Manual LRFD

MANUAL
OF STEEL
CONSTRUCTION
LOAD &
RESISTANCE
FACTOR
DESIGN
Volume I
Structural Members,
Specifications,
& Codes
Volume II
Connections
Second Edition
iv
Copyright © 1994
by
American Institute of Steel Construction, Inc.
ISBN 1-56424-041-X
ISBN 1-56424-042-8
All rights reserved. This book or any part thereof
must not be reproduced in any form without the
written permission of the publisher.
The information presented in this publication has been
prepared in accordance with recognized engineering
principles and is for general information only. While it is
believed to be accurate, this information should not be
used or relied upon for any specific application without
competent professional examination and verification of
its accuracy, suitability, and applicability by a licensed
professional engineer, designer, or architect. The publication of the material contained herein is not intended as a
representation or warranty on the part of the American
Institute of Steel Construction or of any other person
named herein, that this information is suitable for any
general or particular use or of freedom from infringement
of any patent or patents. Anyone making use of this information assumes all liability arising from such use.
Caution must be exercised when relying upon other specifications and codes developed by other bodies and incorporated by reference herein since such material may be
modified or amended from time to time subsequent to the
printing of this edition. The Institute bears no responsibility for such material other than to refer to it and
incorporate it by reference at the time of the initial publication of this edition.
Printed in the United States of America
v
FOREWORD
T
he American Institute of Steel Construction, founded in 1921, is the non-profit
technical specifying and trade organization for the fabricated structural steel industry in
the United States. Executive and engineering headquarters of AISC are maintained in
Chicago, Illinois.
The Institute is supported by three classes of membership: Active Members totaling
400 companies engaged in the fabrication and erection of structural steel, Associate
Members who are allied product manufacturers, and Professional Members who are
individuals or firms engaged in the practice of architecture or engineering. Professional
members also include architectural and engineering educators. The continuing financial
support and active participation of Active Members in the engineering, research, and
development activities of the Institute make possible the publishing of this Second
Edition of the Load and Resistance Factor Design Manual of Steel Construction.
The Institute’s objectives are to improve and advance the use of fabricated structural
steel through research and engineering studies and to develop the most efficient and
economical design of structures. It also conducts programs to improve product quality.
To accomplish these objectives the Institute publishes manuals, textbooks, specifications, and technical booklets. Best known and most widely used are the Manuals of Steel
Construction, LRFD (Load and Resistance Factor Design) and ASD (Allowable Stress
Design), which hold a highly respected position in engineering literature. Outstanding
among AISC standards are the Specifications for Structural Steel Buildings and the Code
of Standard Practice for Steel Buildings and Bridges.
The Institute also assists designers, contractors, educators, and others by publishing
technical information and timely articles on structural applications through two publications, Engineering Journal and Modern Steel Construction. In addition, public appreciation of aesthetically designed steel structures is encouraged through its award programs:
Prize Bridges, Architectural Awards of Excellence, Steel Bridge Building Competition
for Students, and student scholarships.
Due to the expanded nature of the material, the Second Edition of the LRFD Manual
has been divided into two complementary volumes. Volume I contains the LRFD
Specification and Commentary, tables, and other design information for structural
members. Volume II contains all of the information on connections. Like the LRFD
Specification upon which they are based, both volumes of this LRFD Manual apply to
buildings, not bridges.
The Committee gratefully acknowledges the contributions of Roger L. Brockenbrough, Louis F. Geschwindner, Jr., and Cynthia J. Zahn to this Manual.
By the Committee on Manuals, Textbooks, and Codes,
William A. Thornton, Chairman
Barry L. Barger, Vice Chairman
Horatio Allison
Robert O. Disque
Joseph Dudek
William G. Dyker
Ronald L. Hiatt
David T. Ricker
Abraham J. Rokach
Ted W. Winneberger
Charles J. Carter, Secretary
Mark V. Holland
William C. Minchin
Thomas M. Murray
Heinz J. Pak
Dennis F. Randall
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
vi
REFERENCED SPECIFICATIONS, CODES, AND STANDARDS
Part 6 (Volume I) of this LRFD Manual contains the full text of the following:
American Institute of Steel Construction, Inc. (AISC)
Load and Resistance Factor Design Specification for Structural Steel Buildings,
December 1, 1993
Specification for Load and Resistance Factor Design of Single-Angle Members,
December 1, 1993
Seismic Provisions for Structural Steel Buildings, June 15, 1992
Code of Standard Practice for Steel Buildings and Bridges, June 10, 1992
Research Council on Structural Connections (RCSC)
Load and Resistance Factor Design Specifications for Structural Joints Using ASTM
A325 or A490 Bolts, June 8, 1988
Additionally, the following other documents are referenced in Volumes I and II of the
LRFD Manual:
American Association of State Highway and Transportation Officials (AASHTO)
AASHTO/AWS D1.5–88
American Concrete Institute (ACI)
ACI 349–90
American Iron and Steel Institute (AISI)
Load and Resistance Factor Design Specification for Cold-Formed Steel Structural
Members, 1991
American National Standards Institute (ANSI)
ANSI/ASME B1.1–82
ANSI/ASME B18.2.2–86
ANSI/ASME B18.1–72 ANSI/ASME B18.5–78
ANSI/ASME B18.2.1–81
American Society of Civil Engineers (ASCE)
ASCE 7-88
American Society for Testing and Materials (ASTM)
ASTM A6–91b
ASTM A490–91
ASTM A617–92
ASTM A27–87
ASTM A500–90a
ASTM A618–90a
ASTM A36–91
ASTM A501–89
ASTM A668–85a
ASTM A53–88
ASTM A502–91
ASTM A687–89
ASTM A148–84
ASTM A514–91
ASTM A709–91
ASTM A153–82
ASTM A529–89
ASTM A770–86
ASTM A193–91
ASTM A563–91c
ASTM A852–91
ASTM A194–91
ASTM A570–91
ASTM B695–91
ASTM A208(A239–89) ASTM A572–91
ASTM C33–90
ASTM A242–91a
ASTM A588–91a
ASTM C330–89
ASTM A307–91
ASTM A606–91a
ASTM E119–88
ASTM A325–91c
ASTM A607–91
ASTM E380–91
ASTM A354–91
ASTM A615–92b
ASTM F436–91
ASTM A449–91a
ASTM A616–92
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
vii
American Welding Society (AWS)
AWS A2.4–93
AWS A5.25–91
AWS A5.1–91
AWS A5.28–79
AWS A5.5–81
AWS A5.29–80
AWS A5.17–89
AWS B1.0–77
AWS A5.18–79
AWS D1.1–92
AWS A5.20–79
AWS D1.4–92
AWS A5.23–90
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1-1
PART 1
DIMENSIONS AND PROPERTIES
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
STRUCTURAL STEELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Selection of the Appropriate Structural Steel . . . . . . . . . . . . . . . . . . . . . . . . . 1-5
Brittle Fracture Considerations in Structural Design . . . . . . . . . . . . . . . . . . . . . 1-6
Lamellar Tearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8
Jumbo Shapes and Heavy-Welded Built-Up Sections . . . . . . . . . . . . . . . . . . . . 1-8
FIRE-RESISTANT CONSTRUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8
Effect of Shop Painting on Spray-Applied Fireproofing . . . . . . . . . . . . . . . . . . 1-11
EFFECT OF HEAT ON STRUCTURAL STEEL . . . . . . . . . . . . . . . . . . . . . . 1-11
Coefficient of Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-12
Use of Heat to Straighten, Camber, or Curve Members . . . . . . . . . . . . . . . . . . 1-12
EXPANSION JOINTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-13
COMPUTER SOFTWARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14
AISC Database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14
AISC for AutoCAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-14
STRUCTURAL SHAPES: TABLES OF AVAILABILITY, SIZE GROUPINGS,
PRINCIPAL PRODUCERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15
STEEL PIPE AND STRUCTURAL TUBING: TABLES OF AVAILABILITY,
PRINCIPAL PRODUCERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-21
STRUCTURAL SHAPES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-25
Designations, Dimensions, and Properties . . . . . . . . . . . . . . . . . . . . . . . . . 1-25
Tables:
W Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-26
M Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-44
S Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-46
HP Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-48
American Standard Channels (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-50
Miscellaneous Channels (MC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-52
Angles (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-56
STRUCTURAL TEES (WT, MT, ST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-67
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1-2
DIMENSIONS AND PROPERTIES
Use of Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-67
DOUBLE ANGLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-91
Use of Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-91
COMBINATION SECTIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-105
STEEL PIPE AND STRUCTURAL TUBING . . . . . . . . . . . . . . . . . . . . . . . 1-120
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-120
Steel Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-120
Structural Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-120
BARS AND PLATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133
Product Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133
Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133
Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133
Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-133
Floor Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-134
CRANE RAILS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-139
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-139
Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-139
Welded Splices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-141
Fastenings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-141
TORSION PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-145
SURFACE AREAS AND BOX AREAS . . . . . . . . . . . . . . . . . . . . . . . . . . 1-175
CAMBER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-179
Beams and Girders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-179
Trusses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-179
STANDARD MILL PRACTICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-183
General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-183
Methods of Increasing Areas and Weights by Spreading Rolls
. . . . . . . . . . . . . 1-183
Cambering of Rolled Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-185
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-199
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
1-3
OVERVIEW
To facilitate reference to Part 1, the locations of frequently used tables are listed below.
Dimensions and Properties
W Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-26
M Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-44
S Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-46
HP Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-48
American Standard Channels (C) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-50
Miscellaneous Channels (MC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-52
Angles (L) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-56
Structural Tees (WT, MT, ST) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-68
Double Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-92
Combination Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-106
Steel Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-121
Structural Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-122
Torsion Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-146
Surface Areas and Box Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-175
Availability
Availability of Shapes, Plates, and Bars, Table 1-1 . . . . . . . . . . . . . . . . . . . . 1-15
Structural Shape Size Groupings, Table 1-2 . . . . . . . . . . . . . . . . . . . . . . . . 1-16
Principal Producers of Structural Shapes, Table 1-3 . . . . . . . . . . . . . . . . . . . . 1-18
Availability of Steel Pipe and Structural Tubing, Table 1-4 . . . . . . . . . . . . . . . . 1-21
Principal Producers of Structural Tubing (TS), Table 1-5 . . . . . . . . . . . . . . . . . 1-22
Principal Producers of Steel Tubing (Round), Table 1-6 . . . . . . . . . . . . . . . . . . 1-26
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1-4
DIMENSIONS AND PROPERTIES
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL STEELS
1-5
STRUCTURAL STEELS
Availability
Section A3.1 of the AISC Load and Resistance Factor Design Specification for Structural
Steel Buildings lists fifteen ASTM specifications for structural steel approved for use in
building construction.
Five of these steels are available in hot-rolled structural shapes, plates, and bars. Two
steels, ASTM A514 and A852, are available only in plates. Table 1-1 shows five groups
of shapes and eleven ranges of thickness of plates and bars available in the various
minimum yield stress* and tensile strength levels afforded by the seven steels. For
complete information on each steel, reference should be made to the appropriate ASTM
specification. A listing of shape sizes included in each of the five groups follows in
Table 1-2, corresponding with the groupings given in Table A of ASTM Specification A6.
Seven additional grades of steel, other than those covering hot-rolled shapes, plates,
and bars, are listed in Section A3.1a of the LRFD Specification. These steels cover pipe,
cold- and hot-formed tubing, and cold- and hot-rolled sheet and strip.
The principal producers of shapes listed in Part 1 of this Manual are shown in Table 1-3.
Availability and the principal producers of structural tubing are shown in Tables 1-4
through 1-6. For additional information on availability and classification of structural
steel plates and bars, refer to the separate discussion beginning on page 1-129.
Space does not permit inclusion in Table 1-3, or in the listing of shapes and plates in
Part 1 of this Manual, of all rolled shapes or plates of greater thickness that are
occasionally used in construction. For such products, reference should be made to the
various producers’ catalogs.
To obtain an economical structure, it is often advantageous to minimize the number of
different sections. Cost per square foot can often be reduced by designing this way.
Selection of the Appropriate Structural Steel
Steels with 50 ksi yield stress are now widely used in construction, replacing ASTM A36
steel in many applications. The 50 ksi steels listed in Section A3.1a of the LRFD
Specification are ASTM A572 high-strength low-alloy structural steel, ASTM A242 and
A588 atmospheric-corrosion-resistant high-strength low-alloy structural steels, and
ASTM A529 high-strength carbon-manganese structural steel. Yield stresses above 50
ksi can be obtained from two grades of ASTM A572 steel as well as ASTM A514 and
A852 quenched and tempered structural steel plate. These higher-strength steels have
certain advantages over 50 ksi steels in certain applications. They may be economical
choices where lighter members, resulting from use of higher design strengths, are not
penalized because of instability, local buckling, deflection, or other similar reasons. They
may be used in tension members, beams in continuous and composite construction where
deflections can be minimized, and columns having low slenderness ratios. The reduction
of dead load and associated savings in shipping costs can be significant factors. However,
higher strength steels are not to be used indiscriminately. Effective use of all steels
depends on thorough cost and engineering analysis. Normally, connection material is
specified as ASTM A36. The connection tables in this Manual are for A36 steel.
*As used in the AISC LRFD Specification, “yield stress” denotes either the specified minimum yield point (for those that
have a yield point) or specified minimum yield strength (for those steels that do not have a yield point).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1-6
DIMENSIONS AND PROPERTIES
With appropriate procedures and precautions, all steels listed in the AISC Specification
are suitable for welded fabrication. To provide for weldability of ASTM A529 steel, the
specification of a maximum carbon equivalent is recommended.
ASTM A242 and A588 atmospheric-corrosion-resistant, high-strength, low-alloy
steels can be used in the bare (uncoated) condition in most atmospheres. Where boldly
exposed under such conditions, exposure to the normal atmosphere causes a tightly
adherent oxide to form on the surface which protects the steel from further atmospheric
corrosion. To achieve the benefits of the enhanced atmospheric corrosion resistance of
these bare steels, it is necessary that design, detailing, fabrication, erection, and maintenance practices proper for such steels be observed. Designers should consult with the
steel producers on the atmospheric-corrosion-resistant properties and limitations of these
steels prior to use in the bare condition. When either A242 or A588 steel is used in the
coated condition, the coating life is typically longer than with other steels. Although A242
and A588 steels are more expensive than other high-strength, low-alloy steels, the
reduction in maintenance resulting from the use of these steels usually offsets their higher
initial cost.
Brittle Fracture Considerations in Structural Design
As the temperature decreases, an increase is generally noted in the yield stress, tensile
strength, modulus of elasticity, and fatigue strength of the structural steels. In contrast,
the ductility of these steels, as measured by reduction in area or by elongation, and the
toughness of these steels, as determined from a Charpy V-notch impact test, decrease
with decreasing temperatures. Furthermore, there is a temperature below which a
structural steel subjected to tensile stresses may fracture by cleavage,* with little or no
plastic deformation, rather than by shear,* which is usually preceded by a considerable
amount of plastic deformation or yielding.
Fracture that occurs by cleavage at a nominal tensile stress below the yield stress is
commonly referred to as brittle fracture. Generally, a brittle fracture can occur in a
structural steel when there is a sufficiently adverse combination of tensile stress, temperature, strain rate, and geometrical discontinuity (notch) present. Other design and
fabrication factors may also have an important influence. Because of the interrelation of
these effects, the exact combination of stress, temperature, notch, and other conditions
that will cause brittle fracture in a given structure cannot be readily calculated. Consequently, designing against brittle fracture often consists mainly of (1) avoiding conditions
that tend to cause brittle fracture and (2) selecting a steel appropriate for the application.
A discussion of these factors is given in the following sections.
Conditions Causing Brittle Fracture
It has been established that plastic deformation can occur only in the presence of shear
stresses. Shear stresses are always present in a uniaxial or biaxial state-of-stress. However, in a triaxial state-of-stress, the maximum shear stress approaches zero as the
principal stresses approach a common value, and thus, under equal triaxial tensile
stresses, failure occurs by cleavage rather than by shear. Consequently, triaxial tensile
stresses tend to cause brittle fracture and should be avoided. A triaxial state-of-stress can
result from a uniaxial loading when notches or geometrical discontinuities are present.
*Shear and cleavage are used in the metallurgical sense (macroscopically) to denote different fracture mechanisms.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL STEELS
1-7
Increased strain rates tend to increase the possibility of brittle behavior. Thus, structures
that are loaded at fast rates are more susceptible to brittle fracture. However, a rapid strain
rate or impact load is not a required condition for a brittle fracture.
Cold work and the strain aging that normally follows generally increase the likelihood
of brittle fracture. This behavior is usually attributed to the previously mentioned
reduction in ductility. The effect of cold work that occurs in cold forming operations can
be minimized by selecting a generous forming radius and, thus, limiting the amount of
strain. The amount of strain that can be tolerated depends on both the steel and the
application.
The use of welding in construction increases the concerns relative to brittle fracture.
In the as-welded condition, residual stresses will be present in any weldment. These
stresses are considered to be at the yield point of the material. To avoid brittle fracture,
it may be required to utilize steels with higher toughness than would be required for bolted
construction. Welds may also introduce geometric conditions or discontinuities that are
crack-like in nature. These stress risers will additionally increase the requirement for
notch toughness in the weldment. Avoidance of the intersection of welds from multiple
directions reduces the likelihood of triaxial stresses. Properly sized weld-access holes
prohibit the interaction of these various stress fields. As steels being welded become
thicker and more highly restrained, welding procedure issues such as preheat, interpass
temperature, heat input, and cooling rates become increasingly important. The residual
stresses present in a weldment may be reduced by the use of fewer weld passes and
peening of intermittent weld layers. In most cases, weld metal notch toughness exceeds
that of the base materials. However, for fracture-sensitive applications, notch-tough base
and weld metal should be specified.
The residual stresses of welding can be greatly reduced through thermal stress relief.
This reduces the driving force that causes brittle fracture, but if the toughness of the
material is adversely affected by this thermal treatment, no increase in brittle fracture
resistance will be experienced. Therefore, when weldments are to be stress relieved,
investigation into the effects on the weld metal, heat-affected zone, and base material
should be made.
Selecting a Steel To Avoid Brittle Fracture
The best guide in selecting a steel that is appropriate for a given application is
experience with existing and past structures. A36 and Grade 50 (i.e., 50 ksi yield
stress) steels have been used successfully in a great number of applications, such as
buildings, transmission towers, transportation equipment, and bridges, even at the
lowest atmospheric temperatures encountered in the U.S. Therefore, it appears that
any of the structural steels, when designed and fabricated in an appropriate manner,
could be used for similar applications with little likelihood of brittle fracture.
Consequently, brittle fracture is not usually experienced in such structures unless
unusual temperature, notch, and stress conditions are present. Nevertheless, it is
always desirable to avoid or minimize the previously cited adverse conditions that
increase the susceptibility of the steel to brittle fracture.
In applications where notch toughness is considered important, it usually is required
that steels must absorb a certain amount of energy, 15 ft-lb or higher (Charpy V-notch
test), at a given temperature. The test temperature may be higher than the lowest operating
temperature depending on the rate of loading. See Rolfe and Barsom (1986) and Rolfe
(1977).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1-8
DIMENSIONS AND PROPERTIES
Lamellar Tearing
The information on strength and ductility presented in the previous sections generally
pertains to loadings applied in the planar direction (longitudinal or transverse orientation)
of the steel plate or shape. It should be noted that elongation and area reduction values
may well be significantly lower in the through-thickness direction than in the planar
direction. This inherent directionality is of small consequence in many applications, but
does become important in the design and fabrication of structures containing massive
members with highly restrained welded joints.
With the increasing trend toward heavy welded-plate construction, there has been a broader
recognition of the occurrence of lamellar tearing in some highly restrained joints of welded
structures, especially those using thick plates and heavy structural shapes. The restraint
induced by some joint designs in resisting weld deposit shrinkage can impose tensile strain
sufficiently high to cause separation or tearing on planes parallel to the rolled surface of the
structural member being joined. The incidence of this phenomenon can be reduced or
eliminated through greater understanding by designers, detailers, and fabricators of (1) the
inherent directionality of construction forms of steel, (2) the high restraint developed in certain
types of connections, and (3) the need to adopt appropriate weld details and welding
procedures with proper weld metal for through-thickness connections. Further, steels can be
specified to be produced by special practices and/or processes to enhance through-thickness
ductility and thus assist in reducing the incidence of lamellar tearing. Steels produced by such
practices are available from several producers. However, unless precautions are taken in both
design and fabrication, lamellar tearing may still occur in thick plates and heavy shapes of
such steels at restrained through-thickness connections. Some guidelines in minimizing
potential problems have been developed (AISC, 1973). See also Part 8 in Volume II of this
LRFD Manual and ASTM A770, Standard Specification for Through-Thickness Tension
Testing of Steel Plates for Special Applications.
Jumbo Shapes and Heavy Welded Built-up Sections
Although Group 4 and 5 W-shapes, commonly referred to as jumbo shapes, generally are
contemplated as columns or compression members, their use in non-column applications
has been increasing. These heavy shapes have been known to exhibit segregation and a
coarse grain structure in the mid-thickness region of the flange and the web. Because
these areas may have low toughness, cracking might occur as a result of thermal cutting
or welding (Fisher and Pense, 1987). Similar problems may also occur in welded built-up
sections. To minimize the potential of brittle failure, the current LRFD Specification
includes provisions for material toughness requirements, methods of splicing, and
fabrication methods for Group 4 and 5 hot-rolled shapes and welded built-up cross
sections with an element of the cross section more than two inches in thickness intended
for tension applications.
FIRE-RESISTANT CONSTRUCTION
Fire-resistant steel construction may be defined as structural members and assemblies
which can maintain structural stability for the duration of building fire exposure and, in
some cases, prevent the spread of fire to adjacent spaces. Fire resistance of a steel member
is a function of its mass, its geometry, the load to which it is subjected, its structural
support conditions, and the fire to which it is exposed.
Many steel structures have inherent fire resistance through a combination of the above
factors and do not require additional insulation from the effects of fire. However, in many
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FIRE-RESISTANT CONSTRUCTION
1-9
situations, building codes specify the use of fire-rated steel assemblies. In this case,
ASTM Specification E119, Standard Methods of Fire Tests of Building Construction and
Materials, outlines the procedures of fire testing of structural elements.
Structural fire resistance is a major consideration in the design of modern buildings.
In general, building codes define the level of fire protection that is required in specific
applications and structural fire protection is typically implemented in design through
code compliance. In the United States, with a few notable exceptions, the majority of
cities and states now enforce one of the following model codes:
• National Building Code, published by the Building Officials and Code Administrators International.
• Standard Building Code, published by the Southern Building Code Congress International.
• Uniform Building Code, published by the International Conference of Building
Officials.
Building codes specify fire-resistance requirements as a function of building occupancy,
height, area, and whether or not other fire protection systems (e.g., sprinklers) are
provided.
Fire-resistance requirements are specified in terms of hourly ratings based upon tests
conducted in accordance with ASTM E119. This test method specifies a “standard” fire for
evaluating the relative fire-resistance of construction assemblies (i.e., floors, roofs, beams,
girders, and columns). Specific end-point criteria for evaluating the ability of assemblies to
prevent the spread of fire to adjacent spaces and/or to continue to sustain superimposed loads
are included. In effect, ASTM E119 is used to evaluate the length of time that an assembly
continues to perform these functions when exposed to the standard fire. Thus, code requirements and fire-resistance ratings are specified in terms of time (i.e., one hour, two hours, etc.).
The design of fire-resistant buildings is typically accomplished in a very prescriptive fashion
by selecting tested designs that satisfy specific building code requirements. Listings of
fire-resistant designs are available from a number of sources including:
• Fire-Resistance Directory, Underwriters Laboratories.
• Fire-Resistance Ratings, American Insurance Services Group.
• Fire-Resistance Design Manual, Gypsum Association.
In general, due to the very prescriptive nature of fire-resistant design, changes in tested
assemblies can be difficult to justify to the satisfaction of code officials and listing
agencies. In the case of structural steel construction, however, the basic heat transfer and
structural principles are well defined. As a result, relatively simple analytical techniques
have been developed that enable designers to use a variety of different structural steel
shapes in conjunction with tested assemblies. These analytical techniques are specifically
recognized by North American building code authorities and are described in a series of
booklets published by the American Iron and Steel Institute (AISI):
Designing Fire Protection for Steel Columns (1980)
Designing Fire Protection for Steel Beams (1984)
Designing Fire Protection for Steel Trusses (1981)
Since fire-resistant design is currently based on the use of tested assemblies, an
important consideration is the degree to which a test assembly is “representative” of
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 10
DIMENSIONS AND PROPERTIES
actual building construction. In reality, this consideration poses a number of technical
difficulties due to the size of available testing facilities, most of which can only accommodate floor or roof specimens in the range of 15 ft by 18 ft in area. As a result, a test
assembly represents a relatively small sample of a typical floor or roof structure. Most
floor slabs and roof decks are physically, if not structurally, continuous over beams and
girders. Beam and girder spans are often much larger than can be accommodated in
available laboratory furnaces. A variety of connection details are used to frame beams,
girders, and columns. In short, given the cost of testing, the complexity and variety of
modern structural systems, and the size of available test facilities, it is unrealistic to assume
that test assemblies accurately model real construction systems during fire exposure.
In recognition of the practical difficulties associated with laboratory scale testing,
ASTM E119 includes two specific test conditions, “restrained” and “unrestrained.” From
a structural engineering standpoint, the choice of these two terms is unfortunate since the
“restraint” that is contemplated in fire testing is restraint against the thermal expansion,
not structural rotational restraint in the traditional sense. The “restrained” condition
applies when the assembly is supported or surrounded by construction which is “capable
of resisting substantial thermal expansion throughout the range of anticipated elevated
temperatures.” Otherwise, the assembly should be considered free to rotate and expand
at the supports and should be considered “unrestrained.” Thus, a floor system that is
simply supported from a structural standpoint will often be “restrained” from a fireresistance standpoint. In order to provide guidance on the use of restrained and unrestrained ratings, ASTM E119 includes an explanatory Appendix. It should be emphasized
that most common types of steel framing can be considered “restrained” from a fire-resistance standpoint.
The standard fire test also includes other arbitrary assumptions. The specific fire
exposure, for example, is based on furnace capabilities with continuous fuel supply and
does not model real building fires with exhaustible fuel. Also, the test method assumes
that assemblies are fully loaded when a fire occurs. In reality, fires are infrequent, random
events and their design requirements should be probability based. Rarely will design
structural loads occur simultaneously with fire. In addition, many structural elements are
sized for serviceability (i.e., drift, deflection, or vibration) rather than strength, thereby
providing an additional reserve strength during a fire. As a result of these and other
considerations, more rational engineering design standards for structural fire protection
are now being developed (International Fire Engineering Design for Steel Structures:
State-of-the-Art, International Iron and Steel Institute). Although not yet standardized or
recognized in North American building codes, similar design methods have been used in
specific cases, based on code variances.
One such method has been developed by AISI for architecturally exposed structural
steel elements on the exterior of buildings. In effect, ASTM E119 assumes that structural
elements are located within a fire compartment and does not realistically characterize the
fire exposure that will be seen by exterior structural elements. Fire-Safe Structural Steel:
A Design Guide (American Iron and Steel Institute, 1979) defines a step-by-step analytical procedure for determining maximum steel temperatures, based on realistic fire
exposures for exterior structural elements.
Occasionally, structural engineers will be called upon to evaluate fire-damaged steel
structures. Although it is well known that the prolonged exposure to high temperatures
can affect the physical and metallurgical properties of structural steel, in most cases steel
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
EFFECT OF HEAT ON STRUCTURAL STEEL
1 - 11
members that can be straightened in place will be suitable for continued use (Dill, 1960).
Special attention should be given to heat-treated or cold-formed steel elements and
high-strength bolts and welds.
Effect of Shop Painting on Spray-Applied Fireproofing
Spray-applied fireproofing has excellent adhesion to unpainted structural steel. Mechanical anchorage devices, bonding agents, or bond tests are not required to meet Underwriters Laboratories, Inc. (UL) guidelines. In fact, moderate rusting enhances the adhesion
of the fireproofing material, providing the uncoated steel is free of loose rust and mill
scale. Customarily, any loose rust or mill scale as well as any other debris which has
accumulated during the construction process is removed by the fireproofing application
contractor. In many cases, this may be as simple as blowing it off with compressed air.
This ease of application is not realized when fireproofing is applied over painted steel.
In order to meet UL requirements, bond tests in accordance with the ASTM E736 must
be performed to determine if the fireproofing material has adequate adherence to the
painted surface. Frequently, a bonding agent must be added to the fireproofing material
and the bond test repeated to determine if the minimum bond strength can be met. Should
the bond testing still not be satisfactory, mechanical anchorage devices are required to
be applied to the steel before the fireproofing can be applied. The erected steel must still
be cleaned free of any construction debris and scaling or peeling paint before the
fireproofing may be applied.
Once it is determined that the bond tests are adequate, UL guidelines require that if
fireproofing is spray-applied over painted steel, the steel must be wrapped with steel lath
or mechanical anchorage devices must be applied to the steel if the structural shape
exceeds the following dimensional criteria:
• For beam applications, the web depth cannot exceed 16 inches and the flange cannot
exceed 12 inches.
• For column applications, neither the web depth nor the flange width can exceed 16
inches.
A significant number of structural shapes do not meet these restrictions.
The use of primers under spray-applied fireproofing significantly increases the cost of
the steel and the preparation for and the application of the fireproofing material. In an
enclosed structure, primer is insignificant in either the short- or long-term protection of
the steel. LRFD Specification Section M3.1 states that structural steelwork need not be
painted unless required by the contract. For many years, the AISC specifications have
not required that steelwork be painted when it will be concealed by interior building finish
or will be in contact with concrete. The use of primers under spray-applied fireproofing
is strongly discouraged unless there is a compelling reason to paint the steel to protect
against corrosion.
It is suggested that the designer refer to the UL Directory Fire Resistance—Volume 1,
1993, “Coating Materials,” for more specific information on this topic.
EFFECT OF HEAT ON STRUCTURAL STEEL
Short-time elevated-temperature tensile tests on the structural steels permitted by the
AISC Specification indicate that the ratios of the elevated-temperature yield and tensile
strengths to their respective room-temperature values are reasonably similar in the 300°
to 700°F range, except for variations due to strain aging. (The tensile strength ratio may
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 12
DIMENSIONS AND PROPERTIES
increase to a value greater than unity in the 300° to 700°F range when strain aging occurs.)
Below 700°F the strength ratios decrease only slightly. Above 700°F the ratio of
elevated-temperature to room-temperature strength decreases more rapidly as the temperature increases.
The composition of the steels is usually such that the carbon steels (ASTM A36 and
A529) exhibit strain aging with attendant reduced notch toughness. The high-strength
low-alloy steels (ASTM A242, A572, and A588) and heat-treated alloy steels (ASTM
A514 and A852) exhibit less-pronounced or little strain aging. As examples of the
decreased ratio levels obtained at elevated temperature, the yield strength ratios for
carbon and high-strength low-alloy steels are approximately 0.77 at 800°F, 0.63 at
1,000°F, and 0.37 at 1,200°F.
Coefficient of Expansion
The average coefficient of expansion for structural steel between 70°F and 100°F is
0.0000065 for each degree. For temperatures of 100°F to 1,200°F the coefficient is given
by the approximate formula:
ε = (6.1+0.0019t) × 10−6
in which ε is the coefficient of expansion (change in length per unit length) for each
degree Fahrenheit and t is the temperature in degrees Fahrenheit. The modulus of
elasticity of structural steel is approximately 29,000 ksi at 70°F. It decreases linearly to
about 25,000 ksi at 900°F, and then begins to drop at an increasing rate at higher
temperatures.
Use of Heat to Straighten, Camber, or Curve Members
With modern fabrication techniques, a controlled application of heat can be effectively
used to either straighten or to intentionally curve structural members. By this process,
the member is rapidly heated in selected areas; the heated areas tend to expand, but are
restrained by adjacent cooler areas. This action causes a permanent plastic deformation
or “upset” of the heated areas and, thus, a change of shape is developed in the cooled
member.
“Heat straightening” is used in both normal shop fabrication operations and in the field
to remove relatively severe accidental bends in members. Conversely, “heat cambering”
and “heat curving” of either rolled beams or welded girders are examples of the use of
heat to effect a desired curvature.
As with many other fabrication operations, the use of heat to straighten or curve will
cause residual stresses in the member as a result of plastic deformations. These stresses
are similar to those that develop in rolled structural shapes as they cool from the rolling
temperature; in this case, the stresses arise because all parts of the shape do not cool at
the same rate. In like manner, welded members develop residual stresses from the
localized heat of welding.
In general, the residual stresses from heating operations do not affect the ultimate
strength of structural members. Any reduction in strength due to residual stresses is
incorporated in the provisions of the LRFD Specification.
The mechanical properties of steels are largely unaffected by heating operations,
provided that the maximum temperature does not exceed 1,100°F for quenched and
tempered alloy steels (ASTM A514 and A852), and 1,300°F for other steels. The
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
EXPANSION JOINTS
1 - 13
temperature should be carefully checked by temperature-indicating crayons or other
suitable means during the heating process.
EXPANSION JOINTS
Although buildings are typically constructed of flexible materials, expansion joints are
required in roofs and the supporting structure when horizontal dimensions are large. The
maximum distance between expansion joints is dependent upon many variables including
ambient temperature during construction and the expected temperature range during the
lifetime of the building. An excellent reference on the topic of thermal expansion in
buildings and location of expansion joints is the Federal Construction Council’s Technical
Report No. 65, Expansion Joints in Buildings.
Taken from this report, Figure 1-1 provides a guide based on design temperature
change for maximum spacing of structural expansion joints in beam-and-column-framed
buildings with hinged-column bases and heated interiors. The report includes data for
numerous cities and gives five modification factors which should be applied as
appropriate:
MAXIMUM SPACING OF EXPANSION JOINTS (ft)
1. If the building will be heated only and will have hinged-column bases, use the
maximum spacing as specified;
2. If the building will be air-conditioned as well as heated, increase the maximum
spacing by 15 percent provided the environmental control system will run continuously;
3. If the building will be unheated, decrease the maximum spacing by 33 percent;
4. If the building will have fixed column bases, decrease the maximum spacing by 15
percent;
600
500
Rectangular
multiframed
configuration with
Symmetrical stiffness
400
Steel
300
200
Nonrectangular configuration
(L, T, U type)
Any
material
100
10 20 30 40
50 60 70 70 80 90
DESIGN TEMPERATURE CHANGE (°F)
Fig. 1-1. Expansion joint spacing.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 14
DIMENSIONS AND PROPERTIES
5. If the building will have substantially greater stiffness against lateral displacement
in one of the plan dimensions, decrease the maximum spacing by 25 percent.
When more than one of these design conditions prevail in a building, the percentile
factor to be applied should be the algebraic sum of the adjustment factors of all the various
applicable conditions.
Additionally, most building codes include restrictions on location and spacing of fire
walls. Such fire walls often become locations for expansion joints.
The most effective expansion joint is a double line of columns which provides a
complete and positive separation. When expansion joints other than the double-column
type are employed, low-friction sliding elements are generally used. Such systems,
however, are never totally free and will induce some level of inherent restraint to
movement.
COMPUTER SOFTWARE
AISC Database
The AISC Database contains the properties and dimensions of structural steel shapes,
corresponding to Part 1 of this LRFD Manual. LRFD-related properties such as X1 and
X2, as well as torsional properties, are included.
Two versions, one in U.S. customary units and one in metric units, are available.
Dimensions and properties of W, S, M, and HP shapes, American Standard Channels
(C), Miscellaneous Channels (MC), Structural Tees cut from W, M, and S shapes (WT,
MT, ST), Single and Double Angles, Structural Tubing, and Pipe are listed in ASCII
format. Also included are: a BASIC read/write program, a sample search routine, and a
routine to convert the file to Lotus *.PRN file format.
AISC for AutoCAD *
The program will draw the end, elevation, and plan views of W, S, M, and HP shapes,
American Standard Channels (C), Miscellaneous Channels (MC), Structural Tees cut
from W, M, and S shapes (WT, MT, ST), Single and Double Angles, Structural Tubing,
and Pipe to full scale corresponding to data published in Part 1 of this LRFD Manual.
Version 2.0 runs in AutoCAD Release 12 only; Version 1.0 runs in AutoCAD Releases
10 and 11.
*AutoCAD is a registered trademark in the US Patent and Trademark Office by Autodesk, Inc. AISC for AutoCAD is
copyrighted in the US Copyright Office by Bridgefarmer and Associates, Inc.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 15
Table 1-1.
Availability of Shapes, Plates, and Bars According to
ASTM Structural Steel Specifications
Shapes
Fy
Steel
Type
A36
32
58–80
36
58–80c
42
42
60–85
50
50
70–100
42
42
60
50
50
65
60
60
75
65
65
80
A242
42
63
46
67
50
70
HighStrength
Low-alloy
Corrosion
Resistant
Highstrength
Low-alloy
A572 Grade
A529f Grade
Carbon
Group per
Over Over
Mini1⁄ ″
3⁄ ″
ASTM A6
Fu
mum
2
4
ASTM Yield Tensile
To
to
to
a
1⁄ ″
3 ⁄ ″ 11 ⁄ ″
Desig- Stress Stress
2
4
4
b
nation (ksi)
(ksi) 1 2 3 4 5 incl. incl. incl.
A588
42
63
46
67
50
70
Quenched A852e
&
Tempered
Alloy
70
90–110
Quenched A514e
&
Tempered A514e
Low-Alloy
90
100–130
100
110–130
Plates and Bars
Over Over Over Over Over Over Over
11⁄4″ 11⁄2″ 2″ 21⁄2″ 4″
5″
6″
to
to
to
to
to
to
to
11⁄2″ 2″ 21⁄2″ 4″
5″
6″
8″ Over
incl. incl. incl. incl. incl. incl. incl. 8″
d
aMinimum unless a range is shown.
bIncludes bar-size shapes
cFor shapes over 426 lb / ft minimum of 58 ksi only applies.
dPlates to 1 in. thick, 12 in. width; bars to 11⁄ in.
2
ePlates only.
fTo improve the weldability of A529 steel, the specification of a maximum carbon equivalent
(per ASTM Supplementary Requirement S78) is recommended.
Available
Not Available
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 16
DIMENSIONS AND PROPERTIES
Table 1-2.
Structural Shape Size Groupings for Tensile Property Classification
Structural
Shapes
W shapes
Group 1
Group 2
Group 3
W44× 290, 335
Group 4
W24× 55, 62
W44× 230, 262
W21× 44 to 57 incl.
W40× 149 to 264 incl. W40× 431
W18× 35 to 71 incl.
W36× 135 to 210 incl. W40× 277 to 372 incl. W36× 328 to 798 incl.
W16× 26 to 57 incl.
W33× 118 to 152 incl. W36× 230 to 300 incl. W33× 318 to 354 incl.
W14× 22 to 53 incl.
W30× 90 to 211 incl. W33× 169 to 291 incl. W30× 292 to 477 incl.
W12× 14 to 58 incl.
W27× 84 to 178 incl. W30× 235 to 261 incl. W27× 307 to 539 incl.
W10× 12 to 45 incl.
W24× 68 to 162 incl. W27× 194 to 258 incl. W24× 250 to 492 incl.
Group 5
W40×466 to 593 incl. W36× 848
W40× 392
W8× 10 to 48 incl.
W21× 62 to 147 incl. W24× 176 to 229 incl. W18× 211 to 311 incl.
W6× 9 to 25 incl.
W18× 76 to 143 incl. W21× 166 to 201 incl. W14× 233 to 550 incl.
W5× 16,19
W16× 67 to 100 incl. W18× 158 to 192 incl. W12× 210 to 336 incl.
W4× 13
W14× 61 to 132 incl. W14× 145 to 211 incl.
W14× 605 to 808 incl.
W12× 65 to 106 incl. W12× 120 to 190 incl.
W10× 49 to 112 incl.
W8× 58, 67
M Shapes
all
S Shapes
to 35 lb/ft incl.
over 35 lb/ft
HP Shapes
to 102 lb/ft incl.
American
to 20.7 lb/ft incl.
Standard
Channels (C)
over 20.7 lb/ft
Miscellane- to 28.5 lb/ft incl.
ous Channels
(MC)
over 28.5 lb/ft
Angles (L)
to 1⁄2-in. incl.
over 102 lb/ft
over 1⁄2- to 3⁄4-in. incl. over 3⁄4-in.
Notes:
Structural tees from W, M, and S shapes fall into the same group as the structural shapes from which they are cut.
Group 4 and Group 5 shapes are generally contemplated for application as columns or compression components. When used in other applications (e.g., trusses) and when thermal cutting or welding is required, special
material specification and fabrication procedures apply to minimize the possibility of cracking (see Part 6, LRFD
Specification, Sections A3.1c, J1.5, J1.6, J2.3, and M2.2, and corresponding Commentary sections).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 17
Structural Steel Shape Producers
Bayou Steel Corp.
P.O. Box 5000
Laplace, LA 70068
(800) 535-7692
Florida Steel Corp.
P.O. Box 31328
Tampa, FL 33631
(800) 237-0230
Nucor-Yamato Steel
P.O. Box 1228
Blytheville, AR 72316
(800) 289-6977
Bethlehem Steel Corp.
301 East Third St.
Bethlehem, PA 18016-7699
(800) 633-0482
Northwestern Steel & Wire Co.
121 Wallace St.
P.O. Box 618
Sterling, IL 61081-0618
(800) 793-2200
Roanoke Electric Steel Corp.
P.O. Box 13948
Roanoke, VA 24038
(800) 753-3532
British Steel Inc.
475 N. Martingale Road #400
Schaumburg, IL 60173
(800) 542-6244
North Star Steel Co.
1380 Corporate Center Curve
Suite 215
P.O. Box 21620
Eagan, MN 55121-0620
(800) 328-1944
Chaparral Steel Co.
300 Ward Road
Midlothian, TX 76065-9501
(800) 529-7979
Nucor Steel
P.O. Box 126
Jewett, TX 75846
(800) 527-6445
SMI Steel, Inc.
101 South 50th St.
Birmingham, AL 35232
(800) 621-0262
TradeARBED
825 Third Ave.
New York, NY 10022
(212) 486-9890
Structural Tube Producers
American Institute for Hollow
Structural Sections
929 McLaughlin Run Road
Suite 8
Pittsburgh, PA 15017
(412) 221-8880
Acme Roll Forming Co.
812 North Beck St.
Sebewaing, MI 48759-0706
(800) 937-8823
Dallas Tube & Rollform
P.O. Box 540873
Dallas, TX 75354-0873
(214) 556-0234
Independence Tube Corp.
6226 West 74th St.
Chicago, IL 60638
(708) 496-0380
Eugene Welding Co.
P.O. Box 249
Marysville, MI 48040
(313) 364-7421
IPSCO Steel, Inc.
P.O. Box 1670, Armour Road
Regina, Saskatchewan S4P 3C7
CANADA
(416) 271-2312
EXLTUBE, Inc.
905 Atlantic
North Kansas City, MO 64116
(800) 892-8823
Bull Moose
57540 SR 19 S
P.O. Box B-1027
Elkhart, IN 46515
(800) 348-7460
Hanna Steel Corp.
3812 Commerce Ave.
P.O. Box 558
Fairfield, AL 35064
(800) 633-8252
Copperweld Corp.
7401 South Linder Ave.
Chicago, IL 60638
(800) 327-8823
UNR-Leavitt, Div. of UNR Inc.
1717 West 115th St.
Chicago, IL 60643
(800) 532-8488
Valmont Industries, Inc.
P.O. Box 358
Valley, NE 68064
(800) 825-6668
Welded Tube Co. of America
1855 East 122nd St.
Chicago, IL 60633
(800) 733-5683
Steel Pipe Producers
National Association of Steel Pipe
Distributors, Inc.
12651 Briar Forest Dr., Suite 130
Houston, TX 77077
(713) 531-7473
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 18
DIMENSIONS AND PROPERTIES
Table 1-3.
Principal Producers of Structural Shapes
B—Bethlehem Steel
Corp.
C—Chaparral Steel
F—Florida Steel Corp.
I—British Steel
S—North Star Steel
M—SMI Steel Inc.
T—TradeARBED
N—Nucor-Yamato Steel U—Nucor Steel
R—Roanoke Steel
W—Northwestern Steel
& Wire
Y—Bayou Steel Corp.
Section, Weight per ft
Producer Code
Section, Weight per ft
Producer Code
W44× all
T
W40× 321-593
W40× 297
W40× 278
W40× 277
W40× 264
W40× 249
W40× 235
W40× 215
W40× 211
W40× 199
W40× 183
W40× 174
W40× 149-167
T
N
T
N,T
B,T
N,T
B,T
N,T
B,T
N,T
B,I,N,T
T
B,I,N,T
W24× 103
W24× 84-94
W24× 55-76
B,W
B,I,N,W
B,C,I,N,W
W21× 182-201
W21× 166
W21× 83-147
W21× 44-73
I,W
B,I,W
B,I,N,W
B,C,I,N,W
W18× 258-311
W18× 175-234
W18× 130-158
W18× 76-119
W18× 65-71
W18× 35-60
B
B,W
B,N,W
B,N,W
B,I,N,W
B,C,I,N,W
W36× 439-848
W36× 393
W36× 328-359
W36× 260-300
W36× 256
W36× 245
W36× 232
W36× 135-230
T
B,T
B,I,T
B,I,N,T
B,I
B,I,N,T
B,I
B,I,N,T
W16× 67-100
W16× 57
W16× 26-50
B,N,W
B,I,N,W
B,C,I,N,W
W33× 263-354
W33× 201-241
W33× 169
W33× 118-152
B,T
B,N,T
B,T
B,I,N,T
W30× 391-477
W30× 261-326
W30× 173-235
W30× 148
W30× 99-132
W30× 90
W14× 808
W14× 342-730
W14× 311
W14× 90-283
W14× 82
W14× 74
W14× 61-68
W14× 43-53
W14× 38
W14× 22-34
B
B,I,T
B,I,T,W
B,I,N,T,W
B,N,W
B,C,I,N,W
B,C,N,W
B,C,I,N,W
B,I,N,W
B,C,I,N,W
T
B,T
B,I,N,T
B,I,T
B,I,N,T
B,N
W27× 307-539
W27× 258
W27× 235
W27× 146-217
W27× 129
W27× 84-114
T
N,T
N
B,N,T
B,I,T,W
B,I,N,T,W
W12× 252-336
W12× 210-230
W12× 170-190
W12× 65-152
W12× 50-58
W12× 16-45
W12× 14
B
B,T
B,I,T,W
B,I,N,T,W
B,C,I,N,W
B,C,N,W
B,C,W
W24× 279-492
W24× 250
W24× 229
W24× 207
W24× 192
W24× 104-176
T
B,N,W
B,N,T,W
B,N,W
B,I,N,T,W
B,I,N,T,W
W10× 88-112
W10× 49-77
W10× 33-45
W10× 22-30
W10× 15-19
W10× 12
B,I,N,W
B,C,I,N,W
B,C,N,W
B,C,I,N,W
B,C,I,W
B,C,W
W8× 31-67
W8× 18-28
W8× 15
B,C,I,N,W
B,C,N,W
B,C,W,Y
Notes:
For the most recent list of producers, please see the latest January or July issue of the AISC magazine Modern
Steel Construction.
Maximum lengths of shapes obtained vary with producer, but typically range from 60 ft to 75 ft. Lengths up to
100 ft are available for certain shapes. Please consult individual producers for length requirements.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 19
Table 1-3 (cont.).
Principal Producers of Structural Shapes
B—Bethlehem Steel
Corp.
C—Chaparral Steel
F—Florida Steel Corp.
I—British Steel
S—North Star Steel
M—SMI Steel Inc.
T—TradeARBED
N—Nucor-Yamato Steel U—Nucor Steel
R-Roanoke Steel
W—Northwestern Steel
& Wire
Y—Bayou Steel Corp.
Section, Weight per ft
Producer Code
Section, Weight per ft
Producer Code
W8× 10-13
B,C,M,W,Y
W6× 20-25
W6× 16
W6× 15
W6× 12
W6× 9
B,C,I,N,W
B,C,W,Y
B,C,I,N,W
B,C,W,Y
B,C,N,W,Y
W5× 16-19
B
W4× 13
B,C,M,Y
M12× 10.8-11.8
M10× 8-9
M8× 6.5
M5× 18.9
MC18× 42.7-58
MC13× 31.8-50
MC12× 31-50
MC12× 10.6
MC10× 22-41.1
MC10× 8.4
MC9× 23.9-25.4
MC8× 18.7-22.8
MC8× 8.5
MC7× 19.1-22.7
MC6× 18
MC6× 12-16.3
B,N
B,N
B,N
S,N
B
S
B
B,S
M
B
B
B,S
C
C
C
B
S24× 80-121
S20× 66-96
S18× 54.7-70
S15× 42.9-50
S12× 31.8-50
S10× 25.4-35
S8× 18.4-23
S6× 12.5-17.25
S5× 10
S4× 9.5
S4× 7.7
S3× 7.5
S3× 5.7
B,W
B,W
B,W
B,W
B,W
B,S
B,C,S
C,S,Y
C,Y
C
C,Y
C,Y
C,M,Y
HP14× 73-117
HP12× 53-84
HP10× 42-57
HP8× 36
B,I,N,W
B,I,N,W
B,C,I,N,W
B,C,I,N,W
C15× 33.9-50
C12× 30
C12× 20.7-25
C10× 25-30
C10× 15.3-20
C9× 20
C9× 13.4-15
C8× 18.75
C8× 11.5-13.75
C7× 12.25
C7× 9.8
C6× 13
C6× 10.5
C6× 8.2
C5× 9
C5× 6.7
C4× 5.4-7.25
C3× 6
C3× 4.1-5
Section by Leg Length
& Thickness
Producer Code
L8× 8×
B,N,W
B,W
B,C,S,W
B,S,W
B,C,S,W
B
B,S
S,W,Y
C,M,S,U,W,Y
S,U,W
M,S,U,W
M,S,U,W,Y
C,M,S,U,W,Y
C,F,M,U,W,Y,
M,U,W,Y
F,M,U,W,Y
F,M,U,W,Y
M,U,W,Y
F,M,R,U,W,Y
11 ⁄8
1
7⁄
3⁄
5⁄
9⁄
1⁄
L6× 6×
7⁄
5⁄
9⁄
1⁄
7⁄
3⁄
5⁄
7⁄
3⁄
5⁄
1⁄
7⁄
3⁄
5⁄
L4× 4×
4
8
16
2
1
3⁄
L5× 5×
8
3⁄
5⁄
1⁄
7⁄
3⁄
5⁄
1⁄
8
4
8
16
2
16
8
16
8
4
8
2
16
8
16
4
8
2
16
8
16
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
B
B,S
B,S
B,S
B,S
B,S
B,S
B,U,Y
B,U,Y
B,M,U,Y
B,M,U,Y
B,M,U,Y
B,M,S,U,Y
B,M,U,Y
B,M,S,U,Y
M,U,Y
B,U,Y
B,M,U,Y
B,M,U,Y
B,M,U,W,Y
B,M,U,Y
B,M,U,W,Y
B,M,U,W,Y
M,U,Y
M,U,Y
F,M,R,U,W,Y
F,M,U,Y
F,M,R,U,W,Y
F,M,R,U,W,Y
F,M,R,U,W,Y
1 - 20
DIMENSIONS AND PROPERTIES
Table 1-3 (cont.).
Principal Producers of Structural Shapes
B—Bethlehem Steel
Corp.
C—Chaparral Steel
F—Florida Steel Corp.
I—British Steel
S—North Star Steel
M—SMI Steel Inc.
T—TradeARBED
N—Nucor-Yamato Steel U—Nucor Steel
R—Roanoke Steel
W—Northwestern Steel
& Wire
Y—Bayou Steel Corp.
Section by Leg Length
Producer Code
and Thickness
Section by Leg Length
Producer Code
and Thickness
L31 ⁄2 × 31 ⁄2 ×
L6× 31 ⁄2 ×
1⁄
7⁄
3⁄
5⁄
1⁄
L3× 3×
1⁄
7⁄
3⁄
5⁄
1⁄
3⁄
L21 ⁄2 × 21 ⁄2 ×
1⁄
3⁄
5⁄
1⁄
3⁄
L2× 2×
3⁄
5⁄
1⁄
3⁄
1⁄
L8× 6×
7⁄
5⁄
9⁄
1⁄
7⁄
7⁄
5⁄
9⁄
1⁄
7⁄
3⁄
5⁄
1⁄
7⁄
3⁄
L6× 4×
8
16
4
2
16
8
16
4
16
2
8
16
4
16
8
16
4
16
8
8
4
8
16
2
16
1
3⁄
L7× 4×
16
1
3⁄
L8× 4×
2
7⁄
3⁄
5⁄
9⁄
1⁄
7⁄
3⁄
5⁄
8
4
8
16
2
16
4
8
2
16
8
8
4
8
16
2
16
8
16
F,M,R,U,W,Y
U,Y
F,M,R,U,W,Y
F,M,R,U,W,Y
F,M,R,U,W,Y
F,M,U,W,Y
U,Y
F,M,R,S,U,W,Y
F,M,R,S,U,W,Y
F,M,R,S,U,W,Y
F,M,R,U,W,Y
F,U
F,S,U
F,S,U
F,S,U
F,U
F,S,U
F,S,U
F,S,U
F,S,U
F,S,U
B,S
B
B,S
B
B,S
B,S
B,S
B,S
B,S
B,S
B,S
B,S
B,S
B,S
B,Y
B,Y
B,S,Y
B,Y
B,S,Y
B
B,M,S,U,W,Y
B,M,S,U,W,Y
B,M,S,U,W,Y
B,M,S,U,W,Y
B,U,Y
B,M,S,U,W,Y
B,M,S,U,W,Y
1⁄
3⁄
5⁄
L5× 31 ⁄
3⁄
2×
5⁄
1⁄
3⁄
5⁄
1⁄
1⁄
L5× 3×
7⁄
3⁄
5⁄
1⁄
L4× 31 ⁄
1⁄
2×
3⁄
5⁄
1⁄
L4× 3×
5⁄
1⁄
7⁄
3⁄
5⁄
1⁄
L31 ⁄2 × 3×
1⁄
3⁄
5⁄
1⁄
L31 ⁄
2
× 21 ⁄
2×
1⁄
3⁄
1⁄
L3× 21 ⁄2 ×
1⁄
3⁄
5⁄
1⁄
3⁄
L3× 2×
1⁄
3⁄
5⁄
1⁄
3⁄
L21 ⁄
2 × 2×
3⁄
5⁄
1⁄
3⁄
2
8
16
4
8
2
8
16
4
2
16
8
16
4
2
8
16
4
8
2
16
8
16
4
2
8
16
4
2
8
4
2
8
16
4
16
2
8
16
4
16
8
16
4
16
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
M,U,W,Y
B,M,U,W,Y
B,M,U,W,Y
M,U,Y
M,U,Y
M,U,W,Y
M,U,W,Y
M,U,W,Y
M,U,W,Y
F,M,U,W,Y
F,Y
F,M,U,W,Y
F,M,U,W,Y
F,M,U,W,Y
F,M,U,W
F,M,R,U,W
F,M,R,U,W
F,M,R,U,W
M,U,Y
F,M,U,W,Y
U,Y
F,M,R,U,W,Y
F,M,R,U,W,Y
F,M,R,U,W,Y
U,W
M,U,W
M,U,W
M,U,W
U
U
U
U
U,W
U,W,Y
R,U,W
U
F
F,S,U
F,S,U
F,R,S,U
F,R,U
R,S,U
S,U
R,S,U
R,S,U
1 - 21
Table 1-4.
Availability of Steel Pipe and Structural Tubing
According to ASTM Material Specifications
ASTM
Specification
Steel
Fy
Fu
Grade
Minimum
Yield
Stress
(ksi)
Minimum
Tensile
Stress
(ksi)
Shape
Round
Square &
Rectangular
Availability
ElectricResistance
Welded
A53
Type E
B
35
60
Note 3
Seamless
Type S
B
35
60
Note 3
A
33
45
Note 1
B
42
58
Note 1
C
46
62
Note 1
A
39
45
Note 1
B
46
58
Note 2
C
50
62
Note 1
—
36
58
Note 1
I
50
70
Note 1
II
50
70
Note 1
III
50
65
Note 1
Cold
Formed
Hot Formed
HighStrength
Low-Alloy
A500
A501
A618
Notes:
1. Available in mill quantities only; consult with producers.
2. Normally stocked in local steel service centers.
3. Normally stocked by local pipe distributors.
Available
Not Available
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 22
DIMENSIONS AND PROPERTIES
Table 1-5.
Principal Producers of Structural Tubing (TS)
A—Acme Rolling
Forming Co.
B—Bull Moose Tube
Co.
C—Copperweld Corp.
D—Dallas Tube &
I—Independence Tube
Rollform
Corp.
E—Eugene Welding Co. P—IPSCO Steel
H—Hanna Steel Corp.
U—UNR-Leavitt, Div. of
UNR, Inc.
Nominal Size and
Thickness
Producer Code
30× 30× 5⁄8
28× 28× 5⁄8
26× 26× 5⁄8
24× 24× 5⁄8, 1⁄2, 3⁄8
22× 22× 5⁄8, 1⁄2, 3⁄8
20× 20× 5⁄8, 1⁄2, 3⁄8
18× 18× 5⁄8, 1⁄2, 3⁄8
V—Valmont Industries,
Inc.
W—Welded Tube Co. of
America
X—EXLTUBE
Nominal Size and
Thickness
Producer Code
V*
V*
V*
V*
V*
V*
V*
41⁄2× 41⁄2× 3⁄8, 5⁄16
41⁄2× 41⁄2× 1⁄4, 3⁄16
41⁄2× 41⁄2× 1⁄8
I,P,W
A,B,C,D,I,P,W,X
A,B,C,P,I,W
4× 4× 1⁄2
4× 4× 3⁄8, 5⁄16
4× 4× 1⁄4, 3⁄16 , 1⁄8
B,C,P,U,W
A,B,C,D,E,I,P,U,W
A,B,C,D,E,I,P,U,V,W,X
16× 16× 5⁄8
16× 16× 1⁄2, 3⁄8, 5⁄16
V*
V*,W
31⁄2× 31⁄2× 5⁄16
31⁄2× 31⁄2× 1⁄4, 3⁄16 , 1⁄8
I,P,W
A,B,C,D,E,I,P,U,W,X
14× 14× 5⁄8
14× 14× 1⁄2, 3⁄8
14× 14× 5⁄16
V*
V*,W
W
3× 3× 5⁄16
3× 3× 1⁄4, 3⁄16
3× 3× 1⁄8
I,P,W
A,B,C,D,E,I,P,U,W,X
A,B,C,D,E,I,P,U,W
12× 12× 5⁄8
12× 12× 1⁄2, 3⁄8
12× 12× 5⁄16 , 1⁄4
B
B,V*,W
B,W
21⁄2× 21⁄2× 5⁄16
21⁄2× 21⁄2× 1⁄4, 3⁄16
21⁄2× 21⁄2× 1⁄8
I
A,B,C,D,E,I,P,U,V,W,X
A,B,C,D,E,I,P,U,V,W
10× 10× 5⁄8
10× 10× 1⁄2, 3⁄8, 5⁄16 , 1⁄4
10× 10× 3⁄16
B,C
B,C,P,U,W
B,C,P,W
2× 2× 5⁄16
2× 2× 1⁄4
2× 2× 3⁄16 , 1⁄8
I,V
A,B,C,D,I,U,V,W,X
A,B,C,D,E,I,P,U,V,W,X
8× 8× 5⁄8
8× 8× 1⁄2
8× 8× 3⁄8, 5⁄16 , 1⁄4, 3⁄16
B,C
B,C,P,U,W
B,C,D,P,U,W
11⁄2× 11⁄2× 3⁄16
B,E,P,U,V
7× 7× 5⁄8
7× 7× 1⁄2
7× 7× 3⁄8, 5⁄16 , 1⁄4, 3⁄16
B
B,C,P,U,W
B,C,D,P,U,W
30× 24× 1⁄2, 3⁄8, 5⁄16
28× 24× 1⁄2, 3⁄8, 5⁄16
26× 24× 1⁄2, 3⁄8, 5⁄16
24× 22× 1⁄2, 3⁄8, 5⁄16
22× 20× 1⁄2, 3⁄8, 5⁄16
V*
V*
V*
V*
V*
6× 6× 5⁄8
6× 6× 1⁄2
6× 6× 3⁄8, 5⁄16
6× 6× 1⁄4, 3⁄16
6× 6× 1⁄8
B
B,C,P,U,W
B,C,D,I,P,U,W
A,B,C,D,I,P,U,W,X
A,B,C,I,P
20× 18× 1⁄2, 3⁄8, 5⁄16
20× 12× 1⁄2, 3⁄8, 5⁄16
20× 8× 1⁄2, 3⁄8, 5⁄16
20× 4× 1⁄2, 3⁄8, 5⁄16
V*
W
W
W
51⁄2× 51⁄2× 3⁄8, 5⁄16 , 1⁄4, 3⁄16 , 1⁄8,
B,I
18× 12× 1⁄2, 3⁄8, 5⁄16
18× 6× 1⁄2, 3⁄8, 5⁄16
18× 6× 1⁄4
V*
B,W
B
5× 5× 1⁄2
5× 5× 3⁄8, 5⁄16
5× 5× 1⁄4
5× 5× 3⁄16
5× 5× 1⁄8
B,C,P,U,W
B,C,D,I,P,U,W
A,B,C,D,I,P,U,W,X
A,B,C,D,I,P,U,V,W,X
A,B,C,I,P,V,W
16× 12× 1⁄2, 3⁄8, 5⁄16
16× 8× 1⁄2, 3⁄8, 5⁄16
16× 4× 1⁄2, 3⁄8, 5⁄16
V*,W
B,W
B,W
*Size is manufactured by Submerged Arc Welding (SAW) process and is not stocked by steel service centers
(contact producer for specific requirements). All other sizes are manufactured by Electric Resistance Welding
and are available from steel service centers. For the most recent list of producers, please see the latest January or July issue of the AISC magazine Modern Steel Construction.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 23
Table 1-5 (cont.).
Principal Producers of Structural Tubing (TS)
A—Acme Rolling
Forming Co.
B—Bull Moose Tube
Co.
C—Copperweld Corp.
D—Dallas Tube &
I—Independence Tube
Rollform
Corp.
E—Eugene Welding Co. P—IPSCO Steel
H—Hanna Steel Corp.
U—UNR-Leavitt, Div. of
UNR, Inc.
Nominal Size and
Thickness
Producer Code
14× 12× 1⁄2, 3⁄8
14× 10× 1⁄2, 3⁄8, 5⁄16
14× 6× 5⁄8
14× 6× 1⁄2, 3⁄8, 5⁄16 , 1⁄4
14× 4× 5⁄8
14× 4× 1⁄2, 3⁄8, 5⁄16 , 1⁄4
14× 4× 3⁄16
V*
B,W
B
B,W
B
B,W
B
12× 10× 1⁄2, 3⁄8, 5⁄16 , 1⁄4
12× 8× 5⁄8
12× 8× 1⁄2, 3⁄8, 5⁄16 , 1⁄4
12× 8× 3⁄16
12× 6× 5⁄8
12× 6× 1⁄2, 3⁄8, 5⁄16 , 1⁄4
12× 6× 3⁄16
12× 4× 5⁄8
12× 4× 1⁄2, 3⁄8, 5⁄16 , 1⁄4, 3⁄16
12× 3× 5⁄16 , 1⁄4, 3⁄16
12× 2× 1⁄4, 3⁄16
B
B
B,C,U,W
B,C,W
B
B,C,U,W
B,C,W
B
B,U,W
B
B,U
10× 8× 1⁄2, 3⁄8, 5⁄16 , 1⁄4, 3⁄16
10× 6× 1⁄2
10× 6× 3⁄8, 5⁄16 , 1⁄4, 3⁄16
10× 5× 3⁄8, 5⁄16 , 1⁄4, 3⁄16
10× 4× 1⁄2
10× 4× 3⁄8, 5⁄16 , 1⁄4, 3⁄16
10× 3× 3⁄8,5⁄16
10× 3× 1⁄4, 3⁄16
10× 2× 5⁄16
10× 2× 1⁄4, 3⁄16
B,C,U,W
B,C,U,W
B,C,D,P,U,W
B,C,D
B,C,P,U,W
B,C,D,P,U,W
D
B,D
D,P,W
B,D,P,U,W
8× 6× 1⁄2
8× 6× 3⁄8, 5⁄16 , 1⁄4, 3⁄16
8× 4× 5⁄8
8× 4× 1⁄2
8× 4× 3⁄8, 5⁄16
8× 4× 1⁄4, 3⁄16
8× 4× 1⁄8
8× 3× 1⁄2
8× 3× 3⁄8, 5⁄16
8× 3× 1⁄4, 3⁄16
8× 3× 1⁄8
8× 2× 3⁄8
8× 2× 5⁄16
8× 2× 1⁄4, 3⁄16
8× 2× 1⁄8
B,C,P,U,W
B,C,D,P,U,W
B
B,C,P,U,W
B,C,D,H,I,P,U,W
A,B,C,D,H,I,P,U,W,X
A,B,D,I,P
C,P,U
B,C,D,I,P,U,W
A,B,C,D,I,P,U,W
A,B,C,D,I,P
H
H,I,P,W
A,B,D,I,P,U,W
A,B,D,I,P
V—Valmont Industries,
Inc.
W—Welded Tube Co. of
America
X—EXLTUBE
Nominal Size and
Thickness
Producer Code
7× 5× 1⁄2
7× 5× 3⁄8, 5⁄16
7× 5× 1⁄4, 3⁄16
7× 5× 1⁄8
7× 4× 3⁄8, 5⁄16
7× 4× 1⁄4, 3⁄16
7× 4× 1⁄8
7× 3× 3⁄8, 5⁄16
7× 3× 1⁄4, 3⁄16
7× 3× 1⁄8
B,C,P,U,W
B,C,I,P,U,W
A,B,C,H,I,P,U,W
A,B,C,I,P
B,C,D,H,I,P,U,W
A,B,C,D,H,I,P,U,W
A,B,C,H,I,P
B,C,D,H,I,P,W
A,B,C,D,H,I,P,W,X
A,B,C,D,H,I,P
6× 4× 1⁄2
6× 4× 3⁄8, 5⁄16
6× 4× 1⁄4
6× 4× 3⁄16
6× 4× 1⁄8
6× 3× 1⁄2
6× 3× 3⁄8, 5⁄16
6× 3× 1⁄4
6× 3× 3⁄16
6× 3× 1⁄8
6× 2× 3⁄8
6× 2× 5⁄16
6× 2× 1⁄4, 3⁄16
6× 2× 1⁄8
B,C,P,U,W
B,C,D,H,I,P,U,W
A,B,C,D,H,I,P,U,W,X
A,B,C,D,H,I,P,U,V,W,X
A,B,C,D,H,I,P,V,W
P,U
B,D,H,I,P,U
A,B,C,D,H,I,P,U,X
A,B,C,D,H,I,P,U,W,X
A,B,C,D,H,I,P,W
H
H,I,P,W
A,B,C,D,E,H,I,P,U,W,X
A,B,C,D,E,H,I,P,U,W
5× 4× 3⁄8, 5⁄16
5× 4× 1⁄4, 3⁄16
5× 3× 1⁄2
5× 3× 3⁄8, 5⁄16
5× 3× 1⁄4, 3⁄16
5× 3× 1⁄8
5× 2× 5⁄16
5× 2× 1⁄4, 3⁄16
5× 2× 1⁄8
I,P,W
B,C,D,I,P,U,W
C,P,U
B,C,D,H,I,P,U,W
A,B,C,D,E,H,I,P,U,W,X
A,B,C,D,E,H,I,P,U,W
I,P,W
A,B,C,D,E,H,I,P,U,W,X
A,B,C,D,E,H,I,P,U,W
4× 3× 5⁄16
4× 3× 1⁄4, 3⁄16
4× 3× 1⁄8
4× 2× 3⁄8
4× 2× 5⁄16
4× 2× 1⁄4, 3⁄16
4× 2× 1⁄8
B,I,P,W
A,B,C,D,E,H,I,P,U,W,X
A,B,C,D,E,H,I,P,U,W
H
H,I,P,W
A,B,C,D,E,H,I,P,U,W,X
A,B,C,E,H,I,P,U,W
3× 2× 5⁄16
3× 2× 1⁄4, 3⁄16
3× 2× 1⁄8
I
A,B,C,D,E,H,I,P,U,V,W,X
A,B,C,D,E,H,I,P,U,V,W
21⁄2 × 11⁄2 × 1⁄4, 3⁄16
H,X
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 24
DIMENSIONS AND PROPERTIES
Table 1-6.
Principal Producers of Steel Tubing (Round)
C—Copperweld Corp.
P—IPSCO
U—UNR-Leavitt, Div. of
UNR, Inc.
V—Valmont Industries,
Inc.
W—Welded Tube Co.
of America
X—EXLTUBE
Outside Diameter
and Thickness
Producer Code
Outside Diameter
and Thickness
Producer Code
20.000× .500,.375,.250
P*,W
6.626×.250,.188
6.625×.125
P,U,V,W
P,V,W
18.000× .500,.375,.250
P*,W
16.000× .500
16.000× .375,.250
16.000× .188
16.000× .125
P*,W
P,W
P,V*
V*
6.000×.500,.375,.312
6.000×.280
6.000×.250,.188,.125
W
X
V,W
14.000× .500,.438,.375,.250
14.000× .188
14.000× .125
P,W
P,V*
V*
5.563×.375
5.563×.258
5.563×.134
P,U
P,U,V,W
P,V,W
12.750× .500,.406,.375
12.750× .188× .125
P,W
P,V*
5.000×.500,.375,.312
5.000×.258
5.000×.250,.188
5.000×.125
P,C,W
P,X
C,P,U,V,W
P,U,V,W
10.750× .500,.365,.250
P,W
4.500×.237,.188,.125
P,U,V,W
10.000× .625,.500,.375,.312
10.000× .250,.188
10.000× .125
C
C,V
V
4.000×.337,.237
4.000×.266,.250,.188,.125
X
U,V,W
9.625×.500
9.625×.375,.312,.250,.188
C,U
C,P*,U
3.500×.318
3.500×.300
3.500×.250,.203,.188,.125
3.500×.226
X
P,W
P,U,V,W
P,X
8.625×.500
8.625×.375,.322
8.625×.250,.188
8.625×.125
C,P,U
C,P,U,W
C,P,U,V,W
P,V,W
3.000×.300,.216
X
2.875×.276
2.875×.250,.203,.188,.125
W
P,U,V,W
7.000×.500
7.000×.375,.312,.250
7.000×.188
7.000×.125
C,P,U
C,P,U,W
C,P,U,V,W
C,P,V,W
2.375,.250,.218,.188
2.375,.154,.125
P,V,W
P,U,V,W
6.625×.500,.432
6.625×.375,.312,.280
P,U
P,U,W
*Size is manufactured by Submerged Arc Welding (SAW) Process and is typically not stocked by steel service
centers. Other sizes are manufactured by Electric Resistance Welding and typically are available from steel
service centers. For more information contact the manufacturer or the American Institute for Hollow Structural
Sections.
Also, other sizes and wall thicknesses may be available. Contact an individual manufacturer for more details.
Steel Pipe: For availability contact the National Association of Steel Pipe Distributors, Inc.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL SHAPES
1 - 25
STRUCTURAL SHAPES
Designations, Dimensions, and Properties
The hot rolled shapes shown in Part 1 of this Manual are published in ASTM Specification
A6/A6M, Standard Specification for General Requirements for Rolled Steel Plates,
Shapes, Sheet Piling, and Bars for Structural Use.
W shapes have essentially parallel flange surfaces. The profile of a W shape of a given
nominal depth and weight available from different producers is essentially the same
except for the size of fillets between the web and flange.
HP bearing pile shapes have essentially parallel flange surfaces and equal web and
flange thicknesses. The profile of an HP shape of a given nominal depth and weight
available from different producers is essentially the same.
American Standard Beams (S) and American Standard Channels (C) have a slope of
approximately 17 percent (2 in 12 inches) on the inner flange surfaces. The profiles of S
and C shapes of a given nominal depth and weight available from different producers are
essentially the same.
The letter M designates shapes that cannot be classified as W, HP, or S shapes.
Similarly, MC designates channels that cannot be classified as C shapes. Because many
of the M and MC shapes are only available from a limited number of producers, or are
infrequently rolled, their availability should be checked prior to specifying these shapes.
They may or may not have slopes on their inner flange surfaces, dimensions for which
may be obtained from the respective producing mills.
The flange thickness given in the table from S, M, C, and MC shapes is the average
flange thickness.
In calculating the theoretical weights, properties, and dimensions of the rolled shapes
listed in Part 1 of this Manual, fillets and roundings have been included for all shapes
except angles. Because of differences in fillet radii among producers, actual properties
of rolled shapes may vary slightly from those tabulated. Dimensions for detailing are
generally based on the largest theoretical-size fillets produced.
Equal leg and unequal leg angle (L) shapes of the same nominal size available from
different producers have profiles which are essentially the same, except for the size of
fillet between the legs and the shape of the ends of the legs. The k distance given in the
tables for each angle is based on the theoretical largest size fillet available. Availability
of certain angles is subject to rolling accumulation and geographical location, and should
be checked with material suppliers.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 26
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Thickness
tw
tw
2
in.
in.
W44×335
W40×290
W40×262
W40×230
98.3
85.8
77.2
67.7
44.02
43.62
43.31
42.91
44
435⁄8
433⁄8
427⁄8
1.020
0.870
0.790
0.710
W40×593*
W40×503*
W40×431
W40×372
W40×321
W40×297
W40×277
W40×249
W40×215
W40×199
W40×174
174
148
127
109
94.1
87.4
81.3
73.3
63.3
58.4
51.1
42.99
42.05
41.26
40.63
40.08
39.84
39.69
39.38
38.98
38.67
38.20
43
421⁄16
411⁄4
405⁄8
401⁄16
397⁄8
393⁄4
393⁄8
39
385⁄8
381⁄4
1.790 113⁄16
1.540 19⁄16
1.340 15⁄16
1.160 13⁄16
1.000
1
0.930 15⁄16
0.830 13⁄16
3⁄
0.750
4
5⁄
0.650
8
5
0.650
⁄8
5
0.650
⁄8
W40×466*
W40×392*
W40×331
W40×278
W40×264
W40×235
W40×211
W40×183
W40×167
W40×149
137
115
97.6
81.8
77.6
68.9
62.0
53.7
49.1
43.8
42.44 427⁄16
41.57 419⁄16
40.79 4013⁄16
40.16 403⁄16
40.00
40
39.69 393⁄4
39.37 393⁄8
38.98
39
38.59 385⁄8
38.20 381⁄4
1.67
111⁄16
1.42
17⁄16
1.22
11⁄4
1.02
1
0.960
1
13
0.830
⁄16
3
0.750
⁄4
5
⁄8
0.650
5⁄
0.650
8
5⁄
0.630
8
W36×848*
W40×798*
W40×650*
W40×527*
W40×439*
W40×393*
W40×359*
W40×328*
W40×300
W40×280
W40×260
W40×245
W40×230
249
234
190
154
128
115
105
96.4
88.3
82.4
76.5
72.1
67.6
42.45
41.97
40.47
39.21
38.26
37.80
37.40
37.09
36.74
36.52
36.26
36.08
35.90
421⁄2
42
401⁄2
391⁄4
381⁄4
373⁄4
373⁄8
371⁄8
363⁄4
361⁄2
361⁄4
361⁄8
357⁄8
Flange
2.520
2.380
1.970
1.610
1.360
1.220
1.120
1.020
0.945
0.885
0.840
0.800
0.760
1
7⁄
8
13⁄
16
11⁄
16
21⁄2
23⁄8
2
15⁄8
13⁄8
11⁄4
11⁄8
1
15⁄
16
7⁄
8
13⁄
16
13⁄
16
3⁄
4
Width
bf
Thickness
tf
k
in.
k1
in.
in.
1.770
1.580
1.420
1.220
13⁄4
19⁄16
17⁄16
11⁄4
387⁄16 29⁄16
387⁄16 23⁄8
387⁄16 23⁄16
387⁄16
2
15⁄16
11⁄4
13⁄16
11⁄8
3⁄
4
11⁄
16
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
5⁄
16
5⁄
16
5⁄
16
16.690 163⁄4
16.420 167⁄16
16.220 161⁄4
16.060 161⁄16
15.910 157⁄8
15.825 157⁄8
15.830 157⁄8
15.750 153⁄4
15.750 153⁄4
15.750 153⁄4
15.750 153⁄4
3.230
2.760
2.360
2.050
1.770
1.650
1.575
1.420
1.220
1.065
0.830
31⁄4
23⁄4
23⁄8
21⁄16
13⁄4
15⁄8
19⁄16
17⁄16
11⁄4
11⁄16
13⁄
16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
47⁄16 21⁄16
315⁄16 115⁄16
39⁄16 17⁄8
31⁄4
13⁄4
215⁄16 111⁄16
31⁄16 111⁄16
23⁄4
15⁄8
25⁄8 19⁄16
23⁄8
11⁄2
21⁄4
11⁄2
2
11⁄2
13⁄
16
11⁄
16
5⁄
8
1⁄
2
1⁄
2
7⁄
16
3⁄
8
5⁄
16
5⁄
16
5⁄
16
12.640 125⁄8
12.360 123⁄8
12.170 123⁄16
11.970
12
11.930
12
11.890 117⁄8
11.810 113⁄4
11.810 113⁄4
11.810 113⁄4
11.810 113⁄4
2.950 215⁄16
2.520 21⁄2
2.130 21⁄8
1.810 113⁄16
1.730 13⁄4
1.575 17⁄16
1.415 19⁄16
1.220 11⁄4
1.025
1
0.830 13⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
343⁄16
41⁄8
2
311⁄16 17⁄8
35⁄16 113⁄16
3
111⁄16
215⁄16 111⁄16
23⁄4
15⁄8
25⁄8 19⁄16
23⁄8
11⁄2
23⁄16 11⁄2
2
11⁄2
11⁄4
13⁄16
1
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
7⁄
16
7⁄
16
3⁄
8
18.130
17.990
17.575
17.220
16.965
16.830
16.730
16.630
16.655
16.595
16.550
16.510
16.470
181⁄8
18
175⁄8
171⁄4
17
167⁄8
163⁄4
165⁄8
165⁄8
165⁄8
161⁄2
161⁄2
161⁄2
4.530 41⁄2
4.290 45⁄16
3.540 39⁄16
2.910 215⁄16
2.440 27⁄16
2.200 23⁄16
2.010
2
1.850 17⁄8
1.680 111⁄16
1.570 19⁄16
1.440 17⁄16
1.350 13⁄8
1.260 11⁄4
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
311⁄8
511⁄16
57⁄16
411⁄16
41⁄16
39⁄16
35⁄16
31⁄8
3
213⁄16
211⁄16
29⁄16
21⁄2
23⁄8
1
15.950
15.830
15.750
15.750
in.
T
153⁄4
157⁄8
153⁄4
153⁄4
1⁄
2
7⁄
16
3⁄
8
3⁄
8
in.
Distance
*Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
21⁄4
23⁄16
2
13⁄4
15⁄8
15⁄8
19⁄16
11⁄2
11⁄2
11⁄2
11⁄2
17⁄16
17⁄16
STRUCTURAL SHAPES
1 - 27
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
335
290
262
230
4.5
5.0
5.5
6.5
593
503
431
372
321
297
277
249
215
199
174
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
(1/ksi)
in.
38.1
44.7
49.2
54.8
44
32
26
21
2430
2140
1930
1690
5110
8220
12300
21200
31100
27100
24200
20800
2.6
3.0
3.4
3.9
4.5
4.8
5.0
5.5
6.5
7.4
9.5
19.1
22.2
25.5
29.5
34.2
36.8
41.2
45.6
52.6
52.6
52.6
—
—
—
—
—
47
38
31
23
23
23
4790
4110
3550
3100
2690
2500
2350
2120
1830
1690
1500
337
620
1100
1860
3240
4240
5370
7940
14000
20300
36000
466
392
331
278
264
235
211
183
167
149
2.1
2.5
2.9
3.3
3.4
3.8
4.2
4.8
5.8
7.1
20.5
24.1
28.0
33.5
35.6
41.2
45.6
52.6
52.6
54.3
—
—
—
57
50
38
31
23
23
22
4560
3920
3360
2860
2720
2430
2200
1900
1750
1610
848
798
650
527
439
393
359
328
300
280
260
245
230
2.0
2.1
2.5
3.0
3.5
3.8
4.2
4.5
5.0
5.3
5.7
6.1
6.5
12.5
13.2
16.0
19.6
23.1
25.8
28.1
30.9
33.3
35.6
37.5
39.4
41.4
—
—
—
—
—
—
—
—
58
51
46
41
37
7100
6720
5590
4630
3900
3540
3240
2980
2720
2560
2370
2230
2100
S
I
4
Axis Y-Y
r
S
I
4
r
3
Zx
in.
in.
in.
in.
in.3
1410
1240
1120
969
17.8
17.8
17.7
17.5
1200
1050
927
796
150
133
118
101
3.49
3.50
3.46
3.43
1620
1420
1270
1100
236
206
183
157
50400
41700
34800
29600
25100
23200
21900
19500
16700
14900
12200
2340
1980
1690
1460
1250
1170
1100
992
858
769
639
17.0
16.8
16.6
16.4
16.3
16.3
16.4
16.3
16.2
16.0
15.5
2520
2050
1690
1420
1190
1090
1040
926
796
695
541
302
250
208
177
150
138
132
118
101
88.2
68.8
3.81
3.72
3.65
3.60
3.56
3.54
3.58
3.56
3.54
3.45
3.26
2760
2300
1950
1670
1420
1330
1250
1120
963
868
715
481
394
327
277
234
215
204
182
156
137
107
473
851
1560
2910
3510
5310
7890
13700
20500
31400
36300
29900
24700
20500
19400
17400
15500
13300
11600
9780
1710
1440
1210
1020
971
874
785
682
599
512
16.3
16.1
15.9
15.8
15.8
15.9
15.8
15.7
15.3
14.9
1010
803
646
521
493
444
390
336
283
229
160
130
106
87.1
82.6
74.6
66.1
56.9
47.9
38.8
2.72
2.64
2.57
2.52
2.52
2.54
2.51
2.50
2.40
2.29
2050
1710
1430
1190
1130
1010
905
781
692
597
262
212
172
140
132
118
105
89.6
76.0
62.2
71
87
175
365
704
1040
1470
2040
2930
3730
5100
6430
8190
67400
62600
48900
38300
31000
27500
24800
22500
20300
18900
17300
16100
15000
3170
2980
2420
1950
1620
1450
1320
1210
1110
1030
953
895
837
16.4
16.4
16.0
15.8
15.6
15.5
15.4
15.3
15.2
15.1
15.0
15.0
14.9
4550
4200
3230
2490
1990
1750
1570
1420
1300
1200
1090
1010
940
501
467
367
289
235
208
188
171
156
144
132
123
114
4.27
4.24
4.12
4.02
3.95
3.90
3.87
3.84
3.83
3.81
3.78
3.75
3.73
3830
3570
2840
2270
1860
1660
1510
1380
1260
1170
1080
1010
943
799
743
580
454
367
325
292
265
241
223
204
190
176
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
Zy
in.
in.
3
1 - 28
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Flange
Thickness
tw
tw
2
in.
in.
Width
bf
in.
Distance
Thickness
tf
in.
T
k
k1
in.
in.
in.
W36×256
W40×232
W40×210
W40×194
W40×182
W40×170
W40×160
W40×150
W40×135
75.4
68.1
61.8
57.0
53.6
50.0
47.0
44.2
39.7
37.43
37.12
36.69
36.49
36.33
36.17
36.01
35.85
35.55
373⁄8
371⁄8
363⁄4
361⁄2
363⁄8
361⁄8
36
357⁄8
351⁄2
0.960
0.870
0.830
0.765
0.725
0.680
0.650
0.625
0.600
1
7⁄
8
13⁄
16
3⁄
4
3⁄
4
11⁄
16
5⁄
8
5⁄
8
5⁄
8
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
12.215
12.120
12.180
12.115
12.075
12.030
12.000
11.975
11.950
121⁄4
121⁄8
121⁄8
121⁄8
121⁄8
12
12
12
12
1.730
1.570
1.360
1.260
1.180
1.100
1.020
0.940
0.790
13⁄4
19⁄16
13⁄8
11⁄4
13⁄16
11⁄8
1
15⁄
16
13⁄
16
321⁄8
321⁄8
321⁄8
321⁄8
321⁄8
321⁄8
321⁄8
321⁄8
321⁄8
25⁄8
21⁄2
25⁄16
23⁄16
21⁄8
2
115⁄16
17⁄8
111⁄16
15⁄16
11⁄4
11⁄4
13⁄16
13⁄16
13⁄16
11⁄8
11⁄8
11⁄8
W33×354*
W40×318*
W40×291*
W40×263*
W40×241
W40×221
W40×201
104
93.5
85.6
77.4
70.9
65.0
59.1
35.55
35.16
34.84
34.53
34.18
33.93
33.68
351⁄2
351⁄8
347⁄8
341⁄2
341⁄8
337⁄8
335⁄8
1.160
1.040
0.960
0.870
0.830
0.775
0.715
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
16.100
15.985
15.905
15.805
15.860
15.805
15.745
161⁄8
16
157⁄8
153⁄4
157⁄8
153⁄4
153⁄4
2.090
1.890
1.730
1.570
1.400
1.275
1.150
21⁄16
17⁄8
13⁄4
19⁄16
13⁄8
11⁄4
11⁄8
293⁄4
293⁄4
293⁄4
293⁄4
293⁄4
293⁄4
293⁄4
27⁄8
211⁄16
29⁄16
23⁄8
23⁄16
21⁄16
115⁄16
13⁄8
15⁄16
11⁄4
13⁄16
13⁄16
13⁄16
11⁄8
W33×169
W40×152
W40×141
W40×130
W40×118
49.5
44.7
41.6
38.3
34.7
33.82
33.49
33.30
33.09
32.86
337⁄8
331⁄2
331⁄4
331⁄8
327⁄8
0.670
0.635
0.605
0.580
0.550
11⁄
16
5⁄
8
5⁄
8
9⁄
16
9⁄
16
3⁄
8
5⁄
16
5⁄
16
5⁄
16
5⁄
16
11.500
11.565
11.535
11.510
11.480
111⁄2
115⁄8
111⁄2
111⁄2
111⁄2
1.220
1.055
0.960
0.855
0.740
11⁄4
11⁄16
15⁄
16
7⁄
8
3⁄
4
293⁄4
293⁄4
293⁄4
293⁄4
293⁄4
21⁄16
17⁄8
13⁄4
111⁄16
19⁄16
11⁄8
11⁄8
11⁄16
11⁄16
11⁄16
W30×477*
W40×391*
W40×326*
W40×292*
W40×261
W40×235
W40×211
W40×191
W40×173
140
114
95.7
85.7
76.7
69.0
62.0
56.1
50.8
34.21
33.19
32.40
32.01
31.61
31.30
30.94
30.68
30.44
341⁄4
331⁄4
323⁄8
32
315⁄8
311⁄4
31
305⁄8
301⁄2
1.630
1.360
1.140
1.020
0.930
0.830
0.775
0.710
0.655
15⁄8
13⁄8
11⁄8
1
15⁄
16
13⁄
16
3⁄
4
11⁄
16
5⁄
8
13⁄
16
11⁄
16
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
3⁄
8
5⁄
16
15.865
15.590
15.370
15.255
15.155
15.055
15.105
15.040
14.985
157⁄8
155⁄8
153⁄8
151⁄2
151⁄8
15
151⁄8
15
15
2.950
2.440
2.050
1.850
1.650
1.500
1.315
1.185
1.065
3
27⁄16
21⁄16
17⁄8
15⁄8
11⁄2
15⁄16
13⁄16
11⁄16
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
33⁄4
31⁄4
213⁄16
25⁄8
27⁄16
21⁄4
21⁄8
115⁄16
11⁄16
19⁄16
17⁄16
15⁄16
11⁄4
13⁄16
11⁄8
11⁄8
11⁄16
11⁄16
W30×148
W40×132
W40×124
W40×116
W40×108
W40×99
W40×90
43.5
38.9
36.5
34.2
31.7
29.1
26.4
30.67
30.31
30.17
30.01
29.83
29.65
29.53
305⁄8
301⁄4
301⁄8
30
297⁄8
295⁄8
291⁄2
0.650
0.615
0.585
0.565
0.545
0.520
0.470
5⁄
8
5⁄
8
9⁄
16
9⁄
16
9⁄
16
1⁄
2
1⁄
2
5⁄
16
5⁄
16
5⁄
16
5⁄
16
5⁄
16
1⁄
4
1⁄
4
10.480
10.545
10.515
10.495
10.475
10.450
10.400
101⁄2
101⁄2
101⁄2
101⁄2
101⁄2
101⁄2
103⁄8
1.180
1.000
0.930
0.850
0.760
0.670
0.610
13⁄16
1
15⁄
16
7⁄
8
3⁄
4
11⁄
16
9⁄
16
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
263⁄4
2
13⁄4
111⁄16
15⁄8
19⁄16
17⁄16
15⁄16
1
11⁄16
1
1
1
1
1
*Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL SHAPES
1 - 29
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
256
232
210
194
182
170
160
150
135
3.5
3.9
4.5
4.8
5.1
5.5
5.9
6.4
7.6
354
318
291
263
241
221
201
k
Plastic
Modulus
Elastic Properties
Axis X-X
Axis Y-Y
X1
X2 × 106
ksi
ksi
2
(1/ksi)
in.
33.8
37.3
39.1
42.4
44.8
47.8
50.0
52.0
54.1
56
46
42
36
32
28
26
24
22
2840
2580
2320
2140
2020
1900
1780
1680
1520
2870
4160
6560
8850
11300
14500
18600
24200
38000
16800
15000
13200
12100
11300
10500
9750
9040
7800
895
809
719
664
623
580
542
504
439
14.9
14.8
14.6
14.6
14.5
14.5
14.4
14.3
14.0
528
468
411
375
347
320
295
270
225
3.8
4.2
4.6
5.0
5.7
6.2
6.8
25.8
28.8
31.2
34.5
36.1
38.7
41.9
—
—
—
54
49
43
36
3540
3200
2940
2670
2430
2240
2040
1030
1530
2130
3100
4590
6440
9390
21900
19500
17700
15800
14200
12800
11500
1230
1110
1010
917
829
757
684
14.5
14.4
14.4
14.3
14.1
14.1
14.0
169
152
141
130
118
4.7
5.5
6.0
6.7
7.8
44.7
47.2
49.6
51.7
54.5
32
29
26
24
22
2160
1940
1800
1660
1510
8150
12900
17800
25100
37700
9290
8160
7450
6710
5900
549
487
448
406
359
477
391
326
292
261
235
211
191
173
2.7
3.2
3.7
4.1
4.6
5.0
5.7
6.3
7.0
16.6
19.9
23.7
26.5
29.0
32.5
34.9
38.0
41.2
—
—
—
—
—
61
53
44
38
5420
4510
3860
3460
3110
2820
2510
2280
2070
193
386
735
1110
1690
2460
3950
5840
8540
26100
20700
16800
14900
13100
11700
10300
9170
8200
148
132
124
116
108
99
90
4.4
5.3
5.7
6.2
6.9
7.8
8.5
41.5
43.9
46.2
47.8
49.6
51.9
57.5
37
33
30
28
26
24
19
2310
2050
1930
1800
1680
1560
1430
6180
10500
13500
17700
24200
34100
47000
6680
5770
5360
4930
4470
3990
3620
S
I
4
r
S
I
86.5
77.2
67.5
61.9
57.6
53.2
49.1
45.1
37.7
2.65
2.62
2.58
2.56
2.55
2.53
2.50
2.47
2.38
1040
936
833
767
718
668
624
581
509
137
122
107
97.7
90.7
83.8
77.3
70.9
59.7
1460
1290
1160
1030
932
840
749
181
161
146
131
118
106
95.2
3.74
3.71
3.69
3.66
3.63
3.59
3.56
1420
1270
1150
1040
939
855
772
282
250
226
202
182
164
147
13.7
13.5
13.4
13.2
13.0
310
273
246
218
187
53.9
47.2
42.7
37.9
32.6
2.50
2.47
2.43
2.39
2.32
629
559
514
467
415
1530
1250
1030
928
827
746
663
598
539
13.7
13.5
13.2
13.2
13.1
13.0
12.9
12.8
12.7
1970
1550
1240
1100
959
855
757
673
598
249
198
162
144
127
114
100
89.5
79.8
3.75
3.68
3.61
3.58
3.54
3.52
3.49
3.46
3.43
1790
1430
1190
1060
941
845
749
673
605
436
380
355
329
299
269
245
12.4
12.2
12.1
12.0
11.9
11.7
11.7
227
196
181
164
146
128
115
43.3
37.2
34.4
31.3
27.9
24.5
22.1
2.28
2.25
2.23
2.19
2.15
2.10
2.09
500
437
408
378
346
312
283
in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
Zy
in.3
in.
3
Zx
in.
in.
4
r
in.
in.
3
84.4
73.9
66.9
59.5
51.3
390
310
252
223
196
175
154
138
123
68.0
58.4
54.0
49.2
43.9
38.6
34.7
1 - 30
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Flange
Thickness
tw
tw
2
in.
in.
Width
bf
in.
Distance
Thickness
tf
T
in.
k
k1
in.
in.
in.
W27×539*
W40×448*
W40×368*
W40×307*
W40×258
W40×235
W40×217
W40×194
W40×178
W40×161
W40×146
158
131
108
90.2
75.7
69.1
63.8
57.0
52.3
47.4
42.9
32.52
31.42
30.39
29.61
28.98
28.66
28.43
28.11
27.81
27.59
27.38
321⁄2
313⁄8
303⁄8
295⁄8
29
285⁄8
283⁄8
281⁄8
273⁄4
275⁄8
273⁄8
1.970
1.650
1.380
1.160
0.980
0.910
0.830
0.750
0.725
0.660
0.605
2
15⁄8
13⁄8
13⁄16
1
15⁄
16
13⁄
16
3⁄
4
3⁄
4
11⁄
16
5⁄
8
1
13⁄
16
11⁄
16
5⁄
8
1⁄
2
1⁄
2
7⁄
16
3⁄
8
3⁄
8
3⁄
8
5⁄
16
15.255
14.940
14.665
14.445
14.270
14.190
14.115
14.035
14.085
14.020
13.965
151⁄4
15
145⁄8
141⁄2
141⁄4
141⁄4
141⁄8
14
141⁄8
14
14
3.540
2.990
2.480
2.090
1.770
1.610
1.500
1.340
1.190
1.080
0.975
39⁄16
3
21⁄2
21⁄16
13⁄4
15⁄8
11⁄2
15⁄16
13⁄16
11⁄16
1
24
24
24
24
24
24
24
24
24
24
24
41⁄4
311⁄16
33⁄16
213⁄16
21⁄2
25⁄16
23⁄16
21⁄16
17⁄8
113⁄16
111⁄16
15⁄8
11⁄2
15⁄16
11⁄4
11⁄8
11⁄8
11⁄16
1
11⁄16
1
1
W27×129
W40×114
W40×102
W40×94
W40×84
37.8
33.5
30.0
27.7
24.8
27.63
27.29
27.09
26.92
26.71
275⁄8
271⁄4
271⁄8
267⁄8
263⁄4
0.610
0.570
0.515
0.490
0.460
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
5⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
10.010
10.070
10.015
9.990
9.960
10
101⁄8
10
10
10
1.100
0.930
0.830
0.745
0.640
11⁄8
15⁄
16
13⁄
16
3⁄
4
5⁄
8
24
24
24
24
24
113⁄16
15⁄8
19⁄16
17⁄16
13⁄8
15⁄
16
15⁄
16
15⁄
16
15⁄
16
15⁄
16
W24×492*
W40×408*
W40×335*
W40×279*
W40×250*
W40×229
W40×207
W40×192
W40×176
W40×162
W40×146
W40×131
W40×117
W40×104
144
119
98.4
82.0
73.5
67.2
60.7
56.3
51.7
47.7
43.0
38.5
34.4
30.6
29.65
28.54
27.52
26.73
26.34
26.02
25.71
25.47
25.24
25.00
24.74
24.48
24.26
24.06
295⁄8
281⁄2
271⁄2
263⁄4
263⁄8
26
253⁄4
251⁄2
251⁄4
25
243⁄4
241⁄2
241⁄4
24
1.970
1.650
1.380
1.160
1.040
0.960
0.870
0.810
0.750
0.705
0.650
0.605
0.550
0.500
2
15⁄8
13⁄8
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
5⁄
8
9⁄
16
1⁄
2
1
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
1⁄
4
14.115
13.800
13.520
13.305
13.185
13.110
13.010
12.950
12.890
12.955
12.900
12.855
12.800
12.750
141⁄8
133⁄4
131⁄2
131⁄4
131⁄8
131⁄8
13
13
127⁄8
13
127⁄8
127⁄8
123⁄4
123⁄4
3.540
2.990
2.480
2.090
1.890
1.730
1.570
1.460
1.340
1.220
1.090
0.960
0.850
0.750
39⁄16
3
21⁄2
21⁄16
17⁄8
13⁄4
19⁄16
17⁄16
15⁄16
11⁄4
11⁄16
15⁄
16
7⁄
8
3⁄
4
21
21
21
21
21
21
21
21
21
21
21
21
21
21
45⁄16
33⁄4
31⁄4
27⁄8
211⁄16
21⁄2
23⁄8
21⁄4
21⁄8
2
17⁄8
13⁄4
15⁄8
11⁄2
19⁄16
13⁄8
11⁄4
11⁄8
11⁄8
1
1
1
15⁄
16
11⁄16
1
1 ⁄16
11⁄16
1
1
W24×103
W40×94
W40×84
W40×76
W40×68
30.3
27.7
24.7
22.4
20.1
24.53
24.31
24.10
23.92
23.73
241⁄2
241⁄4
241⁄8
237⁄8
233⁄4
0.550
0.515
0.470
0.440
0.415
9⁄
16
1⁄
2
1⁄
2
7⁄
16
7⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
1⁄
4
9.000
9.065
9.020
8.990
8.965
9
91⁄8
9
9
9
0.980
0.875
0.770
0.680
0.585
1
7⁄
8
3⁄
4
11⁄
16
9⁄
16
21
21
21
21
21
13⁄4
15⁄8
19⁄16
17⁄16
13⁄8
13⁄
16
15⁄
16
15⁄
16
15⁄
16
W24×62
W40×55
18.2
16.2
23.74
23.57
233⁄4
235⁄8
0.430
0.395
7⁄
16
3⁄
8
1⁄
4
3⁄
16
7.040
7.005
7
7
0.590
0.505
9⁄
16
1⁄
2
21
21
13⁄8
15⁄16
15⁄
16
15⁄
16
* Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1
STRUCTURAL SHAPES
1 - 31
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
539
448
368
307
258
235
217
194
178
161
146
2.2
2.5
3.0
3.5
4.0
4.4
4.7
5.2
5.9
6.5
7.2
129
114
102
94
84
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
12.3
14.7
17.6
20.9
24.7
26.6
29.2
32.3
33.4
36.7
40.0
—
—
—
—
—
—
—
61
57
47
40
7160
6070
5100
4320
3670
3360
3120
2800
2550
2320
2110
66
123
243
463
873
1230
1640
2520
3740
5370
7900
25500
20400
16100
13100
10800
9660
8870
7820
6990
6280
5630
4.5
5.4
6.0
6.7
7.8
39.7
42.5
47.0
49.4
52.7
41
35
29
26
23
2390
2100
1890
1740
1570
5340
9220
14000
19900
31100
492
408
335
279
250
229
207
192
176
162
146
131
117
104
2.0
2.3
2.7
3.2
3.5
3.8
4.1
4.4
4.8
5.3
5.9
6.7
7.5
8.5
10.9
13.1
15.6
18.6
20.7
22.5
24.8
26.6
28.7
30.6
33.2
35.6
39.2
43.1
—
—
—
—
—
—
—
—
—
—
58
50
42
34
7950
6780
5700
4840
4370
4020
3650
3410
3140
2870
2590
2330
2090
1860
103
94
84
76
68
4.6
5.2
5.9
6.6
7.7
39.2
41.9
45.9
49.0
52.0
42
37
30
27
24
62
55
6.0
6.9
50.1
54.6
25
21
S
I
r
S
3
Zx
in.
in.
in.3
1570
1300
1060
884
742
674
624
556
502
455
411
12.7
12.5
12.2
12.0
11.9
11.8
11.8
11.7
11.6
11.5
11.4
2110
1670
1310
1050
859
768
704
618
555
497
443
277
224
179
146
120
108
99.8
88.1
78.8
70.9
63.5
3.66
3.57
3.48
3.42
3.37
3.33
3.32
3.29
3.26
3.24
3.21
1880
1530
1240
1020
850
769
708
628
567
512
461
437
351
279
227
187
168
154
136
122
109
97.5
4760
4090
3620
3270
2850
345
299
267
243
213
11.2
11.0
11.0
10.9
10.7
184
159
139
124
106
36.8
31.5
27.8
24.8
21.2
2.21
2.18
2.15
2.12
2.07
395
343
305
278
244
57.6
49.3
43.4
38.8
33.2
43
79
156
297
436
605
876
1150
1590
2260
3420
5290
8190
12900
19100
15100
11900
9600
8490
7650
6820
6260
5680
5170
4580
4020
3540
3100
1290
1060
864
718
644
588
531
491
450
414
371
329
291
258
11.5
11.3
11.0
10.8
10.7
10.7
10.6
10.5
10.5
10.4
10.3
10.2
10.1
10.1
1670
1320
1030
823
724
651
578
530
479
443
391
340
297
259
237
191
152
124
110
99.4
88.8
81.8
74.3
68.4
60.5
53.0
46.5
40.7
3.41
3.33
3.23
3.17
3.14
3.11
3.08
3.07
3.04
3.05
3.01
2.97
2.94
2.91
1550
1250
1020
835
744
676
606
559
511
468
418
370
327
289
375
300
238
193
171
154
137
126
115
105
93.2
81.5
71.4
62.4
2400
2180
1950
1760
1590
5280
7800
12200
18600
29000
3000
2700
2370
2100
1830
245
222
196
176
154
9.96
9.87
9.79
9.69
9.55
119
109
94.4
82.5
70.4
26.5
24.0
20.9
18.4
15.7
1.99
1.98
1.95
1.92
1.87
280
254
224
200
177
41.5
37.5
32.6
28.6
24.5
1700
1540
25100
39600
1550
1350
131
114
9.23
9.11
34.5
29.1
1.38
1.34
153
134
15.7
13.3
9.80
8.30
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
Zy
in.
in.
4
r
in.
in.
3
I
in.
(1/ksi)
4
Axis Y-Y
1 - 32
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Flange
Thickness
tw
tw
2
in.
in.
Width
bf
Distance
Thickness
tf
in.
in.
T
k
k1
in.
in.
in.
W21×201
W40×182
W40×166
W40×147
W40×132
W40×122
W40×111
W40×101
59.2
53.6
48.8
43.2
38.8
35.9
32.7
29.8
23.03
22.72
22.48
22.06
21.83
21.68
21.51
21.36
23
223⁄4
221⁄2
22
217⁄8
215⁄8
211⁄2
213⁄8
0.910
0.830
0.750
0.720
0.650
0.600
0.550
0.500
15⁄
16
13⁄
16
3⁄
4
3⁄
4
5⁄
8
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
1⁄
4
12.575
12.500
12.420
12.510
12.440
12.390
12.340
12.290
125⁄8
121⁄2
123⁄8
121⁄2
121⁄2
123⁄8
123⁄8
121⁄4
1.630
1.480
1.360
1.150
1.035
0.960
0.875
0.800
15⁄8
11⁄2
13⁄8
11⁄8
11⁄16
15⁄
16
7⁄
8
13⁄
16
181⁄4
181⁄4
181⁄4
181⁄4
181⁄4
181⁄4
181⁄4
181⁄4
23⁄8
21⁄4
21⁄8
17⁄8
113⁄16
111⁄16
15⁄8
19⁄16
1
1
15⁄
16
11⁄16
1
1
15⁄
16
15⁄
16
W21×93
W40×83
W40×73
W40×68
W40×62
27.3
24.3
21.5
20.0
18.3
21.62
21.43
21.24
21.13
20.99
215⁄8
213⁄8
211⁄4
211⁄8
21
0.580
0.515
0.455
0.430
0.400
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
5⁄
16
1⁄
4
1⁄
4
1⁄
4
3⁄
16
8.420
8.355
8.295
8.270
8.240
83⁄8
83⁄8
81⁄4
81⁄4
81⁄4
0.930
0.835
0.740
0.685
0.615
15⁄
16
13⁄
16
3⁄
4
11⁄
16
5⁄
8
181⁄4
181⁄4
181⁄4
181⁄4
181⁄4
111⁄16
19⁄16
11⁄2
17⁄16
13⁄8
15⁄
16
15⁄
16
7⁄
8
7⁄
8
W21×57
W40×50
W40×44
16.7
14.7
13.0
21.06
20.83
20.66
21
207⁄8
205⁄8
0.405
0.380
0.350
3⁄
8
3⁄
8
3⁄
8
3⁄
16
3⁄
16
3⁄
16
6.555
6.530
6.500
61⁄2
61⁄2
61⁄2
0.650
0.535
0.450
5⁄
8
9⁄
16
7⁄
16
181⁄4
181⁄4
181⁄4
13⁄8
15⁄16
13⁄16
7⁄
8
7⁄
8
7⁄
8
W18×311*
W40×283*
W40×258*
W40×234*
W40×211*
W40×192
W40×175
W40×158
W40×143
W40×130
91.5
83.2
75.9
68.8
62.1
56.4
51.3
46.3
42.1
38.2
22.32
21.85
21.46
21.06
20.67
20.35
20.04
19.72
19.49
19.25
223⁄8
217⁄8
211⁄2
21
205⁄8
203⁄8
20
193⁄4
191⁄2
191⁄4
1.520
1.400
1.280
1.160
1.060
0.960
0.890
0.810
0.730
0.670
11⁄2
13⁄8
11⁄4
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
3⁄
4
11⁄
16
5⁄
8
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
12.005
11.890
11.770
11.650
11.555
11.455
11.375
11.300
11.220
11.160
12
117⁄8
113⁄4
115⁄8
111⁄2
111⁄2
113⁄8
111⁄4
111⁄4
111⁄8
2.740 23⁄4
2.500 21⁄2
2.300 25⁄16
2.110 21⁄8
1.910 115⁄16
1.750 13⁄4
1.590 19⁄16
1.440 17⁄16
1.320 15⁄16
1.200 13⁄16
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
37⁄16
33⁄16
3
23⁄4
9
2 ⁄16
27⁄16
21⁄4
21⁄8
2
17⁄8
13⁄16
13⁄16
11⁄8
1
1
15⁄
16
7⁄
8
7⁄
8
13⁄
16
13⁄
16
W18×119
W40×106
W40×97
W40×86
W40×76
35.1
31.1
28.5
25.3
22.3
18.97
18.73
18.59
18.39
18.21
19
183⁄4
185⁄8
183⁄8
181⁄4
0.655
0.590
0.535
0.480
0.425
5⁄
8
9⁄
16
9⁄
16
1⁄
2
7⁄
16
5⁄
16
5⁄
16
5⁄
16
1⁄
4
1⁄
4
11.265
11.200
11.145
11.090
11.035
111⁄4
111⁄4
111⁄8
111⁄8
11
1.060
0.940
0.870
0.770
0.680
11⁄16
15⁄
16
7⁄
8
3⁄
4
11⁄
16
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
13⁄4
15⁄8
19⁄16
17⁄16
13⁄8
15⁄
16
15⁄
16
7⁄
8
7⁄
8
13⁄
16
W18×71
W40×65
W40×60
W40×55
W40×50
20.8
19.1
17.6
16.2
14.7
18.47
18.35
18.24
18.11
17.99
181⁄2
183⁄8
181⁄4
181⁄8
18
0.495
0.450
0.415
0.390
0.355
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
1⁄
4
1⁄
4
1⁄
4
3⁄
16
3⁄
16
7.635
7.590
7.555
7.530
7.495
75⁄8
75⁄8
71⁄2
71⁄2
71⁄2
0.810
0.750
0.695
0.630
0.570
13⁄
16
3⁄
4
11⁄
16
5⁄
8
9⁄
16
151⁄2
151⁄2
151⁄2
151⁄2
151⁄2
11⁄2
17⁄16
13⁄8
15⁄16
11⁄4
7⁄
8
7⁄
8
13⁄
16
13⁄
16
13⁄
16
W18×46
W40×40
W40×35
13.5
11.8
10.3
18.06
17.90
17.70
18
177⁄8
173⁄4
0.360
0.315
0.300
3⁄
8
5⁄
16
5⁄
16
3⁄
16
3⁄
16
3⁄
16
6.060
6.015
6.000
6
6
6
0.605
0.525
0.425
5⁄
8
1⁄
2
7⁄
16
151⁄2
151⁄2
151⁄2
11⁄4
13⁄16
11⁄8
13⁄
16
13⁄
16
3⁄
4
*Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1
STRUCTURAL SHAPES
1 - 33
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
201
182
166
147
132
122
111
101
3.9
4.2
4.6
5.4
6.0
6.5
7.1
7.7
93
83
73
68
62
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
20.6
22.6
24.9
26.1
28.9
31.3
34.1
37.5
—
—
—
—
—
—
55
45
4290
3910
3590
3140
2840
2630
2400
2200
4.5
5.0
5.6
6.0
6.7
32.3
36.4
41.2
43.6
46.9
61
48
38
34
29
57
50
44
5.0
6.1
7.2
46.3
49.4
53.6
311
283
258
234
211
192
175
158
143
130
2.2
2.4
2.6
2.8
3.0
3.3
3.6
3.9
4.2
4.6
119
106
97
86
76
S
I
4
in.
in.
453
649
904
1590
2350
3160
4510
6400
5310
4730
4280
3630
3220
2960
2670
2420
2680
2400
2140
2000
1820
3460
5250
8380
10900
15900
30
26
22
1960
1730
1550
10.6
11.5
12.5
13.8
15.1
16.7
18.0
19.8
21.9
23.9
—
—
—
—
—
—
—
—
—
—
5.3
6.0
6.4
7.2
8.1
24.5
27.2
30.0
33.4
37.8
71
65
60
55
50
4.7
5.1
5.4
6.0
6.6
46
40
35
5.0
5.7
7.1
Axis Y-Y
r
S
I
4
r
3
Zx
in.
in.
in.
in.
in.3
461
417
380
329
295
273
249
227
9.47
9.40
9.36
9.17
9.12
9.09
9.05
9.02
542
483
435
376
333
305
274
248
86.1
77.2
70.1
60.1
53.5
49.2
44.5
40.3
3.02
3.00
2.98
2.95
2.93
2.92
2.90
2.89
530
476
432
373
333
307
279
253
133
119
108
92.6
82.3
75.6
68.2
61.7
2070
1830
1600
1480
1330
192
171
151
140
127
8.70
8.67
8.64
8.60
8.54
92.9
81.4
70.6
64.7
57.5
22.1
19.5
17.0
15.7
13.9
1.84
1.83
1.81
1.80
1.77
221
196
172
160
144
34.7
30.5
26.6
24.4
21.7
13100
22600
36600
1170
984
843
111
94.5
81.6
8.36
8.18
8.06
30.6
24.9
20.7
1.35
1.30
1.26
129
110
95.4
14.8
12.2
10.2
8160
7520
6920
6360
5800
5320
4870
4430
4060
3710
38
52
71
97
140
194
274
396
557
789
6960
6160
5510
4900
4330
3870
3450
3060
2750
2460
624
564
514
466
419
380
344
310
282
256
8.72
8.61
8.53
8.44
8.35
8.28
8.20
8.12
8.09
8.03
795
704
628
558
493
440
391
347
311
278
132
118
107
95.8
85.3
76.8
68.8
61.4
55.5
49.9
2.95
2.91
2.88
2.85
2.82
2.79
2.76
2.74
2.72
2.70
753
676
611
549
490
442
398
356
322
291
207
185
166
149
132
119
106
94.8
85.4
76.7
—
—
—
57
45
3340
2990
2750
2460
2180
1210
1880
2580
4060
6520
2190
1910
1750
1530
1330
231
204
188
166
146
7.90
7.84
7.82
7.77
7.73
253
220
201
175
152
44.9
39.4
36.1
31.6
27.6
2.69
2.66
2.65
2.63
2.61
261
230
211
186
163
69.1
60.5
55.3
48.4
42.2
32.4
35.7
38.7
41.2
45.2
61
50
43
38
31
2680
2470
2290
2110
1920
3310
4540
6080
8540
12400
1170
1070
984
890
800
127
117
108
98.3
88.9
7.50
7.49
7.47
7.41
7.38
60.3
54.8
50.1
44.9
40.1
15.8
14.4
13.3
11.9
10.7
1.70
1.69
1.69
1.67
1.65
145
133
123
112
101
24.7
22.5
20.6
18.5
16.6
44.6
51.0
53.5
32
25
22
2060
1810
1590
10100
17200
30300
712
612
510
78.8
68.4
57.6
7.25
7.21
7.04
22.5
19.1
15.3
9.35
7.64
6.36
7.43
6.35
5.12
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.29
1.27
1.22
3
Zy
in.
(1/ksi)
3
90.7
78.4
66.5
11.7
9.95
8.06
1 - 34
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Thickness
tw
in.
Flange
tw
2
in.
Width
bf
in.
Distance
Thickness
tf
in.
T
k
in.
in.
k1
in.
W16×100
W16×89
W16×77
W16×67
29.4
26.2
22.6
19.7
16.97
16.75
16.52
16.33
17
163⁄4
161⁄2
163⁄8
0.585
0.525
0.455
0.395
9⁄
16
1⁄
2
7⁄
16
3⁄
8
5⁄
16
1⁄
4
1⁄
4
3⁄
16
10.425
10.365
10.295
10.235
103⁄8
103⁄8
101⁄4
101⁄4
0.985
0.875
0.760
0.665
1
7⁄
8
3⁄
4
11⁄
16
135⁄8 111⁄16
135⁄8 19⁄16
135⁄8 17⁄16
135⁄8 13⁄8
15⁄
16
7⁄
8
7⁄
8
13⁄
16
W16×57
W16×50
W16×45
W16×40
W16×36
16.8
14.7
13.3
11.8
10.6
16.43
16.26
16.13
16.01
15.86
163⁄8
161⁄4
161⁄8
16
157⁄8
0.430
0.380
0.345
0.305
0.295
7⁄
16
3⁄
8
3⁄
8
5⁄
16
5⁄
16
1⁄
4
3⁄
16
3⁄
16
3⁄
16
3⁄
16
7.120
7.070
7.035
6.995
6.985
71⁄8
71⁄8
7
7
7
0.715
0.630
0.565
0.505
0.430
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
135⁄8
135⁄8
135⁄8
135⁄8
135⁄8
13⁄8
15⁄16
11⁄4
13⁄16
11⁄8
7⁄
8
13⁄
16
13⁄
16
13⁄
16
3⁄
4
9.12 15.88
7.68 15.69
157⁄8
153⁄4
0.275
0.250
1⁄
4
1⁄
4
1⁄
5.525
5.500
51⁄2
51⁄2
0.440
0.345
7⁄
16
3⁄
8
135⁄8
135⁄8
11⁄8
11⁄16
3⁄
4
3⁄
4
17⁄8
19⁄16
17⁄16
15⁄16
13⁄16
11⁄8
1
18.560
17.890
17.650
17.415
17.200
17.010
16.835
181⁄2
177⁄8
175⁄8
173⁄8
171⁄4
17
167⁄8
5.120 51⁄8
4.910 415⁄16
4.520 41⁄2
4.160 43⁄16
3.820 313⁄16
3.500 31⁄2
3.210 33⁄16
111⁄4 513⁄16 21⁄2
111⁄4 59⁄16 23⁄16
111⁄4 53⁄16 21⁄16
111⁄4 413⁄16 115⁄16
111⁄4 41⁄2 113⁄16
111⁄4 43⁄16 13⁄4
111⁄4 37⁄8
15⁄8
15⁄
16.695
16.590
16.475
16.360
16.230
16.110
15.995
15.890
15.800
15.710
15.650
15.565
15.500
163⁄4
165⁄8
161⁄2
163⁄8
161⁄4
161⁄8
16
157⁄8
153⁄4
153⁄4
155⁄8
155⁄8
151⁄2
3.035 31⁄16
2.845 27⁄8
2.660 211⁄16
2.470 21⁄2
2.260 21⁄4
2.070 21⁄16
1.890 17⁄8
1.720 13⁄4
1.560 19⁄16
1.440 17⁄16
1.310 15⁄16
1.190 13⁄16
1.090 11⁄16
111⁄4 311⁄16
111⁄4 31⁄2
111⁄4 35⁄16
111⁄4 31⁄8
111⁄4 215⁄16
111⁄4 23⁄4
111⁄4 29⁄16
111⁄4 23⁄8
111⁄4 21⁄4
111⁄4 21⁄8
111⁄4
2
111⁄4 17⁄8
111⁄4 13⁄4
W16×31
W16×26
W14×808*
W16×730*
W16×665*
W16×605*
W16×550*
W16×500*
W16×455*
237
215
196
178
162
147
134
22.84
22.42
21.64
20.92
20.24
19.60
19.02
227⁄8
223⁄8
215⁄8
207⁄8
201⁄4
195⁄8
19
3.740 33⁄4
3.070 31⁄16
2.830 213⁄16
2.595 25⁄8
2.380 23⁄8
2.190 23⁄16
2.015
2
W14×426*
W16×398*
W16×370*
W16×342*
W16×311*
W16×283*
W16×257*
W16×233*
W16×211
W16×193
W16×176
W16×159
W16×145
125
117
109
101
91.4
83.3
75.6
68.5
62.0
56.8
51.8
46.7
42.7
18.67
18.29
17.92
17.54
17.12
16.74
16.38
16.04
15.72
15.48
15.22
14.98
14.78
185⁄8
181⁄4
177⁄8
171⁄2
171⁄8
163⁄4
163⁄8
16
153⁄4
151⁄2
151⁄4
15
143⁄4
1.875
1.770
1.655
1.540
1.410
1.290
1.175
1.070
0.980
0.890
0.830
0.745
0.680
17⁄8
13⁄4
15⁄8
19⁄16
17⁄16
15⁄16
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
1⁄
7⁄
13⁄
13⁄
3⁄
8
8
16
8
16
16
4
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
*Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
19⁄16
11⁄2
17⁄16
13⁄8
15⁄16
11⁄4
13⁄16
13⁄16
11⁄8
11⁄16
11⁄16
1
1
STRUCTURAL SHAPES
1 - 35
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Compact
NomSection
inal
Criteria
Wt.
per
Fy′′′
bf
h
ft
2tf tw
lb
ksi
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
2
(1/ksi)
S
I
4
Axis Y-Y
r
3
in.
in.
175
155
134
117
S
I
4
r
3
Zx
3
Zy
in.3
in.
in.
in.
in.
in.
7.10
7.05
7.00
6.96
186
163
138
119
35.7
31.4
26.9
23.2
2.51
2.49
2.47
2.46
198
175
150
130
54.9
48.1
41.1
35.5
12.1
10.5
9.34
8.25
7.00
1.60
1.59
1.57
1.57
1.52
105
92.0
82.3
72.9
64.0
18.9
16.3
14.5
12.7
10.8
4.49 1.17
3.49 1.12
54.0
44.2
100
89
77
67
5.3
5.9
6.8
7.7
24.3
27.0
31.2
35.9
—
—
—
50
3450
3090
2680
2350
1040
1630
2790
4690
1490
1300
1110
954
57
50
45
40
36
5.0
5.6
6.2
6.9
8.1
33.0
37.4
41.2
46.6
48.1
59
46
38
30
28
2650 3400
2340 5530
2120 8280
1890 12900
1700 20800
758
659
586
518
448
92.2
81.0
72.7
64.7
56.5
6.72
6.68
6.65
6.63
6.51
43.1
37.2
32.8
28.9
24.5
31
26
6.3
8.0
51.6
56.8
24
20
1740 20000
1470 40900
375
301
47.2
38.4
6.41
6.26
12.4
9.59
808
730
665
605
550
500
455
1.8
1.8
2.0
2.1
2.3
2.4
2.6
3.4
3.7
4.0
4.4
4.8
5.2
5.7
—
—
—
—
—
—
—
18900
17500
16300
15100
14200
13100
12200
1.45
1.90
2.50
3.20
4.20
5.50
7.30
16000
14300
12400
10800
9430
8210
7190
1400
1280
1150
1040
931
838
756
8.21
8.17
7.98
7.80
7.63
7.48
7.33
5510
4720
4170
3680
3250
2880
2560
594
527
472
423
378
339
304
4.82
4.69
4.62
4.55
4.49
4.43
4.38
1834
1660
1480
1320
1180
1050
936
927
816
730
652
583
522
468
426
398
370
342
311
283
257
233
211
193
176
159
145
2.8
2.9
3.1
3.3
3.6
3.9
4.2
4.6
5.1
5.5
6.0
6.5
7.1
6.1
6.4
6.9
7.4
8.1
8.8
9.7
10.7
11.6
12.8
13.7
15.3
16.8
—
—
—
—
—
—
—
—
—
—
—
—
—
11500
10900
10300
9600
8820
8120
7460
6820
6230
5740
5280
4790
4400
8.90
11.0
13.9
17.9
24.4
33.4
46.1
64.9
91.8
125
173
249
348
6600
6000
5440
4900
4330
3840
3400
3010
2660
2400
2140
1900
1710
707
656
607
559
506
459
415
375
338
310
281
254
232
7.26
7.16
7.07
6.98
6.88
6.79
6.71
6.63
6.55
6.50
6.43
6.38
6.33
2360
2170
1990
1810
1610
1440
1290
1150
1030
931
838
748
677
283
262
241
221
199
179
161
145
130
119
107
96.2
87.3
4.34
4.31
4.27
4.24
4.20
4.17
4.13
4.10
4.07
4.05
4.02
4.00
3.98
869
801
736
672
603
542
487
436
390
355
320
287
260
434
402
370
338
304
274
246
221
198
180
163
146
133
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.03
5.48
1 - 36
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Thickness
tw
in.
Flange
tw
2
in.
Width
bf
Distance
Thickness
tf
in.
in.
T
k
k1
in.
in.
in.
W14×132
W16×120
W16×109
W16×99
W16×90
38.8
35.3
32.0
29.1
26.5
14.66
14.48
14.32
14.16
14.02
145⁄8
141⁄2
143⁄8
141⁄8
14
0.645
0.590
0.525
0.485
0.440
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
5⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
14.725
14.670
14.605
14.565
14.520
143⁄4
145⁄8
145⁄8
145⁄8
141⁄2
1.030
0.940
0.860
0.780
0.710
1
15⁄
16
7⁄
8
3⁄
4
11⁄
16
111⁄4
111⁄4
111⁄4
111⁄4
111⁄4
111⁄16
15⁄8
19⁄16
17⁄16
13⁄8
15⁄
16
15⁄
16
7⁄
8
7⁄
8
7⁄
8
W14×82
W16×74
W16×68
W16×61
24.1
21.8
20.0
17.9
14.31
14.17
14.04
13.89
141⁄4
141⁄8
14
137⁄8
0.510
0.450
0.415
0.375
1⁄
2
7⁄
16
7⁄
16
3⁄
8
1⁄
4
1⁄
4
1⁄
4
3⁄
16
10.130
10.070
10.035
9.995
101⁄8
101⁄8
10
10
0.855
0.785
0.720
0.645
7⁄
8
13⁄
16
3⁄
4
5⁄
8
11
11
11
11
15⁄8
19⁄16
11⁄2
17⁄16
15⁄
16
15⁄
16
15⁄
16
W14×53
W16×48
W16×43
15.6
14.1
12.6
13.92
13.79
13.66
137⁄8
133⁄4
135⁄8
0.370
0.340
0.305
3⁄
8
5⁄
16
5⁄
16
3⁄
16
3⁄
16
3⁄
16
8.060
8.030
7.995
8
8
8
0.660
0.595
0.530
11⁄
16
5⁄
8
1⁄
2
11
11
11
17⁄16
13⁄8
15⁄16
15⁄
16
7⁄
8
7⁄
8
W14×38
W16×34
W16×30
11.2
10.0
8.85
14.10
13.98
13.84
141⁄8
14
137⁄8
0.310
0.285
0.270
5⁄
16
5⁄
16
1⁄
4
3⁄
16
3⁄
16
1⁄
8
6.770
6.745
6.730
63⁄4
63⁄4
63⁄4
0.515
0.455
0.385
1⁄
2
7⁄
16
3⁄
8
12
12
12
11⁄16
1
15⁄
16
5⁄
8
5⁄
8
5⁄
8
W14×26
W16×22
7.69
6.49
13.91
13.74
137⁄8
133⁄4
0.255
0.230
1⁄
4
1⁄
4
1⁄
8
1⁄
8
5.025
5.000
5
5
0.420
0.335
7⁄
16
5⁄
16
12
12
15⁄
16
7⁄
8
9⁄
16
9⁄
16
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1
STRUCTURAL SHAPES
1 - 37
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
132
120
109
99
90
7.1
7.8
8.5
9.3
10.2
82
74
68
61
5.9
6.4
7.0
7.7
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
17.7
19.3
21.7
23.5
25.9
—
—
—
—
—
4180
3830
3490
3190
2900
22.4
25.3
27.5
30.4
—
—
—
—
53
48
43
6.1 30.8
6.7 33.5
7.5 37.4
38
34
30
26
22
S
I
Axis Y-Y
r
S
in.
in.
428
601
853
1220
1750
1530
1380
1240
1110
999
209
190
173
157
143
6.28
6.24
6.22
6.17
6.14
3600
3290
3020
2720
846
1190
1650
2460
882
796
723
640
123
112
103
92.2
6.05
6.04
6.01
5.98
—
57
46
2830
2580
2320
2250
3220
4900
541
485
428
77.8
70.3
62.7
5.89
5.85
5.82
57.7
51.4
45.2
6.6 39.6
7.4 43.1
8.7 45.4
41
35
31
2190
1970
1750
6850
10600
17600
385
340
291
54.6
48.6
42.0
5.87
5.83
5.73
26.7
23.3
19.6
6.0 48.1
7.5 53.3
28
22
1890
1610
13900
27300
245
199
35.3
29.0
5.65
5.54
(1/ksi)
3
I
4
in.
4
r
Zx
in.
in.
in.3
548
495
447
402
362
74.5
67.5
61.2
55.2
49.9
3.76
3.74
3.73
3.71
3.70
234
212
192
173
157
113
102
92.7
83.6
75.6
148
134
121
107
29.3
26.6
24.2
21.5
2.48
2.48
2.46
2.45
139
126
115
102
44.8
40.6
36.9
32.8
14.3
12.8
11.3
1.92
1.91
1.89
87.1
78.4
69.6
22.0
19.6
17.3
7.88
6.91
5.82
1.55
1.53
1.49
61.5
54.6
47.3
12.1
10.6
8.99
3.54
2.80
1.08
1.04
40.2
33.2
5.54
4.39
8.91
7.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
Zy
in.
in.
3
1 - 38
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Flange
Thickness
tw
tw
2
in.
in.
Width
bf
Distance
Thickness
tf
in.
T
k
k1
in.
in.
in.
in.
2.955 215⁄16
2.705 211⁄16
2.470 21⁄2
2.250 21⁄4
2.070 21⁄16
1.900 17⁄8
1.735 13⁄4
1.560 19⁄16
1.400 13⁄8
1.250 11⁄4
1.105 11⁄8
0.990
1
7⁄
0.900
8
0.810 13⁄16
3
0.735
⁄4
0.670 11⁄16
5⁄
0.605
8
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
91⁄2
311⁄16
37⁄16
33⁄16
215⁄16
23⁄4
25⁄8
27⁄16
21⁄4
21⁄8
115⁄16
113⁄16
111⁄16
15⁄8
11⁄2
17⁄16
13⁄8
15⁄16
11⁄2
17⁄16
13⁄8
15⁄16
11⁄4
11⁄4
13⁄16
11⁄8
11⁄16
1
1
15⁄
16
7⁄
8
7⁄
8
7⁄
8
7⁄
8
13⁄
16
5⁄
8
9⁄
16
91⁄2
91⁄2
13⁄8
11⁄4
13⁄
16
13⁄
16
0.640
0.575
0.515
5⁄
8
9⁄
16
1⁄
2
91⁄2
91⁄2
91⁄2
13⁄8
11⁄4
11⁄4
13⁄
16
13⁄
16
3⁄
4
61⁄2
61⁄2
61⁄2
0.520
0.440
0.380
1⁄
2
7⁄
16
3⁄
8
101⁄2
101⁄2
101⁄2
15⁄
16
7⁄
8
1
9⁄
16
1⁄
2
1⁄
2
4
4
4
4
0.425
0.350
0.265
0.225
7⁄
16
3⁄
8
1⁄
4
1⁄
4
101⁄2
101⁄2
101⁄2
101⁄2
7⁄
8
13⁄
16
3⁄
4
11⁄
16
1⁄
2
1⁄
2
1⁄
2
1⁄
2
W12×336*
W16×305*
W16×279*
W16×252*
W16×230*
W16×210*
W16×190
W16×170
W16×152
W16×136
W16×120
W16×106
W16×96
W16×87
W16×79
W16×72
W16×65
98.8
89.6
81.9
74.1
67.7
61.8
55.8
50.0
44.7
39.9
35.3
31.2
28.2
25.6
23.2
21.1
19.1
16.82
16.32
15.85
15.41
15.05
14.71
14.38
14.03
13.71
13.41
13.12
12.89
12.71
12.53
12.38
12.25
12.12
167⁄8
163⁄8
157⁄8
153⁄8
15
143⁄4
143⁄8
14
133⁄4
133⁄8
131⁄8
127⁄8
123⁄4
121⁄2
123⁄8
121⁄4
121⁄8
1.775
1.625
1.530
1.395
1.285
1.180
1.060
0.960
0.870
0.790
0.710
0.610
0.550
0.515
0.470
0.430
0.390
13⁄4
15⁄8
11⁄2
13⁄8
15⁄16
13⁄16
11⁄16
15⁄
16
7⁄
8
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
7⁄
8
13⁄
16
3⁄
4
11⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
5⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
3⁄
16
13.385
13.235
13.140
13.005
12.895
12.790
12.670
12.570
12.480
12.400
12.320
12.220
12.160
12.125
12.080
12.040
12.000
133⁄8
131⁄4
131⁄8
13
127⁄8
123⁄4
125⁄8
125⁄8
121⁄2
123⁄8
123⁄8
121⁄4
121⁄8
121⁄8
121⁄8
12
12
W12×58
W16×53
17.0
15.6
12.19
12.06
121⁄4
12
0.360
0.345
3⁄
8
3⁄
8
3⁄
16
3⁄
16
10.010
9.995
10
10
0.640
0.575
W12×50
W16×45
W16×40
14.7
13.2
11.8
12.19
12.06
11.94
121⁄4
12
12
0.370
0.335
0.295
3⁄
8
5⁄
16
5⁄
16
3⁄
16
3⁄
16
3⁄
16
8.080
8.045
8.005
81⁄8
8
8
W12×35
W16×30
W16×26
10.3
8.79
7.65
12.50
12.34
12.22
121⁄2
123⁄8
121⁄4
0.300
0.260
0.230
5⁄
16
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
6.560
6.520
6.490
W12×22
W16×19
W16×16
W16×14
6.48
5.57
4.71
4.16
12.31
12.16
11.99
11.91
121⁄4
121⁄8
12
117⁄8
0.260
0.235
0.220
0.200
1⁄
4
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
1⁄
8
4.030
4.005
3.990
3.970
*Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL SHAPES
1 - 39
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
336
305
279
252
230
210
190
170
152
136
120
106
96
87
79
72
65
2.3
2.4
2.7
2.9
3.1
3.4
3.7
4.0
4.5
5.0
5.6
6.2
6.8
7.5
8.2
9.0
9.9
58
53
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
5.5
6.0
6.3
7.0
7.6
8.2
9.2
10.1
11.2
12.3
13.7
15.9
17.7
18.9
20.7
22.6
24.9
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
12800
11800
11000
10100
9390
8670
7940
7190
6510
5850
5240
4660
4250
3880
3530
3230
2940
7.8
8.7
27.0
28.1
—
—
3070
2820
50
45
40
6.3
7.0
7.8
26.2
29.0
32.9
—
—
59
3170
2870
2580
35
30
26
6.3
7.4
8.5
36.2
41.8
47.2
22
19
16
14
4.7
5.7
7.5
8.8
41.8
46.2
49.4
54.3
(1/ksi)
S
I
4
Axis Y-Y
r
3
S
I
4
Zx
3
Zy
in.
in.
177
159
143
127
115
104
93.0
82.3
72.8
64.2
56.0
49.3
44.4
39.7
35.8
32.4
29.1
3.47
3.42
3.38
3.34
3.31
3.28
3.25
3.22
3.19
3.16
3.13
3.11
3.09
3.07
3.05
3.04
3.02
603
537
481
428
386
348
311
275
243
214
186
164
147
132
119
108
96.8
274
244
220
196
177
159
143
126
111
98.0
85.4
75.1
67.5
60.4
54.3
49.2
44.1
in.
in.
4060
3550
3110
2720
2420
2140
1890
1650
1430
1240
1070
933
833
740
662
597
533
483
435
393
353
321
292
263
235
209
186
163
145
131
118
107
97.4
87.9
6.41 1190
6.29 1050
6.16 937
6.06 828
5.97 742
5.89 664
5.82 589
5.74 517
5.66 454
5.58 398
5.51 345
5.47 301
5.44 270
5.38 241
5.34 216
5.31 195
5.28 174
1470
2100
475
425
78.0
70.6
5.28
5.23
107
95.8
21.4
19.2
2.51
2.48
86.4
77.9
32.5
29.1
1410
2070
3110
394
350
310
64.7
58.1
51.9
5.18
5.15
5.13
56.3
50.0
44.1
13.9
12.4
11.0
1.96
1.94
1.93
72.4
64.7
57.5
21.4
19.0
16.8
49
37
29
2420 4340
2090 7950
1820 13900
285
238
204
45.6
38.6
33.4
5.25
5.21
5.17
24.5
20.3
17.3
7.47 1.54
6.24 1.52
5.34 1.51
51.2
43.1
37.2
11.5
9.56
8.17
37
30
26
22
2160 8640
1880 15600
1610 32000
1450 49300
156
130
103
88.6
25.4
21.3
17.1
14.9
4.91
4.82
4.67
4.62
2.31
1.88
1.41
1.19
29.3
24.7
20.1
17.4
3.66
2.98
2.26
1.90
4.66
3.76
2.82
2.36
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
0.847
0.822
0.773
0.753
in.
in.3
in.
6.05
8.17
10.8
14.7
19.7
26.6
37.0
54.0
79.3
119
184
285
405
586
839
1180
1720
in.
r
3
1 - 40
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Flange
Thickness
tw
tw
2
in.
in.
Width
bf
Distance
Thickness
tf
k1
in.
in.
in.
32.9
29.4
25.9
22.6
20.0
17.6
15.8
14.4
11.36
11.10
10.84
10.60
10.40
10.22
10.09
9.98
113⁄8
111⁄8
107⁄8
105⁄8
103⁄8
101⁄4
101⁄8
10
0.755
0.680
0.605
0.530
0.470
0.420
0.370
0.340
3⁄
4
11⁄
16
5⁄
8
1⁄
2
1⁄
2
7⁄
16
3⁄
8
5⁄
16
3⁄
8
3⁄
8
5⁄
16
1⁄
4
1⁄
4
1⁄
4
3⁄
16
3⁄
16
10.415
10.340
10.265
10.190
10.130
10.080
10.030
10.000
103⁄8
103⁄8
101⁄4
101⁄4
101⁄8
101⁄8
10
10
1.250
1.120
0.990
0.870
0.770
0.680
0.615
0.560
11⁄4
11⁄8
1
7⁄
8
3⁄
4
11⁄
16
5⁄
8
9⁄
16
75⁄8
75⁄8
75⁄8
75⁄8
75⁄8
75⁄8
75⁄8
75⁄8
17⁄8
13⁄4
15⁄8
11⁄2
13⁄8
15⁄16
11⁄4
13⁄16
15⁄
16
7⁄
8
13⁄
16
13⁄
16
3⁄
4
3⁄
4
11⁄
16
11⁄
16
W10×45
W10×39
W10×33
13.3
11.5
9.71
10.10
9.92
9.73
101⁄8
97⁄8
93⁄4
0.350
0.315
0.290
3⁄
8
5⁄
16
5⁄
16
3⁄
16
3⁄
16
3⁄
16
8.020
7.985
7.960
8
8
8
0.620
0.530
0.435
5⁄
8
1⁄
2
7⁄
16
75⁄8
75⁄8
75⁄8
11⁄4
11⁄8
11⁄16
11⁄
0.300
0.260
0.240
5⁄
16
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
5.810
5.770
5.750
53⁄4
53⁄4
53⁄4
0.510
0.440
0.360
1⁄
2
7⁄
16
3⁄
8
85⁄8
85⁄8
85⁄8
15⁄
16
7⁄
8
3⁄
4
1⁄
2
1⁄
2
1⁄
2
0.250
0.240
0.230
0.190
1⁄
4
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
1⁄
8
4.020
4.010
4.000
3.960
4
4
4
4
0.395
0.330
0.270
0.210
3⁄
8
5⁄
16
1⁄
4
3⁄
16
85⁄8
85⁄8
85⁄8
85⁄8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
1⁄
2
1⁄
2
7⁄
16
7⁄
16
W10×30
W10×26
W10×22
8.84
7.61
6.49
10.47
10.33
10.17
W10×19
W10×17
W10×15
W10×12
5.62
4.99
4.41
3.54
10.24
10.11
9.99
9.87
101⁄4
101⁄8
10
97⁄8
in.
k
W10×112
W10×100
W10×88
W10×77
W10×68
W10×60
W10×54
W10×49
101⁄2
103⁄8
101⁄8
in.
T
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11⁄
11⁄
16
16
16
STRUCTURAL SHAPES
1 - 41
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
112
100
88
77
68
60
54
49
4.2
4.6
5.2
5.9
6.6
7.4
8.2
8.9
45
39
33
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
in.
in.
10.4
11.6
13.0
14.8
16.7
18.7
21.2
23.1
—
—
—
—
—
—
—
—
7080
6400
5680
5010
4460
3970
3580
3280
56.7
83.8
132
213
334
525
778
1090
716
623
534
455
394
341
303
272
6.5
7.5
9.1
22.5
25.0
27.1
—
—
—
3650
3190
2710
758
1300
2510
30
26
22
5.7
6.6
8.0
29.5
34.0
36.9
—
55
47
2890
2500
2150
2160
3790
7170
19
17
15
12
5.1
6.1
7.4
9.4
35.4
36.9
38.5
46.6
51
47
43
30
2420
2210
1930
1550
5160
7820
14300
35400
(1/ksi)
S
I
4
Axis Y-Y
r
3
S
I
4
r
3
in.3
2.68
2.65
2.63
2.60
2.59
2.57
2.56
2.54
147
130
113
97.6
85.3
74.6
66.6
60.4
69.2
61.0
53.1
45.9
40.1
35.0
31.3
28.3
13.3
11.3
9.20
2.01
1.98
1.94
54.9
46.8
38.8
20.3
17.2
14.0
5.75
4.89
3.97
1.37
1.36
1.33
36.6
31.3
26.0
8.84
7.50
6.10
2.14
1.78
1.45
1.10
0.874
0.844
0.810
0.785
21.6
18.7
16.0
12.6
3.35
2.80
2.30
1.74
in.
in.
in.
126
112
98.5
85.9
75.7
66.7
60.0
54.6
4.66
4.60
4.54
4.49
4.44
4.39
4.37
4.35
236
207
179
154
134
116
103
93.4
45.3
40.0
34.8
30.1
26.4
23.0
20.6
18.7
248
209
170
49.1
42.1
35.0
4.32
4.27
4.19
53.4
45.0
36.6
170
144
118
32.4
27.9
23.2
4.38
4.35
4.27
16.7
14.1
11.4
18.8
16.2
13.8
10.9
4.14
4.05
3.95
3.90
4.29
3.56
2.89
2.18
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
Zy
in.
in.
96.3
81.9
68.9
53.8
Zx
1 - 42
DIMENSIONS AND PROPERTIES
Y
tf
d
X
W SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
Depth
d
2
in.
in.
Thickness
tw
in.
Flange
tw
2
in.
Width
bf
Distance
Thickness
tf
in.
in.
T
k
k1
in.
in.
W8×67
W8×58
W8×48
W8×40
W8×35
W8×31
19.7
17.1
14.1
11.7
10.3
9.13
9.00
8.75
8.50
8.25
8.12
8.00
9
83⁄4
81⁄2
81⁄4
81⁄8
8
0.570
0.510
0.400
0.360
0.310
0.285
9⁄
16
1⁄
2
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
1⁄
4
3⁄
16
3⁄
16
3⁄
16
3⁄
16
8.280
8.220
8.110
8.070
8.020
7.995
81⁄4
81⁄4
81⁄8
81⁄8
8
8
0.935
0.810
0.685
0.560
0.495
0.435
15⁄
16
13⁄
16
11⁄
16
9⁄
16
1⁄
2
7⁄
16
61⁄8
61⁄8
61⁄8
61⁄8
61⁄8
61⁄8
17⁄16
15⁄16
13⁄16
11⁄16
1
15⁄
16
11⁄
W8×28
W8×24
8.25
7.08
8.06
7.93
8
77⁄8
0.285
0.245
5⁄
16
1⁄
4
3⁄
16
1⁄
8
6.535
6.495
61⁄2
61⁄2
0.465
0.400
7⁄
16
3⁄
8
61⁄8
61⁄8
15⁄
16
7⁄
8
9⁄
16
9⁄
16
W8×21
W8×18
6.16
5.26
8.28
8.14
81⁄4
81⁄8
0.250
0.230
1⁄
4
1⁄
4
1⁄
8
1⁄
8
5.270
5.250
51⁄4
51⁄4
0.400
0.330
3⁄
8
5⁄
16
65⁄8
65⁄8
13⁄
16
3⁄
4
1⁄
2
7⁄
16
W8×15
W8×13
W8×10
4.44
3.84
2.96
8.11
7.99
7.89
81⁄8
8
77⁄8
0.245
0.230
0.170
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
4.015
4.000
3.940
4
4
4
0.315
0.255
0.205
5⁄
16
1⁄
4
3⁄
16
65⁄8
65⁄8
65⁄8
3⁄
4
11⁄
16
5⁄
8
1⁄
2
7⁄
16
7⁄
16
W6×25
W8×20
W8×15
7.34
5.87
4.43
6.38
6.20
5.99
63⁄8
61⁄4
6
0.320
0.260
0.230
5⁄
16
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
6.080
6.020
5.990
61⁄8
6
6
0.455
0.365
0.260
7⁄
16
3⁄
8
1⁄
4
43⁄4
43⁄4
43⁄4
13⁄
16
3⁄
4
5⁄
8
7⁄
16
7⁄
16
3⁄
8
W6×16
W8×12
W8×9
4.74
3.55
2.68
6.28
6.03
5.90
61⁄4
6
57⁄8
0.260
0.230
0.170
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
4.030
4.000
3.940
4
4
4
0.405
0.280
0.215
3⁄
8
1⁄
4
3⁄
16
43⁄4
43⁄4
43⁄4
3⁄
4
5⁄
8
9⁄
16
7⁄
16
3⁄
8
3⁄
8
W5×19
W8×16
5.54
4.68
5.15
5.01
51⁄8
5
0.270
0.240
1⁄
4
1⁄
4
1⁄
8
1⁄
8
5.030
5.000
5
5
0.430
0.360
7⁄
16
3⁄
8
31⁄2
31⁄2
13⁄
16
3⁄
4
7⁄
16
7⁄
16
W4×13
3.83
4.16
41⁄8
0.280
1⁄
4
1⁄
8
4.060
4
0.345
3⁄
8
23⁄4
11⁄
16
7⁄
16
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in.
11⁄
16
16
5⁄
8
5⁄
8
9⁄
16
9⁄
16
STRUCTURAL SHAPES
1 - 43
W SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
67
58
48
40
35
31
4.4
5.1
5.9
7.2
8.1
9.2
28
24
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
in.
in.
11.1
12.4
15.8
17.6
20.4
22.2
—
—
—
—
—
—
6620
5820
4860
4080
3610
3230
73.9
122
238
474
761
1180
272
228
184
146
127
110
7.0
8.1
22.2
25.8
—
—
3480
3020
931
1610
21
18
6.6
8.0
27.5
29.9
—
—
2890
2490
15
13
10
6.4
7.8
9.6
28.1
29.9
40.5
—
—
39
25
20
15
6.7 15.5
8.2 19.1
11.5 21.6
16
12
9
5.0
7.1
9.2
19
16
13
(1/ksi)
S
I
4
Axis Y-Y
r
3
S
I
4
r
3
Zx
Zy
in.
3
in.
in.3
in.
in.
in.
60.4
52.0
43.3
35.5
31.2
27.5
3.72
3.65
3.61
3.53
3.51
3.47
88.6
75.1
60.9
49.1
42.6
37.1
21.4
18.3
15.0
12.2
10.6
9.27
2.12
2.10
2.08
2.04
2.03
2.02
70.2
59.8
49.0
39.8
34.7
30.4
32.7
27.9
22.9
18.5
16.1
14.1
98.0
82.8
24.3
20.9
3.45
3.42
21.7
18.3
6.63
5.63
1.62
1.61
27.2
23.2
10.1
8.57
2090
3890
75.3
61.9
18.2
15.2
3.49
3.43
9.77
7.97
3.71
3.04
1.26
1.23
20.4
17.0
5.69
4.66
2670
2370
1760
3440
5780
17900
48.0
39.6
30.8
11.8
9.91
7.81
3.29
3.21
3.22
3.41
2.73
2.09
1.70
1.37
1.06
0.876
0.843
0.841
13.6
11.4
8.87
2.67
2.15
1.66
—
—
—
4410
3550
2740
369
846
2470
53.4
41.4
29.1
16.7
13.4
9.72
2.70
2.66
2.56
17.1
13.3
9.32
5.61
4.41
3.11
1.52
1.50
1.46
18.9
14.9
10.8
8.56
6.72
4.75
19.1
21.6
29.2
—
—
—
4010
3100
2360
591
1740
4980
32.1
22.1
16.4
10.2
7.31
5.56
2.60
2.49
2.47
4.43
2.99
2.19
2.20
1.50
1.11
0.966
0.918
0.905
11.7
8.30
6.23
3.39
2.32
1.72
5.8
6.9
14.0
15.8
—
—
5140
4440
192
346
26.2
21.3
10.2
8.51
2.17
2.13
9.13
7.51
3.63
3.00
1.28
1.27
11.6
9.59
5.53
4.57
5.9
10.6
—
5560
154
11.3
5.46
1.72
3.86
1.90
1.00
6.28
2.92
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 44
DIMENSIONS AND PROPERTIES
Y
tf
d
X
M SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
Thickness
tw
in.
in.
Flange
tw
2
Width
bf
Thickness
tf
in.
in.
T
k
k1
in.
in.
in.
11.91 1115⁄16 0.177
11.87 117⁄8 0.162
3⁄
16
3⁄
16
1⁄
16
1⁄
16
3.065 31⁄16 0.225
3.065 31⁄16 0.206
1⁄
4
3⁄
16
1015⁄16
107⁄8
1⁄
2
1⁄
2
3⁄
8
3⁄
8
97⁄8 0.157
913⁄16 0.139
3⁄
16
1⁄
8
1⁄
16
1⁄
16
2.690 211⁄16 0.206
2.690 211⁄16 0.183
3⁄
16
3⁄
16
87⁄8
813⁄16
1⁄
2
1⁄
2
3⁄
8
3⁄
8
0.133
1⁄
8
1⁄
16
2.280
21⁄4
0.186
3⁄
16
67⁄8
1⁄
2
3⁄
8
0.316
5⁄
16
3⁄
16
5.003
5
0.416
7⁄
16
31⁄4
7⁄
8
1⁄
2
M12×11.8
M12×10.8
3.48
3.20
M10×9
M12×8
2.67
2.38
9.86
9.81
M8×6.5
1.92
7.85
77⁄8
M5×18.9*
5.55
5.00
5
in.
Distance
*This shape has tapered flanges while all other M shapes have parallel flanges.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL SHAPES
1 - 45
M SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
11.8
10.8
6.8
7.4
9
8
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
(1/ksi)
61.4
67.0
17
14
1420
1320
6.5
7.3
56.4
63.7
20
16
6.5
6.1
51.7
18.9
6.0
11.2
S
I
4
Axis Y-Y
r
3
in.
in.
56700
75800
71.7
65.8
12.1
11.1
1570
1400
37100
57800
38.5
34.3
24
1780
20700
—
5710
134
S
I
4
r
3
Zx
Zy
in.
3
in.
in.3
14.3
13.1
1.16
1.05
in.
in.
in.
4.54
4.54
1.09
0.995
0.709
0.649
0.559
0.558
7.82
6.99
3.80
3.80
0.673
0.597
0.501
0.444
0.502
0.502
9.21
8.20
0.815
0.718
18.1
4.62
3.07
0.371
0.325
0.439
5.40
0.527
24.1
9.63
2.08
7.86
3.14
1.19
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11.0
5.02
1 - 46
DIMENSIONS AND PROPERTIES
Y
tf
d
S SHAPES
Dimensions
k
X
X
T
tw
grip
Y
bf
k
Web
Designation
Flange
Distance
Max.
Flge.
FasGrip tener
Area
A
Depth
d
Thickness
tw
tw
2
Width
bf
Thickness
tf
T
k
in.2
in.
in.
in.
in.
in.
in.
in.
in.
in.
1
1
S24×121
S24×106
35.6
31.2
24.50
24.50
241⁄2
241⁄2
0.800
0.620
13⁄
16
5⁄
8
7⁄
16
5⁄
16
8.050
7.870
8
77⁄8
S24×100
S24×90
S24×80
29.3
26.5
23.5
24.00
24.00
24.00
24
24
24
0.745
0.625
0.500
3⁄
4
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
7.245
7.125
7.000
S20×96
S24×86
28.2
25.3
20.30 201⁄4 0.800
20.30 201⁄4 0.660
13⁄
16
11⁄
16
7⁄
16
3⁄
8
S20×75
S24×66
22.0
19.4
20.00
20.00
20
20
0.635
0.505
5⁄
8
1⁄
2
5⁄
16
1⁄
4
6.385
6.255
63⁄8
61⁄4
0.795
0.795
13⁄
16
13⁄
16
163⁄4
163⁄4
15⁄8
15⁄8
13⁄
16
13⁄
16
7⁄
8
7⁄
8
S18×70
20.6
S24×54.7 16.1
18.00
18.00
18
18
0.711
0.461
11⁄
16
7⁄
16
3⁄
4
6.251
6.001
61⁄4
6
0.691
0.691
11⁄
16
11⁄
16
15
15
11⁄2
11⁄2
11⁄
16
11⁄
16
7⁄
8
7⁄
8
S15×50
14.7
S24×42.9 12.6
15.00
15.00
15
15
0.550
0.411
9⁄
16
7⁄
16
5⁄
16
1⁄
4
5.640
5.501
55⁄8
51⁄2
0.622
0.622
5⁄
8
5⁄
8
121⁄4
121⁄4
13⁄8
13⁄8
9⁄
16
9⁄
16
3⁄
4
3⁄
4
S12×50
14.7
S24×40.8 12.0
12.00
12.00
12
12
0.687
0.462
11⁄
16
7⁄
16
3⁄
4
5.477
5.252
51⁄2
51⁄4
0.659
0.659
11⁄
16
11⁄
16
91⁄8
91⁄8
17⁄16
17⁄16
11⁄
16
5⁄
8
3⁄
4
3⁄
4
S12×35
10.3 12.00
S24×31.8 9.35 12.00
12
12
0.428
0.350
7⁄
16
3⁄
8
1⁄
4
3⁄
16
5.078
5.000
51⁄8
5
0.544
0.544
9⁄
16
9⁄
16
95⁄8
95⁄8
13⁄16
13⁄16
1⁄
2
1⁄
2
3⁄
4
3⁄
4
S10×35
10.3 10.00
S24×25.4 7.46 10.00
10
10
0.594
0.311
5⁄
8
5⁄
16
5⁄
16
3⁄
16
4.944
4.661
5
45⁄8
0.491
0.491
1⁄
2
1⁄
2
73⁄4
73⁄4
11⁄8
11⁄8
1⁄
2
1⁄
2
3⁄
4
3⁄
4
4.171
4.001
41⁄8
4
0.426
0.426
7⁄
16
7⁄
16
6
6
1
1
7⁄
16
7⁄
16
3⁄
4
3⁄
4
8
3.565
3.332
35⁄8
33⁄8
0.359
0.359
3⁄
8
3⁄
8
41⁄4
41⁄4
7⁄
8
7⁄
8
3⁄
8
3⁄
8
5⁄
8
—
8
3.004
3
0.326
5⁄
16
33⁄8
13⁄
16
5⁄
16
—
0.293
0.293
5⁄
16
5⁄
16
21⁄2
21⁄2
3⁄
4
3⁄
4
5⁄
16
5⁄
16
—
—
0.260
0.260
1⁄
4
1⁄
4
15⁄8
15⁄8
11⁄
16
11⁄
16
1⁄
4
1⁄
4
—
—
1⁄
1⁄
8
8
1.090
1.090
11⁄16
11⁄16
201⁄2
201⁄2
2
2
11⁄8
11⁄8
71⁄4
71⁄8
7
0.870
0.870
0.870
7⁄
8
7⁄
8
7⁄
8
201⁄2
201⁄2
201⁄2
13⁄4
13⁄4
13⁄4
7⁄
8
7⁄
8
7⁄
8
1
1
1
7.200
7.060
71⁄4
7
0.920
0.920
15⁄
16
15⁄
16
163⁄4
163⁄4
13⁄4
13⁄4
15⁄
16
15⁄
16
1
1
S8×23
S8×18.4
6.77
5.41
8.00
8.00
8
8
0.441
0.271
7⁄
16
1⁄
4
1⁄
S6×17.25
S8×12.5
5.07
3.67
6.00
6.00
6
6
0.465
0.232
7⁄
16
1⁄
4
1⁄
S5×10
2.94
5.00
5
0.214
3⁄
16
1⁄
3⁄
16
1⁄
8
2.796
2.663
23⁄4
25⁄8
3⁄
16
1⁄
8
2.509
2.330
21⁄2
23⁄8
S4×9.5
S8×7.7
2.79
2.26
4.00
4.00
4
4
0.326
0.193
5⁄
16
3⁄
16
S3×7.5
S8×5.7
2.21
1.67
3.00
3.00
3
3
0.349
0.170
3⁄
8
3⁄
16
1⁄
1⁄
4
8
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL SHAPES
1 - 47
S SHAPES
Properties
Y
tf
d
k
X
X
T
tw
Y
bf
grip
Nominal
Wt.
per
ft
Compact
Section
Criteria
bf
2tf
h
tw
Fy′′′
121
106
3.7
3.6
100
90
80
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
(1/ksi)
36.4
34.1
—
55
3310
2960
4.2
4.1
4.0
28.3
33.7
42.1
—
56
36
96
86
3.9
3.8
21.6
26.2
75
66
4.0
3.9
70
54.7
lb
k
S
I
4
Axis Y-Y
r
3
in.
in.
1770
2470
3160
2940
3000
2710
2450
2940
4090
5480
—
—
3730
3350
27.1
34.1
—
55
4.5
4.3
21.8
33.6
50
42.9
4.5
4.4
50
40.8
S
I
4
r
3
Zx
3
Zy
in.3
in.
in.
in.
in.
in.
258
240
9.43
9.71
83.3
77.1
20.7
19.6
1.53
1.57
306
279
36.2
33.2
2390
2250
2100
199
187
175
9.02
9.21
9.47
47.7
44.9
42.2
13.2
12.6
12.1
1.27
1.30
1.34
240
222
204
23.9
22.3
20.7
1160
1630
1670
1580
165
155
7.71
7.89
50.2
46.8
13.9
13.3
1.33
1.36
198
183
24.9
23.0
3140
2800
2290
3250
1280
1190
128
119
7.62
7.83
29.8
27.7
9.32
8.85
1.16
1.19
153
140
16.7
15.3
—
57
3590
2770
1470
3400
926
804
103
89.4
6.71
7.07
24.1
20.8
7.72
6.94
1.08
1.14
125
105
14.4
12.1
23.2
31.0
—
—
3450
2960
1540
2470
486
447
64.8
59.6
5.75
5.95
15.7
14.4
5.57
5.23
1.03
1.07
77.1
69.3
9.97
9.02
4.2
4.0
13.9
20.7
—
—
5070
4050
333
682
305
272
50.8
45.4
4.55
4.77
15.7
13.6
5.74
5.16
1.03
1.06
61.2
53.1
10.3
8.85
35
31.8
4.7
4.6
23.4
28.6
—
—
3500
3190
1310
1710
229
218
38.2
36.4
4.72
4.83
9.87
9.36
3.89
3.74
0.980
1.00
44.8
42.0
6.79
6.40
35
25.4
5.0
4.7
13.8
26.4
—
—
4960
3430
374
1220
147
124
29.4
24.7
3.78
4.07
8.36
6.79
3.38
2.91
0.901
0.954
35.4
28.4
6.22
4.96
23
18.4
4.9
4.7
14.5
23.7
—
—
4770
3770
397
821
64.9
57.6
16.2
14.4
3.10
3.26
4.31
3.73
2.07
1.86
0.798
0.831
19.3
16.5
3.68
3.16
17.25 5.0
12.5
4.6
9.9
19.9
—
—
6250
4290
143
477
26.3
22.1
8.77
7.37
2.28
2.45
2.31
1.82
1.30
1.09
0.675
0.705
10.6
8.47
2.36
1.85
10
4.6
17.4
—
4630
348
12.3
4.92
2.05
1.22
0.809 0.643
5.67
1.37
9.5
7.7
4.8
4.5
8.7
14.7
—
—
6830
5240
87.4
207
6.79
6.08
3.39
3.04
1.56
1.64
0.903
0.764
0.646 0.569
0.574 0.581
4.04
3.51
1.13
0.964
7.5
5.7
4.8
4.5
5.6
11.4
—
—
9160
6160
28.1
106
2.93
2.52
1.95
1.68
1.15
1.23
0.586
0.455
0.468 0.516
0.390 0.522
2.36
1.95
0.826
0.653
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 48
DIMENSIONS AND PROPERTIES
Y
tf
d
X
HP SHAPES
Dimensions
k
k1
X
T
tw
Y
bf
k
Web
Designation
Area
A
2
in.
Depth
d
in.
Thickness
tw
in.
Flange
tw
2
in.
Width
bf
in.
Distance
Thickness
tf
in.
T
k
k1
in.
in.
in.
HP14×117
HP14×102
HP14×89
HP14×73
34.4
30.0
26.1
21.4
14.21
14.01
13.83
13.61
141⁄4
14
137⁄8
135⁄8
0.805
0.705
0.615
0.505
13⁄
16
11⁄
16
5⁄
8
1⁄
2
7⁄
16
3⁄
8
5⁄
16
1⁄
4
14.885
14.785
14.695
14.585
147⁄8
143⁄4
143⁄4
145⁄8
0.805
0.705
0.615
0.505
13⁄
16
11⁄
16
5⁄
8
1⁄
2
111⁄4
111⁄4
111⁄4
111⁄4
11⁄2
13⁄8
15⁄16
13⁄16
11⁄16
1
15⁄
16
7⁄
8
HP12×84
HP14×74
HP14×63
HP14×53
24.6
21.8
18.4
15.5
12.28
12.13
11.94
11.78
121⁄4
121⁄8
12
113⁄4
0.685
0.605
0.515
0.435
11⁄
16
5⁄
8
1⁄
2
7⁄
16
3⁄
8
5⁄
16
1⁄
4
1⁄
4
12.295
12.215
12.125
12.045
121⁄4
121⁄4
121⁄8
12
0.685
0.610
0.515
0.435
11⁄
16
5⁄
8
1⁄
2
7⁄
16
91⁄2
91⁄2
91⁄2
91⁄2
13⁄8
15⁄16
11⁄4
11⁄8
15⁄
16
7⁄
8
7⁄
8
HP10×57
HP14×42
16.8
12.4
9.99
9.70
10
93⁄4
0.565
0.415
9⁄
16
7⁄
16
5⁄
16
1⁄
4
10.225
10.075
101⁄4
101⁄8
0.565
0.420
9⁄
16
7⁄
16
75⁄8
75⁄8
13⁄16
11⁄16
13⁄
16
3⁄
4
HP8×36
10.6
8.02
8
0.445
7⁄
16
1⁄
4
8.155
81⁄8
0.445
7⁄
16
61⁄8
15⁄
16
5⁄
8
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1
STRUCTURAL SHAPES
1 - 49
HP SHAPES
Properties
Y
tf
d
k
k1
X
X
T
tw
Y
bf
Nominal
Wt.
per
ft
Compact
Section
Criteria
h
tw
Fy′′′
lb
bf
2tf
117
102
89
73
9.2
10.5
11.9
14.4
84
74
63
53
9.0
10.0
11.8
13.8
k
Plastic
Modulus
Elastic Properties
Axis X-X
X1
X2 × 106
ksi
ksi
2
14.2
16.2
18.5
22.6
—
—
—
—
14.2
16.0
18.9
22.3
57
42
36
S
I
Axis Y-Y
r
3
S
I
(1/ksi)
4
in.
in.
in.
in.
3870
3400
2960
2450
659
1090
1840
3880
1220
1050
904
729
172
150
131
107
5.96
5.92
5.88
5.84
—
—
—
—
3860
3440
2940
2500
670
1050
1940
3650
650
569
472
393
106
93.8
79.1
66.8
9.0 13.9
12.0 18.9
—
—
3920
2920
631
1970
294
210
9.2 14.2
—
3840
685
119
4
r
3
Zx
Zy
in.
in.
in.
in.3
443
380
326
261
59.5
51.4
44.3
35.8
3.59
3.56
3.53
3.49
194
169
146
118
91.4
78.8
67.7
54.6
5.14
5.11
5.06
5.03
213
186
153
127
34.6
30.4
25.3
21.1
2.94
2.92
2.88
2.86
120
105
88.3
74.0
53.2
46.6
38.7
32.2
58.8
43.4
4.18
4.13
101
71.7
19.7
14.2
2.45
2.41
66.5
48.3
30.3
21.8
29.8
3.36
40.3
1.95
33.6
15.2
9.88
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3
1 - 50
DIMENSIONS AND PROPERTIES
k
T
x
Y
X
CHANNELS
AMERICAN STANDARD
Dimensions
tf
xp
d
X
tw
k
Y
grip
bf
eo
Web
Designation
Area Depth Thickness
A
d
tw
in.2
in.
in.
Flange
Distance
Max.
Flge.
FasGrip tener
tw
2
Width
bf
Thickness
tf
T
k
in.
in.
in.
in.
in.
121⁄8
121⁄8
121⁄8
17⁄16
17⁄16
17⁄16
5⁄
93⁄4
93⁄4
93⁄4
11⁄8
11⁄8
11⁄8
1⁄
2
7⁄
8
7⁄
8
7⁄
8
3⁄
4
3⁄
4
3⁄
4
3⁄
4
3⁄
8
1⁄
4
3⁄
16
in.
3.716
3.520
3.400
33⁄4
31⁄2
33⁄8
0.650
0.650
0.650
5⁄
8
5⁄
8
5⁄
8
3.170
3.047
2.942
31⁄8
3
3
0.501
0.501
0.501
1⁄
2
1⁄
2
1⁄
2
8
8
8
8
1
1
1
1
7⁄
16
7⁄
16
7⁄
16
7⁄
16
in.
C15×50
C15×40
C15×33.9
14.7
11.8
9.96
15.00
15.00
15.00
0.716
0.520
0.400
11⁄
16
1⁄
2
3⁄
8
C12×30
C15×25
C15×20.7
8.82
7.35
6.09
12.00
12.00
12.00
0.510
0.387
0.282
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
3.033
2.886
2.739
2.600
3
27⁄8
23⁄4
25⁄8
0.436
0.436
0.436
0.436
7⁄
16
7⁄
16
7⁄
16
7⁄
16
1⁄
4
1⁄
8
1⁄
8
2.648
2.485
2.433
25⁄8
21⁄2
23⁄8
0.413
0.413
0.413
7⁄
16
7⁄
16
7⁄
16
71⁄8
71⁄8
71⁄8
15⁄
16
15⁄
16
15⁄
16
7⁄
16
7⁄
16
7⁄
16
3⁄
4
3⁄
4
3⁄
4
1⁄
4
1⁄
8
1⁄
8
2.527
2.343
2.260
21⁄2
23⁄8
21⁄4
0.390
0.390
0.390
3⁄
8
3⁄
8
3⁄
8
61⁄8
61⁄8
61⁄8
15⁄
16
15⁄
16
15⁄
16
3⁄
3⁄
4
3⁄
4
3⁄
4
3⁄
16
1⁄
8
2.194
2.090
21⁄4
21⁄8
0.366
0.366
3⁄
8
3⁄
8
51⁄4
51⁄4
7⁄
8
7⁄
8
3⁄
8
5⁄
8
5⁄
8
3⁄
16
3⁄
16
1⁄
8
2.157
2.034
1.920
21⁄8
2
17⁄8
0.343
0.343
0.343
5⁄
16
5⁄
16
5⁄
16
43⁄8
43⁄8
43⁄8
13⁄
16
13⁄
16
13⁄
16
5⁄
16
3⁄
8
5⁄
16
5⁄
8
5⁄
8
5⁄
8
3⁄
16
1⁄
8
1.885
1.750
17⁄8
13⁄4
0.320
0.320
5⁄
16
5⁄
16
31⁄2
31⁄2
3⁄
4
3⁄
4
5⁄
16
5⁄
8
—
5⁄
5⁄
1⁄
1⁄
8
8
8
2
2
1
1
1
C10×30
C15×25
C15×20
C15×15.3
8.82
7.35
5.88
4.49
10.00
10.00
10.00
10.00
0.673
0.526
0.379
0.240
11⁄
16
1⁄
2
3⁄
8
1⁄
4
C9×20
C5×15
C5×13.4
5.88
4.41
3.94
9.00
9.00
9.00
0.448
0.285
0.233
7⁄
C8×18.75
C8×13.75
C8×11.5
5.51
4.04
3.38
8.00
8.00
8.00
0.487
0.303
0.220
C7×12.25
C8×9.8
3.60
2.87
7.00
7.00
0.314
0.210
5⁄
C6×13
C8×10.5
C8×8.2
3.83
3.09
2.40
6.00
6.00
6.00
0.437
0.314
0.200
7⁄
C5×9
C8×6.7
2.64
1.97
5.00
5.00
0.325
0.190
5⁄
C4×7.25
C8×5.4
2.13
1.59
4.00
4.00
0.321
0.184
5⁄
3⁄
16
1⁄
16
1.721
1.584
13⁄4
15⁄8
0.296
0.296
5⁄
16
5⁄
16
25⁄8
25⁄8
11⁄
16
11⁄
16
5⁄
16
16
—
5⁄
8
—
C3×6
C8×5
C8×4.1
1.76
1.47
1.21
3.00
3.00
3.00
0.356
0.258
0.170
3⁄
8
1⁄
4
3⁄
16
3⁄
16
1⁄
8
1⁄
16
1.596
1.498
1.410
15⁄8
11⁄2
13⁄8
0.273
0.273
0.273
1⁄
4
1⁄
4
1⁄
4
15⁄8
15⁄8
15⁄8
11⁄
16
11⁄
16
11⁄
16
—
—
—
—
—
—
5⁄
16
16
1⁄
4
1⁄
2
5⁄
16
1⁄
4
3⁄
5⁄
3⁄
3⁄
3⁄
16
16
16
16
16
16
16
16
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3⁄
3⁄
3⁄
8
8
8
8
—
STRUCTURAL SHAPES
1 - 51
CHANNELS
AMERICAN STANDARD
Properties
k
x
Y
xp
X
T
tf
d
X
tw
Y
k
Nominal
Wt.
per
ft
_
x
Shear
Center PNA
Loca- Location
tion
eo
xp
Axis X-X
Z
I
4
in.
Axis Y-Y
S
3
grip
bf
eo
r
3
Z
I
4
S
3
r
3
lb
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
50
40
33.9
0.798
0.777
0.787
0.583
0.767
0.896
0.488
0.390
0.330
404
349
315
68.2
57.2
50.4
53.8
46.5
42.0
5.24
5.44
5.62
11.0
9.23
8.13
8.17
6.87
6.23
3.78
3.37
3.11
0.867
0.886
0.904
30
25
20.7
0.674
0.674
0.698
0.618
0.746
0.870
0.366
0.305
0.252
162
144
129
33.6
29.2
25.4
27.0
24.1
21.5
4.29
4.43
4.61
5.14
4.47
3.88
4.33
3.84
3.49
2.06
1.88
1.73
0.763
0.780
0.799
30
25
20
15.3
0.649
0.617
0.606
0.634
0.369
0.494
0.637
0.796
0.439
0.366
0.292
0.223
103
91.2
78.9
67.4
26.6
23.0
19.3
15.8
20.7
18.2
15.8
13.5
3.42
3.52
3.66
3.87
3.94
3.36
2.81
2.28
3.78
3.19
2.71
2.35
1.65
1.48
1.32
1.16
0.669
0.676
0.692
0.713
20
15
13.4
0.583
0.586
0.601
0.515
0.682
0.743
0.325
0.243
0.217
60.9
51.0
47.9
16.8
13.5
12.5
13.5
11.3
10.6
3.22
3.40
3.48
2.42
1.93
1.76
2.47
2.05
1.95
1.17
1.01
0.962
0.642
0.661
0.669
18.75
13.75
11.5
0.565
0.553
0.571
0.431
0.604
0.697
0.343
0.251
0.209
44.0
36.1
32.6
13.8
10.9
9.55
11.0
9.03
8.14
2.82
2.99
3.11
1.98
1.53
1.32
2.17
1.73
1.58
1.01
0.854
0.781
0.599
0.615
0.625
12.25
9.8
0.525
0.540
0.538
0.647
0.255
0.203
24.2
21.3
8.40
7.12
6.93
6.08
2.60
2.72
1.17
0.968
1.43
1.26
0.703
0.625
0.571
0.581
13
10.5
8.2
0.514
0.499
0.511
0.380
0.486
0.599
0.317
0.255
0.198
17.4
15.2
13.1
7.26
6.15
5.13
5.80
5.06
4.38
2.13
2.22
2.34
1.05
0.866
0.693
1.36
1.15
0.993
0.642
0.564
0.492
0.525
0.529
0.537
9
6.7
0.478
0.484
0.427
0.552
0.262
0.217
8.90
7.49
4.36
3.51
3.56
3.00
1.83
1.95
0.632
0.479
0.918
0.763
0.450
0.378
0.489
0.493
7.25
5.4
0.459
0.457
0.386
0.502
0.264
0.241
4.59
3.85
2.81
2.26
2.29
1.93
1.47
1.56
0.433
0.319
0.697
0.569
0.343
0.283
0.450
0.449
6
5
4.1
0.455
0.438
0.436
0.322
0.392
0.461
0.291
0.242
0.284
2.07
1.85
1.66
1.72
1.50
1.30
1.38
1.24
1.10
1.08
1.12
1.17
0.305
0.247
0.197
0.544
0.466
0.401
0.268
0.233
0.202
0.416
0.410
0.404
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 52
DIMENSIONS AND PROPERTIES
k
T
x
Y
X
CHANNELS
MISCELLANEOUS
Dimensions
tf
xp
d
X
tw
k
Y
eo
grip
bf
Web
Designation
Area Depth Thickness
A
d
tw
in.2
in.
in.
Flange
Distance
Max.
Flge.
FasGrip tener
tw
2
Width
bf
Thickness
tf
T
k
in.
in.
in.
in.
in.
in.
in.
151⁄4
151⁄4
151⁄4
151⁄4
13⁄8
13⁄8
13⁄8
13⁄8
5⁄
8
5⁄
8
5⁄
8
5⁄
8
1
1
1
1
101⁄4
101⁄4
101⁄4
101⁄4
13⁄8
13⁄8
13⁄8
13⁄8
5⁄
8
9⁄
16
9⁄
16
9⁄
16
1
1
1
1
15⁄16
15⁄16
15⁄16
15⁄16
15⁄16
11⁄
16
11⁄
16
11⁄
16
11⁄
16
11⁄
16
1
1
1
1
1
MC18×58
MC18×51.9
MC18×45.8
MC18×42.7
17.1
15.3
13.5
12.6
18.00
18.00
18.00
18.00
0.700
0.600
0.500
0.450
11⁄
16
5⁄
8
1⁄
2
7⁄
16
MC13×50
MC18×40
MC18×35
MC18×31.8
14.7
11.8
10.3
9.35
13.00
13.00
13.00
13.00
0.787
0.560
0.447
0.375
3⁄
16
9⁄
16
7⁄
16
3⁄
8
3⁄
8
1⁄
4
1⁄
4
3⁄
16
7⁄
16
3⁄
8
5⁄
16
1⁄
4
3⁄
16
4.135
4.012
3.890
3.767
3.670
41⁄
4
37⁄8
33⁄4
35⁄8
0.700
0.700
0.700
0.700
0.700
11⁄
16
11⁄
16
11⁄
16
11⁄
16
11⁄
16
1.500
11⁄2
0.309
5⁄
16
105⁄8
16
—
—
71⁄2
71⁄2
71⁄2
11⁄4
11⁄4
11⁄4
9⁄
16
9⁄
16
9⁄
16
7⁄
8
7⁄
8
7⁄
8
MC12×50
MC18×45
MC18×40
MC18×35
MC18×31
MC12×10.6
3⁄
8
5⁄
16
1⁄
4
1⁄
4
4.200
4.100
4.000
3.950
41⁄
41⁄8
4
4
0.625
0.625
0.625
0.625
5⁄
4.412
4.185
4.072
4.000
43⁄8
41⁄8
41⁄8
4
0.610
0.610
0.610
0.610
5⁄
93⁄8
93⁄8
93⁄8
93⁄8
93⁄8
4
5⁄
5⁄
5⁄
5⁄
5⁄
5⁄
8
8
8
8
8
8
8
8
14.7
13.2
11.8
10.3
9.12
12.00
12.00
12.00
12.00
12.00
0.835
0.712
0.590
0.467
0.370
13⁄
16
11⁄
16
9⁄
16
7⁄
16
3⁄
8
3.10
12.00
0.190
3⁄
16
1⁄
8
3⁄
8
5⁄
16
3⁄
16
4.321
4.100
3.950
43⁄
41⁄8
4
8
0.575
0.575
0.575
9⁄
16
9⁄
16
9⁄
16
8
11⁄
12.1
9.87
8.37
10.00
10.00
10.00
0.796
0.575
0.425
13⁄
16
9⁄
16
7⁄
16
MC10×25
MC18×22
7.35
6.45
10.00
10.00
0.380
0.290
3⁄
8
5⁄
16
3⁄
16
1⁄
8
3.405
3.315
33⁄8
33⁄8
0.575
0.575
9⁄
16
9⁄
16
71⁄2
71⁄2
11⁄4
11⁄4
9⁄
16
9⁄
16
7⁄
8
7⁄
8
MC10×8.4
2.46
10.00
0.170
3⁄
16
1⁄
1.500
11⁄2
0.280
1⁄
85⁄8
11⁄
—
—
MC10×41.1
MC18×33.6
MC18×28.5
16
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4
16
STRUCTURAL SHAPES
1 - 53
CHANNELS
MISCELLANEOUS
Properties
k
x
Y
xp
X
T
tf
d
X
tw
Y
k
Nominal
Wt.
per
ft
_
x
Shear
Center PNA
Loca- Location
tion
eo
xp
Axis X-X
Z
I
4
Axis Y-Y
S
3
grip
bf
eo
r
3
Z
I
4
S
3
r
3
lb
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
58
51.9
45.8
42.7
0.862
0.858
0.866
0.877
0.695
0.797
0.909
0.969
0.472
0.422
0.372
0.347
676
627
578
554
94.6
86.5
78.4
74.4
75.1
69.7
64.3
61.6
6.29
6.41
6.56
6.64
17.8
16.4
15.1
14.4
9.94
9.13
8.42
8.10
5.32
5.07
4.82
4.69
1.02
1.04
1.06
1.07
50
40
35
31.8
0.974
0.963
0.980
1.00
0.815
1.03
1.16
1.24
0.564
0.450
0.394
0.358
314
273
252
239
60.5
50.9
46.2
43.1
48.4
42.0
38.8
36.8
4.62
4.82
4.95
5.06
16.5
13.7
12.3
11.4
10.1
8.57
7.95
7.60
4.79
4.26
3.99
3.81
1.06
1.08
1.10
1.11
50
45
40
35
31
1.05
1.04
1.04
1.05
1.08
0.741
0.844
0.952
1.07
1.18
0.610
0.549
0.488
0.426
0.416
269
252
234
216
203
56.1
51.7
47.3
42.8
39.3
44.9
42.0
39.0
36.1
33.8
4.28
4.36
4.46
4.59
4.71
17.4
15.8
14.3
12.7
11.3
10.2
9.35
8.59
7.91
7.44
5.65
5.33
5.00
4.67
4.39
1.09
1.09
1.10
1.11
1.12
10.6
0.269
0.284
0.129
0.639
0.310
0.351
41.1
33.6
28.5
1.09
1.08
1.12
0.864
1.06
1.21
0.601
0.490
0.415
158
139
127
38.9
33.4
29.6
31.5
27.8
25.3
3.61
3.75
3.89
8.71
7.51
6.83
4.88
4.38
4.02
1.14
1.16
1.17
25
22
0.953
0.990
1.03
1.13
0.364
0.468
110
103
25.8
23.6
22.0
20.5
3.87
3.99
7.35
6.50
5.21
4.86
3.00
2.80
1.00
1.00
0.284
0.332
0.122
3.61
0.328
0.552
0.270
0.365
8.4
55.4
32.0
11.6
7.86
9.23
6.40
4.22
0.382
15.8
13.2
11.4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 54
DIMENSIONS AND PROPERTIES
k
T
x
Y
X
CHANNELS
MISCELLANEOUS
Dimensions
tf
xp
d
X
tw
k
Y
eo
grip
bf
Web
Designation
Area Depth Thickness
A
d
tw
in.2
in.
in.
Flange
Distance
Max.
Flge.
FasGrip tener
tw
2
Width
bf
Thickness
tf
T
k
in.
in.
in.
in.
in.
in.
in.
65⁄8
65⁄8
13⁄16
13⁄16
9⁄
16
9⁄
16
7⁄
8
7⁄
8
55⁄8
55⁄8
13⁄16
13⁄16
1⁄
2
1⁄
2
7⁄
8
7⁄
8
MC9×25.4
MC9×23.9
7.47
7.02
9.00
9.00
0.450
0.400
7⁄
16
3⁄
8
1⁄
4
3⁄
16
3.500
3.450
31⁄
31⁄2
2
0.550
0.550
9⁄
16
9⁄
16
MC8×22.8
MC9×21.4
6.70
6.28
8.00
8.00
0.427
0.375
7⁄
16
3⁄
8
3⁄
3⁄
3.502
3.450
31⁄2
31⁄2
0.525
0.525
1⁄
MC8×20
MC9×18.7
5.88
5.50
8.00
8.00
0.400
0.353
3⁄
8
3⁄
8
3⁄
3.025
2.978
3
3
0.500
0.500
1⁄
16
2
53⁄4
53⁄4
11⁄8
11⁄8
1⁄
2
1⁄
2
7⁄
8
7⁄
8
MC8×8.5
2.50
8.00
0.179
3⁄
16
1⁄
16
1.874
17⁄8
0.311
5⁄
16
61⁄2
3⁄
4
5⁄
16
5⁄
8
MC7×22.7
MC9×19.1
6.67
5.61
7.00
7.00
0.503
0.352
1⁄
2
3⁄
8
3⁄
1⁄
4
3.603
3.452
35⁄8
31⁄2
0.500
0.500
1⁄
16
2
43⁄4
43⁄4
11⁄8
11⁄8
1⁄
2
1⁄
2
7⁄
8
7⁄
8
MC6×18
5.29
6.00
0.379
3⁄
8
3⁄
16
3.504
31⁄2
0.475
1⁄
2
37⁄8
11⁄16
1⁄
2
7⁄
8
MC6×16.3
MC9×15.1
4.79
4.44
6.00
6.00
0.375
0.316
3⁄
8
5⁄
16
3⁄
16
3.000
2.941
3
3
0.475
0.475
1⁄
2
16
2
37⁄8
37⁄8
11⁄16
11⁄16
1⁄
2
1⁄
2
3⁄
4
3⁄
4
MC6×12
3.53
6.00
0.310
5⁄
16
1⁄
8
2.497
21⁄2
0.375
3⁄
8
43⁄8
13⁄
16
3⁄
8
5⁄
8
3⁄
3⁄
16
16
16
1⁄
1⁄
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1⁄
1⁄
2
2
2
2
STRUCTURAL SHAPES
1 - 55
CHANNELS
MISCELLANEOUS
Properties
k
x
Y
xp
X
T
tf
d
X
tw
Y
k
Nominal
Wt.
per
ft
_
x
Shear
Center PNA
Loca- Location
tion
eo
xp
Axis X-X
Z
I
4
Axis Y-Y
S
3
grip
bf
eo
r
3
Z
I
4
S
3
r
3
lb
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
25.4
23.9
0.970
0.981
0.986
1.04
0.411
0.386
88.0
85.0
23.2
22.2
19.6
18.9
3.43
3.48
7.65
7.22
5.23
5.05
3.02
2.93
1.01
1.01
22.8
21.4
1.01
1.02
1.04
1.09
0.415
0.449
63.8
61.6
18.8
18.0
16.0
15.4
3.09
3.13
7.07
6.64
4.88
4.71
2.84
2.74
1.03
1.03
20
18.7
0.840
0.849
0.843
0.889
0.364
0.341
54.5
52.5
16.2
15.4
13.6
13.1
3.05
3.09
4.47
4.20
3.57
3.44
2.05
1.97
0.872
0.874
8.5
0.428
0.542
0.155
23.3
6.91
3.05
0.628
0.882
0.434
0.501
22.7
19.1
1.04
1.08
1.01
1.15
0.473
0.567
47.5
43.2
16.2
14.3
2.67
2.77
7.29
6.11
4.86
4.34
2.85
2.57
1.05
1.04
18
1.12
1.17
0.622
29.7
11.5
9.91
2.37
5.93
4.14
2.48
1.06
16.3
15.1
0.927
0.940
0.930
0.982
0.464
0.537
26.0
25.0
10.2
9.69
8.68
8.32
2.33
2.37
3.82
3.51
3.18
3.00
1.84
1.75
0.892
0.889
12
0.704
0.725
0.292
18.7
7.38
6.24
2.30
1.87
1.79
1.04
0.728
5.83
13.6
12.3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 56
DIMENSIONS AND PROPERTIES
Y
ANGLES
Equal legs and unequal legs
Properties for designing
xp
x
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
in.
Z
k
Weight
per
ft
Axis X-X
Area
2
S
I
4
r
3
y
Z
yp
3
in.
lb
in.
in.
in.
in.
in.
in.
in.
L8×8×11⁄8
L8×8×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×19⁄16
L8×8×11⁄2
13⁄4
15⁄8
11⁄2
13⁄8
11⁄4
13⁄16
11⁄8
56.9
51.0
45.0
38.9
32.7
29.6
26.4
16.7
15.0
13.2
11.4
9.61
8.68
7.75
98.0
89.0
79.6
69.7
59.4
54.1
48.6
17.5
15.8
14.0
12.2
10.3
9.34
8.36
2.42
2.44
2.45
2.47
2.49
2.50
2.50
2.41
2.37
2.33
2.28
2.23
2.21
2.19
31.6
28.5
25.3
22.0
18.6
16.8
15.1
1.05
0.938
0.827
0.715
0.601
0.543
0.484
L8×6×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×19⁄16
L8×8×11⁄2
L8×8×17⁄16
11⁄2
13⁄8
11⁄4
11⁄8
11⁄16
1
15⁄
16
44.2
39.1
33.8
28.5
25.7
23.0
20.2
13.0
11.5
9.94
8.36
7.56
6.75
5.93
80.8
72.3
63.4
54.1
49.3
44.3
39.2
15.1
13.4
11.7
9.87
8.95
8.02
7.07
2.49
2.51
2.53
2.54
2.55
2.56
2.57
2.65
2.61
2.56
2.52
2.50
2.47
2.45
27.3
24.2
21.1
17.9
16.2
14.5
12.8
1.50
1.44
1.38
1.31
1.28
1.25
1.22
L8×4×1
L8×8×17⁄8
L8×8×13⁄4
L8×4×15⁄8
L8×8×19⁄16
L8×8×11⁄2
L8×4×17⁄16
L7×4×3⁄4
L7×4×5⁄8
L7×4×1⁄2
L7×4×7⁄16
L7×4×3⁄8
11⁄2
13⁄8
11⁄4
11⁄8
11⁄16
1
15⁄
16
11⁄4
11⁄8
1
15⁄
16
7⁄
8
37.4
33.1
28.7
24.2
21.9
19.6
17.2
26.2
22.1
17.9
15.7
13.6
11.0
9.73
8.44
7.11
6.43
5.75
5.06
7.69
6.48
5.25
4.62
3.98
69.6
62.5
54.9
46.9
42.8
38.5
34.1
37.8
32.4
26.7
23.7
20.6
14.1
12.5
10.9
9.21
8.35
7.49
6.60
8.42
7.14
5.81
5.13
4.44
2.52
2.53
2.55
2.57
2.58
2.59
2.60
2.22
2.24
2.25
2.26
2.27
3.05
3.00
2.95
2.91
2.88
2.86
2.83
2.51
2.46
2.42
2.39
2.37
24.3
21.6
18.9
16.0
14.5
13.0
11.5
14.8
12.6
10.3
9.09
7.87
2.50
2.44
2.38
2.31
2.28
2.25
2.22
1.88
1.81
1.75
1.72
1.69
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL SHAPES
1 - 57
Y
ANGLES
Equal legs and unequal legs
Properties for designing
x
xp
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
Z
Axis Y-Y
S
I
r
Axis Z-Z
x
Z
xp
r
Tan
in.
in.
in.
in.
in.
in.
in.
α
L8×8×11⁄8
L8×8×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×19⁄16
L8×8×11⁄2
98.0
89.0
79.6
69.7
59.4
54.1
48.6
17.5
15.8
14.0
12.2
10.3
9.34
8.36
2.42
2.44
2.45
2.47
2.49
2.50
2.50
2.41
2.37
2.33
2.28
2.23
2.21
2.19
31.6
28.5
25.3
22.0
18.6
16.8
15.1
1.05
0.938
0.827
0.715
0.601
0.543
0.484
1.56
1.56
1.57
1.58
1.58
1.59
1.59
1.000
1.000
1.000
1.000
1.000
1.000
1.000
L8×6×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×19⁄16
L8×8×11⁄2
L8×8×17⁄16
38.8
34.9
30.7
26.3
24.0
21.7
19.3
8.92
7.94
6.92
5.88
5.34
4.79
4.23
1.73
1.74
1.76
1.77
1.78
1.79
1.80
1.65
1.61
1.56
1.52
1.50
1.47
1.45
16.2
14.4
12.5
10.5
9.52
8.51
7.50
0.813
0.718
0.621
0.522
0.472
0.422
0.371
1.28
1.28
1.29
1.29
1.30
1.30
1.31
0.543
0.547
0.551
0.554
0.556
0.558
0.560
L8×4×1
L8×4×17⁄8
L8×8×13⁄4
L8×4×15⁄8
L8×8×19⁄16
L8×8×11⁄2
L8×4×17⁄16
11.6
10.5
9.36
8.10
7.43
6.74
6.02
3.94
3.51
3.07
2.62
2.38
2.15
1.90
1.03
1.04
1.05
1.07
1.07
1.08
1.09
1.05
0.999
0.953
0.905
0.882
0.859
0.835
7.72
6.77
5.81
4.86
4.38
3.90
3.42
0.688
0.608
0.527
0.444
0.402
0.359
0.316
0.846
0.848
0.852
0.857
0.861
0.865
0.869
0.247
0.253
0.258
0.262
0.265
0.267
0.269
L7×4×3⁄4
L7×4×5⁄8
L7×4×1⁄2
L7×4×7⁄16
L7×4×3⁄8
9.05
7.84
6.53
5.83
5.10
3.03
2.58
2.12
1.88
1.63
1.09
1.10
1.11
1.12
1.13
1.01
0.963
0.917
0.893
0.870
5.65
4.74
3.83
3.37
2.90
0.549
0.463
0.375
0.330
0.285
0.860
0.865
0.872
0.875
0.880
0.324
0.329
0.335
0.337
0.340
in.
4
3
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 58
DIMENSIONS AND PROPERTIES
Y
ANGLES
Equal legs and unequal legs
Properties for designing
xp
x
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
in.
Z
k
Weight
per
ft
Axis X-X
Area
2
S
I
4
r
3
y
Z
yp
3
in.
lb
in.
in.
in.
in.
in.
in.
in.
L6×6×1
L6×6×17⁄8
L6×6×13⁄4
L6×6×15⁄8
L6×6×19⁄16
L6×6×11⁄2
L6×6×17⁄16
L6×6×13⁄8
L6×6×15⁄16
11⁄2
13⁄8
11⁄4
11⁄8
11⁄16
1
15⁄
16
7⁄
8
13⁄
16
37.4
33.1
28.7
24.2
21.9
19.6
17.2
14.9
12.4
11.0
9.73
8.44
7.11
6.43
5.75
5.06
4.36
3.65
35.5
31.9
28.2
24.2
22.1
19.9
17.7
15.4
13.0
8.57
7.63
6.66
5.66
5.14
4.61
4.08
3.53
2.97
1.80
1.81
1.83
1.84
1.85
1.86
1.87
1.88
1.89
1.86
1.82
1.78
1.73
1.71
1.68
1.66
1.64
1.62
15.5
13.8
12.0
10.2
9.26
8.31
7.34
6.35
5.35
0.917
0.811
0.703
0.592
0.536
0.479
0.422
0.363
0.304
L6×4×7⁄8
L6×4×3⁄4
L6×4×5⁄8
L6×4×9⁄16
L6×4×1⁄2
L6×4×7⁄16
L6×4×3⁄8
L6×4×5⁄16
13⁄8
11⁄4
11⁄8
11⁄16
1
15⁄
16
7⁄
8
13⁄
16
27.2
23.6
20.0
18.1
16.2
14.3
12.3
10.3
7.98
6.94
5.86
5.31
4.75
4.18
3.61
3.03
27.7
24.5
21.1
19.3
17.4
15.5
13.5
11.4
7.15
6.25
5.31
4.83
4.33
3.83
3.32
2.79
1.86
1.88
1.90
1.90
1.91
1.92
1.93
1.94
2.12
2.08
2.03
2.01
1.99
1.96
1.94
1.92
12.7
11.2
9.51
8.66
7.78
6.88
5.97
5.03
1.44
1.38
1.31
1.28
1.25
1.22
1.19
1.16
L6×31⁄2×1⁄2
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
1
7⁄
8
13⁄
16
15.3
11.7
9.80
4.50
3.42
2.87
16.6
12.9
10.9
4.24
3.24
2.73
1.92
1.94
1.95
2.08
2.04
2.01
7.50
5.76
4.85
1.50
1.44
1.41
L5×5×7⁄8
L5×5×3⁄4
L5×5×5⁄8
L5×5×1⁄2
L5×5×7⁄16
L5×5×3⁄8
L5×5×5⁄16
13⁄8
11⁄4
11⁄8
1
15⁄
16
7⁄
8
13⁄
16
27.2
23.6
20.0
16.2
14.3
12.3
10.3
7.98
6.94
5.86
4.75
4.18
3.61
3.03
17.8
15.7
13.6
11.3
10.0
8.74
7.42
5.17
4.53
3.86
3.16
2.79
2.42
2.04
1.49
1.51
1.52
1.54
1.55
1.56
1.57
1.57
1.52
1.48
1.43
1.41
1.39
1.37
9.33
8.16
6.95
5.68
5.03
4.36
3.68
0.798
0.694
0.586
0.475
0.418
0.361
0.303
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL SHAPES
1 - 59
Y
ANGLES
Equal legs and unequal legs
Properties for designing
x
xp
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
in.
L6×6×1
L6×6×17⁄8
L6×6×13⁄4
L6×6×15⁄8
L6×6×19⁄16
L6×6×11⁄2
L6×6×17⁄16
L6×6×13⁄8
L6×6×15⁄16
Z
Axis Y-Y
S
I
4
r
Axis Z-Z
x
xp
r
in.
in.
in.
α
1.86
1.82
1.78
1.73
1.71
1.68
1.66
1.64
1.62
15.5
13.8
12.0
10.2
9.26
8.31
7.34
6.35
5.35
0.917
0.811
0.703
0.592
0.536
0.479
0.422
0.363
0.304
1.17
1.17
1.17
1.18
1.18
1.18
1.19
1.19
1.20
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
in.
3
in.
in.
in.
35.5
31.9
28.2
24.2
22.1
19.9
17.7
15.4
13.0
8.57
7.63
6.66
5.66
5.14
4.61
4.08
3.53
2.97
1.80
1.81
1.83
1.84
1.85
1.86
1.87
1.88
1.89
Z
3
Tan
L6×4×7⁄8
L6×4×3⁄4
L6×4×5⁄8
L6×4×9⁄16
L6×4×1⁄2
L6×4×7⁄16
L6×4×3⁄8
L6×4×5⁄16
9.75
8.68
7.52
6.91
6.27
5.60
4.90
4.18
3.39
2.97
2.54
2.31
2.08
1.85
1.60
1.35
1.11
1.12
1.13
1.14
1.15
1.16
1.17
1.17
1.12
1.08
1.03
1.01
0.987
0.964
0.941
0.918
6.31
5.47
4.62
4.19
3.75
3.30
2.85
2.40
0.665
0.578
0.488
0.442
0.396
0.349
0.301
0.252
0.857
0.860
0.864
0.866
0.870
0.873
0.877
0.882
0.421
0.428
0.435
0.438
0.440
0.443
0.446
0.448
L6×31⁄2×1⁄2
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
4.25
3.34
2.85
1.59
1.23
1.04
0.972
0.988
0.996
0.833
0.787
0.763
2.91
2.20
1.85
0.375
0.285
0.239
0.759
0.767
0.772
0.344
0.350
0.352
17.8
15.7
13.6
11.3
10.0
8.74
7.42
5.17
4.53
3.86
3.16
2.79
2.42
2.04
1.49
1.51
1.52
1.54
1.55
1.56
1.57
1.57
1.52
1.48
1.43
1.41
1.39
1.37
9.33
8.16
6.95
5.68
5.03
4.36
3.68
0.798
0.694
0.586
0.475
0.418
0.361
0.303
0.973
0.975
0.978
0.983
0.986
0.990
0.994
1.000
1.000
1.000
1.000
1.000
1.000
1.000
L5×5×7⁄8
L5×5×3⁄4
L5×5×5⁄8
L5×5×1⁄2
L5×5×7⁄16
L5×5×3⁄8
L5×5×5⁄16
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 60
DIMENSIONS AND PROPERTIES
Y
ANGLES
Equal legs and unequal legs
Properties for designing
xp
x
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
in.
Z
k
Weight
per
ft
Axis X-X
Area
2
S
I
4
r
3
y
Z
yp
3
in.
lb
in.
in.
in.
in.
in.
in.
L5×31⁄2×3⁄4
L5×31⁄2×5⁄8
L5×31⁄2×1⁄2
L5×31⁄2×3⁄8
L5×31⁄2×5⁄16
L5×31⁄2×1⁄4
11⁄4
11⁄8
1
7⁄
8
13⁄
16
3⁄
4
19.8
16.8
13.6
10.4
8.70
7.00
5.81
4.92
4.00
3.05
2.56
2.06
13.9
12.0
9.99
7.78
6.60
5.39
4.28
3.65
2.99
2.29
1.94
1.57
1.55
1.56
1.58
1.60
1.61
1.62
1.75
1.70
1.66
1.61
1.59
1.56
7.65
6.55
5.38
4.14
3.49
2.83
1.13
1.06
1.00
0.938
0.906
0.875
L5×3×1⁄2
L5×3×7⁄16
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
1
15⁄
16
7⁄
8
13⁄
16
3⁄
4
12.8
11.3
9.80
8.20
6.60
3.75
3.31
2.86
2.40
1.94
9.45
8.43
7.37
6.26
5.11
2.91
2.58
2.24
1.89
1.53
1.59
1.60
1.61
1.61
1.62
1.75
1.73
1.70
1.68
1.66
5.16
4.57
3.97
3.36
2.72
1.25
1.22
1.19
1.16
1.13
L4×4×3⁄4
L5×3×5⁄8
L5×3×1⁄2
L5×3×7⁄16
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
11⁄8
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
18.5
15.7
12.8
11.3
9.80
8.20
6.60
5.44
4.61
3.75
3.31
2.86
2.40
1.94
7.67
6.66
5.56
4.97
4.36
3.71
3.04
2.81
2.40
1.97
1.75
1.52
1.29
1.05
1.19
1.20
1.22
1.23
1.23
1.24
1.25
1.27
1.23
1.18
1.16
1.14
1.12
1.09
5.07
4.33
3.56
3.16
2.74
2.32
1.88
0.680
0.576
0.469
0.414
0.357
0.300
0.242
L4×31⁄2×1⁄2
L4×31⁄2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
15⁄
16
13⁄
16
3⁄
4
11⁄
16
11.9
9.10
7.70
6.20
3.50
2.67
2.25
1.81
5.32
4.18
3.56
2.91
1.94
1.49
1.26
1.03
1.23
1.25
1.26
1.27
1.25
1.21
1.18
1.16
3.50
2.71
2.29
1.86
0.500
0.438
0.406
0.375
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in.
STRUCTURAL SHAPES
1 - 61
Y
ANGLES
Equal legs and unequal legs
Properties for designing
x
xp
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
Z
Axis Y-Y
S
I
r
Axis Z-Z
x
Z
xp
r
Tan
in.
in.
in.
in.
in.
in.
in.
α
L5×31⁄2×3⁄4
L5×31⁄2×5⁄8
L5×31⁄2×1⁄2
L5×31⁄2×3⁄8
L5×31⁄2×5⁄16
L5×31⁄2×1⁄4
5.55
4.83
4.05
3.18
2.72
2.23
2.22
1.90
1.56
1.21
1.02
0.830
0.977
0.991
1.01
1.02
1.03
1.04
0.996
0.951
0.906
0.861
0.838
0.814
4.10
3.47
2.83
2.16
1.82
1.47
0.581
0.492
0.400
0.305
0.256
0.206
0.748
0.751
0.755
0.762
0.766
0.770
0.464
0.472
0.479
0.486
0.489
0.492
L5×3×1⁄2
L5×3×7⁄16
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
2.58
2.32
2.04
1.75
1.44
1.15
1.02
0.888
0.753
0.614
0.829
0.837
0.845
0.853
0.861
0.750
0.727
0.704
0.681
0.657
2.11
1.86
1.60
1.35
1.09
0.375
0.331
0.286
0.240
0.194
0.648
0.651
0.654
0.658
0.663
0.357
0.361
0.364
0.368
0.371
L4×4×3⁄4
L5×3×5⁄8
L5×3×1⁄2
L5×3×7⁄16
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
7.67
6.66
5.56
4.97
4.36
3.71
3.04
2.81
2.40
1.97
1.75
1.52
1.29
1.05
1.19
1.20
1.22
1.23
1.23
1.24
1.25
1.27
1.23
1.18
1.16
1.14
1.12
1.09
5.07
4.33
3.56
3.16
2.74
2.32
1.88
0.680
0.576
0.469
0.414
0.357
0.300
0.242
0.778
0.779
0.782
0.785
0.788
0.791
0.795
1.000
1.000
1.000
1.000
1.000
1.000
1.000
L4×31⁄2×1⁄2
4×31⁄2×3⁄8
4×31⁄2×5⁄16
4×31⁄2×1⁄4
3.79
2.95
2.55
2.09
1.52
1.16
0.994
0.808
1.04
1.06
1.07
1.07
1.00
0.955
0.932
0.909
2.73
2.11
1.78
1.44
0.438
0.334
0.281
0.227
0.722
0.727
0.730
0.734
0.750
0.755
0.757
0.759
in.
4
3
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 62
DIMENSIONS AND PROPERTIES
Y
ANGLES
Equal legs and unequal legs
Properties for designing
xp
x
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
Z
k
Weight
per
ft
Axis X-X
Area
S
I
2
r
4
y
3
Z
yp
3
in.
in.
lb
in.
in.
in.
in.
in.
in.
L4×3×5⁄8
L4×3×1⁄2
L4×3×7⁄16
L4×3×3⁄8
L4×3×5⁄16
L4×3×1⁄4
11⁄16
15⁄
16
7⁄
8
13⁄
16
3⁄
4
11⁄
16
13.6
11.1
9.80
8.50
7.20
5.80
3.98
3.25
2.87
2.48
2.09
1.69
6.03
5.05
4.52
3.96
3.38
2.77
2.30
1.89
1.68
1.46
1.23
1.00
1.23
1.25
1.25
1.26
1.27
1.28
1.37
1.33
1.30
1.28
1.26
1.24
4.12
3.41
3.03
2.64
2.23
1.82
0.813
0.750
0.719
0.688
0.656
0.625
L31⁄2×31⁄2×1⁄2
L31⁄2×31⁄2×7⁄16
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×5⁄16
L31⁄2×31⁄2×1⁄4
7⁄
8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
11.1
9.80
8.50
7.20
5.80
3.25
2.87
2.48
2.09
1.69
3.64
3.26
2.87
2.45
2.01
1.49
1.32
1.15
0.976
0.794
1.06
1.07
1.07
1.08
1.09
1.06
1.04
1.01
0.990
0.968
2.68
2.38
2.08
1.76
1.43
0.464
0.410
0.355
0.299
0.241
L31⁄2×3×1⁄2
L31⁄2×3×3⁄8
L31⁄2×3×5⁄16
L31⁄2×3×1⁄4
15⁄
16
13⁄
16
3⁄
4
11⁄
16
10.2
7.90
6.60
5.40
3.00
2.30
1.93
1.56
3.45
2.72
2.33
1.91
1.45
1.13
0.954
0.776
1.07
1.09
1.10
1.11
1.13
1.08
1.06
1.04
2.63
2.04
1.73
1.41
0.500
0.438
0.406
0.375
L31⁄2×21⁄2×1⁄2
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×1⁄4
15⁄
16
13⁄
16
11⁄
16
9.40
7.20
4.90
2.75
2.11
1.44
3.24
2.56
1.80
1.41
1.09
0.755
1.09
1.10
1.12
1.20
1.16
1.11
2.53
1.97
1.36
0.750
0.688
0.625
L3×3×1⁄2
L4×3×7⁄16
L4×3×3⁄8
L4×3×5⁄16
L4×3×1⁄4
L4×3×3⁄16
13⁄
16
3⁄
4
11⁄
16
5⁄
8
9⁄
16
1⁄
2
9.40
8.30
7.20
6.10
4.90
3.71
2.75
2.43
2.11
1.78
1.44
1.09
2.22
1.99
1.76
1.51
1.24
0.962
1.07
0.954
0.833
0.707
0.577
0.441
0.898
0.905
0.913
0.922
0.930
0.939
0.932
0.910
0.888
0.865
0.842
0.820
1.93
1.72
1.50
1.27
1.04
0.794
0.458
0.406
0.352
0.296
0.240
0.182
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in.
STRUCTURAL SHAPES
1 - 63
Y
ANGLES
Equal legs and unequal legs
Properties for designing
x
xp
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
Z
Axis Y-Y
S
I
r
Axis Z-Z
x
Z
xp
r
Tan
in.
in.
in.
in.
in.
in.
in.
in.
α
L4×3×5⁄8
L4×3×1⁄2
L4×3×7⁄16
L4×3×3⁄8
L4×3×5⁄16
L4×3×1⁄4
2.87
2.42
2.18
1.92
1.65
1.36
1.35
1.12
0.992
0.866
0.734
0.599
0.849
0.864
0.871
0.879
0.887
0.896
0.871
0.827
0.804
0.782
0.759
0.736
2.48
2.03
1.79
1.56
1.31
1.06
0.498
0.406
0.359
0.311
0.261
0.211
0.637
0.639
0.641
0.644
0.647
0.651
0.534
0.543
0.547
0.551
0.554
0.558
L31⁄2×31⁄2×1⁄2
L31⁄2×31⁄2×7⁄16
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×5⁄16
L31⁄2×31⁄2×1⁄4
3.64
3.26
2.87
2.45
2.01
1.49
1.32
1.15
0.976
0.794
1.06
1.07
1.07
1.08
1.09
1.06
1.04
1.01
0.990
0.968
2.68
2.38
2.08
1.76
1.43
0.464
0.410
0.355
0.299
0.241
0.683
0.684
0.687
0.690
0.694
1.000
1.000
1.000
1.000
1.000
L31⁄2×3×1⁄2
L31⁄2×3×3⁄8
L31⁄2×3×5⁄16
L31⁄2×3×1⁄4
2.33
1.85
1.58
1.30
1.10
0.851
0.722
0.589
0.881
0.897
0.905
0.914
0.875
0.830
0.808
0.785
1.98
1.53
1.30
1.05
0.429
0.328
0.276
0.223
0.621
0.625
0.627
0.631
0.714
0.721
0.724
0.727
L31⁄2×21⁄2×1⁄2
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×1⁄4
1.36
1.09
0.777
0.760
0.592
0.412
0.704
0.719
0.735
0.705
0.660
0.614
1.40
1.07
0.735
0.393
0.301
0.205
0.534
0.537
0.544
0.486
0.496
0.506
L3×3×1⁄2
L3×3×7⁄16
L3×3×3⁄8
L3×3×5⁄16
L3×3×1⁄4
L3×3×3⁄16
2.22
1.99
1.76
1.51
1.24
0.962
1.07
0.954
0.833
0.707
0.577
0.441
0.898
0.905
0.913
0.922
0.930
0.939
0.932
0.910
0.888
0.865
0.842
0.820
1.93
1.72
1.50
1.27
1.04
0.794
0.458
0.406
0.352
0.296
0.240
0.182
0.584
0.585
0.587
0.589
0.592
0.596
1.000
1.000
1.000
1.000
1.000
1.000
4
3
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 64
DIMENSIONS AND PROPERTIES
Y
ANGLES
Equal legs and unequal legs
Properties for designing
xp
x
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
in.
Z
k
Weight
per
ft
Axis X-X
Area
2
S
I
4
r
3
y
Z
yp
3
in.
lb
in.
in.
in.
in.
in.
L3×21⁄2×1⁄2
L3×21⁄2×3⁄8
L3×21⁄2×5⁄16
L3×21⁄2×1⁄4
L3×21⁄2×3⁄16
7⁄
8
3⁄
4
11⁄
16
5⁄
8
9⁄
16
8.50
6.60
5.60
4.50
3.39
2.50
1.92
1.62
1.31
0.996
2.08
1.66
1.42
1.17
0.907
1.04
0.810
0.688
0.561
0.430
0.913
0.928
0.937
0.945
0.954
1.000
0.956
0.933
0.911
0.888
1.88
1.47
1.25
1.02
0.781
0.500
0.438
0.406
0.375
0.344
L3×2×1⁄2
L3×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
L3×2×3⁄16
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7.70
5.90
5.00
4.10
3.07
2.25
1.73
1.46
1.19
0.902
1.92
1.53
1.32
1.09
0.842
1.00
0.781
0.664
0.542
0.415
0.924
0.940
0.948
0.957
0.966
1.08
1.04
1.02
0.993
0.970
1.78
1.40
1.19
0.973
0.746
0.750
0.688
0.656
0.625
0.594
L21⁄2×21⁄2×1⁄2
L21⁄2×21⁄2×3⁄8
L21⁄2×21⁄2×5⁄16
L21⁄2×21⁄2×1⁄4
L21⁄2×21⁄2×3⁄16
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7.70
5.90
5.00
4.10
3.07
2.25
1.73
1.46
1.19
0.902
1.23
0.984
0.849
0.703
0.547
0.724
0.566
0.482
0.394
0.303
0.739
0.753
0.761
0.769
0.778
0.806
0.762
0.740
0.717
0.694
1.31
1.02
0.869
0.711
0.545
0.450
0.347
0.293
0.238
0.180
L21⁄2×2×3⁄8
L21⁄2×2×5⁄16
L21⁄2×2×1⁄4
L21⁄2×2×3⁄16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
5.30
4.50
3.62
2.75
1.55
1.31
1.06
0.809
0.912
0.788
0.654
0.509
0.547
0.466
0.381
0.293
0.768
0.776
0.784
0.793
0.831
0.809
0.787
0.764
0.986
0.843
0.691
0.532
0.438
0.406
0.375
0.344
L2×2×3⁄8
L2×2×5⁄16
L2×2×1⁄4
L2×2×3⁄16
L2×2×1⁄8
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
4.70
3.92
3.19
2.44
1.65
1.36
1.15
0.938
0.715
0.484
0.479
0.416
0.348
0.272
0.190
0.351
0.300
0.247
0.190
0.131
0.594
0.601
0.609
0.617
0.626
0.636
0.614
0.592
0.569
0.546
0.633
0.541
0.445
0.343
0.235
0.340
0.288
0.234
0.179
0.121
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in.
in.
STRUCTURAL SHAPES
1 - 65
ANGLES
Equal legs and unequal legs
Properties for designing
Y
x
xp
Z
X
X
y, yp
k
α
Y
Size
and
Thickness
Z
Axis Y-Y
S
I
r
Axis Z-Z
x
Z
xp
r
Tan
in.
in.
in.
in.
in.
in.
in.
α
L3×21⁄2×1⁄2
L3×21⁄2×3⁄8
L3×21⁄2×5⁄16
L3×21⁄2×1⁄4
L3×21⁄2×3⁄16
1.30
1.04
0.898
0.743
0.577
0.744
0.581
0.494
0.404
0.310
0.722
0.736
0.744
0.753
0.761
0.750
0.706
0.683
0.661
0.638
1.35
1.05
0.889
0.724
0.553
0.417
0.320
0.270
0.219
0.166
0.520
0.522
0.525
0.528
0.533
0.667
0.676
0.680
0.684
0.688
L3×2×1⁄2
L3×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
L3×2×3⁄16
0.672
0.543
0.470
0.392
0.307
0.474
0.371
0.317
0.260
0.200
0.546
0.559
0.567
0.574
0.583
0.583
0.539
0.516
0.493
0.470
0.891
0.684
0.577
0.468
0.357
0.375
0.289
0.244
0.198
0.150
0.428
0.430
0.432
0.435
0.439
0.414
0.428
0.435
0.440
0.446
L21⁄2×21⁄2×1⁄2
L21⁄2×21⁄2×3⁄8
L21⁄2×21⁄2×5⁄16
L21⁄2×21⁄2×1⁄4
L21⁄2×21⁄2×3⁄16
1.23
0.984
0.849
0.703
0.547
0.724
0.566
0.482
0.394
0.303
0.739
0.753
0.761
0.769
0.778
0.806
0.762
0.740
0.717
0.694
1.31
1.02
0.869
0.711
0.545
0.450
0.347
0.293
0.238
0.180
0.487
0.487
0.489
0.491
0.495
1.000
1.000
1.000
1.000
1.000
L21⁄2×2×3⁄8
L21⁄2×2×5⁄16
L21⁄2×2×1⁄4
L21⁄2×2×3⁄16
0.514
0.446
0.372
0.291
0.363
0.310
0.254
0.196
0.577
0.584
0.592
0.600
0.581
0.559
0.537
0.514
0.660
0.561
0.457
0.350
0.309
0.262
0.213
0.162
0.420
0.422
0.424
0.427
0.614
0.620
0.626
0.631
L2×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
L3×2×3⁄16
L3×2×1⁄8
0.479
0.416
0.348
0.272
0.190
0.351
0.300
0.247
0.190
0.131
0.594
0.601
0.609
0.617
0.626
0.636
0.614
0.592
0.569
0.546
0.633
0.541
0.445
0.343
0.235
0.340
0.288
0.234
0.179
0.121
0.389
0.390
0.391
0.394
0.398
1.000
1.000
1.000
1.000
1.000
in.
4
3
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 66
DIMENSIONS AND PROPERTIES
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL TEES (WT, MT, ST)
1 - 67
STRUCTURAL TEES (WT, MT, ST)
Structural tees are obtained by splitting the webs of various beams, generally with the
aid of rotary shears, and straightening to meet established permissible variations listed
in Standard Mill Practice in Part 1 of this Manual.
Although structural tees may be obtained by off-center splitting, or by splitting at two
lines, as specified on order, the Dimensions and Properties are based on a depth of tee
equal to one-half the published beam depth. Values of Qs are given for Fy = 36 ksi and
Fy = 50 ksi, for those tees having stems which exceed the limiting width-thickness ratio
λr of LRFD Specification Section B5. Since the cross section is comprised entirely of
unstiffened elements, Qa = 1.0 and Q = Qs for
_ all tee sections. The Flexural-Torsional
Properties Table lists the dimensional values (ro and H) and cross-section constants (J and
Cw) needed for checking flexural-torsional buckling.
Use of Table
The table may be used as follows for checking the limit states of (1) flexural buckling
about the x-axis and (2) flexural-torsional buckling. The lower of the two limit states
must be used for design. See also Part 3 of this LRFD Manual.
(1) Flexural Buckling About the X-Axis
Where no value of Qs is shown, the design compressive strength for this limit state is
given by LRFD Specification Section E2. Where a value of Qs is shown, the strength
must be reduced in accordance with Appendix B5 of the LRFD Specification.
(2) Flexural-Torsional Buckling
The design compressive strength for this limit
_ state is given by LRFD Specification
Section E3. This involves calculations with J, ro, and H. Refer to the Flexural-Torsional
Properties Tables, later in Part 1.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 68
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Area
Designation in.2
Area
of
Stem
Depth of
Tee
d
Thickness
tw
tw
2
in.
in.
in.
in.2
Flange
Width
bf
in.
Thickness
tf
in.
Distance
k
in.
WT22×167.5
WT22×145
WT22×131
WT22×115
49.1
42.9
38.6
33.8
22.010
22
1.020
21.810 2113⁄16 0.870
21.655 2111⁄16 0.790
21.455 217⁄16 0.710
1
7⁄
8
13⁄
16
11⁄
16
1⁄
2
7⁄
16
3⁄
8
3⁄
8
22.5
19.0
17.1
15.2
15.950
15.830
15.750
15.750
153⁄4
157⁄8
153⁄4
153⁄4
1.770
1.580
1.420
1.220
13⁄4
19⁄16
17⁄16
11⁄4
29⁄16
23⁄8
23⁄16
2
WT20×296.5
WT22×251.5
WT22×215.5
WT22×186
WT22×160.5
WT22×148.5
WT22×138.5
WT22×124.5
WT22×107.5
WT22×99.5
WT22×87
87.0
74.0
63.4
54.7
47.0
43.7
40.7
36.7
31.7
29.2
25.5
21.495
21.025
20.630
20.315
20.040
19.920
19.845
19.690
19.490
19.335
19.100
211⁄2
21
205⁄8
205⁄16
20
1915⁄16
197⁄8
1911⁄16
191⁄2
195⁄16
191⁄8
1.790
1.540
1.340
1.160
1.000
0.930
0.830
0.750
0.650
0.650
0.650
113⁄16
19⁄16
15⁄16
13⁄16
1
15⁄
16
13⁄
16
3⁄
4
5⁄
8
5⁄
8
5⁄
8
1
3⁄
4
11⁄
16
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
5⁄
16
5⁄
16
5⁄
16
38.5
32.4
27.6
23.6
20.0
18.5
16.5
14.8
12.7
12.6
12.4
16.690 163⁄4
16.420 167⁄16
16.220 161⁄4
16.060 161⁄16
15.910 157⁄8
15.825 157⁄8
15.830 157⁄8
15.750 153⁄4
15.750 153⁄4
15.750 153⁄4
15.750 153⁄4
3.230
2.760
2.360
2.050
1.770
1.650
1.575
1.420
1.220
1.065
0.830
31⁄4
23⁄4
23⁄8
21⁄16
13⁄4
15⁄8
19⁄16
17⁄16
11⁄4
11⁄16
13⁄
16
47⁄16
315⁄16
39⁄16
31⁄4
215⁄16
31⁄16
23⁄4
25⁄8
23⁄8
21⁄4
2
WT20×233
WT22×196
WT22×165.5
WT22×139
WT22×132
WT22×117.5
WT22×105.5
WT22×91.5
WT22×83.5
WT22×74.5
68.4
57.7
48.8
40.9
38.8
34.5
31.0
26.9
24.6
21.9
21.220 213⁄16
20.785 203⁄4
20.395 203⁄8
20.080 201⁄8
20.000
20
19.845 197⁄8
19.685 1911⁄16
19.490 191⁄2
19.295 195⁄16
19.100 191⁄8
1.67
1.42
1.22
1.02
0.960
0.830
0.750
0.650
0.650
0.630
111⁄16
17⁄16
11⁄4
1
1
13⁄
16
3⁄
4
5⁄
8
5⁄
8
5⁄
8
13⁄
16
11⁄
16
5⁄
8
1⁄
2
1⁄
2
7⁄
16
3⁄
8
5⁄
16
5⁄
16
5⁄
16
35.4
29.5
24.9
20.5
19.2
16.5
14.8
12.7
12.5
12.0
12.640 125⁄8
12.360 123⁄8
12.170 123⁄16
11.970
12
11.930
12
11.890 117⁄8
11.810 113⁄4
11.810 113⁄4
11.810 113⁄4
11.810 113⁄4
2.950
2.520
2.130
1.810
1.730
1.575
1.415
1.220
1.025
0.830
215⁄16
21⁄2
21⁄8
113⁄16
13⁄4
17⁄16
19⁄16
11⁄4
1
13⁄
16
41⁄8
311⁄16
35⁄16
3
215⁄16
23⁄4
25⁄8
23⁄8
23⁄16
2
WT18×424
WT22×399
WT22×325
WT22×263.5
WT22×219.5
WT22×196.5
WT22×179.5
WT22×164
WT22×150
WT22×140
WT22×130
WT22×122.5
WT22×115
125
117
95.0
77.0
64.0
57.5
52.7
48.2
44.1
41.2
38.2
36.0
33.8
21.225 211⁄4
20.985
21
20.235 201⁄4
19.605 195⁄8
19.130 191⁄8
18.900 187⁄8
18.700 1811⁄16
18.545 189⁄16
18.370 183⁄8
18.260 181⁄4
18.130 181⁄8
18.040
18
17.950
18
2.520
2.380
1.970
1.610
1.360
1.220
1.120
1.020
0.945
0.885
0.840
0.800
0.760
21⁄2
23⁄8
2
15⁄8
13⁄8
11⁄4
11⁄8
1
15⁄
16
7⁄
8
13⁄
16
13⁄
16
3⁄
4
11⁄4
13⁄16
1
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
7⁄
16
7⁄
16
3⁄
8
53.5
49.9
39.9
31.6
26.0
23.1
20.9
18.9
17.4
16.2
15.2
14.4
13.6
18.130
17.990
17.575
17.220
16.965
16.830
16.730
16.630
16.655
16.595
16.550
16.510
16.470
181⁄8
18
175⁄8
171⁄4
17
167⁄8
163⁄4
165⁄8
165⁄8
165⁄8
161⁄2
161⁄2
161⁄2
4.530
4.290
3.540
2.910
2.440
2.200
2.010
1.850
1.680
1.570
1.440
1.350
1.260
41⁄2
45⁄16
39⁄16
215⁄16
27⁄16
23⁄16
2
17⁄8
111⁄16
19⁄16
17⁄16
13⁄8
11⁄4
511⁄16
57⁄16
411⁄16
41⁄16
39⁄16
35⁄16
31⁄8
3
213⁄16
211⁄16
29⁄16
21⁄2
23⁄8
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL TEES (WT, MT, ST)
1 - 69
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
36
Fy, ksi
50
167.5
145
131
115
19.1
22.3
24.6
27.4
2160
1840
1650
1440
131
111
100
88.6
6.63
6.55
6.53
6.53
5.51
5.27
5.20
5.17
233
197
177
157
1.54
1.35
1.23
1.07
600
524
463
398
75.3
66.1
58.8
50.5
3.50
3.49
3.46
3.43
118
103
91.4
78.4
0.982
0.833
0.732
0.608
0.817
0.636
0.532
0.438
296.5
251.5
215.5
186
160.5
148.5
138.5
124.5
107.5
99.5
87
9.5
11.1
12.8
14.7
17.1
18.4
20.6
22.8
26.3
26.3
26.3
3300
2730
2290
1930
1630
1500
1360
1210
1030
987
907
209
175
148
126
107
98.9
88.6
79.3
68.0
66.4
63.8
6.16
6.07
6.01
5.95
5.89
5.87
5.78
5.75
5.72
5.81
5.96
5.67
5.39
5.18
4.97
4.79
4.71
4.51
4.41
4.28
4.48
4.87
379
315
266
225
191
176
157
140
120
117
114
2.61
2.25
1.95
1.70
1.48
1.38
1.28
1.16
1.00
0.927
0.811
1260
1020
843
710
596
546
522
463
398
347
271
151
125
104
88.5
74.9
69.1
65.9
58.8
50.5
44.1
34.4
3.81
3.72
3.65
3.60
3.56
3.54
3.58
3.56
3.55
3.45
3.26
240
197
164
139
117
108
102
91.0
77.9
68.3
53.8
—
—
—
—
—
0.989
0.882
0.782
0.618
0.628
0.643
—
—
—
—
0.895
0.825
0.699
0.580
0.445
0.452
0.463
233
196
165.5
139
132
117.5
105.5
91.5
83.5
74.5
10.2
12.0
14.0
16.8
17.8
20.6
22.8
26.3
26.3
27.1
2770
2270
1880
1540
1450
1260
1120
957
898
815
185
153
128
106
99.3
85.6
76.7
65.8
63.7
59.7
6.36
6.28
6.21
6.14
6.11
6.04
6.01
5.97
6.05
6.10
6.22
5.95
5.74
5.50
5.40
5.17
5.08
4.94
5.20
5.45
333
276
231
190
178
153
137
117
115
119
2.71
2.33
2.01
1.71
1.63
1.45
1.31
1.14
1.04
1.82
504
401
323
261
246
222
195
168
141
115
79.8
65.0
53.1
43.6
41.3
37.3
33.0
28.5
23.9
19.4
2.72
2.64
2.57
2.52
2.52
2.54
2.51
2.50
2.40
2.29
131
106
86.2
70.0
66.2
59.2
52.3
44.8
38.0
31.1
—
—
—
—
—
0.882
0.782
0.618
0.630
0.604
—
—
—
0.913
0.855
0.699
0.581
0.445
0.454
0.435
424
399
325
263.5
219.5
196.5
179.5
164
150
140
130
122.5
115
6.3
6.6
8.0
9.8
11.6
12.9
14.1
15.4
16.7
17.8
18.7
19.7
20.7
4250
3920
3020
2330
1880
1660
1500
1350
1230
1140
1060
995
934
277
257
202
159
130
115
104
94.1
86.1
80.0
75.1
71.0
67.0
5.84
5.79
5.64
5.50
5.42
5.37
5.33
5.29
5.27
5.25
5.26
5.26
5.25
5.86
5.72
5.29
4.89
4.63
4.46
4.33
4.21
4.13
4.07
4.05
4.03
4.01
515
478
373
290
235
207
187
168
153
142
133
125
118
3.43
3.25
2.70
2.24
1.89
1.71
1.58
1.45
1.33
1.24
1.16
1.09
1.03
2270
2100
1610
1240
997
877
786
711
648
599
545
507
470
251
234
184
145
117
104
94.0
85.5
77.8
72.2
65.9
61.4
57.1
4.27
4.24
4.12
4.02
3.95
3.90
3.86
3.84
3.83
3.81
3.78
3.75
3.73
399
371
290
227
184
162
146
132
120
112
102
94.9
88.1
—
—
—
—
—
—
—
—
—
—
0.981
0.943
0.896
—
—
—
—
—
—
—
—
0.927
0.867
0.816
0.770
0.715
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 70
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Area
of
Stem
Flange
DisThickness tance
tf
k
Area
Depth of
Tee
d
Thickness
tw
tw
2
Designation
in.2
in.
in.
in.
WT18×128
WT18×116
WT18×105
WT18×97
WT18×91
WT18×85
WT18×80
WT18×75
WT18×67.5
37.7
34.1
30.9
28.5
26.8
25.0
23.5
22.1
19.9
18.715 1811⁄16
18.560 189⁄16
18.345 183⁄8
18.245 181⁄4
18.165 181⁄8
18.085 181⁄8
18.005
18
17.925 177⁄8
17.775 173⁄4
0.960
0.870
0.830
0.765
0.725
0.680
0.650
0.625
0.600
1
7⁄
8
13⁄
16
3⁄
4
3⁄
4
11⁄
16
5⁄
8
5⁄
8
5⁄
8
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
18.0
16.1
15.2
14.0
13.2
12.3
11.7
11.2
10.7
12.215
12.120
12.180
12.115
12.075
12.030
12.000
11.975
11.950
121⁄4
121⁄8
121⁄8
121⁄8
121⁄8
12
12
12
12
1.730
1.570
1.360
1.260
1.180
1.100
1.020
0.940
0.790
13⁄4
19⁄16
13⁄8
11⁄4
13⁄16
11⁄8
1
15⁄
16
13⁄
16
25⁄8
21⁄2
25⁄16
23⁄16
21⁄8
2
115⁄16
17⁄8
111⁄16
WT16.5×177
WT16.5×159
WT16.5×145.5
WT16.5×131.5
WT16.5×120.5
WT16.5×110.5
WT16.5×100.5
52.1
46.7
42.8
38.7
35.4
32.5
29.5
17.775 173⁄4
17.580 179⁄16
17.420 177⁄16
17.265 171⁄4
17.090 171⁄8
16.965
17
16.840 167⁄8
1.160
1.040
0.960
0.870
0.830
0.775
0.715
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
20.6
18.3
16.7
15.0
14.2
13.1
12.0
16.100
15.985
15.905
15.805
15.860
15.805
15.745
161⁄8
16
157⁄8
153⁄4
157⁄8
153⁄4
153⁄4
2.090
1.890
1.730
1.570
1.400
1.275
1.150
21⁄16
17⁄8
13⁄4
19⁄16
13⁄8
11⁄4
11⁄8
27⁄8
211⁄16
29⁄16
23⁄8
23⁄16
21⁄16
115⁄16
WT16.5×84.5
WT16.5×76
WT16.5×70.5
WT16.5×65
WT16.5×59
24.8
22.4
20.8
19.2
17.3
16.910 1615⁄16
16.745 163⁄4
16.650 165⁄8
16.545 161⁄2
16.430 163⁄8
0.670
0.635
0.605
0.580
0.550
11⁄
3⁄
8
5⁄
16
5⁄
16
5⁄
16
5⁄
16
11.3
10.6
10.1
9.60
9.04
11.500
11.565
11.535
11.510
11.480
111⁄2
115⁄8
111⁄2
111⁄2
111⁄2
1.220
1.055
0.960
0.855
0.740
11⁄4
11⁄16
15⁄
16
7⁄
8
3⁄
4
21⁄16
17⁄8
13⁄4
111⁄16
19⁄16
WT15×238.5
WT15×195.5
WT15×163
WT15×146
WT15×130.5
WT15×117.5
WT15×105.5
WT15×95.5
WT15×86.5
70.0
57.0
47.9
42.9
38.4
34.5
31.0
28.1
25.4
17.105 171⁄8
16.595 165⁄8
16.200 163⁄16
16.005
16
15.805 1513⁄16
15.650 155⁄8
15.470 151⁄2
15.340 153⁄8
15.220 151⁄4
1.630
1.360
1.140
1.020
0.930
0.830
0.775
0.710
0.655
15⁄8
13⁄8
11⁄8
1
15⁄
16
13⁄
16
3⁄
4
11⁄
16
5⁄
8
13⁄
16
11⁄
16
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
3⁄
8
5⁄
16
27.9
22.6
18.5
16.3
14.7
13.0
12.0
10.9
9.97
15.865
15.590
15.370
15.255
15.155
15.055
15.105
15.040
14.985
157⁄8
155⁄8
153⁄8
151⁄2
151⁄8
15
151⁄8
15
15
2.950
2.440
2.050
1.850
1.650
1.500
1.315
1.185
1.065
3
27⁄16
21⁄16
17⁄8
15⁄8
11⁄2
15⁄16
13⁄16
11⁄16
33⁄4
31⁄4
213⁄16
25⁄8
27⁄16
21⁄4
21⁄8
115⁄16
17⁄8
WT15×74
WT18×66
WT18×62
WT18×58
WT18×54
WT18×49.5
WT18×45
21.7
19.4
18.2
17.1
15.9
14.5
13.2
15.335 155⁄16
15.155 151⁄8
15.085 151⁄8
15.005
15
14.915 147⁄8
14.825 147⁄8
14.765 143⁄4
0.650
0.615
0.585
0.565
0.545
0.520
0.470
5⁄
8
5⁄
8
9⁄
16
9⁄
16
9⁄
16
1⁄
2
1⁄
2
5⁄
16
5⁄
16
5⁄
16
5⁄
16
5⁄
16
1⁄
4
1⁄
4
10.0
9.32
8.82
8.48
8.13
7.71
6.94
10.480
10.545
10.515
10.495
10.475
10.450
10.400
101⁄2
101⁄2
101⁄2
101⁄2
101⁄2
101⁄2
103⁄8
1.180
1.000
0.930
0.850
0.760
0.670
0.610
13⁄16
1
15⁄
16
7⁄
8
3⁄
4
11⁄
16
9⁄
16
2
13⁄4
111⁄16
15⁄8
19⁄16
17⁄16
15⁄16
16
5⁄
8
5⁄
8
9⁄
16
9⁄
16
1⁄
Width
bf
in.2
in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in.
in.
STRUCTURAL TEES (WT, MT, ST)
1 - 71
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
Fy, ksi
36
50
128
116
105
97
91
85
80
75
67.5
16.9
18.7
19.6
21.2
22.4
23.9
25.0
26.0
27.1
1200
1080
985
901
845
786
740
698
637
87.4
78.5
73.1
67.0
63.1
58.9
55.8
53.1
49.7
5.66
5.63
5.65
5.62
5.62
5.61
5.61
5.62
5.66
4.92
4.82
4.87
4.80
4.77
4.73
4.74
4.78
4.96
156
140
131
120
113
105
100
95.5
94.3
1.54
1.40
1.27
1.18
1.11
1.04
0.980
0.923
1.24
264
234
206
187
174
160
147
135
113
43.2
38.6
33.8
30.9
28.8
26.6
24.6
22.5
18.9
2.65
2.62
2.58
2.56
2.55
2.53
2.50
2.47
2.38
68.6
61.0
53.5
48.9
45.4
41.9
38.6
35.5
29.8
—
0.994
0.960
0.887
0.831
0.767
0.720
0.677
0.634
0.927
0.831
0.791
0.705
0.635
0.565
0.521
0.486
0.457
177
159
145.5
131.5
120.5
110.5
100.5
12.9
14.4
15.6
17.2
18.1
19.3
21.0
1320
1160
1050
943
871
799
725
96.8
85.8
78.3
70.2
65.8
60.8
55.5
5.03
4.99
4.97
4.94
4.96
4.96
4.95
4.16
4.02
3.94
3.84
3.85
3.81
3.78
174
154
140
125
116
107
97.7
1.62
1.46
1.34
1.22
1.12
1.03
0.938
729
645
581
517
466
420
375
90.6
80.7
73.1
65.5
58.8
53.2
47.6
3.74
3.71
3.69
3.66
3.63
3.59
3.56
141
125
113
101
90.9
82.1
73.4
—
—
—
—
—
0.968
0.896
—
—
0.993
0.907
0.867
0.801
0.715
84.5
76
70.5
65
59
22.4
23.6
24.8
25.8
27.3
649
592
552
513
469
51.1
47.4
44.7
42.1
39.2
5.12
5.14
5.15
5.18
5.20
4.21
4.26
4.29
4.36
4.47
90.8
84.5
79.8
75.6
74.8
1.08
0.967
0.901
0.832
0.862
155
136
123
109
93.6
27.0
23.6
21.3
18.9
16.3
2.50
2.47
2.43
2.39
2.32
42.2
37.0
33.5
29.7
25.7
0.827
0.775
0.728
0.685
0.621
0.630
0.574
0.529
0.492
0.447
238.5
195.5
163
146
130.5
117.5
105.5
95.5
86.5
8.3
9.9
11.8
13.2
14.5
16.2
17.4
19.0
20.6
1550
1210
981
861
764
674
610
549
497
121
96.6
78.9
69.6
62.3
55.1
50.5
45.7
41.7
4.70
4.61
4.53
4.48
4.46
4.42
4.43
4.42
4.42
4.30
4.04
3.76
3.63
3.54
3.42
3.40
3.35
3.31
224
177
143
125
112
98.2
89.5
80.8
73.4
2.21
1.83
1.56
1.40
1.27
1.15
1.03
0.933
0.848
987
774
622
549
480
427
378
336
299
124
99.2
81.0
71.9
63.3
56.8
50.1
44.7
39.9
3.75
3.68
3.61
3.58
3.54
3.52
3.49
3.46
3.43
195
155
126
111
97.9
87.5
77.2
68.9
61.4
—
—
—
—
—
—
—
0.981
0.913
—
—
—
—
—
0.952
0.897
0.816
0.735
74
66
62
58
54
49.5
45
20.8
22.0
23.1
23.9
24.8
26.0
28.7
466
421
396
373
349
322
291
40.6
37.4
35.3
33.7
32.0
30.0
27.1
4.63
4.66
4.66
4.67
4.69
4.71
4.69
3.84
3.90
3.90
3.94
4.01
4.09
4.03
72.2
66.8
63.1
60.4
57.7
57.4
49.4
1.04
0.921
0.867
0.815
0.757
0.912
0.445
113
98.0
90.4
82.1
73.0
63.9
57.3
21.7
18.6
17.2
15.7
13.9
12.2
11.0
2.28
2.25
2.23
2.19
2.15
2.10
2.08
34.0
29.2
27.0
24.6
22.0
19.3
17.3
0.896
0.853
0.801
0.767
0.733
0.685
0.563
0.715
0.664
0.601
0.565
0.533
0.492
0.405
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 72
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Area
of
Stem
Area
Depth of
Tee
d
Thickness
tw
tw
2
Designation
in.2
in.
in.
in.
in.2
WT13.5×269.5
WT13.5×224
WT13.5×184
WT13.5×153.5
WT13.5×129
WT13.5×117.5
WT13.5×108.5
WT13.5×97
WT13.5×89
WT13.5×80.5
WT13.5×73
79.0
65.5
54.0
45.1
37.9
34.6
31.9
28.5
26.1
23.7
21.5
16.260
15.710
15.195
14.805
14.490
14.330
14.215
14.055
13.905
13.795
13.690
161⁄4
1511⁄16
153⁄16
1413⁄16
141⁄2
145⁄16
143⁄16
141⁄16
137⁄8
133⁄4
133⁄4
1.970
1.650
1.380
1.160
0.980
0.910
0.830
0.750
0.725
0.660
0.605
2
15⁄8
13⁄8
13⁄16
1
15⁄
16
13⁄
16
3⁄
4
3⁄
4
11⁄
16
5⁄
8
1
13⁄
16
11⁄
16
5⁄
8
1⁄
2
1⁄
2
7⁄
16
3⁄
8
3⁄
8
3⁄
8
5⁄
16
32.0
25.9
21.0
17.2
14.2
13.0
11.8
10.5
10.1
9.10
8.28
WT13.5×64.5
WT13.5×57
WT13.5×51
WT13.5×47
WT13.5×42
18.9
16.8
15.0
13.8
12.4
13.815 1313⁄16
13.645 135⁄8
13.545 131⁄2
13.460 131⁄2
13.355 133⁄8
0.610
0.570
0.515
0.490
0.460
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
5⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
WT12×246
WT12×204
WT12×167.5
WT12×139.5
WT12×125
WT12×114.5
WT12×103.5
WT12×96
WT12×88
WT12×81
WT12×73
WT12×65.5
WT12×58.5
WT12×52
72.0
59.5
49.2
41.0
36.8
33.6
30.4
28.2
25.8
23.9
21.5
19.3
17.2
15.3
14.825 1413⁄16
14.270 141⁄4
13.760 133⁄4
13.365 133⁄8
13.170 133⁄16
13.010
13
12.855 127⁄8
12.735 123⁄4
12.620 125⁄8
12.500 121⁄2
12.370 123⁄8
12.240 121⁄4
12.130 121⁄8
12.030
12
1.970
1.650
1.380
1.160
1.040
0.960
0.870
0.810
0.750
0.705
0.650
0.605
0.550
0.500
2
15⁄8
13⁄8
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
5⁄
8
9⁄
16
1⁄
2
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
1⁄
4
29.2
23.5
19.0
15.5
13.7
12.5
11.2
10.3
9.47
8.81
8.04
7.41
6.67
6.02
WT12×51.5
WT12×47
WT12×42
WT12×38
WT12×34
15.1
13.8
12.4
11.2
10.0
12.265
12.155
12.050
11.960
11.865
121⁄4
121⁄8
12
12
117⁄8
0.550
0.515
0.470
0.440
0.415
9⁄
16
1⁄
2
1⁄
2
7⁄
16
7⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
1⁄
4
9.11 11.870
8.10 11.785
117⁄8
113⁄4
0.430
0.395
7⁄
16
3⁄
8
1⁄
4
3⁄
16
WT12×31
WT12×27.5
1
Flange
DisThickness tance
tf
k
Width
bf
in.
in.
in.
151⁄4
15
145⁄8
141⁄2
141⁄4
141⁄4
141⁄8
14
141⁄8
14
14
3.540
2.990
2.480
2.090
1.770
1.610
1.500
1.340
1.190
1.080
0.975
39⁄16
3
21⁄2
21⁄16
13⁄4
15⁄8
11⁄2
15⁄16
13⁄16
11⁄16
1
41⁄4
311⁄16
33⁄16
213⁄16
21⁄2
25⁄16
23⁄16
21⁄16
17⁄8
113⁄16
111⁄16
8.43 10.010 10
7.78 10.070 101⁄8
6.98 10.015 10
6.60 9.990 10
6.14 9.960 10
1.100
0.930
0.830
0.745
0.640
11⁄8
15⁄
16
13⁄
16
3⁄
4
5⁄
8
113⁄16
15⁄8
19⁄16
17⁄16
13⁄8
14.115
13.800
13.520
13.305
13.185
13.110
13.010
12.950
12.890
12.955
12.900
12.855
12.800
12.750
141⁄8
133⁄4
131⁄2
131⁄4
131⁄8
131⁄8
13
13
127⁄8
13
127⁄8
127⁄8
123⁄4
123⁄4
3.540
2.990
2.480
2.090
1.890
1.730
1.570
1.460
1.340
1.220
1.090
0.960
0.850
0.750
39⁄16
3
21⁄2
21⁄16
17⁄8
13⁄4
19⁄16
17⁄16
15⁄16
11⁄4
11⁄16
15⁄
16
7⁄
8
3⁄
4
45⁄16
33⁄4
31⁄4
27⁄8
211⁄16
21⁄2
23⁄8
21⁄4
21⁄8
2
17⁄8
13⁄4
15⁄8
11⁄2
6.75
6.26
5.66
5.26
4.92
9.000
9.065
9.020
8.990
8.965
9
91⁄8
9
9
9
0.980
0.875
0.770
0.680
0.585
1
7⁄
8
3⁄
4
11⁄
16
9⁄
16
13⁄4
15⁄8
19⁄16
17⁄16
13⁄8
5.10
4.66
7.040
7.005
7
7
0.590
0.505
9⁄
16
1⁄
2
13⁄8
15⁄16
15.255
14.940
14.665
14.445
14.270
14.190
14.115
14.035
14.085
14.020
13.965
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL TEES (WT, MT, ST)
1 - 73
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
36
50
2.59 1060
2.19
836
1.84
655
1.56
527
1.33
430
1.22
384
1.13
352
1.02
309
0.928 278
0.845 248
0.768 222
138
112
89.3
72.9
60.2
54.2
49.9
44.1
39.4
35.4
31.7
3.66
3.57
3.48
3.42
3.37
3.33
3.32
3.29
3.26
3.24
3.21
218
176
140
113
93.3
83.8
77.0
67.9
60.8
54.5
48.8
—
—
—
—
—
—
—
—
—
—
0.938
—
—
—
—
—
—
—
0.963
0.937
0.851
0.765
18.4
15.8
13.9
12.4
10.6
2.21
2.18
2.15
2.12
2.07
28.8
24.7
21.7
19.4
16.6
0.938
0.883
0.780
0.728
0.664
0.765
0.700
0.578
0.529
0.476
119
95.5
75.9
61.9
54.9
49.7
44.4
40.9
37.2
34.2
30.3
26.5
23.2
20.3
3.41
3.33
3.23
3.17
3.14
3.11
3.08
3.07
3.04
3.05
3.01
2.97
2.94
2.91
187
150
119
96.4
85.3
77.0
68.6
63.1
57.3
52.6
46.6
40.7
35.7
31.2
—
—
—
—
—
—
—
—
—
—
—
—
0.960
0.874
—
—
—
—
—
—
—
—
—
—
0.947
0.887
0.791
0.690
20.7
18.8
16.3
14.3
12.3
0.951
0.896
0.810
0.741
0.681
0.781
0.715
0.610
0.541
0.489
7.87 0.724
6.67 0.626
0.525
0.450
269.5
224
184
153.5
129
117.5
108.5
97
89
80.5
73
6.2
7.4
8.8
10.5
12.4
13.3
14.6
16.2
16.7
18.4
20.0
1520
1190
938
753
613
556
502
444
414
372
336
128
102
81.7
66.4
54.6
50.0
45.2
40.3
38.2
34.4
31.2
4.39
4.27
4.17
4.09
4.02
4.01
3.97
3.95
3.98
3.96
3.95
4.36
4.02
3.71
3.47
3.28
3.21
3.11
3.03
3.05
2.99
2.95
241
191
151
121
98.8
89.8
81.1
71.8
67.6
60.8
55.0
64.5
57
51
47
42
19.9
21.3
23.5
24.7
26.3
323
289
258
239
216
31.0
28.3
25.3
23.8
21.9
4.13
4.15
4.14
4.16
4.18
3.39
3.42
3.37
3.41
3.48
55.1
50.4
45.0
42.4
39.2
0.945
0.833
0.750
0.692
0.621
246
204
167.5
139.5
125
114.5
103.5
96
88
81
73
65.5
58.5
52
5.5
6.5
7.8
9.3
10.4
11.2
12.4
13.3
14.4
15.3
16.6
17.8
19.6
21.6
1130
874
685
546
478
431
382
350
319
293
264
238
212
189
105
83.1
66.3
53.6
47.2
42.9
38.3
35.2
32.2
29.9
27.2
24.8
22.3
20.0
3.96
3.83
3.73
3.65
3.61
3.58
3.55
3.53
3.51
3.50
3.50
3.52
3.51
3.51
4.07
3.74
3.42
3.18
3.05
2.97
2.87
2.80
2.74
2.70
2.66
2.65
2.62
2.59
200
157
123
98.8
86.5
78.1
69.3
63.5
57.8
53.3
48.2
43.9
39.2
35.1
2.55
2.16
1.82
1.54
1.39
1.28
1.17
1.09
1.00
0.921
0.833
0.750
0.672
0.600
51.5
47
42
38
34
19.6
20.9
22.9
24.5
26.0
204
186
166
151
137
22.0
20.3
18.3
16.9
15.6
3.67
3.67
3.67
3.68
3.70
3.01
2.99
2.97
3.00
3.06
39.2
36.1
32.5
30.1
27.9
0.841
0.764
0.685
0.622
0.560
59.7
54.5
47.2
41.3
35.2
13.3
12.0
10.5
9.18
7.85
1.99
1.98
1.95
1.92
1.87
31
27.5
25.1
27.3
131
117
15.6
14.1
3.79
3.80
3.46
3.50
28.4
25.6
1.28
1.53
17.2
14.5
4.90
4.15
1.38
1.34
92.2
79.4
69.6
62.0
52.8
837
659
513
412
362
326
289
265
240
221
195
170
149
130
*Where no value of Qs is shown, the Tee complies with LRFD Specification Sect. E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Fy, ksi
1 - 74
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Area
of
Stem
Flange
DisThickness tance
tf
k
Area
Depth of
Tee
d
Thickness
tw
tw
2
Designation
in.2
in.
in.
in.
in.2
WT10.5×100.5
WT10.5×91
WT10.5×83
WT10.5×73.5
WT10.5×66
WT10.5×61
WT10.5×55.5
WT10.5×50.5
29.6
26.8
24.4
21.6
19.4
17.9
16.3
14.9
11.515
11.360
11.240
11.030
10.915
10.840
10.755
10.680
111⁄2
113⁄8
111⁄4
11
107⁄8
107⁄8
103⁄4
105⁄8
0.910
0.830
0.750
0.720
0.650
0.600
0.550
0.500
15⁄
16
13⁄
16
3⁄
4
3⁄
4
5⁄
8
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
1⁄
4
10.5
9.43
8.43
7.94
7.09
6.50
5.92
5.34
12.575
12.500
12.420
12.510
12.440
12.390
12.340
12.290
125⁄8
121⁄2
123⁄8
121⁄2
121⁄2
123⁄8
123⁄8
121⁄4
1.630
1.480
1.360
1.150
1.035
0.960
0.875
0.800
15⁄8
11⁄2
13⁄8
11⁄8
11⁄16
15⁄
16
7⁄
8
13⁄
16
23⁄8
21⁄4
21⁄8
17⁄8
113⁄16
111⁄16
15⁄8
19⁄16
WT10.5×46.5
WT10.5×41.5
WT10.5×36.5
WT10.5×34
WT10.5×31
13.7
12.2
10.7
10.0
9.13
10.810
10.715
10.620
10.565
10.495
103⁄4
103⁄4
105⁄8
105⁄8
101⁄2
0.580
0.515
0.455
0.430
0.400
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
5⁄
16
1⁄
4
1⁄
4
1⁄
4
3⁄
16
6.27
5.52
4.83
4.54
4.20
8.420
8.355
8.295
8.270
8.240
83⁄8
83⁄8
81⁄4
81⁄4
81⁄4
0.930
0.835
0.740
0.685
0.615
15⁄
16
13⁄
16
3⁄
4
11⁄
16
5⁄
8
111⁄16
19⁄16
11⁄2
17⁄16
13⁄8
8.37 10.530
7.36 10.415
6.49 10.330
101⁄2
103⁄8
103⁄8
0.405
0.380
0.350
3⁄
8
3⁄
8
3⁄
8
3⁄
16
3⁄
16
3⁄
16
4.26
3.96
3.62
6.555
6.530
6.500
61⁄2
61⁄2
61⁄2
0.650
0.535
0.450
5⁄
8
9⁄
16
7⁄
16
13⁄8
15⁄16
13⁄16
WT10.5×28.5
WT10.5×25
WT10.5×22
Width
bf
in.
in.
in.
WT9×155.5
WT9×141.5
WT9×129
WT9×117
WT9×105.5
WT9×96
WT9×87.5
WT9×79
WT9×71.5
WT9×65
45.8
41.6
38.0
34.4
31.1
28.2
25.7
23.2
21.0
19.1
11.160
10.925
10.730
10.530
10.335
10.175
10.020
9.860
9.745
9.625
113⁄16
1015⁄16
103⁄4
101⁄2
105⁄16
103⁄16
10
97⁄8
93⁄4
95⁄8
1.520
1.400
1.280
1.160
1.060
0.960
0.890
0.810
0.730
0.670
11⁄2
13⁄8
11⁄4
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
3⁄
4
11⁄
16
5⁄
8
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
17.0
15.3
13.7
12.2
11.0
9.77
8.92
7.99
7.11
6.45
12.005
11.890
11.770
11.650
11.555
11.455
11.375
11.300
11.220
11.160
12
117⁄8
113⁄4
115⁄8
111⁄2
111⁄2
113⁄8
111⁄4
111⁄4
111⁄8
2.740
2.500
2.300
2.110
1.910
1.750
1.590
1.440
1.320
1.200
23⁄4
21⁄2
25⁄16
21⁄8
115⁄16
13⁄4
19⁄16
17⁄16
15⁄16
13⁄16
37⁄16
33⁄16
3
23⁄4
9
2 ⁄16
27⁄16
21⁄4
21⁄8
2
17⁄8
WT9×59.5
WT9×53
WT9×48.5
WT9×43
WT9×38
17.5
15.6
14.3
12.7
11.2
9.485
9.365
9.295
9.195
9.105
91⁄2
93⁄8
91⁄4
91⁄4
91⁄8
0.655
0.590
0.535
0.480
0.425
5⁄
8
9⁄
16
9⁄
16
1⁄
2
7⁄
16
5⁄
16
5⁄
16
5⁄
16
1⁄
4
1⁄
4
6.21
5.53
4.97
4.41
3.87
11.265
11.200
11.145
11.090
11.035
111⁄4
111⁄4
111⁄8
111⁄8
11
1.060
0.940
0.870
0.770
0.680
11⁄16
15⁄
16
7⁄
8
3⁄
4
11⁄
16
13⁄4
15⁄8
19⁄16
17⁄16
13⁄8
WT9×35.5
WT9×32.5
WT9×30
WT9×27.5
WT9×25
10.4
9.55
8.82
8.10
7.33
9.235
9.175
9.120
9.055
8.995
91⁄4
91⁄8
91⁄8
9
9
0.495
0.450
0.415
0.390
0.355
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
1⁄
1⁄
4
3⁄
16
3⁄
16
4.57
4.13
3.78
3.53
3.19
7.635
7.590
7.555
7.530
7.495
75⁄8
75⁄8
71⁄2
71⁄2
71⁄2
0.810
0.750
0.695
0.630
0.570
13⁄
16
3⁄
4
11⁄
16
5⁄
8
9⁄
16
11⁄2
17⁄16
13⁄8
15⁄16
11⁄4
WT9×23
WT9×20
WT9×17.5
6.77
5.88
5.15
9.030
8.950
8.850
9
9
87⁄8
0.360
0.315
0.300
3⁄
8
5⁄
16
5⁄
16
3⁄
16
3⁄
16
3⁄
16
3.25
2.82
2.66
6.060
6.015
6.000
6
6
6
0.605
0.525
0.425
5⁄
8
1⁄
2
7⁄
16
11⁄4
13⁄16
11⁄8
1⁄
4
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL TEES (WT, MT, ST)
1 - 75
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
36
50
43.1
38.6
35.0
30.0
26.7
24.6
22.2
20.2
3.02
3.00
2.98
2.95
2.93
2.92
2.90
2.89
66.6
59.6
53.9
46.3
41.1
37.8
34.1
30.9
—
—
—
—
—
—
—
0.990
—
—
—
—
—
0.993
0.917
0.826
17.4
15.3
13.3
12.2
10.9
—
—
0.908
0.853
0.784
0.968
0.856
0.730
0.664
0.583
7.42 0.793
6.09 0.733
5.09 0.638
0.592
0.533
0.460
100.5
91
83
73.5
66
61
55.5
50.5
10.3
11.2
12.4
13.0
14.4
15.6
17.1
18.8
285
253
226
204
181
166
150
135
31.9
28.5
25.5
23.7
21.1
19.3
17.5
15.8
3.10
3.07
3.04
3.08
3.06
3.04
3.03
3.01
2.57
2.48
2.39
2.39
2.33
2.28
2.23
2.18
58.6
52.1
46.3
42.4
37.6
34.3
31.0
27.9
1.18
1.07
0.984
0.864
0.780
0.724
0.662
0.605
271
241
217
188
166
152
137
124
46.5
41.5
36.5
34
31
16.2
18.2
20.6
21.8
23.5
144
127
110
103
93.8
17.9
15.7
13.8
12.9
11.9
3.25
3.22
3.21
3.20
3.21
2.74
2.66
2.60
2.59
2.58
31.8
28.0
24.4
22.9
21.1
0.812
0.728
0.647
0.606
0.554
46.4
40.7
35.3
32.4
28.7
11.0
9.75
8.51
7.83
6.97
1.84
1.83
1.81
1.80
1.77
28.5
25
22
23.2
24.7
26.8
90.4
80.3
71.1
11.8
10.7
9.68
3.29
3.30
3.31
2.85
2.93
2.98
21.2
20.8
17.6
0.638
0.771
1.06
15.3
12.5
10.3
4.67
3.82
3.18
1.35
1.30
1.26
155.5
141.5
129
117
105.5
96
87.5
79
71.5
65
5.3
5.7
6.3
6.9
7.5
8.3
9.0
9.9
11.0
11.9
383
337
298
260
229
202
181
160
142
127
46.5
41.5
37.0
32.6
29.0
25.8
23.4
20.8
18.5
16.7
2.89
2.85
2.80
2.75
2.72
2.68
2.66
2.63
2.60
2.58
2.93
2.80
2.68
2.55
2.44
2.34
2.26
2.18
2.09
2.02
90.6
80.1
71.0
62.4
55.0
48.5
43.6
38.5
34.0
30.5
1.91
1.75
1.61
1.48
1.34
1.23
1.13
1.02
0.938
0.856
59.5
53
48.5
43
38
12.3
13.6
15.0
16.7
18.9
119
104
93.8
82.4
71.8
15.9
14.1
12.7
11.2
9.83
2.60
2.59
2.56
2.55
2.54
2.03
1.97
1.91
1.86
1.80
28.7
25.2
22.6
19.9
17.3
0.778 126
0.695 110
0.640 100
0.570 87.6
0.505 76.2
35.5
32.5
30
27.5
25
16.2
17.8
19.3
20.6
22.6
78.2
70.7
64.7
59.5
53.5
11.2
10.1
9.29
8.63
7.79
2.74
2.72
2.71
2.71
2.70
2.26
2.20
2.16
2.16
2.12
20.0
18.0
16.5
15.3
13.8
0.683
0.629
0.583
0.538
0.489
30.1
27.4
25.0
22.5
20.0
23
20
17.5
22.3
25.5
26.8
52.1
44.8
40.1
7.77
6.73
6.21
2.77
2.76
2.79
2.33
2.29
2.39
13.9
12.0
12.0
0.558
0.489
0.450
11.3
9.55
7.67
398
352
314
279
246
220
196
174
156
139
Fy, ksi
66.2
59.2
53.4
47.9
42.7
38.4
34.4
30.7
27.7
24.9
2.95
2.91
2.88
2.85
2.82
2.79
2.76
2.74
2.72
2.70
104
92.5
83.2
74.5
66.2
59.4
53.1
47.4
42.7
38.3
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
22.5
19.7
18.0
15.8
13.8
2.69
2.66
2.65
2.63
2.61
34.6
30.2
27.6
24.2
21.1
—
—
—
—
0.990
—
—
—
0.937
0.826
7.89
7.22
6.63
5.97
5.35
1.70
1.69
1.69
1.67
1.65
12.3
—
11.2
—
10.3 0.964
9.27 0.913
8.29 0.823
0.963
0.877
0.796
0.735
0.625
3.72
3.17
2.56
1.29
1.27
1.22
5.85 0.831
4.97 0.690
4.03 0.638
0.635
0.496
0.460
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 76
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Area
of
Stem
Flange
DisThickness tance
tf
k
Area
Depth of
Tee
d
Thickness
tw
tw
2
Designation
in.2
in.
in.
in.
in.2
WT8×50
WT8×44.5
WT8×38.5
WT8×33.5
14.7
13.1
11.3
9.84
8.485
8.375
8.260
8.165
81⁄2
83⁄8
81⁄4
81⁄8
0.585
0.525
0.455
0.395
9⁄
16
1⁄
2
7⁄
16
3⁄
8
5⁄
16
1⁄
4
1⁄
4
3⁄
16
4.96
4.40
3.76
3.23
10.425
10.365
10.295
10.235
103⁄8
103⁄8
101⁄4
101⁄4
0.985
0.875
0.760
0.665
1
7⁄
8
3⁄
4
11⁄
16
111⁄16
19⁄16
17⁄16
13⁄8
WT8×28.5
WT8×25
WT8×22.5
WT8×20
WT8×18
8.38
7.37
6.63
5.89
5.28
8.215
8.130
8.065
8.005
7.930
81⁄4
81⁄8
81⁄8
8
77⁄8
0.430
0.380
0.345
0.305
0.295
7⁄
16
3⁄
8
3⁄
8
5⁄
16
5⁄
16
1⁄
4
3⁄
16
3⁄
16
3⁄
16
3⁄
16
3.53
3.09
2.78
2.44
2.34
7.120
7.070
7.035
6.995
6.985
71⁄8
71⁄8
7
7
7
0.715
0.630
0.565
0.505
0.430
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
13⁄8
15⁄16
11⁄4
13⁄16
11⁄8
WT8×15.5
WT8×13
4.56
3.84
7.940
7.845
8
77⁄8
0.275
0.250
1⁄
4
1⁄
4
1⁄
2.18
1.96
5.525
5.500
51⁄2
51⁄2
0.440
0.345
7⁄
16
3⁄
8
11⁄8
11⁄16
3.740
3.070
2.830
2.595
2.380
2.190
2.015
33⁄4
31⁄16
213⁄16
25⁄8
23⁄8
23⁄16
2
17⁄8
19⁄16
17⁄16
15⁄16
13⁄16
11⁄8
1
42.7
34.4
30.6
27.1
24.1
21.5
19.2
18.560
17.890
17.650
17.415
17.200
17.010
16.835
181⁄2
177⁄8
175⁄8
173⁄8
171⁄4
17
167⁄8
5.120
4.910
4.520
4.160
3.820
3.500
3.210
51⁄8
415⁄16
41⁄2
43⁄16
313⁄16
31⁄2
33⁄16
513⁄16
59⁄16
53⁄16
413⁄16
41⁄2
43⁄16
37⁄8
1.875
1.770
1.655
1.540
1.410
1.290
1.175
1.070
0.980
0.890
0.830
0.745
0.680
17⁄8
13⁄4
15⁄8
19⁄16
17⁄16
15⁄16
13⁄16
11⁄16
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
15⁄
17.5
16.2
14.8
13.5
12.1
10.8
9.62
8.58
7.70
6.89
6.32
5.58
5.03
16.695
16.590
16.475
16.360
16.230
16.110
15.995
15.890
15.800
15.710
15.650
15.565
15.500
163⁄4
165⁄8
161⁄2
163⁄8
161⁄4
161⁄8
16
157⁄8
153⁄4
153⁄4
155⁄8
155⁄8
151⁄2
3.035
2.845
2.660
2.470
2.260
2.070
1.890
1.720
1.560
1.440
1.310
1.190
1.090
31⁄16
27⁄8
211⁄16
21⁄2
21⁄4
21⁄16
17⁄8
13⁄4
19⁄16
17⁄16
15⁄16
13⁄16
11⁄16
311⁄16
31⁄2
35⁄16
31⁄8
215⁄16
23⁄4
29⁄16
23⁄8
21⁄4
21⁄8
2
17⁄8
13⁄4
WT7×404
WT8×365
WT8×332.5
WT8×302.5
WT8×275
WT8×250
WT8×227.5
119
107
97.8
88.9
80.9
73.5
66.9
WT7×213
WT8×199
WT8×185
WT8×171
WT8×155.5
WT8×141.5
WT8×128.5
WT8×116.5
WT8×105.5
WT8×96.5
WT8×88
WT8×79.5
WT8×72.5
62.6
58.5
54.4
50.3
45.7
41.6
37.8
34.2
31.0
28.4
25.9
23.4
21.3
11.420 117⁄16
11.210 111⁄4
10.820 107⁄8
10.460 101⁄2
10.120 101⁄8
9.800 93⁄4
9.510 91⁄2
9.335
9.145
8.960
8.770
8.560
8.370
8.190
8.020
7.860
7.740
7.610
7.490
7.390
93⁄8
91⁄8
9
83⁄4
81⁄2
83⁄8
81⁄4
8
77⁄8
73⁄4
75⁄8
71⁄2
73⁄8
1⁄
7⁄
13⁄
13⁄
3⁄
8
8
16
8
16
16
4
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
3⁄
8
Width
bf
in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in.
in.
STRUCTURAL TEES (WT, MT, ST)
1 - 77
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
36
50
17.9
15.7
13.4
11.6
2.51
2.49
2.47
2.46
27.4
24.0
20.5
17.7
—
—
—
—
—
—
0.988
0.861
—
0.990
0.904
0.784
0.754
0.942
0.826
0.725
0.583
0.553
50
44.5
38.5
33.5
12.1
13.5
15.6
18.0
76.8
67.2
56.9
48.6
11.4
10.1
8.59
7.36
2.28
2.27
2.24
2.22
1.76
1.70
1.63
1.56
20.7
18.1
15.3
13.0
0.706
0.631
0.549
0.481
93.1
81.3
69.2
59.5
28.5
25
22.5
20
18
16.5
18.7
20.6
23.3
24.1
48.7
42.3
37.8
33.1
30.6
7.77
6.78
6.10
5.35
5.05
2.41
2.40
2.39
2.37
2.41
1.94
1.89
1.86
1.81
1.88
13.8
12.0
10.8
9.43
8.93
0.589
0.521
0.471
0.421
0.378
21.6
18.6
16.4
14.4
12.2
15.5
13
25.8
28.4
27.4
23.5
4.64
4.09
2.45
2.47
2.02
2.09
404
365
332.5
302.5
275
250
227.5
1.5
1.9
2.0
2.2
2.4
2.6
2.8
898
739
622
524
442
375
321
116
95.4
82.1
70.6
60.9
52.7
45.9
2.75
2.62
2.52
2.43
2.34
2.26
2.19
3.70
3.47
3.25
3.05
2.85
2.67
2.51
213
199
185
171
155.5
141.5
128.5
116.5
105.5
96.5
88
79.5
72.5
3.0
3.2
3.4
3.7
4.0
4.4
4.9
5.3
5.8
6.4
6.9
7.7
8.4
287
257
229
203
176
153
133
116
102
89.8
80.5
70.2
62.5
41.4
37.6
33.9
30.4
26.7
23.5
20.7
18.2
16.2
14.4
13.0
11.4
10.2
2.14
2.10
2.05
2.01
1.96
1.92
1.88
1.84
1.81
1.78
1.76
1.73
1.71
2.40
2.30
2.19
2.09
1.97
1.86
1.75
1.65
1.57
1.49
1.43
1.35
1.29
8.27 0.413
8.12 0.372
249
211
182
157
136
117
102
91.7
82.9
74.4
66.2
57.7
50.4
43.9
38.2
33.4
29.4
26.3
22.8
20.2
3.19
3.00
2.77
2.55
2.35
2.16
1.99
6.20
4.80
2760
2360
2080
1840
1630
1440
1280
1.88 1180
1.76 1090
1.65
994
1.54
903
1.41
807
1.29
722
1.18
645
1.08
576
0.980 513
0.903 466
0.827 419
0.751 374
0.688 338
Fy, ksi
6.06
5.26
4.67
4.12
3.50
1.60
1.59
1.57
1.57
1.52
9.43
8.16
7.23
6.37
5.42
2.24
1.74
1.17
1.12
3.52 0.668 0.479
2.74 0.563 0.406
297
264
236
211
189
169
152
4.82
4.69
4.62
4.55
4.49
4.43
4.38
463
408
365
326
292
261
234
—
—
—
—
—
—
—
—
—
—
—
—
—
—
141
131
121
110
99.4
89.7
80.7
72.5
65.0
59.3
53.5
48.1
43.7
4.34
4.31
4.27
4.24
4.20
4.17
4.13
4.10
4.07
4.05
4.02
4.00
3.98
217
201
185
169
152
137
123
110
99.0
90.2
81.4
73.0
66.3
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 78
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Designation
Area
of
Stem
Flange
DisThickness tance
tf
k
Area
Depth of
Tee
d
Thickness
tw
tw
2
in.2
in.
in.
in.
in.2
5⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
4.73
4.27
3.76
3.43
3.08
14.725
14.670
14.605
14.565
14.520
143⁄4
145⁄8
145⁄8
145⁄8
141⁄2
1.030
0.940
0.860
0.780
0.710
1
15⁄
16
7⁄
8
3⁄
4
11⁄
16
111⁄16
15⁄8
19⁄16
17⁄16
13⁄8
1⁄
10.130 101⁄8
10.070 101⁄8
10.035 10
9.995 10
0.855
0.785
0.720
0.645
7⁄
8
13⁄
16
3⁄
4
5⁄
8
15⁄8
19⁄16
11⁄2
17⁄16
Width
bf
in.
in.
in.
WT7×66
WT7×60
WT7×54.5
WT7×49.5
WT7×45
19.4
17.7
16.0
14.6
13.2
7.330
7.240
7.160
7.080
7.010
73⁄8
71⁄4
71⁄8
71⁄8
7
0.645
0.590
0.525
0.485
0.440
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
WT7×41
WT7×37
WT7×34
WT7×30.5
12.0
10.9
9.99
8.96
7.155
7.085
7.020
6.945
71⁄8
71⁄8
7
7
0.510
0.450
0.415
0.375
1⁄
2
7⁄
16
7⁄
16
3⁄
8
1⁄
4
3⁄
16
3.65
3.19
2.91
2.60
WT7×26.5
WT7×24
WT7×21.5
7.81
7.07
6.31
6.960
6.895
6.830
7
67⁄8
67⁄8
0.370
0.340
0.305
3⁄
8
5⁄
16
5⁄
16
3⁄
16
3⁄
16
3⁄
16
2.58
2.34
2.08
8.060
8.030
7.995
8
8
8
0.660
0.595
0.530
11⁄
16
5⁄
8
1⁄
2
17⁄16
13⁄8
15⁄16
WT7×19
WT7×17
WT7×15
5.58
5.00
4.42
7.050
6.990
6.920
7
7
67⁄8
0.310
0.285
0.270
5⁄
16
5⁄
16
1⁄
4
3⁄
16
3⁄
16
1⁄
8
2.19
1.99
1.87
6.770
6.745
6.730
63⁄4
63⁄4
63⁄4
0.515
0.455
0.385
1⁄
2
7⁄
16
3⁄
8
11⁄16
1
15⁄
16
WT7×13
WT7×11
3.85
3.25
6.955
6.870
7
67⁄8
0.255
0.230
1⁄
4
1⁄
4
1⁄
1.77
1.58
5.025
5.000
5
5
0.420
0.335
7⁄
16
5⁄
16
15⁄
1⁄
1⁄
4
4
8
8
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7⁄
16
8
STRUCTURAL TEES (WT, MT, ST)
1 - 79
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
Axis X-X
h
tw
S
I
4
r
3
y
Z
yp
3
S
I
4
in.
in.
in.
in.
in.
in.
66
60
54.5
49.5
45
8.8
9.7
10.9
11.8
13.0
57.8
51.7
45.3
40.9
36.4
9.57
8.61
7.56
6.88
6.16
1.73
1.71
1.68
1.67
1.66
1.29
1.24
1.17
1.14
1.09
18.6
16.5
14.4
12.9
11.5
0.658
0.602
0.549
0.500
0.456
41
37
34
30.5
11.2
12.7
13.7
15.2
41.2
36.0
32.6
28.9
7.14
6.25
5.69
5.07
1.85
1.82
1.81
1.80
1.39
1.32
1.29
1.25
13.2
11.5
10.4
9.16
0.594
0.541
0.498
0.448
74.2
66.9
60.7
53.7
26.5
24
21.5
15.4
16.8
18.7
27.6
24.9
21.9
4.94
4.48
3.98
1.88
1.87
1.86
1.38
1.35
1.31
8.87
8.00
7.05
0.484
0.440
0.395
28.8
25.7
22.6
19
17
15
19.8
21.5
22.7
23.3
20.9
19.0
4.22
3.83
3.55
2.04
2.04
2.07
1.54
1.53
1.58
7.45
6.74
6.25
0.412
0.371
0.329
13
11
24.1
26.7
17.3
14.8
3.31
2.91
2.12
2.14
1.72
1.76
5.89
5.20
0.383
0.325
lb
Qs*
Axis Y-Y
in.
r
3
Z
Fy, ksi
3
in.
in.
in.
36
50
37.2
33.7
30.6
27.6
25.0
3.76
3.74
3.73
3.71
3.70
56.6
51.2
46.4
41.8
37.8
—
—
—
—
—
—
—
—
—
—
14.6
13.3
12.1
10.7
2.48
2.48
2.46
2.45
22.4
20.3
18.5
16.4
—
—
—
—
—
—
—
0.973
7.16
6.40
5.65
1.92
1.91
1.89
11.0
9.82
8.66
—
—
0.947
0.958
0.882
0.775
13.3
11.7
9.79
3.94
3.45
2.91
1.55
1.53
1.49
6.07
5.32
4.49
0.934
0.857
0.810
0.760
0.669
0.610
4.45
3.50
1.77
1.40
1.08
1.04
2.77
2.19
0.737
0.621
0.537
0.447
274
247
223
201
181
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 80
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Designation
Area
of
Stem
Area
Depth of
Tee
d
Thickness
tw
tw
2
in.2
in.
in.
in.
in.2
14.9
13.3
12.1
10.7
9.67
8.68
7.62
6.73
5.96
5.30
4.66
3.93
3.50
3.23
2.91
2.63
2.36
WT6×168
WT6×152.5
WT6×139.5
WT6×126
WT6×115
WT6×105
WT6×95
WT6×85
WT6×76
WT6×68
WT6×60
WT6×53
WT6×48
WT6×43.5
WT6×39.5
WT6×36
WT6×32.5
49.4
44.8
41.0
37.0
33.9
30.9
27.9
25.0
22.4
20.0
17.6
15.6
14.1
12.8
11.6
10.6
9.54
8.410
8.160
7.925
7.705
7.525
7.355
7.190
7.015
6.855
6.705
6.560
6.445
6.355
6.265
6.190
6.125
6.060
83⁄8
81⁄8
77⁄8
73⁄4
71⁄2
73⁄8
71⁄4
7
67⁄8
63⁄4
61⁄2
61⁄2
63⁄8
61⁄4
61⁄4
61⁄8
6
1.775
1.625
1.530
1.395
1.285
1.180
1.060
0.960
0.870
0.790
0.710
0.610
0.550
0.515
0.470
0.430
0.390
13⁄4
15⁄8
11⁄2
13⁄8
15⁄16
13⁄16
11⁄16
15⁄
16
7⁄
8
13⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
1⁄
2
7⁄
16
3⁄
8
7⁄
8
13⁄
16
3⁄
4
11⁄
16
11⁄
16
5⁄
8
9⁄
16
1⁄
2
7⁄
16
7⁄
16
3⁄
8
5⁄
16
5⁄
16
1⁄
4
1⁄
4
1⁄
4
3⁄
16
WT6×29
WT6×26.5
8.52
7.78
6.095
6.030
61⁄8
6
0.360
0.345
3⁄
8
3⁄
8
3⁄
16
3⁄
16
WT6×25
WT6×22.5
WT6×20
7.34
6.61
5.89
6.095
6.030
5.970
61⁄8
6
6
0.370
0.335
0.295
3⁄
8
5⁄
16
5⁄
16
WT6×17.5
WT6×15
WT6×13
5.17
4.40
3.82
6.250
6.170
6.110
61⁄4
61⁄8
61⁄8
0.300
0.260
0.230
WT6×11
WT6×9.5
WT6×8
WT6×7
3.24
2.79
2.36
2.08
6.155
6.080
5.995
5.955
61⁄8
61⁄8
6
6
0.260
0.235
0.220
0.200
Flange
DisThickness tance
tf
k
Width
bf
in.
in.
in.
133⁄8
131⁄4
131⁄8
13
127⁄8
123⁄4
125⁄8
125⁄8
121⁄2
123⁄8
123⁄8
121⁄4
121⁄8
121⁄8
121⁄8
12
12
2.955
2.705
2.470
2.250
2.070
1.900
1.735
1.560
1.400
1.250
1.105
0.990
0.900
0.810
0.735
0.670
0.605
215⁄16
211⁄16
21⁄2
21⁄4
21⁄16
17⁄8
13⁄4
19⁄16
13⁄8
11⁄4
11⁄8
1
7⁄
8
13⁄
16
3⁄
4
11⁄
16
5⁄
8
311⁄16
37⁄16
33⁄16
215⁄16
23⁄4
25⁄8
27⁄16
21⁄4
21⁄8
115⁄16
113⁄16
111⁄16
15⁄8
11⁄2
17⁄16
13⁄8
15⁄16
2.19 10.010
2.08 9.995
10
10
0.640
0.575
5⁄
8
9⁄
16
13⁄8
11⁄4
3⁄
16
3⁄
16
3⁄
16
2.26
2.02
1.76
8.080
8.045
8.005
81⁄8
8
8
0.640
0.575
0.515
5⁄
8
9⁄
16
1⁄
2
13⁄8
11⁄4
11⁄4
5⁄
16
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1.88
1.60
1.41
6.560
6.520
6.490
61⁄2
61⁄2
61⁄2
0.520
0.440
0.380
1⁄
2
7⁄
16
3⁄
8
15⁄
16
7⁄
8
1⁄
4
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
1⁄
8
1.60
1.43
1.32
1.19
4.030
4.005
3.990
3.970
4
4
4
4
0.425
0.350
0.265
0.225
7⁄
16
3⁄
8
1⁄
4
1⁄
4
7⁄
8
13⁄
16
3⁄
4
11⁄
16
13.385
13.235
13.140
13.005
12.895
12.790
12.670
12.570
12.480
12.400
12.320
12.220
12.160
12.125
12.080
12.040
12.000
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1
STRUCTURAL TEES (WT, MT, ST)
1 - 81
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
Axis X-X
h
tw
S
I
4
r
3
y
Qs*
Axis Y-Y
Z
yp
3
S
I
4
r
3
Z
Fy, ksi
3
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.
36
50
168
152.5
139.5
126
115
105
95
85
76
68
60
53
48
43.5
39.5
36
32.5
2.7
3.0
3.2
3.5
3.8
4.1
4.6
5.1
5.6
6.1
6.8
8.0
8.8
9.4
10.3
11.3
12.4
190
162
141
121
106
92.1
79.0
67.8
58.5
50.6
43.4
36.3
32.0
28.9
25.8
23.2
20.6
31.2
27.0
24.1
20.9
18.5
16.4
14.2
12.3
10.8
9.46
8.22
6.91
6.12
5.60
5.03
4.54
4.06
1.96
1.90
1.86
1.81
1.77
1.73
1.68
1.65
1.62
1.59
1.57
1.53
1.51
1.50
1.49
1.48
1.47
2.31
2.16
2.05
1.92
1.82
1.72
1.62
1.52
1.43
1.35
1.28
1.19
1.13
1.10
1.06
1.02
0.985
68.4
59.1
51.9
44.8
39.4
34.5
29.8
25.6
22.0
19.0
16.2
13.6
11.9
10.7
9.49
8.48
7.50
1.84
1.69
1.56
1.42
1.31
1.21
1.10
0.994
0.896
0.805
0.716
0.637
0.580
0.527
0.480
0.439
0.398
593
525
469
414
371
332
295
259
227
199
172
151
135
120
108
97.5
87.2
88.6
79.3
71.3
63.6
57.5
51.9
46.5
41.2
36.4
32.1
28.0
24.7
22.2
19.9
17.9
16.2
14.5
3.47
3.42
3.38
3.34
3.31
3.28
3.25
3.22
3.19
3.16
3.13
3.11
3.09
3.07
3.05
3.04
3.02
137
122
110
97.9
88.4
79.7
71.3
63.0
55.6
49.0
42.7
37.5
33.7
30.2
27.2
24.6
22.0
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
29
26.5
13.5
14.1
19.1
17.7
3.76
3.54
1.50
1.51
1.03
1.02
6.97 0.426
6.46 0.389
53.5
47.9
10.7
9.58
2.51
2.48
16.3
14.6
—
—
—
—
25
22.5
20
13.1
14.5
16.5
18.7
16.6
14.4
3.79
3.39
2.95
1.60
1.58
1.57
1.17
1.13
1.08
6.90 0.454
6.12 0.411
5.30 0.368
28.2
25.0
22.0
6.97
6.21
5.51
1.96
1.94
1.93
10.7
9.50
8.41
—
—
—
—
0.998
0.887
17.5
15
13
18.1
20.9
23.6
16.0
13.5
11.7
3.23
2.75
2.40
1.76
1.75
1.75
1.30
1.27
1.25
5.71 0.394
4.83 0.337
4.20 0.295
12.2
10.2
8.66
3.73
3.12
2.67
1.54
1.52
1.51
5.73
4.78
4.08
—
0.856
0.891 0.710
0.767 0.565
11
9.5
8
7
20.9
23.1
24.7
27.2
11.7
10.1
8.70
7.67
2.59
2.28
2.04
1.83
1.90
1.90
1.92
1.92
1.63
1.65
1.74
1.76
4.63
4.11
3.72
3.32
2.33
1.88
1.41
1.18
1.16
0.939
0.706
0.594
0.847
0.822
0.773
0.753
1.83
1.49
1.13
0.950
0.891
0.797
0.741
0.626
lb
0.402
0.348
0.639
0.760
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
0.710
0.596
0.541
0.450
1 - 82
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Designation
Area
of
Stem
Area
Depth of
Tee
d
Thickness
tw
tw
2
in.2
in.
in.
in.
in.2
Flange
DisThickness tance
tf
k
Width
bf
in.
in.
in.
WT5×56
WT5×50
WT5×44
WT5×38.5
WT5×34
WT5×30
WT5×27
WT5×24.5
16.5
14.7
12.9
11.3
9.99
8.82
7.91
7.21
5.680
5.550
5.420
5.300
5.200
5.110
5.045
4.990
55⁄8
51⁄2
53⁄8
51⁄4
51⁄4
51⁄8
5
5
0.755
0.680
0.605
0.530
0.470
0.420
0.370
0.340
3⁄
4
11⁄
16
5⁄
8
1⁄
2
1⁄
2
7⁄
16
3⁄
8
5⁄
16
3⁄
8
3⁄
8
5⁄
16
1⁄
4
1⁄
4
1⁄
4
3⁄
16
3⁄
16
4.29
3.77
3.28
2.81
2.44
2.15
1.87
1.70
10.415
10.340
10.265
10.190
10.130
10.080
10.030
10.000
103⁄8
103⁄8
101⁄4
101⁄4
101⁄8
101⁄8
10
10
1.250
1.120
0.990
0.870
0.770
0.680
0.615
0.560
11⁄4
11⁄8
1
7⁄
8
3⁄
8
11⁄
16
5⁄
8
9⁄
16
17⁄8
13⁄4
15⁄8
11⁄2
13⁄8
15⁄16
11⁄4
13⁄16
WT5×22.5
WT5×19.5
WT5×16.5
6.63
5.73
4.85
5.050
4.960
4.865
5
5
47⁄8
0.350
0.315
0.290
3⁄
8
5⁄
16
5⁄
16
3⁄
16
3⁄
16
3⁄
16
1.77
1.56
1.41
8.020
7.985
7.960
8
8
8
0.620
0.530
0.435
5⁄
8
1⁄
2
7⁄
16
11⁄4
11⁄8
11⁄16
WT5×15
WT5×13
WT5×11
4.42
3.81
3.24
5.235
5.165
5.085
51⁄4
51⁄8
51⁄8
0.300
0.260
0.240
5⁄
16
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1.57
1.34
1.22
5.810
5.770
5.750
53⁄4
53⁄4
53⁄4
0.510
0.440
0.360
1⁄
2
7⁄
16
3⁄
8
15⁄
16
7⁄
8
3⁄
4
WT5×9.5
WT5×8.5
WT5×7.5
WT5×6
2.81
2.50
2.21
1.77
5.120
5.055
4.995
4.935
51⁄8
5
5
47⁄8
0.250
0.240
0.230
0.190
1⁄
4
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
1⁄
8
1.28
1.21
1.15
0.938
4.020
4.010
4.000
3.960
4
4
4
4
0.395
0.330
0.270
0.210
3⁄
8
5⁄
16
1⁄
4
3⁄
16
13⁄
16
3⁄
4
11⁄
16
5⁄
8
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL TEES (WT, MT, ST)
1 - 83
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
0.791 118
0.711 103
0.631 89.3
0.555 76.8
0.493 66.8
0.438 58.1
0.395 51.7
0.361 46.7
22.6
20.0
17.4
15.1
13.2
11.5
10.3
9.34
2.68
2.65
2.63
2.60
2.59
2.57
2.56
2.54
6.65
5.64
4.60
Fy, ksi
36
50
34.6
30.5
26.5
22.9
20.0
17.5
15.7
14.2
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
2.01
1.98
1.94
10.1
8.59
7.01
—
—
—
—
—
—
56
50
44
38.5
34
30
27
24.5
5.2
5.8
6.5
7.4
8.4
9.4
10.6
11.6
28.6
24.5
20.8
17.4
14.9
12.9
11.1
10.0
6.40
5.56
4.77
4.04
3.49
3.04
2.64
2.39
1.32
1.29
1.27
1.24
1.22
1.21
1.19
1.18
1.21
1.13
1.06
0.990
0.932
0.884
0.836
0.807
13.4
11.4
9.65
8.06
6.85
5.87
5.05
4.52
22.5
19.5
16.5
11.2
12.5
13.6
10.2
8.84
7.71
2.47
2.16
1.93
1.24
1.24
1.26
0.907
0.876
0.869
4.65
3.99
3.48
0.413
0.359
0.305
15
13
11
14.8
17.0
18.4
9.28
7.86
6.88
2.24
1.91
1.72
1.45
1.44
1.46
1.10
1.06
1.07
4.01
3.39
3.02
0.380
0.330
0.282
8.35
7.05
5.71
2.87
2.44
1.99
1.37
1.36
1.33
4.42
3.75
3.05
—
—
0.999
—
0.902
0.836
17.7
18.4
19.2
23.3
6.68
6.06
5.45
4.35
1.74
1.62
1.50
1.22
1.54
1.56
1.57
1.57
1.28
1.32
1.37
1.36
3.10
2.90
3.03
2.50
0.349
0.311
0.306
0.323
2.15
1.78
1.45
1.09
1.07
0.888
0.723
0.551
0.874
0.844
0.810
0.785
1.68
—
1.40
—
1.15 0.977
0.872 0.793
0.872
0.841
0.811
0.592
9.5
8.5
7.5
6
26.7
22.5
18.3
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 84
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from W shapes
Dimensions
k
Y
X
X
d
tw
Y
Stem
Area
of
Stem
Flange
DisThickness tance
tf
k
Area
Depth of
Tee
d
Thickness
tw
tw
2
Designation
in.2
in.
in.
in.
in.2
WT4×33.5
WT4×29
WT4×24
WT4×20
WT4×17.5
WT4×15.5
9.84
8.55
7.05
5.87
5.14
4.56
4.500
4.375
4.250
4.125
4.060
4.000
41⁄2
43⁄8
41⁄4
41⁄8
4
4
0.570
0.510
0.400
0.360
0.310
0.285
9⁄
16
1⁄
2
3⁄
8
3⁄
8
5⁄
16
5⁄
16
5⁄
16
1⁄
4
3⁄
16
3⁄
16
3⁄
16
3⁄
16
2.56
2.23
1.70
1.48
1.26
1.14
8.280
8.220
8.110
8.070
8.020
7.995
81⁄4
81⁄4
81⁄8
81⁄8
8
8
0.935
0.810
0.685
0.560
0.495
0.435
15⁄
16
13⁄
16
11⁄
16
9⁄
16
1⁄
2
7⁄
16
17⁄16
15⁄16
13⁄16
11⁄16
1
15⁄
16
WT4×14
WT4×12
4.12
3.54
4.030
3.965
4
4
0.285
0.245
5⁄
16
1⁄
4
3⁄
16
1⁄
8
1.15
0.971
6.535
6.495
61⁄2
61⁄2
0.465
0.400
7⁄
16
3⁄
8
15⁄
16
7⁄
8
WT4×10.5
WT4×9
3.08
2.63
4.140
4.070
41⁄8
41⁄8
0.250
0.230
1⁄
4
1⁄
4
1⁄
8
1⁄
8
1.03
0.936
5.270
5.250
51⁄4
51⁄4
0.400
0.330
3⁄
8
5⁄
16
13⁄
16
3⁄
4
WT4×7.5
WT4×6.5
WT4×5
2.22
1.92
1.48
4.055
3.995
3.945
4
4
4
0.245
0.230
0.170
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
0.993
0.919
0.671
4.015
4.000
3.940
4
4
4
0.315
0.255
0.205
5⁄
16
1⁄
4
3⁄
16
3⁄
4
11⁄
16
5⁄
8
WT3×12.5
WT4×10
WT4×7.5
3.67
2.94
2.21
3.190
3.100
2.995
31⁄4
31⁄8
3
0.320
0.260
0.230
5⁄
16
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1.02
0.806
0.689
6.080
6.020
5.990
61⁄8
6
6
0.455
0.365
0.260
7⁄
16
3⁄
8
1⁄
4
13⁄
16
3⁄
4
5⁄
8
WT3×8
WT4×6
WT4×4.5
2.37
1.78
1.34
3.140
3.015
2.950
31⁄8
3
3
0.260
0.230
0.170
1⁄
4
1⁄
4
3⁄
16
1⁄
8
1⁄
8
1⁄
8
0.816
0.693
0.502
4.030
4.000
3.940
4
4
4
0.405
0.280
0.215
3⁄
8
1⁄
4
3⁄
16
3⁄
4
5⁄
8
9⁄
16
WT2.5×9.5
WT4.5×8
2.77
2.34
2.575
2.505
25⁄8
21⁄2
0.270
0.240
1⁄
4
1⁄
4
1⁄
8
1⁄
8
0.695
0.601
5.030
5.000
5
5
0.430
0.360
7⁄
16
3⁄
8
13⁄
16
3⁄
4
WT2×6.5
1.91
2.080
21⁄8
0.280
1⁄
4
1⁄
8
0.582
4.060
4
0.345
3⁄
8
11⁄
16
Width
bf
in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
in.
in.
STRUCTURAL TEES (WT, MT, ST)
1 - 85
bf
STRUCTURAL TEES
Cut from W shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
36
Fy, ksi
50
33.5
29
24
20
17.5
15.5
5.6
6.2
7.9
8.8
10.2
11.1
10.9
9.12
6.85
5.73
4.81
4.28
3.05
2.61
1.97
1.69
1.43
1.28
1.05
1.03
0.986
0.988
0.967
0.968
0.936
0.874
0.777
0.735
0.688
0.667
6.29
5.25
3.94
3.25
2.71
2.39
0.594
0.520
0.435
0.364
0.321
0.285
44.3
37.5
30.5
24.5
21.3
18.5
10.7
9.13
7.52
6.08
5.31
4.64
2.12
2.10
2.08
2.04
2.03
2.02
16.3
13.9
11.4
9.25
8.06
7.04
—
—
—
—
—
—
—
—
—
—
—
—
14
12
11.1
12.9
4.22
3.53
1.28
1.08
1.01
0.999
0.734
0.695
2.38
1.98
0.315
0.273
10.8
9.14
3.31
2.81
1.62
1.61
5.05
4.29
—
—
—
—
10.5
9
13.8
15.0
3.90
3.41
1.18
1.05
1.12
1.14
0.831
0.834
2.11
1.86
0.292
0.251
4.89
3.98
1.85
1.52
1.26
1.23
2.84
2.33
—
—
—
—
7.5
6.5
5
14.0
15.0
20.2
3.28
2.89
2.15
1.07
0.974
0.717
1.22
1.23
1.20
0.998
1.03
0.953
1.91
1.74
1.27
0.276
0.240
0.188
1.70
1.37
1.05
0.849 0.876
0.683 0.843
0.532 0.841
1.33
—
1.08
—
0.828 0.913
12.5
10
7.5
7.8
9.6
10.8
2.28
1.76
1.41
0.886
0.693
0.577
0.789
0.774
0.797
0.610
0.560
0.558
1.68
1.29
1.03
0.302
0.244
0.185
8.53
6.64
4.66
2.81
2.21
1.56
4.28
3.36
2.37
—
—
—
—
—
—
8
6
4.5
9.6
10.8
14.6
1.69 0.685
1.32 0.564
0.950 0.408
0.844
0.861
0.842
0.676
0.677
0.623
1.25
1.01
0.720
0.294
0.222
0.170
2.21
1.50
1.10
1.10 0.966
0.748 0.918
0.557 0.905
1.70
1.16
0.858
—
—
—
—
—
—
9.5
8
7.0
7.9
1.01 0.485
0.850 0.413
0.605
0.601
0.487
0.458
0.967
0.798
0.275
0.234
4.56
3.75
1.82
1.50
1.28
1.27
2.76
2.29
—
—
—
—
6.5
5.3
0.530 0.321
0.524
0.440
0.616
0.236
1.93
0.950 1.00
1.46
—
—
1.52
1.50
1.45
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
—
—
0.735
1 - 86
DIMENSIONS AND PROPERTIES
bf
tf
yp , y
STRUCTURAL TEES
Cut from M shapes
Dimensions
k
Y
X
X
d
tw
Y
Designation
Area
Depth
of
Tee
d
in.2
in.
Flange
Stem
Area
of
Thickness tw
2 Stem
tw
in.
in.
in.
1.73
1.59
6.000
5.990
6
6
0.177
0.160
3⁄
16
3⁄
16
1⁄
8
1⁄
16
1.06 3.065
0.958 3.065
31⁄8
31⁄8
0.225
0.210
1⁄
4
1⁄
4
9⁄
16
1⁄
2
1⁄
4
1⁄
4
—
1⁄
2
MT5×4.5
MT5×4
1.32
1.18
5.000
4.980
5
5
0.157
0.141
3⁄
16
3⁄
16
1⁄
8
1⁄
16
0.785 2.690
0.702 2.690
23⁄4
23⁄4
0.206
0.182
3⁄
16
3⁄
16
9⁄
16
7⁄
16
3⁄
16
3⁄
16
—
3⁄
8
MT4×3.25
0.958 4.000
4
0.135
1⁄
8
1⁄
16
0.540 2.281
21⁄4
0.189
3⁄
16
1⁄
2
3⁄
16
—
0.316
5⁄
16
3⁄
16
0.790 5.003
5
0.416
7⁄
16
7⁄
8
7⁄
16
7⁄
8
2.500 21⁄2
in.
in.2
MT6×5.9
MT6×5.4
MT2.5×9.45* 2.78
in.
Width
bf
in.
Max.
DisFlge.
FasThickness tance
Grip tener
tf
k
in.
*This shape has tapered flanges, while all other MT shapes have parallel flanges.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL TEES (WT, MT, ST)
1 - 87
bf
STRUCTURAL TEES
Cut from M shapes
Properties
tf
k
Y
yp , y
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
36
Fy, ksi
50
5.9
5.4
31.3
31.8
6.60
6.03
1.60
1.46
1.95
1.95
1.89
1.85
2.89
2.63
1.09
1.01
0.490
0.453
0.320
0.295
0.532
0.533
0.577
0.525
0.483
0.397
0.348
0.286
4.5
4
29.2
29.7
3.46
3.09
0.997
0.893
1.62
1.62
1.53
1.52
1.81
1.62
0.778
0.778
0.305
0.269
0.227
0.200
0.480
0.477
0.405
0.333
0.549
0.446
0.396
0.321
3.25
26.9
1.57
0.556
1.28
1.17
1.01
0.446
0.172
0.150
0.423
0.265
0.634
0.457
9.45
5.6
1.05
0.527
0.615
0.511
1.03
0.278
3.93
1.57
1.19
2.66
—
—
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 88
DIMENSIONS AND PROPERTIES
bf
tf
y, yp
STRUCTURAL TEES
Cut from S shapes
Dimensions
grip
Y
X
X
d
tw
Y
Designation
Area
Depth
of
Tee
d
in.2
in.
Flange
Stem
Area
of
Thickness tw
2 Stem
tw
Width
bf
Max.
DisFlge.
FasThickness tance
Grip tener
tf
k
in.
in.2
in.
in.
in.
7
13⁄
16 ⁄16
5⁄
5⁄
8
16
9.80
7.60
8.050 8
7.870 77⁄8
1.090
1.090
11⁄16
11⁄16
2
2
11⁄8
11⁄8
1
1
3⁄
8
5⁄
16
1⁄
4
8.94
7.50
6.00
7.245 71⁄4
7.125 71⁄8
7.000 7
0.870
0.870
0.870
7⁄
8
7⁄
8
7⁄
8
13⁄4
13⁄4
13⁄4
7⁄
8
7⁄
8
7⁄
8
1
1
1
7
13⁄
16 ⁄16
3⁄
11⁄
16
8
8.12
6.70
7.200 71⁄4
7.060 7
0.920
0.920
15⁄
16
15⁄
16
13⁄4
13⁄4
15⁄
16
15⁄
16
1
1
in.
in.
in.
in.
ST12×60.5
ST12×53
17.8
15.6
12.250 121⁄4
12.250 121⁄4
0.800
0.620
ST12×50
ST12×45
ST12×40
14.7
13.2
11.7
12.000
12.000
12.000
0.745
0.625
0.500
ST10×48
ST10×43
14.1
12.7
10.150 101⁄8
10.150 101⁄8
0.800
0.660
ST10×37.5
ST10×33
11.0
9.70
10.000
10.000
10
10
0.635
0.505
5⁄
8
1⁄
2
5⁄
16
1⁄
4
6.35
5.05
6.385 63⁄8
6.225 61⁄4
0.795
0.795
13⁄
16
13⁄
16
15⁄8
15⁄8
13⁄
16
13⁄
16
7⁄
8
7⁄
8
ST9×35
ST9×27.35
10.3
8.04
9.000
9.000
9
9
0.711
0.461
11⁄
16
7⁄
16
3⁄
8
1⁄
4
6.40
4.15
6.251 61⁄4
6.001 6
0.691
0.691
11⁄
16
11⁄
16
11⁄2
11⁄2
11⁄
16
11⁄
16
7⁄
8
7⁄
8
12
12
12
3⁄
4
5⁄
8
1⁄
2
ST7.5×25
ST7.5×21.45
7.35
6.31
7.500 71⁄2
7.500 71⁄2
0.550
0.411
9⁄
16
5⁄
16
1⁄
4
4.13
3.08
5.640 55⁄8
5.501 51⁄2
0.622
0.622
5⁄
8
5⁄
8
13⁄8
13⁄8
9⁄
16
9⁄
16
3⁄
4
3⁄
4
ST6×25
ST6×20.4
7.35
6.00
6.000
6.000
6
6
0.687
0.462
11⁄
16
7⁄
16
3⁄
8
1⁄
4
4.12
2.77
5.477 51⁄2
5.252 51⁄4
0.659
0.659
11⁄
16
11⁄
16
17⁄16
17⁄16
11⁄
16
5⁄
8
3⁄
4
3⁄
4
ST6×17.5
ST6×15.9
5.15
4.68
6.000
6.000
6
6
0.428
0.350
7⁄
1⁄
4
3⁄
16
2.57
2.10
5.078 51⁄8
5.000 5
0.545
0.544
9⁄
16
9⁄
16
13⁄16
13⁄16
1⁄
2
1⁄
2
3⁄
4
3⁄
4
ST5×17.5
ST5×12.7
5.15
3.73
5.000
5.000
5
5
0.594
0.311
16
5⁄
16
3⁄
16
2.97
1.56
4.944 5
4.661 45⁄8
0.491
0.491
1⁄
2
1⁄
2
11⁄8
11⁄8
1⁄
2
1⁄
2
3⁄
4
3⁄
4
ST4×11.5
ST4×9.2
3.38
2.70
4.000
4.000
4
4
0.441
0.271
7⁄
16
1⁄
4
1⁄
4
1⁄
8
1.76
1.08
4.171 41⁄8
4.001 4
0.425
0.425
7⁄
16
7⁄
16
1
1
7⁄
16
7⁄
16
3⁄
4
3⁄
4
ST3×8.625
ST3×6.25
2.53
1.83
3.000
3.000
3
3
0.465
0.232
7⁄
16
1⁄
4
1⁄
4
1⁄
8
1.40
0.70
3.565 35⁄8
3.332 33⁄8
0.359
0.359
3⁄
8
3⁄
8
7⁄
8
7⁄
8
3⁄
8
3⁄
8
5⁄
8
—
ST2.5×5
1.47
2.500 21⁄2
0.214
3⁄
16
1⁄
8
0.535 3.004
0.326
5⁄
16
13⁄
16
5⁄
16
—
ST2×4.75
ST2×3.85
1.40
1.13
2.000
2.000
0.326
0.193
5⁄
16
3⁄
16
1⁄
8
0.652 2.796 23⁄4
0.386 2.663 25⁄8
0.293
0.293
5⁄
16
5⁄
16
3⁄
4
3⁄
4
5⁄
16
5⁄
16
—
—
ST1.5×3.75
ST1.5×2.85
1.10
0.835
1.500 11⁄2
1.500 11⁄2
3⁄
16
1⁄
8
0.523 2.509 21⁄2
0.255 2.330 23⁄8
0.260
0.260
1⁄
4
1⁄
4
11⁄
16
11⁄
16
1⁄
4
1⁄
4
—
—
2
2
0.349
0.170
7⁄
16
16
3⁄
8
5⁄
8
5⁄
3⁄
16
3⁄
8
3⁄
16
3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STRUCTURAL TEES (WT, MT, ST)
1 - 89
bf
STRUCTURAL TEES
Cut from S shapes
Properties
tf
grip
Y
y, yp
X
X
d
tw
Y
Nominal
Wt.
per
ft
lb
Axis X-X
h
tw
Qs*
Axis Y-Y
I
S
r
y
Z
yp
I
S
r
Z
in.4
in.3
in.
in.
in.3
in.
in.4
in.3
in.
in.3
60.5
53
13.2
17
259
216
30.1
24.1
3.82
3.72
3.63
3.28
54.5
43.3
1.28
1.03
41.7
38.5
10.4
9.80
1.53
1.57
18.1
16.6
50
45
40
14.1
16.8
21.1
215
190
162
26.3
22.6
18.7
3.83
3.79
3.72
3.84
3.60
3.29
47.5
41.1
33.6
2.20 23.8
1.48 22.5
0.922 21.1
6.58
6.31
6.04
1.27
1.30
1.34
12.0
11.2
10.4
48
43
10.8
13.1
143
125
20.3
17.2
3.18
3.14
3.13
2.91
36.9
31.1
1.40 25.1
0.985 23.4
6.97
6.63
1.33
1.36
12.5
11.6
37.5
33
13.6
17
109
93.1
15.8
12.9
3.15
3.10
3.07
2.81
28.6
23.4
1.40 14.9
0.855 13.8
4.66
4.43
1.16
1.19
35
27.35
10.9
16.8
84.7
62.4
14.0
9.61
2.87
2.79
2.94
2.50
25.1
17.3
1.81 12.1
0.747 10.4
3.86
3.47
25
21.45
11.6
15.5
40.6
33.0
7.73
6.00
2.35
2.29
2.25
2.01
14.0
10.8
0.872
0.613
7.85
7.19
25
20.4
7
10.3
25.2
18.9
6.05
4.28
1.85
1.78
1.84
1.58
11.0
7.71
0.770
0.581
17.5
15.9
11.7
14.3
17.2
14.9
3.95
3.31
1.83
1.78
1.64
1.51
7.12
5.94
17.5
12.7
6.9
13.2
12.5
7.83
3.63
2.06
1.56
1.45
1.56
1.20
11.5
9.2
7.3
11.8
5.03
3.51
1.77
1.15
1.22
1.14
5
10
8.63
6.25
Fy, ksi
36
50
—
—
—
0.907
—
—
—
0.937
0.878 0.695
—
—
—
—
8.37
7.70
—
—
—
0.907
1.08
1.14
7.21
6.07
—
—
—
0.922
2.78
2.61
1.03
1.07
5.01
4.54
—
—
—
0.988
7.85
6.78
2.87
2.58
1.03
1.06
5.19
4.45
—
—
—
—
0.548
0.485
4.94
4.68
1.95
1.87
0.980
1.00
3.41
3.22
—
—
—
—
6.58
3.70
0.702
0.408
4.18
3.39
1.69
1.46
0.901
0.954
3.11
2.49
—
—
—
—
1.15
0.941
3.19
2.07
0.447
0.341
2.15
1.86
1.03 0.798
0.932 0.831
1.84
1.59
—
—
—
—
2.13
1.27
1.02 0.917 0.914
0.552 0.833 0.691
1.85
1.01
0.401
0.275
1.15
0.911
0.648 0.675
0.547 0.705
1.18
0.929
—
—
—
—
5
8.7
0.681
0.353 0.681 0.569
0.650 0.243
0.608
0.405 0.643
0.685
—
—
4.75
3.85
4.3
7.3
0.470
0.316
0.325 0.580 0.553
0.203 0.528 0.448
0.592 0.255
0.381 0.209
0.451
0.382
0.323 0.569
0.287 0.581
0.566
0.483
—
—
—
—
3.75
2.85
2.8
5.7
0.204
0.118
0.191 0.430 0.432
0.101 0.376 0.329
0.351 0.223
0.196 0.175
0.293
0.227
0.234 0.516
0.195 0.522
0.412
0.327
—
—
—
—
*Where no value of Qs is shown, the Tee complies with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 90
DIMENSIONS AND PROPERTIES
DOUBLE ANGLES
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DOUBLE ANGLES
1 - 91
DOUBLE ANGLES
Properties of double angles in contact and separated are listed in the following tables.
Each table shows properties of double angles in contact, and the radius of gyration about
the Y-Y axis when the legs of the angles are separated. Values of Qs are given for Fy = 36
ksi and Fy = 50 ksi for those angles exceeding the width-thickness ratio λr of LRFD
Specification Section B5. Since the cross section is comprised entirely of unstiffened
elements, Qa = 1.0 and Q = Qs, for all _angle sections. The Flexural-Torsional Properties
Table lists the dimensional values (J, ro, and H) needed for checking flexural-torsional
buckling.
Use of Table
The table may be used as follows for checking the limit states of (1) flexural buckling
and (2) flexural-torsional buckling. The lower of the two limit states must be used for
design. See also Part 3 of this LRFD Manual.
(1) Flexural Buckling
Where no value of Qs is shown, the design compressive strength for this limit state is
given by LRFD Specification Section E2. Where a value of Qs is shown, the strength
must be reduced in accordance with Appendix B5 of the LRFD Specification.
(2) Flexural-Torsional Buckling
The design compressive strength for this limit state_ is given by LRFD Specification
Sections E3 and E4. This involves calculations with J, ro, and H. These torsional constants
can be obtained by summing the respective values for single angles listed in the
Flexural-Torsional Properties Tables in Part 1 of this Manual.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 92
DIMENSIONS AND PROPERTIES
Y
X
X
DOUBLE ANGLES
Two equal leg angles
Properties of sections
y, yp
s
Y
Wt.
Area of
per ft
2 Angles 2 Angles
Designation
2
Axis X-X
S
I
4
in.
r
3
y
Z
yp
3
lb
in.
in.
in.
in.
in.
in.
L8×8×11⁄8
L8×8×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×11⁄2
114
102
90.0
77.8
65.4
52.8
33.5
30.0
26.5
22.9
19.2
15.5
195
177
159
139
118
97.3
35.1
31.6
28.0
24.4
20.6
16.7
2.42
2.44
2.45
2.47
2.49
2.50
2.41
2.37
2.32
2.28
2.23
2.19
63.2
56.9
50.5
43.9
37.1
30.1
1.05
0.938
0.827
0.715
0.601
0.484
L6×6×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×11⁄2
L8×8×13⁄8
74.8
66.2
57.4
48.4
39.2
29.8
22.0
19.5
16.9
14.2
11.5
8.72
70.9
63.8
56.3
48.3
39.8
30.8
17.1
15.3
13.3
11.3
9.23
7.06
1.80
1.81
1.83
1.84
1.86
1.88
1.86
1.82
1.78
1.73
1.68
1.64
30.9
27.5
24.0
20.4
16.6
12.7
0.917
0.811
0.703
0.592
0.479
0.363
L5×5×7⁄8
L5×5×3⁄4
L5×5×1⁄2
L5×5×3⁄8
L5×5×5⁄16
54.4
47.2
32.4
24.6
20.6
16.0
13.9
9.50
7.22
6.05
35.5
31.5
22.5
17.5
14.8
10.3
9.06
6.31
4.84
4.08
1.49
1.51
1.54
1.56
1.57
1.57
1.52
1.43
1.39
1.37
18.7
16.3
11.4
8.72
7.35
0.798
0.694
0.475
0.361
0.303
L4×4×3⁄4
L5×5×5⁄8
L5×5×1⁄2
L5×5×3⁄8
L5×5×5⁄16
L5×5×1⁄4
37.0
31.4
25.6
19.6
16.4
13.2
10.9
9.22
7.50
5.72
4.80
3.88
15.3
13.3
11.1
8.72
7.43
6.08
5.62
4.80
3.95
3.05
2.58
2.09
1.19
1.20
1.22
1.23
1.24
1.25
1.27
1.23
1.18
1.14
1.12
1.09
10.1
8.66
7.12
5.49
4.64
3.77
0.680
0.576
0.469
0.357
0.300
0.242
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DOUBLE ANGLES
1 - 93
DOUBLE ANGLES
Two equal leg angles
Properties of sections
Y
X
X
y, yp
s
Y
Qs*
Axis Y-Y
Radii of Gyration
Back to Back of
Angles, in.
Angles in Contact
Angles Separated
0
3⁄
8
3⁄
4
Fy =
36 ksi
Fy =
50 ksi
Fy =
36 ksi
Fy =
50 ksi
L8×8×11⁄8
L8×8×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×11⁄2
3.42
3.40
3.38
3.36
3.34
3.32
3.55
3.53
3.51
3.49
3.47
3.45
3.69
3.67
3.64
3.62
3.60
3.58
—
—
—
—
—
0.995
—
—
—
—
—
0.921
—
—
—
—
0.997
0.911
—
—
—
—
0.935
0.834
L6×6×1
L8×8×17⁄8
L8×8×13⁄4
L8×8×15⁄8
L8×8×11⁄2
L8×8×13⁄8
2.59
2.57
2.55
2.53
2.51
2.49
2.73
2.70
2.68
2.66
2.64
2.62
2.87
2.85
2.82
2.80
2.78
2.75
—
—
—
—
—
0.995
—
—
—
—
—
0.921
—
—
—
—
—
0.911
—
—
—
—
0.961
0.834
L5×5×7⁄8
L5×5×3⁄4
L5×5×1⁄2
L5×5×3⁄8
L5×5×5⁄16
2.16
2.14
2.10
2.09
2.08
2.30
2.28
2.24
2.22
2.21
2.45
2.42
2.38
2.35
2.34
—
—
—
—
0.995
—
—
—
—
0.921
—
—
—
0.982
0.911
—
—
—
0.919
0.834
L4×4×3⁄4
L5×5×5⁄8
L5×5×1⁄2
L5×5×3⁄8
L5×5×5⁄16
L5×5×1⁄4
1.74
1.72
1.70
1.68
1.67
1.66
1.88
1.86
1.83
1.81
1.80
1.79
2.03
2.00
1.98
1.95
1.94
1.93
—
—
—
—
—
0.995
—
—
—
—
—
0.921
—
—
—
—
0.997
0.911
—
—
—
—
0.935
0.834
Designation
*Where no value ofQs is shown, the angles comply with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 94
DIMENSIONS AND PROPERTIES
DOUBLE ANGLES
Two equal leg angles
Properties of sections
Y
X
X
y, yp
s
Y
Wt.
Area of
per ft
2 Angles 2 Angles
2
Axis X-X
S
I
4
r
3
y
Z
yp
3
Designation
lb
in.
in.
in.
in.
in.
in.
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×5⁄16
L31⁄2×31⁄2×1⁄4
17.0
14.4
11.6
4.97
4.18
3.38
5.73
4.90
4.02
2.30
1.95
1.59
1.07
1.08
1.09
1.01
0.990
0.968
4.15
3.52
2.86
0.355
0.299
0.241
L3×3×1⁄2
L3×3×3⁄8
L3×3×5⁄16
L3×3×1⁄4
L3×3×3⁄16
18.8
14.4
12.2
9.80
7.42
5.50
4.22
3.55
2.88
2.18
4.43
3.52
3.02
2.49
1.92
2.14
1.67
1.41
1.15
0.882
0.898
0.913
0.922
0.930
0.939
0.932
0.888
0.865
0.842
0.820
3.87
3.00
2.55
2.08
1.59
0.458
0.352
0.296
0.240
0.182
L21⁄2×21⁄2×3⁄8
L31⁄2×31⁄2×5⁄16
L31⁄2×31⁄2×1⁄4
L31⁄2×31⁄2×3⁄16
11.8
10.0
8.20
6.14
3.47
2.93
2.38
1.80
1.97
1.70
1.41
1.09
1.13
0.964
0.789
0.606
0.753
0.761
0.769
0.778
0.762
0.740
0.717
0.694
2.04
1.74
1.42
1.09
0.347
0.293
0.238
0.180
9.40
7.84
6.38
4.88
3.30
2.72
2.30
1.88
1.43
0.960
0.958
0.832
0.695
0.545
0.380
0.702
0.681
0.494
0.381
0.261
0.594
0.601
0.609
0.617
0.626
0.636
0.614
0.592
0.569
0.546
1.27
1.08
0.890
0.686
0.471
0.340
0.288
0.234
0.179
0.121
L2×2×3⁄8
L3×3×5⁄16
L3×3×1⁄4
L3×3×3⁄16
L3×3×1⁄8
in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DOUBLE ANGLES
1 - 95
DOUBLE ANGLES
Two equal leg angles
Properties of sections
Y
X
X
y, yp
s
Y
Qs*
Axis Y-Y
Radii of Gyration
Angles in Contact
Angles Separated
3⁄
4
Fy =
36 ksi
Fy =
50 ksi
Fy =
36 ksi
Fy =
50 ksi
Back to Back of
Angles, in.
3⁄
8
Designation
0
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×5⁄16
L31⁄2×31⁄2×1⁄4
1.48
1.47
1.46
1.61
1.60
1.59
1.75
1.74
1.73
—
—
—
—
—
0.982
—
—
0.965
—
0.986
0.897
L3×3×1⁄2
L3×3×3⁄8
L3×3×5⁄16
L3×3×1⁄4
L3×3×3⁄16
1.29
1.27
1.26
1.26
1.25
1.43
1.41
1.40
1.39
1.38
1.59
1.56
1.55
1.53
1.52
—
—
—
—
0.995
—
—
—
—
0.921
—
—
—
—
0.911
—
—
—
0.961
0.834
L21⁄2×21⁄2×3⁄8
L21⁄2×21⁄2×5⁄16
L21⁄2×21⁄2×1⁄4
L21⁄2×21⁄2×3⁄16
1.07
1.06
1.05
1.04
1.21
1.20
1.19
1.18
1.36
1.35
1.34
1.32
—
—
—
—
—
—
—
—
—
—
—
0.982
—
—
—
0.919
L2×2×3⁄8
L2×2×5⁄16
L2×2×1⁄4
L2×2×3⁄16
L2×2×1⁄8
0.870
0.859
0.849
0.840
0.831
1.01
1.00
0.989
0.977
0.965
1.17
1.16
1.14
1.13
1.11
—
—
—
—
0.995
—
—
—
—
0.921
—
—
—
—
0.911
—
—
—
—
0.834
*Where no value ofQs is shown, the angles comply with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 96
DIMENSIONS AND PROPERTIES
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Long legs back to back
Y
Wt.
Area of
per ft
2 Angles 2 Angles
Designation
2
Axis X-X
S
I
4
in.
r
3
y
Z
yp
3
lb
in.
in.
in.
in.
in.
in.
L8×6×1
L8×6×13⁄4
L8×6×11⁄2
88.4
67.6
46.0
26.0
19.9
13.5
161
126
88.6
30.2
23.3
16.0
2.49
2.53
2.56
2.65
2.56
2.47
54.5
42.2
29.1
1.50
1.38
1.25
L8×4×1
L8×6×13⁄4
L8×6×11⁄2
74.8
57.4
39.2
22.0
16.9
11.5
139
109
77.0
28.1
21.8
15.0
2.52
2.55
2.59
3.05
2.95
2.86
48.5
37.7
26.1
2.50
2.38
2.25
L7×4×3⁄4
L7×4×1⁄2
L7×4×3⁄8
52.4
35.8
27.2
15.4
10.5
7.97
75.6
53.3
41.1
16.8
11.6
8.88
2.22
2.25
2.27
2.51
2.42
2.37
29.6
20.6
15.7
1.88
1.75
1.69
L6×4×3⁄4
L7×4×5⁄8
L7×4×1⁄2
L7×4×3⁄8
47.2
40.0
32.4
24.6
13.9
11.7
9.50
7.22
49.0
42.1
34.8
26.9
12.5
10.6
8.67
6.64
1.88
1.90
1.91
1.93
2.08
2.03
1.99
1.94
22.3
19.0
15.6
11.9
1.38
1.31
1.25
1.19
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
23.4
19.6
6.84
5.74
25.7
21.8
6.49
5.47
1.94
1.95
2.04
2.01
11.5
9.70
1.44
1.41
L5×31⁄2×3⁄4
L6×31⁄2×1⁄2
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
39.6
27.2
20.8
17.4
11.6
8.00
6.09
5.12
27.8
20.0
15.6
13.2
8.55
5.97
4.59
3.87
1.55
1.58
1.60
1.61
1.75
1.66
1.61
1.59
15.3
10.8
8.28
6.99
1.13
1.00
0.938
0.906
L5×3×1⁄2
L7×4×3⁄8
L7×4×5⁄16
L7×4×1⁄4
25.6
19.6
16.4
13.2
7.50
5.72
4.80
3.88
18.9
14.7
12.5
10.2
5.82
4.47
3.77
3.06
1.59
1.61
1.61
1.62
1.75
1.70
1.68
1.66
10.3
7.95
6.71
5.45
1.25
1.19
1.16
1.13
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DOUBLE ANGLES
1 - 97
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Long legs back to back
Y
Qs*
Axis Y-Y
Radii of Gyration
Back to Back of
Angles, in.
Angles in Contact
Angles Separated
0
3⁄
8
3⁄
4
Fy =
36 ksi
Fy =
50 ksi
Fy =
36 ksi
Fy =
50 ksi
L8×6×1
L8×6×13⁄4
L8×6×11⁄2
2.39
2.35
2.32
2.52
2.48
2.44
2.66
2.62
2.57
—
—
—
—
—
—
—
—
0.911
—
—
0.834
L8×4×1
L8×4×13⁄4
L8×4×11⁄2
1.47
1.42
1.38
1.61
1.55
1.51
1.75
1.69
1.64
—
—
—
—
—
—
—
—
0.911
—
—
0.834
L7×4×3⁄4
L7×4×1⁄2
L7×4×3⁄8
1.48
1.44
1.43
1.62
1.57
1.55
1.76
1.71
1.68
—
—
—
—
—
—
—
0.965
0.839
—
0.897
0.750
L6×4×3⁄4
L7×4×5⁄8
L7×4×1⁄2
L7×4×3⁄8
1.55
1.53
1.51
1.5
1.69
1.67
1.64
1.62
1.83
1.81
1.78
1.76
—
—
—
—
—
—
—
—
—
—
—
0.911
—
—
0.961
0.834
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
1.26
1.26
1.39
1.38
1.53
1.51
—
—
—
—
0.911
0.825
0.834
0.733
L5×31⁄2×3⁄4
L6×31⁄2×1⁄2
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
1.40
1.35
1.34
1.33
1.53
1.49
1.46
1.45
1.68
1.63
1.60
1.59
—
—
—
—
—
—
—
—
—
—
0.982
0.911
—
—
0.919
0.834
L5×3×1⁄2
L7×4×3⁄8
L7×4×5⁄16
L7×4×1⁄4
1.12
1.10
1.09
1.08
1.25
1.23
1.22
1.21
1.40
1.37
1.36
1.34
—
—
—
—
—
—
—
—
—
0.982
0.911
0.804
—
0.919
0.834
0.708
Designation
*Where no value of Qs is shown the angles comply with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 98
DIMENSIONS AND PROPERTIES
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Long legs back to back
Y
Wt.
Area of
per ft
2 Angles 2 Angles
Designation
2
Axis X-X
S
I
4
in.
r
3
y
Z
yp
3
lb
in.
in.
in.
in.
in.
in.
L4×31⁄2×1⁄2
L4×31⁄2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
23.8
18.2
15.4
12.4
7.00
5.34
4.49
3.63
10.6
8.35
7.12
5.83
3.87
2.99
2.53
2.05
1.23
1.25
1.26
1.27
1.25
1.21
1.18
1.16
7.00
5.42
4.59
3.73
0.500
0.438
0.406
0.375
L4×3×1⁄2
L4×3×3⁄8
L4×3×5⁄16
L4×3×1⁄4
22.2
17.0
14.4
11.6
6.50
4.97
4.18
3.38
10.1
7.93
6.76
5.54
3.78
2.92
2.47
2.00
1.25
1.26
1.27
1.28
1.33
1.28
1.26
1.24
6.81
5.28
4.47
3.63
0.750
0.688
0.656
0.625
L31⁄2×3×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
15.8
13.2
10.8
4.59
3.87
3.13
5.45
4.66
3.83
2.25
1.91
1.55
1.09
1.10
1.11
1.08
1.06
1.04
4.08
3.46
2.82
0.438
0.406
0.375
L31⁄2×21⁄2×3⁄8
L31⁄2×21⁄2×1⁄4
14.4
9.80
4.22
2.88
5.12
3.60
2.19
1.51
1.10
1.12
1.16
1.11
3.94
2.73
0.688
0.625
L3×21⁄2×3⁄8
L4×31⁄2×1⁄4
L4×31⁄2×5⁄16
13.2
9.00
6.77
3.84
2.63
1.99
3.31
2.35
1.81
1.62
1.12
0.859
0.928
0.945
0.954
0.956
0.911
0.888
2.93
2.04
1.56
0.438
0.375
0.344
L3×2×3⁄8
L4×3×5⁄16
L4×3×1⁄4
L4×3×3⁄16
11.8
10.0
8.20
6.14
3.47
2.93
2.38
1.80
3.06
2.63
2.17
1.68
1.56
1.33
1.08
0.830
0.940
0.948
0.957
0.966
1.04
1.02
0.993
0.970
2.79
2.38
1.95
1.49
0.688
0.656
0.625
0.594
L21⁄2×2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
L4×31⁄2×3⁄16
10.6
9.00
7.24
5.50
3.09
2.62
2.13
1.62
1.82
1.58
1.31
1.02
1.09
0.932
0.763
0.586
0.768
0.776
0.784
0.793
0.831
0.809
0.787
0.764
1.97
1.69
1.38
1.06
0.438
0.406
0.375
0.344
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DOUBLE ANGLES
1 - 99
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Long legs back to back
Y
Qs*
Axis Y-Y
Radii of Gyration
Angles in Contact
Angles Separated
3⁄
4
Fy =
36 ksi
Fy =
50 ksi
Fy =
36 ksi
Fy =
50 ksi
Back to Back of
Angles, in.
Designation
0
3⁄
8
L4×31⁄2×1⁄2
L4×31⁄2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
1.44
1.42
1.42
1.41
1.58
1.56
1.55
1.54
1.72
1.70
1.69
1.67
—
—
—
—
—
—
—
0.982
—
—
0.997
0.911
—
—
0.935
0.834
L4×3×1⁄2
L4×3×3⁄8
L4×3×5⁄16
L4×3×1⁄4
1.20
1.18
1.17
1.16
1.33
1.31
1.30
1.29
1.48
1.45
1.44
1.43
—
—
—
—
—
—
—
—
—
—
0.997
0.911
—
—
0.935
0.834
L31⁄2×3×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
1.22
1.21
1.20
1.36
1.35
1.33
1.50
1.49
1.48
—
—
—
—
—
—
—
—
0.965
—
0.986
0.897
L31⁄2×21⁄2×3⁄8
L31⁄2×21⁄2×1⁄4
0.976
0.958
1.11
1.09
1.26
1.23
—
—
—
—
—
0.965
—
0.897
L3×21⁄2×3⁄8
L4×31⁄2×1⁄4
L4×31⁄2×5⁄16
1.02
1.00
0.993
1.16
1.13
1.12
1.31
1.28
1.27
—
—
—
—
—
—
—
—
0.911
—
0.961
0.834
L3×2×3⁄8
L4×3×5⁄16
L4×3×1⁄4
L4×3×3⁄16
0.777
0.767
0.757
0.749
0.917
0.903
0.891
0.879
1.07
1.06
1.04
1.03
—
—
—
—
—
—
—
—
—
—
—
0.911
—
—
0.961
0.834
L21⁄2×2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
L4×31⁄2×3⁄16
0.819
0.809
0.799
0.790
0.961
0.948
0.935
0.923
1.12
1.10
1.09
1.07
—
—
—
—
—
—
—
—
—
—
—
0.982
—
—
—
0.919
*Where no value of Qs is shown, the angles comply with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 100
DIMENSIONS AND PROPERTIES
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Short legs back to back
Y
Wt.
Area of
per ft
2 Angles 2 Angles
Designation
2
Axis X-X
S
I
4
in.
r
3
y
Z
yp
3
lb
in.
in.
in.
in.
in.
in.
L8×6×1
L8×6×13⁄4
L8×6×11⁄2
88.4
67.6
46.0
26.0
19.9
13.5
77.6
61.4
43.4
17.8
13.8
9.58
1.73
1.76
1.79
1.65
1.56
1.47
32.4
24.9
17.0
0.813
0.621
0.422
L8×4×1
L8×6×13⁄4
L8×6×11⁄2
74.8
57.4
39.2
22.0
16.9
11.5
23.3
18.7
13.5
7.88
6.14
4.29
1.03
1.05
1.08
1.05
0.953
0.859
15.4
11.6
7.80
0.688
0.527
0.359
L7×4×3⁄4
L5×3×1⁄2
L5×3×3⁄8
52.4
35.8
27.2
15.4
10.5
7.97
18.1
13.1
10.2
6.05
4.23
3.26
1.09
1.11
1.13
1.01
0.917
0.870
11.3
7.66
5.80
0.549
0.375
0.285
L6×4×3⁄4
L5×3×5⁄8
L5×3×1⁄2
L5×3×3⁄8
47.2
40.0
32.4
24.6
13.9
11.7
9.50
7.22
17.4
15.0
12.5
9.81
5.94
5.07
4.16
3.21
1.12
1.13
1.15
1.17
1.08
1.03
0.987
0.941
10.9
9.24
7.50
5.71
0.578
0.488
0.396
0.301
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
23.4
19.6
6.84
5.74
6.68
5.70
2.46
2.08
0.988
0.996
0.787
0.763
4.41
3.70
0.285
0.239
L5×31⁄2×3⁄4
L6×31⁄2×1⁄2
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
39.6
27.2
20.8
17.4
11.6
8.00
6.09
5.12
11.1
8.10
6.37
5.44
4.43
3.12
2.41
2.04
0.977
1.01
1.02
1.03
0.996
0.906
0.861
0.838
8.20
5.65
4.32
3.63
0.581
0.400
0.305
0.256
L5×3×1⁄2
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
25.6
19.6
16.4
13.2
7.50
5.72
4.80
3.88
5.16
4.08
3.49
2.88
2.29
1.78
1.51
1.23
0.829
0.845
0.853
0.861
0.750
0.704
0.681
0.657
4.22
3.21
2.69
2.17
0.375
0.286
0.240
0.194
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DOUBLE ANGLES
1 - 101
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Short legs back to back
Y
Qs*
Axis Y-Y
Radii of Gyration
Back to Back of
Angles, in.
Angles in Contact
Angles Separated
0
3⁄
8
3⁄
4
Fy =
36 ksi
Fy =
50 ksi
Fy =
36 ksi
Fy =
50 ksi
L8×6×1
L8×6×13⁄4
L8×6×11⁄2
3.64
3.60
3.56
3.78
3.74
3.69
3.92
3.88
3.83
—
—
0.995
—
—
0.921
—
—
0.911
—
—
0.834
L8×4×1
L8×4×13⁄4
L8×4×11⁄2
3.95
3.90
3.86
4.10
4.05
4.00
4.25
4.19
4.14
—
—
0.995
—
—
0.921
—
—
0.911
—
—
0.834
L7×4×3⁄4
L7×4×1⁄2
L7×4×3⁄8
3.35
3.30
3.28
3.49
3.44
3.42
3.64
3.59
3.56
—
—
0.926
—
0.982
0.838
—
0.965
0.839
0.897
0.750
L6×4×3⁄4
L7×4×5⁄8
L7×4×1⁄2
L7×4×3⁄8
2.80
2.78
2.76
2.74
2.94
2.92
2.90
2.87
3.09
3.06
3.04
3.02
—
—
—
0.995
—
—
—
0.921
—
—
—
0.911
—
—
0.961
0.834
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
2.81
2.80
2.95
2.94
3.09
3.08
0.995
0.912
0.921
0.822
0.911
0.825
0.834
0.733
L5×31⁄2×3⁄4
L6×31⁄2×1⁄2
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
2.33
2.29
2.27
2.26
2.48
2.43
2.41
2.39
2.63
2.57
2.55
2.54
—
—
—
0.995
—
—
—
0.921
—
—
0.982
0.911
—
—
0.919
0.834
L5×3×1⁄2
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
2.36
2.34
2.33
2.32
2.50
2.48
2.47
2.46
2.65
2.63
2.61
2.60
—
—
0.995
0.891
—
—
0.921
0.797
—
0.982
0.911
0.804
—
0.919
0.834
0.708
Designation
*Where no value of Qs is shown, the angles comply with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 102
DIMENSIONS AND PROPERTIES
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Short legs back to back
Y
Wt.
Area of
per ft
2 Angles 2 Angles
Designation
2
Axis X-X
S
I
4
in.
r
3
y
Z
yp
3
lb
in.
in.
in.
in.
in.
in.
L4×31⁄2×1⁄2
L4×31⁄2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
23.8
18.2
15.4
12.4
7.00
5.34
4.49
3.63
7.58
5.97
5.10
4.19
3.03
2.35
1.99
1.62
1.04
1.06
1.07
1.07
1.00
0.955
0.932
0.909
5.47
4.21
3.56
2.89
0.438
0.334
0.281
0.227
L4×3×1⁄2
L3×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
22.2
17.0
14.4
11.6
6.50
4.97
4.18
3.38
4.85
3.84
3.29
2.71
2.23
1.73
1.47
1.20
0.864
0.879
0.887
0.896
0.827
0.782
0.759
0.736
4.06
3.11
2.63
2.13
0.406
0.311
0.261
0.211
L31⁄2×3×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
15.8
13.2
10.8
4.59
3.87
3.13
3.69
3.17
2.61
1.70
1.44
1.18
0.897
0.905
0.914
0.830
0.808
0.785
3.06
2.59
2.10
0.328
0.276
0.223
L31⁄2×21⁄2×3⁄8
L31⁄2×21⁄2×1⁄4
14.4
9.80
4.22
2.88
2.18
1.55
1.18
0.824
0.719
0.735
0.660
0.614
2.15
1.47
0.301
0.205
L3×21⁄2×3⁄8
L4×31⁄2×1⁄4
L4×31⁄2×3⁄16
13.2
9.00
6.77
3.84
2.63
1.99
2.08
1.49
1.15
1.16
0.808
0.620
0.736
0.753
0.761
0.706
0.661
0.638
2.10
1.45
1.11
0.320
0.219
0.166
L3×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
L3×2×3⁄16
11.8
10.0
8.20
6.14
3.47
2.93
2.38
1.80
1.09
0.941
0.784
0.613
0.743
0.634
0.520
0.401
0.559
0.567
0.574
0.583
0.539
0.516
0.493
0.470
1.37
1.16
0.937
0.713
0.289
0.244
0.198
0.150
L21⁄2×2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
L4×31⁄2×3⁄16
10.6
9.00
7.24
5.50
3.09
2.62
2.13
1.62
1.03
0.893
0.745
0.583
0.725
0.620
0.509
0.392
0.577
0.584
0.592
0.600
0.581
0.559
0.537
0.514
1.32
1.12
0.915
0.701
0.309
0.262
0.213
0.162
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DOUBLE ANGLES
1 - 103
DOUBLE ANGLES
Two unequal leg angles
Properties of sections
Y
X
X
y, yp
s
Short legs back to back
Y
Qs*
Axis Y-Y
Radii of Gyration
Back to Back of
Angles, in.
Angles in Contact
Angles Separated
0
3⁄
8
3⁄
4
Fy =
36 ksi
Fy =
50 ksi
Fy =
36 ksi
Fy =
50 ksi
L4×31⁄2×1⁄2
L4×31⁄2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
1.76
1.74
1.73
1.72
1.89
1.87
1.86
1.85
2.04
2.01
2.00
1.99
—
—
—
0.995
—
—
—
0.921
—
—
0.997
0.911
—
—
0.935
0.834
L4×3×1⁄2
L3×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
1.82
1.80
1.79
1.78
1.96
1.94
1.93
1.92
2.11
2.08
2.07
2.06
—
—
—
0.995
—
—
—
0.921
—
—
0.997
0.911
—
—
0.935
0.834
L31⁄2×3×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
1.53
1.52
1.52
1.67
1.66
1.65
1.82
1.80
1.79
—
—
—
—
—
0.982
—
—
0.965
—
0.986
0.897
L31⁄2×21⁄2×3⁄8
L31⁄2×21⁄2×1⁄4
1.60
1.58
1.74
1.72
1.89
1.86
—
—
—
0.982
—
0.965
—
0.897
L3×21⁄2×3⁄8
L4×31⁄2×1⁄4
L4×31⁄2×3⁄16
1.33
1.31
1.30
1.47
1.45
1.44
1.62
1.60
1.58
—
—
0.995
—
—
0.921
—
—
0.911
—
0.961
0.834
L3×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
L3×2×3⁄16
1.40
1.39
1.38
1.37
1.55
1.53
1.52
1.51
1.70
1.68
1.67
1.66
—
—
—
0.995
—
—
—
0.921
—
—
—
0.911
—
—
0.961
0.834
L21⁄2×2×3⁄8
L4×31⁄2×5⁄16
L4×31⁄2×1⁄4
L4×31⁄2×3⁄16
1.13
1.12
1.11
1.10
1.28
1.26
1.25
1.24
1.43
1.42
1.40
1.39
—
—
—
—
—
—
—
—
—
—
—
0.982
—
—
—
0.911
Designation
*Where no value of Qs is shown the angles comply with LRFD Specification Section E2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 104
DIMENSIONS AND PROPERTIES
COMBINATION SECTIONS
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMBINATION SECTIONS
1 - 105
COMBINATION SECTIONS
Standard rolled shapes are frequently combined to produce efficient and economical
structural members for special applications. Experience has established a demand for
certain combinations. When properly sized and connected to satisfy the design and
specification criteria, these members may be used as struts, lintels, eave struts, and light
crane and trolley runways. The W section with channel attached to the web is not
recommended for use as a trolley or crane runway member. Properties of several
combined sections are tabulated for those combinations that experience has proven to be
in popular demand.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 106
DIMENSIONS AND PROPERTIES
COMBINATION SECTIONS
W shapes and channels
Properties of sections
Y
y
2
X
X
y , yp
1
Y
Beam
Channel
Axis X-X
Total
Weight
per ft
Total
Area
lb
in.2
I
S1 =
I / y1
S2 =
I / y2
r
in.4
in.3
in.3
in.
W12×26
W ×26
C10×15.3
C12×20.7
41.3
46.7
12.14
13.74
299
318
36.3
36.8
70.5
82.2
4.96
4.81
W14×30
W ×30
C10×15.3
C12×20.7
45.3
50.7
13.34
14.94
420
448
46.1
46.8
84.6
98.3
5.61
5.47
W16×36
W ×36
C12×20.7
C15×33.9
56.7
69.9
16.69
20.56
670
748
62.8
64.6
123
160
6.34
6.03
W18×50
W ×50
C12×20.7
C15×33.9
70.7
83.9
20.79
24.66
1120
1250
97.4
100
166
211
7.34
7.11
W21×62
W ×62
W ×68
W ×68
C12×20.7
C15×33.9
C12×20.7
C15×33.9
82.7
95.9
88.7
101.9
24.39
28.26
26.09
29.96
1800
2000
1960
2180
138
142
152
156
218
272
232
287
8.59
8.41
8.68
8.52
W24×68
W ×68
W ×84
W ×84
C12×20.7
C15×33.9
C12×20.7
C15×33.9
88.7
101.9
104.7
117.9
26.19
30.06
30.79
34.66
2450
2720
3040
3340
168
173
212
217
258
321
303
368
9.67
9.50
9.93
9.82
W27×84
W ×94
C15×33.9
C15×33.9
117.9
127.9
34.76
37.66
4050
4530
237
268
404
436
10.8
11.0
W30×99
W ×99
W ×116
W ×116
C15×33.9
C18×42.7
C15×33.9
C18×42.7
132.9
141.7
149.9
158.7
39.06
41.70
44.16
46.80
5540
5830
6590
6900
300
304
360
365
480
533
544
599
11.9
11.8
12.2
12.1
W33×118
W ×118
W ×141
W ×141
C15×33.9
C18×42.7
C15×33.9
C18×42.7
151.9
160.7
174.9
183.7
44.66
47.30
51.56
54.20
7900
8280
9580
10000
395
400
484
490
596
656
689
751
13.3
13.2
13.6
13.6
W36×150
W ×150
C15×33.9
C18×42.7
183.9
192.7
54.16
56.80
11500
12100
546
553
765
832
14.6
14.6
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMBINATION SECTIONS
1 - 107
COMBINATION SECTIONS
W shapes and channels
Properties of sections
Y
y
2
X
X
y , yp
1
Y
Axis X-X
y1
Beam
Z
Axis Y-Y
yp
3
Channel
in.
in.
W12×26
W30×26
C10×15.3
C12×20.7
8.22
8.63
W14×30
W30×30
C10×15.3
C12×20.7
W16×36
W30×36
S
I
4
3
r
Z
in.
in.3
in.
in.
in.
47.0
48.8
11.30
11.55
84.7
146
16.9
24.4
2.64
3.26
24.0
33.6
9.12
9.57
60.5
62.3
12.56
12.87
87.0
149
17.4
24.8
2.55
3.15
24.8
34.4
C12×20.7
C15×33.9
10.67
11.58
83.6
88.6
14.56
15.21
154
340
25.6
45.3
3.03
4.06
36.3
61.3
W18×50
W30×50
C12×20.7
C15×33.9
11.51
12.47
128
134
16.08
16.90
169
355
28.2
47.3
2.85
3.79
42.0
67.0
W21×62
W30×62
W30×68
W30×68
C12×20.7
C15×33.9
C12×20.7
C15×33.9
13.01
14.06
12.93
13.95
182
190
200
208
18.06
19.36
17.60
19.32
187
373
194
380
31.1
49.7
32.3
50.6
2.77
3.63
2.72
3.56
47.2
72.2
49.8
74.8
W24×68
W30×68
W30×84
W30×84
C12×20.7
C15×33.9
C12×20.7
C15×33.9
14.53
15.67
14.35
15.40
224
234
275
288
19.15
21.66
18.49
21.61
199
385
223
409
33.2
51.4
37.2
54.6
2.76
3.58
2.69
3.44
50.0
75.0
58.1
83.1
W27×84
W27×94
C15×33.9
C15×33.9
17.07
16.92
320
357
23.86
23.56
421
439
56.1
58.5
3.48
3.41
83.6
89.2
W30×99
W30×99
W30×116
W30×116
C15×33.9
C18×42.7
C15×33.9
C18×42.7
18.51
19.18
18.30
18.93
408
418
480
492
24.34
26.43
23.77
26.04
443
682
479
718
59.1
75.8
63.9
79.8
3.37
4.04
3.29
3.92
89.1
113
99.6
124
W33×118
W30×118
W30×141
W30×141
C15×33.9
C18×42.7
C15×33.9
C18×42.7
20.01
20.69
19.79
20.42
529
544
634
652
25.43
27.77
24.83
26.96
502
741
561
800
66.9
82.3
74.8
88.9
3.35
3.96
3.30
3.84
102
126
117
141
W36×150
W30×150
C15×33.9
C18×42.7
21.15
21.81
716
738
25.84
27.91
585
824
78.0
91.6
3.29
3.81
121
145
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 108
DIMENSIONS AND PROPERTIES
COMBINATION SECTIONS
S shapes and channels
Properties of sections
Y
y
2
X
X
y , yp
1
Y
Beam
Channel
Axis X-X
Total
Weight
per ft
Total
Area
lb
in.2
I
S1 =
I / y1
S2 =
I / y2
r
in.4
in.3
in.3
in.
S10×25.4
C8×11.5
C10×15.3
36.9
40.7
10.84
11.95
176
186
27.2
27.6
46.6
52.9
4.02
3.94
S12×31.8
C8×11.5
C10×15.3
43.3
47.1
12.73
13.84
299
316
39.8
40.4
63.2
71.4
4.84
4.78
S15×42.9
C8×11.5
C10×15.3
54.4
58.2
15.98
17.09
585
616
64.9
65.8
94.2
105
6.05
6.01
S20×66
C10×15.3
C12×20.7
81.3
86.7
23.89
25.49
1530
1620
130
132
181
203
8.00
7.97
S24×80
C10×15.3
C12×20.7
95.3
100.7
27.99
29.59
2610
2750
188
191
252
278
9.66
9.65
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMBINATION SECTIONS
1 - 109
COMBINATION SECTIONS
S shapes and channels
Properties of sections
Y
y
2
X
X
y , yp
1
Y
Axis X-X
y1
Beam
Z
Axis Y-Y
yp
3
S
I
4
3
r
Z
in.
in.3
Channel
in.
in.
in.
in.
in.
S10×25.4
C8×11.5
C10×15.3
6.45
6.73
35.7
36.9
8.81
9.02
39.4
74.2
9.8
14.8
1.91
2.49
14.5
20.8
S12×31.8
C8×11.5
C10×15.3
7.50
7.82
52.6
53.9
10.30
10.61
42.0
76.8
10.5
15.4
1.82
2.36
16.0
22.2
S15×42.9
C8×11.5
C10×15.3
9.01
9.37
85.7
88.2
11.58
12.77
47.0
81.8
11.8
16.4
1.71
2.19
18.6
24.9
S20×66
C10×15.3
C12×20.7
11.81
12.29
171
178
14.41
15.99
95.1
157
19.0
26.1
2.00
2.48
31.2
40.8
S24×80
C10×15.3
C12×20.7
13.86
14.38
244
254
16.46
18.05
110
171
21.9
28.5
1.98
2.41
36.6
46.2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 110
DIMENSIONS AND PROPERTIES
d
2
Yd
COMBINATION SECTIONS
Two channels
Properties of sections
2
y
2
X
X
x1 , xp
y , yp
1
Y
Vertical Horizontal
Channel Channel
Axis X-X
Total
Weight
per ft
Total
Area
lb
in.2
I
S1 =
I / y1
S2 =
I / y2
r
y1
Z
yp
in.4
in.3
in.3
in.
in.
in.3
in.
C3×4.1
C4×5.4
9.5
2.80
3.0
1.4
3.0
1.04
2.20
2.16
2.67
C4×5.4
C4×5.4
C5×6.7
10.8
12.1
3.18
3.56
6.5
6.9
2.3
2.3
4.9
5.5
1.43
1.39
2.86
2.94
3.39
3.62
3.56
3.61
C5×6.7
C5×6.7
C6×8.2
C7×9.8
13.4
14.9
16.5
3.94
4.37
4.84
12.8
13.4
14.0
3.5
3.6
3.7
8.0
8.9
9.8
1.80
1.75
1.70
3.60
3.70
3.79
5.23
5.50
5.81
4.50
4.57
4.62
C6×8.2
C5×6.7
C6×8.2
C7×9.8
C8×11.5
C9×13.4
C10×15.3
14.9
16.4
18.0
19.7
21.6
23.5
4.37
4.80
5.27
5.78
6.34
6.89
21.5
22.5
23.4
24.3
25.2
26.0
5.1
5.2
5.2
5.3
5.4
5.5
10.9
12.1
13.3
14.5
15.8
16.9
2.22
2.16
2.11
2.05
1.99
1.94
4.22
4.34
4.45
4.55
4.64
4.70
7.31
7.61
7.93
8.30
8.72
9.16
5.37
5.45
5.53
5.58
5.63
5.65
C7×9.8
C6×8.2
C7×9.8
C8×11.5
C9×13.4
C10×15.3
18.0
19.6
21.3
23.2
25.1
5.27
5.74
6.25
6.81
7.36
35.3
36.7
38.0
39.3
40.5
7.1
7.2
7.3
7.4
7.5
15.7
17.3
18.8
20.5
21.9
2.59
2.53
2.47
2.40
2.34
4.95
5.08
5.20
5.31
5.39
10.2
10.6
10.9
11.4
11.8
6.32
6.40
6.48
6.54
6.58
C8×11.5
C6×8.2
C7×9.8
C8×11.5
C9×13.4
C10×15.3
C12×20.7
19.7
21.3
23.0
24.9
26.8
32.2
5.78
6.25
6.76
7.32
7.87
9.47
52.4
54.5
56.4
58.4
60.0
64.4
9.5
9.6
9.7
9.8
9.9
10.2
19.6
21.6
23.6
25.6
27.5
32.6
3.01
2.95
2.89
2.82
2.76
2.61
5.53
5.68
5.82
5.95
6.06
6.30
13.4
13.8
14.2
14.6
15.1
16.4
7.18
7.27
7.35
7.44
7.49
7.62
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMBINATION SECTIONS
1 - 111
COMBINATION SECTIONS
Two channels
Properties of sections
d
2
Yd
2
y
2
X
X
x1 , xp
y , yp
1
Y
Axis Y-Y
Vertical
Channel
Horizontal
Channel
I
S
r
x1
Z
xp
in.4
in.3
in.
in.
in.3
in.
C3×4.1
C4×5.4
4.0
2.0
1.20
0.44
2.67
0.315
C4×5.4
C4×5.4
C5×6.7
4.2
7.8
2.1
3.1
1.14
1.48
0.46
0.46
2.84
4.09
0.281
0.282
C5×6.7
C5×6.7
C6×8.2
C7×9.8
8.0
13.6
21.8
3.2
4.5
6.2
1.42
1.76
2.12
0.48
0.48
0.48
4.29
5.90
7.90
0.264
0.266
0.268
C6×8.2
C5×6.7
C6×8.2
C7×9.8
C8×11.5
C9×13.4
C10×15.3
8.2
13.8
22.0
33.3
48.6
68.1
3.3
4.6
6.3
8.3
10.8
13.6
1.37
1.70
2.04
2.40
2.77
3.14
0.51
0.51
0.51
0.51
0.51
0.51
4.52
6.14
8.13
10.6
13.5
16.8
0.242
0.245
0.247
0.249
0.252
0.254
C7×9.8
C6×8.2
C7×9.8
C8×11.5
C9×13.4
C10×15.3
14.1
22.3
33.6
48.6
68.4
4.7
6.4
8.4
10.9
13.7
1.63
1.97
2.32
2.68
3.05
0.54
0.54
0.54
0.54
0.54
6.41
8.41
10.8
13.8
17.1
0.225
0.228
0.230
0.234
0.235
C8×11.5
C6×8.2
C7×9.8
C8×11.5
C9×13.4
C10×15.3
C12×20.7
14.4
22.6
33.9
49.2
68.7
130
4.8
6.5
8.5
10.9
13.7
21.7
1.58
1.90
2.24
2.59
2.95
3.71
0.57
0.57
0.57
0.57
0.57
0.57
6.73
8.73
11.2
14.1
17.4
27.0
0.218
0.219
0.219
0.220
0.220
0.230
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 112
DIMENSIONS AND PROPERTIES
d
2
Yd
COMBINATION SECTIONS
Two channels
Properties of sections
2
y
2
X
X
x1 , xp
y , yp
1
Y
Vertical Horizontal
Channel Channel
Total
Weight
per ft
Axis X-X
Total
Area
2
lb
in.
C9×13.4
C7×9.8
C8×11.5
C9×13.4
C10×15.3
C12×20.7
23.2
24.9
26.8
28.7
34.1
6.81
7.32
7.88
8.43
10.03
C10×15.3
C8×11.5
C9×13.4
C10×15.3
C12×20.7
C15×33.9
26.8
28.7
30.6
36.0
49.2
7.87
8.43
8.98
10.58
14.45
C12×20.7
C9×13.4
C10×15.3
C12×20.7
C15×33.9
34.1
36.0
41.4
54.6
C15×33.9
C10×15.3
C12×20.7
C15×33.9
MC18×42.7
MC18×42.7 MC12×20.7
MC15×33.9
MC18×42.7
S1 =
I / y1
I
4
in.
3
S2 =
I / y2
3
r
y1
Z
yp
3
in.
in.
in.
in.
in.
in.
12.4
12.6
12.7
12.8
13.1
26.3
28.7
31.2
33.5
39.8
3.38
3.32
3.25
3.19
3.02
6.26
6.42
6.57
6.69
6.98
17.6
18.1
18.5
19.0
20.4
8.11
8.21
8.31
8.37
8.54
110
114
117
126
141
15.8
15.9
16.1
16.4
17.3
34.2
37.2
39.9
47.5
63.7
3.75
3.68
3.61
3.45
3.13
7.00
7.16
7.30
7.64
8.18
22.4
22.9
23.4
24.9
28.3
9.07
9.18
9.26
9.46
9.73
10.03
10.58
12.18
16.05
207
213
228
256
25.2
25.4
25.9
27.0
51.4
55.0
65.3
87.8
4.54
4.48
4.32
4.00
8.21
8.38
8.79
9.48
35.7
36.3
38.0
41.8
10.78
10.88
11.16
11.56
49.2
54.6
67.8
76.6
14.45
16.05
19.92
22.56
474
509
575
608
48.8
49.9
52.0
53.1
85.6
99.8
132
152
5.72
5.63
5.37
5.19
9.71
10.19
11.06
11.45
69.7
72.2
77.4
80.7
12.83
13.31
14.04
14.37
63.4
76.6
85.4
18.69
22.56
25.20
860
975
1030
72.9
76.1
77.6
133
174
200
6.78
6.57
6.40
11.80
12.80
13.29
77.7
80.5
83.3
85.6
91.7
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
106
113
117
15.51
16.50
16.96
COMBINATION SECTIONS
1 - 113
COMBINATION SECTIONS
Two channels
Properties of sections
d
2
Yd
2
y
2
X
X
x1 , xp
y , yp
1
Y
Axis Y-Y
Vertical
Channel
Horizontal
Channel
I
S
r
x1
Z
xp
in.4
in.3
in.
in.
in.3
in.
C9×13.4
C7×9.8
C8×11.5
C9×13.4
C10×15.3
C12×20.7
23.1
34.4
49.7
69.2
131
6.6
8.6
11.0
13.8
21.8
1.84
2.17
2.51
2.86
3.61
0.60
0.60
0.60
0.60
0.60
9.10
11.5
14.5
17.8
27.4
0.226
0.227
0.227
0.227
0.229
C10×15.3
C8×11.5
C9×13.4
C10×15.3
C12×20.7
C15×33.9
34.9
50.2
69.7
131
317
8.7
11.2
13.9
21.9
42.3
2.11
2.44
2.79
3.52
4.69
0.63
0.63
0.63
0.63
0.63
11.9
14.9
18.2
27.8
52.8
0.232
0.232
0.233
0.234
0.239
C12×20.7
C9×13.4
C10×15.3
C12×20.7
C15×33.9
51.8
71.3
133
319
11.5
14.3
22.1
42.5
2.27
2.60
3.30
4.46
0.70
0.70
0.70
0.70
16.0
19.3
29.0
54.0
0.261
0.261
0.262
0.266
C15×33.9
C10×15.3
C12×20.7
C15×33.9
MC18×42.7
75.5
137
323
562
15.1
22.9
43.1
62.5
2.29
2.92
4.03
4.99
0.79
0.79
0.79
0.79
22.1
31.7
56.7
80.7
0.337
0.338
0.342
0.343
MC18×42.7
MC12×20.7
MC15×33.9
MC18×42.7
143
329
568
23.9
43.9
63.2
2.77
3.82
4.75
0.88
0.88
0.88
33.6
58.6
82.6
0.355
0.358
0.359
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 114
DIMENSIONS AND PROPERTIES
COMBINATION SECTIONS
Channels and angles
Properties of sections
Y
y
2
X
X
Long leg of angle turned out
y , yp
1
x1
xp
x2
Y
Total
Weight
per ft
Axis X-X
Total
Area
2
S1 =
I / y1
I
4
3
3
in.
r
y1
Z
yp
3
Angle
lb
in.
in.
in.
in.
in.
in.
C6×8.2
L21⁄2×21⁄2×1⁄4
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L3×21⁄2 ×5⁄16
L4 ×3 ×1⁄4
12.3
12.7
13.6
14.8
14.0
3.59
3.71
3.96
4.33
4.09
17.9
18.5
19.0
19.8
19.5
8.0
8.5
8.9
9.8
9.5
4.8
4.8
4.9
5.0
5.0
2.24
2.23
2.19
2.14
2.19
2.24
2.17
2.13
2.02
2.06
6.75
6.90
7.23
7.54
7.36
1.40
1.26
1.26
1.11
1.13
C7×9.8
L21⁄2×21⁄2×1⁄4
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L3×21⁄2 ×5⁄16
L4 ×3 ×1⁄4
L3×2
×5⁄16
13.9
14.3
15.2
16.4
15.6
17.0
4.06
4.18
4.43
4.80
4.56
4.96
28.5
29.3
30.0
31.2
30.8
32.0
10.6
11.2
11.8
12.9
12.4
13.7
6.6
6.7
6.7
6.8
6.8
6.9
2.65
2.65
2.60
2.55
2.60
2.54
2.68
2.61
2.54
2.42
2.48
2.35
9.13
9.31
9.64
9.99
9.81
10.2
1.67
1.53
1.53
1.35
1.39
1.20
C8×11.5
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L3×21⁄2 ×5⁄16
L4 ×3 ×1⁄4
L3×2
×5⁄16
L5 ×31⁄2×5⁄16
16.0
16.9
18.1
17.3
18.7
20.2
4.69
4.94
5.31
5.07
5.47
5.94
43.9
44.9
46.7
46.0
47.8
49.9
14.3
15.1
16.4
15.8
17.3
18.9
8.9
9.0
9.0
9.0
9.1
9.3
3.06
3.02
2.97
3.01
2.96
2.90
3.07
2.98
2.84
2.91
2.76
2.64
12.2
12.6
13.0
12.8
13.2
13.9
1.81
1.81
1.60
1.67
1.45
1.30
C9×13.4
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L3×21⁄2 ×5⁄16
L4 ×3 ×1⁄4
L3×2
×5⁄16
L5 ×31⁄2×5⁄16
17.9
18.8
20.0
19.2
20.6
22.1
5.25
5.50
5.87
5.63
6.03
6.50
63.1
64.6
67.1
66.0
68.7
71.4
17.8
18.8
20.4
19.6
21.4
23.4
11.6
11.6
11.7
11.7
11.8
12.0
3.47
3.43
3.38
3.42
3.37
3.31
3.54
3.45
3.29
3.37
3.20
3.06
15.8
16.1
16.6
16.3
16.8
17.5
2.11
2.11
1.87
1.98
1.73
1.58
C10×15.3
L31⁄2×3 ×1⁄4
L3×21⁄2 ×5⁄16
L4 ×3 ×1⁄4
L3×2
×5⁄16
L5 ×31⁄2×5⁄16
L3×21⁄2 ×3⁄8
20.7
21.9
21.1
22.5
24.0
25.7
6.05
6.42
6.18
6.58
7.05
7.54
89.3
92.7
91.1
94.7
98.4
102
22.8
24.8
23.8
25.9
28.2
30.6
14.7
14.8
14.8
14.9
15.1
15.2
3.84
3.80
3.84
3.79
3.74
3.67
3.91
3.74
3.83
3.65
3.49
3.33
20.0
20.6
20.3
20.9
21.6
22.2
2.39
2.12
2.26
1.98
1.84
1.61
Channel
in.
S2 =
I / y2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMBINATION SECTIONS
1 - 115
COMBINATION SECTIONS
Channels and angles
Properties of sections
Y
y
2
X
X
Long leg of angle turned out
y , yp
1
x1
xp
x2
Y
Axis Y-Y
S1 =
I / x1
I
3
3
r
x1
Z
xp
3
in.
in.
in.
in.
in.
in.
C6×8.2
L21⁄2×21⁄2×1⁄4
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
2.6
3.6
4.9
5.7
6.5
1.0
1.2
1.4
1.7
1.7
1.4
1.9
2.4
2.7
3.1
0.85
0.98
1.11
1.14
1.26
2.60
3.01
3.40
3.31
3.79
2.02
2.38
2.82
3.27
3.30
2.60
3.09
3.57
3.54
4.06
C7×9.8
L21⁄2×21⁄2×1⁄4
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
L31⁄2
×5⁄16
3.0
4.0
5.4
6.3
7.1
8.3
1.1
1.3
1.6
1.8
18
2.2
1.6
2.0
2.6
2.9
3.2
3.6
0.86
0.98
1.10
1.14
1.25
1.29
2.67
3.09
3.48
3.40
3.88
3.78
2.31
2.66
3.11
3.57
3.59
4.16
2.62
3.11
3.59
3.57
4.08
4.05
C8×11.5
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
L3×3
×5⁄16
L5 ×31⁄2×5⁄16
4.6
6.0
6.9
7.8
9.0
14.7
14
1.7
2.0
2.0
2.3
3.2
2.2
2.7
3.0
3.4
3.8
5.6
0.99
1.10
1.14
1.24
1.28
1.57
3.16
3.56
3.48
3.97
3.87
4.64
3.00
3.45
3.91
3.93
4.51
5.97
3.13
3.61
3.59
4.10
4.08
5.05
C9×13.4
L3 ×21⁄2×1⁄4
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
L3×3
×5⁄16
L5 ×31⁄2×5⁄16
5.2
6.7
7.7
8.5
9.9
15.8
1.6
1.8
2.2
2.1
2.5
3.3
2.3
2.9
3.2
3.6
4.0
5.9
0.99
1.10
1.14
1.23
1.28
1.56
3.22
3.64
3.55
4.05
3.96
4.74
3.38
3.83
4.31
4.32
4.91
6.38
3.14
3.63
3.61
4.12
4.10
5.08
C10×15.3
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
L3×3
×5⁄16
L5 ×31⁄2×5⁄16
L31⁄2×3 ×3⁄8
7.4
8.5
9.4
10.8
16.9
19.2
2.0
2.3
2.3
2.7
3.5
4.1
3.1
3.4
3.8
4.2
6.1
6.7
1.11
1.15
1.23
1.28
1.55
1.60
3.70
3.62
4.12
4.03
4.83
4.73
4.25
4.73
4.74
5.34
6.82
7.70
3.64
3.63
4.14
4.12
5.09
5.07
Channel
Angle
in.
4
S2 =
I / x2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 116
DIMENSIONS AND PROPERTIES
COMBINATION SECTIONS
Channels and angles
Properties of sections
Y
y
2
X
X
Long leg of angle turned out
y , yp
1
x1
xp
x2
Y
Total
Weight
per ft
Axis X-X
Total
Area
2
S1 =
I / y1
I
4
3
S2 =
I / y2
3
r
y1
Z
yp
3
Angle
lb
in.
in.
in.
in.
in.
in.
in.
in.
C12×20.7
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
L31⁄2×3 ×5⁄16
L5 ×31⁄2×5⁄16
L5×31⁄2 ×3⁄8
L6 ×4 ×3⁄8
L5×3
×1⁄2
26.1
27.3
26.5
27.9
29.4
31.1
33.0
36.9
7.65
8.02
7.78
8.18
8.65
9.14
9.70
10.84
164
170
167
173
180
186
192
202
33.2
35.8
34.4
37.2
40.2
43.4
46.6
53.2
23.2
23.5
23.4
23.6
23.9
24.1
24.3
24.7
4.63
4.61
4.63
4.60
4.56
4.51
4.45
4.32
4.94
4.75
4.86
4.66
4.47
4.29
4.12
3.80
31.4
32.2
31.8
32.6
33.5
34.2
35.3
36.7
3.23
2.80
3.01
2.67
2.53
2.25
2.11
1.68
C12×25
L31⁄2×3 ×1⁄4
L5×31⁄2 ×5⁄16
L4 ×3 ×1⁄4
L5×3
×5⁄16
L5 ×31⁄2×5⁄16
L5×31⁄2 ×3⁄8
L6 ×4 ×3⁄8
L5×3
×1⁄2
30.4
31.6
30.8
32.2
33.7
35.4
37.3
41.2
8.91
9.28
9.04
9.44
9.91
10.40
10.96
12.10
180
187
183
190
197
204
211
223
35.4
38.0
36.6
39.3
42.3
45.4
48.7
55.3
26.1
26.4
26.3
26.6
26.9
27.2
27.5
28.0
4.50
4.49
4.50
4.49
4.46
4.43
4.39
4.29
5.09
4.92
5.02
4.84
4.67
4.49
4.33
4.03
35.8
36.8
36.3
37.3
38.3
39.3
40.4
42.2
3.98
3.50
3.82
3.30
3.05
2.77
2.65
2.20
C15×33.9
L4 ×3 ×1⁄4
L5×3
×5⁄16
L5 ×31⁄2×5⁄16
L5×31⁄2 ×3⁄8
L6 ×4 ×3⁄8
L5×3
×1⁄2
39.7
41.1
42.6
44.3
46.2
50.1
11.65
12.05
12.52
13.01
13.57
14.71
383
395
408
421
434
458
58.7
62.4
66.5
70.8
75.4
84.8
45.1
45.6
46.1
46.5
46.9
47.7
5.73
5.73
5.71
5.69
5.65
5.58
6.52
6.33
6.14
5.94
5.76
5.40
60.1
61.8
63.4
64.8
66.2
68.6
5.39
4.89
4.30
3.69
3.48
2.92
Channel
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMBINATION SECTIONS
1 - 117
COMBINATION SECTIONS
Channels and angles
Properties of sections
Y
y
2
X
X
Long leg of angle turned out
y , yp
1
x1
xp
x2
Y
Axis Y-Y
S1 =
I / x1
I
3
3
r
x1
Z
xp
3
in.
in.
in.
in.
in.
in.
C12×20.7
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
L4×3
×5⁄16
L5 ×31⁄2×5⁄16
L31⁄2×3 ×3⁄8
L6 ×4 ×3⁄8
L4×3
×1⁄2
9.5
10.7
11.6
13.2
19.9
22.5
33.2
40.6
2.5
2.8
2.7
3.2
40
4.6
5.8
7.3
3.7
4.0
4.4
4.8
6.8
7.5
10.3
11.9
1.12
1.16
1.22
1.27
1.52
1.57
1.85
1.93
3.84
3.77
4.28
4.20
5.02
4.93
5.72
5.52
5.45
5.94
5.94
6.56
8.06
8.97
11.1
13.7
3.69
3.67
4.18
4.16
5.15
5.13
6.10
6.05
C12×25
L31⁄2×3 ×1⁄4
L31⁄2×3 ×5⁄16
L4 ×3 ×1⁄4
L4×3
×5⁄16
L5 ×31⁄2×5⁄16
L31⁄2×3 ×3⁄8
L6 ×4 ×3⁄8
L4×3
×1⁄2
10.2
11.4
12.3
13.9
20.8
23.5
34.5
42.3
2.6
3.0
2.8
3.3
4.1
4.7
5.9
7.5
3.8
4.2
4.5
5.0
7.0
7.7
10.7
12.4
1.07
1.11
1.17
1.22
1.45
1.50
1.77
1.87
3.87
3.81
4.32
4.25
5.09
5.00
5.81
5.63
5.88
6.40
6.38
7.02
8.54
9.48
11.7
14.3
3.74
3.72
4.23
4.22
5.20
5.18
6.15
6.11
C15×33.9
L4 ×3 ×1⁄4
L4×3
×5⁄16
L5 ×31⁄2×5⁄16
L31⁄2×3 ×3⁄8
L6 ×4 ×3⁄8
L4×3
×1⁄2
16.8
18.7
26.2
29.3
41.3
50.3
3.7
4.2
4.9
5.6
6.8
8.5
5.8
6.3
8.5
9.2
12.4
14.3
1.20
1.25
1.45
1.50
1.75
1.85
4.49
4.43
5.30
5.23
6.06
5.89
8.82
9.47
11.0
12.0
14.2
16.9
4.27
4.26
5.24
5.23
6.21
6.17
Channel
Angle
in.
4
S2 =
I / x2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 118
DIMENSIONS AND PROPERTIES
COMBINATION SECTIONS
Channels and angles
Properties of sections
Y
y
2
X
X
y , yp
1
1
x1
xp
Short leg of angle turned out
2
x2
Y
Total
Weight
per ft
Total
Area
2
3
in.
S2 =
I / y2
3
in.
r
y1
Z
yp
3
in.
in.
in.
in.
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
12.7
13.1
14.0
16.4
18.0
3.71
3.84
4.09
4.80
5.27
6.0
6.1
6.4
7.5
7.7
5.9
6.2
6.2
6.4
6.8
2.61
2.68
2.63
2.55
2.56
4.21
4.56
4.46
4.16
4.45
7.86
8.23
8.32
8.77
9.32
2.79
3.25
3.18
3.00
3.46
C 7×9.8
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
14.3
14.7
15.6
18.0
19.6
4.18
4.31
4.56
5.27
5.74
8.0
8.0
8.5
10.0
10.3
7.8
8.2
8.2
8.5
8.9
3.00
3.07
3.03
2.95
2.96
4.70
5.05
4.93
4.60
4.87
10.5
10.9
1 1.0
11.6
12.2
2.95
3.38
3.29
3.11
3.50
C 8×11.5
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
16.0
16.4
17.3
19.7
21.3
4.69
4.82
5.07
5.78
6.25
10.4
10.4
10.9
12.9
13.3
10.2
10.6
10.6
11.0
11.4
3.39
3.45
3.42
3.36
3.36
5.20
5.55
5.42
5.06
5.31
13.7
14.2
14.3
14.9
15.6
3.52
3.73
3.42
3.21
3.61
C 9×13.4
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
17.9
18.3
19.2
21.6
23.2
5.25
5.38
5.63
6.34
6.81
13.1
13.1
13.8
16.2
16.7
12.9
13.4
13.5
13.9
14.4
3.78
3.84
3.81
3.76
3.77
5.71
6.07
5.93
5.54
5.78
17.4
18.0
18.3
19.0
19.7
4.18
4.42
3.88
3.32
3.71
C10×15.3
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
19.8
20.2
21.1
23.5
25.1
5.80
5.93
6.18
6.89
7.36
16.2
16.1
17.0
19.9
20.5
16.0
16.5
16.6
17.1
17.7
4.17
4.22
4.20
4.17
4.18
6.22
6.58
6.43
6.02
6.25
21.4
22.1
22.5
23.5
24.2
4.77
5.01
4.48
3.44
3.81
C12×20.7
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
25.2
25.6
26.5
28.9
30.5
7.40
7.53
7.78
8.49
8.96
24.3
24.0
25.3
29.2
30.1
24.7
25.3
25.5
26.3
27.1
4.90
4.95
4.95
4.94
4.97
7.32
7.69
7.54
7.11
7.33
32.6
33.4
34.3
36.4
37.5
6.17
6.45
6.01
4.74
4.41
C15×33.9
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
38.8
39.7
42.1
43.7
11.40
11.65
12.36
12.83
42.7
44.5
50.1
51.4
47.2
47.7
49.1
50.3
5.95
5.96
6.01
6.05
9.45
9.31
8.91
9.15
61.1
62.5
66.5
69.0
8.70
8.39
7.50
7.41
Angle
in.
S1 =
I / y1
C 6×8.2
Channel
lb
Axis X-X
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMBINATION SECTIONS
1 - 119
COMBINATION SECTIONS
Channels and angles
Properties of sections
Y
y
2
X
Short leg of angle turned out
X
y , yp
1
1
x1
xp
2
x2
Y
Axis Y-Y
S1 =
I / x1
r
x1
Z
xp
3
in.
in.
in.
in.
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
2.4
2.8
3.8
6.0
8.4
4.4
4.6
6.6
9.3
12.1
1.22
1.26
1.64
2.05
2.47
2.25
2.18
2.85
3.33
3.82
3.70
4.01
5.46
8.29
11.3
2.65
2.59
3.46
4.12
4.84
C 7×9.8
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
2.6
2.9
3.9
6.1
8.6
5.0
5.2
7.5
10.5
13.6
1.19
1.23
1.60
2.01
2.44
2.32
2.25
2.95
3.47
3.98
4.03
4.35
5.82
8.71
11.8
2.72
2.67
3.55
4.24
4.99
C 8×11.5
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
2.7
3.0
4.0
6.3
8.7
5.6
5.8
8.3
11.7
15.2
1.16
1.20
1.55
1.97
2.40
2.37
2.31
3.03
3.58
4 13
4.40
4.73
6.21
9.16
12.3
2.78
2.73
3.62
4.34
5.12
C 9×13.4
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
2.8
3.2
4.2
6.4
8.9
6.2
6.5
9.2
12.9
16.9
1.14
1.18
1.51
1.92
2.36
2.40
2.35
3.10
3.68
4.26
4.81
5.15
6.65
9.66
12.8
2.84
2.79
3.70
4.43
5.23
C10×15.3
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
3.0
3.4
4.3
6.5
9.0
6.8
7.1
10.0
14.0
18.3
1.12
1.16
1.48
1.88
2.31
2.42
2.37
3.15
3.76
4.36
5.25
5.59
7.10
10.1
13.3
2.88
2.84
3.74
4.49
5.31
C12×20.7
L3×21⁄2×1⁄4
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
3.6
4.0
4.7
6.9
9.3
8.6
8.9
12.2
17.0
22.4
1.10
1.13
1.40
1.78
2 19
2.47
2.43
3.25
3.92
4.59
6.47
6.82
8.37
11.5
14.8
3.01
2.97
3.89
4.67
5.52
C15×33.9
L3×3 ×1⁄4
L4×3 ×1⁄4
L5×3 ×5⁄16
L6×31⁄2×5⁄16
5.6
5.9
7.8
10.2
13.5
17.2
23.4
30.7
1.10
1.30
1.61
1.97
2.48
3.35
4.12
4.88
9.54
11.1
14.5
18.0
3.12
4.11
5.02
5.90
Angle
in.
3
C 6×8.2
Channel
in.
3
S2 =
I / x2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 120
DIMENSIONS AND PROPERTIES
STEEL PIPE AND STRUCTURAL TUBING
General
When designing and specifying steel pipe or tubing as compression members, refer to
comments in the notes for Columns, Steel Pipe, and Structural Tubing, in Part 3. For
standard mill practices and tolerances, refer to page 1-183. For material specifications
and availability, see Tables 1-4 through 1-6, Part 1.
Steel Pipe
The Tables of Dimensions and Properties of Steel Pipe (unfilled) list a selected range of
sizes of standard, extra strong, and double-extra strong pipe. For a complete range of
sizes manufactured, refer to catalogs of the manufacturers or to the American Institute
for Hollow Structural Sections (AIHSS).
Structural Tubing
The Tables of Dimensions and Properties of Square and Rectangular Structural Tubing
(unfilled) list a selected range of frequently used sizes. For dimensions and properties of
other sizes, refer to catalogs from the manufacturers or AIHSS.
The tables are based on an outside corner radius equal to two times the specified wall
thickness. Material specifications stipulate that the outside corner radius may vary up to
three times the specified wall thickness. This variation should be considered in those
details where a close match or fit is important.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STEEL PIPE AND STRUCTURAL TUBING
1 - 121
PIPE
Dimensions and properties
Dimensions
Weight
Nominal Outside
Inside
Wall
per ft lbs
Diameter Diameter Diameter Thickness Plain
Ends
in.
in.
in.
in.
Properties
Area
I
S
r
J
Z
in.2
in.4
in.3
in.
in.4
in.3
0.041
0.071
0.133
0.235
0.326
0.561
1.06
1.72
2.39
3.21
5.45
8.50
16.8
29.9
43.8
0.261
0.334
0.421
0.540
0.623
0.787
0.947
1.16
1.34
1.51
1.88
2.25
2.94
3.67
4.38
0.034
0.074
0.175
0.389
0.620
1.33
3.06
6.03
9.58
14.5
30.3
56.3
145
321
559
0.059
0.100
0.187
0.324
0.448
0.761
1.45
2.33
3.22
4.31
7.27
11.2
22.2
39.4
57.4
0.048
0.085
0.161
0.291
0.412
0.731
1.34
2.23
3.14
4.27
7.43
12.2
24.5
39.4
56.7
0.250
0.321
0.407
0.524
0.605
0.766
0.924
1.14
1.31
1.48
1.84
2.19
2.88
3.63
4.33
0.040
0.090
0.211
0.484
0.782
1.74
3.85
8.13
12.6
19.2
41.3
81.0
211
424
723
0.072
0.125
0.233
0.414
0.581
1.02
1.87
3.08
4.32
5.85
10.1
16.6
33.0
52.6
75.1
1.10
2.00
3.42
6.79
12.1
20.0
37.6
0.703
0.844
1.05
1.37
1.72
2.06
2.76
2.62
5.74
12.0
30.6
67.3
133
324
1.67
3.04
5.12
9.97
17.5
28.9
52.8
Standard Weight
1⁄
2
3⁄
4
0.840
1.050
1.315
1.660
1.900
2.375
2.875
3.500
4.000
4.500
5.563
6.625
8.625
10.750
12.750
0.622
0.824
1.049
1.380
1.610
2.067
2.469
3.068
3.548
4.026
5.047
6.065
7.981
10.020
12.000
0.109
0.113
0.133
0.140
0.145
0.154
0.203
0.216
0.226
0.237
0.258
0.280
0.322
0.365
0.375
0.85
1.13
1.68
2.27
2.72
3.65
5.79
7.58
9.11
10.79
14.62
18.97
28.55
40.48
49.56
1
11⁄4
11⁄2
2
21⁄2
3
31⁄2
4
5
6
8
10
12
0.840
1.050
1.315
1.660
1.900
2.375
2.875
3.500
4.000
4.500
5.563
6.625
8.625
10.750
12.750
0.546
0.742
0.957
1.278
1.500
1.939
2.323
2.900
3.364
3.826
4.813
5.761
7.625
9.750
11.750
0.147
0.154
0.179
0.191
0.200
0.218
0.276
0.300
0.318
0.337
0.375
0.432
0.500
0.500
0.500
1.09
1.47
2.17
3.00
3.63
5.02
7.66
10.25
12.50
14.98
20.78
28.57
43.39
54.74
65.42
2
21⁄2
3
4
5
6
8
2.375
2.875
3.500
4.500
5.563
6.625
8.625
1.503
1.771
2.300
3.152
4.063
4.897
6.875
0.436
0.552
0.600
0.674
0.750
0.864
0.875
1
11⁄4
11⁄2
2
21⁄2
3
31⁄2
4
5
6
8
10
12
0.250
0.333
0.494
0.669
0.799
1.07
1.70
2.23
2.68
3.17
4.30
5.58
8.40
11.9
14.6
0.017
0.037
0.087
0.195
0.310
0.666
1.53
3.02
4.79
7.23
15.2
28.1
72.5
161
279
Extra Strong
1⁄
2
3⁄
4
0.320
0.433
0.639
0.881
1.07
1.48
2.25
3.02
3.68
4.41
6.11
8.40
12.8
16.1
19.2
0.020
0.045
0.106
0.242
0.391
0.868
1.92
3.89
6.28
9.61
20.7
40.5
106
212
362
Double-Extra Strong
9.03
13.69
18.58
27.54
38.59
53.16
72.42
2.66
4.03
5.47
8.10
11.3
15.6
21.3
1.31
2.87
5.99
15.3
33.6
66.3
162
The listed sections are available in conformance with ASTM Specification A53 Grade B or A501. Other sections
are made to these specifications. Consult with pipe manufacturers or distributors for availability.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 122
DIMENSIONS AND PROPERTIES
STRUCTURAL TUBING
Square
Dimensions and properties
Dimensions
Properties**
Nominal*
Size
Wall
Thickness
Weight
per ft
Area
I
S
r
J
Z
in.
in.
lb
in.2
in.4
in.3
in.
in.4
in.3
0.6250
5⁄
8
246.47
72.4
10300
690
12.0
16000
794
28×28
0.6250
5⁄
8
229.45
67.4
8360
597
11.1
13000
689
26×26
0.6250
5⁄
8
212.44
62.4
6650
511
10.3
10400
591
24×24
24×24
24×24
0.6250
0.5000
0.3750
5⁄
8
1⁄
2
3⁄
8
195.43
157.74
119.35
57.4
46.4
35.1
5180
4240
3250
432
353
270
9.50
9.56
9.62
8100
6570
4990
500
407
310
22×22
22×22
22×22
0.6250
0.5000
0.3750
5⁄
8
1⁄
2
3⁄
8
178.41
144.13
109.15
52.4
42.4
32.1
3950
3240
2490
359
294
226
8.68
8.74
8.80
6200
5030
3830
418
340
259
20×20
20×20
20×20
0.6250
0.5000
0.3750
5⁄
8
1⁄
2
3⁄
8
161.40
130.52
98.94
47.4
38.4
29.1
2940
2410
1850
294
241
185
7.87
7.93
7.99
4620
3760
2870
342
279
213
18×18
18×18
18×18
0.6250
0.5000
0.3750
5⁄
8
1⁄
2
3⁄
8
144.39
116.91
88.73
42.4
34.4
26.1
2110
1740
1340
234
193
149
7.05
7.11
7.17
3340
2720
2080
274
224
172
30×30
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STEEL PIPE AND STRUCTURAL TUBING
1 - 123
STRUCTURAL TUBING
Square
Dimensions and properties
Dimensions
Properties**
Nominal*
Size
Wall
Thickness
Weight
per ft
Area
I
S
r
J
Z
in.
in.
lb
in.2
in.4
in.3
in.
in.4
in.3
127.37
103.30
78.52
65.87
37.4
30.4
23.1
19.4
1450
1200
931
789
182
150
116
98.6
6.23
6.29
6.35
6.38
2320
1890
1450
1220
214
175
134
113
110.36
89.68
68.31
57.36
32.4
26.4
20.1
16.9
952
791
615
522
136
113
87.9
74.6
5.42
5.48
5.54
5.57
1530
1250
963
812
161
132
102
86.1
93.34
76.07
58.10
48.86
39.43
27.4
22.4
17.1
14.4
11.6
580
485
380
324
265
96.7
80.9
63.4
54.0
44.1
4.60
4.66
4.72
4.75
4.78
943
777
599
506
410
116
95.4
73.9
62.6
50.8
76.33
62.46
47.90
40.35
32.63
24.73
22.4
18.4
14.1
11.9
9.59
7.27
321
271
214
183
151
116
64.2
54.2
42.9
36.7
30.1
23.2
3.78
3.84
3.90
3.93
3.96
3.99
529
439
341
289
235
179
77.6
64.6
50.4
42.8
34.9
26.6
16×16
14×14
12×12
10×10
0.6250
0.5000
0.3750
0.3125
0.6250
0.5000
0.3750
0.3125
0.6250
0.5000
0.3750
0.3125
0.2500
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
5⁄
1⁄
3⁄
8
2
8
5⁄
16
5⁄
1⁄
8
2
3⁄
8
5⁄
16
5⁄
1⁄
8
2
3⁄
8
5⁄
16
1⁄
4
5⁄
1⁄
3⁄
8
2
8
5⁄
16
1⁄
4
3⁄
16
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 124
DIMENSIONS AND PROPERTIES
STRUCTURAL TUBING
Square
Dimensions and properties
Dimensions
Properties**
Nominal*
Size
Wall
Thickness
Weight
per ft
Area
I
S
r
J
Z
in.
in.
lb
in.2
in.4
in.3
in.
in.4
in.3
8×8
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
59.32
48.85
37.69
31.84
25.82
19.63
17.4
14.4
11.1
9.36
7.59
5.77
153
131
106
90.9
75.1
58.2
38.3
32.9
26.4
22.7
18.8
14.6
2.96
3.03
3.09
3.12
3.15
3.18
258
217
170
145
118
90.6
47.2
39.7
31.3
26.7
21.9
16.8
7×7
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
50.81
42.05
32.58
27.59
22.42
17.08
14.9
12.4
9.58
8.11
6.59
5.02
97.5
84.6
68.7
59.5
49.4
38.5
27.9
24.2
19.6
17.0
14.1
11.0
2.56
2.62
2.68
2.71
2.74
2.77
166
141
112
95.6
78.3
60.2
34.8
29.6
23.5
20.1
16.5
12.7
6×6
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
42.30
35.24
27.48
23.34
19.02
14.53
9.86
12.4
10.4
8.08
6.86
5.59
4.27
2.90
57.3
50.5
41.6
36.3
30.3
23.8
16.5
19.1
16.8
13.9
12.1
10.1
7.93
5.52
2.15
2.21
2.27
2.30
2.33
2.36
2.39
99.5
85.6
68.5
58.9
48.5
37.5
25.7
24.3
20.9
16.8
14.4
11.9
9.24
6.35
51⁄2×51⁄2
0.3750
0.3125
0.2500
0.1875
0.1250
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
24.93
21.21
17.32
13.25
9.01
7.33
6.23
5.09
3.89
2.65
31.2
27.4
23.0
18.1
12.6
11.4
9.95
8.36
6.58
4.60
2.07
2.10
2.13
2.16
2.19
51.9
44.8
37.0
28.6
19.7
13.8
12.0
9.91
7.70
5.31
5×5
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
28.43
22.37
19.08
15.62
11.97
8.16
8.36
6.58
5.61
4.59
3.52
2.40
27.0
22.8
20.1
16.9
13.4
9.41
10.8
9.11
8.02
6.78
5.36
3.77
1.80
1.86
1.89
1.92
1.95
1.98
46.8
38.2
33.1
27.4
21.3
14.7
13.7
11.2
9.70
8.07
6.29
4.36
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STEEL PIPE AND STRUCTURAL TUBING
1 - 125
STRUCTURAL TUBING
Square
Dimensions and properties
Dimensions
Properties**
Nominal*
Size
Wall
Thickness
Weight
per ft
Area
I
S
r
J
Z
in.
in.
lb
in.2
in.4
in.3
in.
in.4
in.3
41⁄2×41⁄2
0.3750
0.3125
0.2500
0.1875
0.1250
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
19.82
16.96
13.91
10.70
7.31
5.83
4.98
4.09
3.14
2.15
16.0
14.2
12.1
9.60
6.78
7.10
6.30
5.36
4.27
3.02
1.66
1.69
1.72
1.75
1.78
27.1
23.6
19.7
15.4
10.6
8.81
7.68
6.43
5.03
3.50
4×4
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
1⁄
5⁄
16
1⁄
4
3⁄
16
1⁄
8
21.63
17.27
14.83
12.21
9.42
6.46
6.36
5.08
4.36
3.59
2.77
1.90
12.3
10.7
9.58
8.22
6.59
4.70
6.13
5.35
4.79
4.11
3.30
2.35
1.39
1.45
1.48
1.51
1.54
1.57
21.8
18.4
16.1
13.5
10.6
7.40
8.02
6.72
5.90
4.97
3.91
2.74
31⁄2×31⁄2
0.3125
0.2500
0.1875
0.1250
5⁄
16
1⁄
4
3⁄
16
1⁄
8
12.70
10.51
8.15
5.61
3.73
3.09
2.39
1.65
6.09
5.29
4.29
3.09
3.48
3.02
2.45
1.76
1.28
1.31
1.34
1.37
10.4
8.82
6.99
4.90
4.35
3.69
2.93
2.07
3×3
0.3125
0.2500
0.1875
0.1250
5⁄
16
1⁄
4
3⁄
16
1⁄
8
10.58
8.81
6.87
4.75
3.11
2.59
2.02
1.40
3.58
3.16
2.60
1.90
2.39
2.10
1.73
1.26
1.07
1.10
1.13
1.16
6.22
5.35
4.28
3.03
3.04
2.61
2.10
1.49
21⁄2×21⁄2
0.3125
0.2500
0.1875
0.1250
5⁄
16
1⁄
4
3⁄
16
1⁄
8
8.45
7.11
5.59
3.90
2.48
2.09
1.64
1.15
1.87
1.69
1.42
1.06
1.50
1.35
1.14
0.847
0.868
0.899
0.930
0.961
3.32
2.92
2.38
1.71
1.96
1.71
1.40
1.01
2×2
0.3125
0.2500
0.1875
0.1250
5⁄
16
1⁄
4
3⁄
16
1⁄
8
6.32
5.41
4.32
3.05
1.86
1.59
1.27
0.897
0.815
0.766
0.668
0.513
0.815
0.766
0.668
0.513
0.662
0.694
0.726
0.756
1.49
1.36
1.15
0.846
1.11
1.00
0.840
0.621
11⁄2×11⁄2
0.1875
3⁄
16
3.04
0.894
0.242
0.323
0.521
0.431
0.423
3⁄
2
8
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 126
DIMENSIONS AND PROPERTIES
Y
X
X
STRUCTURAL TUBING
Rectangular
Dimensions and properties
Y
Dimensions
Properties**
Nominal*
Wall
Weight
Size
Thickness per ft Area
in.
in.
2
X-X Axis
S
I
4
Z
3
Y-Y Axis
r
3
S
I
4
Z
3
3
r
J
lb
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.4
178.16
134.67
112.66
52.4
39.6
33.1
7110 474
5430 362
4570 305
555
422
354
11.7
11.7
11.7
5070
3870
3260
422
323
272
477
363
304
9.84
9.89
9.92
9170
6960
5830
30×24
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
28×24
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
171.35
129.56
108.41
50.4
38.1
31.9
6050 432
4630 331
3890 278
503
383
321
11.0
11.0
11.1
4790
3660
3080
399
305
257
454
345
290
9.75
9.81
9.84
8280
6290
5270
26×24
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
164.55
124.46
104.15
48.4
36.6
30.6
5100 392
3900 300
3280 253
454
345
290
10.3
10.3
10.4
4510
3460
2910
376
288
242
430
327
275
9.66
9.72
9.75
7410
5630
4720
24×22
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
150.93
114.25
95.64
44.4
33.6
28.1
3960 330
3040 253
2560 213
383
292
245
9.45 3470
9.51 2660
9.54 2240
315
242
204
361
275
231
8.84
8.90
8.93
5740
4370
3660
22×20
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
137.32
104.04
87.14
40.4
30.6
25.6
3010 273
2310 210
1950 177
318
243
204
8.63 2600
8.69 2000
8.72 1690
260
200
169
298
228
192
8.03
8.09
8.12
4350
3310
2780
20×18
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
123.71
93.83
78.63
36.4
27.6
23.1
2220 222
1710 171
1440 144
259
198
167
7.81 1890
7.88 1460
7.91 1230
210
162
137
242
185
155
7.21
7.27
7.30
3190
2440
2050
20×12
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
103.30
78.52
65.87
30.4
23.1
19.4
1650 165
1280 128
1080 108
201
154
130
7.37
7.45
7.47
750
583
495
125
141
97.2 109
82.5 91.8
4.97
5.03
5.06
1650
1270
1070
20×8
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
89.68
68.31
57.36
26.4
20.1
16.9
1270 127
162
988 98.8 125
838 83.8 105
6.94
7.02
7.05
300
236
202
20×4
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
76.07
58.10
48.86
22.4
17.1
14.4
889
699
596
88.9 123
69.9 95.3
59.6 80.8
6.31
6.40
6.44
61.6
50.3
43.7
75.1
59.1
50.4
84.7
65.6
55.6
3.38
3.43
3.46
806
625
529
30.8
25.1
21.8
36.0
28.5
24.3
1.66
1.72
1.74
205
165
143
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STEEL PIPE AND STRUCTURAL TUBING
1 - 127
STRUCTURAL TUBING
Rectangular
Dimensions and properties
Y
X
X
Y
Dimensions
Properties**
Nominal*
Wall
Weight
Size
Thickness per ft Area
in.
in.
lb
in.2
X-X Axis
Y-Y Axis
I
S
Z
r
I
S
Z
r
J
in.4
in.3
in.3
in.
in.4
in.3
in.3
in.
in.4
6.71
6.78
6.81
684
533
452
114
130
88.8 100
75.3 84.5
4.91
4.97
5.00
1420
1090
920
53.9
42.1
35.8
29.2
2.52
2.57
2.60
2.63
410
322
274
224
103
118
80.3 91.3
68.2 77.2
4.84
4.90
4.93
1200
922
777
18×12
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
96.49
73.42
61.62
28.4
21.6
18.1
18×6
0.5000
0.3750
0.3125
0.2500
1⁄
2
3⁄
8
5⁄
16
1⁄
4
76.07
58.10
48.86
39.43
22.4
17.1
14.4
11.6
818
641
546
447
90.9 119
71.3 92.2
60.7 78.1
49.6 63.5
6.05
6.13
6.17
6.21
141
113
97.0
80.0
16×12
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
89.68
68.31
57.36
26.4
20.1
16.9
962
748
635
120 144
93.5 111
79.4 93.8
6.04
6.11
6.14
618
482
409
16×8
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
76.07
58.10
48.86
22.4
17.1
14.4
722
565
481
90.2 113
70.6 87.6
60.1 74.2
5.68
5.75
5.79
244
193
165
16×4
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
62.46
47.90
40.35
18.4
14.1
11.9
481
382
327
60.2
47.8
40.9
82.2
64.2
54.5
5.12
5.21
5.25
14×12
0.5000
0.3750
1⁄
2
3⁄
8
82.88
63.21
24.4
18.6
699
546
99.9 119
78.0 91.7
5.36
5.42
14×10
0.5000
0.3750
0.3125
1⁄
2
3⁄
8
5⁄
16
76.07
58.10
48.86
22.4
17.1
14.4
608
476
405
86.9 105
68.0 81.5
57.9 69.0
14×6
0.6250
0.5000
0.3750
0.3125
0.2500
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
76.33
62.46
47.90
40.35
32.63
22.4
18.4
14.1
11.9
9.59
504
426
337
288
237
72.0
60.8
48.1
41.2
33.8
1280 142
172
991 110
132
840 93.3 111
94.0
78.3
61.1
51.9
42.3
47.2
37.6
32.3
26.7
61.0
48.2
41.2
69.7
54.2
45.9
3.30
3.36
3.39
599
465
394
24.6
20.2
17.6
29.0
23.0
19.7
1.64
1.69
1.72
157
127
110
552
431
91.9 107
71.9 82.6
4.76
4.82
983
757
5.22
5.28
5.31
361
284
242
72.3
56.8
48.4
83.6
64.8
54.9
4.02
4.08
4.11
730
564
477
4.74
4.82
4.89
4.93
4.97
130
111
89.1
76.7
63.4
43.3
37.1
29.7
25.6
21.1
51.2
42.9
33.6
28.7
23.4
2.41
2.46
2.52
2.54
2.57
352
296
233
199
162
49.3
40.4
35.1
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 128
DIMENSIONS AND PROPERTIES
Y
X
X
STRUCTURAL TUBING
Rectangular
Dimensions and properties
Y
Dimensions
Properties**
Nominal*
Wall
Weight
Size
Thickness per ft Area
in.
in.
lb
in.2
X-X Axis
Y-Y Axis
I
S
Z
r
I
S
Z
r
J
in.4
in.3
in.3
in.
in.4
in.3
in.3
in.
in.4
49.0
43.1
35.4
30.9
25.8
20.2
24.5
21.5
17.7
15.4
12.9
10.1
30.0
25.5
20.3
17.4
14.3
11.1
1.57
1.62
1.68
1.71
1.73
1.76
154
134
108
93.1
77.0
59.7
14×4
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
67.82
55.66
42.79
36.10
29.23
22.18
19.9
16.4
12.6
10.6
8.59
6.52
392
335
267
230
189
146
56.0
47.8
38.2
32.8
27.0
20.9
77.3
64.8
50.8
43.3
35.4
27.1
4.44
4.52
4.61
4.65
4.69
4.74
12×10
0.5000
0.3750
0.3125
0.2500
1⁄
2
3⁄
8
5⁄
16
1⁄
4
69.27
53.00
44.60
36.03
20.4
15.6
13.1
10.6
419
330
281
230
69.9
55.0
46.9
38.4
83.9
65.2
55.2
44.9
4.54
4.60
4.63
4.66
316
249
213
174
63.3
49.8
42.6
34.9
74.1
57.6
48.8
39.7
3.94
4.00
4.03
4.06
581
450
381
309
12×8
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
76.33
62.46
47.90
40.35
32.63
24.73
22.4
18.4
14.1
11.9
9.59
7.27
418
353
279
239
196
151
69.7
58.9
46.5
39.8
32.6
25.1
87.1
72.4
56.5
47.9
39.1
29.8
4.32
4.39
4.45
4.49
4.52
4.55
221
188
149
128
105
81.1
55.3
46.9
37.3
32.0
26.3
20.3
65.6
54.7
42.7
36.3
29.6
22.7
3.14
3.20
3.26
3.28
3.31
3.34
481
401
312
265
216
165
12×6
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
67.82
55.66
42.79
36.10
29.23
22.18
19.9
16.4
12.6
10.6
8.59
6.52
337
287
228
196
161
124
56.2
47.8
38.1
32.6
26.9
20.7
72.9
60.9
47.7
40.6
33.2
25.4
4.11
4.19
4.26
4.30
4.33
4.37
112
96.0
77.2
66.6
55.2
42.8
37.2
32.0
25.7
22.2
18.4
14.3
44.5
37.4
29.4
25.1
20.6
15.8
2.37
2.42
2.48
2.51
2.53
2.56
286
241
190
162
132
101
12×4
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
59.32
48.85
37.69
31.84
25.82
19.63
17.4
14.4
11.1
9.36
7.59
5.77
257
221
178
153
127
98.2
42.8
36.8
29.6
25.5
21.1
16.4
58.6
49.4
39.0
33.3
27.3
21.0
3.84
3.92
4.01
4.05
4.09
4.13
41.8
36.9
30.5
26.6
22.3
17.5
20.9
18.5
15.2
13.3
11.1
8.75
25.8
22.0
17.6
15.1
12.5
9.63
1.55
1.60
1.66
1.69
1.71
1.74
127
110
89.0
76.9
63.6
49.3
12×3
0.3125
0.2500
0.1875
5⁄
16
1⁄
4
3⁄
16
29.72
24.12
18.35
8.73 132
7.09 109
5.39 85.1
22.0
18.2
14.2
29.7
24.4
18.8
3.89
3.93
3.97
13.8
11.7
9.28
9.19 10.6
7.79 8.80
6.19 6.84
1.26
1.28
1.31
43.6
36.5
28.7
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STEEL PIPE AND STRUCTURAL TUBING
1 - 129
STRUCTURAL TUBING
Rectangular
Dimensions and properties
Y
X
X
Y
Dimensions
Properties**
Nominal*
Wall
Weight
Size
Thickness per ft Area
in.
in.
X-X Axis
Y-Y Axis
I
S
Z
r
I
S
Z
r
J
lb
in.2
in.4
in.3
in.3
in.
in.4
in.3
in.3
in.
in.4
92.2 15.4
72.0 12.0
21.4
16.6
3.74
3.79
12×2
0.2500
0.1875
1⁄
4
3⁄
16
22.42
17.08
6.59
5.02
10×8
0.5000
0.3750
0.3125
0.2500
0.1875
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
55.66
42.79
36.10
29.23
22.18
16.4
12.6
10.6
8.59
6.52
226
180
154
127
97.9
45.2
35.9
30.8
25.4
19.6
55.1
43.1
36.7
30.0
23.0
3.72
3.78
3.81
3.84
3.87
160
127
109
90.2
69.7
39.9
31.8
27.3
22.5
17.4
47.2
37.0
31.5
25.8
19.7
3.12
3.18
3.21
3.24
3.27
306
239
203
166
127
10×6
0.5000
0.3750
0.3125
0.2500
0.1875
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
48.85
37.69
31.84
25.82
19.63
14.4
11.1
9.36
7.59
5.77
181
145
125
103
79.8
36.2
29.0
25.0
20.6
16.0
45.6
35.9
30.7
25.1
19.3
3.55
3.62
3.65
3.69
3.72
80.8
65.4
56.5
46.9
36.5
26.9
21.8
18.8
15.6
12.2
31.9
25.2
21.5
17.7
13.6
2.37
2.43
2.46
2.49
2.51
187
147
126
103
79.1
10×5
0.3750
0.3125
0.2500
0.1875
3⁄
8
5⁄
16
1⁄
4
3⁄
16
35.13
29.72
24.12
18.35
10.3 128
8.73 110
7.09 91.2
5.39 70.8
25.5
22.0
18.2
14.2
32.3
27.6
22.7
17.4
3.51
3.55
3.59
3.62
42.9
37.2
31.1
24.3
17.1
14.9
12.4
9.71
19.9
17.0
14.0
10.8
2.04
2.07
2.09
2.12
107
91.5
75.2
58.0
10×4
0.5000
0.3750
0.3125
0.2500
0.1875
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
42.05
32.58
27.59
22.42
17.08
12.4 136
9.58 110
8.11 95.5
6.59 79.3
5.02 61.7
27.1
22.0
19.1
15.9
12.3
36.1
28.7
24.6
20.2
15.6
3.31
3.39
3.43
3.47
3.51
30.8
25.5
22.4
18.8
14.8
15.4
12.8
11.2
9.39
7.39
18.5
14.9
12.8
10.6
8.20
1.58
1.63
1.66
1.69
1.72
86.9
70.4
60.8
50.4
39.1
10×3
0.3750
0.3125
0.2500
0.1875
3⁄
8
5⁄
16
1⁄
4
3⁄
16
30.0
25.5
20.72
15.80
8.83
7.48
6.09
4.64
92.8
80.8
67.4
52.7
18.6
16.2
13.5
10.5
25.1
21.6
17.8
13.8
3.24
3.29
3.33
3.37
13.0
11.5
9.79
7.80
8.66 10.3
7.68 8.92
6.53 7.42
5.20 5.79
1.21
1.24
1.27
1.30
39.8
34.9
29.3
23.0
10×2
0.3750
0.3125
0.2500
0.1875
3⁄
8
5⁄
16
1⁄
4
3⁄
16
27.48
23.34
19.02
14.53
8.08
6.86
5.59
4.27
75.4 15.1
66.1 13.2
55.5 11.1
43.7 8.74
21.5
18.5
15.4
11.9
3.06
3.10
3.15
3.20
4.85
4.42
3.85
3.14
4.85
4.42
3.85
3.14
0.775
0.802
0.830
0.858
16.5
14.9
12.8
10.3
4.62
3.76
4.62
3.76
5.38 0.837
4.24 0.865
6.05
5.33
4.50
3.56
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
15.9
12.8
1 - 130
DIMENSIONS AND PROPERTIES
Y
X
X
STRUCTURAL TUBING
Rectangular
Dimensions and properties
Y
Dimensions
Properties**
Nominal*
Wall
Weight
Size
Thickness per ft Area
in.
in.
lb
in.2
X-X Axis
Y-Y Axis
I
S
Z
r
I
S
Z
r
J
in.4
in.3
in.3
in.
in.4
in.3
in.3
in.
in.4
8×6
0.5000
0.3750
0.3125
0.2500
0.1875
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
42.05
32.58
27.59
22.42
17.08
12.4 103
9.58 83.7
8.11 72.4
6.59 60.1
5.02 46.8
25.8
20.9
18.1
15.0
11.7
32.2
25.6
21.9
18.0
13.9
2.89
2.96
2.99
3.02
3.05
65.7
53.5
46.4
38.6
30.1
21.9
17.8
15.5
12.9
10.0
26.4
21.0
18.0
14.8
11.4
2.31
2.36
2.39
2.42
2.45
135
107
91.3
74.9
57.6
8×4
0.6250
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
42.30
35.24
27.48
23.34
19.02
14.53
9.86
12.4
10.4
8.08
6.86
5.59
4.27
2.90
21.3
18.8
15.5
13.5
11.3
8.83
6.14
28.8
24.7
19.9
17.1
14.1
11.0
7.53
2.62
2.69
2.77
2.80
2.84
2.88
2.91
27.4
24.6
20.6
18.1
15.3
12.0
8.45
13.7
12.3
10.3
9.05
7.63
6.02
4.23
17.3
15.0
12.2
10.5
8.72
6.77
4.67
1.49
1.54
1.60
1.62
1.65
1.68
1.71
73.2
64.1
52.2
45.2
37.5
29.1
20.0
8×3
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
31.84
24.93
21.21
17.32
13.25
9.01
9.36
7.33
6.23
5.09
3.89
2.65
61.0 15.3
51.0 12.7
44.7 11.2
37.6 9.40
29.6 7.40
20.7 5.17
21.0
17.0
14.7
12.2
9.49
6.55
2.55
2.64
2.68
2.72
2.76
2.80
12.1
10.4
9.25
7.90
6.31
4.48
8.05 10.1
6.92 8.31
6.16 7.24
5.26 6.05
4.21 4.73
2.99 3.29
1.14
1.19
1.22
1.25
1.27
1.30
35.7
29.9
26.3
22.1
17.3
12.1
8×2
0.3750
0.3125
0.2500
0.1875
0.1250
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
22.37
19.08
15.62
11.97
8.16
6.58
5.61
4.59
3.52
2.40
40.1 10.0 14.2
35.5 8.87 12.3
30.1 7.52 10.3
23.9 5.97 8.02
16.8 4.20 5.56
2.47
2.51
2.56
2.60
2.65
3.85
3.52
3.08
2.52
1.83
3.85
3.52
3.08
2.52
1.83
4.83
4.28
3.63
2.88
2.03
0.765
0.792
0.819
0.847
0.875
12.6
11.4
9.84
7.94
5.66
7×5
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
35.24
27.48
23.34
19.02
14.53
9.86
10.4
8.08
6.86
5.59
4.27
2.90
63.5
52.2
45.5
38.0
29.8
20.7
23.1
18.5
15.9
13.2
10.2
7.00
2.48
2.54
2.58
2.61
2.64
2.67
37.2
30.8
26.9
22.6
17.7
12.4
14.9
12.3
10.8
9.04
7.10
4.95
18.2
14.6
12.6
10.4
8.10
5.58
1.90
1.95
1.98
2.01
2.04
2.07
79.9
64.2
55.3
45.6
35.3
24.2
7×4
0.3750
0.3125
0.2500
0.1875
0.1250
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
24.93
21.21
17.32
13.25
9.01
7.33
6.23
5.09
3.89
2.65
44.0 12.6 16.0
38.5 11.0 13.8
32.3 9.23 11.5
25.4 7.26 8.91
17.7 5.07 6.15
2.45
2.49
2.52
2.55
2.59
18.1
16.0
13.5
10.7
7.51
9.06 10.8
7.98 9.36
6.75 7.78
5.34 6.06
3.76 4.19
1.57
1.60
1.63
1.66
1.68
43.3
37.5
31.2
24.2
16.7
85.1
75.1
61.9
53.9
45.1
35.3
24.6
18.1
14.9
13.0
10.9
8.50
5.91
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STEEL PIPE AND STRUCTURAL TUBING
1 - 131
STRUCTURAL TUBING
Rectangular
Dimensions and properties
Y
X
X
Y
Dimensions
Properties**
Nominal*
Wall
Weight
Size
Thickness per ft Area
in.
in.
X-X Axis
Y-Y Axis
I
S
Z
r
I
S
Z
r
J
lb
in.2
in.4
in.3
in.3
in.
in.4
in.3
in.3
in.
in.4
7×3
0.3750
0.3125
0.2500
0.1875
0.1250
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
22.37
19.08
15.62
11.97
8.16
6.58
5.61
4.59
3.52
2.40
35.7
31.5
26.6
21.1
14.8
10.2 13.5
9.00 11.8
7.61 9.79
6.02 7.63
4.22 5.29
2.33
2.37
2.41
2.45
2.48
9.08
8.11
6.95
5.57
3.96
6.05
5.41
4.63
3.71
2.64
7.32
6.40
5.36
4.20
2.93
1.18
1.20
1.23
1.26
1.29
25.1
22.0
18.5
14.6
10.2
6×4
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
28.43
22.37
19.08
15.62
11.97
8.16
8.36
6.58
5.61
4.59
3.52
2.40
35.3
29.7
26.2
22.1
17.4
12.2
11.8 15.4
9.90 12.5
8.72 10.9
7.36 9.06
5.81 7.06
4.08 4.88
2.06
2.13
2.16
2.19
2.23
2.26
18.4
15.6
13.8
11.7
9.32
6.57
9.21
7.82
6.92
5.87
4.66
3.29
11.5
9.44
8.21
6.84
5.34
3.71
1.48
1.54
1.57
1.60
1.63
1.66
42.1
34.6
30.1
25.0
19.5
13.5
6×3
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
25.03
19.82
16.96
13.91
10.70
7.31
7.36
5.83
4.98
4.09
3.14
2.15
27.7
23.8
21.1
17.9
14.3
10.1
9.25 12.6
7.92 10.4
7.03 9.11
5.98 7.62
4.76 5.97
3.36 4.15
1.94
2.02
2.06
2.09
2.13
2.17
8.91
7.78
6.98
6.00
4.83
3.45
5.94
5.19
4.65
4.00
3.22
2.30
7.59
6.34
5.56
4.67
3.68
2.57
1.10
1.16
1.18
1.21
1.24
1.27
23.9
20.3
17.9
15.1
11.9
8.27
6×2
0.3750
0.3125
0.2500
0.1875
0.1250
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
17.27
14.83
12.21
9.42
6.46
5.08
4.36
3.59
2.77
1.90
17.8
16.0
13.8
11.1
7.92
5.94
5.34
4.60
3.70
2.64
8.33
7.33
6.18
4.88
3.42
1.87
1.92
1.96
2.00
2.04
2.84
2.62
2.31
1.90
1.39
2.84
2.62
2.31
1.90
1.39
3.61
3.22
2.75
2.20
1.56
0.748
0.775
0.802
0.829
0.857
8.72
7.94
6.88
5.56
3.98
5×4
0.3750
0.3125
0.2500
0.1875
3⁄
8
5⁄
16
1⁄
4
3⁄
16
19.82
16.96
13.91
10.70
5.83
4.98
4.09
3.14
18.7
16.6
14.1
11.2
7.50
6.65
5.65
4.49
9.44
8.24
6.89
5.39
1.79
1.83
1.86
1.89
13.2
11.7
9.98
7.96
6.58
5.85
4.99
3.98
8.08
7.05
5.90
4.63
1.50
1.53
1.56
1.59
26.3
22.9
19.1
14.9
5×3
0.5000
0.3750
0.3125
0.2500
0.1875
0.1250
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
21.63
17.27
14.83
12.21
9.42
6.46
6.36
5.08
4.36
3.59
2.77
1.90
16.9
14.7
13.2
11.3
9.06
6.44
6.75
5.89
5.27
4.52
3.62
2.58
9.20
7.71
6.77
5.70
4.49
3.14
1.63
1.70
1.74
1.77
1.81
1.84
7.33
6.48
5.85
5.05
4.08
2.93
4.88
4.32
3.90
3.37
2.72
1.95
6.34
5.35
4.72
3.98
3.15
2.21
1.07
1.13
1.16
1.19
1.21
1.24
18.2
15.6
13.8
11.7
9.21
6.44
*Outside dimensions across flatsides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 132
DIMENSIONS AND PROPERTIES
Y
X
X
STRUCTURAL TUBING
Rectangular
Dimensions and properties
Y
Dimensions
Properties**
Nominal*
Wall
Weight
Size
Thickness per ft Area
in.
in.
2
X-X Axis
S
I
4
Z
3
Y-Y Axis
r
3
S
I
4
Z
3
3
r
J
lb
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.4
12.70
10.51
8.15
5.61
3.73
3.09
2.39
1.65
9.74
8.48
6.89
4.96
3.90
3.39
2.75
1.98
5.31
4.51
3.59
2.53
1.62
1.66
1.70
1.73
2.16
1.92
1.60
1.17
2.16
1.92
1.60
1.17
2.70
2.32
1.86
1.32
0.762
0.789
0.816
0.844
6.24
5.43
4.40
3.15
5×2
0.3125
0.2500
0.1875
0.1250
5⁄
16
1⁄
4
3⁄
16
1⁄
8
4×3
0.3125
0.2500
0.1875
0.1250
5⁄
16
1⁄
4
3⁄
16
1⁄
8
12.70
10.51
8.15
5.61
3.73
3.09
2.39
1.65
7.45
6.45
5.23
3.76
3.72
3.23
2.62
1.88
4.75
4.03
3.20
2.25
1.41
1.45
1.48
1.51
4.71
4.10
3.34
2.41
3.14
2.74
2.23
1.61
3.88
3.30
2.62
1.85
1.12
1.15
1.18
1.21
9.89
8.41
6.67
4.68
4×2
0.3750
0.3125
0.2500
0.1875
0.1250
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
12.17
10.58
8.81
6.87
4.75
3.58
3.11
2.59
2.02
1.40
5.75
5.32
4.69
3.87
2.82
2.87
2.66
2.35
1.93
1.41
4.00
3.60
3.09
2.48
1.77
1.27
1.31
1.35
1.38
1.42
1.83
1.71
1.54
1.29
0.954
1.83
1.71
1.54
1.29
0.954
2.39
2.17
1.88
1.52
1.09
0.715
0.743
0.770
0.798
0.826
4.97
4.58
4.01
3.26
2.34
3×2
0.3125
0.2500
0.1875
0.1250
5⁄
16
1⁄
4
3⁄
16
1⁄
8
8.45
7.11
5.59
3.90
2.48
2.09
1.64
1.15
2.44
2.21
1.86
1.38
1.63
1.47
1.24
0.920
2.20
1.92
1.57
1.13
0.992
1.03
1.06
1.10
1.26
1.15
0.977
0.733
1.26
1.15
0.977
0.733
1.64
1.44
1.18
0.855
0.714
0.742
0.771
0.800
2.97
2.63
2.16
1.57
21⁄2×11⁄2
0.2500
0.1875
1⁄
4
3⁄
16
5.41
4.32
1.59
1.27
1.05 0.844 1.15 0.815
0.920 0.736 0.964 0.852
0.458
0.405
0.610 0.793 0.537 1.14
0.540 0.669 0.565 0.976
*Outside dimensions across flat sides.
**Properties are based upon a nominal outside corner radius equal to two times the wall thickness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BARS AND PLATES
1 - 133
BARS AND PLATES
Product Availability
Plates are readily available in seven of the structural steel specifications listed in Section
A3.1 of the AISC LRFD Specification. These are: ASTM A36, A242, A529, A572, A588,
A514, and A852. Bars are available in all of these steels except A514 and A852. Table 1-1
shows the availability of each steel in terms of plate thickness.
The Manual user is referred to the discussion on p. 1-5, Selection of the Appropriate
Structural Steel, for guidance in selection of both plate and structural shapes.
Classification
Bars and plates are generally classified as follows:
Bars: 6 in. or less in width, .203 in. and over in thickness.
Over 6 in. to 8 in. in width, .230 in. and over in thickness.
Plates: Over 8 in. to 48 in. in width, .230 in. and over in thickness.
Over 48 in. in width, .180 in. and over in thickness.
Bars
Bars are available in various widths, thicknesses, diameters, and lengths. The preferred
practice is to specify widths in 1⁄4-in. increments and thickness and diameter in 1⁄8-in.
increments.
Plates
Defined according to rolling procedure:
Sheared plates are rolled between horizontal rolls and trimmed (sheared or gas cut) on
all edges.
Universal (UM) plates are rolled between horizontal and vertical rolls and trimmed
(sheared or gas cut) on ends only.
Stripped plates are furnished to required widths by shearing or gas cutting from wider
sheared plates.
Sizes
Plate mills are located in various districts, but the sizes of plates produced differ greatly
and the catalogs of individual mills should be consulted for detail data. The extreme width
of UM plates currently rolled is 60 inches and for sheared plates it is 200 inches, but their
availability together with limiting thickness and lengths should be checked with the mills
before specifying. The preferred increments for width and thickness are:
Widths:
Various. The catalogs of individual mills should be consulted to determine
the most economical widths.
Thickness: 1⁄32-in. increments up to 1⁄2-in.
1⁄ -in. increments over 1⁄ -in. to 1 in.
16
2
1⁄ -in. increments over 1 in. to 3 in.
8
1⁄ -in. increments over 3 in.
4
Ordering
Plate thickness may be specified in inches or by weight per square foot, but no decimal
edge thickness can be assured by the latter method. Separate tolerance tables apply to
each method.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 134
DIMENSIONS AND PROPERTIES
Table 1-7.
Theoretical Weights of Rolled Floor Plates
Gauge
No.
Theoretical
Weight per
sq. ft lb
Nominal
Thickness
in.
18
2.40
1⁄
8
16
3.00
3⁄
14
13
12
Nominal
Thickness
in.
Theoretical
Weight per
sq. ft, lb
6.16
1⁄
2
21.47
8.71
9⁄
16
24.02
3.75
1⁄
4
11.26
5⁄
8
26.58
4.50
5⁄
13.81
3⁄
4
31.68
5.25
3⁄
8
16.37
7⁄
8
36.78
7⁄
18.92
1
41.89
16
16
16
Theoretical
Weight per
sq. ft, lb
Note:
Thickness is measured near the edge of the plate, exclusive of raised pattern.
Invoicing
Standard practice is to invoice plates to the fabricator at theoretical weight at point of
shipment. Permissible variations in weight are in accordance with the tables of ASTM
Specification A6.
All plates are invoiced at theoretical weight and, except as noted, are subject to the
same weight variations which apply to rectangular plates. Odd shapes in most instances
require gas cutting, for which gas cutting extras are applicable.
All plates ordered gas cut for whatever reason, or beyond published shearing limits,
take extras for gas cutting in addition to all other extras. Rolled steel bearing plates are
often gas cut to prevent distortion due to shearing but would also take the regular extra
for the thickness involved.
Extras for thickness, width, length, cutting, quality and quantity, etc., which are added
to the base price of plates, are subject to revision, and should be obtained by inquiry to
the producer. The foregoing general statements are made as a guide toward economy in
design.
Floor Plates
Floor plates having raised patterns are available from several mills, each offering its own
style of surface projections and in a variety of widths, thicknesses, and lengths. A
maximum width of 96 inches and a maximum thickness of one inch are available, but
availability of matching widths, thicknesses, and lengths should be checked with the
producer. Floor plates are generally not specified to chemical composition limits or
mechanical property requirements; a commercial grade of carbon steel is furnished.
However, when strength or corrosion resistance is a consideration, raised pattern floor
plates are procurable in any of the regular steel specifications. As in the case of plain
plates, the individual manufacturers should be consulted for precise information. The
nominal or ordered thickness is that of the flat plate, exclusive of the height or raised
pattern. The usual weights are as shown in Table 1-7.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BARS AND PLATES
1 - 135
SQUARE AND ROUND BARS
Weight and area
Weight
lb per ft
Area
Sq in.
Size
in.
0
Weight
lb per ft
Area
Sq in.
Size
in.
1⁄
16
1⁄
8
3⁄
16
0.013
0.053
0.120
0.010
0.042
0.094
0.0039
0.0156
0.0352
0.0031
0.0123
0.0276
1⁄
16
1⁄
8
3⁄
16
30.63
31.91
33.23
34.57
24.05
25.07
26.10
27.15
9.000
9.379
9.766
10.160
7.069
7.366
7.670
7.980
1⁄
4
5⁄
16
3⁄
8
7⁄
16
0.213
0.332
0.479
0.651
0.167
0.261
0.376
0.512
0.0625
0.0977
0.1406
0.1914
0.0491
0.0767
0.1104
0.1503
1⁄
4
5⁄
16
3⁄
8
7⁄
16
35.94
37.34
38.76
40.21
28.23
29.32
30.44
31.58
10.563
10.973
11.391
11.816
8.296
8.618
8.946
9.281
1⁄
2
9⁄
16
5⁄
8
11⁄
16
0.851
1.077
1.329
1.608
0.668
0.846
1.044
1.263
0.2500
0.3164
0.3906
0.4727
0.1964
0.2485
0.3068
0.3712
1⁄
2
9⁄
16
5⁄
8
11⁄
16
41.68
43.19
44.71
46.27
32.74
33.92
35.12
36.34
12.250
12.691
13.141
13.598
9.621
9.968
10.321
10.680
3⁄
4
13⁄
16
7⁄
8
15⁄
16
1.914
2.246
2.605
2.991
1.503
1.764
2.046
2.349
0.5625
0.6602
0.7656
0.8789
0.4418
0.5185
0.6013
0.6903
3⁄
4
13⁄
16
7⁄
8
15⁄
16
47.85
49.46
51.09
52.76
37.58
38.85
40.13
41.43
14.063
14.535
15.016
15.504
11.045
11.416
11.793
12.177
1⁄
16
1⁄
8
3⁄
16
3.403
3.841
4.307
4.798
2.673
3.017
3.382
3.769
1.0000
1.1289
1.2656
1.4102
0.7854
0.8866
0.9940
1.1075
1⁄
16
1⁄
8
3⁄
16
54.44
56.16
57.90
59.67
42.76
44.11
45.47
46.86
16.000
16.504
17.016
17.535
12.566
12.962
13.364
13.772
1⁄
4
5⁄
16
3⁄
8
7⁄
16
5.317
5.862
6.433
7.032
4.176
4.604
5.053
5.523
1.5625
1.7227
1.8906
2.0664
1.2272
1.3530
1.4849
1.6230
1⁄
4
5⁄
16
3⁄
8
7⁄
16
61.46
63.28
65.13
67.01
48.27
49.70
51.15
52.63
18.063
18.598
19.141
19.691
14.186
14.607
15.033
15.466
1⁄
2
9⁄
16
5⁄
8
11⁄
16
7.656
8.308
8.985
9.690
6.013
6.525
7.057
7.610
2.2500
2.4414
2.6406
2.8477
1.7672
1.9175
2.0739
2.2365
1⁄
2
9⁄
16
5⁄
8
11⁄
16
68.91
70.83
72.79
74.77
54.12
55.63
57.17
58.72
20.250
20.816
21.391
21.973
15.904
16.349
16.800
17.257
3⁄
4
13⁄
16
7⁄
8
15⁄
16
10.421
11.179
11.963
12.774
8.185
8.780
9.396
10.032
3.0625
3.2852
3.5156
3.7539
2.4053
2.5802
2.7612
2.9483
3⁄
4
13⁄
16
7⁄
8
15⁄
16
76.78
78.81
80.87
82.96
60.30
61.90
63.51
65.15
22.563
23.160
23.766
24.379
17.721
18.190
18.666
19.147
1⁄
16
1⁄
8
3⁄
16
13.611
14.475
15.366
16.283
10.690
11.369
12.068
12.789
4.0000
4.2539
4.5156
4.7852
3.1416
3.3410
3.5466
3.7583
1⁄
16
1⁄
8
3⁄
16
85.07
87.21
89.38
91.57
66.81
68.49
70.20
71.92
25.000
25.629
26.266
26.910
19.635
20.129
20.629
21.135
1⁄
4
5⁄
16
3⁄
8
7⁄
16
17.227
18.197
19.194
20.217
13.530
14.292
15.075
15.879
5.0625
5.3477
5.6406
5.9414
3.9761
4.2000
4.4301
4.6664
1⁄
4
5⁄
16
3⁄
8
7⁄
16
93.79
96.04
98.31
100.61
73.66
75.43
77.21
79.02
27.563
28.223
28.891
29.566
21.648
22.166
22.691
23.221
1⁄
2
9⁄
16
5⁄
8
11⁄
16
21.267
22.344
23.447
24.577
16.703
17.549
18.415
19.303
6.2500
6.5664
6.8906
7.2227
4.9087
5.1573
5.4119
5.6727
1⁄
2
9⁄
16
5⁄
8
11⁄
16
102.93
105.29
107.67
110.07
80.84
82.69
84.56
86.45
30.250
30.941
31.641
32.348
23.758
24.301
24.851
25.406
3⁄
4
13⁄
16
7⁄
8
15⁄
16
25.734
26.917
28.126
29.362
20.211
21.140
22.090
23.061
7.5625
7.9102
8.2656
8.6289
5.9396
6.2126
6.4918
6.7771
3⁄
4
13⁄
16
7⁄
8
15⁄
16
112.50
114.96
117.45
119.96
88.36
90.29
92.24
94.22
33.063
33.785
34.516
35.254
25.967
26.535
27.109
27.688
1
2
3
4
5
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 136
DIMENSIONS AND PROPERTIES
SQUARE AND ROUND BARS
Weight and area
Weight
lb per ft
Area
Sq in.
Size
in.
6
Weight
lb per ft
Area
Sq in.
Size
in.
1⁄
16
1⁄
8
3⁄
16
122.50
125.07
127.66
130.28
96.21
98.23
100.26
102.32
36.000
36.754
37.516
38.285
28.274
28.867
29.465
30.069
1⁄
4
5⁄
16
3⁄
8
7⁄
16
132.92
135.59
138.29
141.02
104.40
106.49
108.61
110.75
39.063
39.848
40.641
41.441
1⁄
2
9⁄
16
5⁄
8
11⁄
16
143.77
146.55
149.35
152.18
112.91
115.10
117.30
119.52
3⁄
4
13⁄
16
7⁄
8
15⁄
16
155.04
157.92
160.83
163.77
1⁄
16
1⁄
8
3⁄
16
275.63
279.47
283.33
287.23
216.48
219.49
222.53
225.59
81.000
82.129
83.266
84.410
63.617
64.504
65.397
66.296
30.680
31.296
31.919
32.548
1⁄
4
5⁄
16
3⁄
8
7⁄
16
291.15
295.10
299.07
303.07
228.67
231.77
234.89
238.03
85.563
86.723
87.891
89.066
67.201
68.112
69.029
69.953
42.250
43.066
43.891
44.723
33.183
33.824
34.472
35.125
1⁄
2
9⁄
16
5⁄
8
11⁄
16
307.10
311.15
315.24
319.34
241.20
244.38
247.59
250.81
90.250
91.441
92.641
93.848
70.882
71.818
72.760
73.708
121.77
124.03
126.32
128.63
45.563
46.410
47.266
48.129
35.785
36.451
37.122
37.800
3⁄
4
13⁄
16
7⁄
8
15⁄
16
323.48
327.64
331.82
336.04
254.06
257.33
260.61
263.92
95.063
96.285
97.516
98.754
74.662
75.622
76.589
77.561
1⁄
16
1⁄
8
3⁄
16
166.74
169.73
172.74
175.79
130.95
133.30
135.67
138.06
49.000
49.879
50.766
51.660
38.485
39.175
39.871
40.574
1⁄
16
1⁄
8
3⁄
16
340.28
344.54
348.84
353.16
267.25
270.61
273.98
277.37
100.000
101.254
102.516
103.785
78.540
79.525
80.516
81.513
1⁄
4
5⁄
16
3⁄
8
7⁄
16
178.86
181.96
185.08
188.23
140.48
142.91
145.36
147.84
52.563
53.473
54.391
55.316
41.283
41.997
42.718
43.446
1⁄
4
5⁄
16
3⁄
8
7⁄
16
357.50
361.88
366.28
370.70
280.78
284.22
287.67
291.15
105.063
106.348
107.641
108.941
82.516
83.525
84.541
85.563
1⁄
2
9⁄
16
5⁄
8
11⁄
16
191.41
194.61
197.84
201.10
150.33
152.85
155.38
157.94
56.250
57.191
58.141
59.098
44.179
44.918
45.664
46.415
1⁄
2
9⁄
16
5⁄
8
11⁄
16
375.16
379.64
384.14
388.67
294.65
298.17
301.70
305.26
110.250
111.566
112.891
114.223
86.590
87.624
88.664
89.710
3⁄
4
13⁄
16
7⁄
8
15⁄
16
204.38
207.69
211.03
214.39
160.52
163.12
165.74
168.38
60.063
61.035
62.016
63.004
47.173
47.937
48.707
49.483
3⁄
4
13⁄
16
7⁄
8
15⁄
16
393.23
397.82
402.43
407.07
308.85
312.45
316.07
319.71
115.563
116.910
118.266
119.629
90.763
91.821
92.886
93.957
1⁄
16
1⁄
8
3⁄
16
217.78
221.19
224.64
228.11
171.04
173.73
176.43
179.15
64.000
65.004
66.016
67.035
50.266
51.054
51.849
52.649
1⁄
16
1⁄
8
3⁄
16
411.74
416.43
421.15
425.89
323.38
327.06
330.77
334.50
121.000
122.379
123.766
125.160
95.033
96.116
97.206
98.301
1⁄
4
5⁄
16
3⁄
8
7⁄
16
231.60
235.12
238.67
242.25
181.90
184.67
187.45
190.26
68.063
69.098
70.141
71.191
53.456
54.269
55.088
55.914
1⁄
4
5⁄
16
3⁄
8
7⁄
16
430.66
435.46
440.29
445.14
338.24
342.01
345.80
349.61
126.563
127.973
129.391
130.816
99.402
100.510
101.623
102.743
1⁄
2
9⁄
16
5⁄
8
11⁄
16
245.85
249.48
253.13
256.82
193.09
195.94
198.81
201.70
72.250
73.316
74.391
75.473
56.745
57.583
58.426
59.276
1⁄
2
9⁄
16
5⁄
8
11⁄
16
450.02
454.92
459.85
464.81
353.44
357.30
361.17
365.06
132.250
133.691
135.141
136.598
103.869
105.001
106.139
107.284
3⁄
4
13⁄
16
7⁄
8
15⁄
16
260.53
264.26
268.02
271.81
204.62
207.55
210.50
213.48
76.563
77.660
78.766
79.879
60.132
60.994
61.863
62.737
3⁄
4
13⁄
16
7⁄
8
15⁄
16
469.80
474.81
479.84
484.91
368.98
372.91
376.87
380.85
138.063
139.535
141.016
142.504
108.434
109.591
110.754
111.923
490.00
384.85
144.000
113.098
7
8
9
10
11
12
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BARS AND PLATES
1 - 137
AREA OF RECTANGULAR SECTIONS
Square inches
Width
in.
Thickness, inches
3⁄
16
1⁄
4
5⁄
16
3⁄
8
7⁄
16
1⁄
2
9⁄
16
5⁄
8
11⁄
16
3⁄
4
13⁄
16
1
0.047
0.093
0.141
0.188
0.063
0.125
0.188
0.250
0.078
0.156
0.234
0.313
0.094
0.188
0.281
0.375
0.109
0.219
0.328
0.438
0.125
0.250
0.375
0.500
0.141
0.281
0.422
0.563
0.156
0.313
0.469
0.625
0.172
0.344
0.516
0.688
0.188
0.375
0.563
0.75
0.203
0.406
0.609
0.813
0.219
0.438
0.656
0.875
0.234
0.469
0.703
0.938
0.250
0.500
0.750
1.00
11⁄4
11⁄2
13⁄4
2
0.234
0.281
0.328
0.375
0.313
0.375
0.438
0.500
0.391
0.469
0.547
0.625
0.469
0.563
0.656
0.750
0.547
0.656
0.766
0.875
0.625
0.750
0.875
1.00
0.703
0.844
0.984
1.13
0.781
0.938
1.09
1.25
0.859
1.03
1.20
1.38
0.938
1.13
1.31
1.50
1.02
1.22
1.42
1.63
1.09
1.31
1.53
1.75
1.17
1.41
1.64
1.88
1.25
1.50
1.75
2.00
21⁄4
21⁄2
23⁄4
3
0.422
0.469
0.516
0.563
0.563
0.625
0.688
0.750
0.703
0.781
0.859
0.938
0.844
0.938
1.03
1.13
0.984
1.09
1.20
1.31
1.13
1.25
1.38
1.50
1.27
1.41
1.55
1.69
1.41
1.56
1.72
1.88
1.55
1.72
1.89
2.06
1.69
1.88
2.06
2.25
1.83
2.03
2.23
2.44
1.97
2.19
2.41
2.63
2.11
2.34
2.58
2.81
2.25
2.50
2.75
3.00
31⁄4
31⁄2
33⁄4
4
0.609
0.656
0.703
0.750
0.813
0.875
0.938
1.00
1.02
1.09
1.17
1.25
1.22
1.31
1.41
1.50
1.42
1.53
1.64
1.75
1.63
1.75
1.88
2.00
1.83
1.97
2.11
2.25
2.03
2.19
2.34
2.50
2.23
2.41
2.58
2.75
2.44
2.63
2.81
3.00
2.64
2.84
3.05
3.25
2.84
3.06
3.28
3.50
3.05
3.28
3.52
3.75
3.25
3.50
3.75
4.00
41⁄4
41⁄2
43⁄4
5
0.797
0.844
0.891
0.938
1.06
1.13
1.19
1.25
1.33
1.41
1.48
1.56
1.59
1.69
1.78
1.88
1.86
1.97
2.08
2.19
2.13
2.25
2.38
2.50
2.39
2.53
2.67
2.81
2.66
2.81
2.97
3.13
2.92
3.09
3.27
3.44
3.19
3.38
3.56
3.75
3.45
3.66
3.86
4.06
3.72
3.94
4.16
4.38
3.98
4.22
4.45
4.69
4.25
4.50
4.75
5.00
51⁄4
51⁄2
53⁄4
6
0.984
1.03
1.08
1.13
1.31
1.38
1.44
1.50
1.64
1.72
1.80
1.88
1.97
2.06
2.16
2.25
2.30
2.41
2.52
2.63
2.63
2.75
2.88
3.00
2.95
3.09
3.23
3.38
3.28
3.44
3.59
3.75
3.61
3.78
3.95
4.13
3.94
4.13
4.31
4.50
4.27
4.47
4.67
4.88
4.59
4.81
5.03
5.25
4.92
5.16
5.39
5.63
5.25
5.50
5.75
6.00
61⁄4
61⁄2
63⁄4
7
1.17
1.22
1.27
1.31
1.56
1.63
1.69
1.75
1.95
2.03
2.11
2.19
2.34
2.44
2.53
2.63
2.73
2.84
2.95
3.06
3.13
3.25
3.38
3.50
3.52
3.66
3.80
3.94
3.91
4.06
4.22
4.38
4.30
4.47
4.64
4.81
4.69
4.88
5.06
5.25
5.08
5.28
5.48
5.69
5.47
5.69
5.91
6.13
5.86
6.09
6.33
6.56
6.25
6.50
6.75
7.00
71⁄4
71⁄2
73⁄4
8
1.36
1.41
1.45
1.50
1.81
1.88
1.94
2.00
2.27
2.34
2.42
2.50
2.72
2.81
2.91
3.00
3.17
3.28
3.39
3.50
3.63
3.75
3.88
4.00
4.08
4.22
4.36
4.50
4.53
4.69
4.84
5.00
4.98
5.16
5.33
5.50
5.44
5.63
5.81
6.00
5.89
6.09
6.30
6.50
6.34
6.56
6.78
7.00
6.80
7.03
7.27
7.50
7.25
7.50
7.75
8.00
81⁄2
9
1.59
1.69
2.13
2.25
2.66
2.81
3.19
3.38
3.72
3.94
4.25
4.50
4.78
5.06
5.31
5.63
5.84
6.19
6.38
6.75
6.91
7.31
7.44
7.88
7.97
8.44
8.50
9.00
91⁄2
10
1.78
1.88
2.38
2.50
2.97
3.13
3.56
3.75
4.16
4.38
4.75
5.00
5.34
5.63
5.94
6.25
6.53
6.88
7.13
7.50
7.72
8.13
8.31
8.75
8.91
9.38
9.50
10.0
101⁄2
11
1.97
2.06
2.63
2.75
3.28
3.44
3.94
4.13
4.59
4.81
5.25
5.50
5.91
6.19
6.56
6.88
7.22
7.56
7.88
8.25
8.53
8.94
9.19
9.63
9.84
10.3
10.5
11.0
111⁄2
12
2.16
2.25
2.88
3.00
3.59
3.75
4.31
4.50
5.03
5.25
5.75
6.00
6.47
6.75
7.19
7.50
7.91 8.63
8.25 9.00
9.34
9.75
10.8
11.3
11.5
12.0
1⁄
4
1⁄
2
3⁄
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7⁄
8
10.1
10.5
15⁄
16
1
1 - 138
DIMENSIONS AND PROPERTIES
WEIGHT OF RECTANGULAR SECTIONS
Pounds per linear foot
Width
in.
Thickness, inches
3⁄
16
1⁄
4
5⁄
16
3⁄
8
7⁄
16
1⁄
2
9⁄
16
5⁄
8
11⁄
16
3⁄
4
13⁄
16
7⁄
8
15⁄
16
1
0.160
0.319
0.479
0.638
0.213
0.425
0.638
0.851
0.266
0.532
0.798
1.06
0.319
0.638
0.957
1.28
0.372
0.744
1.12
1.49
0.425
0.851
1.28
1.70
0.479
0.957
1.44
1.91
0.532
1.06
1.60
2.13
0.585
1.17
1.75
2.34
0.638
1.28
1.91
2.55
0.691
1.38
2.07
2.76
0.744
1.49
2.23
2.98
0.798
1.60
2.39
3.19
0.851
1.70
2.55
3.40
11⁄4
11⁄2
13⁄4
2
0.798
0.957
1.12
1.28
1.06
1.28
1.49
1.70
1.33
1.60
1.86
2.13
1.60
1.91
2.23
2.55
1.86
2.23
2.61
2.98
2.13
2.55
2.98
3.40
2.39
2.87
3.35
3.83
2.66
3.19
3.72
4.25
2.92
3.51
4.09
4.68
3.19
3.83
4.47
5.10
3.46
4.15
4.84
5.53
3.72
4.47
5.21
5.95
3.99
4.79
5.58
6.38
4.25
5.10
5.95
6.81
21⁄4
21⁄2
23⁄4
3
1.44
1.60
1.75
1.91
1.91
2.13
2.34
2.55
2.39
2.66
2.92
3.19
2.87
3.19
3.51
3.83
3.35
3.72
4.09
4.47
3.83
4.25
4.68
5.10
4.31
4.79
5.26
5.74
4.79
5.32
5.85
6.38
5.26
5.85
6.43
7.02
5.74
6.38
7.02
7.66
6.22
6.91
7.60
8.29
6.70
7.44
8.19
8.93
7.18
7.98
8.77
9.57
7.66
8.51
9.36
10.2
31⁄4
31⁄2
33⁄4
4
2.07
2.23
2.39
2.55
2.76
2.98
3.19
3.40
3.46
3.72
3.99
4.25
4.15
4.47
4.79
5.10
4.84
5.21
5.58
5.95
5.53
5.95
6.38
6.81
6.22
6.70
7.18
7.66
6.91
7.44
7.98
8.51
7.60
8.19
8.77
9.36
8.29
8.93
9.57
10.2
8.99
9.68
10.4
11.1
9.68
10.4
11.2
11.9
10.4
11.2
12.0
12.8
11.1
11.9
12.8
13.6
41⁄4
41⁄2
43⁄4
5
2.71
2.87
3.03
3.19
3.62
3.83
4.04
4.25
4.52
4.79
5.05
5.32
5.42
5.74
6.06
6.38
6.33
6.70
7.07
7.44
7.23
7.66
8.08
8.51
8.13
8.61
9.09
9.57
9.04
9.57
10.1
10.6
9.94
10.5
11.1
11.7
10.8
11.5
12.1
12.8
11.8
12.4
13.1
13.8
12.7
13.4
14.1
14.9
13.6
14.4
15.2
16.0
14.5
15.3
16.2
17.0
51⁄4
51⁄2
53⁄4
6
3.35
3.51
3.67
3.83
4.47
4.68
4.89
5.10
5.58
5.85
6.11
6.38
6.70
7.02
7.34
7.66
7.82
8.19
8.56
8.93
8.93
9.36
9.78
10.2
10.0
10.5
11.0
11.5
11.2
11.7
12.2
12.8
12.3
12.9
13.5
14.0
13.4
14.0
14.7
15.3
14.5
15.2
15.9
16.6
15.6
16.4
17.1
17.9
16.7
17.5
18.3
19.1
17.9
18.7
19.6
20.4
61⁄4
61⁄2
63⁄4
7
3.99
4.15
4.31
4.47
5.32
5.53
5.74
5.95
6.65
6.91
7.18
7.44
7.98
8.29
8.61
8.93
9.30
9.68
10.0
10.4
10.6
11.1
11.5
11.9
12.0
12.4
12.9
13.4
13.3
13.8
14.4
14.9
14.6
15.2
15.8
16.4
16.0
16.6
17.2
17.9
17.3
18.0
18.7
19.4
18.6
19.4
20.1
20.8
19.9
20.7
21.5
22.3
21.3
22.1
23.0
23.8
71⁄4
71⁄2
73⁄4
8
4.63
4.79
4.94
5.10
6.17
6.38
6.59
6.81
7.71
7.98
8.24
8.51
9.25
9.57
9.89
10.2
10.8
11.2
11.5
11.9
12.3
12.8
13.2
13.6
13.9
14.4
14.8
15.3
15.4
16.0
16.5
17.0
17.0
17.5
18.1
18.7
18.5
19.1
19.8
20.4
20.0
20.7
21.4
22.1
21.6
22.3
23.1
23.8
23.1
23.9
24.7
25.5
24.7
25.5
26.4
27.2
81⁄2
9
5.42
5.74
7.23
7.66
9.04
9.57
10.8
11.5
12.7
13.4
14.5
15.3
16.3
17.2
18.1
19.1
19.9
21.1
21.7
23.0
23.5
24.9
25.3
26.8
27.1
28.7
28.9
30.6
91⁄2
10
6.06
6.38
8.08
8.51
10.1
10.6
12.1
12.8
14.1
14.9
16.2
17.0
18.2
19.1
20.2
21.3
22.2
23.4
24.2
25.5
26.3
27.6
28.3
29.8
30.3
31.9
32.3
34.0
101⁄2
11
6.70
7.02
8.93
9.36
11.2
11.7
13.4
14.0
15.6
16.4
17.9
18.7
20.1
21.1
22.3
23.4
24.6
25.7
26.8
28.1
29.0
30.4
31.3
32.8
33.5
35.1
35.7
37.4
111⁄2
12
7.34
7.66
9.78
10.2
12.2
12.8
14.7
15.3
17.1
17.9
19.6
20.4
22.0
23.0
24.5
25.5
26.9
28.1
29.3
30.6
31.8
33.2
34.2
35.7
36.7
38.3
39.1
40.8
1⁄
4
1⁄
2
3⁄
4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1
CRANE RAILS
1 - 139
CRANE RAILS
General Notes
The ASCE rails and the 104- to 175-lb crane rails shown in Figure 1-2 are recommended
for crane runway use. For complete details and for profiles and properties of rails not
listed, consult manufacturers’ catalogs.
Rails should be arranged so that joints on opposite sides of the crane runway will be
staggered with respect to each other and with due consideration to the wheelbase of the
crane. Rail joints should not occur at crane girder splices. Light 40-lb rails are available
in 30-ft lengths, 60-lb rails in 30-, 33- or 39-ft lengths, standard rails in 33- or 39-ft lengths
and crane rails up to 80 ft. Consult manufacturer for availability of other lengths. Odd
lengths, which must be included to complete a run or obtain the necessary stagger, should
be not less than 10 feet long. For crane rail service, 40-lb rails are furnished to
manufacturers’ specifications and tolerances. 60- and 85-lb rails are furnished to manufacturers’ specifications and tolerances, or to ASTM A1. Crane rails are furnished to
ASTM A759. Rails will be furnished with standard drilling in both standard and odd
lengths unless stipulated otherwise on order. For controlled cooling, heat treatment, and
rail end preparation, see manufacturers’ catalogs. Purchase orders for crane rails should
be noted “For crane service.” (See Table 1-8.)
For maximum wheel loadings see manufacturers’ catalogs.
Splices
Bolted Splices
It is often more desirable to use properly installed and maintained bolted splice bars in
making up rail joints for crane service than welded splice bars.
Standard rail drilling and joint-bar punching, as furnished by manufacturers of light
standard rails for track work, include round holes in rail ends and slotted holes in joint
bars to receive standard oval-neck tack bolts. Holes in rails are oversize and punching in
joint bars is spaced to allow 1⁄16- to 1⁄8-in. clearance between rail ends (see manufacturers’
catalogs for spacing and dimensions of holes and slots). Although this construction is
satisfactory for track and light crane service, its use in general crane service may lead to
joint failure.
For best service in bolted splices, it is recommended that tight joints be stipulated for
all rails for crane service. This will require rail ends to be finished by milling or grinding,
and the special rail drilling and joint-bar punching tabulated below. Special rail drilling
is accepted by some mills, or rails may be ordered blank for shop drilling. End finishing
of standard rails can be done at the mill; light rails must be end-finished in the fabricating
shop or ground at the site prior to erection. In the crane rail range, from 104 to 175 lbs
per yard, rails and joint bars are manufactured to obtain a tight fit and no further special
end finishing, drilling, or punching is required. Because of cumulative tolerance variations in holes, bolt diameters, and rail ends, a slight gap may sometimes occur in the
so-called tight joints. Conversely, it may sometimes be necessary to ream holes through
joined bar and rail to permit entry of bolts.
Joint bars for crane service are provided in various sections to match the rails. Joint
bars for light and standard rails may be purchased blank for special shop punching to
obtain tight joints. See Bethlehem Steel Corp. Booklet 3351 for dimensions, material
specifications, and the identification necessary to match the crane rail section.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 140
DIMENSIONS AND PROPERTIES
c
Bars can be
sheared off
r
13°
c of g
y
13°
1/
4 Rad.
R
X
X
h
1/
4 Rad.
t
1/
2 Rad.
d
1/
2 Rad.
h
g
13°
13°
m
m
n
b
A.S.C.E. 40, 60 & 85 lb.
c
BETHLEHEM 104 lb.
c
4
3 (approx.)
12°
13°
3
4
Rad.
3
4
Rad.
7/
8
7/
8 Rad.
h
13°
h
12°
m
BETHLEHEM 135 lb.
Rad.
m
BETHLEHEM 171 lb.
c
4 1/32 (approx.)
12°
2 Rad.
11/8 Rad.
12°
h
2 53/64
m
BETHLEHEM 175 lb.
Nomenclature of sketch for A.S.C.E. rails also applies to the other sections.
Fig. 1-2. Crane rails.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CRANE RAILS
1 - 141
Table 1-8.
Crane Rails
Dimensions and Properties
Type
Nominal
Wt.
per
Classi- Yd. d
fication lb in.
Sx
Gage
g
b
m
n
c
r
t
h
R
Area
lx
in.
in.
in.
in.
in.
in.
in.
in.
in.
in.2
in.4
17⁄
32
5⁄
8
11⁄
16
48⁄
64
13⁄
16
7⁄
8
57⁄
64
31⁄
32
11⁄16
11⁄16
11⁄4
19⁄64
11⁄
64
7⁄
32
1⁄
4
9⁄
32
9⁄
32
19⁄
64
19⁄
64
10⁄
32
1⁄
2
15⁄
32
5⁄
8
1⁄
2
111⁄16
12
12
3.00 4.10 2.55
12
155⁄64
12
3.94 6.54 3.59 3.89 1.68
21⁄8
12
23⁄8
12
27⁄16
12
21⁄2
12
29⁄16
12
23⁄4
12
21⁄
64
25⁄
64
7⁄
16
31⁄
64
33⁄
64
35⁄
64
9⁄
16
9⁄
16
123⁄32
17⁄8
21⁄2
12
1
ASCE
Light
30
31⁄8
125⁄64
31⁄8
ASCE
Light
40
31⁄2
171⁄128
31⁄2
ASCE
Light
50
37⁄8
123⁄32
37⁄8
ASCE
Light
60
41⁄4 1115⁄128 41⁄4
ASCE
70
45⁄8
23⁄64
45⁄8
ASCE
80
5
23⁄16
5
ASCE
Std.
85
53⁄16
217⁄64
53⁄16
ASCE
Std.
100
53⁄4
265⁄128
53⁄4
Bethlehem
Crane
104
5
27⁄16
5
Bethlehem
Crane
135
53⁄4
215⁄32
53⁄16
Bethlehem
Crane
171
6
25⁄8
6
Bethlehem
Crane
175
6
221⁄32
6
Hd. Base
y
in.3
in.3
in.
—
—
21⁄16
12
4.90 10.1
5.10
217⁄64
12
5.93 14.6
6.64 7.12 2.05
215⁄32
12
6.81 19.7
8.19 8.87 2.22
25⁄8
12
7.86 26.4 10.1 11.1 2.38
23⁄4
12
8.33 30.1 11.1 12.2 2.47
25⁄64
12
9.84 44.0 14.6 16.1 2.73
27⁄16
31⁄2
10.3 29.8 10.7 13.5 2.21
12
13.3 50.8 17.3 18.1 2.81
—
1.88
37⁄16
14
11⁄4 213⁄16
4.3
Flat
11⁄4
23⁄4 Vert. 16.8 73.4 24.5 24.4 3.01
41⁄4
18
11⁄2
37⁄64 Vert. 17.1 70.5 23.4 23.6 2.98
Joint-bar bolts, as distinguished from oval-neck track bolts, have straight shanks to the
head and are manufactured to ASTM A449 specifications. Nuts are manufactured to
ASTM A563 Gr. B specifications. ASTM A325 bolts and nuts may be used. Bolt assembly
includes an alloy steel spring washer, furnished to AREA specifications.
After installation, bolts should be retightened within 30 days and every three months
thereafter.
Welded Splices
When welded splices are specified, consult the manufacturer for recommended rail-end
preparation, welding procedure, and method of ordering. Although joint continuity, made
possible by this method of splicing, is desirable, it should be noted that the careful control
required in all stages of the welding operation may be difficult to meet during crane rail
installation.
Rails should not be attached to structural supports by welding. Rails with holes for
joint bar bolts should not be used in making welded splices.
Fastenings
Hook Bolts
Hook bolts (Figure 1-3) are used primarily with light rails when attached to beams too
narrow for clamps. Rail adjustment to ±1⁄2-in. is inherent in the threaded shank. Hook
bolts are paired alternately three to four inches apart, spaced at about 24-in. centers. The
special rail drilling required must be done at the fabricator’s shop. Hook bolts are not
recommended for use with heavy duty cycle cranes (CMAA Classes, D, E, and F). It is
generally recommended that hook bolts should not be used in runway systems which are
longer than 500 feet because the bolts do not allow for longitudinal movement of the rail.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 142
DIMENSIONS AND PROPERTIES
Table 1-9.
Splices for Tight Joints
g
A
B
C
C
B
D
C
B
L
Rail End
Joint Bar
l
l
Grip
Grip
H
H
G
Cut when specified
40-60-85-104
Rail
Joint Bar
Drilling
Wt.
Per
Yard
g
lb
in.
40 171⁄128
60 1115⁄128
85 217⁄64
104
27⁄16
135 215⁄32
171
25⁄8
175
221⁄32
Hole
Dia. A
in.
13⁄ *
16
13⁄ *
16
15⁄ *
16
11⁄16
13⁄16
13⁄16
13⁄16
105-135-171-175
B C
in. in. in.
21⁄2 5
—
21⁄2 5
—
21⁄2 5
—
4
5
6
4
5
6
4
5
6
4
Bolt
Washer
Punching
5
6
Wt. 2 Bars
Bolts, Nuts,
Washers
ThickIn- ness
side and With Less
Dia. Width Fig. Fig.
Hole
Dia.
D
B C
L
G
Dia.
Grip
I
H
in.
in.
in. in. in.
in.
in.
in.
in.
in.
in.
in.
lb
lb
13⁄ *
16
13⁄ *
16
15⁄ *
16
11⁄16
13⁄16
13⁄16
13⁄16
415⁄16*
5
— 20 23⁄16
3⁄
4
115⁄16
31⁄2
21⁄2
16.5
5
— 24 211⁄16
3⁄
4
219⁄32
4
211⁄16
36.5
29.6
415⁄16*
5
— 24 311⁄32
7⁄
8
35⁄32
43⁄4
33⁄16
56.6
45.3
715⁄16
5
6
34
31⁄2
1
31⁄2
51⁄4
31⁄2
715⁄16
5
6
34
—
11⁄8
35⁄8
51⁄2
311⁄16
715⁄16
5
6
34
—
11⁄8
47⁄16
61⁄4
41⁄16
—
11⁄8
41⁄8
61⁄4
315⁄16
7⁄ ×3⁄
16 8
7⁄ ×3⁄
16 8
7⁄ ×3⁄
16 8
7⁄ ×1⁄
16 2
7⁄ ×1⁄
16 2
7⁄ ×1⁄
16 2
7⁄ ×1⁄
16 2
20.0
415⁄16*
13⁄
16
13⁄
16
15⁄
16
11⁄16
13⁄16
13⁄16
13⁄16
715⁄16
5
6
34
73.5
55.4
—
75.3
—
90.8
—
87.7
*Special rail drilling and joint-bar punching.
Rail Clips
Rail clips are forged or cast devices which are shaped to match specific rail profiles. They
are usually bolted to the runway girder flange with one bolt or are sometimes welded.
Rail clips have been used satisfactorily with all classes of cranes. However, one drawback
is that when a single bolt is used the clip can rotate in response to rail longitudinal
movement. This clip rotation can cause a camming action, thus forcing the rail out of
alignment. Because of this limitation, rail clips should only be used in crane systems
subject to infrequent use, and for runways less than 500 feet in length.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CRANE RAILS
1 - 143
Rail Clamps
Rail clamps are a common method of attachment for heavy duty cycle cranes. Rail clamps
are detailed to provide two types: tight and floating (Figure 1-4). Each clamp consists of
two plates: an upper clamp plate and a lower filler plate.
The lower plate is flat and roughly matches the height of the toe of the rail flange. The
upper plate covers the lower plate and extends over the top of the lower rail flange. In
the tight clamp the upper plate is detailed to fit tightly to the lower tail flange top, thus
“clamping” it tightly in place when the fasteners are tightened. In the past, the tight clamp
had been illustrated with the filler plates fitted tightly against the rail flange toe. This
tight fit-up was rarely achieved in practice and is not considered to be necessary to achieve
a tight type clamp. In the floating type clamp, the pieces are detailed to provide a clearance
both alongside the rail flange toe and below the upper plate. The floating type does not,
in reality, clamp the rail but merely holds the rail within the limits of the clamp clearances.
Fig. 1-3. Hook bolts.
Reversible
1 1/2
fillers
Reversible
fillers
Clamp
plates
3
Off-center
punching
11/2
Clamp
plates
3
Off-center
punching
11/2
1 1/2
Rail base +
1/
4
( 1/2 to 9/16 ) "float"
Max. adjustment
Self-locking nut or
nut and lock washer
Filler
Machine bolt
Gage
Gage
Tight clamp
Floating clamp
Fig. 1-4. Rail clamps.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 144
DIMENSIONS AND PROPERTIES
High strength bolts are recommended for both clamp types. Both types should be spaced
three feet or less apart.
Dimensions shown above are suggested. See manufacturers’ catalogs for recommended gages, bolt sizes, and detail dimensions not shown.
Patented Rail Clips
Each manufacturer’s literature presents in detail the desirable aspects of the various
designs. In general patented rail clips are easy to install due to their range of adjustment
while providing the proper limitations of lateral movement and allowance for longitudinal movement. Patented rail clips should be considered as a viable alternative to
conventional hook bolts, clips, or clamps. Because of their desirable characteristics,
patented rail clips can be used without restriction except as limited by the specific
manufacturer’s recommendations. Installations using patented rail clips sometimes incorporate pads beneath the rail. When this is done the lateral float of the rail should be
limited as in the case of the tight rail clamps.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 145
TORSION PROPERTIES
Torsional analysis is not required for the routine design of most structural steel members.
When torsional analysis is required, the Table of Torsion Properties will be of assistance
in utilizing current analysis methods. The reader is referred to the AISC publication
Torsional Analysis of Steel Members (American Institute of Steel Construction, 1983) for
additional information and appropriate design aids.
Torsion Properties are also required to determine the design compressive strength for
torsional and flexural-torsional buckling as specified in the AISC LRFD Specification
Appendix E3.
Nomenclature
= warping constant for section, in.6*
= modulus of elasticity of steel (29,000 ksi)
= shear modulus of elasticity of steel (11,200 ksi)
= flexural constant in Equation E3-1, LRFD Specification
= torsional constant for a section, in.4
= statical moment for a point in the flange directly above the vertical edge of the
web, in.3
3
_Qw = statical moment at mid-depth of the section, in.
ro = polar radius of gyration about the shear center, in.
Sw = warping statical moment at a point in the section, in.4
Wno = normalized warping function at a point at the flange edge, in.2
Cw
E
G
H
J
Qf
*Calculated values of Cw are given for all tabulated shapes. However, for many angles and T shapes, Cw is so small that for
practical purposes it can be taken as zero.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 146
DIMENSIONS AND PROPERTIES
TORSION PROPERTIES
W shapes

√
EC
w
GJ
Normalized
Warping
Constant
Wno
Warping
Statical
Moment
Sw
Qf
Qw
in.
in.2
in.4
in.3
in.3
137
153
167
190
168
166
165
164
1190
1040
922
789
282
251
225
194
811
709
636
551
989000
649000
577000
511000
446000
397000
378000
333000
283000
245000
189000
75.4
95.1
103
110
121
130
138
151
173
187
209
166
158
156
154
152
151
151
149
149
148
147
2240
1540
1380
1240
1100
986
940
836
714
621
481
484
354
323
294
264
240
230
208
179
157
119
1380
992
894
813
730
665
624
560
481
434
364
393000
306000
242000
192000
181000
161000
140000
119000
99300
79600
60.6
67.9
76.8
87.6
91.3
101
109
125
136
147
125
121
118
115
114
113
112
111
111
110
1160
940
762
622
589
530
468
402
336
270
322
272
228
192
184
168
151
134
113
92.0
1030
856
715
596
566
506
453
391
346
299
1620000
1480000
1090000
816000
637000
554000
493000
441000
398000
366000
330000
306000
282000
57.5
59.8
68.6
80.0
92.0
100
108
116
127
134
143
151
160
172
169
162
156
152
150
148
146
146
145
144
143
143
3530
3270
2520
1960
1570
1390
1240
1130
1020
944
858
799
740
674
634
513
415
344
309
281
258
235
219
200
187
175
1910
1790
1420
1130
928
830
757
691
628
585
538
505
472
168000
148000
128000
116000
107000
98500
90200
82200
68100
90.3
98.1
109
116
123
130
137
145
159
109
108
108
107
106
105
105
105
104
576
512
446
407
378
349
321
294
245
408000
357000
319000
281000
250000
224000
198000
95.8
105
113
122
134
145
158
135
133
132
130
130
129
128
1130
1000
906
808
721
650
580
Torsional
Constant
J
Warping
Constant
Cw
Designation
in.4
in.6
W44×335
W ×290
W ×262
W ×230
74.4
51.5
37.7
24.9
536000
463000
406000
346000
W40×593
W ×503
W ×431
W ×372
W ×321
W ×297
W ×277
W ×249
W ×215
W ×199
W ×174
451
186
142
109
79.4
61.2
51.1
37.7
24.4
18.1
11.2
W40×466
W ×392
W ×331
W ×278
W ×264
W ×235
W ×211
W ×183
W ×167
W ×149
277
172
106
64.7
56.1
41.3
30.4
19.6
14.0
9.60
W36×848
W ×798
W ×650
W ×527
W ×439
W ×393
W ×359
W ×328
W ×300
W ×280
W ×260
W ×245
W ×230
W36×256
W ×232
W ×210
W ×194
W ×182
W ×170
W ×160
W ×150
W ×135
W33×354
W ×318
W ×291
W ×263
W ×241
W ×221
W ×201
W33×169
W ×152
W ×141
W ×130
W ×118
1270
1070
600
330
195
143
109
84.5
64.2
52.6
41.5
34.6
28.6
53.3
39.8
28.0
22.2
18.4
15.1
12.4
10.1
6.99
115
84.4
65.0
48.5
35.8
27.5
20.5
17.7
12.4
9.70
7.37
5.30
82400
71700
64400
56600
48300
110
122
131
141
154
93.7
93.8
93.3
92.8
92.2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
329
286
258
228
196
Statical
Moment
176
159
138
128
120
111
103
95.1
79.9
520
468
416
383
359
334
312
291
255
263
237
216
195
174
158
142
709
634
577
519
469
428
386
109
95.1
86.5
76.9
66.6
314
279
257
233
207
TORSION PROPERTIES
1 - 147
TORSION PROPERTIES
W shapes
Designation
W30×477
W ×391
W ×326
W ×292
W ×261
W ×235
W ×211
W ×191
W ×173
W30×148
W ×132
W ×124
W ×116
W ×108
W ×99
W ×90
W27×539
W ×448
W ×368
W ×307
W ×258
W ×235
W ×217
W ×194
W ×178
W ×161
W ×146

√
EC
w
GJ
Normalized
Warping
Constant
Wno
Warping
Statical
Moment
Sw
Qf
Qw
in.6
in.
in.2
in.4
in.3
in.3
480000
364000
286000
249000
215000
190000
166000
146000
129000
63.6
73.6
84.8
92.8
102
111
124
135
148
329
268
223
200
177
160
141
126
113
896
716
595
530
470
422
374
337
303
49400
42100
38600
34900
30900
26800
24000
93.6
106
112
119
127
136
146
77.3
77.3
76.9
76.5
76.1
75.7
75.0
239
204
188
171
152
133
119
86.8
74.0
68.8
62.8
56.1
49.5
45.0
250
219
204
189
173
156
142
440000
336000
254000
199000
159000
140000
128000
111000
98300
87300
77200
47.8
54.1
62.4
71.4
82.2
88.5
94.6
104
114
124
135
111
106
102
99.4
98.2
96.0
95.0
93.9
93.7
92.9
92.2
1490
1190
930
750
613
548
503
442
393
352
314
342
283
231
192
161
146
135
120
107
96.6
87.0
940
766
620
511
424
384
354
314
284
256
231
Torsional
Constant
J
Warping
Constant
Cw
in.4
307
174
103
74.9
53.8
40.0
27.9
20.6
15.3
14.6
9.72
7.99
6.43
4.99
3.77
2.92
499
297
169
101
61.0
46.3
37.0
26.5
19.5
14.7
10.9
124
120
117
115
114
112
112
111
110
1450
1140
919
812
710
633
556
494
439
Statical
Moment
W27×129
W ×114
W ×102
W ×94
W ×84
11.2
7.33
5.29
4.03
2.81
32500
27600
24000
21300
17900
86.7
98.7
108
117
128
66.4
66.4
65.7
65.4
64.9
183
155
137
122
103
69.5
59.2
52.7
47.3
40.6
197
171
153
139
122
W24×492
W ×408
W ×335
W ×279
W ×250
W ×229
W ×207
W ×192
W ×176
W ×162
W ×146
W ×131
W ×117
W ×104
456
271
154
91.7
67.3
51.8
38.6
31.0
24.1
18.5
13.4
9.50
6.72
4.72
283000
214000
160000
125000
108000
95800
83900
76200
68400
62600
54600
47100
40800
35200
40.1
45.2
51.9
59.4
64.5
69.2
75.0
79.8
85.7
93.6
103
113
125
139
92.1
88.1
84.6
82.0
80.6
79.6
78.5
77.7
77.0
77.0
76.3
75.6
74.9
74.3
1150
909
709
570
502
451
401
367
333
304
268
233
204
178
281
233
189
157
141
128
116
107
97.8
89.4
79.5
69.7
61.5
54.1
774
626
509
418
372
338
303
280
255
234
209
185
164
144
W24×103
W ×94
W ×84
W ×76
W ×68
7.10
5.26
3.70
2.68
1.87
16600
15000
12800
11100
9430
77.8
85.9
94.6
104
114
53.0
53.1
52.6
52.2
51.9
117
105
91.3
79.8
68.0
49.4
44.4
39.0
34.4
29.5
140
127
112
100
88.3
W24×62
W ×55
1.71
1.18
4620
3870
83.6
92.2
40.7
40.4
42.3
35.7
23.2
19.8
76.6
67.1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 148
DIMENSIONS AND PROPERTIES
TORSION PROPERTIES
W shapes

√
EC
w
GJ
Normalized
Warping
Constant
Wno
Warping
Statical
Moment
Sw
Qf
Qw
in.6
in.
in.2
in.4
in.3
in.3
41.3
31.1
23.9
15.4
11.3
8.98
6.83
5.21
61800
54300
48500
41100
36000
32700
29200
26200
62.2
67.2
72.5
83.1
90.8
97.1
105
114
67.0
66.0
65.6
65.4
64.7
64.2
63.7
63.2
345
307
277
235
208
191
172
155
W21×93
W ×83
W ×73
W ×68
W ×62
6.03
4.34
3.02
2.45
1.83
9940
8630
7410
6760
5960
65.3
71.8
79.7
84.5
91.8
43.6
43.0
42.5
42.3
42.0
85.3
75.0
65.2
59.9
53.2
38.2
34.2
30.3
28.0
25.1
110
98.0
86.2
79.9
72.2
W21×57
W ×50
W ×44
1.77
1.14
0.77
3190
2570
2110
68.3
76.4
84.2
33.4
33.1
32.8
35.6
28.9
24.0
20.9
17.2
14.5
64.3
55.0
47.7
75700
65600
57400
49900
43200
37900
33200
28900
25700
22700
33.3
35.5
37.8
40.3
43.4
46.6
50.1
54.3
58.6
63.2
58.8
57.5
56.4
55.2
54.2
53.3
52.5
51.6
51.0
50.4
483
427
382
339
299
267
237
210
189
169
Torsional
Constant
J
Warping
Constant
Cw
Designation
in.4
W21×201
W ×182
W ×166
W ×147
W ×132
W ×122
W ×111
W ×101
W18×311
W ×283
W ×258
W ×234
W ×211
W ×192
W ×175
W ×158
W ×143
W ×130
177
135
104
79.7
59.3
45.2
34.2
25.4
19.4
14.7
Statical
Moment
102
92.3
84.4
71.4
64.0
59.2
53.7
49.0
141
127
116
105
94.3
85.7
77.2
69.4
63.2
57.1
265
238
216
187
167
154
139
127
376
338
306
274
245
221
199
178
161
145
W18×119
W ×106
W ×97
W ×86
W ×76
10.6
7.48
5.86
4.10
2.83
20300
17400
15800
13600
11700
70.4
77.6
83.6
92.7
103
50.4
49.8
49.4
48.9
48.4
151
131
120
104
90.7
50.6
44.6
41.2
36.3
31.9
131
115
105
92.8
81.4
W18×71
W ×65
W ×60
W ×55
W ×50
3.48
2.73
2.17
1.66
1.24
4700
4240
3850
3430
3040
59.1
63.4
67.8
73.1
79.7
33.7
33.4
33.1
32.9
32.6
52.1
47.5
43.5
39.0
34.9
25.8
23.8
22.1
19.9
18.0
72.7
66.6
61.4
55.9
50.4
W18×46
W ×40
W ×35
1.22
0.81
0.51
1710
1440
1140
60.2
67.8
76.1
26.4
26.1
25.9
24.2
20.6
16.5
15.3
13.3
10.7
45.3
39.2
33.2
W16×100
W ×89
W ×77
W ×67
7.73
5.45
3.57
2.39
11900
10200
8590
7300
63.1
69.6
78.9
88.9
41.7
41.1
40.6
40.1
107
93.3
79.3
68.2
39.0
34.4
29.7
25.9
99.0
87.3
75.0
64.9
W16×57
W ×50
W ×45
W ×40
W ×36
2.22
1.52
1.11
0.79
0.54
2660
2270
1990
1730
1460
55.7
62.2
68.1
75.3
83.7
28.0
27.6
27.4
27.1
26.9
35.6
30.8
27.2
23.9
20.2
19.0
16.7
15.0
13.4
11.4
52.6
46.0
41.1
36.5
32.0
W16×31
W ×26
0.46
0.26
739
565
64.5
75.0
21.3
21.1
13.0
10.0
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9.17
7.20
27.0
22.1
TORSION PROPERTIES
1 - 149
TORSION PROPERTIES
W shapes
Torsional
Constant
J
Designation
W14×808
W ×730
W ×665
W ×605
W ×550
W ×500
W ×455
W14×426
W ×398
W ×370
W ×342
W ×311
W ×283
W ×257
W ×233
W ×211
W ×193
W ×176
W ×159
W ×145
4
in.
1860
1450
1120
870
670
514
395
331
273
222
178
136
104
79.1
59.5
44.6
34.8
26.5
19.8
15.2
Warping
Constant
Cw
6
in.
√

EC
w
GJ
Normalized
Warping
Constant
Wno
2
Warping
Statical
Moment
Sw
4
Statical
Moment
Qf
3
Qw
in.3
in.
in.
in.
in.
433000
362000
305000
258000
219000
187000
160000
24.6
25.4
26.6
27.7
29.1
30.7
32.4
82.2
78.3
75.5
73.0
70.6
68.5
66.5
1950
1720
1510
1320
1160
1020
899
337
319
287
259
233
209
189
916
831
740
660
588
524
468
144000
129000
116000
103000
89100
77700
67800
59000
51500
45900
40500
35600
31700
33.6
35.0
36.8
38.7
41.2
44.0
47.1
50.7
54.7
58.4
62.9
68.2
73.5
65.3
64.1
62.9
61.6
60.3
59.1
57.9
56.9
55.9
55.1
54.4
53.7
53.0
827
756
689
623
553
493
438
389
345
312
279
248
224
176
163
151
138
125
113
102
91.7
82.3
75.4
68.0
61.3
55.8
434
401
368
336
301
271
243
218
195
177
160
143
130
190
171
154
138
125
49.9
45.3
41.2
37.2
33.7
117
106
95.9
86.6
78.3
W14×132
W ×120
W ×109
W ×99
W ×90
12.3
9.37
7.12
5.37
4.06
25500
22700
20200
18000
16000
73.3
79.2
85.7
93.2
101
50.2
49.7
49.1
48.7
48.3
W14×82
W ×74
W ×68
W ×61
5.08
3.88
3.02
2.20
6710
5990
5380
4710
58.5
63.2
67.9
74.5
34.1
33.7
33.4
33.1
73.8
66.6
60.4
53.3
28.1
25.7
23.5
21.0
69.3
62.8
57.3
51.1
W14×53
W ×48
W ×43
1.94
1.46
1.05
2540
2240
1950
58.2
63.0
69.3
26.7
26.5
26.2
35.5
31.6
27.8
17.3
15.6
13.9
43.6
39.2
34.8
W14×38
W ×34
W ×30
0.80
0.57
0.38
1230
1070
887
63.1
69.7
77.7
23.0
22.8
22.6
20.0
17.5
14.7
11.5
10.2
8.59
30.7
27.3
23.6
W14×26
W ×22
0.36
0.21
405
314
54.0
62.2
16.9
16.8
6.98
5.58
20.1
16.6
243
185
143
108
83.8
64.7
48.8
35.6
25.8
18.5
12.9
9.13
6.86
5.10
3.84
2.93
2.18
57000
48600
42000
35800
31200
27200
23600
20100
17200
14700
12400
10700
9410
8270
7330
6540
5780
24.6
26.1
27.6
29.3
31.0
33.0
35.4
38.2
41.5
45.4
49.9
55.1
59.6
64.8
70.3
76.0
82.9
46.4
45.0
44.0
42.8
41.8
41.0
40.1
39.2
38.4
37.7
37.0
36.4
35.9
35.5
35.2
34.9
34.5
W12×336
W ×305
W ×279
W ×252
W ×230
W ×210
W ×190
W ×170
W ×152
W ×136
W ×120
W ×106
W ×96
W ×87
W ×79
W ×72
W ×65
8.94
7.02
459
403
357
313
279
249
220
192
168
146
126
110
98.2
87.2
78.1
70.3
62.7
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
119
107
96.3
86.4
78.4
71.1
64.1
56.9
50.4
44.5
38.9
34.6
31.3
28.0
25.3
22.9
20.6
301
269
241
214
193
174
156
137
121
107
93.2
81.9
73.6
66.0
59.5
53.9
48.4
1 - 150
DIMENSIONS AND PROPERTIES
TORSION PROPERTIES
W shapes

√
EC
w
GJ
Normalized
Warping
Constant
Wno
Warping
Statical
Moment
Sw
Qf
Qw
in.
in.2
in.4
in.3
in.3
3570
3160
66.3
72.0
28.9
28.7
46.3
41.2
18.2
16.3
43.2
39.0
1.78
1.31
0.95
1880
1650
1440
52.3
57.1
62.6
23.3
23.1
22.9
30.2
26.7
23.6
14.7
13.1
11.8
36.2
32.4
28.8
W12×35
W ×30
W ×26
0.74
0.46
0.30
879
720
607
55.5
63.7
72.4
19.6
19.4
19.2
16.8
13.9
11.8
W12×22
W ×19
W ×16
W ×14
0.29
0.18
0.10
0.07
164
131
96.9
80.4
38.3
43.4
50.1
54.5
12.0
11.8
11.7
11.6
W10×112
W ×100
W ×88
W ×77
W ×68
W ×60
W ×54
W ×49
15.1
10.9
7.53
5.11
3.56
2.48
1.82
1.39
6020
5150
4330
3630
3100
2640
2320
2070
32.1
35.0
38.6
42.9
47.5
52.5
57.5
62.1
26.3
25.8
25.3
24.8
24.4
24.0
23.8
23.6
85.7
74.7
64.2
54.9
47.6
41.2
36.6
33.0
30.8
27.2
23.8
20.7
18.1
15.9
14.3
13.0
73.7
64.9
56.4
48.8
42.6
37.3
33.3
30.2
W10×45
W ×39
W ×33
1.51
0.98
0.58
1200
992
790
45.4
51.2
59.4
19.0
18.7
18.5
23.6
19.8
16.0
11.5
9.77
7.98
27.5
23.4
19.4
W10×30
W ×26
W ×22
0.62
0.40
0.24
414
345
275
41.6
47.3
54.5
14.5
14.3
14.1
10.7
9.05
7.30
7.09
6.08
4.95
18.3
15.6
13.0
W10×19
W ×17
W ×15
W ×12
0.23
0.16
0.10
0.05
104
85.1
68.3
50.9
34.2
37.1
42.1
51.3
3.93
3.24
2.62
1.99
3.76
3.13
2.56
2.00
10.8
9.33
8.00
6.32
W8×67
W ×58
W ×48
W ×40
W ×35
W ×31
5.06
3.34
1.96
1.12
0.77
0.54
1440
1180
931
726
619
530
27.1
30.2
35.1
41.0
45.6
50.4
16.7
16.3
15.8
15.5
15.3
15.1
14.7
12.5
10.4
8.42
7.39
6.46
35.1
29.9
24.5
19.9
17.3
15.2
W8×28
W ×24
0.54
0.35
312
259
38.7
43.8
12.4
12.2
9.43
7.94
5.64
4.83
13.6
11.6
W8×21
W ×18
0.28
0.17
152
122
37.5
43.1
10.4
10.3
5.47
4.44
4.03
3.31
10.2
8.52
W8×15
W ×13
W ×10
0.14
0.09
0.04
51.8
40.8
30.9
31.0
34.3
44.7
7.82
7.74
7.57
2.47
1.97
1.53
2.39
1.93
1.56
6.78
5.70
4.43
W6×25
W ×20
W ×15
0.46
0.24
0.10
150
113
76.5
29.1
34.9
44.5
9.01
8.78
8.58
6.23
4.82
3.34
3.92
3.10
2.18
9.46
7.45
5.39
W6×16
W ×12
W ×9
0.22
0.09
0.04
38.2
24.7
17.7
21.2
26.7
33.8
5.92
5.75
5.60
2.42
1.61
1.19
2.28
1.55
1.19
5.84
4.15
3.12
W5×19
W ×16
0.31
0.19
50.8
40.6
20.6
23.5
5.94
5.81
3.21
2.62
2.44
2.02
5.81
4.82
W4×13
0.15
14.0
15.5
3.87
1.36
1.27
3.14
Torsional
Constant
J
Warping
Constant
Cw
Designation
in.4
in.6
W12×58
W ×53
2.10
1.58
W12×50
W ×45
W ×40
9.89
9.80
9.72
9.56
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.13
4.14
3.09
2.59
32.3
27.2
22.0
17.5
15.2
13.1
Statical
Moment
9.86
8.30
7.15
25.6
21.6
18.6
4.87
4.01
3.04
2.59
14.7
12.4
10.0
8.72
TORSION PROPERTIES
1 - 151
TORSION PROPERTIES
M shapes

√
EC
w
GJ
Normalized
Warping
Constant
Wno
Warping
Statical
Moment
Sw
Qf
Qw
in.6
in.
in.2
in.4
in.3
in.3
0.05
0.04
34.0
31.3
42.0
45.0
9.02
9.01
1.56
1.45
1.98
1.86
7.14
6.58
M10×9
M ×8
0.03
0.02
14.6
12.8
35.5
40.7
6.59
6.57
0.91
0.80
1.32
1.18
4.60
4.06
M8×6.5
0.02
26.0
4.45
0.48
0.82
2.72
M5×18.9
0.34
17.7
5.73
2.98
2.28
5.53
Torsional
Constant
J
Warping
Constant
Cw
Designation
in.4
M12×11.8
M ×10.8
5.23
41.3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Statical
Moment
1 - 152
DIMENSIONS AND PROPERTIES
TORSION PROPERTIES
S shapes
Designation
S24×121
S ×106

√
EC
w
GJ
Normalized
Warping
Constant
Wno
Warping
Statical
Moment
Sw
Qf
Qw
in.6
in.
in.2
in.4
in.3
in.3
11400
10600
48.0
52.1
47.1
46.1
103
98.8
47.1
47.1
154
141
121
112
103
Torsional
Constant
J
Warping
Constant
Cw
in.4
12.8
10.1
Statical
Moment
S24×100
S ×90
S ×80
7.58
6.04
4.88
6380
6000
5640
46.7
50.7
54.7
41.9
41.2
40.5
66.0
63.8
61.6
33.5
33.5
33.5
S20×96
S ×86
8.39
6.64
4710
4390
38.1
41.4
34.9
34.2
57.8
55.5
29.2
29.2
99.7
92.5
S20×75
S ×66
4.59
3.58
2750
2550
39.4
42.9
30.7
30.0
38.9
37.3
22.6
22.6
77.0
70.5
S18×70
S ×54.7
4.15
2.37
1800
1560
33.5
41.3
27.0
26.0
29.2
26.9
17.1
17.1
63.0
52.9
S15×50
S ×42.9
2.12
1.54
811
744
31.5
35.4
20.3
19.8
17.8
16.9
11.8
11.8
39.0
35.1
S12×50
S ×40.8
2.82
1.75
505
437
21.5
25.4
15.5
14.9
14.0
12.9
9.30
9.30
31.0
26.9
S12×35
S ×31.8
1.08
0.90
324
307
27.9
29.7
14.5
14.3
10.0
9.74
7.48
7.48
22.7
21.3
S10×35
S ×25.4
1.29
0.60
189
153
19.5
25.7
11.8
11.1
7.13
6.34
5.24
5.24
17.9
14.4
S8×23
S ×18.4
0.55
0.34
61.8
53.5
17.1
20.2
7.90
7.58
3.50
3.22
3.10
3.10
9.74
8.38
S6×17.25
S ×12.5
0.37
0.17
18.4
14.5
11.3
14.9
5.03
4.70
1.61
1.41
1.63
1.63
5.35
4.30
S5×10
0.11
6.66
12.3
3.51
0.86
1.11
2.88
S4×9.5
S ×7.7
0.12
0.07
3.10
2.62
8.18
9.84
2.59
2.47
0.53
0.48
0.70
0.70
2.05
1.79
S3×7.5
S ×5.7
0.09
0.04
1.10
0.85
5.63
7.42
1.72
1.60
0.28
0.24
0.40
0.40
1.20
1.00
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 153
TORSION PROPERTIES
HP shapes

√
EC
w
GJ
Normalized
Warping
Constant
Wno
Warping
Statical
Moment
Sw
Qf
Qw
in.6
in.
in.2
in.4
in.3
in.3
8.02
5.40
3.60
2.01
19900
16800
14200
11200
80.2
89.8
101
120
49.9
49.2
48.5
47.8
149
128
110
88.0
38.5
33.5
29.1
23.8
97.2
84.3
72.9
59.2
HP13×100
HP ×87
HP ×73
HP ×60
6.25
4.12
2.54
1.39
11300
9430
7680
6020
68.4
77.0
88.5
106
40.9
40.2
39.6
39.0
103
87.7
72.8
57.8
29.9
25.8
21.8
17.7
76.3
65.6
55.2
44.5
HP12×84
HP ×74
HP ×63
HP ×53
4.24
2.98
1.83
1.12
7160
6170
4990
4090
66.1
73.2
84.0
97.2
35.6
35.2
34.6
34.2
75.0
65.5
54.1
44.7
23.5
20.8
17.5
14.7
59.8
52.7
44.2
37.0
HP10×57
HP ×42
1.97
0.81
2240
1540
54.3
70.2
24.1
23.4
34.8
24.7
13.1
9.64
33.2
24.2
HP8×36
0.77
578
44.1
15.4
14.0
6.62
16.8
Torsional
Constant
J
Warping
Constant
Cw
Designation
in.4
HP14×117
HP ×102
HP ×89
HP ×73
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Statical
Moment
1 - 154
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Channels
Designation
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
C15×50
C15×40
C15×33.9
2.67
1.46
1.02
492
411
358
5.49
5.72
5.94
.937
.927
.920
C12×30
C15×25
C15×20.7
0.87
0.54
0.37
151
130
112
4.55
4.72
4.93
.919
.909
.899
C10×30
C1××25
C5××20
C10×15.3
1.23
0.69
0.37
0.21
79.3
68.4
56.9
45.6
3.63
3.75
3.93
4.19
.921
.912
.900
.883
C9×20
C9×15
C9×13.4
0.43
0.21
0.17
39.4
31.0
28.2
3.46
3.69
3.79
.899
.882
.874
C8×18.75
C9×13.75
C9×11.5
0.44
0.19
0.13
25.1
19.2
16.5
3.06
3.27
3.42
.894
.874
.862
C7×12.25
C9×9.8
0.16
0.10
11.2
9.18
2.87
3.02
.862
.846
C6×13
C9×10.5
C9×8.2
0.24
0.13
0.08
7.22
5.95
4.72
2.37
2.49
2.65
.858
.843
.824
C5×9
C9×6.7
0.11
0.06
2.93
2.22
2.10
2.26
.814
.790
C4×7.25
C9×5.4
0.08
0.04
1.24
0.92
1.75
1.89
.768
.741
C3×6
C9×5
C9×4.1
0.07
0.04
0.03
0.46
0.38
0.31
1.39
1.45
1.53
.689
.674
.656
*See LRFD Specification Appendix E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 155
FLEXURAL-TORSIONAL PROPERTIES
Channels
Designation
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
MC18×58
MC10×51.9
MC10×45.8
MC10×42.7
2.81
2.03
1.45
1.23
1070
986
897
852
6.56
6.70
6.88
6.97
.944
.939
.933
.930
MC13×50
MC10×40
MC10×35
MC10×31.8
2.98
1.57
1.14
0.94
558
463
413
380
5.07
5.33
5.50
5.64
.875
.860
.849
.842
MC12×50
MC10×45
MC10×40
MC10×35
MC10×31
MC10×10.6
3.24
2.35
1.70
1.25
1.01
0.06
411
374
336
297
268
11.7
4.77
4.87
5.01
5.18
5.34
4.27
.859
.851
.842
.832
.821
.983
MC10×41.1
MC10×33.6
MC10×28.5
2.27
1.21
0.79
270
224
194
4.26
4.47
4.68
.790
.771
.752
MC10×25
MC10×22
0.64
0.51
125
111
4.46
4.63
.802
.790
MC10×8.4
0.04
3.68
.972
MC9×25.4
MC9×23.9
0.69
0.60
4.08
4.15
.770
.763
MC8×22.8
MC9×21.4
MC9×20
MC9×18.7
MC9×8.5
0.57
0.50
0.44
0.38
0.06
75.3
70.9
47.9
45.1
8.22
3.85
3.91
3.59
3.65
3.24
.716
.709
.780
.773
.910
MC7×22.7
MC9×19.1
0.63
0.41
58.5
49.4
3.53
3.71
.662
.638
MC6×18
0.38
34.6
3.46
.562
MC6×16.3
MC9×15.1
0.34
0.29
22.1
20.6
3.11
3.18
.643
.634
MC6×12
0.15
11.2
2.80
.740
7.01
104
98.2
*See LRFD Specification Appendix E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 156
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Single Angles
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.6
in.
No Units
×1
×17⁄8
×13⁄4
×15⁄8
×19⁄16
×11⁄2
7.13
5.08
3.46
2.21
1.30
0.960
0.682
32.5
23.4
16.1
10.4
6.16
4.55
3.23
4.31
4.35
4.37
4.41
4.45
4.47
4.48
0.632
0.630
0.629
0.627
0.627
0.627
0.624
L8×6×1
L × × 3⁄4
L × ×19⁄16
L × ×11⁄2
L × ×17⁄16
4.35
1.90
0.822
0.584
0.396
16.3
7.28
3.20
2.28
1.55
3.89
3.96
4.01
4.02
4.04
—
—
—
—
—
L8×4×1
L8×4×17⁄8
L × ×13⁄4
L8×4×15⁄8
L × ×19⁄16
L × ×11⁄2
L8×4×17⁄16
3.68
2.48
1.61
0.933
0.704
0.501
0.328
12.9
8.89
5.75
3.42
2.53
1.80
1.22
3.77
3.79
3.82
3.85
3.86
3.88
3.89
—
—
—
—
—
—
—
L7×4×3⁄4
L × ×5⁄8
L × ×1⁄2
L7×4×7⁄16
L × ×3⁄8
1.47
0.873
0.459
0.300
0.200
3.33
3.36
3.38
3.40
3.42
—
—
—
—
—
Designation
L8×8×11⁄8
L
L
L
L
L
L
×
×
×
×
×
×
Torsional
Constant
J
Warping
Constant
Cw
in.4
3.97
2.37
1.25
0.851
0.544
*See LRFD Specification Appendix E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 157
FLEXURAL-TORSIONAL PROPERTIES
Single Angles
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
L6×6×1
L6×6×17⁄8
L6×6×13⁄4
L6×6×15⁄8
L6×6×19⁄16
L6×6×11⁄2
L6×6×17⁄16
L6×6×13⁄8
L6×6×15⁄16
3.68
2.51
1.61
0.954
0.704
0.501
0.340
0.218
0.129
9.24
6.41
4.17
2.50
1.85
1.32
0.899
0.575
0.338
3.19
3.22
3.26
3.29
3.31
3.32
3.34
3.36
3.38
0.637
0.632
0.629
0.628
0.627
0.627
0.627
0.626
0.625
L6×4×3⁄4
L6×4×5⁄8
L6×4×9⁄16
L6×4×1⁄2
L6×4×7⁄16
L6×4×3⁄8
L6×4×5⁄16
1.33
0.792
0.585
0.417
0.284
0.183
0.108
2.64
1.59
1.18
0.843
0.575
0.369
0.217
2.86
2.89
2.9
2.92
2.94
2.96
2.97
—
—
—
—
—
—
—
L6×31⁄2×1⁄2
L6×31⁄2×3⁄8
L6×31⁄2×5⁄16
0.396
0.174
0.103
0.779
0.341
0.201
2.88
2.92
2.93
—
—
—
L5×5×7⁄8
L6×4×3⁄4
L6×4×5⁄8
L6×4×1⁄2
L6×4×7⁄16
L6×4×3⁄8
L6×4×5⁄16
2.07
1.33
0.792
0.417
0.284
0.183
0.108
3.53
2.32
1.40
0.744
0.508
0.327
0.193
2.65
2.68
2.71
2.74
2.77
2.79
2.81
0.634
0.634
0.630
0.630
0.629
0.627
0.626
Designation
*See LRFD Specification Appendix E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 158
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Single Angles
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
L5×31⁄2×3⁄4
L5×31⁄2×5⁄8
L5×31⁄2×1⁄2
L5×31⁄2×3⁄8
L5×31⁄2×5⁄16
L5×31⁄2×1⁄4
1.11
0.660
0.348
0.153
0.0905
0.0479
1.52
0.918
0.491
0.217
0.128
0.0670
2.37
2.40
2.44
2.47
2.49
2.50
—
—
—
—
—
—
L5×3×1⁄2
L5×3×7⁄16
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
0.322
0.219
0.141
0.0832
0.0438
0.444
0.304
0.196
0.116
0.0606
2.39
2.41
2.42
2.43
2.45
—
—
—
—
—
L4×4×3⁄4
L5×3×5⁄8
L5×3×1⁄2
L5×3×7⁄16
L5×3×3⁄8
L5×3×5⁄16
L5×3×1⁄4
1.02
0.610
0.322
0.219
0.141
0.0832
0.0438
1.12
0.680
0.366
0.252
0.162
0.0963
0.0505
2.11
2.14
2.17
2.19
2.20
2.22
2.23
0.639
0.631
0.632
0.631
0.625
0.623
0.627
L4×31⁄2×1⁄2
L5×31⁄2×3⁄8
L5×31⁄2×5⁄16
L5×31⁄2×1⁄4
0.301
0.132
0.0782
0.0412
0.302
0.134
0.0798
0.0419
2.04
2.08
2.09
2.11
—
—
—
—
Designation
*See LRFD Specification Appendix E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 159
FLEXURAL-TORSIONAL PROPERTIES
Single Angles
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
L4×3×5⁄8
L4×3×1⁄2
L4×3×7⁄16
L4×3×3⁄8
L4×3×5⁄16
L4×3×1⁄4
0.529
0.281
0.192
0.123
0.0731
0.0386
0.472
0.255
0.176
0.114
0.0676
0.0356
1.91
1.95
1.96
1.98
2.00
2.01
—
—
—
—
—
—
L31⁄2×31⁄2×1⁄2
L31⁄2×31⁄2×7⁄16
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×5⁄16
L31⁄2×31⁄2×1⁄4
0.281
0.192
0.123
0.0731
0.0386
0.238
0.164
0.106
0.0634
0.0334
1.89
1.91
1.91
1.93
1.95
0.631
0.629
0.628
0.627
0.626
L31⁄2×3×1⁄2
L31⁄2×3×3⁄8
L31⁄2×3×5⁄16
L31⁄2×3×1⁄4
0.260
0.114
0.0680
0.0360
0.191
0.0858
0.0512
0.0270
1.76
1.79
1.81
1.83
—
—
—
—
L31⁄2×21⁄2×1⁄2
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×1⁄4
0.234
0.103
0.0322
0.159
0.0714
0.0225
1.67
1.70
1.73
—
—
—
L3×3×1⁄2
L4×3×7⁄16
L4×3×3⁄8
L4×3×5⁄16
L4×3×1⁄4
L4×3×3⁄16
0.234
0.160
0.103
0.0611
0.0322
0.0142
0.144
0.100
0.0652
0.0390
0.0206
0.00899
1.60
1.61
1.63
1.65
1.66
1.68
0.634
0.632
0.629
0.628
0.627
0.626
Designation
*See LRFD Specification Appendix E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 160
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Single Angles
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
L3×21⁄2×1⁄2
L3×21⁄2×7⁄16
L3×21⁄2×3⁄8
L3×21⁄2×5⁄16
L3×21⁄2×1⁄4
L3×21⁄2×3⁄16
0.213
0.146
0.0943
0.0560
0.0296
0.0131
0.112
0.0777
0.0507
0.0304
0.0161
0.00705
1.47
1.49
1.50
1.52
1.54
1.55
—
—
—
—
—
—
L3×2×1⁄2
L2×2×3⁄8
L2×2×5⁄16
L2×2×1⁄4
L2×2×3⁄16
0.192
0.0855
0.0509
0.0270
0.0120
0.0908
0.0413
0.0248
0.0132
0.00576
1.40
1.43
1.45
1.46
1.48
—
—
—
—
—
L21⁄2×21⁄2×1⁄2
L21⁄2×21⁄2×3⁄8
L21⁄2×21⁄2×5⁄16
L21⁄2×21⁄2×1⁄4
L21⁄2×21⁄2×3⁄16
0.185
0.0816
0.0483
0.0253
0.0110
0.0791
0.0362
0.0218
0.0116
0.00510
1.31
1.34
1.36
1.37
1.39
0.639
0.632
0.630
0.628
0.627
L21⁄2×2×3⁄8
L3×21⁄2×5⁄16
L3×21⁄2×1⁄4
L3×21⁄2×3⁄16
0.0728
0.0432
0.0227
0.00990
0.0268
0.0162
0.00868
0.00382
1.22
1.24
1.25
1.27
—
—
—
—
L2×2×3⁄8
L2×2×5⁄16
L2×2×1⁄4
L2×2×3⁄16
L2×2×1⁄8
0.0640
0.0381
0.0201
0.00880
0.00274
0.0174
0.0106
0.00572
0.00254
0.00079
1.05
1.07
1.09
1.10
1.12
0.637
0.633
0.630
0.628
0.626
Designation
*See LRFD Specification Appendix E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 161
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.6
in.
No Units
37.2
25.7
18.9
12.4
434
279
204
139
8.81
8.67
8.65
8.67
0.724
0.733
0.731
0.723
WT20×296.5**
WT ×251.5**
WT ×215.5
WT ×186
WT ×160.5
WT ×148.5
WT ×138.5
WT ×124.5
WT ×107.5
WT ×99.5
WT ×87
223
140
88.5
58.2
37.7
30.6
25.8
19.1
12.4
9.14
5.60
2340
1420
881
559
350
279
218
158
101
83.5
65.3
8.30
8.17
8.09
8.00
7.92
7.88
7.75
7.71
7.66
7.83
8.12
0.761
0.760
0.756
0.756
0.756
0.756
0.770
0.770
0.770
0.746
0.699
WT20×233**
WT ×196**
WT ×165.5
WT ×139
WT ×132
WT ×117.5
WT ×105.5
WT ×91.5
WT ×83.5
WT ×74.5
139
86.1
53.0
32.4
28.0
20.6
15.2
10.0
7.01
4.68
1360
802
485
278
233
156
113
72.1
62.9
51.9
8.39
8.27
8.19
8.07
8.02
7.88
7.84
7.79
8.02
8.24
0.680
0.678
0.674
0.676
0.680
0.690
0.690
0.691
0.658
0.626
WT18×424**
WT ×399**
WT ×325**
WT ×263.5**
WT ×219.5**
WT ×196.5**
WT ×179.5**
WT ×164**
WT ×150
WT ×140
WT ×130
WT ×122.5
WT ×115
622
527
295
163
96.7
70.7
54.3
42.1
32.0
26.2
20.7
17.3
14.3
6880
5700
3010
1570
894
637
480
363
278
226
181
151
125
8.08
8.02
7.82
7.63
7.52
7.44
7.38
7.32
7.30
7.27
7.28
7.28
7.27
0.802
0.801
0.797
0.797
0.794
0.796
0.797
0.799
0.797
0.796
0.791
0.788
0.784
Designation
WT22×167.5
WT ×145
WT ×131
WT ×115
Torsional
Constant
J
Warping
Constant
Cw
in.4
*See LRFD Specification Section E3.
**Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 162
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
WT18×128
WT ×116
WT ×105
WT ×97
WT ×91
WT ×85
WT ×80
WT ×75
WT ×67.5
26.6
19.8
13.9
11.1
9.19
7.51
6.17
5.04
3.48
205
151
119
92.7
77.6
63.2
53.6
46.0
37.3
7.43
7.40
7.49
7.45
7.45
7.44
7.46
7.50
7.65
0.703
0.703
0.687
0.687
0.686
0.684
0.678
0.670
0.644
WT16.5×177**
WT
×159**
WT
×145.5**
WT
×131.5**
WT
×120.5
WT
×110.5
WT
×100.5
57.2
42.1
32.4
24.2
17.9
13.7
10.2
468
335
256
188
146
113
84.9
7.00
6.94
6.90
6.86
6.91
6.90
6.89
0.802
0.803
0.801
0.802
0.792
0.788
0.784
8.83
6.16
4.84
3.67
2.64
55.4
43.0
35.4
29.3
23.4
6.74
6.82
6.85
6.93
7.02
0.714
0.700
0.691
0.678
0.659
151
85.9
50.8
37.2
26.7
19.9
13.9
10.3
7.61
1170
636
361
257
184
132
96.4
71.2
53.0
6.65
6.54
6.40
6.34
6.31
6.25
6.27
6.25
6.25
0.819
0.815
0.817
0.818
0.815
0.817
0.809
0.806
0.802
7.27
4.85
3.98
3.21
2.49
1.88
1.42
37.6
28.5
23.9
20.5
17.3
14.3
10.5
6.10
6.19
6.20
6.24
6.31
6.38
6.34
0.716
0.698
0.693
0.683
0.669
0.654
0.655
Designation
WT16.5×84.5
WT
×76
WT
×70.5
WT
×65
WT
×59
WT15×238.5**
WT ×195.5**
WT ×163**
WT ×146**
WT ×130.5
WT ×117.5
WT ×105.5
WT ×95.5
WT ×86.5
WT15×74
WT ×66
WT ×62
WT ×58
WT ×54
WT ×49.5
WT ×45
*See LRFD Specification Section E3.
**Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 163
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Designation
WT13.5×269.5**
WT
×224**
WT
×184**
WT
×153.5**
WT
×140.5**
WT
×129
WT
×117.5
WT
×108.5
WT
×97
WT
×89
WT
×80.5
WT
×73
WT13.5×64.5
WT
×57
WT
×51
WT
×47
WT
×42
WT12×246**
WT ×204**
WT ×167.5**
WT ×139.5**
WT ×125**
WT ×114.5
WT ×103.5
WT ×96
WT ×88
WT ×81
WT ×73
WT ×65.5
WT ×58.5
WT ×52
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
245
146
83.6
49.8
39.0
30.2
23.0
18.5
13.2
9.74
7.31
5.44
1740
977
532
304
232
178
135
105
74.3
57.7
42.7
31.7
6.27
6.11
5.97
5.85
5.80
5.77
5.74
5.72
5.66
5.70
5.67
5.65
0.830
0.829
0.828
0.828
0.830
0.828
0.825
0.830
0.826
0.815
0.813
0.810
5.48
5.54
5.52
5.57
5.63
0.731
0.716
0.714
0.703
0.685
5.71
5.55
5.40
5.28
5.22
5.19
5.14
5.11
5.09
5.09
5.08
5.09
5.08
5.07
0.838
0.836
0.837
0.837
0.838
0.836
0.836
0.836
0.835
0.831
0.827
0.818
0.813
0.809
5.60
3.65
2.64
2.01
1.40
223
133
76.0
45.3
33.3
25.7
19.1
15.4
12.0
9.22
6.70
4.74
3.35
2.35
24.0
17.5
12.6
10.2
7.79
1340
748
405
230
165
125
91.3
72.5
55.8
43.8
31.9
23.1
16.4
11.6
WT12×51.5
WT ×47
WT ×42
WT ×38
WT ×34
3.54
2.62
1.84
1.34
0.932
12.3
9.57
6.90
5.30
4.08
4.88
4.89
4.89
4.93
4.99
0.733
0.727
0.721
0.709
0.692
WT12×31
WT ×27.5
0.850
0.588
3.92
2.93
5.13
5.18
0.619
0.606
*See LRFD Specification Section E3.
**Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 164
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Designation
WT10.5×100.5
WT10.5×91
WT10.5×83
WT10.5×73.5
WT10.5×66
WT10.5×61
WT10.5×55.5
WT10.5×50.5
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
20.6
15.4
11.9
7.69
5.62
4.47
3.40
2.60
85.4
63.0
47.3
32.5
23.4
18.4
13.8
10.4
4.67
4.64
4.59
4.64
4.61
4.58
4.56
4.54
0.859
0.859
0.861
0.847
0.845
0.846
0.846
0.846
WT10.5×46.5
WT10.5×41.5
WT10.5×36.5
WT10.5×34
WT10.5×31
3.01
2.16
1.51
1.22
0.513
9.33
6.50
4.42
3.62
2.78
4.37
4.33
4.31
4.31
4.31
0.729
0.732
0.732
0.727
0.722
WT10.5×28.5
WT10.5×25
WT10.5×22
0.884
0.570
0.383
2.50
1.89
1.40
4.36
4.44
4.49
0.665
0.640
0.623
4.42
4.36
4.30
4.23
4.19
4.14
4.10
4.06
4.03
3.99
0.875
0.873
0.874
0.875
0.873
0.875
0.872
0.872
0.874
0.874
WT9×155.5**
WT9×141.5**
WT9×129**
WT9×117**
WT9×105.5**
WT9×96
WT9×87.5
WT9×79
WT9×71.5
WT9×65
87.2
66.5
51.5
39.4
29.4
22.4
17.0
12.6
9.70
7.30
339
251
189
140
102
75.7
56.5
41.2
30.7
22.8
WT9×59.5
WT9×53
WT9×48.5
WT9×43
WT9×38
5.30
3.73
2.92
2.04
1.41
17.4
12.1
9.29
6.42
4.37
4.03
4.00
3.97
3.95
3.92
0.862
0.860
0.862
0.860
0.862
WT9×35.5
WT9×32.5
WT9×30
WT9×27.5
WT9×25
1.74
1.36
1.08
0.829
0.613
3.96
3.01
2.35
1.84
1.36
3.72
3.69
3.67
3.68
3.66
0.751
0.755
0.756
0.749
0.748
WT9×23
WT9×20
WT9×17.5
0.609
0.403
0.252
1.20
0.788
0.598
3.67
3.65
3.74
0.694
0.692
0.662
*See LRFD Specification Section E3.
**Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 165
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
WT8×50
WT ×44.5
WT ×38.5
WT ×33.5
3.85
2.72
1.78
1.19
10.4
7.19
4.61
3.01
3.62
3.60
3.56
3.53
0.877
0.877
0.877
0.879
WT8×28.5
WT ×25
WT ×22.5
WT ×20
WT ×18
1.10
0.760
0.655
0.396
0.271
1.99
1.34
0.974
0.673
0.516
3.30
3.28
3.27
3.24
3.30
0.770
0.770
0.767
0.769
0.745
WT8×15.5
WT ×13
0.229
0.130
0.366
0.243
3.26
3.32
0.695
0.667
5.67
5.47
5.36
5.25
5.15
5.06
4.98
0.959
0.966
0.966
0.966
0.967
0.967
0.967
4.92
4.87
4.81
4.77
4.71
4.66
4.61
4.56
4.52
4.49
4.46
4.42
4.40
0.968
0.968
0.968
0.968
0.968
0.969
0.969
0.970
0.970
0.971
0.971
0.971
0.971
Designation
WT7×404**
WT ×365**
WT ×332.5**
WT ×302.5**
WT ×275**
WT ×250**
WT ×227.5**
918
714
555
430
331
255
196
6970
5250
3920
2930
2180
1620
1210
WT7×213**
WT ×199**
WT ×185**
WT ×171**
WT ×155.5**
WT ×141.5**
WT ×128.5**
WT ×116.5**
WT ×105.5
WT ×96.5
WT ×88
WT ×79.5
WT ×72.5
164
135
110
88.3
67.5
51.8
39.3
29.6
22.2
17.3
13.2
9.84
7.56
991
801
640
502
375
281
209
154
113
87.2
65.2
47.9
36.3
*See LRFD Specification Section E3.
**Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 166
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
WT7×66
WT ×60
WT ×54.5
WT ×49.5
WT ×45
6.13
4.67
3.55
2.68
2.03
26.6
20.0
15.0
11.1
8.31
4.21
4.18
4.16
4.14
4.12
0.966
0.966
0.968
0.968
0.968
WT7×41
WT ×37
WT ×34
WT ×30.5
2.53
1.94
1.51
1.10
5.63
4.19
3.21
2.29
3.25
3.21
3.19
3.18
0.912
0.917
0.915
0.915
WT7×26.5
WT ×24
WT ×21.5
0.970
0.726
0.524
1.46
1.07
0.751
2.89
2.87
2.85
0.868
0.866
0.866
WT7×19
WT ×17
WT ×15
0.398
0.284
0.190
0.554
0.400
0.287
2.87
2.86
2.90
0.800
0.793
0.772
WT7×13
WT ×11
0.179
0.104
0.207
0.134
2.82
2.86
0.713
0.691
Designation
*See LRFD Specification Section E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 167
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Designation
WT6×168**
WT ×152.5**
WT ×139.5**
WT ×126**
WT ×115**
WT ×105**
WT ×95
WT ×85
WT ×76
WT ×68
WT ×60
WT ×53
WT ×48
WT ×43.5
WT ×39.5
WT ×36
WT ×32.5
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
120
92.0
70.9
53.5
41.6
32.2
24.4
17.7
12.8
9.22
6.43
4.55
3.42
2.54
1.92
1.46
1.09
481
356
267
195
148
112
82.1
58.3
41.3
28.9
19.7
13.6
10.1
7.34
5.43
4.07
2.97
4.07
4.00
3.94
3.88
3.84
3.79
3.74
3.69
3.65
3.61
3.58
3.54
3.51
3.49
3.46
3.45
3.43
0.958
0.959
0.957
0.958
0.958
0.958
0.959
0.960
0.960
0.960
0.959
0.961
0.961
0.960
0.960
0.961
0.960
WT6×29
WT ×26.5
1.05
0.788
2.08
1.53
3.01
3.00
0.944
0.940
WT6×25
WT ×22.5
WT ×20
0.889
0.656
0.476
1.23
0.885
0.620
2.67
2.64
2.62
0.899
0.898
0.901
WT6×17.5
WT ×15
WT ×13
0.369
0.228
0.150
0.437
0.267
0.174
2.56
2.55
2.54
0.835
0.830
0.826
WT6×11
WT ×9.5
WT ×8
WT ×7
0.146
0.0899
0.0511
0.0350
0.137
0.0934
0.0678
0.0493
2.52
2.54
2.62
2.64
0.683
0.663
0.624
0.610
*See LRFD Specification Section E3.
**Group 4 or Group 5 shape. See Notes in Table 1-2.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 168
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
WT5×56
WT5×50
WT5×44
WT5×38.5
WT5×34
WT5×30
WT5×27
WT5×24.5
7.50
5.41
3.75
2.55
1.78
1.23
0.909
0.693
16.9
11.9
8.02
5.31
3.62
2.46
1.78
1.33
3.04
3.00
2.98
2.93
2.92
2.89
2.87
2.85
0.963
0.964
0.964
0.964
0.965
0.965
0.966
0.966
WT5×22.5
WT5×19.5
WT5×16.5
0.753
0.487
0.291
0.981
0.616
0.356
2.44
2.42
2.40
0.940
0.936
0.927
WT5×15
WT5×13
WT5×11
0.310
0.201
0.119
0.273
0.173
0.107
2.17
2.15
2.17
0.848
0.848
0.831
WT5×9.5
WT5×8.5
WT5×7.5
WT5×6
0.116
0.0776
0.0518
0.0272
0.0796
0.061
0.0475
0.0255
2.08
2.12
2.16
2.16
0.728
0.702
0.672
0.662
Designation
*See LRFD Specification Section E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 169
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
WT4×33.5
WT ×29
WT ×24
WT ×20
WT ×17.5
WT ×15.5
2.52
1.66
0.979
0.559
0.385
0.268
3.56
2.28
1.30
0.715
0.480
0.327
2.41
2.39
2.34
2.31
2.29
2.29
0.962
0.961
0.966
0.961
0.963
0.961
WT4×14
WT ×12
0.268
0.173
0.230
0.144
1.97
1.96
0.935
0.936
WT4×10.5
WT ×9
0.141
0.0855
0.0916
0.0562
1.80
1.81
0.877
0.863
WT4×7.5
WT ×6.5
WT ×5
0.0679
0.0433
0.0212
0.0382
0.0269
0.0114
1.72
1.74
1.69
0.762
0.732
0.748
WT3×12.5
WT ×10
WT ×7.5
0.229
0.120
0.0504
0.171
0.0858
0.0342
1.76
1.73
1.71
0.952
0.952
0.937
WT3×8
WT ×6
WT ×4.5
0.111
0.0449
0.0202
0.0426
0.0178
0.0074
1.37
1.37
1.34
0.880
0.846
0.852
WT2.5×9.5
WT ×8
0.154
0.0930
0.0775
0.0453
1.44
1.43
0.964
0.962
WT2×6.5
0.0750
0.0213
1.16
0.947
Designation
*See LRFD Specification Section E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 170
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.6
in.
No Units
0.0307
0.0196
0.0330
0.0252
2.69
2.67
0.564
0.572
MT5×4.5
MT ×4
0.0213
0.0116
0.0133
0.00916
2.21
2.21
0.584
0.582
MT4×3.25
0.0146
0.00421
1.73
0.611
MT2.5×9.45**
0.165
0.0732
1.37
0.951
Torsional
Constant
J
Warping
Constant
Cw
in.4
MT6×5.9
MT ×5.4
Designation
*See LRFD Specification Section E3.
**This shape has tapered flanges while other MT shapes have parallel flanges.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 171
FLEXURAL-TORSIONAL PROPERTIES
Structural Tees
Designation
Torsional
Constant
J
Warping
Constant
Cw
Polar
Radius of
Gyration
_
ro*
Flexural
Constant
H*
in.4
in.6
in.
No Units
ST12×60.5
ST ×53
6.38
5.04
27.5
15.0
5.14
4.87
0.640
0.685
ST12×50
ST ×45
ST ×40
3.76
3.01
2.43
19.5
12.1
6.94
5.27
5.12
4.89
0.584
0.616
0.657
ST10×48
ST ×43
4.15
3.30
15.0
9.17
4.36
4.20
0.625
0.661
ST10×37.5
ST ×33
2.28
1.78
7.21
4.02
4.28
4.10
0.612
0.655
ST9×35
ST ×27.35
2.05
1.18
7.03
2.26
4.01
3.71
0.583
0.662
ST7.5×25
ST ×21.45
1.05
0.767
2.02
0.995
3.22
3.04
0.637
0.689
ST6×25
ST ×20.4
1.39
0.872
1.97
0.787
2.60
2.42
0.663
0.733
ST6×17.5
ST ×15.9
0.538
0.449
0.556
0.364
2.49
2.39
0.697
0.731
ST5×17.5
ST ×12.7
0.633
0.300
0.725
0.173
2.23
1.98
0.653
0.768
ST4×11.5
ST ×9.2
0.271
0.167
0.168
0.0642
1.74
1.59
0.707
0.789
ST3×8.625
ST ×6.25
0.182
0.0838
0.0772
0.0197
1.36
1.21
0.706
0.820
ST2.5×5
0.0568
0.0100
1.02
0.842
ST2×4.75
ST ×3.85
0.0589
0.0364
0.00995
0.00457
0.907
0.841
0.800
0.872
ST1.5×3.75
ST ×2.85
0.0440
0.0220
0.00496
0.00189
0.737
0.672
0.832
0.913
*See LRFD Specification Section E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 172
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Double Angles
Long Legs Vertical
Short Legs Vertical
Back to Back of Angles, in.
3⁄
8
0
Back to Back of Angles, in.
3⁄
4
3⁄
8
0
3⁄
4
Designation
ro*
H*
ro*
H*
ro*
H*
ro*
H*
ro*
H*
ro*
H*
L8×8×11⁄8
L × ×1
L × × 7⁄8
L × × 3⁄4
L × × 5⁄8
L × × 1⁄2
4.58
4.58
4.58
4.58
4.58
4.59
0.837
0.833
0.831
0.828
0.825
0.822
4.68
4.68
4.68
4.68
4.68
4.69
0.844
0.840
0.838
0.835
0.832
0.829
4.79
4.79
4.78
4.78
4.78
4.78
0.851
0.847
0.845
0.842
0.839
0.836
4.58
4.58
4.58
4.58
4.58
4.59
0.837
0.833
0.831
0.828
0.825
0.822
4.68
4.68
4.68
4.68
4.68
4.69
0.844
0.840
0.838
0.835
0.832
0.829
4.79
4.79
4.78
4.78
4.78
4.78
0.851
0.847
0.845
0.842
0.839
0.836
L8×6×1
L × × 3⁄4
L × × 1⁄2
4.07
4.08
4.11
0.721
0.714
0.708
4.15
4.16
4.18
0.731
0.724
0.718
4.23
4.24
4.26
0.742
0.735
0.728
4.19
4.17
4.17
0.925
0.919
0.914
4.31
4.29
4.28
0.929
0.924
0.919
4.44
4.41
4.40
0.933
0.928
0.923
L8×4×1
L × × 3⁄4
L × × 1⁄2
3.87
3.89
3.93
0.566
0.562
0.558
3.93
3.94
3.97
0.578
0.573
0.568
3.99
4.00
4.03
0.591
0.586
0.580
4.12
4.08
4.05
0.982
0.980
0.977
4.26
4.22
4.19
0.983
0.981
0.979
4.41
4.36
4.33
0.984
0.982
0.980
L7×4×3⁄4
L × ×1⁄2
L × ×3⁄8
3.42
3.45
3.46
0.609
0.604
0.602
3.48
3.5
3.51
0.623
0.616
0.614
3.55
3.57
3.57
0.637
0.629
0.627
3.58
3.55
3.54
0.968
0.965
0.963
3.71
3.68
3.67
0.971
0.967
0.965
3.85
3.82
3.80
0.973
0.969
0.968
L6×6×1
L × × 7⁄8
L × × 3⁄4
L × × 5⁄8
L × × 1⁄2
L × × 3⁄8
3.43
3.43
3.44
3.44
3.44
3.44
0.843
0.838
0.833
0.830
0.827
0.822
3.54
3.54
3.54
3.54
3.54
3.54
0.852
0.847
0.842
0.839
0.836
0.831
3.65
3.65
3.65
3.64
3.64
3.64
0.861
0.856
0.852
0.848
0.845
0.841
3.43
3.43
3.44
3.44
3.44
3.44
0.843
0.838
0.833
0.830
0.827
0.822
3.54
3.54
3.54
3.54
3.54
3.54
0.852
0.847
0.842
0.839
0.836
0.831
3.65
3.65
3.65
3.64
3.64
3.64
0.861
0.856
0.852
0.848
0.845
0.841
L6×4×3⁄4
L × ×5⁄8
L × ×1⁄2
L × ×3⁄8
2.98
2.98
3.00
3.01
0.672
0.668
0.663
0.661
3.05
3.05
3.06
3.07
0.687
0.683
0.678
0.675
3.13
3.13
3.14
3.15
0.704
0.699
0.693
0.690
3.10
3.09
3.08
3.07
0.948
0.946
0.943
0.940
3.23
3.21
3.20
3.19
0.952
0.950
0.947
0.944
3.36
3.34
3.34
3.32
0.956
0.954
0.951
0.948
L6×31⁄2×3⁄8
L × 1⁄2×5⁄16
2.97
2.97
0.610
0.610
3.02
3.02
0.624
0.624
3.09
3.09
0.640
0.639
3.05
3.03
0.961
0.960
3.17
3.16
0.964
0.963
3.31
3.29
0.967
0.966
L5×5×7⁄8
L × ×3⁄4
L × ×1⁄2
L × ×3⁄8
L × ×5⁄16
2.87
2.85
2.86
2.87
2.87
0.844
0.839
0.830
0.824
0.821
2.97
2.96
2.96
2.96
2.97
0.855
0.850
0.841
0.835
0.833
3.09
3.07
3.07
3.07
3.07
0.865
0.861
0.852
0.846
0.844
2.87
2.85
2.86
2.87
2.87
0.844
0.839
0.830
0.824
0.821
2.97
2.96
2.96
2.96
2.97
0.855
0.850
0.841
0.835
0.833
3.09
3.07
3.07
3.07
3.07
0.865
0.861
0.852
0.846
0.844
*See LRFD Specification Section E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TORSION PROPERTIES
1 - 173
FLEXURAL-TORSIONAL PROPERTIES
Double Angles
Long Legs Vertical
Short Legs Vertical
Back to Back of Angles, in.
Back to Back of Angles, in.
3⁄
8
0
3⁄
4
3⁄
8
0
3⁄
4
Designation
ro*
H*
ro*
H*
ro*
H*
ro*
H*
ro*
H*
ro*
H*
L5×31⁄2×3⁄4
L5×31⁄2×1⁄2
L5×31⁄2×3⁄8
L5×31⁄2×5⁄16
2.50
2.51
2.52
2.53
0.697
0.685
0.682
0.679
2.58
2.59
2.59
2.60
0.715
0.703
0.699
0.695
2.67
2.67
2.67
2.68
0.734
0.722
0.717
0.713
2.61
2.59
2.58
2.58
0.943
0.936
0.932
0.930
2.74
2.71
2.70
2.70
0.948
0.941
0.938
0.936
2.87
2.84
2.83
2.82
0.953
0.947
0.943
0.942
L5×3×1⁄2
L3×3×3⁄8
L3×3×5⁄16
L3×3×1⁄4
2.45
2.46
2.47
2.48
0.626
0.623
0.621
0.618
2.52
2.52
2.53
2.54
0.645
0.641
0.638
0.634
2.59
2.60
2.60
2.61
0.665
0.661
0.657
0.653
2.55
2.54
2.54
2.53
0.962
0.959
0.957
0.956
2.69
2.67
2.67
2.66
0.965
0.963
0.961
0.960
2.82
2.80
2.80
2.79
0.969
0.966
0.965
0.964
L4×4×3⁄4
L3×3×5⁄8
L3×3×1⁄2
L3×3×3⁄8
L3×3×5⁄16
L3×3×1⁄4
2.29
2.29
2.29
2.29
2.29
2.29
0.847
0.839
0.834
0.827
0.824
0.823
2.40
2.40
2.39
2.39
2.39
2.39
0.861
0.853
0.848
0.841
0.838
0.837
2.52
2.51
2.50
2.50
2.50
2.49
0.873
0.867
0.862
0.855
0.852
0.850
2.29
2.29
2.29
2.29
2.29
2.29
0.847
0.839
0.834
0.827
0.824
0.823
2.40
2.40
2.39
2.39
2.39
2.39
0.861
0.853
0.848
0.841
0.838
0.837
2.52
2.51
2.50
2.50
2.50
2.49
0.873
0.867
0.862
0.855
0.852
0.850
L4×31⁄2×1⁄2
L5×31⁄2×3⁄8
L5×31⁄2×5⁄16
L5×31⁄2×1⁄4
2.15
2.15
2.15
2.16
0.783
0.774
0.774
0.770
2.24
2.24
2.24
2.24
0.801
0.792
0.791
0.787
2.34
2.34
2.34
2.34
0.818
0.809
0.808
0.805
2.17
2.17
2.17
2.17
0.881
0.875
0.872
0.870
2.29
2.28
2.28
2.28
0.892
0.887
0.884
0.882
2.41
2.40
2.40
2.39
0.903
0.898
0.895
0.893
L4×3×1⁄2
L3×3×3⁄8
L3×3×5⁄16
L3×3×1⁄4
2.04
2.04
2.05
2.06
0.719
0.714
0.710
0.706
2.12
2.12
2.13
2.13
0.740
0.735
0.731
0.726
2.22
2.21
2.22
2.22
0.762
0.757
0.752
0.747
2.10
2.09
2.09
2.09
0.924
0.919
0.917
0.914
2.22
2.21
2.21
2.20
0.933
0.928
0.925
0.923
2.35
2.34
2.33
2.33
0.940
0.935
0.933
0.931
L31⁄2×31⁄2×3⁄8
L31⁄2×31⁄2×1⁄4
2.00
2.01
0.831
0.824
2.10
2.10
0.847
0.839
2.22
2.21
0.862
0.855
2.00
2.01
0.831
0.824
2.10
2.10
0.847
0.839
2.22
2.21
0.862
0.855
L31⁄2×3×3⁄8
L5×31⁄2×5⁄16
L5×31⁄2×1⁄4
1.86
1.87
1.87
0.771
0.766
0.762
1.95
1.96
1.96
0.791
0.787
0.782
2.06
2.06
2.06
0.812
0.807
0.803
1.89
1.89
1.89
0.884
0.881
0.878
2.00
2.00
2.00
0.897
0.894
0.891
2.13
2.12
2.12
0.909
0.906
0.903
L31⁄2×21⁄2×3⁄8
L31⁄2×31⁄2×1⁄4
1.76
1.77
0.696
0.691
1.84
1.85
0.721
0.715
1.94
1.93
0.748
0.740
1.82
1.81
0.932
0.927
1.94
1.93
0.941
0.936
2.08
2.06
0.948
0.944
L3×3×1⁄2
L3×3×3⁄8
L3×3×5⁄16
L3×3×1⁄4
L3×3×3⁄16
1.72
1.72
1.72
1.72
1.72
0.842
0.834
0.830
0.825
0.822
1.83
1.82
1.82
1.82
1.82
0.860
0.852
0.848
0.844
0.841
1.95
1.94
1.93
1.93
1.93
0.877
0.869
0.866
0.862
0.858
1.72
1.72
1.72
1.72
1.72
0.842
0.834
0.830
0.825
0.822
1.83
1.82
1.82
1.82
1.82
0.860
0.852
0.848
0.844
0.841
1.95
1.94
1.93
1.93
1.93
0.877
0.869
0.866
0.862
0.858
*See LRFD Specification Section E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 174
DIMENSIONS AND PROPERTIES
FLEXURAL-TORSIONAL PROPERTIES
Double Angles
Long Legs Vertical
Short Legs Vertical
Back to Back of Angles, in.
3⁄
8
0
Back to Back of Angles, in.
3⁄
4
3⁄
8
0
3⁄
4
Designation
ro*
H*
ro*
H*
ro*
H*
ro*
H*
ro*
H*
ro*
H*
L3×21⁄2×3⁄8
L3×21⁄2×1⁄4
L3×21⁄2×3⁄16
1.58
1.59
1.59
0.763
0.754
0.750
1.67
1.67
1.67
0.789
0.779
0.775
1.78
1.78
1.77
0.813
0.804
0.800
1.61
1.61
1.61
0.896
0.889
0.885
1.73
1.72
1.72
0.910
0.903
0.899
1.86
1.84
1.84
0.922
0.916
0.912
L3×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
L3×2×3⁄16
1.49
1.50
1.50
1.50
0.672
0.667
0.664
0.661
1.57
1.57
1.57
1.57
0.704
0.698
0.694
0.690
1.66
1.66
1.66
1.66
0.737
0.730
0.726
0.721
1.55
1.55
1.54
1.54
0.949
0.946
0.943
0.940
1.68
1.68
1.67
1.66
0.956
0.954
0.951
0.949
1.82
1.82
1.80
1.80
0.963
0.961
0.958
0.956
L21⁄2×21⁄2×3⁄8
L21⁄2×21⁄2×5⁄16
L21⁄2×21⁄2×1⁄4
L21⁄2×21⁄2×3⁄16
1.43
1.43
1.43
1.43
0.839
0.834
0.829
0.825
1.54
1.54
1.53
1.53
0.861
0.856
0.851
0.847
1.66
1.66
1.65
1.65
0.880
0.876
0.871
0.867
1.43
1.43
1.43
1.43
0.839
0.834
0.829
0.825
1.54
1.54
1.53
1.53
0.861
0.856
0.851
0.847
1.66
1.66
1.65
1.65
0.880
0.876
0.871
0.867
L21⁄2×2×3⁄8
L3×21⁄2×5⁄16
L3×21⁄2×1⁄4
L3×21⁄2×3⁄16
1.29
1.30
1.30
1.31
0.752
0.746
0.741
0.736
1.39
1.39
1.39
1.39
0.785
0.779
0.773
0.767
1.50
1.50
1.50
1.49
0.816
0.810
0.804
0.798
1.33
1.33
1.33
1.32
0.912
0.908
0.903
0.899
1.45
1.45
1.45
1.44
0.927
0.923
0.919
0.915
1.59
1.58
1.58
1.57
0.939
0.935
0.932
0.928
L2×2×3⁄8
L3×2×5⁄16
L3×2×1⁄4
L3×2×3⁄16
L3×2×1⁄8
1.15
1.15
1.15
1.15
1.15
0.846
0.840
0.834
0.828
0.822
1.26
1.26
1.25
1.25
1.25
0.873
0.867
0.861
0.855
0.850
1.39
1.38
1.38
1.37
1.37
0.896
0.890
0.885
0.880
0.875
1.15
1.15
1.15
1.15
1.15
0.846
0.840
0.834
0.828
0.822
1.26
1.26
1.25
1.25
1.25
0.873
0.867
0.861
0.855
0.850
1.39
1.38
1.38
1.37
1.37
0.896
0.890
0.885
0.880
0.875
*See LRFD Specification Section E3.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SURFACE AREAS AND BOX AREAS
1 - 175
SURFACE AREAS AND BOX AREAS
W shapes
Square feet per foot of length
Case A Case B Case C Case D
Designation
Case A Case B Case C Case D
Designation
W44×335
W44×290
W44×262
W44×230
W44
W40×593
W44×503
W44×431
W44×372
W44×321
W44×297
W44×277
W44×249
W44×215
W44×199
W44×174
11.0
11.0
10.9
10.9
12.4
12.3
12.2
12.2
8.67
8.59
8.53
8.46
10.0
9.91
9.84
9.78
10.9
10.7
10.5
10.4
10.3
10.3
10.3
10.2
10.2
10.1
10.0
12.3
12.1
11.9
11.8
11.6
11.6
11.6
11.5
11.5
11.4
11.3
8.56
8.38
8.23
8.11
8.01
7.96
7.93
7.88
7.81
7.76
7.68
9.95
9.75
9.58
9.45
9.33
9.28
9.25
9.19
9.12
9.07
8.99
W40×466
W44×392
W44×331
W44×278
W44×264
W44×235
W36×211
W36×183
W36×167
W36×149
9.79
9.61
9.47
9.35
9.32
9.28
9.22
9.17
9.11
9.05
10.8
10.6
10.5
10.3
10.3
10.3
10.2
10.2
10.1
10.0
8.13
7.96
7.81
7.69
7.66
7.61
7.55
7.48
7.42
7.35
9.18
8.99
8.83
8.69
8.66
8.60
8.53
8.47
8.40
8.34
W36×848
W36×798
W36×650
W36×527
W36×439
W36×393
W36×359
W36×328
W36×300
W36×280
W36×260
W36×245
W36×230
11.1
11.0
10.7
10.4
10.3
10.2
10.1
10.0
9.99
9.95
9.90
9.87
9.84
12.6
12.5
12.1
11.9
11.7
11.6
11.5
11.4
11.4
11.3
11.3
11.2
11.2
8.59
8.49
8.21
7.97
7.79
7.70
7.63
7.57
7.51
7.47
7.42
7.39
7.36
10.1
9.99
9.67
9.41
9.20
9.10
9.02
8.95
8.90
8.85
8.80
8.77
8.73
W36×256
W44×232
W44×210
W44×194
W36×182
W36×170
W36×160
W36×150
W36×135
9.02
8.96
8.91
8.88
8.85
8.82
8.79
8.76
8.71
10.0
9.97
9.93
9.89
9.85
9.82
9.79
9.76
9.70
7.26
7.20
7.13
7.09
7.06
7.03
7.00
6.97
6.92
8.27
8.21
8.15
8.10
8.07
8.03
8.00
7.97
7.92
W33×354
W36×318
W36×291
W36×263
W36×241
W36×221
W33×201
9.66
9.58
9.52
9.46
9.42
9.38
9.33
11.0
10.9
10.8
10.8
10.7
10.7
10.6
7.27
7.19
7.13
7.07
7.02
6.97
6.93
8.61
8.52
8.46
8.39
8.34
8.29
8.24
W33×169
W36×152
W36×141
W36×130
W36×118
8.30
8.27
8.23
8.20
8.15
9.26
9.23
9.19
9.15
9.11
6.60
6.55
6.51
6.47
6.43
7.55
7.51
7.47
7.43
7.39
W30×477
W36×391
W36×326
W36×292
W36×261
W36×235
W36×211
W36×191
W36×173
9.30
9.11
8.96
8.88
8.81
8.75
8.71
8.66
8.62
10.6
10.4
10.2
10.2
10.1
10.0
9.97
9.92
9.87
7.02
6.83
6.68
6.61
6.53
6.47
6.42
6.37
6.32
8.35
8.13
7.96
7.88
7.79
7.73
7.67
7.62
7.57
W30×148
W36×132
W36×124
W36×116
W36×108
W36×99
W36×90
7.53
7.49
7.47
7.44
7.41
7.37
7.35
8.40
8.37
8.34
8.31
8.28
8.25
8.22
5.99
5.93
5.90
5.88
5.84
5.81
5.79
6.86
6.81
6.78
6.75
6.72
6.68
6.66
Case A: Shape perimeter, minus one flange surface.
Case B: Shape perimeter.
Case C: Box perimeter, equal to one flange surface plus twice the depth.
Case D: Box perimeter, equal to two flange surfaces plus twice the depth.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 176
DIMENSIONS AND PROPERTIES
SURFACE AREAS AND BOX AREAS
W shapes
Square feet per foot of length
Case A Case B Case C Case D
Designation
Case A Case B Case C Case D
Designation
W27×539
W ×448
W ×368
W ×307
W ×281
W ×258
W ×235
W ×217
W ×194
W ×178
W ×161
W ×146
8.82
8.61
8.42
8.27
8.21
8.15
8.09
8.04
7.98
7.95
7.91
7.87
10.09
9.86
9.64
9.47
9.40
9.34
9.27
9.22
9.15
9.12
9.08
9.03
6.69
6.48
6.29
6.14
6.08
6.02
5.96
5.91
5.85
5.81
5.77
5.73
7.96
7.73
7.51
7.34
7.27
7.21
7.14
7.09
7.02
6.98
6.94
6.89
W27×129
W ×114
W ×102
W ×94
W ×84
6.92
6.88
6.85
6.82
6.78
7.75
7.72
7.68
7.65
7.61
5.44
5.39
5.35
5.32
5.28
6.27
6.23
6.18
6.15
6.11
W24×492
W ×408
W ×335
W ×279
W ×250
W ×229
W ×207
W ×192
W ×176
W ×162
W ×146
W ×131
W ×117
W ×104
8.07
7.86
7.66
7.51
7.44
7.38
7.32
7.27
7.23
7.22
7.17
7.12
7.08
7.04
9.25
9.01
8.79
8.62
8.54
8.47
8.40
8.35
8.31
8.30
8.24
8.19
8.15
8.11
6.12
5.91
5.71
5.56
5.49
5.43
5.37
5.32
5.28
5.25
5.20
5.15
5.11
5.07
7.29
7.06
6.84
6.67
6.59
6.52
6.45
6.40
6.35
6.33
6.27
6.22
6.18
6.14
W24×103
W ×94
W ×84
W ×76
W ×68
6.18
6.16
6.12
6.09
6.06
6.93
6.92
6.87
6.84
6.80
4.84
4.81
4.77
4.74
4.70
5.59
5.56
5.52
5.49
5.45
W24×62
W ×55
5.57
5.54
6.16
6.13
4.54
4.51
5.13
5.10
W21×201
W18×182
W18×166
W18×147
W18×132
W18×122
W18×111
W18×101
6.75
6.69
6.65
6.61
6.57
6.54
6.51
6.48
7.80
7.74
7.68
7.66
7.61
7.57
7.54
7.50
4.89
4.83
4.78
4.72
4.68
4.65
4.61
4.58
5.93
5.87
5.82
5.76
5.71
5.68
5.64
5.61
W21×93
W18×83
W18×73
W ×68
W18×62
5.54
5.50
5.47
5.45
5.42
6.24
6.20
6.16
6.14
6.11
4.31
4.27
4.23
4.21
4.19
5.01
4.96
4.92
4.90
4.87
W21×57
W18×50
W18×44
5.01
4.97
4.94
5.56
5.51
5.48
4.06
4.02
3.99
4.60
4.56
4.53
W18×311
W18×283
W18×258
W18×234
W18×211
W18×192
W18×175
W18×158
W18×143
W18×130
6.41
6.32
6.24
6.17
6.10
6.03
5.97
5.92
5.87
5.83
7.41
7.31
7.23
7.14
7.06
6.99
6.92
6.86
6.81
6.76
4.72
4.63
4.56
4.48
4.41
4.35
4.29
4.23
4.18
4.14
5.72
5.62
5.54
5.45
5.37
5.30
5.24
5.17
5.12
5.07
W18×119
W18×106
W18×97
W ×86
W18×76
5.81
5.77
5.74
5.70
5.67
6.75
6.70
6.67
6.62
6.59
4.10
4.06
4.03
3.99
3.95
5.04
4.99
4.96
4.91
4.87
W18×71
W18×65
W18×60
W ×55
W18×50
4.85
4.82
4.80
4.78
4.76
5.48
5.46
5.43
5.41
5.38
3.71
3.69
3.67
3.65
3.62
4.35
4.32
4.30
4.27
4.25
Case A: Shape perimeter, minus one flange surface.
Case B: Shape perimeter.
Case C: Box perimeter, equal to one flange surface plus twice the depth.
Case D: Box perimeter, equal to two flange surfaces plus twice the depth.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
SURFACE AREAS AND BOX AREAS
1 - 177
SURFACE AREAS AND BOX AREAS
W shapes
Square feet per foot of length
Case A Case B Case C Case D
Designation
Case A Case B Case C Case D
Designation
W18×46
W ×40
W ×35
4.41
4.38
4.34
4.91
4.88
4.84
3.51
3.48
3.45
4.02
3.99
3.95
W16×100
W ×89
W ×77
W ×67
5.28
5.24
5.19
5.16
6.15
6.10
6.05
6.01
3.70
3.66
3.61
3.57
4.57
4.52
4.47
4.43
W16×57
W ×50
W ×45
W ×40
W ×36
4.39
4.36
4.33
4.31
4.28
4.98
4.95
4.92
4.89
4.87
3.33
3.30
3.27
3.25
3.23
3.93
3.89
3.86
3.83
3.81
W16×31
W ×26
3.92
3.89
4.39
4.35
3.11
3.07
3.57
3.53
W14×808
W ×730
W ×665
W ×605
W ×550
W ×500
W ×455
7.74
7.61
7.46
7.32
7.19
7.07
6.96
9.28
9.10
8.93
8.77
8.62
8.49
8.36
5.35
5.23
5.08
4.94
4.81
4.68
4.57
6.90
6.72
6.55
6.39
6.24
6.10
5.98
W14×426
W ×398
W ×370
W ×342
W ×311
W ×283
W ×257
W ×233
W ×211
W ×193
W ×176
W ×159
W ×145
6.89
6.81
6.74
6.67
6.59
6.52
6.45
6.38
6.32
6.27
6.22
6.18
6.14
8.28
8.20
8.12
8.03
7.94
7.86
7.78
7.71
7.64
7.58
7.53
7.47
7.43
4.50
4.43
4.36
4.29
4.21
4.13
4.06
4.00
3.94
3.89
3.84
3.79
3.76
5.89
5.81
5.73
5.65
5.56
5.48
5.40
5.32
5.25
5.20
5.15
5.09
5.05
W14×132
W ×120
W ×109
W ×99
W ×90
5.93
5.90
5.86
5.83
5.81
7.16
7.12
7.08
7.05
7.02
3.67
3.64
3.60
3.57
3.55
4.90
4.86
4.82
4.79
4.76
W14×82
W14×74
W14×68
W ×61
4.75
4.72
4.69
4.67
5.59
5.56
5.53
5.50
3.23
3.20
3.18
3.15
4.07
4.04
4.01
3.98
W14×53
W14×48
W14×43
4.19
4.16
4.14
4.86
4.83
4.80
2.99
2.97
2.94
3.66
3.64
3.61
W14×38
W14×34
W14×30
3.93
3.91
3.89
4.50
4.47
4.45
2.91
2.89
2.87
3.48
3.45
3.43
W14×26
W ×22
3.47
3.44
3.89
3.86
2.74
2.71
3.16
3.12
W12×336
W ×305
W14×279
W14×252
W14×230
W14×210
W14×190
W14×170
W14×152
W ×136
W14×120
W14×106
W14×96
W14×87
W14×79
W14×72
W14×65
5.77
5.67
5.59
5.50
5.43
5.37
5.30
5.23
5.17
5.12
5.06
5.02
4.98
4.95
4.92
4.89
4.87
6.88
6.77
6.68
6.58
6.51
6.43
6.36
6.28
6.21
6.15
6.09
6.03
5.99
5.96
5.93
5.90
5.87
3.92
3.82
3.74
3.65
3.58
3.52
3.45
3.39
3.33
3.27
3.21
3.17
3.13
3.10
3.07
3.05
3.02
5.03
4.93
4.83
4.74
4.66
4.58
4.51
4.43
4.37
4.30
4.24
4.19
4.15
4.11
4.08
4.05
4.02
W12×58
W14×53
4.39
4.37
5.22
5.20
2.87
2.84
3.70
3.68
W12×50
W14×45
W ×40
3.90
3.88
3.86
4.58
4.55
4.52
2.71
2.68
2.66
3.38
3.35
3.32
Case A: Shape perimeter, minus one flange surface.
Case B: Shape perimeter.
Case C: Box perimeter, equal to one flange surface plus twice the depth.
Case D: Box perimeter, equal to two flange surfaces plus twice the depth.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 178
DIMENSIONS AND PROPERTIES
SURFACE AREAS AND BOX AREAS
W shapes
Square feet per foot of length
Case A Case B Case C Case D
Designation
Case A Case B Case C Case D
Designation
W12×35
W12×30
W12×26
3.63
3.60
3.58
4.18
4.14
4.12
2.63
2.60
2.58
3.18
3.14
3.12
W12×22
W12×19
W12×16
W12×14
2.97
2.95
2.92
2.90
3.31
3.28
3.25
3.23
2.39
2.36
2.33
2.32
2.72
2.69
2.66
2.65
W10×112
W12×100
W12×88
W12×77
W12×68
W12×60
W12×54
W12×49
4.30
4.25
4.20
4.15
4.12
4.08
4.06
4.04
5.17
5.11
5.06
5.00
4.96
4.92
4.89
4.87
2.76
2.71
2.66
2.62
2.58
2.54
2.52
2.50
3.63
3.57
3.52
3.47
3.42
3.38
3.35
3.33
W10×45
W12×39
W12×33
3.56
3.53
3.49
4.23
4.19
4.16
2.35
2.32
2.29
3.02
2.98
2.95
W10×30
W12×26
W12×22
3.10
3.08
3.05
3.59
3.56
3.53
2.23
2.20
2.17
2.71
2.68
2.65
W10×19
W12×17
W12×15
W12×12
2.63
2.60
2.58
2.56
2.96
2.94
2.92
2.89
2.04
2.02
2.00
1.97
2.38
2.35
2.33
2.30
W8×67
W8×58
W8×48
W8×40
W8×35
W8×31
3.42
3.37
3.32
3.28
3.25
3.23
4.11
4.06
4.00
3.95
3.92
3.89
2.19
2.14
2.09
2.05
2.02
2.00
2.88
2.83
2.77
2.72
2.69
2.67
W8×28
W8×24
2.87
2.85
3.42
3.39
1.89
1.86
2.43
2.40
W8×21
W8×18
2.61
2.59
3.05
3.03
1.82
1.79
2.26
2.23
W8×15
W8×13
W8×10
2.27
2.25
2.23
2.61
2.58
2.56
1.69
1.67
1.64
2.02
2.00
1.97
W6×25
W ×20
W8×15
2.49
2.46
2.42
3.00
2.96
2.92
1.57
1.54
1.50
2.08
2.04
2.00
W6×16
W8×12
W8×9
1.98
1.93
1.90
2.31
2.26
2.23
1.38
1.34
1.31
1.72
1.67
1.64
W5×19
W8×16
2.04
2.01
2.45
2.43
1.28
1.25
1.70
1.67
W4×13
1.63
1.96
1.03
1.37
Case A: Shape perimeter, minus one flange surface.
Case B: Shape perimeter.
Case C: Box perimeter, equal to one flange surface plus twice the depth.
Case D: Box perimeter, equal to two flange surfaces plus twice the depth.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
CAMBER
1 - 179
CAMBER
Beams and Girders
Camber and sweep are used to form a desired curvature in either rolled beams or welded
girders. Camber denotes a curve in the vertical plane. Beams and girders can be cambered
to compensate for the anticipated deflection or for architectural reasons. Note that the
required camber is determined at service (unfactored) load levels. Sweep denotes a curve
in the horizontal plane. Camber and sweep may be induced through cold bending or
through the application of heat.
The minimum radius for cold cambering in members up to a nominal depth of 30 inches
is between 10 and 14 times the depth of the member; deeper members will require a larger
minimum radius. Cold bending may be used to provide sweep in members to practically
any radius desired. Note that a length limit of 40 to 50 feet is practical.
Heat cambering, sweeping, and straightening are provided through controlled heat application. The member is rapidly heated in selected areas which tend to expand, but are restrained by
the adjacent cooler areas, causing plastic deformation of the heated areas and a change in the
shape of the cooled member. The mechanical properties of steels are largely unaffected by such
heating operations, provided the maximum temperature does not exceed 1,100°F for quenched
and tempered alloy steels, and 1,300°F for other steels. The temperature should be carefully
checked by temperature-indicating crayons or other suitable means during the heating process.
Cambering and sweeping induces residual stresses similar to those that develop in rolled
structural shapes as elements of the shape cool from the rolling temperature at different
rates. In general, these residual stresses do not affect the ultimate strength of structural
members. Additionally, the effect of residual stresses is incorporated in the provisions of
the LRFD Specification.
Note that when a cambered beam bearing on a wall or other support is loaded,
expansion of the unrestrained end must be considered. In Figure 1-5(a), the end will move
a distance ∆, where
∆=
4Cd
L
If instead the cambered beam is supported on a simple shear connection at both ends,
the top and bottom flange will each move a distance of one-half ∆ since end rotation will
occur approximately about the neutral axis. The designer should be aware of the
magnitude of these movements and make provisions to accommodate them. Figure 1-5(a)
considers the geometry of a girder in the horizontal position, and Figure 1-5(b) illustrates
the condition when the girder is not level.
Trusses
“Cambering” of trusses is accomplished by geometric relocation of panel points and
adjustment of member lengths; it does not involve physical cold bending or the application of heat as with beams and girders.
The following discussion of cambering to compensate for the anticipated deflection
of a truss is applicable for any parabolic condition; large-radius circular curves will be
approximated very closely by the technique described. Cambering to compensate for the
axial deformation of the members of a truss is beyond the scope of this Manual; refer to
a textbook on mechanics of materials.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 180
DIMENSIONS AND PROPERTIES
Distances approximately
equal for small angles
Distances equal for
parabolic curve, approximately
equal for circular curve.
See sketch below.
∆
∆
θ
d
C
90°
C
L
/2
∆
L
/2
tanθ = 2C
Fixed
End
L
/2
∆ = d tanθ
Unrestrained
End
∆ = 4Cd
L
θ
2θ for circular curve
2C for parabolic curve
(a) Beam or Girder Ends at
Same Elevations
4Cd
∆= L
4Cd
∆= L
∆ = 4Cd
L
∆ = 4Cd
L
d
B
Grade
angle
B
L
L approx
.
(b) Beam or Girder Ends at
Different Elevations
Fig. 1-5. Camber for beams and girders.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
B
A+B
A
B
A
Horiz. line
Vert.
A
°
90
A
B
°
e
B
90
Grade lin
A+B
A
C
A
CAMBER
1 - 181
The usual method of providing camber in building trusses is to progressively raise each
panel point. The lengths of the verticals are not changed, but the lengths of the diagonals
are calculated on the basis of the adjusted elevation for the several panel points. For any
simple-span truss, the offset above a straight base line, at the several panel points, can be
computed from the following equations if the vertical curve forming the camber is taken
as a parabola.
2
2

B
B 
D = C − C   = C 1 −   
A
 
A 

where
A = Horizontal distance from end panel point to mid-span of the truss (half the truss span).
B = Horizontal distance from mid-span of the truss to panel point for which offset is
to be determined.
C = Required mid-span camber.
D = Offset from the base-line at panel point corresponding to distance B.
A and B must be expressed in the same units; similarly C and D must be expressed in
the same units, but not necessarily the same units as A and B. When the truss is divided
into any number of approximately equal panels, it may be convenient to express distances
A and B in panel lengths.
For the truss of Figure 1-6(a) with eight equal panels, distance A is taken as four panel
lengths. Assuming the camber at the midpoint is specified as 11⁄2-in., the offset at panel
point 1, where B equals three panel lengths, is:
2

3 
D = 1 -in. 1 −   
4 

= 21⁄32-in.
1⁄
2
The offset at panel point 2, where B equals two panel lengths, is:
2

2 
D = 1 -in. 1 −   

4 
= 11⁄8-in.
1⁄
2
The offset at panel point 3, where B equals one panel length, is:
2

1 
D = 1 -in. 1 −   
4 

= 113⁄32-in.
1⁄
2
Finally, the offset at panel point 4, where B equals zero, is
D = C = 11⁄2-in.
An alternative method of determining the amount of camber at intermediate panel
points when all panel points are approximately the same distance apart is as follows.
Using the truss in Figure 1-6(a) as an example, sketch the camber diagram and number
the panel points, starting with the first panel point from the end of the truss, from 1 to 4,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 182
DIMENSIONS AND PROPERTIES
as shown in Figure 1-6(b) on line A. Next, on line B, reverse the numbering as shown.
Finally, on line C, enter the product of the numbers on lines A and B.
The camber at any panel point is the amount of camber at the centerline of the truss
multiplied by the fraction whose numerator is the figure on line C at the given panel point,
and whose denominator is the figure on line C at the center line of the truss. Thus, at
panel point 1, the camber is
7⁄
16
× 11⁄2jin. = 21⁄32jin.
at panel point 2, the camber is
12⁄
16
× 11⁄2jin. = 11⁄8jin.
at panel point 3, the camber is
15⁄
16
× 11⁄2jin. = 113⁄32jin.
and at panel point 4, the camber is
16⁄
16
× 11⁄2jin. = 11⁄2jin.
cL
4
3
2
1
21/
32
0
1 1/2
1 13/32
11/8
Baseline
EQ
EQ
EQ
EQ
(a) Calculated camber ordinates by formula
1
2
3
cL
4
line A
line B
1
x7
2
x6
3
x5
4
x4
line C
7
12
15
16
Panel point
(b) Alternative calculation method for approximately equal panels
Fig. 1-6. Camber for trusses.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STANDARD MILL PRACTICE
1 - 183
STANDARD MILL PRACTICE
General Information
Rolling structural shapes and plates involves such factors as roll wear, subsequent roll
dressing, temperature variations, etc., which cause the finished product to vary from
published profiles. Such variations are limited by the provisions of the American Society
for Testing and Materials Specification A6. Contained in this section is a summary of
these provisions, not a reproduction of the complete specification. In its entirety, A6
covers a group of common requirements, which, unless otherwise specified in the
purchase order or in an individual specification, apply to rolled steel plates, shapes, sheet
piling, and bars.
As indicated in Table 1-1, carbon steel refers to ASTM designations A36 and A529;
high-strength, low-alloy steel refers to designations A242, A572, and A588; alloy steel
refers to designation A514; and low-alloy steel refers to A852.
For further information on mill practices, including permissible variations for rolled
tees, zees, and bulb angles in structural and bar sizes, pipe, tubing, sheets, and strip, and
for other grades of steel, see ASTM A6, A53, A500, A568, and A618; the Steel Products
Manuals of the Iron and Steel Society (American Institute of Mining, Metallurgical, and
Petroleum Engineers); and producers’ catalogs.
The data on spreading rolls to increase areas and weights, and mill cambering of beams,
is not a part of ASTM A6.
Additional material on mill practice is included in the descriptive material preceding
the “Dimensions and Properties” tables for shapes and plates.
Letter symbols representing dimensions on sketches shown herein are in accordance
with ASTM A6, AISI and mill catalogs and not necessarily as defined by the general
nomenclature of this manual.
Methods of increasing areas and weights by spreading rolls
Cambering of rolled beams . . . . . . . . . . . . . . . . . .
Positions for measuring camber and sweep . . . . . . . . .
W Shapes, permissible variations . . . . . . . . . . . . . .
S Shapes, M Shapes, and Channels, permissible variations .
Tees split from W , M, and S Shapes, permissible variations
Angles split from Channels, permissible variations . . . . .
Angles, structural size, permissible variations . . . . . . . .
Angles, bar size, permissible variations . . . . . . . . . . .
Steel Pipe and Tubing, permissible variations . . . . . . . .
Plates, permissible variations for sheared, length and width .
Plates, permissible variations for universal mill, length . . .
Plates, permissible variations for universal mill, width . . .
Plates, permissible variations for camber . . . . . . . . . .
Plates, permissible variations for flatness . . . . . . . . . .
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1-183
1-186
1-187
1-188
1-190
1-191
1-191
1-192
1-193
1-194
1-196
1-196
1-196
1-197
1-198
Methods of Increasing Areas and Weights by Spreading Rolls
W Shapes
To vary the area and weight within a given nominal size, the flange width, the flange
thickness, and the web thickness are changed as shown in Figure 1-7(a).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 184
DIMENSIONS AND PROPERTIES
S Shapes and American Standard Channels
To vary the area and weight within a given nominal size, the web thickness and the flange
width are changed by an equal amount as shown in Figures 1-7(b) and (c).
Angles
To vary area and weight for a given leg length, the thickness of each leg is changed. Note
that the leg length is changed slightly by this method (Figure 1-7(d)).
Constant for a given
nominal size
(a)
Constant for a given
nominal size
(except S24 and S20)
(b)
Constant for a given
nominal size
(c)
(d)
Fig. 1-7. Varying areas and weights.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STANDARD MILL PRACTICE
1 - 185
Cambering of Rolled Beams
All beams are straightened after rolling to meet permissible variations for sweep and
camber listed hereinafter for W shapes and S shapes. The following data refer to the
subsequent cold cambering of beams to produce a predetermined dimension.
The maximum lengths that can be cambered depend on the length to which a given
section can be rolled, with a maximum of 100 feet. Table 1-10 outlines the maximum and
minimum induced camber of W shapes and S shapes.
Consult the producer for specific camber and/or lengths outside the above listed
available lengths and sections.
Mill camber in beams of less depth than tabulated should not be specified.
A single minimum value for camber, within the ranges shown above for the length
ordered, should be specified.
Camber is measured at the mill and will not necessarily be present in the same amount
in the section of beam as received due to release of stress induced during the cambering
operation. In general 75 percent of the specified camber is likely to remain.
Camber will approximate a simple regular curve nearly the full length of the beam, or
between any two points specified.
Camber is ordinarily specified by the ordinate at the mid-length of the portion of the
beam to be curved. Ordinates at the other points should not be specified.
Although mill cambering to achieve reverse or other compound curves is not considered practical, fabricating shop facilities for cambering by heat can accomplish such
results as well as form regular curves in excess of the limits tabulated above. Refer to the
earlier section Effect of Heat of Steel for further information.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 186
DIMENSIONS AND PROPERTIES
Table 1-10.
Cambering of Rolled Beams
Maximum and Minimum Induced Camber
Sections, Nominal
Depth, in.
Specified Length of Beam, ft
Over 30 to
42, incl.
Over 42 to
52, incl.
Over 52 to
65, incl.
Over 65 to
85, incl.
Over 85 to
100, incl.
Max. and Min. Camber Acceptable, in.
W shapes, 24 and over
W shapes, 14 to 21, incl.
and S shapes, 12 in.
and over
1 to 2,
incl.
3⁄
4
to 21⁄2,
incl.
1 to 3,
incl.
2 to 4,
incl.
3 to 5,
incl.
3 to 6,
incl.
1 to 3,
incl.
—
—
—
Permissible Variations for Camber Ordinate
Lengths
Plus Variation
1⁄
50 ft and less
Over 50 ft
1⁄ -in.
2
2-in.
1⁄ -in.
8
plus
for each 10 ft or
fraction thereof in excess of 50 ft
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Minus Variation
0
0
STANDARD MILL PRACTICE
1 - 187
Table 1-11.
Positions for Measuring Camber and Sweep
Camber
Sweep
Camber
Sweep*
Horizontal
surface
W SHAPES
Camber
S SHAPES and M SHAPES
Sweep*
Camber
Horizontal
surface
Horz
Camber
onta
CHANNELS
ANGLES
l sur
face
TEES
*Due to the extreme variations in flexibility of these shapes, straightness tolerances for sweep are subject to
negotiations between manufacturer and purchaser for individual sections involved.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 188
DIMENSIONS AND PROPERTIES
Table 1-12.
W Shapes, HP Shapes
B
1/
2 B±
B
1/
2 B±
E
E
T′
C
T′
C
A
A
T
T
1/2 B±E
1/
2 B±
E
Permissible Variations in Cross Section
Section
Nominal
Size, in.
A, Depth, in.
B, Fig. Width, in.
Over
Theoretical
Under
Theoretical
Over
Theoretical
To 12, inc.
1⁄
2
1⁄
8
1⁄
4
3⁄
Over 12
1⁄
8
1⁄
8
1⁄
4
3⁄
T+T′
Flanges,
out of
square,
Max, in.
E a,
Web off
Center,
Max, in.
C, Max.
Depth at
any Crosssection
over Theoretical
Depth, in.
16
1⁄
4
3⁄
16
1⁄
4
16
5⁄
3⁄
16
1⁄
4
Under
Theoretical
16
Permissible Variations in Length
Variations from Specified Length for Lengths for Given, in.
30 ft and Under
W Shapes
Over 30 ft
Over
Under
Over
Under
Beams 24 in. and
under in nominal depth
3⁄
8
3⁄
8
3⁄
1
8 plus ⁄16 for each
additional 5 ft or
fraction thereof
3⁄
8
Beams over 24 in. nom.
depth; all columns
1⁄
2
1⁄
2
1⁄
1⁄
2
1
2 plus ⁄16 for each
additional 5 ft or
fraction thereof
Notes:
aVariation of 5⁄ in. max. for sections over 426 lb / ft.
16
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Continued on next page
STANDARD MILL PRACTICE
1 - 189
Table 1-12 (cont.).
WP Shapes, HP Shapes
Other Permissible Variations
Area and weight variation: ±2.5 percent theorectical or specified amount.
Ends out-of-square: 1⁄64-in. per in. of depth, or of flange width if it is greater than the depth.
Camber and Sweep
Permissible Variation, in.
Sizes
Length
Sizes with flange width
equal to or greater than
6 in.
All
Sizes with flange width
less than 6 in.
All
45 ft. and under
Certain sections with a
flange width approx.
equal to depth &
specified on order as
b
columns
Over 45 ft.
Camber
1⁄
8
1⁄
8
in. ×
Sweep
in. ×
(total length ft.)
10
(total length ft.)
10
1⁄
8
in. ×
(total length ft.)
5
(total length ft.)
with 3⁄8 in. max.
10
1⁄
8
in. ×
3⁄
8

(total length ft. − 45) 
in. + 1⁄8 in. ×

10


bApplies only to W8×31 and heavier, W10×49 and heavier, W12×65 and heavier, W14×90 and heavier. If the
other sections are specified on the order as columns, the tolerance will be subject to negotiation with the
manufacturer.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 190
DIMENSIONS AND PROPERTIES
Table 1-13.
S Shapes, M Shapes, and Channels
Permissible Variations in Cross Section
B
B
T′
T′
*
A
A
T
T
* Back of square and centerline of web to be parallel when measuring “out-of-square”
A, Depth in.a
Section
T + T ′b,
Out of
Square per
Inch of
Over
Under
Over
Under
B, in.
Theoretical Theoretical Theoretical Theoretical
Nominal
Size in.
S shapes 3 to 7, incl.
Over 7 to 14,
and M
incl.
shapes
Over 14 to 24,
incl.
1⁄
2
1⁄
8
1⁄
16
3⁄
32
1⁄
8
5⁄
32
1⁄
8
5⁄
32
1⁄
3⁄
16
1⁄
8
3⁄
16
3⁄
16
1⁄
32
32
1⁄
8
1⁄
16
3⁄
32
1⁄
8
1⁄
8
1⁄
8
5⁄
32
1⁄
32
3⁄
1⁄
8
1⁄
8
3⁄
16
1⁄
3⁄
Channels 3 to 4, incl.
Over 7 to 14,
incl.
Over 14
B, Flange Width, in.
16
1⁄
1⁄
32
32
32
32
Permissible Variations in Length
Variations from Specified Length for Lengths Given, in.
Over
30 to 40 ft.,
incl.
to 30 ft.,
incl.
Section
S shapes,
M shapes and
Channels
Over
40 to 50 ft.,
incl.
Over
Under
Over
Under
Over
1⁄
1⁄
4
3⁄
4
1⁄
1
2
4
Under
1⁄
4
Over
50 to 65 ft.,
incl.
Over 65 ft.
Over
Under
Over
Under
11⁄8
1⁄
4
11⁄4
1⁄
4
Other Permissible Variations
Area and weight variation: ±2.5 percent theoretical or specified amount.
Ends out-of square: S shapes and channels 1⁄64-in. per in. of depth.
total length,ft
Camber = 1⁄8-in. ×
5
Notes:
aA is measured at center line of web for beams; and at back of web for channels.
bT + T′ applies when flanges of channels are toed in or out.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STANDARD MILL PRACTICE
1 - 191
Table 1-14.
Tees Split from W, M, and S Shapes,
Angles Split from Channels
Permissible Variations in Depth
A
A
A
Dimension A may be approximately one-half beam or channel depth, or any dimension resulting
from off-center splitting, or splitting on two lines as specified on the order.
Depth of Beam from which
Tees or Angles are Split
Variations in Depth A Over and Under
Tees
Angles
To 6 in., excl.
1⁄
8
1⁄
8
6 to 16, excl.
3⁄
16
3⁄
16
16 to 20, excl.
1⁄
4
1⁄
4
20 to 24, excl.
5⁄
16
—
24 and over
3⁄
8
—
The above variations for depths to tees or angles include the permissible variations in depth for
the beams and channels before splitting.
Other Permissible Variations
Other permissible variations in cross section as well as permissible variations in length, area,
and weight variation, and ends out-of-square will correspond to those of the beam or channel before splitting, except
total length,ft
Camber = 1⁄8-in. ×
5
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 192
DIMENSIONS AND PROPERTIES
Table 1-15.
Angles, Structural Size
Permissible Variations in Cross Section
T
B
B
T
B Length of Leg, in.
Nominal Size,
in.a
Section
Angles
Over
Theoretical
Under
Theoretical
T, Out of Square
per in. of B, in.
1⁄
8
3⁄
32
b
3⁄
128
3 to 4, incl.
Over 4 to 6, incl.
1⁄
8
1⁄
8
b
3⁄
128
Over 6
3⁄
16
1⁄
8
b
3⁄
128
Permissible Variations in Length
Variations from Specified Length for Lengths Given, in.
Over
30 to 40 ft.,
incl.
to 30 ft.,
incl.
Section
Angles
Over
40 to 50 ft.,
incl.
Over
50 to 65 ft.,
incl.
Over 65 ft.
Over
Under
Over
Under
Over
Under
Over
Under
Over
Under
1⁄
2
1⁄
4
3⁄
4
1⁄
4
1
1⁄
4
11⁄8
1⁄
4
11⁄4
1⁄
4
Other Permissible Variations
Area and weight variation: ±2.5 percent theoretical or specified amount.
Ends out-of square: 3⁄128-in. per in. of leg length, or 11⁄2 degrees. Variations based on the longer
leg of unequal angle.
total length,ft
Camber = 1⁄8-in. ×
, applied to either leg
5
Notes;
aFor unequal leg angles, longer leg determines classification.
1
b1⁄
128 in. per in. = 1 ⁄2 deg.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STANDARD MILL PRACTICE
1 - 193
Table 1-16.
Angles, Bar Size*
Permissible Variation in Cross Section
T
B
B
a
Specified
Length of Leg,
in.
T
Variations from Thickness for Thicknesses
Given, Over and Under, in.
3⁄
16
and
Under
Over 3⁄16 to
3⁄ incl.
8
1 and Under
0.008
0.010
Over 1 to 2, incl.
0.010
0.010
Over 2 to 3, excl.
0.012
0.015
Over 3⁄8
B Length of
T, Out of
Leg Over
Square per
and Under, in. Inch of B, in.
1⁄
32
b
3⁄
128
0.012
3⁄
64
b
3⁄
128
0.015
1⁄
16
b
3⁄
128
Permissible Variations in Length
Variations Over Specified Length for Lengths Given
No Variation Under
Section
All sizes of barsize angles
50 to 10 ft.
excl.
10 to 20 ft.
excl.
20 to 30 ft.
excl.
30 to 40 ft.
excl.
40 to 65 ft.
excl.
5⁄
8
1
11⁄2
2
21⁄2
Other Permissible Variations
total length,ft
5
Straightness: Because of warpage, permissible variations for straightness do not apply to bars if
any subsequent heating operation has been performed.
Ends out-of-square: 3⁄128-in. per inch of leg length or 11⁄2 degrees. Variation based on longer leg
of an unequal angle.
Camber: 1⁄4-in. in any 5 feet, or 1⁄4 in. ×
Notes:
*A member is ‘‘bar size’’ when its greatest cross-sectional dimension is less than three inches.
aFor unequal leg angles, longer leg determines classification.
1
b1⁄
128 in. per in. = 1 ⁄2 degrees.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 194
DIMENSIONS AND PROPERTIES
Table 1-17.
Steel Pipe and Tubing
Dimensions and Weight Tolerances
Round Tubing and Pipe (see also Table 1-4)
ASTM A53
Weight—The weight of the pipe as specified in Table X2 and Table X3 (ASTM Specification
A53) shall not vary by more than ±10 percent.
Note that the weight tolerance of ±10 percent is determined from the weights of the customary lifts of pipe as produced for shipment by the mill, divided by the number of feet of
pipe in the lift. On pipe sizes over four inches where individual lengths may be weighed, the
weight tolerance is applicable to the individual length.
Diameter—For pipe two inches and over in nominal diameter, the outside diameter shall not
vary more than ±1 percent from the standard specified.
Thickness—The minimum wall thickness at any point shall not be more than 12.5 percent
under the nominal wall thickness specified.
ASTM 500
Diameter—For pipe two inches and over in nominal diameter, the outside diameter shall not
vary more than ±0.75 percent from the standard specified.
Thickness—The wall thickness at any point shall not be more than 10 percent under or over
the nominal wall thickness specified.
ASTM A501 and ASTM 618
Outside dimensions—For round hot-formed structural tubing two inches and over in nominal
size, the outside diameter shall not vary more than ±1 percent from the standard specified.
Weight (A501 only)—The weight of structural tubing shall be less than the specified value by
more than 3.5 percent.
Mass (A618 only)—The mass of structural tubing shall not be less than the specified value
by more than 3.5 percent.
Length—Structural tubing is commonly produced in random mill lengths and in definite cut
lengths. When cut lengths are specified for structural tubing, the length tolerances shall be in
accordance with the following table:
Over 22 to
44 ft, incl.
22 ft and under
Length tolerance for specified cut lengths, in.
Over
Under
Over
Under
1⁄
1⁄
3⁄
1⁄
2
4
4
4
Straightness—The permissible variation for straightness of structural tubing shall be 1⁄8-in.
times the number of feet of total length divided by 5.
Continued on next page
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STANDARD MILL PRACTICE
1 - 195
Table 1-17 (cont.).
Steel Pipe and Tubing
Dimensions and Weight Tolerances
Square and Rectangular Tubing (see also Table 1-4)
ASTM A500 and ASTM A618
Outside Dimensions—The specified dimensions, measured across the flats at positions at
least two inches from either end-of-square or rectangular tubing and including an allowance
for convexity or concavity, shall not exceed the plus and minus tolerance shown in the following table:
a
Largest Outside Dimension Across Flats, in.
Tolerance Plus an Minus, in.
21⁄2 and under
Over 21⁄2 to 31⁄2, incl.
Over 31⁄2 to 51⁄2, incl.
Over 51⁄2
0.020
0.025
0.030
1 percent
aThe respective outside dimension tolerances
include the allowances for convexity and concavity.
Lengths—Structural tubing is commonly produced in random lengths, in multiple lengths, and
in definite cut lengths. When cut lengths are specified for structural tubing, the length tolerances shall be in accordance with the following table:
22 ft and under
Length tolerance for specified cut lengths, in.
Over 22 to 44 ft, incl.
Over
Under
Over
Under
1⁄
1⁄
3⁄
1⁄
2
4
4
4
Mass (A618 only)—The mass of structural tubing shall not be less than the specified value
by more than 3.5 percent.
Straightness—The permissible variation for straightness of structural tubing shall be 1⁄8-in.
times the number of feet of total length divided by five.
Squareness of sides—For square or rectangular structural tubing, adjacent sides may deviate from 90 degrees by a tolerance of plus or minus two degrees maximum.
Radius of corners—For square or rectangular structural tubing, the radius of any outside corner of the section shall not exceed three times the specified wall thickness.
Twists—The tolerances for twist or variation with respect to axial alignment of the section, for
square and rectangular structural tubing, shall be as shown in the following table:
Specified Dimension of Longest Side, in.
Maximum Twist per 3 ft of Length, in.
11⁄
2 and under
Over 11⁄2 to 21⁄2, incl.
Over 21⁄2 to 4, incl.
Over 4 to 6 incl.
Over 6 to 8, incl.
Over 8
0.050
0.062
0.075
0.087
0.100
0.112
Twist is measured by holding down one end of a square or rectangular tube on a flat surface plate with the bottom side of the tube parallel to the surface plate and noting the height
that either corner, at the opposite end of the bottom side of the tube, extends above the surface plate.
Wall thickness (A500 only)—The tolerance for wall thickness exclusive of the weld area shall
be plus and minus 10 percent of the nominal wall thickness specified. The wall thickness is
to be measured at the center of the flat.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 196
DIMENSIONS AND PROPERTIES
Table 1-18.
Rectangular Sheared Plates and Universal Mill Plates
Permissible Variations in Width and Length for Sheared Plates
(11⁄2-in. and under in thickness)
Permissible Variations in Length Only for Universal Mill Plates
(21⁄2-in. and under in thickness)
Specified
Dimensions, in.
Variations over Specified Width and Length for Thickness,
in., and Equivalent Weights, lb per sq. ft., Given
To 3⁄8 excl.
To 15.3,
excl.
Length
To 120, excl.
Width
to 5⁄8 excl.
15.3 to 25.5,
excl.
5⁄
8
to 1, excl.
1 to 2, incl.a
25.5 to 40.8,
excl.
40.8 to 81.7,
incl.
Width Length Width Length Width Length Width Length
To 60, excl.
60 to 84, excl.
84 to 108, excl
108 and over
120 to 240, excl. To 60, excl.
60 to 84, excl.
84 to 108, excl.
108 and over
240 to 360, excl. To 60, excl.
60 to 84, excl.
84 to 108, excl.
108 and over
3⁄
8
7⁄
16
1⁄
2
5⁄
8
1⁄
2
5⁄
8
3⁄
4
7⁄
8
7⁄
16
1⁄
2
5⁄
8
3⁄
4
3⁄
3⁄
1⁄
1⁄
16
5⁄
8
1
9⁄
3⁄
1⁄
8
2
9⁄
16
11⁄
16
480 to 600, excl. To 60, excl.
60 to 84, excl.
84 to 108, excl.
108 and over
7⁄
To 60, excl.
60 to 84, excl.
84 to 108, excl.
108 and over
4
3⁄
7⁄
600 to 720, excl. To 60, excl.
60 to 84, excl.
84 to 108, excl.
108 and over
8
2
360 to 480, excl. To 60, excl.
60 to 84, excl.
84 to 108, excl.
108 and over
720 and over,
excl.
3⁄
8
16
1⁄
2
9⁄
16
3⁄
4
16
1⁄
2
5⁄
8
3⁄
4
1⁄
5⁄
5⁄
7⁄
2
8
8
8
9⁄
16
3⁄
4
3⁄
4
1
7⁄
4
8
5⁄
11⁄
2
8
16
3⁄
4
1
1
1
11 ⁄8
1⁄
11 ⁄8
11 ⁄4
11 ⁄4
13 ⁄8
1⁄
11 ⁄4
13 ⁄8
13 ⁄8
11 ⁄2
1⁄
11 ⁄4
13 ⁄8
13 ⁄8
11 ⁄2
5⁄
2
2
2
2
3⁄
5⁄
3⁄
7⁄
5⁄
3⁄
7⁄
5⁄
3⁄
7⁄
3⁄
3⁄
2
8
4
8
2
8
4
8
2
8
4
8
8
4
4
1
7⁄
7⁄
4
8
8
11 ⁄8
5⁄
8
11⁄
16
7⁄
8
1
7⁄
7⁄
15 ⁄
8
8
16
11 ⁄8
1⁄
2
5⁄
3⁄
7⁄
5⁄
3⁄
13 ⁄
7⁄
11 ⁄8
11 ⁄8
11 ⁄8
11 ⁄4
5⁄
11 ⁄4
13 ⁄8
13 ⁄8
11 ⁄2
5⁄
11 ⁄2
11 ⁄2
11 ⁄2
15 ⁄8
5⁄
17 ⁄8
17 ⁄8
17 ⁄8
2
3⁄
21 ⁄8
21 ⁄8
21 ⁄8
23 ⁄8
3⁄
7⁄
8
4
8
8
4
16
8
8
4
8
1
3⁄
7⁄
8
4
8
1
3⁄
7⁄
8
4
8
1
7⁄
7⁄
4
8
8
11 ⁄8
7⁄
8
1
1
11 ⁄4
3⁄
4
7⁄
8
5⁄
8
3⁄
4
1
11 ⁄8
1
11 ⁄8
1
1
11 ⁄8
11 ⁄4
3⁄
11 ⁄4
11 ⁄4
13 ⁄8
13 ⁄8
13 ⁄8
11 ⁄2
11 ⁄2
15 ⁄8
15 ⁄8
15 ⁄8
15 ⁄8
13 ⁄4
7⁄
4
8
1
11 ⁄8
3⁄
7⁄
4
8
1
11 ⁄4
3⁄
7⁄
4
8
1
11 ⁄4
3⁄
7⁄
4
8
1
11 ⁄4
7⁄
1
1
11 ⁄ 8
11 ⁄ 4
11 ⁄ 8
11 ⁄ 4
13 ⁄ 8
13 ⁄ 8
11 ⁄ 2
11 ⁄ 2
11 ⁄ 2
13 ⁄ 4
15 ⁄ 8
15 ⁄ 8
17 ⁄ 8
17 ⁄ 8
17 ⁄ 8
17 ⁄ 8
17 ⁄ 8
17 ⁄ 8
17 ⁄8
17 ⁄8
17 ⁄8
21 ⁄4
1
11 ⁄8
11 ⁄4
21 ⁄ 4
21 ⁄ 4
21 ⁄ 4
21 ⁄ 2
21 ⁄4
21 ⁄4
21 ⁄4
21 ⁄2
1
11 ⁄8
11 ⁄4
13 ⁄8
23 ⁄ 4
23 ⁄ 4
23 ⁄ 4
3
8
Notes:
aPermissible variations in length apply also to Universal Mill plates up to 12 in. width for thicknesses over 2 to
21⁄2-in., incl. except for alloy steels up to 13⁄4-in. thick.
Permissible variations under specified width and length, 1⁄4-in. Table applies to all steels listed in ASTM A6.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
STANDARD MILL PRACTICE
1 - 197
Table 1-19.
Rectangular Sheared Plates and Universal Mill Plates
Permissible Variations from Flatness (Carbon Steel Only)
Variations from Flatness for Specified Widths, in.
Specified
Thickness,
in.
To 36
excl.
To 1⁄4, excl.
1⁄ to 3⁄ , excl.
4
8
3⁄ to 1⁄ , excl.
8
2
1⁄ to 3⁄ , excl.
2
4
3⁄ to 1, excl.
4
1 to 2, excl.
2 to 4, excl.
4 to 6, excl.
6 to 8, excl.
9⁄
16
1⁄
2
1⁄
2
7⁄
16
7⁄
16
3⁄
8
5⁄
16
3⁄
8
7⁄
16
36 to 48, 48 to 60, 60 to 72, 72 to 84, 84 to 96, 96 to 108, 108 to
excl.
excl.
excl.
excl.
excl.
excl. 120, excl.
3⁄
4
5⁄
8
9⁄
16
1⁄
2
1⁄
2
1⁄
2
3⁄
8
7⁄
16
1⁄
2
15⁄
3⁄
5⁄
16
4
8
9⁄
16
9⁄
16
1⁄
2
7⁄
16
1⁄
2
1⁄
2
11⁄4
15⁄
16
5⁄
8
5⁄
8
5⁄
8
9⁄
16
1⁄
2
1⁄
2
5⁄
8
13⁄8
11⁄8
3⁄
4
5⁄
8
5⁄
8
9⁄
16
1⁄
2
9⁄
16
11⁄
16
11⁄2
11⁄4
7⁄
8
3⁄
4
5⁄
8
5⁄
8
1⁄
2
9⁄
16
3⁄
4
15⁄8
13⁄8
1
1
3⁄
4
5⁄
8
1⁄
2
5⁄
8
7⁄
8
13⁄4
11⁄2
11⁄8
1
7⁄
8
5⁄
8
9⁄
16
3⁄
4
7⁄
8
Permissible Variations in Camber for Carbon Steel
Sheared and Gas Cut Rectangular Plates
Maximum permissible camber, in. (all thicknesses) = 1⁄8-in. ×
total length,ft
5
Permissible Variations in Camber for Carbon Steel Universal Mill Plates,
High-Strength Low-Alloy Steel Sheared and Gas Cut Rectangular Plates,
Universal Mill Plates, Special Cut Plates
Dimension, in.
Thickness
To 2, incl.
Over 2 to 15, incl.
Over 2 to 15, incl.
Width
Camber for Thicknesses
and Widths Given
All
To 30, incl.
Over 30 to 60, incl.
1⁄ in. × (total length, ft / 5)
8
3⁄ in. × (total length, ft / 5)
16
1⁄ in. × (total length, ft / 5)
4
General Notes:
1. The longer dimension specified is considered the length, and permissible variations in flatness along the
length should not exceed the tabular amount for the specified width in plates up to 12 feet in length.
2. The flatness variations across the width should not exceed the tabular amount for the specified width.
3. When the longer dimension is under 36 inches, the permissible variation should not exceed 1⁄4-in. When the
longer dimension is from 36 to 72 inches, inclusive, the permissible variation should not exceed 75 percent of
the tabular amount for the specified width, but in no case less than 1⁄4-in.
4. These variations apply to plates which have a specified minimum tensile strength of not more than 60 ksi or
compatible chemistry or hardness. The limits in the table are increased 50 percent for plates specified to a
higher minimum tensile strength or compatible chemistry or hardness.
See also next page.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1 - 198
DIMENSIONS AND PROPERTIES
Table 1-20.
Rectangular Sheared Plates and Universal Milled Plates
Permissible Variations from Flatness
(High-Strength Low-Alloy and Alloy Steel, Hot Rolled or Thermally Treated)
Variations from Flatness for Specified Widths, in.
Specified
Thickness,
in.
To 36
excl.
To 1⁄4, excl.
1⁄ to 3⁄ , excl.
4
8
3⁄ to 1⁄ , excl.
8
2
1⁄ to 3⁄ , excl.
2
4
3⁄ to 1, excl.
4
1 to 2, excl.
2 to 4, excl.
4 to 6, excl.
6 to 8, excl.
13⁄
16
3⁄
4
3⁄
4
5⁄
8
5⁄
8
9⁄
16
1⁄
2
9⁄
16
5⁄
8
36 to 48, 48 to 60, 60 to 72, 72 to 84, 84 to 96, 96 to 108, 108 to
excl.
excl.
excl.
excl.
excl.
excl. 120, excl.
11⁄8
15⁄
7⁄
3⁄
3⁄
5⁄
13⁄8
11⁄8
15⁄
16
15⁄
16
7⁄
8
3⁄
4
9⁄
16
3⁄
4
3⁄
4
16
8
4
4
8
9⁄
16
11⁄
16
3⁄
4
17⁄8
13⁄8
15⁄
16
7⁄
8
7⁄
8
13⁄
16
3⁄
4
3⁄
4
15⁄
16
21⁄4
17⁄8
15⁄16
11⁄8
1
15⁄
16
3⁄
4
7⁄
8
11⁄8
2
13⁄4
11⁄8
1
15⁄
16
7⁄
8
3⁄
4
7⁄
8
1
23⁄8
2
11⁄2
11⁄4
11⁄8
1
3⁄
4
15⁄
16
11⁄4
25⁄8
21⁄4
15⁄8
13⁄8
15⁄16
1
7⁄
8
11⁄8
15⁄16
General Notes:
1. The longer dimension specified is considered the length, and variations from a flat surface along the length
should not exceed the tabular amount for the specified width in plates up to 12 feet in length.
2. The flatness variation across the width should not exceed the tabular amount for the specified width.
3. When the longer dimension is under 36 inches, the variation should not exceed 3⁄8-in. When the longer
dimension is from 36 to 72 inches, inclusive the variation should not exceed 75 percent of the tabular amount
for the specified width.
Permissible Variations in Width for Universal Mill Plates
(15 inches and under in thickness)
Variations Over Specified Width for Thickness, in.,
and Equivalent Weights, lb per sq. ft., Given
To 3⁄8,
excl.
3⁄
8
to 5⁄8
excl.
5⁄
8
to 1,
excl.
Specified
Width, in.
To 15.3,
excl.
15.3 to
25.5, excl.
25.5 to
40.8, excl.
Over 8 to 20, excl.
20 to 36, excl.
36 and over
1⁄
8
3⁄
16
5⁄
16
1⁄
1⁄
3⁄
16
5⁄
16
7⁄
16
3⁄
8
4
8
1 to 2,
excl.
Over 2 to
10, incl.
Over 10 to
15, incl.
40.8 to
81.7 to
409.0 to
81.7, incl. 409.0, incl. 613.0, incl.
1⁄
3⁄
1⁄
4
8
2
Notes:
Permissible variation under specified width, 1⁄8-in.
Table applies to all steels listed in ASTM A6.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3⁄
8
7⁄
16
9⁄
16
1⁄
2
9⁄
16
5⁄
8
REFERENCES
1 - 199
REFERENCES
American Institute of Steel Construction, 1973, “Commentary on Highly Restrained
Welded Connections,” Engineering Journal, 3rd Qtr., AISC, Chicago, IL.
American Iron and Steel Institute, 1979, Fire Safe Structural Steel: A Design Guide, AISI,
Washington, DC.
AISI, 1980, Designing Fire Protection for Steel Columns, 3rd Edition.
AISI, 1981, Designing Fire Protection for Steel Trusses, 2nd Edition.
AISI, 1984, Designing Fire Protection for Steel Beams.
Brockenbrough, R. L. and B. G. Johnston, 1981, USS Steel Design Manual, R. L.
Brockenbrough & Assoc. Inc., Pittsburgh, PA.
Dill, F. H., 1960, “Structural Steel After a Fire,” Proceedings of the 1960 National
Engineering Conference, AISC, New York, NY.
Fisher, J. W. and A. W. Pense, 1987, “Experience with Use of Heavy W Shapes in
Tension,” Engineering Journal, 2nd Qtr., AISC, Chicago.
Lightner, M. W. and R. W. Vanderbeck, 1956, “Factors Involved in Brittle Fracture,”
Regional Technical Meetings, AISI, Washington, DC.
Rolfe, S. T. and J. M. Barsom, 1986, Fracture and Fatigue Control in Structures:
Applications of Fracture Mechanics, Prentice-Hall, Inc., Englewood Cliffs, NJ.
Rolfe, S. T., 1977, “Fracture and Fatigue Control in Steel Structures,” Engineering
Journal, 1st Qtr., AISC, Chicago.
Welding Research Council, 1957, Control of Steel Construction to Avoid Brittle Failure,
New York.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2-1
PART 2
ESSENTIALS OF LRFD
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3
INTRODUCTION TO LRFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
A. GENERAL PROVISIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8
B. DESIGN REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11
C. FRAMES AND OTHER STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . 2-14
D. TENSION MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19
E. COLUMNS AND OTHER COMPRESSION MEMBERS . . . . . . . . . . . . . . . . 2-22
F. BEAMS AND OTHER FLEXURAL MEMBERS . . . . . . . . . . . . . . . . . . . . 2-27
H. MEMBERS UNDER COMBINED FORCES AND TORSION . . . . . . . . . . . . . 2-34
I. COMPOSITE MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42
COMPUTER SOFTWARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-44
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-45
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2-2
ESSENTIALS OF LRFD
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
2-3
OVERVIEW
The following LRFD topics are covered herein (with the letters A through I in the section
headings referring to the corresponding chapters in the LRFD Specification):
INTRODUCTION TO LRFD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
LRFD Versus ASD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
LRFD Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
A. GENERAL PROVISIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8
Loads and Load Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8
B. DESIGN REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11
Gross, Net, and Effective Net Areas for Tension Members . . . . . . . . . . . . . . . . 2-11
Gross, Net, and Effective Net Areas for Flexural Members . . . . . . . . . . . . . . . . 2-12
Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-12
Limiting Slenderness Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-13
C. FRAMES AND OTHER STRUCTURES . . . . . . . . . . . . . . . . . . . . . . . . . 2-14
Second Order Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-14
Effective Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-17
“Leaning” Columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-18
D. TENSION MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19
Design Tensile Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-19
Built-Up Members, Eyebars, and Pin-Connected Members . . . . . . . . . . . . . . . . 2-21
E. COLUMNS AND OTHER COMPRESSION MEMBERS . . . . . . . . . . . . . . . . 2-22
Effective Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-22
Design Compressive Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-22
Flexural-Torsional Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27
Built-Up and Pin-Connected Members . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27
F. BEAMS AND OTHER FLEXURAL MEMBERS . . . . . . . . . . . . . . . . . . . . 2-27
Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27
Design for Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-29
Design for Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-33
Web Openings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-34
H. MEMBERS UNDER COMBINED FORCES AND TORSION . . . . . . . . . . . . . 2-34
Symmetric Members Subject to Bending and Axial Tension . . . . . . . . . . . . . . . 2-34
Symmetric Members Subject to Bending and Axial Compression . . . . . . . . . . . . 2-37
Bending and Axial Compression—Preliminary Design . . . . . . . . . . . . . . . . . . 2-37
Torsion and Combined Torsion, Flexure, and/or Axial Force . . . . . . . . . . . . . . . 2-40
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2-4
ESSENTIALS OF LRFD
I. COMPOSITE MEMBERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42
Compression Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42
Flexural Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-43
Combined Compression and Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-44
COMPUTER SOFTWARE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-44
ELRFD (Electronic LRFD Specification) . . . . . . . . . . . . . . . . . . . . . . . . . 2-44
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-45
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
INTRODUCTION TO LRFD
2-5
INTRODUCTION TO LRFD
The intent of this part of the LRFD Manual is to provide a general introduction to the
subject. It was written primarily for:
(1) engineers experienced in allowable stress design (ASD) who are unfamiliar with
LRFD and
(2) students and novice engineers.
The emphasis is on understanding the most common cases, rather than on completeness
and efficiency in design. Regular users of LRFD may also find it helpful to refer to the
information provided herein. It should be noted, however, that the governing document
is the LRFD Specification (in Part 6 of this volume of the Manual). For optimum design
the use of the design aids elsewhere in this Manual is recommended. Among the topics
not covered herein are:
(1) connections, the subject of Volume II, and
(2) noncompact beams and plate girders, for which the reader is referred to Appendices
F and G of the LRFD Specification and Part 4 of this volume of the Manual.
LRFD Versus ASD
The primary objective of the LRFD Specification is to provide a uniform reliability for
steel structures under various loading conditions. This uniformity cannot be obtained with
the allowable stress design (ASD) format.
The ASD method can be represented by the inequality
ΣQi ≤ Rn / F.S.
(2-1)
The left side is the summation of the load effects, Qi (i.e., forces or moments). The right
side is the nominal strength or resistance Rn divided by a factor of safety. When divided
by the appropriate section property (e.g., area or section modulus), the two sides of the
inequality become the calculated stress and allowable stress, respectively. The left side
can be expanded as follows:
ΣQi = the maximum (absolute value) of the combinations
D + L′
(D + L′ + W) × 0.75*
(D + L′ + E) × 0.75*
D−W
D−E
where D, L′, W, and E are, respectively, the effects of the dead, live, wind, and earthquake
loads; total live load L′ = L + (Lr or S or R)
L = Live load due to occupancy
Lr = Roof live load
S = Snow load
R = Nominal load due to initial rainwater or ice exclusive of the ponding
contribution
*0.75 is the reciprocal of 1.33, which represents the 1/3 increase in allowable stress permitted when wind or earthquake is
taken simultaneously with live load.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2-6
ESSENTIALS OF LRFD
ASD, then, is characterized by the use of unfactored service loads in conjunction with a
single factor of safety applied to the resistance. Because of the greater variability and,
hence, unpredictability of the live load and other loads in comparison with the dead load,
a uniform reliability is not possible.
LRFD, as its name implies, uses separate factors for each load and for the resistance.
Considerable research and experience were needed to establish the appropriate factors.
Because the different factors reflect the degree of uncertainty of different loads and
combinations of loads and the accuracy of predicted strength, a more uniform reliability
is possible.
The LRFD method may be summarized by the formula
ΣγiQi ≤ φRn
(2-2)
On the left side of the inequality, the required strength is the summation of the various
load effects Qi multiplied by their respective load factors γi. The design strength, on the
right side, is the nominal strength or resistance Rn multiplied by a resistance factor φ.
Values of φ and Rn for columns, beams, etc. are provided throughout the LRFD Specification and will be covered here, as well.
According to the LRFD Specification (Section A4.1), ΣγiQi = the maximum absolute
value of the following combinations
1.4D
1.2D + 1.6L + 0.5(Lr or S or R)
1.2D + 1.6(Lr or S or R) + (0.5L or 0.8W)
1.2D + 1.3W + 0.5L + 0.5(Lr or S or R)
1.2D ± 1.0E + 0.5L + 0.2S
0.9D ± (1.3W or 1.0E)
(A4-1)
(A4-2)
(A4-3)
(A4-4)
(A4-5)
(A4-6)
(Exception: The load factor on L in combinations A4-3, A4-4, A4-5 shall equal 1.0 for
garages, areas occupied as places of public assembly, and all areas where the live load is
greater than 100 psf).
The load effects D, L, Lr, S, R, W, and E are as defined above. The loads should be
taken from the governing building code or from ASCE 7, Minimum Design Loads in
Buildings and Other Structures (American Society of Civil Engineers, 1988). Where
applicable, L should be determined from the reduced live load specified for the given
member in the governing code. Earthquake loads should be from the AISC Seismic
Provisions for Structural Steel Buildings, which appears in Part 6 of this Manual.
LRFD Fundamentals
The following is a brief discussion of the basic concepts of LRFD. A more complete
treatment of the subject is available in the Commentary on the LRFD Specification
(Section A4 and A5) and in the references cited therein.
LRFD is a method for proportioning structures so that no applicable limit state is
exceeded when the structure is subjected to all appropriate factored load combinations.
Strength limit states are related to safety and load carrying capacity (e.g., the limit states
of plastic moment and buckling). Serviceability limit states (e.g., deflections) relate to
performance under normal service conditions. In general, a structural member will have
several limit states. For a beam, for example, they are flexural strength, shear strength,
vertical deflection, etc. Each limit state has associated with it a value of Rn, which defines
the boundary of structural usefulness.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
INTRODUCTION TO LRFD
2-7
Because the AISC Specification is concerned primarily with safety, strength limit states
are emphasized. The load combinations for determining the required strength were given
in expressions A4-1 through A4-6. (Other load combinations, with different values of
γi, are appropriate for serviceability; see Chapter L in the LRFD Specification and
Commentary.)
The AISC load factors (A4-1 through A4-6) are based on ASCE 7. They were originally
developed by the A58 Load Factor Subcommittee of the American National Standards
Institute, ANSI, (U.S. Department of Commerce, 1980) and are based strictly on load
statistics. Being material-independent, they are applicable to all structural materials.
Although others have written design codes similar in format to the LRFD Specification,
the AISC was the first specification group to adopt the ANSI probability-based load
factors.
The AISC load factors recognize that when several loads act in combination, only one
assumes its maximum lifetime value at a time, while the others are at their “arbitrarypoint-in-time” (APT) values. Each combination models the total design loading condition
when a different load is at its maximum:
Load Combination
A4-1
A4-2
A4-3
A4-4
A4-5
A4-6
Load at its Lifetime (50-year) Maximum
D (during construction; other loads not present)
L
Lr or S or R (a roof load)
W (acting in direction of D)
E (acting in direction of D)
W or E (opposing D)
The other loads, which are APT loads, have mean values considerably lower than the
lifetime maximums. To achieve a uniform reliability, every factored load (lifetime
maximum or APT) is larger than its mean value by an amount depending on its variability.
The AISC resistance factors are based on research recommendations published by
Washington University in St. Louis (Galambos et al., 1978) and reviewed by the AISC
Specification Advisory Committee. Test data were analyzed to determine the variability
of each resistance. In general, the resistance factors are less than one (φ < 1). For uniform
reliability, the greater the scatter in the data for a given resistance, the lower its φ factor.
Several representative LRFD φ factors for steel members (referenced to the corresponding chapters in the LRFD Specification) are:
φt = 0.90 for tensile yielding (Chapter D)
φt = 0.75 for tensile fracture (Chapter D)
φc = 0.85 for compression (Chapter E)
φb = 0.90 for flexure (Chapter F)
φv = 0.90 for shear yielding (Chapter F)
Resistance factors for other member and connection limit states are given in the LRFD
Specification.
The following sections (A through I) summarize and explain the corresponding
chapters of the LRFD Specification.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2-8
ESSENTIALS OF LRFD
A. GENERAL PROVISIONS
In the LRFD Specification, Sections A4 and A5 define Load and Resistance Factor
Design. The remainder of Chapter A contains general provisions which are essentially
the same as in the earlier ASD editions of the Specification.
Reference is made to the Code of Standard Practice for Steel Buildings and Bridges
(adopted in 1992 by AISC), which appears with a Commentary in Part 6 of this LRFD
Manual. The Code defines the practices and commonly accepted standards in the
structural steel fabricating industry. In the absence of other instructions in the contract
documents, these trade practices govern the fabrication and erection of structural steel.
The types of construction recognized by the AISC Specification have not changed,
except that both “simple framing” (formerly Type 2) and “semi-rigid framing” (formerly
Type 3) have been combined into one category, Type PR (partially restrained). “Rigid
framing” (formerly Type 1) is now Type FR (fully restrained). Type FR construction is
permitted unconditionally. Type PR is allowed only upon evidence that the connections
to be used are capable of furnishing, as a minimum, a predictable portion of full end
restraint. Type PR construction may necessitate some inelastic, but self-limiting, deformation of a structural steel part. When specifying Type PR construction, the designer
should take into account the effects of reduced connection stiffness on the stability of the
structure, lateral deflections, and second order bending moments.
Semi-rigid connections, once common, are again becoming popular. They offer
economies in connection fabrication (compared with FR connections) and reduced
member size (compared with simple framing). For information on connections, please
refer to Volume II of this LRFD Manual.
The yield stresses of the grades of structural steel approved for use range from 36 ksi
for the common A36 steel to 100 ksi for A514 steel. Not all rolled shapes and plate
thicknesses are available for every yield stress. Availability tables for structural shapes,
plates and bars are at the beginning of Part 1 of this LRFD Manual.
A36, for many years the dominant structural steel for buildings, is being replaced by
the more economical 50 ksi steels. ASTM designations for structural steels with 50 ksi
yield stress are: A572 for most applications, A529 for thin-plate members only, and A242
and A588 weathering steels for atmospheric corrosion resistance. A more complete
explanation is provided by Table 1-1 in Part 1 of this Manual. However, A36 is still
normally specified for connection material, where no appreciable savings can be realized
from higher strength steels.
Complete and accurate drawings and specifications are necessary for all stages of steel
construction. The requirements for design documents are set forth in Section A7 of the
LRFD Specification and Section 3 of the AISC Code of Standard Practice. When beam
end reactions are not shown on the drawings, the structural steel detailer will refer to the
appropriate tables in Part 4 of the LRFD Manual. These tables, which are for uniform
loads, may significantly underestimate the effects of the concentrated loads. The recording of beam end reactions on design drawings, which is recommended in all cases, is,
therefore, absolutely essential when there are concentrated loads. Beam reactions,
column loads, etc., shown on design drawings should be the required strengths calculated
from the factored load combinations and should be so noted.
Loads and Load Combinations
LRFD Specification Sections A4 (Loads and Load Combinations) and A5 (Design Basis)
describe the basic criteria of LRFD. This information was discussed above under
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
A. GENERAL PROVISIONS
2-9
Introduction to LRFD. To illustrate the application of load factors, the AISC load
combinations will be repeated here with design examples.
The required strength is the maximum absolute value of the combinations
1.4D
1.2D + 1.6L + 0.5(Lr or S or R)
1.2D + 1.6(Lr or S or R) + (0.5L or 0.8W)
1.2D + 1.3W + 0.5L + 0.5(Lr or S or R)
1.2D ± 1.0E + 0.5L + 0.2S
0.9D ± (1.3W or 1.0E)
(A4-1)
(A4-2)
(A4-3)
(A4-4)
(A4-5)
(A4-6)
(The load factor on L in combinations A4-3, A4-4 and A4-5 shall equal 1.0 for garages,
areas occupied as placed of public assembly, and all areas where the live load is greater
than 100 psf).
In the combinations the loads or load effects (i.e., forces or moments) are:
D = dead load due to the weight of the structural elements and the permanent features on the structure
L = live load due to occupancy and moveable equipment (reduced as permitted by
the governing code)
Lr = roof live load
W= wind load
S = snow load
E = earthquake load
R = nominal load due to initial rainwater or ice exclusive of the ponding contribution
The loads are to be taken from the governing building code. In the absence of a code, one
may use ASCE 7 Minimum Design Loads for Buildings and Other Structures (American
Society of Civil Engineers, 1988). Earthquake loads should be determined from the AISC
Seismic Provisions for Structural Steel Buildings, in Part 6 of this Manual.
Whether the loads themselves or the load effects are combined, the results are the same,
provided the principle of superposition is valid. This is usually true because deflections
are small and the stress-strain behavior is linear elastic; consequently, second order effects
can usually be neglected. (The analysis of second order effects is covered in Chapter C
of the LRFD Specification.) The linear elastic assumption, although not correct at the
strength limit states, is valid under normal in-service loads and is permissible as a design
assumption under the LRFD Specification. In fact, the Specification (in Section A.5.1)
allows the designer the option of elastic or plastic analysis using the factored loads.
However, to simplify this presentation, it is assumed that the more prevalent elastic
analysis option has been selected.
EXAMPLE A-1
Given:
Solution:
Roof beams W16×31, spaced 7′′-0 center-to-center, support a superimposed dead load of 40 psf. Code specified roof loads are 30 psf
downward (due to roof live load, snow, or rain) and 20 psf upward or
downward (due to wind). Determine the critical loading for LRFD.
D
= 31 plf + 40 psf × 7.0 ft = 311 plf
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 10
ESSENTIALS OF LRFD
L
=0
(Lr or S or R) = 30 psf × 7.0 ft = 210 plf
W
= 20 psf × 7.0 ft = 140 plf
E
=0
Load
Combinations
A4-1
A4-2
A4-3
A4-4
A4-5
A4-6a
A4-6b
Factored Loads
1.4(311 plf)
1.2(311 plf) + 0 + 0.5(210 plf)
1.2(311 plf) + 1.6 (210 plf) +
0.8(140 plf)
1.2(311 plf) + 1.3(140 plf) + 0 +
0.5(210 plf)
1.2(311 plf) + 0 + 0 + 0.2(210 plf)
0.9 (311 plf) + 1.3 (140 plf)
0.9(311 plf) − 1.3(140 plf)
= 435 plf
= 478 plf
= 821 plf
= 660 plf
= 415 plf
= 462 plf
= 98 plf
The critical factored load combination for design is the third, with a
total factored load of 821 plf.
EXAMPLE A-2
Given:
Solution:
The axial loads on a building column resulting from the code-specified
service loads have been calculated as: 100 kips from dead load, 150
kips from (reduced) floor live load, 30 kips from the roof (Lr or S or
R), 60 kips due to wind, and 50 kips due to earthquake. Determine the
required strength of this column.
Load
Combination
A4-1
A4-2
A4-3a
A4-3b
A4-4
A4-5a
A4-5b
A4-6a
A4-6b
A4-6c
A4-6d
Factored Axial Load
1.4(100 kips)
1.2(100 kips) + 1.6(150 kips) +
0.5(30 kips)
1.2(100 kips) + 1.6(30 kips) +
0.5(150 kips)
1.2(100 kips) + 1.6(30 kips) +
0.8(60 kips)
1.2(100 kips) + 1.3(60 kips) +
0.5(150 kips) + 0.5(30 kips)
1.2(100 kips) + 1.0(50 kips) +
0.5(150 kips) + 0.2(30 kips)
1.2(100 kips) − 1.0(50 kips) +
0.5(150 kips) + 0.2(30 kips)
0.9(100 kips) + 1.3(60 kips)
0.9(100 kips) − 1.3(60 kips)
0.9(100 kips) + 1.0(50 kips)
0.9(100 kips) − 1.0(50 kips)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
= 140 kips
= 375 kips
= 243 kips
= 216 kips
= 288 kips
= 251 kips
= 151 kips
= 168 kips
= 12 kips
= 140 kips
= 40 kips
B. DESIGN REQUIREMENTS
2 - 11
The required strength of the column is 375 kips based on the second
combination of factored axial loads. As none of the results above are
negative, net tension need not be considered in the design of this
column.
B. DESIGN REQUIREMENTS
Gross, Net, and Effective Net Areas for Tension Members
The concept of effective net area, which in earlier editions of the Specification was
applied only to bolted members, has been extended to cover members connected by
welding as well. As in the past, when tensile forces are transmitted directly to all elements
of the member, the net area is used to determine stresses. However, when the tensile forces
are transmitted through some, but not all, of the cross-sectional elements of the member,
a reduced effective net area Ae is used instead. According to Section B3 of the LRFD
Specification
Ae = AU
(B3-1)
where
A = area as defined below
U = reduction
coefficient
_
=
1
−
(x
/
L)
≤ 0.9, or as defined in (c) or (d)
(B3-2)
_
x = connection eccentricity. (See Commentary on the LRFD Specification, Section
B3 and Figure C-B3.1.)
L = length of connection in the direction of loading
a. When the forces are transmitted only by bolts
A = An
= net area of member, in.2
b. When the forces are transmitted by longitudinal welds only or in combination with
transverse welds
A = Ag
= gross area of member, in.2
c. When the forces are transmitted only by transverse welds
A = area of directly connected elements, in.2
U = 1.0
d. When the forces are transmitted to a plate by longitudinal welds along both edges
at the end of the plate
A = area of plate, in.2
l ≥w
For l ≥ 2w
For 2w > l ≥ 1.5w
For 1.5w > l ≥ w
U = 1.00
U = 0.87
U = 0.75
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 12
ESSENTIALS OF LRFD
where
l = weld length
w = plate width (distance between welds), in.
In computing the net area for tension and shear, the width of a bolt hole is taken as 1⁄16-in.
greater than the nominal dimension of the hole, which, for standard holes, is 1⁄16-in. larger
than the diameter of the bolt. Chains of holes, treated as in the past, are covered in Section
B2 of the LRFD Specification.
Gross, Net, and Effective Net Areas for Flexural Members
Gross areas are used for elements in compression, in beams and columns. According to
Section B10 of the LRFD Specification, the properties of beams and other flexural
members are based on the gross section (with no deduction for holes in the tension flange)
if
0.75Fu Afn ≥ 0.9Fy Afg
(B10-1)
where
Afg = gross flange area, in.2
Afn = net flange area (deducting bolt holes), in.2
Fy = specified minimum yield stress, ksi
Fu = minimum tensile strength, ksi
Otherwise, an effective tension flange area Afe is used to calculate flexural properties
Afe =
5 Fu
A
6 Fy fn
(B10-3)
Local Buckling
Steel sections are classified as either compact, noncompact, or slender element sections:
• If the flanges are continuously connected to the web and the width-thickness ratios
of all the compression elements do not exceed λp, then the section is compact.
• If the width-thickness ratio of at least one of its compression elements exceeds λp,
but does not exceed λr, the section is noncompact.
• If the width-thickness ratio of any compression element exceeds λr, that element is
called a slender compression element.
Columns with compact and noncompact cross sections are covered by Chapter E of
the LRFD Specification. Column cross sections with slender elements require the special
design procedure in Appendix B5.3 of the Specification.
Beams with compact sections are covered by Chapter F of the LRFD Specification.
All other cross sections in bending must be designed in accordance with Appendices
B5.3, F1 and/or G.
In general, reference to the appendices of the Specification is required for the design
of members controlled by local buckling. In slender element sections, local buckling,
occurring prior to initial yielding, will limit the strength of the member. Noncompact
sections will yield first, but local buckling will precede the development of a fully plastic
stress distribution. In actual practice, such cases are not common and can be easily
avoided by designing so that:
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
B. DESIGN REQUIREMENTS
2 - 13
Table B-1.
Limiting Width-Thickness Ratios for Compression Elements*
WidthThickness Ratio
Beam Element
Limiting Width-Thickness Ratio, λp
General
For Fy = 50 ksi
Flanges of I shapes and channels
b/t
65 / √
F
y
9.2
Flanges of square and rectangular
box beams
b/t
190 / √
Fy
26.9
Webs in flexural compression
h / tw
640 / √
Fy
90.5
Webs in combined flexural and axial
compression
h / tw
253 / √
Fy **
35.8
Column Element
WidthThickness Ratio
Limiting Width-Thickness Ratio, λr
General
For Fy = 50 ksi
Flanges of I shapes and channels
and plates projecting from
compression elements
b/t
95 / √
F
y
13.4
Webs in axial compression
h / tw
253 / √
Fy
35.8
*For the complete table, see LRFD Specification, Section B5, Table B5.1.
**This is a simplified, conservative version of the corresponding entry in Table B5.1 of the LRFD Specification.
• for beams, the width-thickness ratios of all compression elements ≤ λp;
• for columns, the width-thickness ratios of all elements ≤ λr.
Table B-1, which is an abridged version of Table B5.1 in the LRFD Specification,
should be useful for this purpose. The formulas for λp for beam elements and λr for column
elements are tabulated, together with the corresponding numerical values for 50 ksi steel.
The definitions of “width” for use in determining the width-thickness ratios of the
elements of various structural shapes are stated in Section B5 of the LRFD Specification.
They are shown graphically in Figure B-1. Compact section criteria for W shapes and
other I-shaped cross sections are listed in the Properties Tables in Part 1 of LRFD Manual.
Limiting Slenderness Ratios
For members whose design is based on compressive force, the slenderness ratio Kl / r
preferably should not exceed 200.
For members whose design is based on tensile force, the slenderness ratio l / r
preferably should not exceed 300. The above limitation does not apply to rods in tension.
K = effective length factor, defined in Section C below
l = distance between points of lateral support (lx or ly), in.
r = radius of gyration (rx or ry), in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 14
ESSENTIALS OF LRFD
C. FRAMES AND OTHER STRUCTURES
Second Order Effects
As stated in Section C1 of the LRFD Specification, an analysis of second order effects
is required; i.e., the additional moments due to the axial loads acting on the deformed
structure must be considered. In lieu of a second order analysis for Mu, the required
flexural strength, the LRFD Specification (in Section C1) presents the following simplified method:
Mu = B1Mnt + B2Mlt
(C1-1)
The components of the total factored moment, determined from a first order elastic
analysis (neglecting second order effects) are divided into two groups, Mnt and Mlt. Each
group is in turn multiplied by a magnification factor B1 or B2 and the results are added to
approximate the actual second order factored moment Mu. (The method, as explained
here, is valid where the moment connections are Type FR, fully restrained. The analysis
for Type PR, or partially restrained, moment connections is beyond the scope of this
section.)
Beam-columns are generally columns in frames, which are either braced (Mlt = 0) or
unbraced (Mlt ≠ 0). Mnt is the moment in the member assuming there is no lateral
translation of the frame; Mlt is the moment due to lateral translation. Mnt includes the
moments resulting from the gravity loads, as determined manually or by computer, using
one of the customary (elastic, first order) methods. The moments from the lateral loads
are classified as Mlt; i.e., due to lateral translation. If both the frame and its vertical loads
are symmetric, Mlt from the vertical loads is zero. However, if either the vertical loads or
the frame is asymmetric and the frame is not braced, lateral translation occurs and Mlt ≠ 0.
The procedure for obtaining Mlt in this case involves:
b=
bf
b=
2
bf
bf
b = bf
2
bf
bf
h
h
h
bf
b
t
hw
t
h
b = b f – 3t
h = h w – 3t
Fig. B-1. Definitions of widths (b and h) for use in Table B-1.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
C. FRAMES AND OTHER STRUCTURES
2 - 15
a. applying fictitious horizontal reactions at each floor level to prevent lateral translation, and
b. using the reverse of these reactions as the “sway forces” for determining Mlt.
In general, Mlt for an unbraced frame is the sum of the moments due to the lateral loads
and these “sway forces,” as illustrated in Figure C-1.
The magnification factors applied to Mnt and Mlt are, respectively, B1 and B2. As shown
in Figure C-2, B1 accounts for the secondary Pδ member effect in all frames (including
sway-inhibited) and B2 covers the P∆ story effect in unbraced frames. The expressions
for B1 and B2 follow:
B1 =
Cm
≥ 1.0
(1 − Pu / Pe1 )
(C1-2)
where
Pu = the factored axial compressive force on the member, kips
Pe1 = Pe as listed in Table C-1 as a function of the slenderness ratio Kl / r, with effective length factor K = 1.0 and considering l / r in the plane of bending only
l = unbraced length of the member, in.
r = radius of gyration of its cross section, in.
Cm = a coefficient to be taken as follows:
V1
V2
V3
P1
P1
R1
V1 +R1
P2
P2 R
2
V2 +R2
P3
P3
Original
Frame
=
R3
Nonsway
Frame
for M nt
V3 +R3
Sway
Frame
for M t
+
Fig. C-1. Frame models for Mnt and Mlt.
∆P
P
H
δ
M1=Mnt+Pδ
=B1Mnt
(a) Column in Braced Frame
L
M t =HL
M2=M t +P∆
=B2M t
(b) Column in Unbraced Frame
Fig. C-2. Illustrations of secondary effects.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 16
ESSENTIALS OF LRFD
Table C-1.
Values of Pe / Ag for Use in Equation C1-2 and C1-5 for Steel of Any Yield Stress
Note: Multiply tabulated values by Ag (the gross cross-sectional area of the member) to obtain Pe
Kl / r
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Pe / Ag
Pe / Ag
Pe / Ag
Pe / Ag
Pe / Ag
Pe / Ag
(ksi) Kl / r (ksi) Kl / r (ksi) Kl / r (ksi) Kl / r (ksi) Kl / r (ksi)
649.02
591.36
541.06
496.91
457.95
423.40
392.62
365.07
340.33
318.02
297.83
279.51
262.83
247.59
233.65
220.85
209.07
198.21
188.18
178.89
170.27
162.26
154.80
147.84
141.34
135.26
129.57
124.23
119.21
114.49
Note: Pe / Ag =
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
110.04
105.85
101.89
98.15
94.62
91.27
88.08
85.08
82.22
79.51
76.92
74.46
72.11
69.88
67.74
65.71
63.76
61.90
60.12
58.41
56.78
55.21
53.71
52.57
50.88
49.55
48.27
47.04
45.86
44.72
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
43.62
42.57
41.55
40.56
39.62
38.70
37.81
36.96
36.13
35.34
34.56
33.82
33.09
32.39
31.71
31.06
30.42
29.80
29.20
28.62
28.06
27.51
26.98
26.46
25.96
25.47
25.00
24.54
24.09
23.65
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
23.23
22.82
22.42
22.02
21.64
21.27
20.91
20.56
20.21
19.88
19.55
19.23
18.92
18.61
18.32
18.03
17.75
17.47
17.20
16.94
16.68
16.43
16.18
15.94
15.70
15.47
15.25
15.03
14.81
14.60
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
14.40
14.19
14.00
13.80
13.61
13.43
13.25
13.07
12.89
12.72
12.55
12.39
12.23
12.07
11.91
11.76
11.61
11.47
11.32
11.18
11.04
10.91
10.77
10.64
10.51
10.39
10.26
10.14
10.02
9.90
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
9.79
9.67
9.56
9.45
9.35
9.24
9.14
9.03
8.93
8.83
8.74
8.64
8.55
8.45
8.36
8.27
8.18
8.10
8.01
7.93
7.85
7.76
7.68
7.60
7.53
7.45
7.38
7.30
7.23
7.16
π2E
(K l /r)2
a. For compression members not subject to transverse loading between their supports
in the plane of bending,
Cm = 0.6 − 0.4(M1 / M2)
(C1-3)
where M1 / M2 is the ratio of the smaller to larger moment at the ends of that portion
of the member unbraced in the plane of bending under consideration. M1 / M2 is
positive when the member is bending in reverse curvature, negative when bending
in single curvature.
b. For compression members subjected to transverse loading between their supports,
the value of Cm can be determined by rational analysis, or the following values may
be used:
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
C. FRAMES AND OTHER STRUCTURES
2 - 17
for members with ends restrained against rotation . . . . . . . . . . Cm = 0.85
for members with ends unrestrained against rotation . . . . . . . . . Cm = 1.0
Two alternative equations are given for B2 in the LRFD Specification
B2 =
1
ΣPu  ∆oh 
1−
 
ΣH  L 
B2 =
1
ΣPu
1−
ΣPe2
(C1-4)
(C1-5)
where
ΣPu = required axial strength of all columns in a story, i.e., the total factored gravity
load above that level, kips
∆oh = translational deflection of the story under consideration, in.
ΣH = sum of all story horizontal forces producing ∆oh, kips
L = story height, in.
ΣPe2 = the summation of Pe2 for all rigid-frame columns in a story; Pe2 is determined
from Table C-1, considering the actual slenderness ratio Kl / r of each column in its plane of bending
K = effective length factor (see below)
Of the two expressions for B2, the first (Equation C1-4) is better suited for design office
practice. The quantity (∆oh / L) is the story drift index. For many structures, particularly
tall buildings, a maximum drift index is one of the design criteria. Using this value in
Equation C1-4 will facilitate the evaluation of B2.
In general, two values of B2 are obtained for each story of a building, one for each of
the major directions. B1 is evaluated separately for every column; two values of B1 are
needed for biaxial bending. Using Equations C1-1 through C1-5, the appropriate Mux and
Muy are determined for each column.
Effective Length
As in previous editions of the AISC Specification, the effective length of Kl is used
(instead of the actual unbraced length l) to account for the influence of end-conditions in
the design of compression members. A number of acceptable methods have been utilized
to evaluate K, the effective length factor. They are discussed in Section C2 of the
Commentary on the LRFD Specification. One method will be shown here.
Table C-2, which is also Table C-C2.1 in the Commentary, is taken from the Structural
Stability Research Council (SSRC) Guide to Stability Design Criteria for Metal Structures. It relates K to the rotational and translational restraints at the ends of the column.
Theoretical values for K are given, as well as the recommendations of the SSRC. The
basic case is d, the classical pin-ended column, for which K = 1.0. Theoretical K values
for the other cases are determined by the distances between points of inflection. The more
conservative SSRC recommendations reflect the fact that perfect fixity can never be
attained in actual structures.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 18
ESSENTIALS OF LRFD
Table C-2.
Effective Length Factors (K) for Columns
Buckled shape of column is shown
by dashed line
(a)
(b)
(c)
Theoretical K value
0.5
0.7
1.0
Recommended design value when
ideal conditions are approximated
0.65
0.80
1.2
End condition code
(d)
(e)
(f)
1.0
2.0
2.0
1.0
2.10
2.0
Rotation fixed and translation fixed
Rotation free and translation fixed
Rotation fixed and translation free
Rotation free and translation free
Like its predecessors, the LRFD Specification (in Section C2) distinguishes between
columns in braced and unbraced frames. In braced frames, sidesway is inhibited by
attachment to diagonal bracing or shear walls. Cases a, b, and d in Table C-2 represent
columns in braced frames; K ≤ 1.0. The LRFD Specification requires that for compression
members in braced frames, K “shall be taken as unity, unless structural analysis shows
that a smaller value may be used.” Common practice is to assume conservatively K = 1.0
for columns in braced frames and compression members in trusses.
The other cases in Table C-2, c, e, and f, are in unbraced frames (sidesway uninhibited);
K ≥ 1.0. The SSRC recommendations given in Table C-2 are appropriate for design.
“Leaning” Columns
The concept of the “leaning” column, although not related exclusively to LRFD, is new
to the 1993 LRFD Specification. A leaning column is one which is pin ended and does
not participate in providing lateral stability to the structure. As a result it relies on the
columns in other parts of the structure for stability. In analyzing and designing unbraced
frames, the effects of the leaning columns must be considered (as required by Section
C2.2 of the LRFD Specification). For further information the reader is referred to:
(1) Part 3 of this Manual.
(2) the Commentary on the LRFD Specification, Section C2, and
(3) a paper on this subject (Geschwindner, 1993).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
D. TENSION MEMBERS
2 - 19
D. TENSION MEMBERS
Design Tensile Strength
The design philosophy for tension members is the same in the LRFD and ASD
Specifications:
a. The limit state of yielding in the gross section is intended to prevent excessive
elongation of the member. Usually, the portion of the total member length occupied
by fastener holes is small. The effect of early yielding at the reduced cross sections
on the total member elongation is negligible. Use of the area of the gross section is
appropriate.
b. The second limit state involves fracture at the section with the minimum effective
net area.
The design strength of tension members, φtPn, as given in Section D1 of the LRFD
Specification, is the lesser of the following:
a. For yielding in the gross section,
φt = 0.90
Pn = Fy Ag
(D1-1)
b. For fracture in the net section,
φt = 0.75
Pn = Fu Ae
(D1-2)
where
Ae
Ag
Fy
Fu
Pn
= effective net area, in.2 (see Section B, above)
= gross area of member, in.2
= specified minimum yield stress, ksi
= specified minimum tensile strength, ksi
= nominal axial strength, kips
For 50 ksi steels, Fy = 50 ksi and minimum Fu = 65 ksi. Accordingly
a. For yielding in the gross section,
φtPn = 0.9 × 50 ksi × Ag = 45.0 ksi × Ag
(2-3)
b. For fracture in the net section,
φtPn = 0.75 × 65 ksi × Ae = 48.8 ksi × Ae
(2-4)
The limit state of block shear rupture may govern the design tensile strength. For
information on block shear, see Section J4.3 of the LRFD Specification and Part 8 (in
Volume II) of this LRFD Manual.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 20
ESSENTIALS OF LRFD
EXAMPLE D-1
Given:
Determine the design strength of a W8×24 as a tension member in
50 ksi steel. How much dead load can it support?
Solution:
If there are no holes in the member, Ae = Ag and Equation 2-3 governs
φtPn = 45.0 ksi × Ag = 45.0 ksi × 7.08 in.2 = 319 kips
Assuming that dead load is the only load, the governing load combination from Section A is 1.4D. Then, the required tensile strength
Pu = 1.4PD ≤φtPn = 319 kips
PD≤ 319 kips/1.4 = 228 kips maximum dead load that can be supported
by the member.
EXAMPLE D-2
Given:
Repeat Example D-1 for a W8×24 in 50 ksi steel with four 1-in.
diameter holes, two per flange, along the member (i.e., not at its ends)
for miscellaneous attachments. See Figure D-1(a).
Solution:
a. For yielding in the gross section
φtPn = 319 kips, as in Example D-1.
b. For fracture in the net section
Ae = An = Ag − 4 × (dhole + 1⁄16-in.) × tf
= 7.08 in.2 − 4 × (1 + 1⁄16-in.) × 0.400 in.
= 5.38 in.2
φtPn = 48.8 ksi × Ae
= 48.8 ksi × 5.38 in.2 = 263 kips < 319 kips
Fracture in the net section governs.
Pu = 1.4 PD ≤ φtPn = 263 kips
PD ≤ 263 kips / 1.4 = 188 kips
W8x24
x=y=0.695 in.
tf
WT4x12
WT4x12
(a)
(b)
Fig. D-1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
D. TENSION MEMBERS
2 - 21
Note: If the holes had been at the end connection of the tension
member, the U reduction coefficient would apply in the calculation of
an effective net area.
EXAMPLE D-3
Given:
Repeat Example D-2 for holes at a bolted end-connection. There are a
total of eight 1-in. diameter holes, as shown in Figure D-1(a), on two
planes, 4 in. center-to-center.
Solution:
a. For yielding in the gross section φtPn = 319 kips, as in Example D-1.
b. For fracture in the net section, according to Equation B3-1 in
Section B above, the effective net area
Ae = AU = AnU
where
An = 5.38 in.2 as in Example D-2
_
x
U = 1 − , L = 4 in.*
L
_
According to Commentary Figure C-B3.1(a), x for a W8×24 in this
case is taken as that for a WT4×12.
_ From the properties of a WT4×12
given in Part 1 of this Manual, x = y = 0.695 in. See Figure D-1(b).
U=1−
0.695 in.
= 0.826
4 in.
Thus
Ae = 5.38 in.2 × 0.826 = 4.45 in.2
φtPn = 48.8 ksi × Ae
= 48.8 ksi × 4.45 in.2 = 217 kips < 319 kips
Fracture in the net section governs. Again, assuming that dead load is
the only load,
Pu = 1.4PD ≤ φtPn = 217 kips
PD ≤ 217 kips / 1.4 = 155 kips maximum dead load that can be supported
by the member.
Built-Up Members, Eyebars, and Pin-Connected Members
See Section D2 and D3 in the LRFD Specification.
*In lieu of calculating U, the Commentary on the LRFD Specification (Section B3) permits the use of more conservative
values of U listed therein.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 22
ESSENTIALS OF LRFD
E. COLUMNS AND OTHER COMPRESSION MEMBERS
Effective Length
For a discussion of the effective length Kl for columns, refer to Section C above.
Design Compressive Strength
Although the column strength equations have been revised for compatibility with LRFD
and recent research on column behavior, the philosophy and procedures of column design
in LRFD are similar with those in ASD. The direct design of columns with W and other
rolled shapes is facilitated by the column strength tables in Part 3 of this LRFD Manual,
which show the design compressive strength φcPn as a function of KL (the effective
unbraced length in feet). Columns with cross sections not tabulated (e.g., built-up
columns) can be designed iteratively, as in the past, with the aid of tables listing design
stresses versus Kl / r, the slenderness ratio. Such tables are given in the Appendix of the
LRFD Specification for 36 and 50 ksi structural steels, and below (Table E-1) for 50 ksi
steel.
There are two equations governing column strength, based on the limit state of flexural
buckling, one for inelastic buckling (Equation E2-2) and the other (Equation E2-3) for
elastic, or Euler, buckling. Equation E2-2 is an empirical relationship for the inelastic
range, while Equation E2-3 is the familiar Euler formula multiplied by 0.877. Both
equations include the effects of residual stresses and initial out-of-straightness. The
boundary between inelastic and elastic instability is λc = 1.5, where the parameter
λc =
Kl
rπ

√
Fy
E
(E2-4)
For axially loaded columns with all elements having width-thickness ratios < λr (in
Section B5.1 of the LRFD Specification), the design compressive strength = φcPn
where
φc = 0.85
Pn = AgFcr
(E2-1)
Ag = gross area of member, in.2
a. For λc ≤ 1.5
2
Fcr = (0.658λc)Fy
(E2-2)
As is done in the Commentary on Section E2, this equation can be expressed in
exponential form
Fcr = [exp (−0.419λ2c )]Fy
where exp(x) = ex
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(C-E2-1)
E. COLUMNS AND OTHER COMPRESSION MEMBERS
2 - 23
Table E-1.
Design Stress for Compression Members of 50 ksi Specified
Minimum Yield Stress Steel, φc = 0.85*
Kl
r
F cr (ksi)
Kl
r
F cr (ksi)
1
2
3
4
5
42.50
42.49
42.47
42.45
42.42
41
42
43
44
45
37.59
37.36
37.13
36.89
36.65
6
7
8
9
10
42.39
42.35
42.30
42.25
42.19
46
47
48
49
50
11
12
13
14
15
42.13
42.05
41.98
41.90
41.81
16
17
18
19
20
Kl
r
F cr (ksi)
Kl
r
F cr (ksi)
Kl
r
F cr (ksi)
81
82
83
84
85
26.31
26.00
25.68
25.37
25.06
121
122
123
124
125
14.57
14.33
14.10
13.88
13.66
161
162
163
164
165
8.23
8.13
8.03
7.93
7.84
36.41
36.16
35.91
35.66
35.40
86
87
88
89
90
24.75
24.44
24.13
23.82
23.51
126
127
128
129
130
13.44
13.23
13.02
12.82
12.62
166
167
168
169
170
7.74
7.65
7.56
7.47
7.38
51
52
53
54
55
35.14
34.88
34.61
34.34
34.07
91
92
93
94
95
23.20
22.89
22.58
22.28
21.97
131
132
133
134
135
12.43
12.25
12.06
11.88
11.71
171
172
173
174
175
7.30
7.21
7.13
7.05
6.97
41.71
41.61
41.51
41.39
41.28
56
57
58
59
60
33.79
33.51
33.23
32.95
32.67
96
97
98
99
100
21.67
21.36
21.06
20.76
20.46
136
137
138
139
140
11.54
11.37
11.20
11.04
10.89
176
177
178
179
180
6.89
6.81
6.73
6.66
6.59
21
22
23
24
25
41.15
41.02
40.89
40.75
40.60
61
62
63
64
65
32.38
32.09
31.80
31.50
31.21
101
102
103
104
105
20.16
19.86
19.57
19.28
18.98
141
142
143
144
145
10.73
10.58
10.43
10.29
10.15
181
182
183
184
185
6.51
6.44
6.37
6.30
6.23
26
27
28
29
30
40.45
40.29
40.13
39.97
39.79
66
67
68
69
70
30.91
30.61
30.31
30.01
29.70
106
107
108
109
110
18.69
18.40
18.12
17.83
17.55
146
147
148
149
150
10.01
9.87
9.74
9.61
9.48
186
187
188
189
190
6.17
6.10
6.04
5.97
5.91
31
32
33
34
35
39.62
39.43
39.25
39.06
38.86
71
72
73
74
75
29.40
20.09
28.79
28.48
28.17
111
112
113
114
115
17.27
16.99
16.71
16.42
16.13
151
152
153
154
155
9.36
9.23
9.11
9.00
8.88
191
192
193
194
195
5.85
5.79
5.73
5.67
5.61
36
37
38
39
40
38.66
38.45
38.24
38.03
37.81
76
77
78
79
80
27.86
27.55
27.24
26.93
26.62
116
117
118
119
120
15.86
15.59
15.32
15.07
14.82
156
157
158
159
160
8.77
8.66
8.55
8.44
8.33
196
197
198
199
200
5.55
5.50
5.44
5.39
5.33
* When element width-to-thickness ratio exceeds λr, see Appendix B5.3 of LRFD Specification
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 24
ESSENTIALS OF LRFD
b. For λc > 1.5
0.877
Fcr =  2  Fy
 λc 
(E2-3)
where
Fy = specified minimum yield stress, ksi
E = modulus of elasticity, ksi
K = effective length factor
l = unbraced length of member, in.
r = governing radius of gyration about plane of buckling, in.
For 50 ksi steel
λc =
Kl 1
r π

√
Kl Kl
50 ksi
= 0.0132
or
= 75.7λc
r
r
29,000 ksi
(2-5)
The boundary between inelastic and elastic buckling (λc = 1.5) for 50 ksi steel is
Kl
= 75.7 × 1.5 = 113.5
r
The column strength equations in terms of Kl / r for 50 ksi steel become
φcPn = (φcFcr )Ag
(2-6)
Fcr = {exp[−7.3 × 10−5(Kl / r)2]} × 50 ksi
(2-7)
where φc = 0.85
a. For Kl / r ≤ 113.5
b. For Kl / r ≤ 113.5
Fcr =
2.51 × 105
ksi
(Kl / r)2
(2-8)
Based on Equations 2-7 and 2-8, Table E-1 gives the design stresses for 50 ksi steel
columns for the full range of slenderness ratios. Determining the design strength of a
given 50 ksi steel column merely involves using Equation 2-6 in connection with
Table E-1. The appropriate design stress (φcFcr) from Table E-1 is multiplied by the
cross-sectional area to obtain the design strength φcPn.
EXAMPLE E-1
Given:
Design a 25-ft high, free standing A618 (Fy = 50 ksi) steel pipe column
to support a water tank with a weight of 75 kips at full capacity. See
Figure E-1.
Solution:
For a live load of 75 kips, the required column strength (from Section
A) is Pu = 1.6PL = 1.6 × 75 kips = 120 kips.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
E. COLUMNS AND OTHER COMPRESSION MEMBERS
2 - 25
From Table C-2, case e, recommended K = 2.1. KL = 2.1 × 25.0 ft =
52.5 ft.
Try a standard 12-in. diameter pipe (A = 14.6 in.2, I = 279 in.4):
r =√

I/A =√

279 in. / 14.6 in.2 = 4.37 in.
Kl 52.5 ft × 12 in./ft
=
= 144.2
4.37 in
r
From Table E-1, φcFcr = 10.3 ksi
The design compressive strength
φcPn = (φcFcr )Ag = 10.3 ksi × 14.6 in.2
= 150 kips > 120 kips required o.k.
To complete the design, bending due to lateral loads (i.e., wind and
earthquake) should also be considered. See Sections F and H.
EXAMPLE E-2
Determine the adequacy of a W14×120 building column.
Given:
50 ksi steel; K = 1.0; story height = 12.0 ft; required strength based on
the maximum total factored load is 1,300 kips.
KxLx = Ky Ly = 1.0 × 12.0 ft = 12.0 ft
Because ry < rx,
 Kl 
Ky Ly 12.0 ft × 12 in./ft
=
= 38.5
  maximum =
ry
3.74 in.
r
From Table E-1, φcFcr = 38.14 ksi
Design compressive strength
φcPn = (φcFcr)Ag = 38.14 ksi × 35.3 in.2
= 1,346 kips > 1,300 kips required o.k.
L = 25.0 ft.
Solution:
Fig. E-1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 26
Select the most economical W14 column for the case shown in Figures
E-2 and E-3.
Lower
Level
Intermediate
Level
Upper
Level
Fig. E-2. Plan views.
12 -0
Upper
Level
Intermediate
Level
12 -0
EXAMPLE E-3
ESSENTIALS OF LRFD
Lower
Level
Fig. E-3. Elevation.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
F. BEAMS AND OTHER FLEXURAL MEMBERS
2 - 27
Given:
50 ksi steel; K = 1.0; required strength based on the maximum total
factored load is 1,300 kips. The column is braced in both directions at
the upper and lower levels, and in the weak direction at the intermediate
level.
Solution:
Try a W14×120 (as in Example E-2):
Kx lx
rx
=
1.0 × 24.0 ft × 12 in./ft
= 46.2
6.24 in.
Ky ly
ry
=
1.0 × 12.0 ft × 12 in./ft
= 38.5
3.74 in.
Kx lx
Kl
max =
= 46.2
rx
r
From Table E-1, φcFcr = 36.35 ksi
Required Ag =
1,300 kips
= 35.8 in.2 > 35.3 in.2 provided
36.35 ksi
W14×120 n.g.
By inspection W14×132 is o.k.
Use W14×132
Flexural-Torsional Buckling
As stated in Section E3 of the LRFD Specification and Commentary, torsional and
flexural-torsional buckling generally do not govern the design of doubly symmetric rolled
shapes in compression. For other cross sections, see Section E3 and Appendix E3 of the
LRFD Specification.
Built-Up and Pin-Connected Members
These members are covered, respectively, in Section E4 and E5 of the LRFD
Specification.
F. BEAMS AND OTHER FLEXURAL MEMBERS
Chapter F of the LRFD Specification covers compact beams. Compactness criteria are
given in Table B5.1 of the LRFD Specification and are summarized in Table B-1 above.
To prevent torsion, wide-flange shapes must be loaded in either plane of symmetry,
channels must be loaded through the shear center parallel to the web, or restraint against
twisting must be provided at load points and points of support. Torsion combined with
flexure and axial force combined with flexure are covered in Chapter H of the LRFD
Specification.
This section explains the provisions of the LRFD Specification for compact rolled
beams. For other compact and noncompact flexural members, refer to Appendix F of the
Specification; plate girders are in Appendix G.
Flexure
To understand the provisions of the LRFD Specification regarding flexural design, it is
helpful to review briefly some aspects of elementary beam theory.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 28
ESSENTIALS OF LRFD
Under working loads (and until initial yielding) the distributions of flexural strains and
stresses over the cross-section of a beam are linear. As shown in Figure F-1, they vary
from maximum compression at the extreme fibers on one side (the top) to zero at the
neutral, or centroidal, axis to maximum tension at the extreme fibers on the other side
(the bottom).
The relationship between moment and maximum bending stress (tension or compression) at a given cross section is
M = Sfb
(2-9)
where
M= bending moment due to the applied loads, kip-in.
S = elastic section modulus, in the direction of bending, in.3
I
=
c
fb = maximum bending stress, ksi
I = moment of inertia of the cross section about its centroidal axis, in.4
c = distance from the elastic neutral axis to the extreme fiber, in.
Similarly, at initial yielding
Mr = SFy
(2-10)
where
Mr = bending moment coinciding with first yielding, kip-in.
If additional load is applied, the strains continue to increase; the stresses, however, are,
limited to Fy. Yielding proceeds from the outer fibers inward until a plastic hinge is
developed, as shown in Figure F-1. At full plastification of the cross section
Mp = ZFy
(2-11)
where
Mp = plastic moment, kip-in
Z = plastic section modulus, in the direction of bending, in.3
Due to the presence of residual stresses (prior to loading, as a consequence of the rolling
operation), yielding begins at an applied stress of (Fy − Fr). Equation 2-10 should be
modified to
STRAINS
BEAM
Cross
Section
Compression
STRESSES
Fy
Fy
Working
Load
Fy
Initial
Yielding
Tension
Fig. F-1. Flexural strains and stresses.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Fy
Plastic
Hinge
F. BEAMS AND OTHER FLEXURAL MEMBERS
Mr = S(Fy − Fr )
2 - 29
(2-12)
where
Fr = the maximum compressive residual stress in either flange, ksi
= 10 ksi for rolled shapes, 16.5 ksi for welded shapes
The definition of plastic moment in Equation 2-11 is still valid, because it is not affected
by residual stresses.
Design for Flexure
a. Assuming Cb = 1.0
Compact sections will not experience local buckling before the formation of a plastic
hinge. The occurrence of lateral-torsional buckling of the member depends on the
unbraced length Lb. As implied by the term lateral-torsional buckling, overall instability
of a beam requires that twisting of the member occur simultaneously with lateral buckling
of the compression flange. Lb is the distance between points braced to prevent twist of
the cross section. Many beams can be considered continuously braced; e.g., beams
supporting a metal deck, if the deck is intermittently welded to the compression flange.
Compact wide flange and channel members bending about their major (or x) axes can
develop their full plastic moment Mp without buckling if Lb ≤ Lp. If Lb = Lr, the nominal
flexural strength is Mr, the moment at first yielding adjusted for residual stresses. The
nominal moment capacity (Mn) for Lp < Lb < Lr is Mr < Mn < Mp. Compact shapes bent
about their minor (or y) axes will not buckle before developing Mp, regardless of Lb.
Flexural design strength, governed by the limit state of lateral-torsional buckling, is
φbMn, where φb = 0.90 and Mn the nominal flexural strength is as follows:
Mn = Mp = ZxFy for bending about the major axis if Lb ≤ Lp
Mn = Mp = ZyFy for bending about the minor axis regardless of Lb
Lp =
300ry
= 42.4ry for 50 ksi steel
Fy
√
Mn = Mr = Sx(Fy − Fr )
= Sx(Fy − 10 ksi) for rolled shapes bending about the major axis if Lb = Lr
(2-13)
(2-14)
(2-15)
(2-16)
Mn for bending about the major axis, if Lp < Lb < Lr, is determined by linear interpolation
between Equations 2-13 and 2-16; i.e.,
 Lb − Lp 
Mn = Mp − (Mp − Mr) 

 Lr − Lp 
(2-17)
The definition for the limiting laterally unbraced length Lr is given in the LRFD
Specification (in Equations F1-6, 8, and 9) and will not be repeated here. For bending
about the major axis if Lb > Lr,
Mn = Mcr ≤ Mr
(2-18)
The case of Lb > Lr is beyond the scope of this section. The reader is referred to Section
F1.2b of LRFD Specification (specifically Equation F1-13, where the critical moment
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 30
ESSENTIALS OF LRFD
Table F-1.
Values of Cb for Simply Supported Beams Braced at Ends of Span
Load
Lateral Bracing Along Span
Cb
Concentrated at center
None
1.32
At centerline only
1.67
None
1.14
At centerline only
1.30
Uniform
Mcr is controlled by lateral-torsional buckling). This case is also covered in the beam
graphs in Part 4 of this LRFD Manual.
b. All values of Cb
Cb is the bending coefficient. A new expression for Cb is given in the LRFD Specification. (It is more accurate than the one previously shown.)
Cb =
12.5Mmax
2.5Mmax + 3MA + 4MB + 3Mc
(F1-3)
where M is the absolute value of a moment in the unbraced beam segment as follows:
Mmax, the maximum
MA, at the quarter point
MB, at the centerline
Mc, at the three-quarter point
The purpose of Cb is to account for the influence of moment gradient on lateral-torsional buckling. The flexural strength equations with Cb = 1.0 are based on a uniform
moment along a laterally unsupported beam segment causing single curvature buckling
of the member. Other loadings are less severe, resulting in higher flexural strengths;
Cb ≥ 1.0. Typical values of Cb are given in Table F-1. For unbraced cantilevers, Cb = 1.0.
Cb can conservatively be taken as 1.0 for all cases.
For all values of Cb, the flexural design strength φbMn, where φb = 0.90, is given in the
LRFD Specification in terms of a nominal flexural strength Mn varying as follows:
Mn = Mp = ZxFy
(2-13)
for bending about the major axis if Lb ≤ Lm
Mn = CbMr = CbSx(Fy − 10 ksi) ≤ Mp
(2-19)
for bending about the major axis if Lb = Lr.
For bending about the major axis if Lm < Lb < Lr, linear interpolation is used
 Lb − Lp 

Mn = Cb Mp − (Mp − Mr) 
 ≤ Mp
 Lr − Lp 

(F1-2)
Mn = Mcr ≤ CbMr and Mp
(2-20)
If Lb > Lr,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
F. BEAMS AND OTHER FLEXURAL MEMBERS
2 - 31
The determination of Mn for a given Lb can best be done graphically, as illustrated in
Figure F-2. The required parameters for each W shape are given in the beam design table
in Part 4 of the LRFD Manual, an excerpt of which is shown herein as Table F-2. If Cb =
1.0, the coordinates for constructing the graph are (Lp, Mp), and (Lr, Mr). For Cb > 1.0, the
key coordinates are (Lp, Cb Mp) and (Lr, Cb Mr). Note that Mn cannot exceed the plastic
moment Mp. Lm, then, can be derived graphically as the upper limit of Lb for which Mn =
Mp. If Lb > Lr, the beam graphs in Part 4 of the LRFD Manual can be used to determine
Mcr.
EXAMPLE F-1
Select the required W shape for a 30-foot simple floor beam with full
lateral support carrying a dead load (including its own weight) of 1.5
kips per linear foot and a live load of 3.0 kips per linear foot. Assume
50 ksi steel and:
Given:
a. There is no member depth limitation
b. The deepest member is a W18
The governing load combination in Section A is A4-2:
Solution:
1.2D + 1.6L + 0.5(Lr or S or R) = 1.2 × 1.5 klf + 1.6 × 3.0 klf + 0
= 6.6 klf
Required Mu =
wL2 6.6 klf × (30.0 ft)2
=
= 743 kip-ft
8
8
Flexural design strength φbMn ≥ 743 kip-ft
CbMp
Mn for Cb=1.0
Mn for Cb>1.0
Mp
Mn
Mcr for Cb=1.0
CbMr
Mcr for Cb >1.0
Mr
Lm
Lp
Lr
Lb
Fig. F-2. Determination of nominal flexural strength M n.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 32
ESSENTIALS OF LRFD
Table F-2.
Excerpt from Load Factor Design Selection Table
(LRFD Manual, Part 4)
For Fy = 50 ksi
Zx (in.3)
Shape
φbMp
(kip-ft)
φbMr
(kip-ft)
Lp (ft)
Lr (ft)
224
221
212
211
W24×
×84
W21×93
W14×120
W18×97
840
829
795
791
588
576
570
564
6.9
6.5
13.2
9.4
18.6
19.4
46.2
27.4
200
198
196
192
186
186
W24×
×76
W16×100
W21×83
W14×109
W18×86
W12×120
750
743
735
720
698
698
528
525
513
519
498
489
6.8
8.9
6.5
13.2
9.3
11.1
18.0
29.3
18.5
43.2
26.1
50.0
177
175
W24×
×68
W16×89
664
656
462
465
6.6
8.8
17.4
27.3
Note: Flexural design strength φbMn = φbMp, as tabulated is valid for Lb ≤ Lm. If Cb = 1.0, Lm = Lp; otherwise,
Lm > Lp. φb = 0.90.
a. In Table F-2, the most economical beams are in boldface print. Of
the boldfaced beams, the lightest one with φbMn = φbMp ≥ 743 kip-ft
is a W24×76
b. By inspection of Table F-2, the lightest W18 with φbMn = φbMp ≥
743 kip-ft is a W18×97.
EXAMPLE F-2
Given:
Determine the flexural design strength of a 30-ft long simply supported
W24×76 girder (of 50 ksi steel) with a concentrated load and lateral
support, both at midspan.
Solution:
From Table F-1, Cb = 1.67
Lb = 30.0 ft/2 = 15.0 ft
From Equation F1-2:
 Lb − Lp  

φbMn = Cb φbMp − (φbMp − φbMr) 
  ≤ φbMp
 Lr − Lp  

From Table F-2 for a W24×76:
φbMp = 750 kip-ft
φbMr = 528 kip-ft
Lp = 6.8 ft
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
F. BEAMS AND OTHER FLEXURAL MEMBERS
Lr
2 - 33
= 18.0 ft
15.0 ft − 6.8 ft 

φbMn = 1.67 750 kip−ft − (750 − 528) kip−ft ×
18.0 ft − 6.8 ft 

= 981 kip-ft > 750 kip-ft
Use φb Mn = φb Mp = 750 kip-ft
In this case, even though the unbraced length Lb > Lp, the design
flexural strength is φbMp because Cb > 1.0.
Design for Shear
The design shear strength is defined by the equations in Section F2 of the LRFD
Specification. Shear in wide-flange and channel sections is resisted by the area of the
web (Aw), which is taken as the overall depth d times the web thickness tw. For webs of
50 ksi steel without transverse stiffeners, the design shear strength φvVn, where φv = 0.90,
and the nominal shear strength Vn are as follows:
For
h
≤ 59 (including all rolled W and channel shapes),
tw
Vn = 30.0 ksi × dtw
φvVn= 27.0 ksi × dtw
For 59 <
(2-21)
h
≤ 74,
tw
= 30.0 ksi × dtw ×
59
h / tw
φvVn = 27.0 ksi × dtw ×
59
h / tw
Vn
For
(2-22)
h
> 74,
tw
=
132,000
dtw ksi
(h / tw)2
φvVn =
118,000
dtw ksi
(h / tw)2
Vn
h
(2-23)
tw
d
tw
h
Fig. F-3. Definitions of d, h, and tw for W and channel shapes.
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
2 - 34
ESSENTIALS OF LRFD
Shear strength is governed by the following limit states; Equation 2-21 by yielding of the
web; Equation 2-22, by inelastic buckling of the web; and Equation 2-23 by elastic
buckling.
EXAMPLE F-3
Given:
Solution:
Check the adequacy of a W30×99 beam of 50 ksi steel to carry a load
resulting in maximum shears of 100 kips due to dead load and 150 kips
due to live load.
Required shear strength = Vu = 1.2D + 1.6L
= 1.2 × 100 kips + 1.6 × 150 kips
= 360 kips
Design shear strength = φvVn = 27.0 ksi × dtw
= 27.0 ksi × 29.65 in. × 0.520 in.
= 416 kips > 360 kips required o.k.
Web Openings
See Section F4 of the LRFD Specification and Commentary, and the references given in
the Commentary.
H. MEMBERS UNDER COMBINED FORCES AND TORSION
Symmetric Members Subject to Bending and Axial Tension
The interaction of flexure and tension in singly and doubly symmetric shapes is governed
by Equations H1-1a and H1-1b, as follows:
For
For
Pu
≥ 0.2,
φPn
Pu
< 0.2,
φPn
Muy 
Pu 8  Mux
+ 
+
 ≤ 1.0
9
φPn
 φb Mnx φb Mny 
(H1-1a)
 Mux
Muy 
Pu
+
+
 ≤ 1.0
2φPn  φb Mnx φb Mny
(H1-1b)
where
= required tensile strength; i.e., the total factored tensile force, kips
= design tensile strength, φtPn, kips
= resistance factor for tension, φt = 0.90
= nominal tensile strength as defined in Chapter D of the LRFD Specification,
kips
Mu = required flexural strength; i.e., the moment due to the total factored load, kipin. or kip-ft. (Subscript x or y denotes the axis about which bending occurs.)
φb Mn = design flexural strength, kip-in. or kip-ft
= resistance factor for flexure = 0.90
φb
Pu
φPn
φ
Pn
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
H. MEMBERS UNDER COMBINED FORCES AND TORSION
Mn
2 - 35
= nominal flexural strength determined in accordance with the appropriate equations in Chapter F of the LRFD Specification, kip-in. or kip-ft
Interaction Equations H1-1a and H1-1b cover the general case of biaxial bending
combined with axial force. They are also valid for uniaxial bending (i.e., when Mux = 0
or Muy = 0). In this case, they reduce to the form plotted in Figure H-1. Pure biaxial bending
(with Pu = 0) is covered by Equation H1-1b.
EXAMPLE H-1
Given:
Check the adequacy of a W10×22 tension member of 50 ksi steel to
carry loads resulting in the following factored load combination:
Pu = 55 kips
Muy = 20 kip-ft
Mux = 0
Solution:
From Section D above for 50 ksi steel,
φPn = φtPn = 45.0 ksi × Ag = 45.0 ksi × 6.49 in.2 = 292 kips
Pu
55 kips
=
= 0.188 < 0.20; therefore, Equation H1-1b governs.
φPn 292 kips
For bending about the y axis only, Equation H1-1b becomes:
Pu
Muy
+
≤ 1.0
2φPn φb Mny
φ Pn
Pu
Pu
φ Pn
+
8 Mu
=
9 φb M n
0.2 φPn
( )
1 Pu
2 φPn
Mu
+
Mu
=1
φb M n
0.9 φb M n
φb M n
Fig. H-1. Interaction Equations H1-1a and H1-1b modified for
axial load combined with bending about one axis only.
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
2 - 36
ESSENTIALS OF LRFD
From Section F above for 50 ksi steel, Mn = Mp = ZyFy = 50 ksi × Zy for
minor-axis bending (regardless of the unbraced length).
φbMny = 0.90 × 50 ksi × Zy = 45.0 ksi × Zy
= 45.0 ksi ×
6.10 in.3
12 in./ft
= 22.9 kip-ft for a W10×22 member
20 kip−ft
Pu
Muy
0.188
+
=
+
= 0.094 + 0.873
2
22.9 kip−ft
2φPn φb Mny
= 0.967 < 1.0 o.k.
EXAMPLE H-2
Given:
Check the same tension member, a W10×22 in 50 ksi steel, 4.0 ft long,
subjected to the following combination of factored loads:
Pu = 140 kips
Mux = 55 kip-ft
Muy = 0
Cb = 1.0
Solution:
Again, φPn = 292 kips
Pu
φPn
=
140 kips
= 0.479 > 0.20; Equation H1-1a governs.
292 kips
For bending about the x axis only, Equation H1-1a becomes
Pu 8 Mux
+
≤ 1.0
φPn 9 φb Mnx
From Section F above for 50 ksi steel, Mn = Mp = ZxFy = 50 ksi × Zx for
major-axis bending if Lb ≤ Lp for (Cb = 1.0).
Assume unbraced length, Lb = 4.0 ft.
By Equation 2-15 in Section F, Lp = 42.4ry for 50 ksi steel.
For a W10×22, ry = 1.33 in., Zx = 26.0 in.3
Lp =
42.4 × 1.33 in.
= 4.7 ft
12 in./ft
Lb = 4.0 ft < Lp = 4.7 ft
Then Mnx = 50 ksi × Zx
φb Mnx
0.90 × 50 ksi × 26.0 in.3
12 in./ft
= 97.5 kip-ft for a W10×22 member
=
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
H. MEMBERS UNDER COMBINED FORCES AND TORSION
2 - 37
55 kip−ft
Pu
8Mux
8
+
= 0.479 + ×
9 97.5 kip−ft
φPn 9φb Mnx
= 0.479 + 0.501 = 0.980 < 1.0 o.k.
Symmetric Members Subject to Bending and Axial Compression
The interaction of compression and flexure in beam-columns with singly and doubly
symmetric cross sections is governed by Equations H1-1a and H1-1b, repeated here for
convenience:
For
For
Pu
≥ 0.2,
φPn
Pu
< 0.2,
φPn
Muy 
Pu 8  Mux
+ 
+
 ≤ 1.0
φPn 9  φb Mnx φb Mny
(H1-1a)
 Mux
Muy 
Pu
+
+
 ≤ 1.0
2φPn  φb Mnx φb Mny
(H1-1b)
The definitions of the ter ms in the for mulas, which differ in some cases from those given
above, are as follows:
= required compressive strength; i.e., the total factored compressive force, kips
= design compressive strength, φc Pn, kips
= resistance factor for compression, φc = 0.85
= nominal compressive strength as defined in Chapter E of the LRFD Specification, kips
Mu = required flexural strength including second-order effects, kip-in. or kip-ft
φb Mn = design flexural strength, kip-in. or kip-ft
= resistance factor for flexure = 0.90
φb
Mn = nominal flexural strength from Chapter F of the LRFD Specification, kip-in.
or kip-ft
Pu
φPn
φ
Pn
The second-order analysis required for Mu involves the determination of the additional
moment due to the action of the axial compressive forces on a deformed structure. In lieu
of a second-order analysis, the simplified method given in Chapter C of the LRFD
Specification (and in Section C above) may be used. However, in applying the simplified
method, the additional moments obtained for beam-columns must also be distributed to
connected members and connections (to satisfy equilibrium).
Bending and Axial Compression—Preliminary Design
The design of a beam-column is a trial and error process which can become tedious,
particularly with the repeated solution of Interaction Equation H1-1a or H1-1b. A rapid
method for the selection of a trial section is given in this LRFD Manual, Part 3, under
the heading Combined Axial and Bending Loading (Interaction). As in earlier editions
of the AISC Manual, the Interaction Equations are approximated by an equation which
converts bending moments to equivalent axial loads:
Pu eq = Pu + Muxm + Muymu
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
2 - 38
ESSENTIALS OF LRFD
where
= equivalent axial load to be checked against the column load table, kips
Pu eq
Pu, Mux, Muy are defined in the Interaction Equations for compression and bending
m, u
are factors tabulated in this LRFD Manual, Part 3
As soon as a satisfactory trial section has been found (i.e., one for which Pu eq ≤ tabulated
φc Pn), a final verification should be made with the appropriate Interaction Equation,
H1-1a or H1-1b
EXAMPLE H-3
Given:
Check the adequacy of a W14×176 beam-column, 14.0 ft in height
floor-to-floor, in a braced symmetrical frame in 50 ksi steel. The
member is subjected to the following factored forces due to symmetrical gravity loads: Pu = 1,400 kips; Mx = 200 kip-ft, My = 70 kip-ft
(reverse curvature bending with equal end moments about both axes);
and no loads along the member.
Solution:
For a braced frame, K = 1.0 KxLx = KyLy = 14.0 ft
For a W14×176:
A
Zx
Zy
rx
ry
Kl / rx
Kl / ry
= 51.8 in.2
= 320 in.3
= 163 in.3
= 6.43 in.
= 4.02 in.
= (14.0 ft × 12 in./ft) / 6.43 in. = 26.1
= (14.0 ft × 12 in./ft) / 4.02 in. = 41.8
From Table E-1, above, φcFcr = 37.4 ksi for Kl / r = 41.8 in 50 ksi steel.
φcPn = (φc Fcr) A = 37.4 ksi × 51.8 in.2 = 1,940 kips
Pu
1,400 kips
=
= 0.72 > 0.2, Interaction Equation H1-1a
φc Pn 1,940 kips
governs.
Since
For a braced frame, Mlt = 0. From Equation C1-1:
Mux = B1x Mntx , where Mntx = 200 kip-ft; and
Muy = B1y Mnty , where Mnty = 70 kip-ft
From Equations C1-2 and C1-3:
B1 =
Cm
> 1.0
(1 − Pu / Pe1 )
where in this case (a braced frame with no transverse loading),
Cm = 0.6 − 0.4(M1 / M2)
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
H. MEMBERS UNDER COMBINED FORCES AND TORSION
2 - 39
For reverse curvature bending and equal end moments:
M1 / M2 = +1.0
= 0.6 − 0.4(1.0) = 0.2
Cm
From Table C-1:
Pe1x = 420 ksi × Ag = 420 ksi × 51.8 in.2 = 21,756 kips
From Table C-1:
Pe1y = 164 ksi × Ag = 164 ksi × 51.8 in.2 = 8,495 kips
B1x =
Cmx
0.2
=
= 0.2
(1 − Pu / Pe1x ) (1 − 1,400 kips / 21,756 kips)
Use B1x = 1.0, per Equation C1-2.
B1y =
Cmy
0.2
=
= 0.2
(1 − Pu / Pe1y ) 1 − 1,400 kips / 8,495 kips)
Use B1y = 1.0, per Equation C1-2.
Mux = 1.0 × 200 kip-ft
Muy = 1.0 × 70 kip-ft
From Equation 2-15 for 50 ksi steel,
Lp = 42.4ry =
42.4 × 4.02 in.
= 14.2 ft
12 in./ft
Since Lb = 14.0 ft < Lp = 14.2 ft, Mnx = Mpx = ZxFy
Mny
= Mpy = Zy Fy
φbFy
= 0.90 × 50 ksi = 45.0 ksi
φb Mnx = φbFy Zx =
45.0 ksi × 320 in.3
= 1,200 kip-ft
12 in./ft
φb Mny = φbFy Zy =
45.0 ksi × 163 in.3
= 611 kip-ft
12 in./ft
By Interaction Equation H1-1a
70 kip−ft 
8
1,400 kips 8  200 kip−ft
+ 
+
 = 0.72 + (0.17+0.11)
1,940 kips 9  1,200 kip−ft 611 kip−ft 
9
= 0.72 + 0.25
= 0.97 < 1.0
W14×176 is o.k.
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
2 - 40
ESSENTIALS OF LRFD
EXAMPLE H-4
Given:
Check the adequacy of a W14×176 beam-column (Fy = 50 ksi) in an
unbraced symmetrical frame subjected to the following factored
forces:
Pu
Mux
My
KxLx
= 1,400 kips (due to gravity plus wind)
= 300 kip-ft (due to wind only)
=0
= Ky Ly = 14.0 ft
Drift index, ∆oh / L ≤ 0.0025 (or 1⁄400)
ΣPu = 24,000 kips
ΣH = 800 kips
Solution:
As in Example H-3, for a W14×176 with KL = 14.0 ft, φcPn = 1,940
kips.
Pu
1,400 kips
=
= 0.72 > 0.2, Interaction Equation H1-1a
φcPn 1,940 kips
governs.
Since
Because Mntx = Mnty = Mlty = 0 and only Mltx ≠ 0, Mux = B2Mltx and
Muy = 0.
Mltx = 300 kip-ft
According to Equation C1-4,
B2 =
1
1
=
= 1.08
ΣPu  ∆oh 1 − 24,000 kips (0.0025)
1−
 
800 kips
ΣH  L 
Mux = 1.08 × 300 kip-ft = 324 kip-ft
Because Lb < Lp = 14.2 ft, Mnx = Mpx = ZxFy; φb Mnx = 1,200 kip-ft as in
Example H-3.
By Interaction Equation H1-1a:
8
1,400 kips 8 324 kip−ft
+
= 0.72 + 0.27 = 0.96 < 1.0
9
1,940 kips 9 1,200 kip−ft
W14×176 is o.k.
Torsion and Combined Torsion, Flexure, and/or Axial Force
Criteria for members subjected to torsion and torsion combined with other forces are
given in Section H2 of the LRFD Specification. They require the calculation of normal
and shear stresses by elastic analysis of the member under the factored loads. The AISC
book Torsional Analysis of Steel Members (American Institute of Steel Construction,
1983) provides design aids and examples for the determination of torsional stresses.
Extensive coverage is given there to wide-flange shapes (W, S, and HP), channels (C
and MC) and Z shapes. For these members, the charts and formulas simplify considerably
AMERICAN INSTITUTE OF
STEEL CONSTRUCTION
H. MEMBERS UNDER COMBINED FORCES AND TORSION
2 - 41
the calculation of torsional rotations, torsional normal and shear stresses, and the
combination of torsional with flexural stresses.
In the LRFD Specification,
fun = the total normal stress under factored load (ksi) from torsion and all other causes
fuv = the total shear stress under factored load (ksi) from torsion and all other causes
The criteria are as follows:
a. For the limit state of yielding under normal stress
fun ≤ φFy, where φ = 0.90
(H2-1)
fun ≤ 0.90 × 50 ksi = 45.0 ksi
(2-24)
For 50 ksi steel,
b. For the limit state of yielding under shear stress,
fuv ≤ 0.60φFy, where φ = 0.90
(H2-2)
fuv ≤ 0.60 × 0.90 × 50 ksi = 27.0 ksi
(2-25)
For 50 ksi steel,
c. For the limit state of buckling,
fun ≤ φcFcr or fuv ≤ φcFcr, as applicable, where φc = 0.85
(H2-3)
For 50 ksi steel, values of φcFcr are given in Table E-1, in Section E above.
Torsion will accompany flexure when the line of action of a lateral load does not pass
through the shear center. For wide flange and other doubly symmetric shapes, the shear
center is located at the centroid. Singly symmetric shapes have their shear centers on the
axis of symmetry, but not at the centroid. (The location of the shear center of channel
sections is given in the Properties tables in Part 1 of this LRFD Manual.)
Open sections, such as wide-flange and channel, are very inefficient in resisting
torsion; i.e., torsional rotations can be large and torsional stresses relatively high. It is
best to avoid torsion by detailing the loads and reactions to act through the shear center
of the member. In the case of spandrel members supporting building facade elements,
this may not be possible. Heavy exterior masonry walls and stone panels can impose
severe torsional loads on spandrel beams. The following are suggestions for eliminating
or reducing this kind of torsion:
1. Wall elements may span between floors. The moment due to the eccentricity of the
wall with respect to the edge beams can be resisted by lateral forces acting through
the floor diaphragms. Torsion would not be imposed on the spandrel beams.
2. If facade panels extend only a partial story height below the floor line, the use of
diagonal steel “kickers” may be possible. These light members would provide lateral
support to the wall panels. Torsion from the panels would be resisted by forces
originating from structural elements other than the spandrel beams.
3. Even if torsion must be resisted by the edge members, providing intermediate
torsional supports can be helpful. Reducing the span over which the torsion acts will
reduce torsional stresses. If there are secondary beams framing into a spandrel girder,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 - 42
ESSENTIALS OF LRFD
the beams can act as intermediate torsional supports for the girder. By adding top
and bottom moment plates to the connections of the beams with the girder, the
bending resistances of the beams can be mobilized to provide the required torsional
reactions along the girder.
4. Closed sections provide considerably better resistance to torsion than open sections;
torsional rotations and stresses are much lower for box beams than for wide-flange
members. For members subjected to torsion, it may be advisable to use box sections
or to simulate a box shape by welding one or two side plates to a W shape.
I. COMPOSITE MEMBERS
Chapter I of the LRFD Specification covers composite members. Included are concreteencased and concrete-filled steel columns and beam columns, as well as steel beams
interactive with the concrete slabs they support and steel beams encased in concrete.
Unlike traditional structural steel design, which considers only the strength of the steel,
composite design assumes that the steel and concrete work together in resisting loads.
This results in more economical designs, as the quantity of steel can be reduced.
Compression Members
Composite columns (concrete-encased and concrete-filled) must satisfy the limitations
in Section I2 of the LRFD Specification. The design strength of axially loaded composite
columns is φcPn, where φc = 0.85 and the nominal axial compressive strength is determined
from Equations E2-1 through E2-4 above with the following modifications:
As replaces Ag, rm replaces r, Fmy replaces Fy, and Em replaces E.
Fmy = Fy + c1Fyr
Ar
Ac
+ c2 fc′
As
As
(I2-1)
Ac
As
(I2-2)
Em = E + c3Ec
rm = radius of gyraton of the steel shape, pipe, or tubing, in. (For steel shapes it shall
not be less than 0.3 times the overall thickness of the composite cross section
in the plane of buckling.)
where
Ec = w1.5√
fc′
and
Fmy
Fy
Fyr
fc′
Em
E
Ec
w
Ac
Ar
= modified yield stress for the design of composite columns, ksi
= specified minimum yield stress of the structural steel shape, ksi
= specified minimum yield stress of the longitudinal reinforcing bars, ksi
= specified compressive strength of the concrete, ksi
= modified modulus of elasticity for the design of composite columns, ksi
= modulus of elasticity of steel = 29,000 ksi
= modulus of elasticity of concrete, ksi
= unit weight of concrete, lb/ft3
= cross-sectional area of concrete, in.2
= cross-sectional area of longitudinal reinforcing bars, in.2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
I. COMPOSITE MEMBERS
2 - 43
As
= cross-sectional area of structural steel, in.2
c1, c2, c3 = numerical coefficients. For concrete-filled pipe and tubing: c1 = 1.0,
c2 = 0.85, and c3 = 0.4; for concrete-encased shapes c1 = 0.7, c2 = 0.6,
and c3 = 0.2
Composite columns can be designed by using the Composite Columns Tables in Part 5
of this LRFD Manual (or the numerous tables in AISC Steel Design Guide No. 6: Load
and Resistance Factor Design of W-Shapes Encased in Concrete) for the cross sections
tabulated therein, or the above equations for all cross sections.
Flexural Members
The most common case of a composite flexural member is a steel beam interacting with
a concrete slab by means of stud or channel shear connectors. The slab can be a solid
reinforced concrete slab, but is usually concrete on a corrugated metal deck.
The effective width of concrete slab acting compositely with a steel beam is determined
by three criteria. On either side of the beam centerline, the effective width of concrete
slab cannot exceed:
a. one-eighth of the beam span,
b. one-half the distance to the centerline of the adjacent beam, or
c. the distance to the edge of the slab.
The following pertains to rolled W shapes in regions of positive moment, the predominant use of composite beam design. Other cases (e.g., plate girders and negative
moments) are covered in Chapter I of the LRFD Specification.
The horizontal shear force between the steel beam and concrete slab, to be transferred
by the shear connectors between the points of zero and maximum positive moments, is
the minimum of:
a. 0.85fc′Ac (the maximum possible compressive force in the concrete),
b. AsFy (the maximum possible tensile force in the steel), and
c. ΣQn (the strength of the shear connectors).
For W shapes, the design flexural strength φb Mn, with φb = 0.85, is based on:
a. a uniform compressive stress of 0.85fc′ and zero tensile strength in the concrete
b. a uniform steel stress of Fy in the tension area and compression area (if any) of the
steel section, and
c. equilibrium; i.e., the sum of the tensile forces equals the sum of the compressive
forces.
The above is valid for shored and unshored construction. However, in the latter case, it
is also necessary to check the bare steel beam for adequacy to support the wet concrete
and other construction loads (properly factored).
The number of shear connectors required between a point of maximum moment and
the nearest location of zero moment is
n=
Vh
Qn
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(2-26)
2 - 44
ESSENTIALS OF LRFD
where
Vh = the total horizontal shear force to be transferred, kips
= the minimum of 0.85fc′Ac, AsFy, and ΣQn
Qn = the shear strength of one connector
The nominal strength of a single stud shear connector in a solid concrete slab is

fc′Ec ≤ AscFu
Qn = 0.5Asc√
(I5-1)
where
Asc = cross-sectional area of a stud shear connector, in.2
fc′ = specified compressive strength of concrete, ksi
Fu = minimum specified tensile strength of a stud shear connector, ksi
Ec = modulus of elasticity of concrete, ksi
Special provisions for shear connectors embedded in concrete on formed steel deck are
given in Section I3.5 of the LRFD Specification. Among them are reduction factors (given
by Equation I3-1 and I3-2) to be applied to the middle term of Equation I5-1 above.
The design of composite beams and the selection of shear connectors can be accomplished with the tables in Part 5 of this LRFD Manual.
The design shear strength for composite beams is determined by the shear strength of
the steel web, as for noncomposite beams; see Section F above.
Combined Compression and Flexure
Composite beam-columns are covered in Section I4 of the LRFD Specification.
COMPUTER SOFTWARE
ELRFD* (Electronic LRFD Specification)
ELRFD is a sophisticated computer program for interactively checking structural steel
building components for compliance with the AISC Specification. All provisions of
Chapters A through H and K of the LRFD Specification are included in the knowledge
base of ELRFD.
The ELRFD program checks whether the member satisfies all limit states and limitation requirements set by the LRFD Specification and reports which sections of the
specification are satisfied or violated. One can review in detail the formulas and rules
used in the evaluation and interactively assess any mathematical expression appearing
on the screen. Design data produced by the software can be viewed and/or printed in
report form for permanent record. ELRFD has a fully interactive Windows-based user
interface.
*ELRFD is copyright AISC and Visual Edge Software, Ltd.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
REFERENCES
2 - 45
REFERENCES
American Institute of Steel Construction, Inc., 1983, Torsional Analysis of Steel Members, AISC, Chicago, IL.
American Society of Civil Engineers, 1988, Minimum Design Loads for Buildings and
Other Structures, ASCE 7-88, New York, NY.
Galambos, T. V., et al., 1978, Eight LRFD Papers, Journal of the Structural Division,
ASCE, Vol. 104, No. ST9 (September 1978), New York.
Geschwindner, L., 1993, “The ‘Leaning’ Column in ASD and LRFD,” Proceedings of
the 1993 National Steel Construction Conference, AISC, Chicago.
U.S. Department of Commerce, 1980, Development of a Probability Based Criterion for
American National Standard A58, NBS (National Bureau of Standards) Special
Publication 577, Washington, DC.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3-1
PART 3
COLUMN DESIGN
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-3
DESIGN STRENGTH OF COLUMNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5
W and HP Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-15
Steel Pipe and Structural Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-35
Double Angles and WT Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-53
Single-Angle Struts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-104
COLUMN BASE PLATES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-117
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-117
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3-2
COLUMN DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
3-3
OVERVIEW
Column tables with design compressive strengths, in kips, are located as follows:
W shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-16
HP shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-31
Steel pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-36
Structural tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-39
Double angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-57
WT shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-83
Single angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-104
Additional information related to column design is provided as follows:
Effective length factor (K) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5
Alignment charts, Figure 3-1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6
Stiffness reduction factors (SRF), Table 3-1 . . . . . . . . . . . . . . . . . . . . . . . . 3-7
“Leaning” columns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10
Combined axial and bending loading (Interaction) . . . . . . . . . . . . . . . . . . . . 3-11
Preliminary design of beam-columns, Table 3-2 . . . . . . . . . . . . . . . . . . . . 3-12
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3-4
COLUMN DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3-5
DESIGN STRENGTH OF COLUMNS
General Notes
Column Load Tables
Column Load Tables are presented for W, WT, and HP shapes, pipe, structural tubing,
double angles, and single angles. Tabular loads are computed in accordance with the
AISC LRFD Specification, Sections E2 and E3 and Appendix E3, for axially loaded
members having effective unsupported lengths indicated to the left of each table. The
effective length KL is the actual unbraced length, in feet, multiplied by the factor K, which
depends on the rotational restraint at the ends of the unbraced length and the means
available to resist lateral movements.
Table C-C2.1 in the Commentary on the LRFD Specification is a guide in selecting
the K-factor. Interpolation between the idealized cases is a matter of engineering judgment. Once sections have been selected for the several framing members, the alignment
charts in Figure 3-1 [reproduced from the Structural Stability Research Council Guide
(Galambos, 1988) here and in Figure C-C2.2 of the Commentary on the LRFD Specification] afford a means to obtain more precise values for K, if desired. For column behavior
in the inelastic range, the values of G as defined in Figure 3-1 may be reduced by the
values given in Table 3-1, as illustrated in Example 3-3.
Tables for W, WT, and HP shapes and for double and single angles are provided for
36 ksi and 50 ksi yield stress steels. Tables for steel pipe are provided for 36 ksi, and for
structural tubing for 46 ksi yield stress steel. All design strengths are tabulated in kips.
Values are not shown when Kl / r exceeds 200.
In all tables, except double angle and WT tables, design strengths are given for effective
lengths with respect to the minor axis calculated by LRFD Specification Section E2.
When the minor axis is braced at closer intervals than the major axis, the strength of the
column must be investigated with reference to both major (X-X) and minor (Y-Y) axes.
The ratio rx / ry included in these tables provides a convenient method for investigating
the strength of a column with respect to its major axis. To obtain an effective length with
respect to the minor axis equivalent in load carrying capacity to the actual effective length
about the major axis, divide the major axis effective length by rx / ry ratio. Compare this
length with the actual effective length about the minor axis. The longer of the two lengths
will control the design, and the design strength may be taken from the table opposite the
longer of the two effective lengths with respect to the minor axis. The double angle and
WT tables show values for effective lengths about both axes.
Properties useful to the designer are listed at the bottom of the column design strength
tables. Additional notes relating specifically to the W and HP shape tables, the steel pipe
and structural tubing tables, and the double and single angle tables precede each of these
groups of tables.
EXAMPLE 3-1
Given:
Design the lightest W shape of Fy = 50 ksi steel to support a factored
concentric load of 1,400 kips. The effective length with respect to
its minor axis is 16 feet. The effective length with respect to its
major axis is 31 feet.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3-6
COLUMN DESIGN
Solution:
Enter the appropriate Column Load Table for W shapes at effective
length of KL = 16 ft. Since W14 columns are generally most efficient,
begin with the W14 table and work downward, weightwise.
Select W14×145, good for 1,530 kips > 1,400 kips
rx / ry = 1.59. Equivalent L = 31 ft / 1.59 = 19.5 ft > 16 ft
Equivalent effective length for X-X axis controls.
GA
∞
50.0
K
GB
∞
1.0
50.0
10.0
10.0
5.0
3.0
5.0
0.9
5.0
100.0
50.0
30.0
20.0
4.0
20.0
10.0
9.0
8.0
7.0
3.0
2.0
0.5
0.5
0.4
0.4
0.3
0.3
pl
am
2
0.6
0.7
6.0
5.0
10.0
9.0
8.0
7.0
-3
e3
Ex
3-
0.8
0.7
ple
1.0
0.8
0.7
am
1.0
Ex
0.8
0.2
GB
∞
20.0
10.0
100.0
50.0
30.0
3.0
2.0
0.6
K
GA
∞
6.0
5.0
2.2
4.0
4.0
2.0
3.0
3.0
1.75
2.0
2.36
2.0
1.5
0.6
0.2
1.0
0.1
1.0
0.1
0.26
0
0.5
0
SIDESWAY INHIBITED
1.0
0
0
SIDESWAY UNINHIBITED
Fig. 3-1. Alignment charts for effective length of columns in continuous frames.
The subscripts A and B refer to the joints at the two ends of the column section
being considered. G is defined as
Σ(Ic / Lc)
G=
Σ(Ig / Lg)
in which Σ indicates a summation of all members rigidly connected to that joint and
lying on the plane in which buckling of the column is being considered. Ic is the
moment of inertia and Lc the unsupported length of a column section, and Ig is the
moment of inertia and Lg is the unsupported length of a girder or other restraining
member. Ic and Ig are taken about axes perpendicular to the plane of buckling being
considered.
For column ends supported but not rigidly connected to a footing or foundation,
G is theoretically infinity, but, unless actually designed a true friction free pin, may
be taken as 10 for practical designs. If the column end is rigidly attached to a properly
designed footing, G may be taken as 1.0. Smaller values may be used if justified by
analysis.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3-7
Table 3-1.
Stiffness Reduction Factors (SRF) for Columns
Pu / A
Fy
Pu / A
ksi
42
41
40
39
38
37
36
35
34
33
32
31
30
29
28
27
Fy
ksi
36 ksi
50 ksi
—
—
—
—
—
—
—
—
—
—
—
—
0.05
0.14
0.22
0.30
0.03
0.09
0.16
0.21
0.27
0.33
0.38
0.44
0.49
0.53
0.58
0.63
0.67
0.71
0.75
0.79
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
36 ksi
50 ksi
0.38
0.45
0.52
0.58
0.65
0.70
0.76
0.81
0.85
0.89
0.92
0.95
0.97
0.99
1.00
↓
0.82
0.85
0.88
0.90
0.93
0.95
0.97
0.98
0.99
1.00
↓
— indicates not applicable.
Re-enter table for effective length of 19.5 ft to satisfy axial load of
1,400 kips, select W14×145.
By interpolation, the column is good for 1,410 kips.
Use W14×145 column
EXAMPLE 3-2
Given:
Design an 11-ft long W12 interior bay column to support a factored
concentric axial roof load of 1,100 kips. The column is rigidly framed at
the top by 30-ft long W30×116 girders connected to each flange. Column
moment is zero due to the assumption of equal and offsetting moments in
the girders. The column is braced normal to its web at top and base so that
sidesway is inhibited in this plane. Use Fy = 50 ksi steel.
Solution:
a. Check Y-Y axis:
Assume the column is pin-connected at the top and bottom with
sidesway inhibited.
From Table C-C2.1 in the Commentary for condition (d), K = 1.0:
Effective length = 11 ft
Enter Column Load Table:
W12×106 good for 1,160 kips > 1,100 kips o.k.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3-8
COLUMN DESIGN
b. Check X-X axis:
1. Preliminary selection:
Assume sidesway uninhibited and pin-connected at base.
From Table C-C2.1 for condition (f):
K = 2.0
Approximate effective length relative to X-X axis:
2.0 × 11 = 22.0 ft
From Properties section in tables, for W12 column:
rx / ry ≈ 1.76
Equivalent effective length relative to the Y-Y axis:
22.0
1.76
≈ 12.5 ft > 11.0 ft
Therefore, effective length for X-X axis is critical.
Enter Column Load Table with an effective length of 12.5 ft:
W12×106 column, by interpolation, good for 1,115 kips > 1,100 kips
o.k.
1. Final selection
Try W12×106
Using Figure 3-1 (sidesway uninhibited):
Ix for W12×106 column = 933 in.4
Ix for W30×116 girder = 4,930 in.4
G (base)
= 10 (assume supported but not rigidly connected)
G (top)
=
933 / 11
= 0.258, say 0.26
(4,930 × 2) / 30
Connect points GA = 10 and GB = 0.26, read K = 1.75
For W12×106, rx / ry = 1.76
Actual effective length relative to Y-Y axis:
1.75
× 11.0 = 10.9 ft < 11.0 ft
1.76
Since the effective length for Y-Y axis is not critical,
Use W12×106 column
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3-9
EXAMPLE 3-3
Given:
Using the alignment chart, Figure 3-1 (sidesway uninhibited) and Table
3-1 (Stiffness Reduction Factors), design columns for the bent shown,
by the inelastic K-factor procedure. Let Fy = 50 ksi. Assume continuous
support in the transverse direction.
Solution:
The alignment charts in Figure 3-1 are applicable to elastic columns.
By multiplying G-values times the stiffness reduction factor Et / E, the
charts may be used for inelastic columns.
Since Et / E ≈ Fcr, inelastic / Fcr, elastic, the relationship may be written as
Ginelastic = (Fcr, inelastic / Fcr, elastic)Gelastic.
By utilizing the calculated stress Pu / A a direct solution is possible,
using the following steps:
1. For a known value of factored axial load, Pu = 1,100 kips, select a
trial column size.
Assume W12×120
A = 35.3 in.2, Ix = 1,070 in.4, rx = 5.51 in.
2. Calculate Pu / A:
Pu / A = 1,100 kips / 35.3 in.2 = 31.2 ksi
3. From Table 3-1, determine the Stiffness Reduction Factor (SRF);
SRF = 0.62. For values of Pu / A smaller than those with entries in
Table 3-1, the column is elastic, and the reduction factor is 1.0.
4. Determine Gelastic:
Gelastic (bottom) = 10
1,100 k
1,100 k
W16x31
IX = 375
15′
20′
Fig. 3-2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 10
COLUMN DESIGN
Gelastic (top)
=
1,070 / 15
= 3.80
375 / 20
5. Calculate Ginelastic = SRF × Gelastic:
Ginelastic(top) = 0.62 × 3.80 = 2.36
6. Determine K from Figure 3-1 using Ginelastic
For G (top) = 2.36 and G (bottom) = 10,
Read from Figure 3-1, K = 2.2
7. KLx = 2.2 × 15 ft = 33.0 ft
8. Calculate equivalent of KLy:
KLx 33.0 ft
=
= 18.75 ft
1.76
rx / ry
9. From the column tables (for 50 ksi steel):
φc Pn = 1,030 kips < 1,100 kips req’d. n.g.
Try a stronger column.
1. Try a W12×136
A = 39.9 in.2, Ix = 1,240 in.4, rx = 5.58 in.
2. Pu / A = 1,100 kips / 39.9 in.2 = 27.6 ksi
3. From Table 3-1: SRF = 0.77
4. Gelastic (top) =
1,240 / 15
= 4.41
375 / 20
5. Ginelastic(top) = 0.77 × 4.41 = 3.39
6. K = 2.3
7. KLx = 2.3 × 15 ft = 34.5 ft
8. Equivalent KLy:
KLx 34.5 ft
=
= 19.5 ft
1.77
rx / ry
9. φc Pn = 1,135 kips > 1,100 kips req’d o.k.
Use W12×136
“Leaning” Columns
A “leaning” column is one which is considered pin-ended and does not participate in
providing lateral stability to the structure. As a result, it relies on other parts of the
structure for stability. The LRFD Specification in Section C2.2 requires that for unbraced
frames, “the destabilizing effects of gravity-loaded columns whose simple connections
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 11
to the frame do not provide resistance to lateral loads shall be included in the design of
the moment-frame columns.”
Normal practice is to design leaning columns for their required strength with an
effective length factor K = 1. To account for the effects of leaning columns on unbraced
frames, one of the methods given in the Commentary on the LRFD Specification (Section
C2) or in Geschwindner (1993) may be utilized. The simplest methods are:
1. The slightly conservative approach of adjusting the effective lengths of the rigidframe columns,
Ki′ = 
√NKi
where
Ki′ = the modified effective length factor of a column
Ki = the actual effective length factor of a column
N = ratio of the factored gravity load supported by all columns in the given story
to that supported by the columns in the rigid frame
2. The more conservative approach of providing sufficient design compressive
strength in the rigid-frame columns of a story to enable them to support the total
factored gravity load of the story at their actual effective lengths.
Combined Axial and Bending Loading (Interaction)
Loads given in the Column Tables are for concentrically loaded columns. For columns
subjected to both axial and bending stress, see Chapters C and H of the LRFD
Specification.
The design of a beam-column is a trial and error process in which a trial section is
checked for compliance with Equations H1-1a and H1-1b. A fast method for selecting an
economical trial W section, using an equivalent axial load, is illustrated in the example
problem, using Table 3-2 and the u values listed in the column properties at the bottom
of the column load tables.
The procedure is as follows:
1. With the known value of KL (effective length), select a first approximate value of
m from Table 3-2. Let u equal 2.
2. Solve for Pu eq = Pu + Mux m + Muy mu
where
Pu
Mux
Muy
m
u
= actual factored axial load, kips
= factored bending moment about the strong axis, kip-ft
= factored bending moment about the weak axis, kip-ft
= factor taken from Table 3-2
= factor taken from column load table
3. From the appropriate Column Load Table, select a tentative section to support Pu eq.
4. Based on the section selected in Step 3, select a “subsequent approximate” value of
m from Table 3-2 and a u value from the column load table.
5. With the values selected in Step 4, solve for Pu eq.
6. Repeat Steps 3 and 4 until the values of m and u stabilize.
7. Check section obtained in Step 6 per Equation H1-1a or H1-1b, as applicable.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 12
COLUMN DESIGN
Table 3-2.
Preliminary Beam-Column Design
Fy = 36 ksi, Fy = 50 ksi
Values of m
Fy
KL (ft)
36 ksi
10
12
14
16
18
50 ksi
20
22 and
over
10
12
14
16
18
20
22 and
over
1.8
1.7
1.6
1.4
1.3
1.2
1.4
1.7
1.8
2.0
1.8
1.5
1.4
1.1
1.4
1.5
1.7
1.7
1.5
1.3
1.0
1.1
1.3
1.5
1.5
1.4
1.3
0.9
1.0
1.2
1.3
1.4
1.3
1.2
0.8
0.9
1.1
1.2
1.3
1.2
1.2
1st Approximation
All
Shapes
2.0
1.9
1.8
1.7
1.6
1.5
1.3
1.9
Subsequent Approximation
W4
W6
W8
W8
W10
W12
W14
3.1
3.2
2.8
2.5
2.1
1.7
1.5
2.3
2.7
2.5
2.3
2.0
1.7
1.5
1.7
2.1
2.1
2.2
1.9
1.6
1.4
1.4
1.7
1.8
2.0
1.8
1.5
1.4
1.1
1.4
1.5
1.8
1.7
1.5
1.3
1.0
1.2
1.3
1.6
1.6
1.4
1.3
0.8
1.0
1.1
1.4
1.4
1.3
1.2
2.4
2.8
2.5
2.4
2.0
1.7
1.5
1.8
2.2
2.2
2.2
1.9
1.6
1.4
This table is from a paper in AISC Engineering Journal by Uang, Wattar, and Leet (1990).
EXAMPLE 3-4
Given:
Design the following column:
Pu = 400 kips
Mntx = 250 kip-ft
Mltx = 0 (braced frame)
Mnty = 80 kip-ft
Mlty = 0 (braced frame)
KLx = KLy = 14 ft
Lb = 14 ft
Cm = 0.85
Fy = 50 ksi
Solution:
1. For KL = 14 ft, from Table 3-2 select a first trial value of m = 1.7.
Let u = 2
2. Pu eq = Pu + Mux m + Muy mu = 400 + 250 × 1.7 + 80 × 1.7 × 2 =
1,097 kips
3. From Column Load Tables select W14×109 (φc Pn = 1,170 kips) or
W12×120 (φc Pn = 1,220 kips).
4. Select the W14 column, so the second trial value of m is 1.4. (Note:
If a W14 column were required for architectural or other reasons,
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 13
the selection process could have started with m = 1.4). With m = 1.4
and u = 1.97 (for a W14×109) from Column Load Table,
Pu eq = 400 + 250 × 1.4 + 80 × 1.4 × 1.97 = 971 kips
5. From Column Load Tables select W14×90 (φc Pn = 969 kips).
6. For W14×90, m = 1.4, u = 1.94. Repeat of Steps 3 and 4 not required.
7. Check W14×90 with the appropriate interaction formula.
A
= 26.5 in.2
ry
= 3.70 in.,
 Kl 14 × 12
= 45.4
 =
3.70
 ry 
rx
= 6.14 in.,
 Kl 14 × 12
= 27.4
 =
6.14
 rx 
Thesecond-or der moments,Mux and Muy, will be evaluated using the
approximate method given in Section C1 of the LRFD Specification.
Because Mltx = Mlty = 0 (braced frames in both directions), Specification Equation C1-1 reduces to Mu = B1Mnt, where B1 is a function
of Pe1 (Equation C1-2). The values of Pe1 with respect to the x and y
axes can be determined from LRFD Specification Table 8 as follows:
Pex
Pey
= 382 × 26.5 = 10,123 kips
= 139 × 26.5 = 3,684 kips
B1x
=
0.85
< 1.0. Use B1x = 1.0
1 − 400 / 10,123
B1y
=
0.85
< 1.0. Use B1y = 1.0
1 − 400 / 3,684
= 1.0 × 250 = 250 kip-ft
= 1.0 × 80 = 80 kip-ft
0.9 × 50 × 75.6
= 284 kip-ft
φb Mny = φb Mpy =
12
Mux
Muy
From the beam selection table in Part 4 of this Manual:
φb Mnx = 577 kip-ft for Lb < Lp = 15.0 ft
Pu
φcPn
=
400
= 0.412 > 0.2. Therefore, Equation H1-1a applies.
969
400 8  250 80 
+ 
+
 = 0.412 + 0.636 = 1.05 < 1.0 n.g.
969 9  577 284
Use W14×99
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 14
COLUMN DESIGN
Column Stiffening
Values of Pwo, Pwi, Pwb, and Pfb, listed in the Properties Section of the Column Load Tables
for W and HP shapes, are useful in determining if a column requires stiffening because
of forces transmitted into it from the flanges or connecting flange plates of a rigid beam
connection to the column flange.
The parameters are defined as follows:
Pwo
Pwi
Pwb
Pfb
= φ5Fyw tw k (kips), φ = 1.0
= φFyw tw (kips/in.), φ = 1.0
= φ4,100tw3 √
Fyw / h (kips), φ = 0.9
= φ6.25tf2Fyf (kips), φ = 0.9
Column stiffening or a heavier column* is required if Pbf, the factored force transmitted
into the column web, exceeds any one of the following three resisting forces:
Pwb
Pfb
Pwi tb + Pwo, where tb is the thickness of the beam flange delivering the concentrated force.
For a complete explanation of these design parameters, see the section Column
Stiffening in Part 10 (Volume II) of this LRFD Manual.
*The designer should consider selecting a heavier column section to eliminate the need for stiffening. Although this will
increase the material cost of the column, this heavier section may provide a more economical solution due to the reduction in
labor cost associated with the elimination of stiffening.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 15
W and HP Shapes
The design strengths in the tables that follow are tabulated for the effective lengths in
feet KL (with respect to the minor axis), indicated at the left of each table. They are
applicable to axially loaded members in accordance with Section E2 of the LRFD
Specification. Two yield stresses are covered, 36 and 50 ksi.
The heavy horizontal lines appearing within the tables indicate Kl / r = 200. No values
are listed beyond Kl / r = 200.
For discussion of effective length, range of l / r, strength about the major axis,
combined axial and bending stress, and sample problems, see General Notes, above.
Properties and factors are listed at the bottom of the tables for checking strength about
the strong axis, combined loading conditions, and column stiffener requirements.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 16
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
W14
Wt./ft
808
Effective length KL (ft) with respect to least radius of gyration ry
Fy
730
665
605
550
36
50
36
50
36
50
36
50
36
50
0
7250
10100
6580
9140
6000
8330
5450
7570
4960
6890
11
12
13
14
15
5610
5480
5350
5230
5110
7440
7240
7040
6850
6660
6310
6260
6210
6150
6090
8620
8530
8430
8320
8200
5750
5700
5650
5590
5540
7850
7760
7660
7560
7450
5210
5170
5120
5070
5020
7110
7030
6940
6850
6750
4740
4700
4650
4600
4560
6460
6390
6300
6220
6120
16
17
18
19
20
4990
4870
4760
4650
4540
6480
6310
6130
5970
5810
6020
5960
5880
5810
5730
8080
7960
7820
7690
7550
5480
5410
5350
5280
5200
7340
7220
7100
6970
6840
4960
4900
4840
4770
4700
6640
6530
6420
6300
6170
4500
4450
4390
4330
4260
6020
5920
5810
5700
5590
22
24
26
28
30
4340
4140
3950
3770
3600
5490
5200
4920
4660
4410
5570
5390
5210
5020
4820
7250
6940
6610
6280
5940
5050
4890
4720
4540
4360
6560
6270
5970
5660
5340
4560
4410
4250
4090
3920
5910
5640
5360
5080
4790
4130
3990
3840
3690
3530
5350
5100
4840
4570
4300
32
34
36
38
40
3430
3280
3130
2980
2850
4170
3950
3740
3540
3350
4620
4420
4210
4000
3790
5600
5250
4910
4580
4250
4170
3980
3790
3590
3400
5030
4710
4400
4090
3780
3740
3570
3390
3210
3030
4490
4200
3910
3630
3350
3370
3210
3050
2880
2720
4030
3760
3500
3240
2990
42
44
46
48
50
2720
2590
2470
2360
2250
3170
3000
3860
3540
3260
3580
3380
3170
2970
2780
3930
3620
3310
3040
2800
3210
3020
2830
2650
2470
3490
3200
2930
2690
2480
2860
2680
2510
2340
2180
3080
2820
2580
2370
2180
2550
2390
2240
2080
1940
2740
2500
2290
2100
1940
2.03
2.03
2.03
3910
5430
3070
135
187
111
103000 122000 56400
5310
7370
4880
20.1
17.0
19.5
415
270
372
2.03
4270
154
66500
6780
16.6
241
2.02
3670
142
52200
5750
16.3
222
2.02
2250
93.4
33900
3500
19.0
313
2.01
3120
130
39900
4870
16.1
203
2.02
1930
85.7
26100
2950
18.7
288
2.01
2680
119
30800
4100
15.9
188
Properties
u
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
237
16000
5510
4.82
1.70
457000
158000
215
14300
4720
4.69
1.74
411000
135000
2.02
2640
102
44300
4140
19.3
342
196
12400
4170
4.62
1.73
357000
120000
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
178
10800
3680
4.55
1.71
310000
105000
162
9430
3250
4.49
1.70
270000
93500
DESIGN STRENGTH OF COLUMNS
3 - 17
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
W14
Wt./ft
500
Fy
455
426
398
370
50
36
50
36
50
36
50
36
50
4500
6250
4100
5700
3830
5310
3580
4970
3340
4630
11
12
13
14
15
4290
4250
4210
4170
4120
5850
5780
5710
5620
5540
3910
3870
3840
3790
3750
5330
5260
5190
5110
5030
3640
3610
3570
3530
3490
4970
4900
4830
4760
4680
3410
3380
3340
3300
3270
4640
4580
4520
4450
4380
3170
3140
3110
3070
3040
4320
4260
4200
4140
4070
16
17
18
19
20
4070
4020
3970
3910
3850
5450
5350
5250
5150
5040
3710
3660
3610
3560
3500
4950
4860
4770
4670
4570
3450
3400
3360
3310
3260
4600
4520
4430
4340
4250
3230
3180
3140
3090
3040
4300
4220
4140
4050
3960
3000
2960
2920
2870
2820
4000
3920
3840
3760
3680
22
24
26
28
30
3730
3600
3460
3320
3180
4820
4590
4350
4100
3850
3390
3270
3140
3010
2870
4370
4150
3930
3700
3480
3150
3030
2910
2790
2660
4050
3850
3640
3430
3210
2940
2830
2720
2600
2480
3780
3590
3390
3190
2990
2730
2630
2520
2410
2290
3500
3320
3140
2950
2750
32
34
36
38
40
3030
2880
2730
2580
2420
3610
3360
3120
2880
2650
2740
2600
2460
2320
2180
3250
3020
2800
2580
2370
2530
2400
2270
2140
2010
3000
2780
2570
2370
2170
2360
2230
2110
1990
1860
2780
2580
2390
2190
2010
2180
2060
1950
1830
1710
2560
2380
2190
2010
1840
42
44
46
48
50
2280
2130
1990
1850
1710
2420
2210
2020
1860
1710
2040
1910
1780
1650
1520
2160
1970
1800
1650
1520
1880
1750
1630
1510
1400
1980
1800
1650
1510
1400
1740
1620
1510
1400
1290
1830
1660
1520
1400
1290
1600
1490
1380
1280
1180
1670
1520
1390
1280
1180
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.01
1650
78.8
20400
2480
18.5
264
2.00
2290
110
24100
3450
15.7
172
1.99
1410
72.5
15800
2090
18.3
242
1.99
1950
101
18600
2900
15.5
157
1.99
1730
93.8
15000
2590
15.3
148
1.99
1120
63.7
10800
1640
18.0
213
1.98
1550
88.5
12800
2280
15.2
139
1.98
987
59.6
8790
1430
17.8
199
1.97
1370
82.8
10400
1990
15.1
129
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
147
8210
2880
4.43
1.69
235000
82600
134
7190
2560
4.38
1.67
206000
73600
2.00
1240
67.5
12800
1870
18.1
227
125
6600
2360
4.34
1.67
189000
67400
117
6000
2170
4.31
1.66
172000
62200
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
109
5440
1990
4.27
1.66
156000
56900
3 - 18
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
W14
Wt./ft
342
Fy
311
283
257
233
50
36
50
36
50
36
50
36
50
3090
4290
2800
3880
2550
3540
2310
3210
2100
2910
6
7
8
9
10
3040
3030
3010
2990
2960
4200
4170
4130
4090
4050
2750
2740
2720
2700
2680
3800
3770
3740
3700
3660
2510
2500
2480
2460
2440
3460
3440
3410
3370
3330
2280
2260
2250
2230
2210
3140
3120
3090
3060
3020
2060
2050
2040
2020
2000
2850
2820
2800
2770
2730
11
12
13
14
15
2940
2910
2880
2850
2810
4000
3950
3890
3830
3760
2660
2630
2600
2570
2540
3610
3560
3510
3460
3400
2420
2390
2370
2340
2310
3290
3240
3200
3140
3090
2190
2170
2150
2120
2090
2980
2940
2890
2850
2800
1980
1960
1940
1920
1890
2700
2660
2620
2570
2530
16
17
18
19
20
2770
2740
2700
2650
2610
3690
3620
3550
3470
3400
2510
2470
2430
2390
2360
3330
3270
3200
3130
3060
2280
2250
2210
2180
2140
3030
2970
2910
2850
2780
2060
2030
2000
1970
1940
2740
2690
2630
2570
2510
1870
1840
1810
1780
1750
2480
2430
2380
2320
2270
22
24
26
28
30
2520
2420
2320
2220
2110
3230
3060
2890
2710
2530
2270
2180
2090
2000
1900
2910
2750
2590
2430
2270
2060
1980
1900
1810
1720
2640
2500
2350
2200
2050
1870
1790
1710
1630
1550
2380
2250
2120
1980
1840
1690
1620
1550
1470
1400
2150
2030
1910
1780
1660
32
34
36
38
40
2010
1900
1790
1680
1570
2360
2180
2010
1840
1680
1800
1700
1600
1500
1410
2110
1950
1790
1640
1490
1630
1540
1450
1360
1270
1900
1760
1620
1480
1340
1470
1380
1300
1220
1140
1710
1570
1440
1320
1190
1320
1240
1170
1090
1020
1530
1410
1290
1180
1070
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
1.98
866
55.4
7100
1240
17.7
185
1.97
1200
77.0
8360
1720
15.0
120
1.97
746
50.8
5430
1030
17.5
168
1.96
1040
70.5
6400
1440
14.8
110
1.95
887
64.5
4930
1210
14.7
100
1.96
542
42.3
3150
723
17.2
140
1.94
753
58.8
3710
1000
14.6
91.6
1.95
457
38.5
2370
599
17.1
127
1.93
635
53.5
2790
832
14.5
83.4
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
101
4900
1810
4.24
1.65
141000
52000
91.4
4330
1610
4.2
1.64
124000
46100
1.97
639
46.4
4190
868
17.4
154
83.3
3840
1440
4.17
1.63
110000
41500
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
75.6
3400
1290
4.13
1.62
97400
36900
68.5
3010
1150
4.1
1.62
86200
33000
DESIGN STRENGTH OF COLUMNS
3 - 19
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
W14
Wt./ft
211
Fy
193
176
159
145
50
36
50
36
50
36
50
36
50
1900
2640
1740
2410
1590
2200
1430
1980
1310
1810
6
7
8
9
10
1870
1860
1840
1830
1810
2580
2550
2530
2500
2470
1710
1700
1690
1670
1660
2360
2340
2320
2290
2260
1560
1550
1540
1530
1510
2150
2130
2110
2090
2060
1400
1400
1390
1380
1360
1940
1920
1900
1880
1860
1280
1280
1270
1260
1250
1770
1760
1740
1720
1700
11
12
13
14
15
1790
1780
1760
1730
1710
2440
2400
2370
2330
2280
1640
1630
1610
1590
1570
2230
2200
2170
2130
2090
1500
1480
1460
1450
1430
2030
2000
1970
1940
1900
1350
1330
1320
1300
1280
1830
1810
1780
1740
1710
1230
1220
1210
1190
1170
1670
1650
1620
1590
1560
16
17
18
19
20
1690
1660
1640
1610
1580
2240
2190
2140
2090
2040
1540
1520
1500
1470
1440
2050
2010
1960
1910
1870
1410
1380
1360
1340
1310
1860
1820
1780
1740
1700
1270
1250
1230
1200
1180
1680
1640
1600
1570
1530
1160
1140
1120
1100
1080
1530
1500
1460
1430
1390
22
24
26
28
30
1520
1460
1390
1330
1260
1940
1830
1710
1600
1490
1390
1330
1270
1210
1150
1770
1670
1560
1460
1350
1260
1210
1150
1100
1040
1610
1510
1420
1320
1220
1140
1090
1040
990
930
1440
1360
1270
1180
1100
1040
992
946
898
849
1320
1240
1160
1080
998
32
34
36
38
40
1190
1120
1050
980
912
1370
1260
1160
1050
951
1080
1020
955
892
830
1250
1150
1050
956
863
980
920
863
805
748
1130
1040
946
859
775
880
830
773
721
670
1010
928
846
767
692
800
752
703
655
608
919
842
767
694
626
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
1.95
397
35.3
1830
493
17.0
116
1.93
551
49.0
2160
684
14.4
76.0
1.96
340
32.0
1370
420
16.9
106
1.93
473
44.5
1610
583
14.3
70.1
1.92
415
41.5
1310
483
14.2
64.5
1.94
251
26.8
803
287
16.7
88.6
1.92
349
37.3
947
398
14.1
59.0
1.93
214
24.5
609
241
16.6
81.5
1.90
298
34.0
718
334
14.1
54.7
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
62.0
2660
1030
4.07
1.61
76100
29400
56.8
2400
931
4.05
1.60
68700
26700
1.94
299
29.9
1110
348
16.8
97.5
51.8
2140
838
4.02
1.60
61300
24000
46.7
1900
748
4
1.60
54400
21400
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
42.7
1710
677
3.98
1.59
49000
19400
3 - 20
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
W14
Wt./ft
132
Fy
120
109
50
90
36
50
36
50
36
50†
36
50†
0
1190
1650
1080
1500
979
1360
890
1240
811
1130
6
7
8
9
10
1160
1160
1150
1140
1130
1610
1590
1570
1550
1530
1060
1050
1040
1030
1020
1460
1450
1430
1410
1390
960
953
946
937
927
1320
1310
1300
1280
1260
873
867
860
852
843
1200
1190
1180
1160
1150
795
789
783
775
767
1100
1080
1070
1060
1040
11
12
13
14
15
1110
1100
1080
1070
1050
1510
1480
1450
1430
1390
1010
999
986
971
956
1370
1350
1320
1290
1270
917
905
893
880
866
1240
1220
1200
1170
1150
833
823
811
799
787
1130
1110
1090
1060
1040
758
749
738
727
716
1030
1010
989
969
947
16
17
18
19
20
1030
1020
997
978
958
1360
1330
1300
1260
1220
940
924
906
888
870
1240
1210
1180
1140
1110
852
837
821
804
787
1120
1090
1060
1030
1000
773
759
745
730
714
1020
991
965
938
911
704
691
678
664
650
925
902
878
853
828
22
24
26
28
30
916
872
826
780
733
1150
1070
997
920
844
831
791
749
706
663
1040
972
902
832
762
752
715
677
639
600
943
879
815
751
688
682
648
614
578
542
854
796
737
679
621
620
589
558
525
493
776
723
670
616
564
32
34
36
38
686
639
593
547
769
697
627
563
620
577
535
494
694
628
565
507
560
522
483
446
627
567
509
457
507
471
436
402
565
511
458
411
460
428
396
365
512
463
415
372
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.03
196
23.2
520
215
15.7
73.7
1.99
272
32.3
613
298
13.3
49.7
2.04
173
21.2
399
179
15.6
67.9
1.99
240
29.5
471
249
13.2
46.3
1.97
205
26.3
331
208
13.2
43.2
2.02
125
17.5
222
123
15.5
58.1
1.95
174
24.3
261
171
13.4
40.6
2.02
109
15.8
165
102
15.4
54.2
1.94
151
22.0
195
142
15.0
38.4
Effective length KL (ft) with respect to least radius of gyration ry
36
99
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
38.8
1530
548
3.76
1.67
43800
15700
35.3
1380
495
3.74
1.67
39300
14100
2.02
148
18.9
281
150
15.5
62.7
32
1240
447
3.73
1.67
35400
12700
†Flange is noncompact; see discussion preceding column load tables.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
29.1
1110
402
3.71
1.66
31700
11500
26.5
999
362
3.70
1.66
28600
10400
DESIGN STRENGTH OF COLUMNS
3 - 21
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
W14
Wt./ft
82
Fy
36
50
68
61
53
48
43
36
50
36
50
36
50
36
50
36
50
36
50†
737 1020 667
927
612
850
548
761
477
663
431
599
386
536
6
7
8
9
10
705
694
682
667
652
963
942
918
892
863
638
628
616
604
590
871
852
830
807
781
585
576
565
553
540
798
781
760
738
714
523
515
505
494
483
714
698
680
660
638
443
432
418
404
389
598
576
552
526
498
400
390
378
365
351
540
520
498
474
449
357
347
337
325
312
482
463
443
422
399
11
12
14
16
18
635
618
579
538
495
833
800
732
661
588
575
559
524
487
447
753
724
662
598
532
526
511
479
444
408
689
662
604
544
484
470
457
428
396
364
615
591
539
486
431
372
355
319
282
245
469
439
379
319
263
336
320
287
253
220
423
395
340
286
235
298
284
254
224
194
375
350
301
252
206
20
22
24
26
28
450
406
363
321
280
516
447
381
325
280
407
367
328
290
253
467
405
345
294
253
371
334
297
262
229
424
366
311
265
229
331
297
265
233
203
377
325
276
236
203
210
176
148
126
109
213
176
148
126
109
188
157
132
113
97
191
157
132
113
97
165
138
116
99
85
167
138
116
99
85
30
31
32
34
36
244
229
214
190
169
244
229
214
190
169
221
207
194
172
153
221
207
194
172
153
199
187
175
155
138
199
187
175
155
138
177
166
155
138
123
177
166
155
138
123
95
89
83
95
89
83
85
79
85
79
74
69
74
69
38
152
152 138
138
124
124
110
110
3.2 2.7 3.12 2.56 2.97
95.7 133 84.2 117 72.1
13.3 18.5 12.2 17.0 11.0
98.4 116 76.4 90.0 55.1
88.2 123 71.7 100 56.9
8.00 6.79 7.96 6.75 7.88
28.0 20.1 26.4 19.2 24.7
2.37
100
15.3
64.9
79.0
6.68
18.2
0
Effective length KL (ft) with respect to least radius of gyration ry
74
Properties
u
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
2.85
149
18.4
257
148
10.3
43.0
2.68
207
25.5
303
206
8.77
29.6
24.1
882
148
2.48
2.44
25200
4240
2.82
127
16.2
177
125
10.3
40.0
2.62
176
22.5
209
173
8.77
27.9
21.8
796
134
2.48
2.44
22800
3840
2.80
112
14.9
139
105
10.3
37.3
2.56
156
20.8
163
146
8.70
26.4
20
723
121
2.46
2.44
20700
3460
2.74
97.0
13.5
102
84.2
10.2
34.7
2.44
135
18.8
121
117
8.66
25.0
17.9
640
107
2.45
2.44
18300
3080
15.6
541
57.7
1.92
3.07
15500
1650
14.1
485
51.4
1.91
3.06
13800
1470
12.6
428
45.2
1.89
3.08
12200
1290
†Web may be noncompact for combined axial and bending stress; see AISC LRFD Specification Section B5.
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 22
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
W12
Wt./ft
336
Fy
305
279
252
230
50
36
50
36
50
36
50
36
50
3020
4200
2740
3810
2510
3480
2270
3150
2070
2880
6
7
8
9
10
2960
2930
2900
2870
2840
4070
4020
3970
3910
3850
2680
2660
2630
2600
2570
3690
3640
3590
3540
3480
2450
2430
2400
2370
2350
3370
3330
3280
3230
3170
2210
2190
2170
2150
2120
3040
3010
2960
2920
2870
2020
2000
1980
1960
1930
2780
2740
2710
2660
2610
11
12
13
14
15
2800
2760
2720
2670
2620
3780
3700
3620
3540
3450
2530
2500
2460
2410
2370
3420
3350
3270
3190
3110
2310
2280
2240
2200
2160
3110
3050
2980
2910
2830
2090
2060
2020
1980
1950
2810
2750
2680
2620
2550
1910
1880
1840
1810
1770
2560
2500
2450
2380
2320
16
17
18
19
20
2570
2520
2470
2410
2350
3360
3260
3160
3060
2960
2320
2270
2220
2170
2120
3020
2940
2840
2750
2660
2110
2070
2020
1970
1920
2750
2670
2580
2500
2410
1910
1860
1820
1770
1730
2470
2400
2320
2240
2160
1740
1700
1660
1610
1570
2250
2180
2110
2030
1960
22
24
26
28
30
2230
2100
1980
1850
1720
2750
2540
2330
2120
1910
2000
1890
1770
1650
1530
2460
2270
2070
1880
1690
1820
1710
1600
1490
1380
2230
2050
1870
1690
1520
1630
1530
1430
1330
1230
1990
1830
1660
1500
1350
1480
1390
1300
1200
1110
1810
1650
1500
1350
1210
32
34
36
38
40
1590
1460
1340
1220
1100
1720
1520
1360
1220
1100
1410
1300
1180
1080
971
1510
1340
1200
1080
971
1270
1160
1060
960
866
1350
1200
1070
960
866
1130
1030
940
848
766
1200
1060
945
848
766
1020
931
845
761
687
1070
951
848
761
687
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.18
1180
64
12700
1770
14.5
202
2.17
1640
89
15000
2460
12.3
131
2.18
1010
59
9740
1480
14.3
184
2.16
1400
81
11500
2060
12.1
120
2.15
1220
77
9700
1720
12.0
110
2.16
738
50
6150
1030
13.9
154
2.14
1020
70
7250
1420
11.8
100
2.15
636
46
4810
868
13.8
141
2.13
883
64
5670
1210
11.7
92.0
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
98.8
4060
1190
3.47
1.85
116000
34000
89.6
3550
1050
3.42
1.84
101000
30000
2.16
878
55
8230
1240
14.1
169
81.9
3110
937
3.38
1.82
88900
26800
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
74.1
2720
828
3.34
1.81
77900
23700
67.7
2420
742
3.31
1.80
69100
21200
DESIGN STRENGTH OF COLUMNS
3 - 23
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
W12
Wt./ft
210
Fy
190
170
152
136
120
50
36
50
36
50
36
50
36
50
36
50
1890
2630
1710
2370
1530
2120
1370
1900
1220
1700
1080
1500
6
7
8
9
10
1840
1830
1810
1790
1760
2540
2500
2470
2430
2380
1660
1650
1630
1610
1590
2290
2260
2220
2190
2150
1490
1480
1460
1440
1420
2050
2020
1990
1960
1920
1330
1320
1300
1290
1270
1830
1810
1780
1750
1710
1190
1180
1160
1150
1130
1630
1610
1590
1560
1530
1050
1040
1030
1010
1000
1440
1420
1400
1380
1350
11
12
13
14
15
1740
1710
1680
1650
1610
2330
2280
2230
2170
2110
1570
1540
1510
1480
1450
2100
2050
2000
1950
1900
1400
1380
1350
1330
1300
1880
1840
1790
1740
1690
1250
1230
1210
1180
1160
1680
1640
1590
1550
1510
1110
1090
1070
1050
1030
1490
1460
1420
1380
1340
984
966
948
928
908
1320
1290
1250
1220
1180
16
17
18
19
20
1580
1540
1510
1470
1430
2040
1980
1910
1840
1780
1420
1390
1350
1320
1280
1840
1780
1720
1650
1590
1270
1240
1210
1180
1140
1640
1580
1530
1470
1420
1130
1100
1070
1050
1020
1460
1410
1360
1310
1260
1010
980
955
928
901
1290
1250
1210
1160
1110
886
864
841
817
793
1140
1100
1060
1020
976
22
24
26
28
30
1340
1260
1170
1090
1000
1640
1490
1360
1220
1090
1210
1130
1050
973
895
1460
1340
1210
1090
967
1070
1000
933
862
792
1300
1180
1070
959
852
954
891
827
763
700
1150
1050
944
844
749
846
788
731
673
617
1020
924
831
742
656
743
692
640
589
538
892
808
726
646
569
32
34
36
38
40
919
837
759
682
616
962
852
760
682
616
819
745
674
605
546
853
755
674
605
546
724
657
593
532
480
750
664
593
532
480
638
578
520
467
421
658
583
520
467
421
561
508
456
409
369
577
511
456
409
369
489
442
395
355
320
500
443
395
355
320
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.16
558
42
3760
731
13.7
129
2.13
774
59
4430
1020
11.6
84.2
2.14
465
38
2700
610
13.5
117
2.11
646
53
3190
847
11.5
76.6
2.15
333
31
1500
397
13.3
94.7
2.11
462
44
1760
551
11.3
62.1
2.13
276
28
1120
316
13.2
84.6
2.09
383
40
1320
439
11.2
55.7
2.12
232
26
815
247
13.0
75.5
2.07
322
36
960
343
11.1
50.0
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
61.8
2140
664
3.28
1.80
61400
19000
55.8
1890
589
3.25
1.79
54100
16900
2.14
389
35
2020
493
13.4
105
2.11
540
48
2380
684
11.4
68.9
50.0
1650
517
3.22
1.78
47100
14800
44.7
1430
454
3.19
1.77
41000
13000
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
39.9
1240
398
3.16
1.77
35600
11400
35.3
1070
345
3.13
1.76
30700
9900
3 - 24
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
W12
Wt./ft
106
Fy
96
87
79
72
65
50
36
50
36
50
36
50
36
50
36
50†
955
1330
863
1200
783
1090
710
986
646
897
584
812
6
7
8
9
10
928
919
908
896
883
1280
1260
1240
1210
1190
839
830
820
809
797
1150
1140
1120
1100
1070
761
753
744
734
723
1050
1030
1010
994
973
689
682
674
665
654
947
933
917
900
880
627
620
613
604
595
861
848
834
818
800
567
561
554
546
538
779
767
754
739
723
11
12
13
14
15
868
853
836
819
800
1160
1130
1100
1070
1040
784
770
755
739
722
1050
1020
995
966
935
711
698
684
669
654
950
926
901
874
846
643
631
619
605
591
860
838
814
790
764
585
574
562
550
537
781
761
740
717
694
529
519
508
497
485
706
687
668
647
626
16
17
18
19
20
781
761
741
719
698
1000
968
932
895
858
704
686
667
648
628
904
871
838
805
771
638
621
604
586
568
817
788
758
727
696
576
561
545
529
512
738
711
683
655
627
523
509
495
480
465
670
645
620
594
569
472
460
446
433
419
604
581
558
535
512
22
24
26
28
30
653
608
562
516
472
783
708
635
565
497
588
546
505
463
422
703
635
569
505
443
531
493
455
417
380
634
572
511
453
397
479
444
409
375
341
570
514
459
406
355
434
403
371
339
309
517
465
415
367
321
391
362
333
305
277
464
417
372
328
287
32
34
36
38
40
428
386
345
310
279
437
387
345
310
279
383
345
308
276
249
390
345
308
276
249
344
309
276
248
223
349
309
276
248
223
308
277
247
221
200
312
277
247
221
200
279
250
223
200
181
282
250
223
200
181
250
223
199
179
161
252
223
199
179
161
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.12
185
22
518
198
13.0
67.2
2.06
257
31
611
276
11.0
44.9
2.10
161
20
378
164
12.9
61.4
2.04
223
28
446
228
10.9
41.4
2.09
122
17
236
109
12.7
51.8
2.01
169
24
278
152
10.8
35.7
2.08
106
15
181
91
12.7
48.2
1.98
148
22
213
126
10.7
33.6
2.06
92.1
14
135
74
12.6
44.7
1.95
128
20
159
103
11.8
31.7
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
31.2
933
301
3.11
1.76
26700
8640
28.2
833
270
3.09
1.76
23900
7710
2.10
139
19
311
133
12.8
56.3
2.02
193
26
366
185
10.9
38.3
25.6
740
241
3.07
1.75
21200
6910
23.2
662
216
3.05
1.75
18900
6180
†Flange is noncompact; see discussion preceding column load tables.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
21.1
597
195
3.04
1.75
17000
5580
19.1
533
174
3.02
1.75
15200
4990
DESIGN STRENGTH OF COLUMNS
3 - 25
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
W12
Wt./ft
58
Fy
53
50
45
40
50
36
50
36
50
36
50
36
50
520
723
477
663
450
625
404
561
361
502
6
7
8
9
10
498
490
482
472
461
680
666
649
631
611
457
449
441
432
422
623
610
594
577
559
419
408
396
383
369
566
546
524
500
475
376
366
355
343
330
507
489
469
447
424
336
327
317
306
295
453
437
419
399
378
11
12
13
14
15
450
437
424
411
397
590
568
545
521
496
411
400
388
375
362
539
518
496
474
451
354
339
322
306
289
448
421
393
365
337
317
302
287
272
257
400
375
350
324
299
282
269
256
242
228
356
334
311
288
266
16
18
20
22
24
382
352
321
291
260
471
420
370
322
276
348
320
292
263
235
428
381
334
290
247
271
237
204
173
145
310
257
209
173
145
241
210
180
152
128
274
227
184
152
128
214
187
160
135
113
243
201
163
135
113
26
28
30
32
34
231
202
176
155
137
235
202
176
155
137
207
181
158
139
123
210
181
158
139
123
124
107
93
82
124
107
93
82
109
94
82
72
109
94
82
72
96
83
72
64
96
83
72
64
38
41
110
94
110
94
98
85
98
85
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.41
89
13
106
83
10.5
38.3
2.22
124
18
125
115
8.9
27.0
2.39
78
12
94
67
10.3
35.8
2.16
108
17
111
93
8.8
25.6
2.51
127
19
136
115
6.9
21.6
2.79
75
12
86
67
8.1
28.4
2.37
105
17
101
93
6.9
20.3
2.69
66
11
59
54
8.0
26.5
2.22
92
15
69
75
6.8
19.3
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
17.0
475
107
2.51
2.10
13600
3070
15.6
425
95.8
2.48
2.11
12200
2750
2.85
92
13
116
83
8.2
30.8
14.7
394
56.3
1.96
2.64
11300
1620
13.2
350
50
1.94
2.65
10000
1420
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11.8
310
44.1
1.93
2.66
8890
1260
3 - 26
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
W10
Wt./ft
112
Fy
100
88
77
68
50
36
50
36
50
36
50
36
50
1010
1400
900
1250
793
1100
692
961
612
850
6
7
8
9
10
969
956
941
924
906
1330
1300
1270
1240
1210
865
853
840
824
808
1180
1160
1140
1110
1080
762
751
739
725
710
1040
1020
999
973
945
664
655
644
632
618
908
890
869
847
822
588
579
569
558
547
803
787
769
749
727
11
12
13
14
15
886
865
842
819
794
1170
1130
1090
1050
1010
789
770
750
728
706
1040
1010
970
931
892
694
677
659
639
619
916
884
851
817
782
604
588
572
555
537
796
768
738
708
677
534
520
506
490
475
703
678
652
625
597
16
17
18
19
20
768
742
715
688
660
961
915
870
824
778
682
659
634
609
584
851
810
769
727
686
599
577
556
534
511
746
709
672
635
599
519
500
481
461
442
645
612
580
547
515
458
441
424
407
389
569
540
511
482
454
22
24
26
28
30
604
548
493
440
389
688
601
518
447
389
534
483
434
386
340
605
527
453
390
340
466
422
378
336
295
527
458
393
339
295
402
362
324
287
252
452
392
335
289
252
354
319
285
252
221
398
344
294
254
221
32
34
36
38
40
342
303
270
242
219
342
303
270
242
219
299
265
236
212
191
299
265
236
212
191
259
230
205
184
166
259
230
205
184
166
221
196
175
157
141
221
196
175
157
141
194
172
153
138
124
194
172
153
138
124
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.06
255
27
1210
316
11.2
86.4
2.02
354
38
1430
439
9.5
56.5
2.06
214
24
883
254
11.0
77.4
2.01
298
34
1040
353
9.4
50.8
1.99
246
30
735
276
9.3
45.1
2.03
143
19
420
153
10.8
60.0
1.96
199
27
495
213
9.2
39.8
2.01
116
17
293
120
10.8
53.8
1.93
162
24
345
167
9.2
36.0
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
32.9
716
236
2.68
1.74
20400
6760
29.4
623
207
2.65
1.74
17800
5910
2.04
177
22
623
198
11.0
68.4
25.9
534
179
2.63
1.73
15300
5130
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
22.6
455
154
2.60
1.73
13000
4370
20.0
394
134
2.59
1.71
11300
3840
DESIGN STRENGTH OF COLUMNS
3 - 27
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
W10
Wt./ft
60
Fy
54
49
45
39
33
50
36
50
36
50
36
50
36
50
36
50
539
748
483
672
441
612
407
565
352
489
297
413
6
7
8
9
10
517
509
500
491
480
706
692
675
657
638
464
457
449
440
431
634
621
606
590
572
422
416
409
401
392
577
565
551
536
520
380
371
361
350
337
515
497
478
458
436
328
320
311
301
290
444
428
412
393
374
276
269
261
252
243
373
360
345
329
312
11
12
13
14
15
469
457
444
430
416
617
595
571
547
523
420
409
398
385
373
553
533
512
490
468
382
372
361
350
338
502
484
464
444
424
324
311
296
282
267
412
388
364
339
314
278
266
254
241
228
353
332
310
289
267
233
222
211
200
189
294
276
257
238
220
16
17
18
19
20
401
387
371
356
340
497
472
446
421
395
360
346
332
318
304
445
422
399
376
353
326
314
301
288
275
403
382
361
340
319
252
237
222
207
192
290
266
243
221
199
215
201
188
175
162
246
225
205
185
167
177
166
155
144
133
202
184
167
150
135
22
24
26
28
30
309
278
248
219
191
346
299
255
220
191
276
248
221
195
170
309
266
227
196
170
250
224
199
175
153
278
239
204
176
153
164
138
118
102
88
164
138
118
102
88
138
116
99
85
74
138
116
99
85
74
112
94
80
69
60
112
94
80
69
60
32
33
34
36
168
158
149
133
168
158
149
133
150
141
133
118
150
141
133
118
134
126
119
106
134
126
119
106
78
73
78
73
65
61
65
61
53
53
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.00
99
15
209
94
10.7
48.1
1.90
138
21
246
130
9.1
32.6
1.97
83
13
143
77
10.7
43.9
1.87
116
19
168
106
9.1
30.2
2.37
79
13
121
78
8.4
35.2
2.17
109
18
142
108
7.1
24.1
2.31
64
11
88
57
8.3
31.2
2.04
89
16
104
79
7.0
21.9
2.23
55
10
69
38
8.1
27.4
1.87
77
14
81
53
6.9
19.7
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
17.6
341
116
2.57
1.71
9710
3330
15.8
303
103
2.56
1.71
8640
2960
1.96
73
12
111
64
10.6
40.7
1.83
101
17
131
88
9.0
28.3
14.4
272
93.4
2.54
1.71
7800
2660
13.3
248
53.4
2.01
2.15
7100
1540
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11.5
209
45.0
1.98
2.16
6000
1290
9.71
170
36.6
1.94
2.16
4880
1050
3 - 28
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
W8
Wt./ft
67
Fy
58
48
40
35
31
50
36
50
36
50
36
50
36
50
36
50
603
837
523
727
431
599
358
497
315
438
279
388
6
7
8
9
10
567
555
541
526
509
770
746
721
693
662
492
481
469
455
441
667
647
624
599
572
405
396
386
374
362
549
532
513
492
470
335
327
319
309
298
454
439
423
405
386
295
288
280
272
262
399
386
372
356
339
261
255
248
240
232
354
342
329
315
300
11
12
13
14
15
492
473
453
433
412
631
598
564
529
494
425
409
391
374
355
544
515
485
455
425
349
335
321
306
291
446
422
397
372
347
287
275
263
251
238
366
345
324
303
281
252
242
231
220
208
321
303
284
265
246
223
214
204
194
184
284
268
251
234
217
16
17
18
19
20
391
370
349
328
307
460
425
392
359
328
337
318
300
281
263
394
365
335
307
279
276
260
245
229
214
321
297
272
249
226
225
211
198
185
173
260
239
219
199
180
197
185
174
162
151
228
209
191
174
157
174
163
153
143
133
200
184
168
153
138
22
24
26
28
30
266
228
194
167
146
271
228
194
167
146
228
194
165
143
124
231
194
165
143
124
185
157
134
115
100
187
157
134
115
100
148
125
107
92
80
149
125
107
92
80
129
109
93
80
70
130
109
93
80
70
114
96
82
70
61
114
96
82
70
61
32
33
34
35
128
120
113
107
128
120
113
107
109
103
97
91
109
103
97
91
88
83
78
88
83
78
70
66
62
70
66
62
61
58
61
58
54
51
54
51
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.03
147
21
648
177
8.8
64.0
1.96
205
28
764
246
7.5
41.9
2
120
18
464
133
8.8
55.9
1.93
167
26
547
185
7.4
36.8
1.93
69
13
163
64
8.5
39.1
1.8
96
18
192
88
7.2
26.5
1.89
56
11
104
50
8.5
35.1
1.74
78
16
123
69
7.2
24.1
1.85
48
10
81
38
8.4
32.0
1.65
67
14
95
53
7.1
22.4
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
19.7
272
88.6
2.12
1.75
7800
2530
17.1
228
75.1
2.10
1.74
6520
2160
1.97
86
14
224
95
8.7
46.7
1.87
119
20
264
132
7.4
31.1
14.1
184
60.9
2.08
1.74
5260
1750
11.7
146
49.1
2.04
1.73
4170
1390
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10.3
127
42.6
2.03
1.73
3630
1210
9.13
110
37.1
2.02
1.72
3150
1070
DESIGN STRENGTH OF COLUMNS
3 - 29
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
W8
Wt./ft
W6
28
Fy
24
25
20
15
†
50
36
50
36
50
36
50
36
50†
252
351
217
301
225
312
180
249
136
188
6
7
8
9
10
228
219
210
200
189
303
288
271
253
235
195
188
180
171
162
260
247
232
217
200
200
191
182
172
162
265
250
233
216
198
159
152
145
137
128
211
198
185
171
156
119
114
108
102
95
158
148
137
126
115
11
12
13
14
15
178
167
155
143
132
216
197
178
160
142
152
142
132
122
112
184
168
151
136
121
151
140
129
118
107
180
162
144
128
112
119
111
102
93
84
142
127
113
100
87
88
81
74
68
61
104
92
82
71
62
16
17
18
19
20
121
110
99
89
80
125
111
99
89
80
102
93
84
75
68
106
94
84
75
68
97
87
78
70
63
98
87
78
70
63
76
68
60
54
49
76
68
60
54
49
55
48
43
39
35
55
48
43
39
35
22
24
25
26
27
66
56
51
47
44
66
56
51
47
44
56
47
44
40
56
47
44
40
52
44
40
52
44
40
40
34
31
40
34
31
29
24
29
24
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
2.17
48
10
81
44
6.8
27.2
1.87
67
14
95
61
5.7
18.8
2.07
39
9
52
32
6.7
24.3
1.71
54
12
61
45
5.7
17.2
1.98
65
16
172
58
5.4
21.0
2.03
35
9
78
27
6.3
25.6
1.91
49
13
92
37
5.3
17.6
1.98
26
8
54
14
6.7
20.8
1.75
36
12
64
19
6.8
15.0
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
u
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
8.25
98.0
21.7
1.62
2.13
2810
620
7.08
82.8
18.3
1.61
2.12
2370
525
2.07
47
12
146
42
6.3
31.2
7.34
53.4
17.1
1.52
1.78
1530
485
5.87
41.4
13.3
1.50
1.77
1190
378
†Flange is noncompact; see discussion preceding column load tables.
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.43
29.1
9.32
1.46
1.75
831
270
3 - 30
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
X
COLUMNS
W shapes
Design axial strength in kips (φ = 0.85)
Y
Designation
W6
Wt./ft
16
Effective length KL (ft) with respect to least radius of gyration ry
Fy
W5
12
9
W4
19
16
13
36
50
36
50
36
50
36
50
36
50
36
50
0
145
201
109
151
82
114
170
235
143
199
117
163
2
3
4
5
6
140
135
127
118
108
193
182
168
152
134
105
100
94
87
79
144
135
124
110
96
79
75
71
65
59
108
101
93
83
72
166
163
157
151
144
229
222
212
201
187
141
137
133
127
121
194
188
179
169
157
114
109
104
97
89
156
148
138
125
111
7
8
9
10
11
97
86
75
64
54
116
98
81
66
54
70
61
52
44
37
82
68
55
44
37
52
45
39
32
27
61
50
40
33
27
135
126
117
107
97
172
156
140
124
108
114
106
98
90
81
144
131
117
104
90
81
72
63
55
47
97
83
69
57
47
12
13
14
15
16
46
39
33
29
26
46
39
33
29
26
31
26
23
20
31
26
23
20
23
19
17
14
23
19
17
14
87
78
68
60
53
93
80
69
60
53
73
65
57
50
44
78
66
57
50
44
39
34
29
25
22
39
34
29
25
22
47
42
37
34
30
47
42
37
34
30
39
35
31
28
25
39
35
31
28
25
1.84
39
10
115
37
5.3
30.3
1.72
55
14
136
52
4.5
20.1
1.79
32
9
81
26
5.3
26.2
1.63
45
12
95
36
4.5
17.6
1.89
35
10
164
24
4.2
25.5
1.77
48
14
193
33
3.5
16.8
17
18
19
20
21
Properties
u
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
2.84
35
9
78
33
4.0
18.3
2.5
49
13
92
46
3.4
12.5
4.74
32.1
4.43
0.966
2.69
917
127
2.62
26
8
54
16
3.8
14.3
2.13
36
12
64
22
3.2
10.2
3.55
22.1
2.99
0.918
2.71
630
85.6
2.24
17
6
22
9
3.8
12.0
1.72
24
9
26
13
3.2
8.9
2.68
16.4
2.19
0.905
2.73
468
62.8
5.54
26.2
9.13
1.28
1.70
747
260
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.68
21.3
7.51
1.27
1.68
608
216
3.83
11.3
3.86
1.00
1.72
324
110
DESIGN STRENGTH OF COLUMNS
3 - 31
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
HP shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
HP14
Wt./ft
117
Fy
HP13
102
89
73
100
50
36
50
36
50
36
50
36
50
1050
1460
918
1280
799
1110
655
909
900
1250
6
7
8
9
10
1030
1020
1010
1000
993
1420
1400
1390
1370
1350
898
891
884
875
865
1240
1220
1210
1190
1170
781
775
768
760
752
1080
1060
1050
1040
1020
640
635
629
623
615
882
872
861
848
834
875
867
857
846
834
1200
1190
1170
1150
1120
11
12
13
14
15
980
967
953
938
922
1320
1300
1270
1250
1220
854
842
830
816
802
1150
1130
1110
1080
1060
742
732
721
709
696
1000
982
962
940
917
607
599
589
580
569
819
803
786
768
749
821
806
791
775
758
1100
1070
1050
1020
986
16
17
18
19
20
905
888
870
851
832
1190
1150
1120
1090
1050
788
772
756
740
723
1030
1000
974
945
915
683
670
656
641
626
893
869
844
818
791
558
547
535
523
511
729
708
687
666
644
741
722
703
684
664
954
921
888
854
820
22
24
26
28
30
792
750
707
664
620
985
913
842
771
701
687
650
613
574
536
853
790
727
665
604
595
563
529
496
462
737
682
627
572
519
485
458
430
402
374
599
553
507
462
418
623
581
539
496
454
750
681
613
547
483
32
34
36
38
40
576
533
491
450
411
633
568
507
455
411
498
460
423
387
352
545
487
435
390
352
428
395
363
332
301
467
417
372
334
301
346
319
292
267
241
375
334
298
267
241
413
374
336
301
272
425
376
336
301
272
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
217
29
1010
131
15.0
66.0
302
40
1191
182
12.7
45.1
174
25
679
101
14.8
59.0
242
35
801
140
12.6
41.1
202
31
533
106
12.5
37.6
108
18
250
52
14.5
46.8
150
25
294
72
12.3
34.2
198
28
953
119
13.2
60.1
275
38
1123
165
11.2
40.9
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
34.4
1220
443
3.59
1.66
35000
12700
30.0
1050
380
3.56
1.66
30100
10900
145
22
453
77
14.7
53.0
26.1
904
326
3.53
1.67
25800
9310
21.4
729
261
3.49
1.67
20900
7460
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
29.4
886
294
3.16
1.74
25400
8400
3 - 32
COLUMN DESIGN
Y
Fy = 36 ksi
Fy = 50 ksi
X
COLUMNS
HP shapes
Design axial strength in kips (φ = 0.85)
X
Y
Designation
HP13
Wt./ft
87
Fy
HP12
73
60
84
74
50
36
50
36
50
36
50
36
50
780
1080
661
918
536
744
753
1050
667
927
6
7
8
9
10
759
751
743
733
722
1040
1030
1010
993
973
642
636
628
620
611
882
870
856
840
823
520
515
509
502
494
714
704
692
679
665
729
721
712
701
690
1000
985
967
947
926
646
639
630
621
610
886
872
856
838
819
11
12
13
14
15
711
698
685
670
656
952
928
904
878
851
601
590
578
566
553
804
784
763
741
717
486
477
467
457
447
650
633
616
597
578
677
663
649
634
618
902
877
851
823
795
599
587
574
560
546
798
776
752
727
702
16
17
18
19
20
640
624
607
590
573
823
794
765
735
705
540
526
512
497
482
693
669
644
618
592
436
424
413
401
388
559
539
518
497
476
601
584
567
548
530
765
735
705
674
642
531
516
500
484
467
675
648
621
593
565
22
24
26
28
30
537
500
462
425
389
644
584
524
467
411
451
420
388
356
325
540
488
438
389
342
363
337
311
285
260
433
391
350
310
272
492
454
416
378
342
580
518
459
402
350
434
400
366
332
300
510
455
402
351
306
32
34
36
38
40
353
319
286
256
231
361
320
286
256
231
295
266
237
213
192
300
266
237
213
192
235
211
189
169
153
239
211
189
169
153
307
273
243
218
197
308
273
243
218
197
268
238
213
191
172
269
238
213
191
172
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
165
24
624
90
13.0
53.2
229
33
735
124
11.1
36.9
127
20
384
65
12.9
47.0
177
28
453
90
11.0
33.4
129
23
243
60
10.9
30.2
170
25
732
95
12.3
54.0
235
34
862
132
10.4
36.9
143
22
506
75
12.2
48.9
199
30
597
105
10.3
34.0
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
25.5
755
250
3.13
1.74
21700
7150
21.6
630
207
3.10
1.74
18000
5940
93
17
206
43
12.8
41.2
17.5
503
165
3.07
1.75
14400
4720
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
24.6
650
213
2.94
1.75
18600
6090
21.8
569
186
2.92
1.75
16300
5320
DESIGN STRENGTH OF COLUMNS
3 - 33
Y
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
HP shapes
Design axial strength in kips (φ = 0.85)
X
X
Y
Designation
HP12
Wt./ft
HP10
63
Fy
53
HP8
57
42
36
50
36
50
36
50
36
50
36
50
563
782
474
659
514
714
379
527
324
451
6
7
8
9
10
545
538
531
523
514
747
735
721
706
689
459
453
447
440
432
629
618
607
594
579
491
483
474
464
453
670
655
638
619
599
362
356
349
341
333
494
482
469
455
440
302
294
286
276
266
408
393
377
360
342
11
12
13
14
15
504
494
482
471
458
671
651
631
610
588
424
415
406
396
385
564
547
530
512
493
441
429
415
401
387
577
555
531
506
481
324
314
304
294
283
423
406
388
369
350
255
243
232
219
207
322
302
282
262
242
16
17
18
19
20
446
432
419
405
391
565
542
518
495
471
374
363
351
339
327
474
454
434
414
394
372
357
341
326
310
456
430
404
379
354
272
260
249
237
225
331
312
293
274
255
195
182
170
158
146
222
202
184
165
149
22
24
26
28
30
362
333
304
275
247
423
376
332
288
251
303
278
253
229
206
353
314
276
240
209
279
248
219
191
166
305
259
221
191
166
202
179
157
136
119
219
185
158
136
119
123
104
88
76
66
123
104
88
76
66
32
34
36
38
40
221
196
174
157
141
221
196
174
157
141
183
163
145
130
117
183
163
145
130
117
146
129
115
103
93
146
129
115
103
93
104
92
82
74
67
104
92
82
74
67
58
52
46
41
37
58
52
46
41
37
P wo (kips)
P wi (kips/in.)
P wb (kips)
P fb (kips)
L p (ft)
L r (ft)
116
19
311
54
12.0
43.0
161
26
366
75
10.2
30.7
88
16
188
38
11.9
38.7
122
22
221
53
10.1
28.3
168
28
599
90
8.7
31.1
79
15
202
36
10.0
35.9
110
21
238
50
8.5
25.6
75
16
309
40
8.1
35.7
104
22
364
56
6.9
24.4
Effective length KL (ft) with respect to least radius of gyration ry
36
0
Properties
A (in.2)
Ix (in.4)
Iy (in.4)
ry (in.)
Ratio rx / ry
Pex (KL )2 / 10 4
Pey (KL )2 / 10 4
18.4
472
153
2.88
1.76
13500
4370
15.5
393
127
2.86
1.76
11200
3630
121
20
508
65
10.2
45.6
16.8
294
101
2.45
1.71
8400
2890
12.4
210
71.7
2.41
1.71
6050
2060
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10.6
119
40.3
1.95
1.72
3420
1150
3 - 34
COLUMN DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 35
Steel Pipe and Structural Tubing
The design strengths in the tables that follow are tabulated for the effective lengths in
feet KL (with respect to the least radius of gyration, r or ry), indicated at the left of each
table. They are applicable to axially loaded members in accordance with Section E2 of
the LRFD Specification.
For discussion of effective length, range of l / r, strength about major axis, combined
axial and bending stress, and sample problems, see General Notes. Properties and factors
are listed at the bottom of the tables for checking strength about the strong axis.
Steel Pipe Columns
Design strengths for unfilled pipe columns are tabulated for Fy = 36 ksi. Steel pipe
manufactured to ASTM A501 furnishes Fy = 36 ksi, and ASTM A53, Type E or S, Gr. B
furnishes Fy = 35 ksi and may be designed for the strengths permitted for Fy = 36 ksi steel.
The heavy horizontal lines within the table indicate Kl / r = 200. No values are listed
beyond Kl / r = 200.
Structural Tube Columns
Design strengths for square and rectangular structural tube columns are tabulated for Fy
= 46 ksi. Structural tubing is manufactured to Fy = 46 ksi under ASTM A500, Gr. B.
All tubes listed in the column load tables satisfy Section B5 of the LRFD Specification.
The heavy horizontal lines appearing within the tables indicate Kl / r = 200. No values
are listed beyond Kl / r = 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 36
COLUMN DESIGN
Fy = 36 ksi
COLUMNS
Standard steel pipe
Design axial strength in kips (φ = 0.85)
Nominal Dia.
12
10
8
6
5
4
31⁄2
3
Wall Thickness
0.375
0.365
0.322
0.280
0.258
0.237
0.226
0.216
Weight per ft
49.56
40.48
28.55
18.97
14.62
10.79
9.11
7.58
Fy
Effective length KL (ft)
36 ksi
0
447
364
257
171
132
97
82
68
6
7
8
9
10
440
438
436
433
429
357
354
351
348
344
249
246
243
239
235
162
159
155
151
147
122
118
115
111
106
86
82
78
74
70
70
67
63
58
54
56
52
48
43
39
11
12
13
14
15
426
422
418
413
409
340
336
331
326
321
231
227
222
216
211
142
138
133
127
122
102
97
92
86
81
65
60
55
51
46
49
45
40
36
32
35
30
26
23
20
16
17
18
19
20
404
399
393
387
381
315
309
303
297
291
205
199
193
187
181
116
111
105
99
94
76
71
66
61
56
41
37
33
30
27
28
25
22
20
18
17
15
14
12
22
24
25
26
28
369
356
349
342
328
277
263
256
249
234
168
155
149
142
129
83
72
67
62
53
47
39
36
33
29
22
19
17
15
30
31
32
34
36
313
306
298
283
268
219
212
205
190
176
117
111
105
93
83
47
44
41
36
32
25
23
37
38
40
260
253
237
169
162
148
79
75
67
31
3.17
7.23
1.51
2.68
4.79
1.34
Properties
2
Area A (in. )
I (in.4)
r (in.)
14.6
279
4.38
11.9
161
3.67
8.40
72.5
2.94
5.58
28.1
2.25
4.30
15.2
1.88
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.23
3.02
1.16
DESIGN STRENGTH OF COLUMNS
3 - 37
Fy = 36 ksi
COLUMNS
Extra strong steel pipe
Design axial strength in kips (φ = 0.85)
Nominal Dia.
12
10
8
6
5
4
31⁄2
3
Wall Thickness
0.500
0.500
0.500
0.432
0.375
0.337
0.318
0.300
Weight per ft
65.42
54.74
43.39
28.57
20.78
14.98
12.50
10.25
Effective length KL (ft)
Fy
36 ksi
0
588
493
392
257
187
135
113
92
6
7
8
9
10
579
576
573
569
564
483
479
475
470
465
379
375
369
364
357
243
238
232
226
219
172
168
162
156
149
119
114
108
102
95
96
91
85
79
72
75
69
64
58
52
11
12
13
14
15
559
554
549
543
536
460
453
447
440
433
351
343
336
327
319
212
205
197
189
180
143
135
128
121
113
89
82
75
68
62
66
60
53
47
42
46
40
34
30
26
16
18
19
20
21
530
515
508
500
492
425
409
400
391
382
310
291
282
272
262
172
154
145
137
128
105
91
83
76
70
56
44
40
36
32
37
29
26
23
21
23
18
16
22
24
26
28
30
483
465
447
428
408
373
354
334
314
294
252
231
211
191
172
120
103
88
76
66
63
53
45
39
34
30
25
32
34
36
38
40
388
368
348
328
308
273
253
234
215
196
154
136
121
109
98
58
52
46
19.2
362
4.33
16.1
212
3.63
12.8
106
2.88
6.11
20.7
1.84
4.41
9.61
1.48
3.68
6.28
1.31
3.02
3.89
1.14
Properties
Area A (in.2)
I (in.4)
r (in.)
8.40
40.5
2.19
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 38
COLUMN DESIGN
Fy = 36 ksi
COLUMNS
Double-extra strong steel pipe
Design axial strength in kips (φ = 0.85)
Nominal Dia.
8
6
5
4
3
Wall Thickness
0.875
0.864
0.750
0.674
0.600
Weight per ft
72.42
53.16
38.55
27.54
18.58
Effective length KL (ft)
Fy
36 ksi
0
652
477
346
248
167
6
7
8
9
10
629
621
612
601
590
448
437
426
413
399
315
305
293
281
268
214
203
191
179
165
131
120
108
96
84
11
12
13
14
15
578
565
551
536
521
385
369
353
336
319
254
239
224
209
194
152
139
125
112
100
73
62
53
46
40
16
17
18
19
20
505
489
472
455
438
302
285
268
250
234
179
165
151
137
124
88
78
70
62
56
35
31
22
24
26
28
30
403
367
333
299
266
201
170
145
125
109
102
86
73
63
47
32
34
36
38
40
235
208
186
166
150
96
85
21.3
162
2.76
15.6
66.3
2.06
11.3
33.6
1.72
8.10
15.3
1.37
Properties
Area A (in.2)
I (in.4)
r (in.)
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.47
5.99
1.05
DESIGN STRENGTH OF COLUMNS
3 - 39
Fy = 46 ksi
COLUMNS
Square structural tubing
Design axial strength in kips (φ = 0.85)
Nominal Size
16×
×16
Thickness
1⁄
Wt./ft
103.30
89.68
68.31
0
1190
1030
786
6
7
8
9
10
1180
1170
1170
1170
1160
1020
1020
1010
1010
1000
11
12
13
14
15
1150
1150
1140
1130
1120
16
17
18
19
20
2
14×
×14
1⁄
2
12×
×12
3⁄
8
8
93.34
1⁄
2
3⁄
8
5⁄
16
76.07
58.10
48.86
1070
876
669
563
777
774
770
766
761
1050
1050
1040
1030
1020
862
857
851
845
838
658
655
650
645
640
554
551
548
544
539
993
985
977
969
960
756
751
745
739
732
1010
1000
992
979
966
830
821
812
803
792
634
628
621
614
606
535
529
524
518
511
1120
1110
1100
1090
1080
950
940
930
919
907
725
717
710
701
693
953
939
924
908
892
781
770
758
746
733
598
590
581
571
562
504
497
490
482
474
21
22
23
24
25
1070
1060
1040
1030
1020
895
883
870
857
844
684
675
665
655
645
875
858
841
823
805
719
706
692
677
663
552
542
531
520
510
466
457
449
440
431
26
27
28
29
30
1010
994
981
967
954
830
816
802
787
772
635
624
614
603
592
786
767
748
729
710
648
633
617
602
586
498
487
475
464
452
421
412
402
392
383
32
34
36
38
40
925
896
865
835
803
742
711
680
648
616
569
546
522
498
474
670
631
592
553
515
555
523
491
460
429
428
404
381
357
333
363
343
323
303
283
30.4
1200
6.29
26.4
791
5.48
27.4
580
4.60
22.4
485
4.66
17.1
380
4.72
14.4
324
4.75
Fy
Effective length KL (ft)
5⁄
46 ksi
Properties
A (in2)
I (in.4)
r (in.)
20.1
615
5.54
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 40
COLUMN DESIGN
Fy = 46 ksi
COLUMNS
Square structural tubing
Design axial strength in kips (φ = 0.85)
10×
×10
Nominal Size
Thickness
Wt./ft
76.33
62.46
47.90
40.35
32.63
0
876
719
551
465
375
6
7
8
9
10
855
847
839
829
818
703
697
690
682
674
539
534
529
524
517
455
451
447
442
437
11
12
13
14
15
807
794
781
767
752
664
655
644
633
621
510
503
495
487
478
16
17
18
19
20
736
720
703
686
668
608
595
582
568
553
21
22
23
24
25
650
631
612
593
573
26
27
28
29
30
32
34
36
38
40
8
1⁄
2
3⁄
8×
×8
5⁄
8
5⁄
16
4
5⁄
8
59.32
1⁄
2
3⁄
8
5⁄
16
1⁄
4
48.85
37.69
31.84
25.82
680
563
434
366
297
367
364
360
357
353
654
644
634
622
609
542
535
526
517
507
418
413
407
400
392
353
349
343
338
331
287
283
279
274
269
431
425
418
411
404
348
343
338
332
326
595
580
564
548
531
496
484
471
458
444
384
375
366
356
345
324
317
309
301
293
264
258
252
245
238
468
459
449
438
427
396
388
380
371
362
320
314
307
300
293
513
494
476
456
437
430
415
400
385
369
335
324
312
301
289
284
275
265
256
246
231
224
216
209
201
538
523
508
493
477
416
405
394
382
370
353
343
334
324
314
286
278
270
263
255
418
398
379
360
341
354
338
322
307
291
277
266
254
242
230
236
226
216
206
196
193
185
177
169
161
554
534
515
495
476
461
446
430
414
398
358
347
335
323
311
305
295
285
275
265
247
239
231
223
215
322
304
286
268
251
276
261
246
232
218
219
207
196
185
174
187
177
168
158
149
153
146
138
131
123
437
400
364
328
296
367
337
307
278
251
287
264
242
220
199
245
225
206
188
170
199
184
168
154
139
221
195
174
156
141
191
169
151
136
122
153
136
121
109
98
132
117
104
93
84
109
97
86
77
70
22.4
321
3.78
18.4
271
3.84
14.1
214
3.90
11.9
183
3.93
17.4
153
2.96
14.4
131
3.03
11.1
106
3.09
9.36
90.9
3.12
7.59
75.1
3.15
Fy
Effective length KL (ft)
1⁄
46 ksi
Properties
A (in2)
I (in.4)
r (in.)
9.59
151
3.96
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 41
Fy = 46 ksi
COLUMNS
Square structural tubing
Design axial strength in kips (φ = 0.85)
7×
×7
Nominal Size
Thickness
5⁄
8
1⁄
2
3⁄
8
6×
×6
5⁄
16
1⁄
4
3⁄
16
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
50.81 42.05 32.58 27.59 22.42 17.08 42.30 35.24 27.48 23.34 19.02 14.53
Fy
46 ksi
Effective length KL (ft)
Wt./ft
0
584
485
375
317
258
196
486
407
316
268
219
167
6
7
8
9
10
553
543
531
518
503
461
452
443
432
421
357
351
344
336
327
302
297
291
285
278
246
242
237
232
226
188
185
181
177
173
451
438
425
410
394
379
369
358
346
333
295
288
280
271
262
251
245
239
231
223
205
200
195
189
183
157
153
149
145
140
11
12
13
14
15
488
472
454
437
418
409
396
382
368
353
318
308
298
288
277
270
262
254
245
236
220
214
207
200
193
168
164
159
153
148
377
359
341
322
303
320
306
291
276
260
252
241
230
219
207
215
206
197
187
178
176
169
162
154
146
135
130
124
119
113
16
17
18
19
20
399
380
361
342
323
338
322
307
291
276
265
254
242
230
218
226
217
207
197
187
185
177
170
162
154
142
136
130
124
118
284
265
246
227
210
245
229
214
199
184
195
184
172
160
149
168
158
148
138
129
138
131
123
115
107
107
101
95
89
83
22
24
26
28
30
285
248
214
184
161
245
215
187
161
140
195
172
151
130
113
167
148
130
113
98
138
123
108
94
81
107
95
84
73
63
175
147
125
108
94
155
131
111
96
84
127
107
91
79
69
111
93
80
69
60
92
78
67
57
50
72
61
52
45
39
32
34
141
125
123
109
100
88
86
76
72
63
56
49
83
73
73
65
60
53
53
47
44
39
34
30
35
36
37
38
39
118
111
106
100
95
103
97
92
87
83
83
79
74
71
67
72
68
64
61
58
60
57
54
51
48
47
44
42
40
38
69
61
58
50
48
45
44
41
39
37
37
35
33
31
29
27
26
24
23
40
90
79
64
55
46
36
12.4
57.3
2.15
10.4
50.5
2.21
8.08
41.6
2.27
6.86
36.3
2.30
5.59
30.3
2.33
4.27
23.8
2.36
Properties
2
A (in )
I (in.4)
r (in.)
14.9
97.5
2.56
12.4
84.6
2.62
9.58
68.7
2.68
8.11
59.5
2.71
6.59
49.4
2.74
5.02
38.5
2.77
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 42
COLUMN DESIGN
Fy = 46 ksi
COLUMNS
Square structural tubing
Design axial strength in kips (φ = 0.85)
51⁄2×51⁄2
Nominal Size
5×
×5
Thickness
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
Wt./ft
24.93
21.21
17.32
13.25
28.43
22.37
19.08
15.62
11.97
8.16
Effective length KL (ft)
Fy
46 ksi
0
286
244
199
152
327
257
219
179
138
94
6
7
8
9
10
264
256
248
238
228
225
219
212
204
195
184
179
173
167
161
141
137
133
129
124
294
282
270
257
242
233
224
215
205
194
199
192
184
176
167
163
158
152
145
138
126
121
117
112
107
86
83
80
77
73
11
12
13
14
15
218
207
195
184
172
187
177
168
158
148
154
146
139
131
123
118
113
107
101
95
228
213
197
182
167
183
172
160
149
137
158
148
139
129
119
131
123
115
107
99
101
95
89
84
78
70
66
62
58
54
16
17
18
19
20
160
149
137
126
115
139
129
119
110
101
115
107
99
92
84
89
83
77
72
66
152
138
124
111
100
126
115
104
93
84
110
100
91
82
74
92
84
77
69
63
72
66
60
55
50
50
46
42
38
35
22
24
26
28
30
96
80
68
59
51
84
70
60
52
45
70
59
50
43
38
55
47
40
34
30
83
70
59
51
45
70
59
50
43
37
61
52
44
38
33
52
44
37
32
28
41
34
29
25
22
29
24
21
18
15
31
32
33
34
35
48
45
43
40
42
40
37
35
35
33
31
29
28
28
26
25
23
22
35
31
26
24
21
19
15
14
13
6.58
22.8
1.86
5.61
20.1
1.89
4.59
16.9
1.92
3.52
13.4
1.95
2.40
9.41
1.98
Properties
2
A (in )
I (in.4)
r (in.)
7.33
31.2
2.07
6.23
27.4
2.10
5.09
23.0
2.13
3.89
18.1
2.16
8.36
27.0
1.80
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 43
Fy = 46 ksi
COLUMNS
Square structural tubing
Design axial strength in kips (φ = 0.85)
41⁄2×41⁄2
Nominal Size
4×
×4
Thickness
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
Wt./ft
19.82
16.96
13.91
10.70
7.31
Effective length KL (ft)
Fy
1⁄
2
3⁄
8
21.63
17.27
5⁄
16
1⁄
4
14.83 12.21
3⁄
16
1⁄
8
9.42
6.46
46 ksi
0
228
195
160
123
84
249
199
170
140
108
74
6
7
8
9
10
201
192
182
171
160
172
165
157
148
139
142
136
130
123
115
110
105
100
95
90
75
72
69
65
62
208
195
180
166
151
168
158
148
137
125
145
137
128
119
110
120
114
107
100
92
93
89
83
78
72
64
61
58
54
50
11
12
13
14
15
149
137
125
114
103
129
119
110
100
91
107
100
92
84
76
84
78
72
66
60
58
54
50
46
42
136
121
107
93
81
114
102
91
81
70
100
90
81
72
63
84
76
68
61
54
66
60
54
49
43
46
42
38
34
31
16
17
18
19
20
92
82
73
66
59
81
73
65
58
53
69
62
55
49
45
55
49
44
39
36
38
35
31
28
25
71
63
56
50
46
62
55
49
44
40
55
49
44
39
35
47
42
37
34
30
38
34
30
27
24
27
24
21
19
17
21
22
23
24
25
54
49
45
41
38
48
43
40
36
34
41
37
34
31
29
32
29
27
25
23
23
21
19
17
16
41
38
34
36
33
30
27
32
29
27
25
28
25
23
21
19
22
20
18
17
16
16
14
13
12
11
26
35
31
26
21
15
27
28
29
32
29
27
25
23
20
18
17
14
13
12
10
Properties
2
A (in )
I (in.4)
r (in.)
5.83
16.0
1.66
4.98
14.2
1.69
4.09
12.1
1.72
3.14
9.60
1.75
2.15
6.78
1.78
6.36
12.3
1.39
5.08
10.7
1.45
4.36
9.58
1.48
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.59
8.22
1.51
2.77
6.59
1.54
1.90
4.70
1.57
3 - 44
COLUMN DESIGN
Fy = 46 ksi
COLUMNS
Square structural tubing
Design axial strength in kips (φ = 0.85)
31⁄2×31⁄2
Nominal Size
3×
×3
Thickness
5⁄
16
1⁄
4
3⁄
16
1⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
Wt./ft
12.7
10.51
8.15
5.61
10.58
8.81
6.87
4.75
0
146
121
93
65
122
101
79
55
6
7
8
9
10
118
109
100
90
81
99
92
84
76
69
77
72
66
60
54
54
50
46
42
39
90
80
71
61
52
76
68
61
53
45
60
54
49
43
37
42
39
35
31
27
11
12
13
14
15
71
62
54
46
40
61
54
46
40
35
49
43
38
32
28
35
31
27
23
20
44
37
31
27
23
38
32
27
24
21
32
27
23
19
17
23
20
17
14
12
16
17
18
19
20
35
31
28
25
23
31
27
24
22
20
25
22
20
18
16
18
16
14
13
11
21
18
18
16
14
15
13
12
11
10
9
8
21
22
21
18
14
13
10
9
3.73
6.09
1.28
3.09
5.29
1.31
2.39
4.29
1.34
3.11
3.58
1.07
2.59
3.16
1.10
2.02
2.60
1.13
1.40
1.90
1.16
Effective length KL (ft)
Fy
46 ksi
Properties
A (in2)
I (in.4)
r (in.)
1.65
3.09
1.37
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 45
Fy = 46 ksi
Y
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
X
X
Y
Nominal Size 16×
×12
16×
×8
14×
×12
14×
×10
Thickness
1⁄
1⁄
1⁄
Wt./ft
89.68
76.07
82.88
63.21
76.07
0
1030
876
952
726
876
6
7
8
9
10
1020
1010
1010
998
990
848
838
827
815
801
938
933
927
920
912
715
712
707
702
697
11
12
13
14
15
982
973
963
952
941
786
771
754
736
717
904
895
886
876
865
16
17
18
19
20
929
916
903
889
875
697
677
657
635
614
22
24
26
28
30
845
813
781
746
711
32
34
36
38
40
676
640
604
568
533
2
2
2
3⁄
8
2
12×
×10
3⁄
8
58.10
1⁄
2
3⁄
8
5⁄
16
1⁄
4
69.27
53.00
44.60
36.03
669
796
609
513
414
857
850
843
834
825
655
650
644
638
631
778
772
765
757
748
596
591
586
580
573
502
498
493
488
483
405
402
399
395
390
691
684
677
669
661
815
803
791
779
765
623
615
606
597
587
738
728
716
704
692
566
558
550
541
531
477
470
463
456
448
386
380
375
369
363
854
842
829
816
803
653
644
634
625
615
751
737
721
705
689
576
565
554
542
530
679
665
650
636
620
522
511
501
489
478
440
431
422
413
404
356
349
342
335
327
569
525
480
436
393
774
744
713
681
648
593
571
548
524
499
655
620
584
547
511
504
478
451
424
396
589
556
522
488
454
454
430
404
379
353
384
363
342
321
300
311
295
278
261
244
352
313
279
250
226
615
581
547
514
480
474
448
423
398
372
474
438
403
369
335
368
341
315
289
264
420
387
355
324
293
328
302
278
254
231
278
257
237
217
197
227
210
193
177
162
17.1
476
284
1.29
4.08
20.4
419
316
1.15
3.94
15.6
330
249
1.15
4.00
13.1
281
213
1.15
4.03
10.6
230
174
1.15
4.06
Fy
Effective length KL (ft) with respect to least radius of gyration
1⁄
46 ksi
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
26.4
962
618
1.25
4.84
22.4
722
244
1.72
3.30
24.4
699
552
1.13
4.76
18.6
546
431
1.13
4.82
22.4
608
361
1.30
4.02
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 46
COLUMN DESIGN
Fy = 46 ksi
Y
X
X
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
Y
12×
×8
Nominal Size
12×
×6
Thickness
5⁄
8
1⁄
2
3⁄
8
5⁄
16
5⁄
8
1⁄
2
3⁄
8
5⁄
16
Wt./ft
76.33
62.46
47.90
40.35
67.82
55.66
42.79
36.10
0
876
719
551
465
778
641
493
414
6
7
8
9
10
845
835
822
809
794
695
687
677
666
655
534
527
520
512
503
450
445
439
433
425
731
715
697
677
655
604
591
577
561
543
466
456
445
434
421
392
384
376
366
355
11
12
13
14
15
778
760
742
722
702
642
628
613
598
582
494
483
473
461
449
417
409
400
390
380
632
607
581
555
528
525
505
485
464
442
407
393
378
362
346
344
332
320
307
293
16
17
18
19
20
681
659
637
614
591
565
547
530
511
493
437
424
410
397
383
370
359
348
336
325
500
473
445
418
390
420
398
375
353
331
329
313
296
279
262
280
266
252
238
224
22
24
26
28
30
544
497
451
405
362
455
417
380
343
307
355
326
298
270
243
301
277
253
230
207
338
288
245
211
184
288
247
211
182
158
230
199
170
146
128
197
171
146
126
110
32
34
36
38
39
320
283
252
227
215
273
241
215
193
184
217
192
171
154
146
185
164
146
131
125
162
143
128
115
109
139
123
110
99
94
112
99
89
80
75
97
86
76
69
65
40
205
174
139
119
89
72
62
16.4
287
96.0
1.73
2.42
12.6
228
77.2
1.72
2.48
10.6
196
66.6
1.71
2.51
Effective length KL (ft) with respect to least radius of gyration
Fy
46 ksi
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
22.4
418
221
1.38
3.14
18.4
353
188
1.37
3.20
14.1
279
149
1.37
3.26
11.9
239
128
1.37
3.28
19.9
337
112
1.73
2.37
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 47
Fy = 46 ksi
Y
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
X
X
Y
10×
×8
Nominal Size
10×
×6
Thickness
1⁄
2
3⁄
8
5⁄
16
1⁄
4
1⁄
2
3⁄
8
5⁄
16
1⁄
4
Wt./ft
55.66
42.79
36.10
29.23
48.85
37.69
31.84
25.82
0
641
493
414
336
563
434
366
297
6
7
8
9
10
619
611
602
592
581
476
470
463
456
448
401
396
390
384
377
325
321
317
312
306
529
517
504
490
474
409
400
391
380
368
345
338
330
321
312
281
275
269
261
254
11
12
13
14
15
568
556
542
528
513
439
429
419
408
397
370
362
354
345
335
300
294
287
280
273
457
439
421
402
382
356
343
329
315
300
302
291
279
267
255
246
237
228
218
209
16
17
18
19
20
497
481
465
448
431
386
374
361
349
336
326
316
306
295
285
265
257
249
241
232
362
342
322
302
282
285
270
255
240
225
243
230
218
205
193
199
189
179
169
159
22
24
26
28
30
396
361
327
294
262
310
284
258
232
208
263
241
220
198
178
215
197
180
163
146
244
208
177
153
133
196
169
144
124
108
169
146
124
107
93
139
121
103
89
77
32
34
36
38
39
231
205
183
164
156
184
163
146
131
124
158
140
125
112
106
130
116
103
93
88
117
104
92
83
79
95
84
75
67
64
82
73
65
58
55
68
60
54
48
46
40
148
118
101
84
61
52
44
11.1
145
65.4
1.49
2.43
9.36
125
56.5
1.48
2.46
7.59
103
46.9
1.48
2.49
Effective length KL (ft) with respect to least radius of gyration
Fy
46 ksi
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
16.4
226
160
1.19
3.12
12.6
180
127
1.19
3.18
10.6
154
109
1.19
3.21
8.59
127
90.2
1.19
3.24
14.4
181
80.8
1.50
2.37
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 48
COLUMN DESIGN
Fy = 46 ksi
Y
X
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
X
Y
10×
×5
Nominal Size
8×
×6
Thickness
3⁄
8
5⁄
16
1⁄
4
1⁄
2
3⁄
8
5⁄
16
1⁄
4
Wt./ft
35.13
29.72
24.12
42.05
32.58
27.59
22.42
0
403
341
277
485
375
317
258
6
7
8
9
10
370
359
347
334
319
315
306
295
284
272
256
249
241
232
222
454
444
432
419
404
352
344
335
325
315
298
292
284
276
268
243
238
232
225
218
11
12
13
14
15
304
288
272
255
239
260
246
233
219
205
212
201
191
179
168
389
373
357
340
322
303
292
279
266
253
258
248
238
227
217
211
203
195
186
178
16
17
18
19
20
222
206
189
174
159
191
178
164
151
138
157
146
135
124
114
305
287
269
252
235
240
227
213
200
187
205
194
183
172
161
169
160
151
142
133
22
24
26
28
30
131
110
94
81
71
115
96
82
71
62
95
80
68
59
51
201
170
145
125
109
161
137
117
101
88
140
119
102
88
76
116
99
85
73
64
32
34
36
38
39
62
55
54
48
45
40
96
85
76
68
77
68
61
55
52
67
59
53
48
45
56
49
44
40
38
Effective length KL (ft) with respect to least radius of gyration
Fy
46 ksi
36
40
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
10.3
128
42.9
1.72
2.04
8.73
110
37.2
1.71
2.07
7.09
91.2
31.1
1.72
2.09
12.4
103
65.7
1.25
2.31
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9.58
83.7
53.5
1.25
2.36
8.11
72.4
46.4
1.25
2.39
6.59
60.1
38.6
1.25
2.42
DESIGN STRENGTH OF COLUMNS
3 - 49
Fy = 46 ksi
Y
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
X
X
Y
8×
×4
Nominal Size
7×
×5
Thickness
5⁄
8
1⁄
2
3⁄
8
5⁄
16
1⁄
4
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
Wt./ft
42.30
35.24
27.48
23.34
19.02
35.24
27.48
23.34
19.02
14.53
0
486
407
316
268
219
407
316
268
219
167
6
7
8
9
10
415
393
368
341
314
351
333
313
292
270
276
262
248
233
216
235
224
212
199
185
192
184
174
164
153
369
357
342
327
311
288
279
268
257
245
245
238
229
220
210
200
194
187
180
172
154
149
144
138
132
11
12
13
14
15
287
259
233
207
182
248
226
204
183
162
200
183
167
150
135
172
158
144
130
117
142
131
120
109
98
294
276
258
240
222
232
219
205
192
178
199
188
177
165
154
164
155
146
137
127
126
119
113
106
99
16
17
18
19
20
160
141
126
113
102
143
126
113
101
91
120
106
95
85
77
104
92
82
74
67
88
78
70
62
56
205
187
170
154
139
165
151
138
126
114
142
131
120
110
100
118
109
101
92
84
92
85
79
72
66
22
24
25
26
27
84
71
76
63
58
63
53
49
45
55
46
43
39
37
47
39
36
33
31
115
97
89
82
76
94
79
73
67
62
82
69
64
59
55
69
58
54
50
46
54
46
42
39
36
71
66
62
58
58
54
51
47
44
51
47
44
41
39
43
40
37
35
33
34
31
29
27
26
37
31
24
23
6.86
45.5
26.9
1.30
1.98
5.59
38.0
22.6
1.30
2.01
4.27
29.8
17.7
1.29
2.04
Effective length KL (ft) with respect to least radius of gyration
Fy
46 ksi
28
29
30
31
32
33
34
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
12.4
85.1
27.4
1.76
1.49
10.4
75.1
24.6
1.75
1.54
8.08
61.9
20.6
1.73
1.60
6.86
53.9
18.1
1.73
1.62
5.59
45.1
15.3
1.72
1.65
10.40
63.5
37.2
1.31
1.90
8.08
52.2
30.8
1.30
1.95
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 50
COLUMN DESIGN
Fy = 46 ksi
Y
X
X
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
Y
7×
×4
Nominal Size
6×
×4
Thickness
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
Wt./ft
24.93
21.21
17.32
13.25
28.43
22.37
19.08
15.62
11.97
0
287
244
199
152
327
257
219
179
138
6
7
8
9
10
249
236
223
208
193
213
202
191
179
167
175
166
158
148
138
134
128
121
114
107
279
263
246
228
210
222
211
198
185
171
190
181
171
160
148
157
149
141
132
123
121
115
109
102
96
11
12
13
14
15
178
163
148
133
118
154
141
129
116
104
128
118
107
97
88
99
92
84
76
69
191
173
155
137
121
157
143
129
116
103
136
125
113
102
91
114
104
95
85
77
89
81
74
67
61
16
17
18
19
20
105
93
83
74
67
92
82
73
65
59
78
69
62
56
50
62
55
49
44
40
106
94
84
75
68
90
80
71
64
58
80
71
63
57
51
68
60
54
48
44
54
48
43
38
35
21
22
23
24
25
61
55
51
46
43
54
49
45
41
38
45
41
38
35
32
36
33
30
28
25
62
56
51
47
52
48
44
40
37
46
42
39
36
33
39
36
33
30
28
31
29
26
24
22
26
27
40
35
30
27
23
22
30
26
20
19
5.61
26.2
13.8
1.38
1.57
4.59
22.1
11.7
1.37
1.60
3.52
17.4
9.32
1.37
1.63
Effective length KL (ft) with respect to least radius of gyration
Fy
46 ksi
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
7.33
44.0
18.1
1.56
1.57
6.23
38.5
16.0
1.56
1.60
5.09
32.3
13.5
1.55
1.63
3.89
25.4
10.7
1.54
1.66
8.36
35.3
18.4
1.39
1.48
6.58
29.7
15.6
1.38
1.54
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 51
Fy = 46 ksi
Y
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
X
X
Y
6×
×3
Nominal Size
5×
×4
Thickness
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
3⁄
8
5⁄
16
1⁄
4
3⁄
16
Wt./ft
25.03
19.82
16.96
13.91
10.70
19.82
16.96
13.91
10.70
0
288
228
195
160
123
228
195
160
123
6
7
8
9
10
216
194
172
150
129
176
160
144
127
111
152
138
125
111
97
126
116
105
94
83
98
90
82
74
65
195
185
173
161
148
168
159
149
139
129
139
132
124
116
107
107
102
96
90
84
11
12
13
14
15
109
92
78
67
59
95
81
69
59
52
84
71
61
52
46
72
62
53
45
39
57
50
42
36
32
135
123
110
98
86
118
107
97
87
77
99
90
82
73
65
77
71
64
58
52
16
17
18
19
20
52
46
41
45
40
36
32
40
36
32
28
35
31
27
25
22
28
25
22
20
18
76
67
60
54
49
67
60
53
48
43
58
51
46
41
37
46
41
36
33
29
44
40
37
34
31
39
36
33
30
28
33
30
28
26
24
27
24
22
20
19
22
17
4.09
14.1
9.98
1.19
1.56
3.14
11.2
7.96
1.19
1.59
Effective length KL (ft) with respect to least radius of gyration
Fy
46 ksi
21
22
23
24
25
26
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
7.36
27.7
8.91
1.76
1.10
5.83
23.8
7.78
1.74
1.16
4.98
21.1
6.98
1.75
1.18
4.09
17.9
6.00
1.73
1.21
3.14
14.3
4.83
1.72
1.24
5.83
18.7
13.2
1.19
1.50
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.98
16.6
11.7
1.20
1.53
3 - 52
COLUMN DESIGN
Fy = 46 ksi
Y
X
X
COLUMNS
Rectangular structural tubing
Design axial strength in kips (φ = 0.85)
Y
5×
×3
Nominal Size
4×
×3
Thickness
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
Wt./ft
21.63
17.27
14.83
12.21
9.42
6.46
12.70
10.51
8.15
5.61
0
249
199
170
140
108
74
146
121
93
64
6
7
8
9
10
183
164
145
125
107
151
137
122
107
93
132
120
108
95
83
110
100
91
81
71
85
78
71
63
56
59
55
50
45
40
110
100
89
78
67
93
84
76
67
58
73
66
60
53
47
51
47
42
38
33
11
12
13
14
15
89
75
64
55
48
79
67
57
49
43
71
60
51
44
39
61
52
45
38
33
49
42
36
31
27
35
30
26
22
19
57
48
41
35
31
50
42
36
31
27
40
34
29
25
22
29
25
21
18
16
16
17
18
19
20
42
37
38
33
30
34
30
27
24
29
26
23
21
23
21
19
17
15
17
15
13
12
11
27
24
21
24
21
19
17
19
17
15
14
14
12
11
10
9
1.90
6.44
2.93
1.48
1.24
3.73
7.45
4.71
1.26
1.12
3.09
6.45
4.10
1.26
1.15
2.39
5.23
3.34
1.25
1.18
1.65
3.76
2.41
1.25
1.21
Effective length KL (ft) with respect to least radius of gyration
Fy
46 ksi
Properties
2
A (in )
Ix (in.4)
Iy (in.4)
rx / ry
ry (in.)
6.36
16.9
7.33
1.52
1.07
5.08
14.7
6.48
1.50
1.13
4.36
13.2
5.85
1.50
1.16
3.59
11.3
5.05
1.49
1.19
2.77
9.06
4.08
1.50
1.21
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 53
Double Angles and WT Shapes
Double Angles
Design strengths are tabulated for the effective length KL in feet with respect to both the
X-X and Y-Y axes. Design strengths about the X-X axis are in accordance with LRFD
Specification Section E2. For buckling about the Y-Y axis the shear deformation of the
connectors may require the slenderness to be increased in accordance with the equations
for (Kl / r)m in Section E4. Incorporating this slenderness ratio, the design strengths are
determined from Section E2 or E3, whichever governs. In addition to the usual limit state
of flexural buckling for columns, double angle and WT shapes in compression may also
be governed by the limit state of flexural-torsional buckling, in accordance with Section
E3 of the LRFD Specification. This has been included in the tables. Discussion under
Section C2 of the LRFD Specification Commentary points out that for trusses it is usual
practice to take K = 1.0. No values are listed beyond KL / r = 200.
For buckling about the X-X axis, both angles move parallel so that the design strength
is not affected by the connectors. For buckling about the Y-Y axis, the design strengths
are tabulated for the indicated number n of intermediate connectors. For connectors with
snug-tight bolts or different spacings, the design strength must be recalculated using the
corresponding modified slenderness and LRFD Specification Section E4. The number of
intermediate connectors given in the table was selected so the design strength about the
Y-Y axis is 90 percent or greater of that for buckling of the two angles acting as a unit.
If fewer connectors are used, the strength must be reduced accordingly. According to
Section E4 of the LRFD Specification, the connectors must be spaced so that the
slenderness ratio a / rz of the individual angle does not exceed 75 percent of the governing
slenderness ratio of the built-up member.
In designing members fabricated of two angles connected to opposite faces of a gusset
plate, Chapter J of the LRFD Specification states that eccentricity between the gage lines
and gravity axis may be neglected. In the following tables, this eccentricity is neglected.
The tabulated loads for double angles referred to in the Y-Y axis assume a 3⁄8-in. spacing
between angles. These values are conservative when a wider spacing is provided.
Example 3-5 illustrates a method for determining the design strength when a 3⁄4-in. gusset
plate is used.
Examples 3-6 and 3-7 demonstrate how to determine the number of connectors when
Klx / rx governs and when the modified (Kly / ry)m governs.
EXAMPLE 3-5
Given:
Solution:
Using 50 ksi steel, determine the design strength with respect to the
Y-Y axis of a double angle member of 8×8×1 angles with an effective
length equal to 12 ft, and connected to a 3⁄4-in. thick gusset plate.
ry = 3.53 in. (from Double Angle Column Design Strength Table
for two L8×8×1 with 3⁄8-in. plate)
ry′ = 3.67 in. (from Part 1, Properties, Two Equal-Leg Angles, two
L8×8×1 with 3⁄4-in. plate)
ry 3.53
=
= 0.962
ry′ 3.67
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 54
COLUMN DESIGN
Equivalent effective length = 0.962 × 12 ft = 11.5 ft
Enter Column Design Strength Table for two L8×8×1 with reference
to Y-Y axis for effective lengths between 10 and 15 feet, read 1,120
and 1,000 kips, respectively.

Equivalent design strength = 1,120 − (1,120 − 1,000) ×

11.5 − 10 
15 − 10 
= 1,084 kips
EXAMPLE 3-6
Given:
Solution:
Using a double angle member of 5×3×1⁄2 angles (short legs back to
back) and 36 ksi steel, with Lx = 10 ft and Ly = 20 ft, and a factored
axial load of 70 kips, determine the number of connectors required.
Assume K = 1.0 and that the intermediate connectors are snug-tight
bolted.
Kx Lx = 10 ft, Kx lx / rx = (10 × 12) / 0.829 = 145
Ky Ly = 20 ft, Ky ly / ry = (20 × 12) / 2.5 = 96
The X-X axis governs. From the X-X axis portion of the table
φPn = 76 kips > 70 kips o.k.
Find number of connectors required based on Section E4:
a / rz ≤ 0.75KLx / rx
a
≤ 0.75(KLx / rx)rz = 0.75 (145) 0.648 = 70 in.
Assume two connectors are required; a = (10 × 12) / 3 = 40 in.
a / rz = 40 / rz = 40.0 / 0.648 = 61.7
Check that modified (Ky ly / ry)m does not govern.
According to Specification Equation E4-1,

962 + 61.7
 2 = 114
(Ky ly / ry)m = √
Modified ly′ = 114ry / Ky = 114 (2.50 in.) / 1.0 = 285 in. = 23.8 ft
Inspection of the tables indicates that Kxlx / rx still governs, therefore
one connector is required every 40 inches.
EXAMPLE 3-7
Given:
Using the same steel shape and bolts as Example 3-6, with Lx = 10 ft
and Ly = 30 ft, determine the number of connectors required and the
corresponding maximum design strength. Assume K = 1.0.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
Solution:
3 - 55
Kx Lx = 10 ft, Kx lx / rx = (10 × 12) / 0.829 = 145
Ky Ly = 30 ft, Ky ly / ry = (30 × 12) / 2.5 = 144
Kx lx / rx appears to govern, so try one connector in the 10-ft length.
Check (Ky ly / ry)m with a / rz = 5 × 12 / 0.648 = 93

1442 + 932 = 171
(Ky ly / ry)m = √
Since (Ky ly / ry)m governs, the Y-Y portion of the table gives a design
strength of 72 kips provided four connectors are used in the 30-ft length.
This gives a spacing of 30 ft / 5 = 6.0 ft. Check if (Kyly / ry)m governs with
= (6.0 × 12) / 0.648 = 111
a / rz

1442 + 111 2 = 182
(Kyly / ry)m = √
(Ky ly / ry)m still governs, so four connectors at 6.0 ft would be
appropriate.
Verify that a / rz < 0.75 governing Kl / r :
111 < (0.75 × 182 = 137) o.k.
Modified ly′ = 182ry / Ky = 182(2.5 in.) / 1.0 = 455 in. = 37.9 ft
From the tables, the design strength is 45 kips.
The design strength can be increased by closer spacing of the connectors, which reduces (Kyly / ry)m .
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 56
COLUMN DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 57
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Equal legs
8
in. back to back of angles
3/ ′′
8
8×
×8
Size
11⁄8
Thickness
Wt./ft
36
7⁄
8
1
113.8
Fy
X-X AXIS
Y
102.0
50
3⁄
4
90.0
5⁄
8
77.8
1⁄
2
65.4
52.8
36
50
36
50
36
50
36
50
36
50
0
1030 1420
918
1280
811
1130
701
973
586
763
432
550
10
14
18
22
26
901 1190
795 1000
674 795
548 596
427 430
808
715
608
496
388
1070
902
719
542
391
715
633
539
440
345
945
799
638
482
349
619
549
469
384
303
819
694
556
422
306
518
461
395
325
257
651
559
456
354
261
387
348
302
253
205
478
417
349
278
212
30
34
38
39
40
323
251
201
191
182
323
251
201
191
182
294
229
183
174
165
294
229
183
174
165
262
204
163
155
147
262
204
163
155
147
230
179
143
136
129
230
179
143
136
129
196
153
122
116
110
196
153
122
116
110
159
124
99
94
90
159
124
99
94
90
123
123
105
105
85
85
0
1030 1420
918
1280
811
1130
701
973
586
763
432
550
10
15
20
25
30
939 1260
869 1130
779 975
677 803
570 632
834
772
692
601
506
1120
1000
864
711
560
726
670
599
517
432
965
865
741
606
473
615
569
509
440
368
808
728
626
514
402
495
460
413
359
302
609
555
486
407
325
345
324
297
263
226
406
378
341
295
244
35
40
45
50
55
465
366
290
235
194
477
366
290
235
194
412
324
257
208
172
422
324
257
208
172
349
272
216
175
145
354
272
216
175
145
297
232
184
150
124
301
232
184
150
124
244
191
152
124
103
248
191
152
124
103
188
150
120
98
82
193
150
120
98
82
56
57
58
59
188
181
175
169
188
181
175
169
166
161
155
166
161
155
140
135
130
140
135
130
120
116
112
120
116
112
99
96
99
96
79
76
79
76
No. of
a
Connectors
3⁄
Effective length KL (ft) with respect to indicated axis
b
Y-Y AXIS
41
2
3
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
33.5
2.42
3.55
30.0
2.44
3.53
26.5
2.45
3.51
22.9
2.47
3.49
19.2
2.49
3.47
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
15.5
2.50
3.45
3 - 58
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
3⁄
8
Equal legs
in. back to back of angles
6×
×6
Size
Thickness
Wt./ft
74.8
Y-Y AXIS
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
7⁄
8
1
3⁄
4
66.2
57.4
1⁄
2
48.4
3⁄
8
39.2
29.8
36
50
36
50
36
50
36
50
36
50
36
50
0
673
935
597
829
517
718
435
604
352
470
243
309
8
10
12
14
16
580
533
481
426
370
759
676
586
495
407
515
473
428
379
330
675
601
522
441
364
447
412
373
332
290
587
524
457
388
321
377
347
315
280
245
495
442
386
328
272
306
283
257
229
201
389
351
308
265
222
214
200
183
166
147
264
241
216
190
164
18
22
26
30
31
315
218
156
117
326
218
156
117
282
196
140
105
292
196
140
105
248
173
124
93
259
173
124
93
210
147
105
79
220
147
105
79
173
122
87
65
61
182
122
87
65
61
129
94
68
51
48
138
94
68
51
48
0
673
935
597
829
517
718
435
604
352
470
243
309
10
12
14
16
18
595
567
537
503
468
787
738
683
625
565
523
499
472
442
410
690
647
598
547
494
449
428
404
379
352
590
552
511
468
422
371
353
334
313
291
483
453
420
385
348
289
275
260
244
226
359
338
315
289
262
187
180
172
163
153
219
210
199
186
173
20
22
24
26
28
431
394
357
321
286
505
446
389
334
288
378
345
312
280
249
441
388
338
290
250
324
295
267
239
213
377
332
288
247
214
268
244
221
198
176
310
273
238
204
176
208
189
171
152
135
235
207
181
155
135
142
131
120
109
97
158
143
128
113
98
30
32
34
36
38
252
221
196
175
157
252
221
196
175
157
218
192
170
152
137
218
192
170
152
137
187
164
146
130
117
187
164
146
130
117
154
136
120
108
97
154
136
120
108
97
118
104
92
82
74
118
104
92
82
74
86
76
68
61
55
86
76
68
61
55
40
42
43
44
45
142
129
123
117
112
142
129
123
117
112
123
112
107
102
98
123
112
107
102
98
106
96
91
87
106
96
91
87
87
79
76
72
87
79
76
72
67
61
58
56
67
61
58
56
50
45
43
50
45
43
Properties of 2
A (in2)
rx (in.)
ry (in.)
5⁄
8
22.0
1.80
2.73
19.5
1.81
2.70
No. of
a
Connectors
Y
3/ ′′
8
b
2
3
angles—3⁄8
in. back to back
16.9
1.83
2.68
14.2
1.84
2.66
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11.5
1.86
2.64
8.72
1.88
2.62
DESIGN STRENGTH OF COLUMNS
3 - 59
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Equal legs
in. back to back of angles
5×
×5
Size
7⁄
8
Thickness
Wt./ft
X-X AXIS
3⁄
4
54.5
Fy
Effective length KL (ft) with respect to indicated axis
1⁄
2
47.2
3⁄
8
32.4
5⁄
16
24.6
20.6
36
50
36
50
36
50
36
50
36
50
0
490
680
425
591
291
404
217
282
169
215
6
8
10
12
14
433
393
348
299
251
573
502
423
343
268
377
344
305
264
222
500
440
372
304
239
259
237
211
183
155
344
304
259
213
169
194
178
160
140
119
244
219
189
159
129
152
141
127
113
97
189
171
150
128
107
16
18
20
22
24
204
162
132
109
91
206
162
132
109
91
182
145
117
97
82
183
145
117
97
82
128
103
83
69
58
130
103
83
69
58
99
80
65
54
45
102
80
65
54
45
82
68
55
46
38
86
68
55
46
38
75
75
53
53
42
39
42
39
35
33
35
33
25
26
Y-Y AXIS
3/ ′′
8
Y
0
490
680
425
591
291
404
217
282
169
215
6
8
10
12
14
457
438
414
388
358
617
582
540
492
441
394
377
357
334
309
531
501
464
423
379
260
249
236
221
204
345
326
303
277
249
184
176
168
157
145
224
214
201
186
168
136
131
126
119
111
160
154
146
137
127
16
18
20
22
24
327
295
263
231
201
389
337
287
240
202
282
254
226
199
172
334
289
246
205
173
186
168
149
131
114
219
190
161
135
114
133
120
107
93
81
150
132
113
95
81
103
94
84
75
66
115
103
90
78
66
26
28
30
32
34
172
149
130
114
101
172
149
130
114
101
148
127
111
98
87
148
127
111
98
87
97
84
73
65
57
97
84
73
65
57
69
60
52
46
41
69
60
52
46
41
57
49
43
38
34
57
49
43
38
34
36
37
38
90
85
81
90
85
81
77
73
69
77
73
69
51
48
51
48
37
35
37
35
30
30
A (in )
rx (in.)
ry (in.)
16.0
1.49
2.30
13.9
1.51
2.28
b
2
3
Properties of 2 angles—3⁄8 in. back to back
2
No. of
a
Connectors
3⁄
8
9.50
1.54
2.24
7.22
1.56
2.22
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.05
1.57
2.21
3 - 60
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
3⁄
8
Equal legs
in. back to back of angles
4×
×4
Size
3⁄
4
Thickness
Wt./ft
37.0
X-X AXIS
Fy
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
5⁄
8
1⁄
2
31.4
3⁄
8
25.6
5⁄
16
19.6
1⁄
4
16.4
13.2
36
50
36
50
36
50
36
50
36
50
36
50
0
334
463
282
392
230
319
175
243
146
191
108
138
4
6
8
10
12
306
275
237
195
154
411
354
288
220
159
259
233
201
167
132
349
301
245
189
137
212
191
166
138
110
285
247
203
157
115
162
146
127
106
85
217
189
156
121
89
135
123
107
90
72
172
152
127
101
76
101
92
82
70
57
126
112
96
78
61
14
16
18
19
20
117
89
71
63
117
89
71
63
100
77
61
54
49
100
77
61
54
49
84
65
51
46
41
84
65
51
46
41
65
50
40
36
32
65
50
40
36
32
56
43
34
30
27
56
43
34
30
27
45
35
28
25
22
46
35
28
25
22
0
334
463
282
392
230
319
175
243
146
191
108
138
6
8
10
12
14
303
284
262
237
210
406
371
332
288
245
254
238
219
198
176
339
311
277
241
204
204
191
176
158
140
270
247
220
191
161
151
141
130
117
104
196
180
161
141
119
121
114
106
96
85
148
138
125
110
95
85
81
76
70
63
100
94
87
79
70
16
18
20
22
24
183
157
132
109
92
202
163
132
109
92
153
131
109
91
76
168
135
109
91
76
122
104
86
72
60
133
106
86
72
60
90
77
64
53
45
98
79
64
53
45
74
63
53
44
37
79
64
53
44
37
56
48
41
35
29
60
50
41
35
29
26
28
29
30
31
78
67
63
59
55
78
67
63
59
55
65
56
52
49
46
65
56
52
49
46
51
44
41
39
51
44
41
39
38
33
31
29
38
33
31
29
32
27
26
24
32
27
26
24
25
22
20
25
22
20
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
10.9
1.19
1.88
9.22
1.20
1.86
7.50
1.22
1.83
5.72
1.23
1.81
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.80
1.24
1.80
3.88
1.25
1.79
No. of
a
Connectors
Y
3/ ′′
8
b
3
DESIGN STRENGTH OF COLUMNS
3 - 61
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Equal legs
8
in. back to back of angles
31⁄2×31⁄2
Size
3⁄
8
Thickness
Wt./ft
X-X AXIS
5⁄
16
17.0
Fy
Effective length KL (ft) with respect to indicated axis
Y
1⁄
4
14.4
11.6
36
50
36
50
36
50
0
152
211
128
175
100
129
2
4
6
8
10
148
137
120
100
78
204
182
152
117
84
125
115
101
84
67
169
152
127
99
72
97
90
80
67
54
125
114
97
77
58
12
14
16
17
18
59
43
33
29
59
43
33
29
50
37
28
25
22
50
37
28
25
22
41
30
23
21
18
41
30
23
21
18
0
152
211
128
175
100
129
6
8
10
12
14
130
120
108
94
81
170
152
131
109
88
107
98
89
78
67
136
123
106
89
72
80
74
67
60
52
96
88
78
67
56
16
18
20
22
24
67
54
44
37
31
69
54
44
37
31
56
45
37
30
26
57
45
37
30
26
43
36
29
24
20
44
36
29
24
20
26
26
26
22
22
17
17
3/ ′′
8
No. of
a
Connectors
3⁄
b
Y-Y axis
3
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
4.97
1.07
1.61
4.18
1.08
1.60
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.38
1.09
1.59
3 - 62
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
Y
3⁄
8
Equal legs
in. back to back of angles
3×
×3
Size
1⁄
2
Thickness
Wt./ft
18.8
X-X AXIS
Fy
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
3⁄
8
5⁄
16
14.4
1⁄
4
12.2
3⁄
16
9.8
7.42
36
50
36
50
36
50
36
50
36
50
0
168
234
129
179
109
151
88
118
61
77
2
4
5
6
7
162
145
133
120
106
222
190
169
146
123
125
112
103
93
83
171
147
131
114
97
105
94
87
79
70
144
124
111
97
82
85
77
71
64
57
112
98
88
77
66
59
54
50
46
41
74
66
60
54
47
8
9
10
11
12
92
79
66
54
46
101
81
66
54
46
72
62
52
43
36
80
64
52
43
36
61
53
45
37
31
68
55
45
37
31
50
43
37
31
26
56
46
37
31
26
37
32
28
24
20
41
34
28
24
20
13
14
15
39
34
39
34
31
27
23
31
27
23
26
23
20
26
23
20
22
19
16
22
19
16
17
15
13
17
15
13
0
168
234
129
179
109
151
88
118
61
77
2
4
6
8
10
163
155
143
128
111
223
209
187
161
132
123
117
108
97
84
167
156
140
121
99
101
97
89
80
70
136
128
115
99
82
79
75
70
63
55
100
95
86
75
63
50
48
45
42
37
59
57
53
48
42
12
14
16
18
20
94
76
60
47
38
104
78
60
47
38
70
57
45
36
29
78
58
45
36
29
58
47
37
29
24
64
48
37
29
24
46
38
29
23
19
50
38
29
23
19
32
27
22
17
14
35
28
22
17
14
22
23
32
29
32
29
24
22
24
22
20
18
20
18
16
14
16
14
12
11
12
11
A (in )
rx (in.)
ry (in.)
b
3
Properties of 2 angles—3⁄8 in. back to back
2
No. of
a
Connectors
3/ ′′
8
5.50
0.898
1.43
4.22
0.913
1.41
3.55
0.922
1.40
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.88
0.930
1.39
2.18
0.939
1.38
DESIGN STRENGTH OF COLUMNS
3 - 63
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Equal legs
8
in. back to back of angles
21⁄2×21⁄2
Size
3⁄
8
Thickness
Wt./ft
X-X AXIS
Y-Y AXIS
5⁄
16
11.8
Fy
Effective length KL (ft) with respect to indicated axis
Y
1⁄
4
10.0
3⁄
16
8.2
6.14
36
50
36
50
36
50
36
50
0
106
147
90
125
73
101
54
70
2
3
4
5
6
101
94
86
76
66
137
125
110
93
76
85
80
73
65
56
116
106
93
79
65
69
65
59
53
46
94
86
76
65
53
52
48
44
40
35
66
61
54
47
40
7
8
9
10
11
55
45
36
29
24
59
46
36
29
24
47
39
31
25
21
51
39
31
25
21
39
32
26
21
17
42
33
26
21
17
30
25
20
16
13
32
25
20
16
13
12
20
20
17
17
14
14
11
11
0
106
147
90
125
73
101
54
70
2
3
4
5
6
101
99
95
90
85
138
133
126
118
109
84
82
79
75
71
114
110
105
98
90
67
65
63
60
56
89
86
82
77
71
46
45
44
42
40
57
55
53
50
47
7
8
9
10
11
79
73
66
60
53
98
88
77
67
57
66
61
55
50
44
82
73
64
55
47
52
48
44
40
35
64
58
51
44
37
37
35
32
29
26
44
40
35
31
27
12
13
14
15
16
47
41
35
31
27
48
41
35
31
27
39
34
29
26
22
40
34
29
26
22
31
27
23
20
18
32
27
23
20
18
23
20
17
15
13
23
20
17
15
13
17
18
19
20
24
21
19
17
24
21
19
17
20
18
16
14
20
18
16
14
16
14
13
16
14
13
12
11
9
12
11
9
Properties of 2 angles—3⁄8 in. back to back
A (in2)
rx (in.)
ry (in.)
3.47
0.753
1.21
2.93
0.761
1.20
2.38
0.769
1.19
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.80
0.778
1.18
3/ ′′
8
No. of
a
Connectors
3⁄
b
3
3 - 64
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
Y
3⁄
8
Equal legs
in. back to back of angles
2×
×2
Size
3⁄
8
Thickness
Wt./ft
9.4
X-X AXIS
Fy
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
5⁄
16
1⁄
4
7.84
3⁄
16
6.38
1⁄
8
4.88
3.30
36
50
36
50
36
50
36
50
36
50
0
83
116
70
98
58
80
44
61
27
34
2
3
4
5
6
76
69
59
49
38
103
88
72
55
39
65
58
50
42
33
87
75
61
47
34
53
48
41
35
28
71
62
51
39
29
40
37
32
27
21
54
47
39
30
22
25
23
20
17
14
31
28
24
19
15
7
8
9
10
29
22
18
29
22
18
25
19
15
12
25
19
15
12
21
16
13
10
21
16
13
10
16
13
10
8
16
13
10
8
11
9
7
6
11
9
7
6
0
83
116
70
98
58
80
44
61
27
34
2
3
4
5
6
79
76
72
67
61
108
102
95
86
76
67
64
60
56
51
90
86
79
72
63
54
51
49
45
41
72
68
63
57
51
39
38
36
33
31
52
49
46
42
37
22
21
20
19
18
26
25
24
22
20
7
8
9
10
11
55
49
43
37
31
66
55
46
37
31
46
41
36
30
26
55
46
38
31
26
37
33
29
24
21
44
37
30
25
21
27
24
21
18
15
32
27
22
18
15
16
15
13
11
10
18
16
14
12
10
12
13
14
15
16
26
22
19
17
15
26
22
19
17
15
22
18
16
14
12
22
18
16
14
12
17
15
13
11
10
17
15
13
11
10
13
11
9
8
7
13
11
9
8
7
8
7
6
5
5
8
7
6
5
5
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
2.72
0.594
1.01
2.30
0.601
1.00
1.88
0.609
0.989
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.43
0.617
0.977
0.960
0.626
0.965
No. of
a
Connectors
3/ ′′
8
b
3
DESIGN STRENGTH OF COLUMNS
3 - 65
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
Long legs 3⁄8 in. back to back of angles
3⁄
4
1⁄
2
Wt./ft
88.4
67.6
46.0
Fy
36
X-X AXIS
1⁄
2
57.4
39.2
36
50
36
50
36
50
846
376
479
0
673
935 517 718 321 408
10
12
14
16
18
704
667
626
582
535
932
865
792
715
637
541
513
483
450
415
717
667
613
555
496
339
323
306
287
267
419
395
368
340
310
10
12
14
16
18
597
567
533
496
457
792
736
676
612
546
460
437
412
384
354
611
569
523
475
425
289
276
262
246
230
358
338
315
292
267
20
22
24
26
28
488
440
393
348
305
560
486
415
353
305
379
343
308
273
241
438
381
328
279
241
247
226
205
185
165
280
250
221
193
167
20
22
24
26
28
418
378
338
300
264
482
419
359
306
264
324
294
264
235
207
376
328
283
241
208
212
195
177
160
143
242
216
192
168
146
30
32
34
36
38
265
233
207
184
165
265
233
207
184
165
210
184
163
146
131
210
184
163
146
131
146
128
113
101
91
146
128
113
101
91
30
32
34
36
38
230 230
202 202
179 179
160 160
143 143
181
159
141
126
113
181 127 127
159 112 112
141
99
99
126
88
88
113
79
79
41
42
142
142 112
107
112
107
78
74
78
74
40
42
43
129 129 102 102
117 117
92
92
0
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
3⁄
4
74.8
796 1110 609
0
50
8×
×4
1
b
50
36
50
71
65
62
796 1110 609
846
376
479
0
729
703
672
636
595
978
932
876
811
741
537
519
496
470
440
709
677
638
593
543
301
293
282
270
256
357
346
331
314
295
6
8
10
12
14
568 741 416 533 234 275
520 657 381 473 217 251
464 562 339 405 197 223
404 463 294 333 175 192
342 368 248 263 150 159
935 517 718 321 408
16
18
20
22
24
551
506
459
412
366
667
592
517
445
378
408
375
340
305
271
490
435
381
328
279
240
223
205
187
169
273
249
225
200
176
16
18
20
22
24
282
238
194
160
135
300
238
194
160
135
203
162
132
110
93
26
28
32
321
279
214
323
279
214
238
207
159
239
207
159
151
133
103
152
133
103
25
26
125
115
125
115
85
34
36
40
41
42
190
170
138
131
125
190
170
138
131
125
141
126
103
98
141
126
103
98
92
82
67
92
82
67
A
rx (in.)
ry (in.)
26.0
2.49
2.52
19.9
2.53
2.48
13.5
2.56
2.44
22.0
2.52
1.61
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2
204 126 127
162 103 103
132
84
84
110
70
70
93
60
60
85
55
55
3
Properties of 2 angles—3⁄8 in. back to back
(in2)
b
71
65
62
6
8
10
12
14
2
673
36
No. of a
Connectors
1
No. of a
Connectors
8×
×6
Size
Thickness
Y
16.9
2.55
1.55
11.5
2.59
1.51
3 - 66
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
3⁄
4
1⁄
2
3⁄
8
Wt./ft
52.4
35.8
27.2
Fy
36
50
36
50
36
50
X-X AXIS
Effective length KL (ft) with respect to indicated axis
0 471 655 310 401 205 254
3⁄
4
5⁄
8
1⁄
2
3⁄
8
47.2
40.0
32.4
24.6
36
0
50
36
50
36
50
36
50
425 591 358 497 291 388 201 256
8
10
12
14
16
427
404
378
349
318
571
529
481
431
379
283
268
252
233
214
355
332
306
278
248
189
181
171
161
149
230
218
204
188
172
8
10
12
14
16
371
343
312
279
246
488
439
385
329
276
313
290
265
237
209
413
371
327
281
236
18
20
22
24
26
286
255
224
194
166
328
278
232
195
166
194
174
154
135
117
219
190
162
137
117
137
125
113
101
89
155
138
121
105
90
18
20
22
24
26
212
180
150
126
108
225
182
150
126
108
181
155
129
109
93
193 148 158 110 119
156 127 128 96 100
129 106 106 82 82
109 89 89 69 69
93 76 76 59 59
28 143 143 100 100
30 125 125 88 88
32 110 110 77 77
34 97 97 68 68
78
68
59
53
78
68
59
53
28
30
31
32
93
81
76
93
81
76
80
70
65
36
37
47
44
47
44
87
82
87
82
61
58
61
58
b
0 471 655 310 401 205 254
Y-Y AXIS
6×
×4
No. of a
Connectors
7×
×4
Size
Thickness
6
8
10
12
14
394
362
325
284
242
511
456
393
327
262
238
221
200
176
151
286
260
229
196
161
146
137
127
115
101
167
156
142
126
108
16
18
20
22
24
201
162
132
110
92
204 126 128
162 103 103
132 84 84
110 70 70
92 59 59
87
74
61
51
43
90
74
61
51
43
25
26
27
85
79
73
40
40
0
80
70
65
254
236
216
193
171
65
57
53
325
294
260
225
191
65
57
53
179
167
154
140
125
51
44
41
39
220
202
182
161
140
b
51
44
41
39
425 591 358 497 291 388 201 256
6
8
10
12
14
367
339
306
270
232
481
432
375
315
256
302
279
252
222
191
394
354
308
259
210
236
218
197
174
150
293
266
233
198
162
153
144
132
118
104
181
167
151
132
112
16
18
20
22
24
195
160
136
113
95
211 161 165 126 129
167 132 132 103 103
136 107 107 84 84
113 89 89 70 70
95 75 75 59 59
89
75
61
51
43
93
75
61
51
43
26
27
28
81
75
70
37
35
37
35
2
85
79
73
55
51
55
51
2
81
75
70
64
59
64
59
50
47
50
47
3
Properties of 2 angles—3⁄8 in. back to back
A (in2)
rx (in.)
ry (in.)
No. of a
Connectors
Long legs 3⁄8 in. back to back of angles
Y
15.4
2.22
1.62
10.5
2.25
1.57
7.97
2.27
1.55
13.9
1.88
1.69
11.7
1.90
1.67
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9.50
1.91
1.64
7.22
1.93
1.62
DESIGN STRENGTH OF COLUMNS
3 - 67
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
Long legs 3⁄8 in. back to back of angles
Wt./ft
23.4
Y-Y AXIS
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
5⁄
16
19.6
36
50
36
50
0
191
243
145
179
8
10
12
14
16
170
159
146
133
119
209
192
173
153
133
130
123
114
105
95
157
146
134
120
106
18
20
22
24
26
105
92
78
66
56
114
95
79
66
56
85
75
65
56
48
93
79
67
56
48
28
30
32
49
42
37
49
42
37
41
36
32
0
191
243
4
6
8
10
12
148
139
127
113
98
14
16
18
20
22
23
3⁄
4
1⁄
2
39.6
3⁄
8
27.2
5⁄
16
20.8
50
36
50
0
355
493
245
340 183 238 143 182
4
6
8
10
12
337
317
290
259
225
460 233
421 219
372 202
318 181
262 158
14
16
18
20
22
191
158
127
103
85
209
161
127
103
85
41
36
32
24
25
26
72
66
72
66
51
47
44
145
179
0
355
493
245
176
163
147
127
105
107
101
94
85
75
122
115
106
94
80
4
6
8
10
12
325
303
274
241
206
437 215
396 200
345 182
289 160
232 136
284
258
226
189
152
152
142
129
114
98
81
66
53
43
36
84
66
53
43
36
64
53
43
35
29
66
53
43
35
29
14
16
18
20
22
170
144
114
93
77
188
144
114
93
77
113
90
72
58
48
117
90
72
58
48
82
65
52
43
35
84
65
52
43
35
65
53
43
35
29
68
53
43
35
29
33
33
27
27
24
25
65
60
65
60
41
41
30
30
25
25
b
318
292
260
223
185
36
17.4
36
175
165
152
137
120
50
36
50
224
208
187
163
138
137
130
120
109
97
172
161
146
129
111
135 149 104 113
113 116
87
90
91
91
71
71
74
74
58
58
61
61
48
48
85
72
60
49
41
93
76
61
49
41
34
31
29
34
31
29
51
47
44
40
37
34
40
37
34
A (in )
rx (in.)
ry (in.)
186 113 134
171 107 125
152
98 114
130
88
99
107
77
84
2
6.84
1.94
1.39
5.74
1.95
1.38
b
340 183 238 143 182
2
3
Properties of 2 angles—3⁄8 in. back to back
2
No. of a
Connectors
3⁄
8
Thickness
5×
×31⁄2
No. of a
Connectors
6×
×31⁄2
Size
Y
11.6
1.55
1.53
8.00
1.58
1.49
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.09
1.60
1.46
5.12
1.61
1.45
3 - 68
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
5×
×3
Size
1⁄
2
Thickness
Wt./ft
25.6
X-X AXIS
Fy
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
3⁄
8
5⁄
16
19.6
1⁄
4
16.4
13.2
36
50
36
50
36
50
36
50
0
230
319
172
223
134
170
95
117
2
4
6
8
10
227
219
206
189
170
313
298
274
244
210
170
164
155
143
129
220
210
195
176
154
132
128
122
113
103
168
161
151
137
121
95
92
88
82
76
115
112
105
97
88
12
14
16
18
20
149
128
107
87
70
175
141
110
87
70
114
98
82
68
55
130
107
86
68
55
91
79
68
56
46
104
88
71
57
46
68
61
53
45
38
78
67
56
47
38
22
24
26
27
58
49
42
58
49
42
45
38
32
45
38
32
38
32
27
38
32
27
31
26
22
21
31
26
22
21
0
230
319
172
223
134
170
95
117
2
4
6
8
10
207
195
177
153
128
276
255
223
184
143
146
138
125
110
92
179
167
149
126
101
107
102
94
84
72
128
121
110
95
78
71
68
64
58
51
80
77
72
64
55
12
14
16
18
20
101
81
62
49
40
109
81
62
49
40
74
57
44
35
28
76
57
44
35
28
59
46
36
29
23
61
46
36
29
23
43
35
28
22
18
45
35
28
22
18
No. of
a
Connectors
Long legs 3⁄8 in. back to back of angles
Y
b
2
3
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
7.50
1.59
1.25
5.72
1.61
1.23
4.80
1.61
1.22
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.88
1.62
1.21
DESIGN STRENGTH OF COLUMNS
3 - 69
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
Long legs 3⁄8 in. back to back of angles
1⁄
2
Thickness
Wt./ft
23.8
Fy
X-X AXIS
3⁄
8
5⁄
16
18.2
15.4
12.4
36
50
36
50
36
50
36
50
0
214
298
163
227
137
179
101
129
2
4
6
8
10
210
198
179
155
130
289
266
232
191
148
160
151
137
120
101
221
204
178
147
116
134
127
115
101
85
174
162
143
120
96
99
94
87
77
66
126
118
106
91
75
12
14
16
18
20
104
80
61
48
39
109
80
61
48
39
81
63
48
38
31
86
63
48
38
31
69
54
41
33
26
73
54
41
33
26
55
44
34
27
22
59
44
34
27
22
24
24
20
20
0
214
298
163
227
137
179
101
129
2
4
6
8
10
203
196
183
167
148
276
262
240
211
180
150
144
135
124
110
200
190
174
155
132
121
116
110
101
90
150
143
133
120
104
84
81
77
72
65
99
96
91
83
74
12
14
16
18
20
128
108
88
74
60
147
116
93
74
60
95
80
66
53
43
108
86
66
53
43
78
66
54
43
35
87
70
54
43
35
58
50
42
34
28
64
53
42
34
28
22
24
25
26
50
42
39
36
50
42
39
36
35
30
28
25
35
30
28
25
29
25
23
29
25
23
23
20
18
23
20
18
b
21
Y-Y AXIS
1⁄
4
No. of
a
Connectors
4×
×31⁄2
Size
Effective length KL (ft) with respect to indicated axis
Y
2
3
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
7.00
1.23
1.58
5.34
1.25
1.56
4.49
1.26
1.55
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.63
1.27
1.54
3 - 70
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
4×
×3
Size
1⁄
2
Thickness
Wt./ft
22.2
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
3⁄
8
17.0
1⁄
4
14.4
11.6
36
50
36
50
36
50
36
50
0
199
276
152
211
127
166
94
120
2
4
6
8
10
195
184
167
146
122
269
248
217
179
141
149
141
128
112
94
206
190
166
138
109
125
118
108
94
80
162
151
133
112
90
93
88
81
72
62
117
110
99
85
70
12
14
16
18
20
99
77
59
46
38
105
77
59
46
38
76
60
46
36
29
81
60
46
36
29
65
51
39
31
25
69
51
39
31
25
51
41
32
25
21
55
42
32
25
21
27
27
23
23
19
19
0
199
276
152
211
127
166
94
120
2
4
6
8
10
187
177
161
142
120
253
235
207
173
137
138
131
119
105
89
183
171
151
127
101
111
105
96
85
73
137
129
116
99
81
77
74
69
62
54
92
88
80
71
59
12
14
16
18
20
97
76
61
49
39
108
80
61
49
39
72
56
43
35
28
76
56
43
35
28
59
46
36
29
23
62
46
36
29
23
45
36
28
23
18
47
36
28
23
18
21
22
36
33
36
33
25
25
21
21
17
17
b
21
Y-Y AXIS
5⁄
16
2
3
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
No. of
a
Connectors
Long legs 3⁄8 in. back to back of angles
Y
6.50
1.25
1.33
4.97
1.26
1.31
4.18
1.27
1.30
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.38
1.28
1.29
DESIGN STRENGTH OF COLUMNS
3 - 71
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
Long legs 3⁄8 in. back to back of angles
Wt./ft
15.8
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
5⁄
16
1⁄
4
13.2
10.8
36
50
36
50
36
50
0
140
195
118
162
92
119
2
4
6
8
10
137
127
112
93
74
188
169
142
111
80
115
107
95
79
63
157
141
119
94
69
90
84
75
63
51
116
106
91
73
55
12
14
16
17
18
56
41
32
28
25
56
41
32
28
25
48
35
27
24
21
48
35
27
24
21
39
29
22
20
18
0
140
195
118
162
2
4
6
8
10
131
124
114
101
86
176
164
146
123
99
107
102
94
83
71
12
14
71
56
76
59
16
18
20
45
36
29
22
24
3⁄
8
1⁄
4
14.4
9.8
36
50
36
50
0
129
179
85
110
2
4
6
8
10
126
117
103
86
69
173
156
131
103
75
83
77
69
59
47
107
97
84
68
52
40
29
22
20
18
12
14
16
18
52
39
30
23
53
39
30
23
37
27
21
17
37
27
21
17
92
119
0
129
179
85
110
140
131
118
100
81
79
76
70
63
54
97
92
83
73
60
2
4
6
8
10
118
109
96
80
63
158
142
119
92
69
71
67
59
50
40
87
80
69
56
42
59
46
62
47
45
36
48
36
12
14
49
36
49
36
30
22
30
22
45
36
29
36
29
23
36
29
23
28
22
18
28
22
18
16
18
28
22
28
22
17
14
17
14
24
19
19
15
15
b
No. of a
Connectors
3⁄
8
Thickness
31⁄2×21⁄2
No. of a
Connectors
31⁄2×3
Size
Y
b
2
Y-Y AXIS
2
3
3
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
4.59
1.09
1.36
3.87
1.10
1.35
3.13
1.11
1.33
4.22
1.10
1.11
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.88
1.12
1.09
3 - 72
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
Y
X
COLUMNS
Double angles
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
3⁄
8
Thickness
13.2
Wt./ft
Y-Y AXIS
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
1⁄
4
36
3⁄
16
9.0
6.77
50
36
50
36
50
0 118 163
80
107
55
71
2 113 155
3 109 146
4 102 134
5 94 120
6 86 105
78
75
70
65
59
103
97
90
81
71
54
52
49
46
42
68
65
60
55
50
3×
×2
No. of
a
Connectors
3×
×21⁄2
Size
3⁄
8
5⁄
16
11.8
36
1⁄
4
10.0
3⁄
16
8.2
36
6.1
50
36
50
50
0
106 147
90
125
73
97
50
64
2
3
4
5
6
103
98
93
86
78
141
132
122
109
96
87
83
78
73
66
119
112
103
93
82
70
68
64
59
54
93
88
81
74
65
49
47
45
42
38
61
59
55
50
45
7
8
9
10
11
70
61
53
45
38
82
69
56
45
38
59
52
45
39
32
70
59
48
39
32
49
43
37
32
27
57
48
40
32
27
35
31
28
24
20
40
35
30
25
21
12
13
14
15
16
32
27
23
20
32
27
23
20
27
23
20
17
27
23
20
17
22
19
16
14
22
19
16
14
17
15
13
11
10
17
15
13
11
10
7
8
9
10
11
76
67
58
49
40
90
75
60
49
40
53
47
40
34
29
62
52
43
35
29
38
34
30
26
22
44
38
32
27
22
12
13
14
15
34
29
25
22
34
29
25
22
24
21
18
15
24
21
18
15
19
16
14
12
19
16
14
12
0 118 163
80
107
55
71
0
106 147
90
125
73
97
50
64
2 110 149
3 107 143
4 102 135
5 97 125
6 90 114
71
69
66
63
59
90
87
83
77
71
45
44
43
41
39
54
53
51
48
45
2
3
4
5
6
97 131
93 122
86 111
79 98
71 84
80
76
71
65
58
107
100
91
81
69
63
60
56
51
46
79
74
68
61
53
40
39
37
34
31
48
46
43
39
35
7
8
9
10
11
62
53
47
39
32
70
60
48
39
32
51
44
37
32
27
58
49
39
32
27
40
35
29
25
21
45
37
31
25
21
28
24
21
17
15
30
26
21
17
15
12
13
14
15
27
23
20
18
27
23
20
18
22
19
17
14
22
19
17
14
18
15
13
18
15
13
12
11
10
12
11
10
7
8
9
10
11
83 102
76 90
68 77
61 66
53 58
54
50
45
40
35
64
57
49
42
35
36
34
31
28
25
41
38
34
30
26
12
13
14
15
16
48
42
36
31
28
49
42
36
31
28
30
26
23
20
18
30
26
23
20
18
22
19
16
14
13
22
19
16
14
13
17
18
19
24
22
20
24
22
20
16
14
16
14
11
10
11
10
b
2
3
Properties of 2 angles—3⁄8 in. back to back
A
(in2)
rx (in.)
ry (in.)
3.84
0.928
1.16
2.63
0.945
1.13
1.99
0.954
1.12
3.47
0.940
0.917
2.93
0.948
0.903
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.38
0.957
0.891
1.80
0.966
0.879
No. of a
Connectors
Long legs 3⁄8 in. back to back of angles
Y
b
2
3
DESIGN STRENGTH OF COLUMNS
3 - 73
Fy = 36 ksi
Fy = 50 ksi
Y
COLUMNS
Double angles
X
X
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
Long legs 3⁄8 in. back to back of angles
3⁄
8
Thickness
Wt./ft
10.6
X-X AXIS
Fy
Y-Y AXIS
5⁄
16
1⁄
4
9.0
3⁄
16
7.2
5.5
36
50
36
50
36
50
36
50
0
95
131
80
111
65
91
49
63
2
3
4
5
6
90
84
77
69
60
122
112
99
84
69
76
72
66
59
51
104
95
84
72
59
62
58
54
48
42
85
78
69
59
49
46
44
40
36
32
59
55
49
43
36
7
8
9
10
11
50
42
33
27
22
55
42
33
27
22
43
36
29
23
19
47
37
29
23
19
36
30
24
19
16
39
30
24
19
16
27
23
19
15
12
30
24
19
15
12
12
13
19
19
16
16
13
11
13
11
10
9
10
9
0
95
131
80
111
65
91
49
63
2
3
4
5
6
89
85
80
74
67
120
113
104
93
82
74
71
66
61
55
99
93
85
76
66
58
56
52
48
44
77
73
67
60
52
41
39
37
34
31
50
48
44
40
36
7
8
9
10
11
60
52
45
38
32
70
58
47
38
32
49
42
36
32
26
56
48
39
32
26
39
33
28
25
21
44
36
31
25
21
28
24
21
17
15
31
26
22
18
15
12
13
14
15
16
27
23
20
17
15
27
23
20
17
15
22
19
16
14
22
19
16
14
17
15
13
11
17
15
13
11
13
11
10
8
13
11
10
8
b
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
No. of
a
Connectors
21⁄2×2
Size
Effective length KL (ft) with respect to indicated axis
Y
3.09
0.768
0.961
2.62
0.776
0.948
2.13
0.784
0.935
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.62
0.793
0.923
2
3
3 - 74
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
X
Unequal legs
8×
×6
Size
Thickness
Wt./ft
88.4
Fy
36
X-X AXIS
Y-Y AXIS
67.6
46.0
50
36
50
796 1110 609
846
376
479
8
12
16
20
24
677
552
416
288
200
882
666
449
288
200
521
428
325
228
159
680
518
354
228
159
328
276
217
159
111
402
323
237
160
111
28
29
147
147 116
109
116
109
82
76
796 1110 609
846
12
16
20
24
28
725
681
628
569
506
970
890
796
695
591
547
514
474
429
382
32
36
40
44
48
443
380
320
265
223
490
396
321
265
223
52
56
60
61
62
190
164
143
138
134
190
164
143
138
134
63
130
130
0
50
1⁄
2
36
0
Effective length KL (ft) with respect to indicated axis
3⁄
4
1
8×
×4
3⁄
4
1
74.8
1⁄
2
57.4
50
0
673
935 517 718 321 408
4
6
8
10
12
600
521
426
329
240
798
654
495
346
240
82
76
14
16
17
18
176 176 141 141 101 101
135 135 108 108
78
78
120 120
96
96
69
69
61
61
376
479
0
673
935 517 718 321 408
727
667
598
522
444
325
308
287
263
237
393
368
338
304
267
12
16
20
24
28
628
596
558
514
467
849
790
720
643
563
480
455
426
392
355
647
602
548
489
426
295
281
264
245
224
365
344
318
290
258
333
286
240
199
168
368
297
241
199
168
210
183
156
131
110
229
192
157
131
110
32
36
40
44
48
418
369
320
274
231
483
405
333
275
231
317
279
242
206
174
364
305
250
206
174
202
179
157
135
115
227
195
165
137
115
143
123
108
104
101
143
123
108
104
101
94
81
71
69
94
81
71
69
52
56
60
64
66
197
170
148
130
122
197 148 148
170 128 128
148 111 111
130
98
98
122
92
92
98
85
74
65
61
98
85
74
65
61
67
68
119 119
115 115
b
3
36
39.2
36
463
404
333
260
192
50
616
509
390
276
192
89
36
292
259
219
177
137
50
361
311
252
192
138
89
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
26.0
1.73
3.78
19.9
1.76
3.74
13.5
1.79
3.69
22.0
1.03
4.10
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
16.9
1.05
4.05
11.5
1.08
4.00
No. of a
Connectors
Short legs 3⁄8 in. back to back of angles
No. of a
Connectors
Y
Design axial strength in kips (φ = 0.85)
3/ ′′
8
b
6
DESIGN STRENGTH OF COLUMNS
3 - 75
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
X
Unequal legs
7×
×4
Size
3⁄
4
Thickness
Wt./ft
1⁄
2
52.4
Fy
36
50
3⁄
8
35.8
36
50
27.2
36
50
No. of a
Connectors
Short legs 3⁄8 in. back to back of angles
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
0 471 655 310 401 205 254
4
6
8
10
12
426
375
313
249
188
568
476
371
270
188
282
250
212
171
132
354
304
245
186
133
189
171
149
124
100
230
203
171
137
104
14 138 138
16 106 106
18 84 84
98
75
59
98
75
59
77
59
47
3/ ′′
8
Y
6×
×4
3⁄
4
5⁄
8
47.2
50
0
36
50
1⁄
2
40.0
36
3⁄
8
32.4
50
36
24.6
50
36
50
425 591 358 497 291 388 201 256
4
6
8
10
12
386
342
289
232
178
436
370
293
218
154
265
236
201
164
127
343
295
238
181
129
186
168
146
122
97
231
203
170
135
102
77
59
47
14
16
18
19
132 132 113 113
101 101 86 86
80 80 68 68
95
73
57
52
95
73
57
52
75
57
45
41
75
57
45
41
0 471 655 310 401 205 254
0
8
12
16
20
24
449
427
397
362
324
611
570
516
454
389
291
277
259
236
212
368
346
317
282
245
28
32
36
40
44
283
243
204
168
139
323
261
207
168
139
186
160
135
111
92
207 129 143
171 113 122
137 98 102
111 83 83
92 69 69
48 117 117
52 99 99
56 86 86
57 83 83
58 80 80
77
66
57
55
77
66
57
55
188
181
171
158
144
58
49
43
41
b
225
215
201
184
164
58
49
43
41
5
517
437
345
255
179
326
289
245
198
152
A (in )
rx (in.)
ry (in.)
15.4
1.09
3.49
10.5
1.11
3.44
7.97
1.13
3.42
b
425 591 358 497 291 388 201 256
8
12
16
20
24
398
370
334
293
249
538
486
422
352
282
28
32
36
40
44
206
166
131
106
88
216 172 179 138 143 100 105
165 138 138 110 110 81 82
131 109 109 87 87 65 65
106 88 88 71 71 52 52
88 73 73 58 58 43 43
45
46
47
48
49
84
80
77
74
71
84
80
77
74
71
333
310
279
245
208
70
67
64
61
449
406
352
294
235
70
67
64
61
267
249
224
197
167
56
53
51
49
346
314
275
230
186
56
53
51
49
181
170
155
138
119
42
40
38
222
205
184
158
131
42
40
38
Properties of 2 angles—3⁄8 in. back to back
2
No. of a
Connectors
Design axial strength in kips (φ = 0.85)
13.9
1.12
2.94
11.7
1.13
2.92
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9.50
1.15
2.90
7.22
1.17
2.87
4
3 - 76
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
X
Unequal legs
6×
×31⁄2
Size
3⁄
8
Thickness
Wt./ft
23.4
Y-Y AXIS
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
5⁄
16
19.6
36
50
36
50
0
191
243
145
179
4
6
8
10
170
148
121
94
210
175
136
99
131
115
97
77
158
135
109
82
12
14
16
69
50
39
69
50
39
58
43
33
59
43
33
0
191
243
145
8
12
16
20
24
173
160
144
125
112
213
194
170
142
124
28
32
36
40
44
94
76
63
51
42
48
49
36
34
5×
×31⁄2
3⁄
4
1⁄
2
39.6
3⁄
8
27.2
5⁄
16
20.8
50
36
50
0
355
493
245
340 183 238 143 182
2
4
6
8
10
344
313
267
214
160
472 238 326
413 217 288
331 187 234
243 152 176
164 116 121
12
14
16
17
114
84
64
114
84
64
84
62
47
179
0
355
493
245
340 183 238 143 182
130
122
111
98
84
154
143
128
110
98
8
10
12
14
16
318
300
279
257
233
423
390
354
334
297
217
205
191
175
159
287
265
240
214
201
99
80
63
51
42
75
62
53
43
35
80
66
53
43
35
18
20
22
24
26
224
201
179
157
144
260
225
201
169
144
152
136
121
106
96
175 106 127
151 101 111
134
90
95
113
79
84
96
69
72
36
34
30
29
30
29
28
30
32
34
36
125
109
95
85
75
125
109
95
85
75
83
72
64
56
50
83
72
64
56
50
62
54
48
42
38
62
54
48
42
38
49
43
38
33
30
49
43
38
33
30
38
39
40
68
64
61
68
64
61
45
43
41
45
43
41
34
32
31
34
32
31
27
25
27
25
41
58
58
b
5
36
17.4
36
178
163
141
116
89
84
62
47
50
50
229 139 176
205 129 159
170 113 135
131
94 107
94
74
79
65
48
37
32
160
151
141
130
118
36
65
48
37
32
198
185
169
153
143
56
41
31
28
123
117
110
102
94
6.84
0.988
2.95
5.74
0.996
2.94
11.6
0.977
2.48
8.00
1.01
2.43
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
6.09
1.02
2.41
b
56
41
31
28
149
140
130
119
106
85 100
81
89
73
77
65
66
57
57
Properties of 2 angles—3⁄8 in. back to back
A (in2)
rx (in.)
ry (in.)
No. of a
Connectors
Short legs 3⁄8 in. back to back of angles
No. of a
Connectors
Y
Design axial strength in kips (φ = 0.85)
3/ ′′
8
5.12
1.03
2.39
4
DESIGN STRENGTH OF COLUMNS
3 - 77
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
X
Unequal legs
Short legs 3⁄8 in. back to back of angles
5×
×3
Size
1⁄
2
Thickness
Wt./ft
X-X AXIS
Y-Y AXIS
3⁄
8
25.6
Fy
Effective length KL (ft) with respect to indicated axis
Y
5⁄
16
19.6
1⁄
4
16.4
13.2
36
50
36
50
36
50
36
50
0
230
319
172
223
134
170
95
117
2
4
6
8
10
220
192
154
113
76
300
249
184
119
76
165
146
118
88
61
212
180
137
94
61
129
115
95
73
52
162
140
110
79
52
92
84
71
56
42
112
99
81
61
43
12
13
14
53
45
53
45
42
36
31
42
36
31
36
31
26
36
31
26
30
25
22
30
25
22
0
230
319
172
223
134
170
95
117
8
10
12
14
16
205
194
181
167
152
273
253
230
205
194
152
144
135
125
114
190
178
163
147
139
118
112
106
98
90
144
135
126
115
103
83
79
75
71
66
96
92
87
81
75
18
20
22
24
26
146
132
117
103
95
170
147
132
112
95
109
99
88
78
68
124
109
94
84
71
82
79
71
63
56
98
87
76
66
59
61
56
54
49
44
68
65
58
51
45
28
30
32
34
36
82
72
63
56
50
82
72
63
56
50
62
54
47
42
37
62
54
47
42
37
51
45
39
35
31
51
45
39
35
31
39
36
31
28
25
41
36
31
28
25
38
40
41
45
40
38
45
40
38
34
30
29
34
30
29
28
25
24
28
25
24
22
20
19
22
20
19
3/ ′′
8
No. of
a
Connectors
Design axial strength in kips (φ = 0.85)
b
4
5
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
7.50
0.829
2.50
5.72
0.845
2.48
4.80
0.853
2.47
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.88
0.861
2.46
3 - 78
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
Y
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
Short legs 3⁄8 in. back to back of angles
4×
×31⁄2
Size
1⁄
2
Thickness
Wt./ft
23.8
X-X AXIS
Fy
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
3⁄
8
5⁄
16
18.2
1⁄
4
15.4
12.4
36
50
36
50
36
50
36
50
0
214
298
163
227
137
179
101
129
2
4
6
8
10
208
191
166
137
106
286
255
210
160
112
159
147
128
106
83
219
195
162
125
89
133
123
108
90
71
172
156
131
103
76
99
92
81
69
55
125
114
98
79
60
12
14
16
17
78
57
44
39
78
57
44
39
62
45
35
31
62
45
35
31
53
39
30
26
53
39
30
26
42
31
24
21
43
31
24
21
0
214
298
163
227
137
179
101
129
4
6
8
10
12
201
190
177
161
143
271
252
228
200
181
150
142
132
120
107
200
187
169
149
127
122
116
108
99
89
152
143
132
117
102
86
83
78
72
66
103
99
92
84
75
14
16
18
20
22
132
115
98
86
71
153
126
106
86
71
94
86
73
61
53
114
94
75
61
53
77
71
61
51
42
92
77
62
51
42
58
54
47
40
33
65
59
49
40
33
24
26
28
30
31
60
51
44
38
36
60
51
44
38
36
45
38
33
29
27
45
38
33
29
27
36
30
26
23
21
36
30
26
23
21
28
24
21
18
28
24
21
18
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
7.00
1.04
1.89
5.34
1.06
1.87
4.49
1.07
1.86
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.63
1.07
1.85
No. of
a
Connectors
X
b
3
DESIGN STRENGTH OF COLUMNS
3 - 79
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
X
Unequal legs
Short legs 3⁄8 in. back to back of angles
4×
×3
Size
1⁄
2
Thickness
Wt./ft
X-X AXIS
Y-Y AXIS
3⁄
8
22.2
Fy
Effective length KL (ft) with respect to indicated axis
Y
5⁄
16
17.0
1⁄
4
14.4
11.6
36
50
36
50
36
50
36
50
0
199
276
152
211
127
166
94
120
2
4
6
8
10
191
169
138
104
72
261
220
166
112
72
146
130
107
81
57
200
170
129
88
57
123
109
90
69
49
158
136
106
75
49
91
82
69
54
40
115
101
81
59
40
12
14
50
37
50
37
40
29
40
29
34
25
34
25
28
21
28
21
0
199
276
152
211
127
166
94
120
4
6
8
10
12
190
182
172
160
146
259
245
226
204
180
143
137
130
121
110
193
183
169
153
135
118
113
107
99
91
149
142
132
120
107
85
82
78
73
67
103
99
93
86
78
14
16
18
20
22
131
116
101
86
73
156
131
108
88
73
99
87
76
65
54
117
98
81
66
54
81
72
62
53
44
93
79
65
53
44
61
55
48
41
35
69
60
51
42
35
24
26
28
30
32
61
52
45
39
34
61
52
45
39
34
46
39
34
29
26
46
39
34
29
26
37
32
27
24
21
37
32
27
24
21
30
25
22
19
17
30
25
22
19
17
3/ ′′
8
No. of
a
Connectors
Design axial strength in kips (φ = 0.85)
b
3
4
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
6.50
0.864
1.96
4.97
0.879
1.94
4.18
0.887
1.93
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.38
0.896
1.92
3 - 80
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
X
Unequal legs
31⁄2×3
Size
3⁄
8
Thickness
Wt./ft
15.8
X-X AXIS
Fy
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
5⁄
16
1⁄
4
13.2
10.8
36
50
36
50
36
50
0
140
195
118
162
92
2
4
6
8
10
135
121
100
77
55
185
158
122
84
55
114
102
85
65
47
154
132
103
72
47
12
14
15
38
28
38
28
33
24
21
0
140
195
4
6
8
10
12
130
123
114
103
91
14
16
18
20
22
24
26
27
31⁄2×21⁄2
3⁄
8
1⁄
4
14.4
9.8
50
36
50
36
50
119
0
129
179
85
110
89
80
67
53
38
114
100
79
58
39
2
4
6
8
10
122
102
76
51
32
165
129
86
51
32
81
68
52
36
23
102
83
59
36
23
33
24
21
27
20
17
27
20
17
11
12
27
27
19
16
19
16
118
162
92
119
0
129
179
85
110
175
162
146
127
107
108
102
94
85
75
142
132
119
104
88
82
77
72
66
58
100
94
86
77
66
4
6
8
10
12
122
116
108
98
87
165
154
139
122
105
78
74
69
63
57
97
91
84
75
65
78
66
54
44
36
87
68
54
44
36
65
55
45
37
30
72
57
45
37
30
51
43
36
29
24
55
45
36
29
24
14
16
18
20
22
76
65
55
45
37
87
70
55
45
37
50
43
36
30
25
55
46
37
30
25
31
26
24
31
26
24
26
22
20
26
22
20
20
17
16
20
17
16
24
26
28
29
31
27
23
21
31
27
23
21
21
18
15
21
18
15
b
3
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
4.59
0.897
1.67
3.87
0.905
1.66
3.13
0.914
1.65
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.22
0.719
1.74
2.88
0.735
1.72
No. of a
Connectors
Short legs 3⁄8 in. back to back of angles
No. of
a
Connectors
Y
Design axial strength in kips (φ = 0.85)
3/ ′′
8
b
4
DESIGN STRENGTH OF COLUMNS
3 - 81
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
X
Unequal legs
3×
×21⁄2
Size
3⁄
8
Thickness
Wt./ft
13.2
X-X AXIS
Fy
36
3⁄
16
9.0
6.77
50
36
50
36
50
0 118 163
80
107
55
71
2 111 151
3 104 137
4 94 120
5 83 100
6 71 81
76
71
65
58
50
100
91
81
69
56
53
50
46
41
36
66
62
55
48
41
45
35
27
22
18
31
26
21
17
14
34
27
21
17
14
3/ ′′
8
Y
3×
×2
3⁄
8
5⁄
16
11.8
50
36
1⁄
4
10.0
3⁄
16
8.2
6.1
50
36
50
36
50
36
50
0
106 147
90
125
73
97
50
64
2
3
4
5
6
96 129
85 109
72 86
58 64
44 45
82
73
61
50
38
109
93
74
55
39
66
59
50
41
32
86
74
59
45
32
46
42
36
30
24
58
51
42
33
25
7
8
9
33
25
20
33
25
20
28
22
17
28
22
17
24
18
14
24
18
14
18
14
11
18
14
11
106 147
90
125
73
97
50
64
b
7
8
9
10
11
59
48
38
31
25
63
48
38
31
25
42
34
27
22
18
12
21
b
21
15
15
12
12
0 118 163
80
107
55
71
0
2 113 155
4 109 146
6 101 132
8 91 114
10 79 95
75
72
67
60
53
97
92
84
73
62
49
47
45
41
36
59
57
53
48
41
2
4
6
8
10
104
100
93
85
76
143
135
123
109
92
87
84
78
71
63
119
113
103
91
77
70
67
63
57
51
92
87
80
70
60
47
45
43
39
35
58
55
52
47
41
12
14
16
18
20
67
56
44
35
28
76
58
44
35
28
45
37
29
23
19
50
38
29
23
19
32
27
22
17
14
35
28
22
17
14
12
14
16
18
20
65
55
45
36
29
75
59
46
36
29
54
46
37
30
24
62
49
38
30
24
44
37
30
24
19
49
39
30
24
19
31
26
22
18
14
35
28
22
18
14
22
24
23
20
23
20
16
13
16
13
12
10
12
10
22
24
25
24
20
19
24 20
20 17
19 15
20 16
17 13
15 12
16
13
12
12
10
9
12
10
9
3
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
1⁄
4
No. of a
Connectors
Short legs 3⁄8 in. back to back of angles
No. of a
Connectors
Design axial strength in kips (φ = 0.85)
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
3.84
0.736
1.47
2.63
0.753
1.45
1.99
0.761
1.44
3.47
0.559
1.55
2.93
0.567
1.53
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.38
0.574
1.52
1.80
0.583
1.51
4
3 - 82
COLUMN DESIGN
Fy = 36 ksi
Fy = 50 ksi
COLUMNS
Double angles
Y
X
Y
Design axial strength in kips (φ = 0.85)
Unequal legs
3/ ′′
8
Short legs 3⁄8 in. back to back of angles
21⁄2×2
Size
3⁄
8
Thickness
Wt./ft
10.6
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
5⁄
16
1⁄
4
9.0
3⁄
16
7.2
5.5
36
50
36
50
36
50
36
50
0
95
131
80
111
65
91
49
63
2
3
4
5
6
86
77
66
54
42
116
99
79
60
42
73
66
56
46
36
98
84
68
51
37
60
54
46
38
30
80
69
56
43
31
45
40
35
29
23
57
50
41
32
24
7
8
9
10
31
24
19
31
24
19
27
21
16
27
21
16
23
17
14
23
17
14
18
14
11
9
18
14
11
9
0
95
131
80
111
65
91
49
63
2
4
6
8
10
92
86
78
69
58
126
116
101
84
66
77
73
66
57
47
105
97
84
69
54
62
58
53
46
38
84
77
67
55
43
45
42
38
33
28
56
52
46
39
31
12
14
16
18
20
46
36
28
22
18
49
36
28
22
18
38
29
22
17
14
39
29
22
17
14
30
23
18
14
11
31
23
18
14
11
22
17
13
10
9
23
17
13
10
9
21
16
16
13
13
No. of
a
Connectors
X
b
Y-Y AXIS
3
4
Properties of 2 angles—3⁄8 in. back to back
2
A (in )
rx (in.)
ry (in.)
3.09
0.577
1.28
2.62
0.584
1.26
2.13
0.592
1.25
aFor Y-Y axis, welded or fully tensioned bolted connectors only.
bFor number of connectors, see double angle column discussion.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.62
0.600
1.24
DESIGN STRENGTH OF COLUMNS
3 - 83
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Designation
X-X AXIS
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
Y
WT 18
150
Wt./ft
Fy
X
140
130
122.5
115
36
50
36
50
36
50
36
50
36
50
0
1350
1730
1260
1510
1150
1330
1040
1170
925
1030
10
12
14
16
18
1310
1300
1280
1260
1240
1670
1650
1620
1590
1550
1230
1210
1190
1180
1150
1470
1440
1420
1390
1360
1120
1100
1090
1070
1050
1290
1270
1250
1220
1200
1010
998
985
970
953
1140
1130
1110
1090
1070
903
893
882
869
855
998
986
972
956
939
20
22
24
26
28
1210
1180
1150
1120
1090
1510
1460
1420
1370
1320
1130
1100
1080
1050
1020
1330
1290
1250
1210
1170
1030
1010
983
957
930
1170
1140
1110
1070
1040
935
915
893
870
847
1050
1020
993
964
934
839
822
803
784
763
920
899
876
853
828
30
32
34
36
38
1060
1020
984
947
910
1260
1210
1160
1100
1040
984
951
917
883
847
1120
1080
1030
987
940
901
871
841
810
778
1000
965
926
886
847
822
796
769
742
714
903
871
838
804
770
742
719
696
673
649
802
776
748
720
692
40
872
989
812
893
746
806
686
736
624
663
0
1350
1730
1260
1510
1150
1330
1040
1170
925
1030
10
12
14
16
18
1210
1190
1160
1130
1090
1510
1470
1430
1370
1320
1120
1100
1070
1040
1010
1320
1290
1250
1210
1160
1010
990
966
938
908
1140
1120
1090
1050
1010
906
888
867
843
817
1010
985
959
930
898
803
788
770
750
728
874
857
836
812
786
20
22
24
26
28
1050
1010
962
916
868
1260
1190
1130
1060
988
972
932
891
848
804
1110
1060
1000
943
884
876
841
804
766
726
971
927
880
833
784
789
759
727
693
659
863
826
787
747
705
704
679
651
623
593
758
728
696
662
628
30
32
34
36
38
820
771
721
672
624
918
848
780
713
647
758
713
667
622
577
825
766
708
650
595
686
645
604
563
523
734
684
634
585
537
623
587
551
515
480
662
619
577
534
493
563
532
501
469
438
592
557
521
485
450
40
577
585
533
540
484
490
445
452
408
415
Properties
A (in2)
rx (in.)
ry (in.)
44.1
5.27
3.83
41.2
5.25
3.81
38.2
5.26
3.78
36.0
5.26
3.75
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
33.8
5.25
3.73
3 - 84
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
105
Wt./ft
X-X AXIS
Fy
36
97
50
91
85
80
75
67.5
36
50
36
50
36
50
36
50
36
50
36
50
0
908 1040 772
851
683
726
587
601
518
521
458
457
385
385
10
12
14
16
18
887 1010 755
878 1000 748
868 986 740
856 971 731
843 954 720
831
822
812
801
788
670
664
657
649
640
710
704
696
687
677
576
571
566
560
553
590
585
579
572
565
509
505
500
495
489
512
508
503
498
492
451
448
444
440
435
449
446
442
438
433
380
377
374
371
367
380
377
374
371
367
20
22
24
26
28
828
813
796
778
759
935
915
893
870
846
709
696
683
668
653
775
759
743
726
708
631
620
609
597
584
667
655
642
629
614
545
537
528
518
508
557
548
539
529
518
483
476
468
460
452
486
479
471
463
454
429
424
417
411
403
428
422
416
409
402
363
359
354
348
343
363
359
354
348
343
30
32
36
40
739
719
675
630
821
795
740
684
637
621
586
549
689
669
628
585
571
557
527
496
599
584
551
517
497
486
462
437
507
495
470
444
443
433
413
392
445
436
415
394
396
388
371
353
395
387
370
352
337
331
317
303
337
331
317
303
908 1040 772
851
683
726
587
601
518
521
458
457
385
385
10
12
14
16
18
716
687
654
617
578
791
756
715
670
622
607
585
559
530
499
653
627
597
563
527
534
515
494
470
444
558
538
515
488
460
457
442
425
406
385
465
450
432
412
391
397
385
371
356
339
399
387
373
357
340
344
335
323
311
297
344
334
323
310
296
268
261
253
244
234
268
261
253
244
234
20
22
24
26
28
537
494
450
407
364
572
521
469
418
367
465
431
395
360
325
489
449
409
369
330
416
387
358
327
297
430
398
366
333
301
363
340
315
291
266
368
344
319
293
268
320
301
280
260
239
321
302
281
260
239
281
265
248
231
213
281
265
248
231
213
223
211
198
185
172
223
211
198
185
172
30
32
34
36
39
323
285
254
228
195
323
285
254
228
195
291
258
230
206
176
291
258
230
206
176
268
239
213
191
164
269
239
213
191
164
242
218
194
174
150
242
218
194
174
150
218
197
177
159
137
218
197
177
159
137
196
178
161
144
124
195
178
161
144
124
158
144
131
118
102
158
144
131
118
102
41
42
43
177
169
161
177 160
169 153
161
160
153
149
142
149
142
136
130
136
130
124
124
113
113
0
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
WT 18
Properties
A (in2)
rx (in.)
ry (in.)
30.9
5.65
2.58
28.5
5.62
2.56
26.8
5.62
2.55
25.0
5.61
2.53
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
23.5
5.61
2.50
22.1
5.62
2.47
19.9
5.66
2.38
DESIGN STRENGTH OF COLUMNS
3 - 85
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
Y-Y AXIS
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
WT 16.5
120.5
Wt./ft
Y
36
50
110.5
36
50
100.5
76
70.5
65
59
36
50
36
50
36
50
36
50
0 1080 1300 964 1110 810
899
532
548
463
467
402
401
330
330
10
12
14
16
18
1050
1040
1020
1000
980
1260
1240
1210
1190
1160
935
923
909
893
875
1070
1050
1030
1010
990
788
779
767
755
741
872
860
847
831
814
521
516
510
503
495
535
530
524
516
508
453
449
444
439
433
457
453
448
442
436
394
391
387
383
378
393
390
386
382
377
324
321
318
315
311
324
321
318
315
311
20
22
24
26
28
958
933
907
880
851
1120
1090
1050
1020
975
855
834
811
787
762
965
937
908
878
846
725
708
690
672
652
795
775
753
730
706
487
478
468
458
447
500
490
480
469
458
426
419
411
402
393
429
422
414
405
396
372
366
360
353
345
371
365
359
352
345
307
303
298
293
287
307
303
298
293
287
30
32
34
36
40
821
790
759
727
662
934
892
849
806
720
737
710
682
654
598
813
779
745
710
639
631
610
588
565
520
681
656
630
603
549
436
424
411
399
373
446
433
420
407
379
384
374
364
354
332
387
377
366
356
334
338
330
321
313
295
337
329
321
312
295
282
276
269
263
249
282
276
269
263
249
0 1080 1300 964 1110 810
899
532
548
463
467
402
401
330
330
10
12
14
16
18
951
929
904
876
845
1110
1080
1050
1010
967
833
815
793
769
743
934
911
884
854
821
692
678
661
643
622
753
736
717
695
671
420
406
389
370
349
429
414
396
377
355
358
346
333
318
301
360
348
335
319
302
300
291
280
268
255
299
290
280
268
255
234
228
220
212
203
234
228
220
212
203
20
22
24
26
28
811
775
738
699
659
922
874
824
772
720
714
683
651
617
583
785
747
707
666
624
600
576
551
525
497
644
616
587
556
525
327
305
281
257
234
332
309
284
260
235
283
264
245
225
206
284
266
246
226
206
241
226
211
195
179
241
226
210
195
178
192
181
170
158
146
192
181
170
158
146
30
34
36
38
39
618
537
497
458
439
667
564
514
464
441
548
477
442
408
391
581
496
455
414
394
470
413
385
357
343
492
427
395
363
348
211
167
150
135
129
211
167
150
135
129
186
149
134
121
115
187
149
134
121
115
162
131
118
107
102
162
131
118
107
102
134
109
98
89
134
109
98
89
40
41
420
401
420 375
401 358
375 330
358 316
332
317
123
117
123
117
109
109
Properties
A (in2)
rx (in.)
ry (in.)
35.4
4.96
3.63
32.5
4.96
3.59
29.5
4.95
3.56
22.4
5.14
2.47
20.8
5.15
2.43
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
19.2
5.18
2.39
17.3
5.20
2.32
3 - 86
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
105.5
Wt./ft
Fy
36
Effective length KL (ft) with respect to indicated axis
X-X AXIS
0
50
95.5
36
50
86.5
36
66
50
36
62
50
36
58
50
36
54
50
36
49.5
50
36
50
949 1180 844 974 708 791 505 546 447 465 402 412 357 361 304 303
10
12
14
16
18
913
897
879
859
837
1130
1100
1080
1050
1010
812
799
783
765
746
932
914
894
870
845
684
673
661
647
632
761
748
733
715
696
490
484
477
468
459
529
521
513
503
492
434
429
423
416
408
452
446
439
432
423
392
387
382
376
369
401
396
391
384
377
348
344
340
335
329
352
348
343
338
332
297
294
290
286
282
296
293
290
286
281
20
22
24
26
28
813
787
759
731
701
976
938
897
855
811
724
702
678
652
626
817
787
756
724
690
615
597
578
558
537
676
654
630
606
581
449
437
426
413
400
480
467
454
439
424
399
390
380
370
359
414
404
393
382
370
361
353
345
336
326
369
361
352
343
333
323
316
309
301
293
326
319
311
304
295
277
271
266
259
253
276
271
265
259
253
30
32
34
36
40
670
639
607
575
511
767
723
678
634
547
599
571
543
515
459
656
621
586
551
482
515
493
471
448
402
555
528
501
474
421
387
373
358
344
314
409
393
377
360
327
347
335
323
311
285
358
345
332
319
292
316
306
295
284
262
322
311
300
289
266
284
276
267
257
238
287
278
269
259
240
246
239
232
224
209
246
239
232
224
209
0
Y-Y AXIS
WT 15
949 1180 844 974 708 791 505 546 447 465 402 412 357 361 304 303
10
12
14
16
18
838 1010 734 828 609 667
817 982 716 805 595 651
793 946 695 778 579 631
766 907 672 749 561 610
736 864 646 717 541 586
389
371
350
328
303
411
391
368
343
316
340
325
308
290
269
350
335
317
297
275
298
286
271
256
238
303
290
276
259
241
254
244
233
220
206
256
246
234
221
207
207
199
191
181
170
206
199
191
181
170
20
22
24
26
28
704
670
635
598
561
818
769
720
669
617
619
589
559
527
495
682
645
607
568
528
520
497
473
448
422
561
533
505
475
445
278
252
227
201
176
288
259
231
203
176
248
226
204
183
161
253
230
207
184
161
220
201
182
163
145
223
203
183
164
145
191
175
159
143
127
192
176
160
143
127
159
147
134
121
108
159
146
134
121
108
30
32
34
35
36
523
486
449
430
412
567
517
468
444
420
462
429
397
381
365
488
448
410
391
372
396
370
344
331
318
415
384
354
339
325
155
137
122
115
109
155
137
122
115
109
142
125
112
106
100
142 127 127 112 112
125 113 113 100 100
112 100 100 89 89
106 95 95 84 84
100 90 90
96
85
76
96
85
76
37
38
40
395
377
342
398 349 353 305 310 103 103
378 334 335 293 296
342 303 303 268 268
95
95
Properties
A (in2)
rx (in.)
ry (in.)
31.0
4.43
3.49
28.1
4.42
3.46
25.4
4.42
3.43
19.4
4.66
2.25
18.2
4.66
2.23
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
17.1
4.67
2.19
15.9
4.69
2.15
14.5
4.71
2.10
DESIGN STRENGTH OF COLUMNS
3 - 87
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
WT 13.5
89
Wt./ft
Fy
36
X-X AXIS
50
73
57
51
47
42
50
36
50
36
50
36
50
36
50
36
50
799 1040 725
857
617
698
453
498
358
369
308
311
251
250
10
12
14
16
18
761
745
727
707
684
978
951
921
887
850
691
676
660
641
620
810
790
767
741
712
589
577
564
549
532
663
648
631
612
591
436
428
420
410
399
477
468
458
447
434
346
341
334
328
320
356
350
344
337
329
298
294
289
284
278
301
297
292
286
280
244
241
238
234
229
243
240
236
232
228
20
22
24
26
28
660
634
606
578
549
811
770
727
683
638
598
574
549
523
496
682
650
617
583
548
514
495
474
453
431
568
544
519
493
466
388
375
362
348
334
420
405
390
373
357
312
303
293
283
273
320
310
300
290
279
271
264
256
248
240
273
266
258
250
241
224
219
213
207
201
223
218
212
206
200
30
32
34
36
38
519
489
459
430
400
594
550
506
464
423
469
442
415
388
361
513
478
443
409
376
409
387
364
342
319
439
412
385
358
332
319
304
289
274
259
339
322
304
287
269
262
251
240
229
218
268
256
244
233
221
231
222
213
204
194
233
223
214
205
195
194
187
180
173
166
193
187
180
173
165
371
40
383 335
344
298
306
244
252
206
209
185
186
159
158
799 1040 725
857
617
698
453
498
358
369
308
311
251
250
10
12
14
16
18
701
681
658
632
604
877
845
808
768
725
627
609
588
565
540
720
696
669
639
606
527
513
497
479
459
583
566
546
524
500
349
331
311
288
264
374
353
330
304
277
275
263
248
232
215
281
268
253
236
218
231
221
210
197
184
233
223
211
198
185
181
174
166
157
147
180
173
165
156
147
20
22
24
26
28
574
542
509
476
442
678
631
582
533
484
513
485
456
426
395
571
534
497
458
420
437
415
391
367
342
474
446
418
389
359
240
215
191
167
145
249
221
193
167
145
197
179
160
142
125
199
180
161
143
125
169
154
140
125
110
170
155
140
125
110
137
126
114
103
92
136
125
114
103
92
30
32
34
35
36
408
374
342
326
310
436
390
347
328
310
365
335
305
291
277
382
345
309
292
277
317
292
268
256
244
330
301
273
259
245
127
112
100
94
89
127
112
100
94
89
109
97
86
81
109
97
86
81
97
86
76
72
97
86
76
72
81
72
64
81
72
64
40
252
252 225
225
200
200
0
Y-Y AXIS
80.5
36
0
Effective length KL (ft) with respect to indicated axis
Y
Properties
A (in2)
rx (in.)
ry (in.)
26.1
3.98
3.26
23.7
3.96
3.24
21.5
3.95
3.21
16.8
4.15
2.18
15.0
4.14
2.15
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
13.8
4.16
2.12
12.4
4.18
2.07
3 - 88
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
WT 12
81
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
73
65.5
58.5
52
36
50
36
50
36
50
36
50
36
50
0
731
1020
658
864
591
726
506
580
410
450
10
12
14
16
18
687
669
648
624
598
932
898
858
815
769
618
602
583
562
538
797
769
737
702
664
556
541
524
505
484
673
652
627
599
569
477
465
451
435
418
542
526
508
487
465
389
379
369
357
344
424
413
401
387
371
20
22
24
26
28
571
542
512
481
450
720
670
619
568
518
514
488
461
433
405
624
583
541
499
457
462
439
415
391
366
537
504
471
437
403
400
380
360
339
318
442
418
392
367
341
331
316
301
285
269
355
338
320
302
283
30
32
34
36
38
419
388
358
328
299
469
421
375
335
300
377
349
322
295
269
416
376
338
301
270
341
316
291
267
244
369
336
304
273
245
297
276
255
235
215
315
290
265
241
217
252
236
220
204
188
264
246
227
209
192
40
271
271
244
244
221
221
196
196
173
175
0
731
1020
658
864
591
726
506
580
410
450
10
12
14
16
18
648
626
601
574
544
858
819
775
727
675
575
555
533
508
482
723
691
656
617
575
505
487
468
446
422
597
573
545
515
482
424
410
395
377
358
472
455
435
414
390
338
328
317
304
290
363
352
339
324
308
20
22
24
26
28
512
480
446
412
378
622
568
514
460
409
453
424
393
363
332
532
487
442
398
355
397
371
345
317
290
448
412
376
340
305
338
316
294
272
249
365
339
313
286
259
275
260
243
226
209
291
273
254
235
216
30
32
34
36
38
345
312
281
251
225
359
316
281
251
225
303
273
245
219
197
313
276
245
219
197
264
238
213
190
171
271
239
213
190
171
227
206
184
165
149
233
207
184
165
149
192
175
159
143
129
196
178
159
143
129
40
204
204
178
178
155
155
135
135
117
117
Properties
A (in2)
rx (in.)
ry (in.)
23.9
3.50
3.05
21.5
3.50
3.01
19.3
3.52
2.97
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
17.2
3.51
2.94
15.3
3.51
2.91
DESIGN STRENGTH OF COLUMNS
3 - 89
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
WT 12
47
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
Y
42
38
34
31
27.5
36
50
36
50
36
50
36
50
36
50
36
50
0
378
419
307
321
254
258
209
208
202
203
155
155
10
12
14
16
18
360
352
343
332
321
396
387
376
363
350
293
287
280
273
265
306
299
292
284
275
244
240
234
229
222
247
243
237
231
225
201
198
194
189
185
200
197
193
189
184
194
191
187
183
178
196
192
188
184
179
150
148
145
142
139
150
148
145
142
139
20
22
24
26
28
309
296
283
269
255
335
320
304
287
271
256
246
236
225
215
265
255
244
233
221
215
208
200
192
184
218
210
202
194
185
179
174
168
162
155
179
173
167
161
155
173
168
162
156
150
174
169
163
157
150
136
132
128
124
120
136
132
128
124
120
30
32
34
36
38
240
226
211
197
183
254
237
220
203
187
204
192
181
170
159
209
197
185
173
161
175
166
157
148
140
176
167
158
149
140
148
142
135
128
121
148
141
135
128
121
143
136
130
123
116
144
137
130
123
117
115
111
106
101
96
115
111
106
101
96
40
169
171
148
150
131
131
114
114
109
110
92
92
0
378
419
307
321
254
258
209
208
202
203
155
155
10
12
14
16
18
288
269
248
226
202
310
288
263
237
211
231
218
202
185
168
239
224
208
190
171
188
178
166
154
140
190
179
167
155
141
148
140
132
123
113
147
140
132
123
113
121
110
97
84
71
122
110
98
84
71
91
84
75
67
57
91
84
75
67
57
20
22
23
24
26
179
156
145
134
115
184
158
145
134
115
150
132
124
115
99
152
134
124
115
99
126
113
106
99
86
127
113
106
99
86
103
92
87
82
71
103
92
87
82
71
59
49
46
59
49
46
48
41
48
41
28
30
31
32
33
99
87
82
77
72
99
87
82
77
72
86
75
71
66
86
75
71
66
74
65
61
58
74
65
61
58
62
55
51
62
55
51
Properties
A (in2)
rx (in.)
ry (in.)
13.8
3.67
1.98
12.4
3.67
1.95
11.2
3.68
1.92
10.0
3.70
1.87
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
9.11
3.79
1.38
8.10
3.80
1.34
3 - 90
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
WT 10.5
73.5
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
66
61
55.5
50.5
36
50
36
50
36
50
36
50
36
50
0
661
918
594
825
548
757
499
637
452
524
10
12
14
16
18
610
589
565
539
510
822
782
739
691
641
547
528
507
483
457
737
701
661
618
573
505
487
466
444
420
676
643
606
566
524
459
443
424
404
382
573
547
518
486
453
416
401
384
366
346
476
457
434
410
384
20
22
24
26
28
480
449
417
385
353
589
536
484
434
385
429
401
372
343
315
526
478
431
386
341
395
368
341
315
288
481
437
394
352
311
358
334
310
285
261
418
382
347
312
279
324
303
280
258
236
357
329
301
274
247
30
32
34
36
38
322
292
262
234
210
337
296
263
234
210
286
259
233
208
186
299
263
233
208
186
262
236
212
189
170
272
239
212
189
170
237
214
192
171
154
246
217
192
171
154
214
193
173
154
139
221
195
173
154
139
40
190
190
168
168
153
153
139
139
125
125
0
661
918
594
825
548
757
499
637
452
524
10
12
14
16
18
587
566
542
515
486
778
740
697
650
601
522
503
482
458
432
689
655
617
576
532
478
461
441
419
396
626
596
562
524
485
430
415
397
377
356
526
503
476
447
415
385
372
356
339
320
434
417
397
375
352
20
22
24
26
28
456
424
392
360
328
550
498
447
397
349
405
377
348
320
291
487
441
395
351
308
371
345
319
293
267
444
402
361
321
281
334
311
287
263
239
383
349
316
283
251
300
279
258
237
216
327
301
275
249
223
30
32
34
36
38
297
267
238
213
191
305
268
238
213
191
263
237
210
188
169
269
237
210
188
169
241
216
193
172
155
246
217
193
172
155
216
194
172
154
139
220
194
172
154
139
195
175
156
139
125
199
175
156
139
125
40
173
173
153
153
140
140
125
125
113
113
Properties
A (in2)
rx (in.)
ry (in.)
21.6
3.08
2.95
19.4
3.06
2.93
17.9
3.04
2.92
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
16.3
3.03
2.90
14.9
3.01
2.89
DESIGN STRENGTH OF COLUMNS
3 - 91
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
Fy
36
X-X AXIS
Effective length KL (ft) with respect to indicated axis
0
50
41.5
36
50
36.5
36
34
50
36
31
50
36
28.5
50
36
50
25
36
22
50
36
50
419 562 373 444 297 331 261 283 219 225 203 210 165 167 127 127
6
8
10
12
14
409
400
390
378
364
543
529
511
489
466
364
356
347
336
323
430
420
407
392
374
290
284
278
270
260
322
316
307
297
286
255
251
245
239
231
276
271
264
256
247
214
211
206
201
195
221
217
212
207
201
199
196
192
187
182
206
203
199
194
188
162
160
157
153
149
164
161
158
155
151
125
123
121
119
116
125
123
121
119
116
16
18
20
22
24
349
332
315
296
277
439
412
383
353
323
310
295
279
262
245
355
335
314
291
269
250
239
227
215
202
274
260
246
231
216
222
213
203
192
182
237
227
215
203
191
189
181
174
165
157
194
186
178
169
160
176
170
163
155
147
182
175
167
159
151
145
140
134
129
123
146
141
136
130
124
113
110
106
102
98
113
110
106
102
98
26
28
30
32
34
258
239
220
201
183
293
264
236
209
185
228
210
193
177
160
247
225
203
182
162
189
176
163
150
137
200
185
169
155
140
170
159
148
137
126
178
165
153
140
128
148
139
130
121
112
151
142
132
123
114
139
131
123
115
107
143 117 118
134 111 111
125 104 105
117 98 98
108 91 92
94
90
85
81
76
94
90
85
81
76
36
38
40
165 165 145 145 125 126 115 117 104 104
148 148 130 130 113 113 105 105 95 96
134 134 117 117 102 102 95 95 87 87
71
67
63
71
67
63
0
Y-Y AXIS
WT 10.5
46.5
Wt./ft
Y
99 100
91 92
84 84
85
79
73
85
79
73
419 562 373 444 297 331 261 283 219 225 203 210 165 167 127 127
6
8
10
12
14
357
337
313
285
256
452
420
381
338
293
311
294
273
250
224
357
334
307
276
243
245
233
218
201
182
267
252
235
214
192
213
203
191
177
161
227
215
202
186
168
152
147
141
133
123
153
142
128
113
97
16
18
20
21
22
226
195
166
151
138
247
203
166
151
138
198
171
145
132
121
210
177
145
132
121
162
142
122
113
103
169
146
124
113
103
145
128
111
103
95
150 112 113
131 101 102
112 90 90
103 84 84
95 78 78
81
66
54
49
45
24
26
28
29
30
117 117 102 102
100 100 88 88
86 86 76 76
80 80 71 71
75 75 66 66
87
75
65
60
57
87
75
65
60
57
80
69
60
56
52
80
69
60
56
52
149
145
138
131
122
67
58
51
47
157 116 117
145 108 109
131 99 99
115 88 88
98 76 76
82
66
54
49
45
64
52
43
39
64
52
43
39
85
80
74
67
59
85
80
74
67
59
51
42
35
32
51
42
35
32
67
58
51
47
Properties
A
(in2)
rx (in.)
ry (in.)
13.7
3.25
1.84
12.2
3.22
1.83
10.7
3.21
1.81
10.0
3.20
1.80
9.13
3.21
1.77
8.37
3.29
1.35
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.36
3.30
1.30
6.49
3.31
1.26
3 - 92
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
WT 9
59.5
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
53
48.5
43
38
36
50
36
50
36
50
36
50
36
50
0
536
744
477
663
438
608
389
507
339
393
10
12
14
16
18
479
456
430
402
372
636
594
548
499
449
426
406
383
357
331
567
529
487
444
399
390
370
349
325
301
518
482
444
403
361
346
329
309
288
266
436
407
376
344
310
302
287
270
252
233
343
323
302
278
254
20
22
24
26
28
342
311
281
251
222
399
350
303
259
224
304
276
249
222
197
354
310
268
229
198
275
250
225
200
177
320
279
241
205
177
244
221
199
177
156
276
243
211
181
156
213
193
174
155
136
229
205
181
158
137
30
34
38
42
43
195
152
121
99
95
195
152
121
99
95
172
134
107
88
84
172
134
107
88
84
154
120
96
79
154
120
96
79
136
106
85
69
136
106
85
69
119
93
74
61
119
93
74
61
0
536
744
477
663
438
608
389
507
339
393
10
12
14
16
18
471
450
427
401
374
622
584
543
499
453
415
397
376
353
329
546
513
477
438
397
379
362
343
322
300
496
467
434
398
361
331
317
300
282
263
411
388
362
334
305
285
272
258
243
226
320
304
287
267
246
20
22
24
26
28
346
318
289
260
233
407
361
317
274
237
304
279
253
228
203
356
315
276
238
206
277
254
230
207
185
324
286
251
216
187
242
222
201
181
161
275
245
216
188
163
209
192
174
156
139
225
203
182
161
140
30
34
38
42
43
206
161
129
106
101
206
161
129
106
101
180
140
112
92
88
180
140
112
92
88
163
127
102
84
80
163
127
102
84
80
142
111
89
73
70
142
111
89
73
70
123
96
77
63
61
123
96
77
63
61
44
96
96
84
84
76
76
Properties
A (in2)
rx (in.)
ry (in.)
17.5
2.60
2.69
15.6
2.59
2.66
14.3
2.56
2.65
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
12.7
2.55
2.63
11.2
2.54
2.61
DESIGN STRENGTH OF COLUMNS
3 - 93
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
Fy
36
X-X AXIS
Effective length KL (ft) with respect to indicated axis
0
32.5
50
36
30
50
36
27.5
50
36
25
50
36
23
50
36
20
50
36
17.5
50
36
50
318 426 292 356 261 299 226 253 184 194 172 183 124 124 101 101
10
12
14
16
18
288
275
261
246
229
372
351
327
302
275
264
252
239
225
210
314
297
279
259
238
236
226
214
202
189
266
253
239
223
206
206
197
188
178
167
227
217
206
193
180
169
163
156
148
140
177
171
163
154
145
168
161
154
146
138
116
112
108
104
99
116
112
108
104
99
95
92
89
86
82
95
92
89
86
82
20
22
24
26
28
212
195
178
161
144
248
222
196
171
148
194
178
162
146
131
216
195
173
153
134
175
161
147
133
119
189
172
155
138
122
155
143
131
120
108
166
152
138
124
111
131
122
113
103
94
135 124 129
126 116 120
116 107 111
106 99 101
96 90 92
94
89
84
78
72
94
89
83
78
72
78
74
70
66
62
78
74
70
66
62
30
32
34
36
38
128 129 116 116 106 107
113 113 102 102 94 94
100 100 91 91 83 83
89 89 81 81 74 74
80 80 72 72 66 66
97
86
76
68
61
98
86
76
68
61
85
77
68
61
55
86
77
68
61
55
82
74
67
59
53
83
75
67
59
53
67
61
56
51
46
67
61
56
51
46
57
53
49
45
41
57
53
49
45
41
55
50
48
44
55
50
48
44
49
45
43
39
49
45
43
39
48
44
42
38
36
48
44
42
38
36
41
38
36
33
31
41
38
36
33
31
37
34
32
29
28
37
34
32
29
28
40
42
43
45
46
0
Y-Y AXIS
WT 9
35.5
Wt./ft
Y
72
66
63
57
72
66
63
57
65
59
57
52
65
59
57
52
60
54
52
47
60
54
52
47
318 426 292 356 261 299 226 253 184 194 172 183 124 124 101 101
10
12
14
16
18
231
207
182
157
132
279
242
204
167
133
210
188
165
142
119
238
209
179
149
120
187
168
149
129
109
204
182
158
134
111
161
146
130
113
96
20
21
22
24
26
109 109
99 99
90 90
76 76
65 65
98
89
82
69
59
98
89
82
69
59
90
82
75
63
54
90
82
75
63
54
80
73
67
57
48
80
73
67
57
48
70
64
59
50
43
70
64
59
50
43
55
51
55
51
50
47
50
47
45
45
40
40
27
28
159
153
147
140
132
60
56
60
56
173 132 137 107 111
155 121 125 92 94
136 109 111 77 78
117 96 98 62 62
98 83 84 50 50
40
37
40
37
80
71
61
51
41
80
71
61
51
41
61
54
47
40
32
61
54
47
40
32
34
31
34
31
27
27
Properties
A (in2)
rx (in.)
ry (in.)
10.4
2.74
1.70
9.55
2.72
1.69
8.82
2.71
1.69
8.10
2.71
1.67
7.33
2.70
1.65
6.77
2.77
1.29
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.88
2.76
1.27
5.15
2.79
1.22
3 - 94
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
WT 8
50
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
44.5
38.5
33.5
36
50
36
50
36
50
36
50
0
450
625
401
557
346
476
301
361
10
12
14
16
18
389
365
338
310
280
510
467
420
372
324
346
324
300
275
249
454
415
373
330
287
297
278
257
235
212
386
353
316
279
243
258
241
223
203
183
300
277
251
225
199
20
22
24
26
28
251
222
194
167
144
278
234
197
167
144
223
197
172
148
128
246
207
174
148
128
189
166
145
124
107
207
174
146
124
107
163
143
124
106
92
173
148
125
106
92
30
32
34
36
37
126
111
98
87
83
126
111
98
87
83
111
98
87
77
73
111
98
87
77
73
93
82
73
65
61
93
82
73
65
61
80
70
62
55
52
80
70
62
55
52
38
78
78
0
450
625
401
557
346
476
301
361
10
12
14
16
18
391
371
349
325
300
514
479
440
399
357
346
328
309
287
265
453
422
388
351
314
295
280
263
245
226
382
356
327
297
265
254
241
226
211
194
294
276
257
236
214
20
22
24
26
28
274
248
223
198
174
315
275
236
201
174
242
219
196
173
152
277
241
206
176
152
206
186
166
147
129
234
203
174
149
129
177
160
143
127
111
192
170
148
128
111
30
32
34
36
38
151
133
118
105
95
151
133
118
105
95
133
117
103
92
83
133
117
103
92
83
112
99
88
78
70
112
99
88
78
70
97
85
75
67
61
97
85
75
67
61
41
81
81
71
71
60
60
52
52
Properties
A (in2)
rx (in.)
ry (in.)
14.7
2.28
2.51
13.1
2.27
2.49
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
11.3
2.24
2.47
9.84
2.22
2.46
DESIGN STRENGTH OF COLUMNS
3 - 95
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
Y-Y AXIS
X-X AXIS
Fy
Effective length KL (ft) with respect to indicated axis
WT 8
28.5
Wt./ft
Y
25
22.5
20
18
15.5
13
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
256
336
223
259
184
205
141
145
122
124
93
93
66
66
6
8
10
12
14
245
236
225
212
199
316
301
283
262
240
213
205
196
185
173
245
235
223
208
193
176
170
163
154
145
195
188
179
169
157
136
132
127
121
115
140
136
130
124
117
118
114
111
106
101
120
116
112
108
102
91
88
86
83
79
90
88
85
82
79
65
63
62
60
58
65
63
62
60
58
16
18
20
22
24
184
168
152
136
121
217
193
169
147
125
160
146
133
119
105
176
159
141
125
108
135
124
114
103
92
145
133
120
107
95
108
100
92
85
77
110
102
94
86
78
95
89
82
76
69
96
90
83
76
70
75
71
67
62
57
75
71
66
62
57
55
53
50
47
44
55
53
50
47
44
26
28
30
32
34
106
92
80
70
62
107
92
80
70
62
93
80
70
61
54
93
80
70
61
54
82
72
62
55
49
83
72
62
55
49
69
62
54
48
42
70
62
54
48
42
63
56
50
44
39
63
57
50
44
39
53
48
44
39
35
53
48
44
39
35
41
38
35
32
29
41
38
35
32
29
36
38
39
40
41
56
50
47
45
56
50
47
45
49
44
41
39
49
44
41
39
43
39
37
43
39
37
38
34
32
38
34
32
35
31
30
28
35
31
30
28
31
28
27
25
31
28
27
25
27
24
23
22
21
27
24
23
22
21
0
256
336
223
259
184
205
141
145
122
124
93
93
66
66
6
8
10
12
14
216
200
181
160
138
268
243
214
182
151
185
171
155
137
119
207
190
170
148
125
153
143
130
116
101
167
155
140
123
106
116
110
102
92
82
119
112
104
94
84
95
90
84
76
68
97
91
85
77
69
70
65
58
50
42
70
64
57
50
42
47
44
40
35
30
47
44
40
35
30
16
18
20
22
116
96
78
65
120
96
78
65
100
83
67
56
103
83
67
56
87
72
59
49
89
72
59
49
72
62
52
43
73
62
52
43
60
51
43
36
60
51
43
36
34
27
34
27
25
21
25
21
24
25
26
54
50
46
54
50
46
47
43
40
47
43
40
41
38
35
41
38
35
36
34
31
36
34
31
30
28
30
28
Properties
A (in2)
rx (in.)
ry (in.)
8.38
2.41
1.60
7.37
2.40
1.59
6.63
2.39
1.57
5.89
2.37
1.57
5.28
2.41
1.52
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4.56
2.45
1.17
3.84
2.47
1.12
3 - 96
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
WT 7
66
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
60
54.5
49.5
45
36
50
36
50
36
50
36
50
36
50
0
594
825
542
752
490
680
447
621
404
561
2
4
6
8
10
588
570
542
505
461
813
779
726
658
580
536
520
493
459
418
741
710
661
597
525
484
469
444
412
374
670
641
595
536
468
442
428
405
375
340
611
584
542
487
425
399
387
366
339
307
552
528
489
439
383
12
14
16
18
20
412
361
310
261
215
497
414
335
266
215
373
326
279
234
192
448
371
299
237
192
333
289
246
205
167
397
327
261
207
167
302
262
223
185
151
360
296
236
186
151
272
236
200
166
135
324
265
211
166
135
22
24
26
27
28
178
149
127
118
110
178
149
127
118
110
158
133
113
105
98
158
133
113
105
98
138
116
99
92
85
138
116
99
92
85
125
105
89
83
125
105
89
83
111
94
80
74
111
94
80
74
0
594
825
542
752
490
680
447
621
404
561
6
8
10
12
14
578
570
559
546
531
794
778
758
734
706
526
519
509
497
483
722
708
689
667
642
475
468
459
448
436
651
638
621
601
578
432
426
418
408
396
591
579
564
546
525
389
384
376
367
357
531
520
506
490
472
16
18
20
22
24
514
496
476
455
434
675
642
607
571
533
468
451
433
414
394
614
584
551
518
484
422
407
391
373
355
553
526
497
467
436
384
370
355
339
322
502
477
451
423
395
346
333
320
305
290
451
429
405
381
355
26
28
30
32
34
411
388
365
341
318
495
457
420
383
347
373
352
331
309
288
449
414
380
346
314
337
317
298
279
260
404
373
342
311
282
305
288
270
253
235
366
337
309
281
255
275
259
243
227
211
329
303
278
253
229
36
38
40
295
273
251
312
281
253
267
247
227
282
253
229
241
222
204
253
227
205
218
201
184
228
205
185
196
180
166
205
184
166
Properties
A (in2)
rx (in.)
ry (in.)
19.4
1.73
3.76
17.7
1.71
3.74
16.0
1.68
3.73
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
14.6
1.67
3.71
13.2
1.66
3.70
DESIGN STRENGTH OF COLUMNS
3 - 97
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
WT 7
41
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
Y
37
34
30.5
26.5
24
21.5
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
367
510
334
463
306
425
274
370
239
318
216
265
183
208
4
6
8
10
12
354
339
319
294
267
486
457
419
375
327
322
307
288
265
240
440
413
378
337
293
295
281
264
243
219
403
378
346
308
267
264
252
236
217
196
352
330
302
270
235
231
221
208
193
175
303
287
265
239
211
209
200
188
174
158
254
241
224
203
181
177
170
160
149
136
200
191
179
164
148
14
16
18
20
22
238
208
179
151
126
279
232
188
152
126
213
186
159
134
111
248
205
165
134
111
194
169
144
121
100
226
186
150
121
100
173
151
128
108
89
199
165
133
108
89
157
138
119
101
85
182
153
126
102
85
141
124
107
91
76
158
134
112
92
76
122
108
93
80
67
131
114
97
81
67
24
26
28
30
31
106
90
78
68
106
90
78
68
93
79
68
59
93
79
68
59
84
72
62
54
84
72
62
54
75
64
55
48
75
64
55
48
71
61
52
45
43
71
61
52
45
43
64
54
47
41
38
64
54
47
41
38
56
48
41
36
34
56
48
41
36
34
0
367
510
334
463
306
425
274
370
239
318
216
265
183
208
8
10
12
14
16
334
320
303
285
265
447
421
391
359
324
303
290
275
258
240
405
382
355
325
294
276
265
251
235
218
369
347
322
295
267
246
236
223
210
195
320
302
281
258
233
203
189
173
156
139
256
233
208
181
154
183
170
156
140
124
215
197
177
156
135
154
144
132
119
106
171
158
144
128
112
18
20
22
24
26
244
222
201
179
159
289
254
221
188
161
221
202
182
163
144
262
231
200
171
146
201
183
165
147
130
238
209
181
154
131
179
163
147
131
116
209
184
160
137
117
121
104
87
73
63
129
105
87
73
63
108
93
78
66
56
114
94
78
66
56
93
80
68
57
49
97
82
68
57
49
28
30
31
32
34
139
121
113
106
94
139
121
113
106
94
126
110
103
97
86
126
110
103
97
86
113
99
93
87
77
113
99
93
87
77
101
88
82
77
69
101
88
82
77
69
54
47
44
41
54
47
44
41
48
42
40
48
42
40
42
37
34
42
37
34
36
40
41
84
68
65
84
68
65
76
62
59
76
62
59
69
56
53
69
56
53
61
50
61
50
Properties
A
(in2)
rx (in.)
ry (in.)
12.0
1.85
2.48
10.9
1.82
2.48
9.99
1.81
2.46
8.96
1.80
2.45
7.81
1.88
1.92
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
7.07
1.87
1.91
6.31
1.86
1.89
3 - 98
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
WT 7
19
Wt./ft
X-X AXIS
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
Fy
17
15
13
11
36
50
36
50
36
50
36
50
36
50
0
159
180
131
142
109
114
87
88
62
62
2
4
6
8
10
158
155
150
143
134
178
174
168
159
148
130
128
124
119
112
141
138
134
127
120
109
107
104
100
95
114
112
108
104
98
87
85
83
80
77
88
86
84
81
78
62
61
60
58
56
62
61
60
58
56
12
14
16
18
20
125
114
103
92
81
136
123
110
97
83
105
96
88
79
70
111
102
92
82
72
89
83
76
69
62
92
85
78
70
63
73
68
63
58
53
73
69
64
58
53
53
51
48
44
41
53
51
48
44
41
22
24
26
28
30
70
60
51
44
38
71
60
51
44
38
62
53
46
39
34
63
54
46
39
34
55
48
42
36
31
55
48
42
36
31
48
42
37
33
28
48
43
38
33
28
38
34
31
28
24
38
34
31
28
24
32
34
35
34
30
34
30
30
27
30
27
27
24
27
24
25
22
21
25
22
21
22
19
18
22
19
18
0
159
180
131
142
109
114
87
88
62
62
6
8
10
12
14
132
123
111
99
86
146
134
120
105
89
108
101
92
82
72
115
107
97
86
74
86
81
74
67
59
89
83
76
68
60
65
58
50
41
32
66
58
50
41
32
45
41
35
30
24
45
41
35
30
24
16
17
18
20
22
72
66
60
49
40
74
66
60
49
40
61
56
51
42
35
63
57
52
42
35
50
46
42
35
29
51
47
42
35
29
25
22
20
25
22
20
19
17
19
17
24
25
34
31
34
31
30
27
30
27
25
25
Properties
A (in2)
rx (in.)
ry (in.)
5.58
2.04
1.55
5.00
2.04
1.53
4.42
2.07
1.49
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.85
2.12
1.08
3.25
2.14
1.04
DESIGN STRENGTH OF COLUMNS
3 - 99
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Designation
X-X AXIS
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
Y
WT 6
29
Wt./ft
Fy
X
26.6
25
22.5
20
36
50
36
50
36
50
36
50
36
50
0
261
362
238
331
225
312
202
280
180
221
2
4
6
8
10
257
247
231
210
186
355
336
306
268
227
235
226
211
192
171
325
307
280
246
208
222
214
202
186
167
307
292
269
240
207
200
193
181
167
149
276
262
241
214
184
178
172
161
148
133
218
208
193
174
152
12
14
16
18
20
160
135
110
88
71
185
145
111
88
71
147
124
102
81
66
170
134
103
81
66
147
126
105
86
70
173
139
109
86
70
131
112
93
75
61
153
123
96
75
61
116
99
82
66
54
129
106
84
66
54
22
24
25
26
59
49
45
59
49
45
54
46
42
54
46
42
58
48
45
41
58
48
45
41
51
42
39
36
51
42
39
36
44
37
34
32
44
37
34
32
0
261
362
238
331
225
312
202
280
180
221
6
8
10
12
14
246
238
228
216
203
333
318
300
279
257
223
216
206
196
184
301
287
271
252
231
205
194
181
166
150
274
255
232
206
179
183
174
162
148
134
244
227
206
183
159
162
154
143
131
118
194
182
167
150
132
16
18
20
22
24
189
175
160
144
129
233
208
184
160
137
171
157
144
130
116
209
187
164
143
122
134
117
101
86
72
152
127
103
86
72
119
104
89
75
63
135
112
91
75
63
105
92
79
66
56
114
97
80
66
56
26
28
30
32
34
115
101
88
77
69
117
101
88
77
69
103
90
78
69
61
104
90
78
69
61
61
53
46
41
61
53
46
41
54
47
41
36
54
47
41
36
48
41
36
32
48
41
36
32
36
38
41
61
55
47
61
55
47
54
49
42
54
49
42
Properties
A
(in2)
rx (in.)
ry (in.)
8.52
1.50
2.51
7.78
1.51
2.48
7.34
1.60
1.96
6.61
1.58
1.94
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5.89
1.57
1.93
3 - 100
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
17.5
Wt./ft
X-X AXIS
Fy
15
13
11
9.5
8
7
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
158
188
120
132
90
92
88
98
68
71
53
54
40
40
2
4
6
8
10
157
152
145
135
124
186
179
169
156
140
119
116
111
104
96
131
127
121
113
104
89
87
84
80
74
91
89
86
81
76
88
86
83
78
73
97
95
91
86
80
68
66
64
61
58
70
69
67
63
60
53
52
51
48
46
54
53
51
49
46
40
39
38
37
35
40
39
38
37
35
12
14
16
18
20
111
98
85
72
59
124
106
89
73
59
87
78
68
59
50
93
82
71
60
50
68
62
55
48
42
70
63
56
49
42
68
61
55
48
42
73
65
58
50
43
54
49
44
40
35
55
50
45
40
35
43
40
36
33
29
43
40
36
33
29
33
31
29
26
24
33
31
29
26
24
22
24
26
28
29
49
41
35
30
28
49
41
35
30
28
41
35
30
25
24
41
35
30
25
24
36
30
26
22
21
36
30
26
22
21
36
30
26
22
21
36
30
26
22
21
30
26
22
19
18
30
26
22
19
18
26
22
19
16
15
26
22
19
16
15
21
19
17
14
14
21
19
17
14
14
19
18
19
18
17
16
17
16
14
13
13
14
13
13
13
12
11
13
12
11
30
31
32
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
WT 6
0
158
188
120
132
90
92
88
98
68
71
53
54
40
40
2
4
6
8
10
147
142
134
123
110
172
165
154
139
123
109
106
101
93
85
119
115
109
100
90
81
79
75
71
65
83
80
77
72
66
73
67
57
45
33
80
72
60
46
33
54
49
43
34
26
55
51
44
35
26
37
34
30
24
18
37
34
30
25
18
26
25
22
19
15
26
25
22
19
15
12
13
14
16
18
96
89
82
68
55
105
95
87
69
55
75
70
65
55
45
79
73
67
56
45
59
55
52
45
38
59
56
52
45
38
23
20
17
23
20
17
18
16
18
16
13
13
11
11
20
22
24
25
45
37
31
29
45
37
31
29
37
31
26
24
37
31
26
24
31
26
22
20
31
26
22
20
Properties
A
(in2)
rx (in.)
ry (in.)
5.17
1.76
1.54
4.40
1.75
1.52
3.82
1.75
1.51
3.24
1.90
0.847
2.79
1.90
0.822
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.36
1.92
0.773
2.08
1.92
0.753
DESIGN STRENGTH OF COLUMNS
3 - 101
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
WT 5
22.5
Wt./ft
19.5
16.5
15
13
11
36
50
36
50
36
50
36
50
36
50
36
50
0
203
282
175
244
148
206
135
188
117
146
99
115
2
4
6
8
10
199
187
170
148
124
274
253
220
182
142
172
162
147
128
107
237
218
190
157
123
146
137
125
109
92
201
185
162
135
106
133
128
119
107
94
184
173
157
136
114
115
110
102
92
81
144
136
124
109
92
98
94
87
79
69
113
108
99
88
76
12
14
16
18
20
100
77
59
47
38
105
77
59
47
38
86
67
51
40
33
91
67
51
40
33
75
58
45
35
29
79
58
45
35
29
80
67
54
42
34
91
70
54
42
34
69
57
46
36
29
76
60
46
36
29
59
49
40
32
26
64
51
40
32
26
26
26
31
28
24
31
28
24
27
24
20
27
24
20
23
21
18
23
21
18
21
22
24
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
Y
0
203
282
175
244
148
206
135
188
117
146
99
115
2
4
6
8
10
199
195
188
178
167
274
266
253
235
214
171
167
161
153
143
235
227
216
201
183
143
140
134
127
119
194
188
179
166
151
128
122
113
101
88
174
163
147
126
104
109
104
96
86
75
134
126
115
100
84
89
85
78
70
61
101
96
88
78
66
12
14
16
18
20
153
139
125
110
95
191
167
143
120
99
131
119
106
93
80
163
142
121
101
83
109
98
87
76
66
134
116
99
82
67
74
60
47
38
30
82
62
47
38
30
63
51
40
32
26
68
52
40
32
26
51
41
32
26
21
54
42
32
26
21
22
24
26
28
30
81
69
59
50
44
82
69
59
50
44
68
57
49
42
37
68
57
49
42
37
55
47
40
34
30
55
47
40
34
30
25
25
21
21
17
17
32
33
39
36
39
36
32
30
32
30
26
26
Properties
A (in2)
rx (in.)
ry (in.)
6.63
1.24
2.01
5.73
1.24
1.98
4.85
1.26
1.94
4.42
1.45
1.37
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3.81
1.44
1.36
3.24
1.46
1.33
3 - 102
COLUMN DESIGN
Fy = 36 ksi
Y
Fy = 50 ksi
X
COLUMNS
Structural tees
cut from W shapes
X
Design axial strength in kips (φ = 0.85)
Y
Designation
WT 5
9.5
Wt./ft
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
8.5
7.5
6
36
50
36
50
36
50
36
50
0
86
104
77
90
66
76
43
45
2
4
6
8
10
85
82
77
70
62
103
98
91
81
71
76
73
68
63
56
88
85
79
71
62
65
63
59
54
49
75
72
67
61
54
43
41
39
37
34
44
43
41
38
35
12
14
16
18
20
54
46
38
30
25
60
49
39
30
25
49
42
34
28
23
53
44
35
28
23
43
37
31
25
20
46
39
31
25
20
30
27
23
19
16
31
27
23
20
16
22
24
25
26
20
17
16
20
17
16
19
16
14
13
19
16
14
13
17
14
13
12
17
14
13
12
13
11
10
10
13
11
10
10
0
86
104
77
90
66
76
43
45
2
4
6
8
10
74
67
56
43
31
87
77
62
46
31
62
56
47
36
25
70
62
51
37
25
49
45
37
29
20
54
48
40
29
20
30
28
24
19
14
30
28
24
20
14
12
13
14
22
18
16
22
18
16
18
15
13
18
15
13
14
12
14
12
10
9
10
9
Properties
A (in2)
rx (in.)
ry (in.)
2.81
1.54
0.874
2.50
1.56
0.844
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.21
1.57
0.810
1.77
1.57
0.785
DESIGN STRENGTH OF COLUMNS
3 - 103
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Structural tees
cut from W shapes
X
X
Design axial strength in kips (φ = 0.85)
Designation
WT 4
14
Wt./ft
12
10.5
9
7.5
6.5
5
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
126
175
108
150
94
131
80
112
68
94
59
82
41
46
2
3
4
5
6
122
118
112
105
96
168
160
148
135
121
105
101
96
90
82
144
137
127
116
103
92
89
86
81
76
127
121
114
106
97
79
76
73
70
65
108
104
98
91
83
67
65
63
60
57
92
89
84
79
73
58
56
54
52
49
79
77
73
69
64
41
40
38
37
35
45
44
42
40
38
8
10
12
14
16
78
60
43
32
24
90
62
43
32
24
67
51
36
27
20
77
52
36
27
20
64
52
39
29
22
76
57
40
29
22
55
45
35
26
20
67
50
35
26
20
49
41
33
25
19
60
47
34
25
19
43
36
29
22
17
52
41
30
22
17
30
26
21
16
12
33
27
21
16
12
18
18
16
14
16
14
15
14
12
15
14
12
13
12
11
13
12
11
10
9
8
10
9
8
18
19
20
Y-Y AXIS
Effective length KL (ft) with respect to indicated axis
X-X AXIS
Fy
Y
0
126
175
108
150
94
131
80
112
68
94
59
82
41
46
2
4
6
8
10
123
119
112
104
93
169
161
149
133
116
105
101
96
88
80
143
137
127
113
98
89
85
77
68
57
121
113
99
83
66
75
70
64
56
47
100
93
82
68
54
60
54
45
35
25
79
68
53
37
25
49
44
36
28
19
63
55
43
29
19
33
30
25
20
15
35
32
27
21
15
12
14
16
18
20
82
71
60
49
40
97
79
62
49
40
70
60
51
42
34
83
67
53
42
34
47
37
28
22
18
49
37
28
22
18
38
30
23
18
15
40
30
23
18
15
17
13
17
13
14
10
14
10
10
8
10
8
21
22
24
26
27
36
33
28
24
22
36
33
28
24
22
31
28
24
20
31
28
24
20
16
16
Properties
A
(in2)
rx (in.)
ry (in.)
4.12
1.01
1.62
3.54
.999
1.61
3.08
1.12
1.26
2.63
1.14
1.23
2.22
1.22
0.876
Note: Heavy line indicates Kl / r of 200.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.92
1.23
0.843
1.48
1.20
0.841
3 - 104
COLUMN DESIGN
Single-Angle Struts
Design strengths of single-angle struts were formerly not tabulated in this Manual
because of the difficulty in loading such struts concentrically. Concentric loading can be
accomplished by milling the ends of an angle and loading it through bearing plates.
However, in common practice, the eccentricity of loading is relatively large, and its
neglect in design may lead to an under-designed member.
The design of single-angle struts is governed by the AISC Specification for Load and
Resistance Factor Design of Single-Angle Members, which is reproduced in Part 6 of this
Manual.
The following example illustrates the design procedure for an equal-leg angle loaded
eccentrically. The design strengths for concentric loading, tabulated below, are useful in
solving the interaction equations for combined axial force and bending. The tables below
are based on Zureick (1993), revised to conform with the AISC Single-Angle Specification (LRFD).
EXAMPLE 3-8
An angle 2×2×1⁄4 is loaded by a gusset plate attached to one leg with
an eccentricity of 0.8 in. from the centroid, as shown in Figure 3-3.
Determine the factored compressive load Pu which may be applied. The
effective length KL is 4.0 ft.
Given:
A = 0.938 in.2
rz = 0.391 in.
Ix = Iy = 0.348 in.4
3
84
′
7′
′′
7
.2
0
0.
Z
Pn
W
0.8′′
0.592 ′′
37
′′
α
8
0.
W
Z
′
4′
41
1.
Fig. 3-3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 105
α = 45°
Fy = 50 ksi
Solution:
Determine the properties for the principal axes Z-Z and W-W as
follows:
Iz = Arz2 = 0.938(0.391)2 = 0.143 in.2
Iw + Iz = Ix + Iy
Iw = 0.348 + 0.348 − 0.143 = 0.552 in.4
rw
=
 √
√

Iw
=
A
0.552
= 0.767 in.
0.938
From the tables which follow, the design compressive strength φcPn =
14 kips for KL = 4 ft.
For combined axial compression and bending, the latter is taken about
the principal axes in accordance with the Single-Angle LRFD Specification (Section 6).
For equal leg angles—
Major principal axis (W-W) bending (Section 5.3.1):
0.46Eb2t 2
l
0.46(29,000 ksi)(2 in.)2(0.25 in.)2
= 1.0 ×
48 in.
= 69.5 k-in.
Iw
0.552 in.4
My = Fy Sw = Fy = 50 ksi ×
cw
1.414 in.
= 19.5 k-in.
Mob = Cb
Since Mob > My (Section 5.1.3),
Mnw = [1.58 − 0.83 
√
My / Mob ] My ≤ 1.25My
= [1.58 − 0.83 
√
19.5 / 69.5 ] My = 1.14My
= 1.14 × 19.5 k-in.
= 22 k-in.
According to Section 5.1.1,
(= 2 in. / 0.25 in. = 8) < 0.382 √

E /Fy
(= 0.382 √

29,000 / 50
 = 9.2),
Mnw ≤ 1.25Fy Sc = 1.25Fy Sw = 1.25My
for b / t
This is satisfied since Mnw = 1.14My.
Minor principal axis (Z-Z) bending (Section 5.3.1):
With the leg tips of the angle in tension and the angle corner in
compression
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 106
COLUMN DESIGN
Mnz = 1.25My = 1.25Fy Sz = 1.25Fy
= 1.25 × 50 ksi ×
Iz
cz
0.143 in.4
0.837 in.
= 11 k-in.
Assuming
Pu
≥ 0.2, Interaction Equation 6-1a governs.
φcPn
Muz  
 Pu 8  Muw
 φ P + 9  φ M + φ M   ≤ 1.0
b nz  
 b nw
 c n
According to Section 6.1.1, for flexural compression Mu shall be
multiplied by B1 (Equation 6-2).
Major principal axis (W-W) bending:
Kl / rw = 1.0 × 48 / 0.767 = 62.2
From LRFD Specification Table 8, Pe / Ag = 73.1
Pe1w = 73.1(0.938) = 68.6 kips
B1w =
Cm
0.85
=
< 1. Use B1w = 1.0.
1 − Pu / Pe1w 1 − Pu / 68.6
Minor principal axis (Z-Z) bending:
Kl / rw = 1.0 × 48 / 0.391 = 122.8
From LRFD Specification Table 8, Pe / Ag = 19.0
Pe1z = 19.0(0.938) = 17.8 kips
B1z =
Cm
0.85
=
1 − Pu / Pe1z 1 − Pu / 17.8
Conservatively adding the maximum axial and flexural terms, Equation 6-1a becomes
Pu ×0.277 in.
Pu
8  Pu ×0.843 in. × 1.0
0.85 
+ 
+
 ≤ 1.0
14 kips 9  0.9×22 kip−in.
0.9×11 kip−in. 1−Pu / 17.8 
Pu = 7 kips
Checking
Pu
7 kips
=
= 0.5 > 0.2 o.k.
14
kips
φcPn
A less conservative approach would have involved applying the interaction equation separately at the corner and the two leg tips of the
angle, with the proper signs (+ or −) for compression and tension.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 107
Fy = 36 ksi
z
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
Design axial strength in kips (φ = 0.90)
x
w
Y z
8×
×6
Size
Thickness
1
7⁄
8
3⁄
4
5⁄
8
9⁄
16
1⁄
2
7⁄
16
Wt./ft
44.2
39.1
33.8
28.5
25.7
23.0
20.2
Effective length KL (ft)
Fy
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
421
585
373
518
322
447
270
352
235
303
199
253
163
203
1
2
3
4
5
406
398
393
384
371
555
541
531
515
490
355
347
342
336
325
484
468
460
448
429
301
292
288
284
277
408
391
383
375
363
246
235
231
228
224
311
294
287
282
276
210
199
195
193
190
262
245
239
235
230
174
163
160
158
156
213
197
192
188
185
138
128
125
123
122
166
151
146
144
141
6
7
8
9
10
353
333
311
287
263
458
422
383
344
305
311
293
274
253
232
402
371
338
303
268
266
252
236
219
201
343
319
291
262
233
217
208
195
182
167
265
250
231
210
189
186
179
170
159
148
224
214
200
184
167
153
149
143
135
126
181
175
166
155
142
120
118
115
110
104
139
136
131
124
116
11
12
13
14
15
239
215
192
169
147
266
230
196
169
147
211
190
169
149
130
235
203
173
149
130
183
165
147
130
114
204
177
151
130
114
152
137
123
109
95
167
146
125
109
95
135
123
111
99
87
149
131
114
99
87
117
107
96
87
77
128
114
101
88
77
97
90
82
75
67
107
97
87
77
67
16
17
18
19
20
130
115
103
92
83
130
115
103
92
83
115
102
91
81
74
115
102
91
81
74
100
89
79
71
64
100
89
79
71
64
84
74
66
60
54
84
74
66
60
54
77
68
61
55
49
77
68
61
55
49
68
60
54
49
44
68
60
54
49
44
60
53
48
43
39
60
53
48
43
39
21
76
76
67
67
58
58
49
49
45
45
40
40
35
35
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 108
COLUMN DESIGN
z
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
x
Design axial strength in kips (φ = 0.90)
w
Y z
8×
×4
Size
Thickness
Wt./ft
37.4
Fy
Effective length KL (ft)
7⁄
8
1
3⁄
4
33.1
5⁄
8
28.7
24.2
1⁄
2
21.9
7⁄
16
19.6
17.2
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
356
495
315
438
273
380
230
299
200
258
170
216
139
174
1
2
3
4
5
342
331
315
293
267
468
446
417
378
332
300
289
275
257
234
408
387
363
330
290
256
245
235
220
201
346
326
307
280
248
209
198
190
179
165
264
246
233
216
194
179
169
162
154
142
223
207
197
184
167
149
139
134
128
119
182
168
160
150
138
118
109
105
101
95
142
128
122
116
108
6
7
8
9
10
238
208
177
148
121
283
234
187
149
121
209
183
156
131
107
248
205
164
131
107
180
157
135
113
92
212
176
141
113
92
148
130
112
94
77
169
142
117
94
77
129
114
99
84
70
146
125
104
84
70
109
98
86
73
61
123
107
90
74
61
88
80
71
62
53
98
87
75
63
53
11
12
13
14
100
85
72
62
100
85
72
62
89
75
64
55
89
75
64
55
77
65
56
48
77
65
56
48
65
55
47
41
65
55
47
41
58
49
42
37
58
49
42
37
52
44
38
33
52
44
38
33
45
38
33
29
45
38
33
29
7×
×4
Size
3⁄
4
Thickness
Wt./ft
5⁄
8
26.2
Fy
Effective length KL (ft)
9⁄
16
1⁄
2
22.1
7⁄
16
17.9
3⁄
8
15.7
13.6
36
50
36
50
36
50
36
50
36
50
0
249
346
210
288
164
212
136
173
108
134
1
2
3
4
5
236
228
219
205
188
320
306
289
264
233
194
187
180
170
156
258
245
233
215
191
146
139
134
128
119
182
171
164
154
140
118
111
107
103
97
144
133
128
122
113
90
85
82
79
76
107
99
95
91
86
6
7
8
9
10
168
147
126
106
87
200
166
134
107
87
140
123
106
89
73
165
138
113
90
73
108
96
84
71
59
124
106
89
72
59
89
80
71
61
51
101
88
75
62
51
70
64
57
50
43
79
70
61
52
43
11
12
13
14
72
61
52
45
72
61
52
45
61
52
44
38
61
52
44
38
49
42
36
31
49
42
36
31
43
37
31
27
43
37
31
27
37
31
27
23
37
31
27
23
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 109
Fy = 36 ksi
z
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
Design axial strength in kips (φ = 0.90)
Wt./ft
7⁄
8
3⁄
4
27.2
Fy
Effective length KL (ft)
Y z
6×
×4
Size
Thickness
36
5⁄
8
23.6
50
36
9⁄
16
20.0
50
36
1⁄
2
18.1
50
36
7⁄
16
16.2
50
36
3⁄
8
14.3
50
36
5⁄
16
10.3
12.3
50
36
50
36
50
0
259 359 225 312 190 264 172 239 154 205 132 171 107 136
81
100
1
2
3
4
5
250
244
233
217
198
343
331
310
282
248
91 111
87 105
85 102
82 97
78 91
66
63
61
59
57
78
73
70
68
65
6
7
8
9
10
177
155
133
111
91
212 154 184 129 155 117 139 104 121
176 135 153 113 129 102 116 91 102
142 115 124 98 105 88 94 79 84
112 97 98 82 83 74 75 67 67
91 80 80 67 67 61 61 55 55
89 102
79 87
68 73
58 59
48 48
72
65
57
49
41
82
72
61
50
41
54
50
45
39
34
61
55
48
41
34
11
12
13
14
75
63
54
47
40
34
29
25
34
29
25
22
34
29
25
22
29
24
21
18
29
24
21
18
75
63
54
47
215
210
201
188
172
293
284
268
244
215
66
55
47
41
66
55
47
41
178
174
168
157
144
56
47
40
35
241
233
222
203
180
56
47
40
35
159
155
150
141
130
51
43
37
32
214
206
197
182
162
139
135
131
125
115
51
43
37
32
46
38
33
28
180
172
166
155
139
46
38
33
28
116
112
109
105
98
145
138
133
126
116
40
34
29
25
6×
×31⁄2
Size
1⁄
2
Thickness
Wt./ft
3⁄
8
15.3
Fy
Effective length KL (ft)
x
w
5⁄
16
11.7
9.8
36
50
36
50
36
50
0
146
195
101
128
77
95
1
2
3
4
5
132
127
121
112
100
171
162
152
137
118
86
82
79
75
69
105
99
94
88
79
63
59
57
55
51
74
69
66
63
58
6
7
8
9
10
87
74
60
48
39
98
78
61
48
39
61
53
44
36
30
68
56
45
36
30
47
41
36
30
25
51
44
37
30
25
11
12
33
28
33
28
25
21
25
21
21
18
21
18
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 110
COLUMN DESIGN
z
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
x
Design axial strength in kips (φ = 0.90)
w
Y z
5×
×31⁄2
Size
3⁄
4
Thickness
Wt./ft
19.8
Fy
Effective length KL (ft)
5⁄
8
1⁄
2
16.8
3⁄
8
13.6
10.4
1⁄
4
8.7
7.0
36
50
36
50
36
50
36
50
36
50
36
50
0
188
261
159
221
130
180
97
126
76
96
54
66
1
2
3
4
5
182
176
165
150
133
249
238
218
192
162
152
148
139
127
113
207
199
183
162
137
120
117
112
103
91
162
156
146
130
111
85
82
80
75
68
107
102
98
90
79
64
61
60
57
53
77
74
71
67
61
43
41
40
38
36
49
47
45
44
41
6
7
8
9
10
115
96
79
63
51
132
103
79
63
51
97
82
67
53
43
112
88
67
53
43
79
67
55
44
35
90
71
55
44
35
59
50
42
33
27
66
54
42
33
27
47
41
34
28
23
52
44
35
28
23
34
30
26
22
18
37
32
27
22
18
11
12
42
35
42
35
36
30
36
30
29
25
29
25
23
19
23
19
19
16
19
16
15
13
15
13
5×
×3
Size
1⁄
2
Thickness
Wt./ft
7⁄
16
12.8
Fy
Effective length KL (ft)
5⁄
16
3⁄
8
11.3
5⁄
16
9.8
1⁄
4
8.2
6.6
36
50
36
50
36
50
36
50
36
50
0
122
169
107
146
91
118
71
90
51
62
1
2
3
4
5
112
108
100
88
75
151
143
128
108
87
97
93
87
77
66
127
120
109
93
76
80
76
72
65
56
100
94
87
76
63
60
57
54
50
44
72
68
64
58
49
40
38
36
34
31
46
44
42
39
34
6
7
8
9
10
62
49
38
30
24
66
49
38
30
24
54
43
33
27
22
58
43
33
27
22
46
37
29
23
19
49
37
29
23
19
37
30
24
19
16
40
31
24
19
16
27
23
19
15
13
29
24
19
15
13
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 111
Fy = 36 ksi
z
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
Design axial strength in kips (φ = 0.90)
1⁄
Thickness
Wt./ft
3⁄
8
2
11.9
Fy
Effective length
KL (ft)
Y z
4×
×31⁄2
Size
5⁄
16
9.1
1⁄
4
7.7
6.2
36
50
36
50
36
50
36
50
0
113
158
87
120
73
95
53
68
1
2
3
4
5
107
105
99
90
79
146
142
131
114
95
78
77
75
68
60
104
102
98
87
73
63
61
60
57
51
79
76
74
69
59
43
42
42
41
38
52
50
49
48
44
6
7
8
9
10
67
56
45
35
29
76
58
45
35
29
51
43
35
27
22
58
45
34
27
22
43
36
29
23
19
48
38
29
23
19
33
28
23
19
15
37
30
24
19
15
11
12
24
20
24
20
18
15
18
15
15
13
15
13
13
11
13
11
4×
×3
Size
5⁄
8
Thickness
Wt./ft
1⁄
2
13.6
Fy
Effective length
KL (ft)
x
w
7⁄
16
11.1
3⁄
8
9.8
5⁄
16
8.5
1⁄
4
7.2
5.8
36
50
36
50
36
50
36
50
36
50
36
50
0
129
179
105
146
93
129
80
112
67
88
50
63
1
2
3
4
5
124
119
108
95
81
170
160
141
118
93
100
96
88
78
66
136
129
114
96
76
87
84
78
68
58
117
112
101
84
67
73
71
66
59
50
98
94
86
73
58
59
57
55
49
42
74
71
67
58
47
41
40
39
36
32
50
48
46
42
36
6
7
8
9
10
66
52
39
31
25
70
51
39
31
25
54
42
32
26
21
57
42
32
26
21
47
37
29
23
18
51
37
29
23
18
41
32
25
20
16
44
32
25
20
16
35
27
21
17
14
37
27
21
17
14
27
22
17
14
11
29
22
17
14
11
31⁄2×3
Size
Thickness
1⁄
2
3⁄
8
5⁄
16
1⁄
4
Wt./ft
10.2
7.9
6.6
5.4
Effective length
KL (ft)
Fy
36
50
36
50
36
50
36
0
97
135
75
104
63
86
49
63
1
2
3
4
5
93
89
81
71
59
127
120
105
87
68
69
67
62
54
46
93
90
81
67
53
56
55
52
46
38
73
71
66
56
44
41
40
39
36
30
51
49
48
42
34
6
7
8
9
10
48
37
28
22
18
50
37
28
22
18
37
29
22
17
14
39
29
22
17
14
31
24
19
15
12
33
24
19
15
12
25
20
15
12
10
27
20
15
12
10
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
50
3 - 112
COLUMN DESIGN
z
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
x
Design axial strength in kips (φ = 0.90)
w
Y z
31⁄2×21⁄2
Size
1⁄
2
Thickness
3⁄
8
9.4
Wt./ft
Effective length
KL (ft)
Fy
1⁄
4
7.2
4.9
36
50
36
50
36
50
0
89
124
68
95
45
58
1
2
3
4
5
6
7
8
9
85
79
70
58
46
116
105
88
68
49
34
25
19
63
60
53
44
35
26
19
15
85
79
67
52
38
26
19
15
38
37
34
29
24
18
13
10
8
47
45
41
33
25
18
13
10
8
34
25
19
3×
×21⁄2
Size
Thickness
1⁄
2
3⁄
8
5⁄
16
1⁄
4
3⁄
16
Wt./ft
8.5
6.6
5.6
4.5
3.39
Effective length
KL (ft)
Fy
36
50
36
50
36
50
36
50
36
50
0
81
113
62
86
52
73
42
57
29
37
1
2
3
4
5
78
72
63
52
40
107
96
79
60
42
58
55
48
40
31
79
73
61
46
33
48
46
41
34
26
65
61
51
39
28
37
36
33
27
21
48
46
40
31
23
24
23
22
19
16
29
28
26
22
17
6
7
8
29
22
17
29
22
17
23
17
13
23
17
13
19
14
11
19
14
11
16
12
9
16
12
9
12
9
7
12
9
7
3×
×2
Size
1⁄
2
Thickness
7.7
Wt./ft
Fy
Effective length
KL (ft)
3⁄
8
5⁄
16
5.9
5.0
3⁄
16
4.1
3.07
36
50
36
50
36
50
36
50
36
50
0
1
2
3
4
5
73
69
61
50
37
26
101
94
80
60
40
26
56
52
47
38
29
20
78
71
61
46
31
20
47
43
39
32
24
17
66
58
51
39
26
17
39
34
31
26
20
14
51
43
39
30
21
14
27
22
21
18
14
10
34
27
25
21
15
10
6
7
18
13
18
13
14
10
14
10
12
9
12
9
10
7
10
7
7
5
7
5
21⁄2×2
Size
3⁄
8
Thickness
5⁄
16
5.3
Wt./ft
Fy
Effective length
KL (ft)
1⁄
4
0
1
2
3
4
5
6
7
1⁄
4
4.5
3⁄
16
3.62
2.75
36
50
36
50
36
50
36
50
50
48
42
34
25
17
12
9
70
65
55
41
27
17
12
9
42
40
36
29
21
15
10
7
59
54
46
34
23
15
10
7
34
31
29
23
17
12
8
6
48
42
37
28
18
12
8
6
26
22
21
17
13
9
6
5
33
27
25
20
14
9
6
5
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 113
Fy = 36 ksi
z
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
Design axial strength in kips (φ = 0.90)
Y z
8×
×8
Size
11⁄8
Thickness
Wt./ft
7⁄
8
1
56.9
Fy
Effective length KL (ft)
x
w
51.0
3⁄
4
45.0
5⁄
8
38.9
9⁄
16
32.7
1⁄
2
29.6
26.4
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
541
752
486
675
428
594
369
513
310
405
270
348
229
291
6
7
8
9
10
484
465
444
421
397
643
608
570
530
488
435
417
398
378
356
578
546
512
476
438
383
368
351
334
315
510
482
452
421
388
320
318
304
289
273
420
417
392
365
337
254
252
251
243
230
311
309
306
294
273
213
212
210
209
202
256
255
253
250
240
173
172
171
170
168
203
202
201
199
197
11
12
13
14
15
372
346
320
294
269
446
404
363
323
283
334
311
288
264
242
401
363
326
290
255
295
275
255
234
215
355
322
289
258
227
256
239
221
204
187
308
280
252
225
198
215
201
186
172
157
251
230
208
187
167
191
178
166
154
141
222
204
186
169
151
165
155
144
134
124
191
177
162
148
133
16
17
18
19
20
244
221
197
177
159
249
221
197
177
159
219
198
177
159
143
224
198
177
159
143
195
176
158
141
128
199
177
158
141
128
170
154
138
124
112
174
154
138
124
112
143
130
116
104
94
147
130
116
104
94
129
118
107
95
86
134
119
106
95
86
114
104
95
85
77
120
106
95
85
77
21
22
23
24
25
145
132
121
111
102
145
132
121
111
102
130
118
108
99
92
130
118
108
99
92
116
105
96
89
82
116
105
96
89
82
101
92
84
78
71
101
92
84
78
71
85
78
71
65
60
85
78
71
65
60
78
71
65
60
55
78
71
65
60
55
70
64
58
53
49
70
64
58
53
49
26
94
94
85
85
76
76
66
66
56
56
51
51
45
45
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 114
COLUMN DESIGN
z
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
x
Design axial strength in kips (φ = 0.90)
w
Y z
6×
×6
Size
Thickness
Wt./ft
7⁄
8
1
37.4
Fy
36
3⁄
4
33.1
50
36
5⁄
8
28.7
50
36
9⁄
16
24.2
50
36
50
1⁄
2
21.9
36
7⁄
16
19.6
50
36
3⁄
8
17.2
50
36
5⁄
16
14.9
50
36
12.4
50
36
50
Effective length KL (ft)
0 356 495 315 438 273 380 230 320 208 289 186 249 159 206 129 164 98 120
1
2
3
4
5
346
343
339
326
310
476
469
462
438
409
304
300
298
289
275
416
408
404
387
361
260
255
253
250
238
354
345
342
336
314
214
209
207
205
201
289
279
275
273
265
190
184
182
181
180
255
244
241
238
236
166
160
158
157
155
213
202
199
197
195
137
131
129
128
127
170 107 129 77
160 100 119 71
157 99 117 69
156 98 115 69
154 97 114 68
89
81
79
78
77
6
7
8
9
10
292
272
250
228
205
376
340
303
266
230
258
241
221
202
181
332
301
268
235
203
224
209
192
175
157
288
261
232
204
176
189
177
163
148
134
244
221
197
174
151
171
160
147
134
121
221
200
179
157
136
153
143
132
120
108
192
174
156
138
120
126
124
114
105
95
152
149
134
120
105
96 113 68
95 112 67
94 110 66
87 99 66
79 88 63
76
76
75
74
71
11
12
13
14
15
183
161
140
121
105
196
164
140
121
105
162
142
124
107
93
173 140 150 119 128 108 116
145 123 126 105 108 95 98
124 108 107 92 92 83 83
107 92 92 79 79 72 72
93 81 81 69 69 62 62
97 103
85 87
74 74
64 64
56 56
85
75
66
57
50
92
78
67
57
50
71
64
57
49
43
77
67
57
49
43
58
52
47
42
37
63
56
49
42
37
16
17
18
19
92
82
73
65
92
82
73
65
82
72
64
58
49
43
39
35
44
39
35
31
44
39
35
31
38
34
30
27
38
34
30
27
32
29
25
23
32
29
25
23
82
72
64
58
71
63
56
50
71
63
56
50
61
54
48
43
61
54
48
43
55
49
43
39
49
43
39
35
5×
×5
Size
7⁄
8
Thickness
Wt./ft
3⁄
4
27.2
Fy
Effective length KL (ft)
55
49
43
39
5⁄
8
23.6
1⁄
2
20.0
7⁄
16
16.2
3⁄
8
14.3
5⁄
16
12.3
10.3
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
259
359
225
312
190
264
154
214
135
184
115
149
89
114
1
2
3
4
5
251
249
241
228
212
345
341
325
301
272
216
214
209
198
184
296
291
283
262
237
179
177
176
167
156
244
239
236
221
200
141
138
137
135
127
189
183
181
179
163
121
117
116
115
112
157
152
150
148
141
99
95
94
93
92
122
117
115
114
112
73
70
69
68
67
88
83
81
80
79
6
7
8
9
10
194
175
155
135
116
241
209
177
146
119
169
152
135
118
102
210
182
154
128
104
143
129
114
100
86
178
154
131
108
88
116
105
93
82
70
145
126
107
89
72
102
93
82
72
62
126
110
94
78
64
87
79
71
62
54
105
92
80
67
56
67
64
57
51
45
78
74
65
55
47
11
12
13
14
15
98
82
70
60
53
98
82
70
60
53
86
72
61
53
46
86
72
61
53
46
73
61
52
45
39
73
61
52
45
39
60
50
43
37
32
60
50
43
37
32
53
44
38
33
28
53
44
38
33
28
46
39
33
28
25
46
39
33
28
25
38
33
28
24
21
39
33
28
24
21
16
46
46
40
40
34
34
28
28
25
25
22
22
18
18
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF COLUMNS
3 - 115
Fy = 36 ksi
z
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
Design axial strength in kips (φ = 0.90)
Wt./ft
3⁄
4
Effective length KL (ft)
5⁄
8
18.5
Fy
1⁄
2
15.7
7⁄
16
12.8
3⁄
8
11.3
5⁄
16
9.8
1⁄
4
8.2
6.6
36
50
36
50
36
50
36
50
36
50
36
50
36
50
0
176
245
149
207
122
169
107
149
93
129
78
101
57
73
1
2
3
4
5
171
168
158
144
129
236
228
209
185
159
144
142
134
122
109
196
194
178
157
135
114
113
109
100
89
155
152
145
128
110
99
97
96
88
79
133
130
128
113
97
83
81
80
76
68
110
107
106
98
84
66
64
64
63
57
82
79
78
77
68
46
44
44
43
43
55
52
51
51
50
6
7
8
9
10
112
96
79
64
52
131
105
81
64
52
95
81
67
54
44
111
89
69
54
44
78
66
55
44
36
91
73
56
44
36
69
59
49
40
32
81
65
50
40
32
60
51
43
34
28
70
56
44
34
28
50
43
36
29
24
57
47
37
29
24
39
34
29
24
19
44
37
30
24
19
11
12
13
43
36
43
36
36
30
36
30
30
25
21
30
25
21
26
22
19
26
22
19
23
19
16
23
19
16
19
16
14
19
16
14
16
13
11
16
13
11
31⁄2×31⁄2
Size
1⁄
2
Thickness
Wt./ft
7⁄
16
11.1
Fy
Effective length KL (ft)
Y z
4×
×4
Size
Thickness
3⁄
8
9.8
5⁄
16
8.5
1⁄
4
7.2
5.8
36
50
36
50
36
50
36
50
36
50
0
105
146
93
129
80
112
68
93
53
68
1
2
3
4
5
100
99
91
81
70
137
134
119
102
83
87
86
80
72
62
118
116
106
90
74
74
73
70
62
54
99
97
91
78
64
60
59
58
53
46
78
76
75
65
54
44
43
42
41
36
53
52
51
50
42
6
7
8
9
10
59
48
37
29
24
65
49
37
29
24
52
42
33
26
21
58
43
33
26
21
45
37
29
23
18
50
37
29
23
18
38
31
24
19
16
42
32
24
19
16
31
25
20
16
13
34
26
20
16
13
11
20
20
17
17
15
15
13
13
11
11
3×
×3
Size
1⁄
2
Thickness
Wt./ft
7⁄
16
9.4
Fy
Effective length
KL (ft)
x
w
3⁄
8
8.3
5⁄
16
7.2
1⁄
4
6.1
3⁄
16
4.9
3.71
36
50
36
50
36
50
36
50
36
50
36
50
0
89
124
79
109
68
95
58
80
47
62
32
41
1
2
3
4
5
86
82
73
62
51
117
109
94
76
57
75
72
65
55
45
102
97
83
67
51
64
63
56
48
40
86
84
72
58
44
52
52
47
41
33
70
69
61
49
38
40
39
38
33
27
51
50
48
39
30
25
25
24
24
20
30
29
29
28
22
6
7
8
9
40
30
23
18
41
30
23
18
36
27
20
16
36
27
20
16
31
23
18
14
32
23
18
14
26
20
15
12
27
20
15
12
21
16
12
10
22
16
12
10
16
12
9
7
17
12
9
7
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
3 - 116
COLUMN DESIGN
z
Fy = 36 ksi
Y
Fy = 50 ksi
COLUMNS
Single angles
w
x
x
Design axial strength in kips (φ = 0.90)
w
Y z
21⁄2×21⁄2
Size
1⁄
2
Thickness
Wt./ft
7.7
Fy
Effective length KL (ft)
3⁄
8
5⁄
16
5.9
1⁄
4
5.0
3⁄
16
4.1
3.07
36
50
36
50
36
50
36
50
36
50
0
73
101
56
78
47
66
39
54
29
37
1
2
3
4
5
71
64
55
44
33
97
85
68
50
33
53
49
42
34
25
73
65
52
38
26
44
42
36
29
21
59
55
44
33
22
34
34
29
23
18
46
45
36
27
18
24
23
22
18
13
29
28
26
20
14
6
7
8
23
17
13
23
17
13
18
13
10
18
13
10
15
11
9
15
11
9
13
9
7
13
9
7
10
7
5
10
7
5
2×
×2
Size
Thickness
3⁄
8
5⁄
16
1⁄
4
3⁄
16
1⁄
8
Wt./ft
4.7
3.92
3.19
2.44
1.65
Fy
50
36
50
36
50
36
50
36
50
44
61
37
52
30
42
23
32
14
18
1
2
3
4
5
42
36
28
20
13
57
46
33
20
13
35
31
24
17
11
48
39
28
17
11
28
25
19
14
9
38
32
23
14
9
20
19
15
11
7
27
25
18
11
7
11
11
10
7
5
13
13
11
8
5
6
9
9
8
8
6
6
5
5
3
3
Effective length KL (ft)
36
0
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
REFERENCES
3 - 117
COLUMN BASE PLATES
The design of column base plates is covered in Part 11 (Volume II) of this LRFD Manual.
REFERENCES
Galambos, T. V. (ed.), 1988, Guide to Stability Design Criteria for Metal Structures,
Fourth Edition, Structural Stability Research Council, John Wiley & Sons, New York,
NY.
Geschwindner, L., 1993, “The ‘Leaning’ Column in ASD and LRFD,” Proceedings of
the 1993 National Steel Construction Conference, AISC, Chicago, IL.
Uang, C. M., S. W. Wattar, and K. M. Leet, 1990, “Proposed Revision of the Equivalent Axial
Load Method for LRFD Steel and Composite Beam-Column Design,” Engineering
Journal, 1st Qtr., AISC, Chicago.
Zureick, A., 1993, “Design Strength of Concentrically Loaded Single-Angle Struts,”
Engineering Journal, 4th Qtr., AISC, Chicago.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4-1
PART 4
BEAM AND GIRDER DESIGN
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-3
DESIGN STRENGTH OF BEAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5
General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5
Design Strength If Elastic Analysis Is Used . . . . . . . . . . . . . . . . . . . . . . . . . 4-5
Flexural Design Strength for Cb = 1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-6
Flexural Design Strength for Cb > 1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8
Design Strength If Plastic Analysis Is Used . . . . . . . . . . . . . . . . . . . . . . . . 4-10
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS . . . 4-11
Use of the Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12
MOMENT OF INERTIA SELECTION TABLES FOR W AND M SHAPES . . . . . . . . 4-23
FACTORED UNIFORM LOAD TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . 4-28
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-28
Use of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-30
Reference Notes on Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-32
Tables, Fy = 36 ksi: W Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-35
Tables, Fy = 36 ksi: S Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-61
Tables, Fy = 36 ksi: Channels (C, MC) . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-64
Tables, Fy = 50 ksi: W Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-72
Tables, Fy = 50 ksi: S Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-98
Tables, Fy = 50 ksi: Channels (C, MC)) . . . . . . . . . . . . . . . . . . . . . . . . . . 4-101
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH
GREATER THAN Lp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-109
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-109
Charts (Fy = 36 ksi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-113
Charts (Fy = 50 ksi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-139
PLATE GIRDER DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-167
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-167
Flexure and Shear Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-167
Table of Dimensions and Properties of Built-up Wide-Flange Section . . . . . . . . . . 4-167
Design Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-168
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4-2
BEAM AND GIRDER DESIGN
BEAM DIAGRAMS AND FORMULAS . . . . . . . . . . . . . . . . . . . . . . . . . . 4-187
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-187
Frequently Used Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-188
Table of Concentrated Load Equivalents . . . . . . . . . . . . . . . . . . . . . . . . . 4-189
Static Loading Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-190
Design Properties of Cantilevered Beams . . . . . . . . . . . . . . . . . . . . . . . . 4-205
FLOOR DEFLECTIONS AND VIBRATIONS . . . . . . . . . . . . . . . . . . . . . . . 4-207
Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-207
Deflections and Camber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-207
Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-208
BEAMS: OTHER SUBJECTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-211
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-213
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
4-3
OVERVIEW
Beam tables are located as follows:
Load Factor Design Selection Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-15
Moment of Inertia Selection Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-24
Factored Uniform Load Tables, Fy = 36 ksi, begin on . . . . . . . . . . . . . . . . . . . 4-35
Factored Uniform Load Tables, Fy = 50 ksi, begin on . . . . . . . . . . . . . . . . . . . 4-72
Beam charts are located as follows:
Beam Design Moments, Fy = 36 ksi, begin on . . . . . . . . . . . . . . . . . . . . . . . 4-113
Beam Design Moments, Fy = 50 ksi, begin on . . . . . . . . . . . . . . . . . . . . . . . 4-139
Plate Girder Design Tables are on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-183
Beam Diagrams and Formulas begin on . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-187
Additional information related to beam design is provided as follows:
Floor deflections and vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-207
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4-4
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF BEAMS
4-5
DESIGN STRENGTH OF BEAMS
General
Beams are proportioned so that no applicable strength limit state is exceeded when
subjected to factored load combinations and that no serviceability limit state is exceeded
when subjected to service loads. Strength limit states for beams include local buckling,
lateral torsional buckling, and yielding. Serviceability limit states may include, but are
not limited to, deflection and vibration.
The flexural design strength for beams must equal or exceed the required strength
based on the factored loads. The design strength φbMn for each applicable limit state shall
equal or exceed the maximum moment Mu as determined from the applicable factored
load combinations given in Section A4 of the LRFD Specification. Values of φbMn are
tabulated in the pages to follow. These values are based on beam behavior as shown in
Figure 4-1 and explained in the following discussion.
It should be noted that the LRFD Specification expresses values for moments and
lengths in kip-in. and inches. In this and other parts of the LRFD Manual, these values
are tabulated in kip-ft and feet.
The required strength can be determined by either elastic or plastic analysis.
Design Strength If Elastic Analysis Is Used
The flexural design strength of rolled I and C shape beams designed using elastic analysis,
according to LRFD Specification Section F1 is:
φbMn
where
φb = 0.90
Mp
M n′
Mn
Mr
(CbMn – Mn)
CbMn
Mn
Lp
L ′p
Lm
Lm′
Lr
Lb
Fig. 4-1
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4-6
BEAM AND GIRDER DESIGN
Mn = nominal flexural strength as determined by the limit state of yielding, lateraltorsional buckling, or local buckling
Flexural Design Strength for Cb = 1.0
Compact Sections (Cb = 1.0)
When Lb ≤ Lp
The flexural design strength of compact (flange and web local buckling λ ≤ λp)
I-shaped and C-shaped rolled beams (as defined in Section B5 of the LRFD Specification)
bent about the major or minor axis is:
φbMn = φbMp = φbZFy / 12
In minor axis flexure this is true for all unbraced lengths, but for bending about the major
axis the distance Lb between points braced against lateral movement of the compression
flange or between points braced to prevent twist of the cross-section shall not exceed the
value Lp (see Figure 4-1).
Lp =
300ry
Fy
√
(F1-4)
When Lp < Lb ≤ Lr
The flexural design strength of compact I or C rolled shapes bent about the major axis,
from LRFD Specification Section F1.2, is:
 Lb − Lp 
φbMn = φbMp − φb(Mp − Mr)
 ≤ φbMp
 Lr − Lp 
where the limiting length Lr and the corresponding buckling moment Mr (see Figure 4-1)
are determined as follows:
Lr =
ryX1
(Fy − Fr )

√
1+√

1 + X2(Fy − Fr)2
(F1-6)
where
X1 =
π
Sx

√
4Cw
X2 =
Iy
EGJA
2
 Sx 
 
 GJ 
(F1-8)
2
φbMr = φbSx(Fy − Fr ) / 12 kip-ft
Sx = section modulus about major axis, in.3
E = modulus of elasticity of steel, 29,000 ksi
G = shear modulus of steel, 11,200 ksi
J = torsional constant, in.4
A = cross-sectional area of beam, in.2
Cw = warping constant, in.6
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(F1-9)
DESIGN STRENGTH OF BEAMS
4-7
Fr = compressive residual stress in flange: for rolled shapes Fr = 10 ksi; for welded
shapes Fr = 16.5 ksi
Values of J and Cw are tabulated for some shapes in Part 1 of the LRFD Manual. For
values not shown, see Torsional Analysis of Steel Members (AISC, 1983).
Compact and Noncompact Sections (Cb = 1.0)
When Lb > Lr
According to LRFD Specification Section F1.2b, the flexural design strength of
compact and noncompact I or C rolled shapes bent about the major axis is:
π
φbMn = φbMcr = φb  
 Lb 

√
2
 πE 
EIyGJ +   IyCw
 Lb 
 SxX1√
2 
= φb 

 (Lb / ry) 

√
1+
X21X2
≤ φbMr
2(Lb / ry)2
Noncompact Sections (Cb = 1.0)
When Lb ≤ Lp′
All rolled W shapes are compact except the W40×174, W14×99, W14×90, W12×65,
W10×12, W8×10, and W6×15 for 50 ksi and the W6×15 for 36 ksi. The flexural design
strength φbMn′ (see Figure 4-1) for noncompact (flange or web local buckling λp < λ ≤
λr) I and C rolled shapes bent about the major or minor axis is the smaller value for either
local flange buckling or local web buckling as determined by:
 λ − λp 
φbMn′ = φbMp − φb(Mp − Mr) 

 λr − λp 
For local flange buckling:
λ = bf / 2tf for I-shaped members
λ = bf / tf for C-shaped members
Fy
λp = 65 / √
λr = 141 / √

Fy − 10

For local web buckling:
λ = h / tw
λp = 640 / √
Fy
Fy
λr = 970 / √
 Mp − Mn′ 
Lp′ = Lp + (Lr − Lp) 

 Mp − Mr 
Sections with a width-to-thickness ratio exceeding the specified values for λr are
slender shapes and must be analyzed using LRFD Specification Appendix B5.3.
When Lp′ < Lb ≤ Lr
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4-8
BEAM AND GIRDER DESIGN
The flexural design strength of noncompact I or C rolled shapes bent about the major
axis is determined by:
 Lb − Lp 
φbMn = φbMp − φb(Mp − Mr) 
 ≤ φbMn′
 Lr − Lp 
In the Load Factor Design Selection Table, in the case of the noncompact shapes, the
values of φbMn′ and Lp′ are tabulated as φbMp and Lp. The formula above may be used with
the tabulated values.
Flexural Design Strength for Cb > 1.0
Cb is a factor which varies with the moment gradient between bracing points (Lb). For
Cb greater than 1.0, the design flexural strength is equal to the tabulated value of the
design flexural strength (with Cb = 1.0) multiplied by the calculated Cb value. The
maximum value is φbMp for compact shapes or φbMn′ for noncompact shapes. The
maximum unbraced lengths associated with the maximum flexural design strengths
φbMp and φbMn′ are Lm and Lm′ (see Figure 4-1).
A new expression for Cb is given in the LRFD Specification. (It is more accurate than
the one previously shown.)
Cb =
12.5Mmax
2.5Mmax + 3MA + 4MB + 3Mc
(F1-3)
where M is the absolute value of a moment in the unbraced beam segment as follows:
Mmax , the maximum
MA , at the quarter point
MB , at the centerline
Mc , at the three-quarter point
Values for Cb for some typical loading conditions are given in Table 4-1.
Compact Sections (Cb > 1.0)
When Lb ≤ Lm
The flexural design strength for rolled I and C shapes is:
φbMn = φbMp
When Lb > Lm
The flexural design strength is:
φbMn = Cb[φbMn (for Cb = 1.0)] ≤ φbMp
For Lm ≤ Lr
Lm = Lp +
(CbMp − Mp)(Lr − Lp)
Cb(Mp − Mr)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN STRENGTH OF BEAMS
4-9
Table 4-1.
Values of Cb for Simply Supported Beams
Lateral Bracing
Along Span
Load
Cb
None
1.32
At load points
1.67
1.67
None
1.14
At load points
1.67
1.00
1.67
None
1.14
At load points
1.67
1.11
None
At centerline
Cbπ
Mp
1.30
 √
√


√
EIyGJ
2
1+
1+
4CwM2p
IyC2bG2J2
The value of Cb for which Lm or Lm′ equals Lr for any rolled shape is:
Cb =
Fy Zx
(Fy − 10)Sx
Noncompact Sections (Cb > 1.0)
When Lb ≤ Lm′
The flexural design strength for rolled I and C shapes is:
φbMn = φbMn′ < φbMp
When Lb > Lm′
The flexural design strength is:
φbMn = Cb[φbMn (for Cb = 1.0)] ≤ φbMn′
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.67
1.14
For Lm > Lr
Lm =
1.11
1.30
4 - 10
BEAM AND GIRDER DESIGN
For Lm′ ≤ Lr
Lm′ = Lp′ +
(CbMn′ − Mn′)(Lr − Lp)
Cb(Mp − Mr)
For Lm′ > Lr
Lm =
Cbπ
Mp
 √
√


√
EIyGJ
2
1+
1+
4CwM2p
IyC2bG2J2
Design Strength If Plastic Analysis Is Used
The design flexural strength for plastic analysis is:
φbMn = φbMp
where
φb = 0.90
Mp = ZxFy / 12 kip-ft
The yield strength of material that may be used with plastic analysis is limited to 65 ksi. Plastic
analysis is limited to compact shapes as defined in Table B5.1 of the LRFD Specification as:
λp = bf / 2tf ≤ 65 / √
Fy for the flanges of I shapes in flexure
Fy for the flanges of C shapes in flexure
λp = bf / tf ≤ 65 / √
and
λp = h / tw ≤ 640 / √
Fy for beam webs in flexural compression
where
.
λp = limiting slenderness parameter for compact element
bf = width of flange for I and C shapes, in.
tf = flange thickness, in.
h = clear distance between flanges less the fillet at each flange, in.
tw = beam web thickness, in
In addition, LRFD Specification Section F1.2d states: for a section bent about the major
axis, the laterally unbraced length of the compression flange at plastic hinge locations
associated with the failure mechanism shall not exceed:
Lpd =
3,600 + 2,220(M1 / M2)
ry
Fy
where
Fy
M1
M2
ry
(M1 / M2)
= specified yield strength of compression flange, ksi
= smaller moment at end of unbraced length of beam, kip-in.
= larger moment at end of unbraced length of beam, kip-in.
= radius of gyration about minor axis, in.
is positive when the moments cause reverse curvature
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(F1-17)
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS
4 - 11
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS
This table facilitates the selection of beams designed on the basis of flexural strength in
accordance with Section F of the LRFD Specification. It includes only W and M shapes
designed as beams. A laterally supported beam can be selected by entering the table with
the required plastic section modulus or factored bending moment, and comparing it with
tabulated values of Zx or φbMp respectively.
The table is applicable to adequately braced beams with unbraced lengths not exceeding Lr, i.e., Lb ≤ Lr. For beams with unbraced lengths greater than Lp, it may be convenient
to use the unbraced beam charts. For most loading conditions, it is convenient to use this
selection table. However, for adequately braced, simply supported beams with a uniform
load over the entire length, or equivalent symmetrical loading, the tables of Factored
Uniform Loads can also be used.
In this table, shapes are listed in groups by descending order plastic section modulus
Zx. Included also for steel of Fy = 36 ksi and 50 ksi are values for the maximum flexural
design strength φbMp; the limiting buckling moment φbMr; the limiting laterally unbraced
compression flange length for full plastic moment capacity and uniform moment (Cb =
1.0) Lp; limiting laterally unbraced length for inelastic lateral-torsional buckling Lr; and
BF, a factor that can be used to calculate the resisting moment φbMn for beams with
unbraced lengths between the limiting bracing lengths Lp and Lr.
For noncompact shapes, as determined by Section B5 of the LRFD Specification, the
maximum flexural design strength φbMn, max as determined by LRFD Specification
Formula A-F1-3 is tabulated as φbMp. The associated maximum unbraced length is
tabulated as Lp. (See the previous discussion under Design Strength of Beams for further
explanation.)
The symbols used in this table are:
Zx = plastic section modulus, X-X axis, in.3
φbMp = design plastic bending moment, kip-ft
= φbZxFy / 12 if shape is compact
 λ − λp 
= φbM′n = φbMp − φb(Mp − Mr) 
 if shape is noncompact
 λr − λp 
φbMr = limiting design buckling moment, kip-ft
= φbSx(Fy − Fr ) / 12
where
Fr = 10 ksi for rolled shapes
Lp = limiting laterally unbraced length for inelastic LTB, ft, uniform moment case
(Cb = 1)
Lr = limiting laterally unbraced length for elastic lateral-torsional buckling, ft
BF = a factor that can be used to calculate the design flexural strength for unbraced
lengths Lb, between Lp and Lr, kip-ft
φb(Mp − Mr)
=
Lr − Lp
where
φbMn = Cb[φbMp − BF(Lb − Lp)] ≤ φbMp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 12
BEAM AND GIRDER DESIGN
Use of the Table
Determine the required plastic section modulus Zx from the maximum factored moment
Mu (kip-ft) using the desired steel yield strength.
Zx =
12Mu
φbFy
Enter the column headed Zx and find a value equal to or greater than the plastic section
modulus required. Alternatively, enter the φbMp column and find a value of φbMp equal
to or greater than the required factored load moment. The beam opposite these values
(Zx or φbMp) in the shapes column, and all beams above it, have sufficient flexural strength
based only on these parameters. The first beam appearing in boldface type adjacent to or
above the required Zx or φbMp is the lightest section that will serve for the steel yield stress
used in the calculations. If the beam must not exceed a certain depth, proceed up the
column headed “Shape” until a beam within the required depth is reached.
After a shape has been selected, the following checks should be made. If the lateral
bracing of the compressive flange exceeds Lp, but is less than Lr, the design flexural
strength may be calculated as follows:
φbMn = Cb[φbMp − BF(Lb − Lp)] ≤ φbMp
If the bracing length Lb is substantially greater than Lp, i.e., Lb > Lr, it is recommended
the unbraced beam charts be used. A check should be made of the beam web shear strength
by referring to the Factored Uniform Load Tables or by use of the formula:
φvVn = φv0.6FywAw (from LRFD Specification Section F2)
where
φv = 0.90
If a deflection limitation also exists, the adequacy of the selected beam should be checked
accordingly.
EXAMPLE 4-1
Given:
Solution
(Zx method):
Select a beam of Fy = 50 ksi steel subjected to a factored uniform
bending moment of 256 kip-ft, having its compression flange braced
at 5.0 ft intervals. Assume Cb = 1.0.
Zx (req’d) =
Mu(12) 256(12)
=
= 68.3 in.3
φbFy
0.9(50)
Enter the Load Factor Design Selection Table and find the nearest
higher tabulated value of Zx is 69.6 in., which corresponds to a
W14×43. This beam, however, is not in boldface type. Proceed up the
shape column and locate the first beam in boldface, W16×40. Note the
values tabulated for φbMp and Lp are 273 kip-ft and 5.6 ft, respectively.
Use W16x40
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS
4 - 13
Alternatively, proceed up the shape column and select a W18×40. The
tabulated values for φbMp and Lp are 294 kip-ft and 4.5 ft, respectively.
Since the bracing length Lb is larger than Lp and smaller than Lr, the
maximum resisting moment may be calculated as follows:
φbMn = Cb[φbMp − BF(Lb − Lp)]
= 1.0[294 − (11.7)(5.0 − 4.5)]
= 288 kip-ft > 256 kip-ft req’d o.k.
A W18×40 is satisfactory.
Alternate
solution
(Mp method):
Enter the column of φbMp values and note the tabulated value nearest
and higher than the required factored moment (Mu) is 261 kip-ft, which
corresponds to a W14×43. Scanning the φbMp values for shapes listed
higher in the column, a W16×40 is found to be the lightest suitable
shape with Lb < Lp.
Use W16×40
EXAMPLE 4-2
Given:
Determine the design flexural strength of a W16×40 of Fy = 36 ksi and
Fy = 50 ksi steel with the compression flange braced at intervals of
9.0 ft. Assume Cb = 1.1.
Solution:
Enter the Load Factor Design Table and note that for a W16×40, Fy =
36 ksi:
φbMp = 197 kip-ft
Lp = 6.5 ft
Lr = 19.3 ft
BF = 5.54 kips
φbMn = Cb[φbMp − BF(Lb − Lp)] ≤ φb Mp
= 1.1[197 − 5.54(9 − 6.5)] ≤ 197 kip-ft
= 197 kip-ft
Enter the Load Factor Design Selection Table and note that for a
W16×40, Fy = 50 ksi:
φbMp = 273 kip-ft
Lp = 5.6 ft
Lr = 14.7 ft
BF = 8.67 kips
φbMn = Cb[φbMp − BF(Lb − Lp)] ≤ φb Mp
= 1.1[273 − 8.67(9 − 5.6)] ≤ 273 kip-ft
= 268 kip-ft
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 14
BEAM AND GIRDER DESIGN
EXAMPLE 4-3
Given:
Select a beam of Fy = 50 ksi steel subjected to a factored uniform
bending moment of 30 kip-ft having its compression flange braced at
4.0-ft intervals and a depth of eight inches or less. Assume Cb = 1.0.
Solution
(Zx method):
Assume shape is compact and Lb ≤ Lp.
Zx req’d =
12Mu 12(30)
=
= 8.0 in.3
φbFy 0.9(50)
Enter the Load Factor Design Selection Table and note that for a
W8×10, Fy = 50 ksi, the shape is noncompact, however, the maximum
resisting moment φbMn listed in the φbMp column is adequate. Further
note:
φbMn = 33.0 kip-ft
Lp = 3.1 ft
Lr = 7.8 ft
BF = 2.03 kips
Since Lp < Lb ≤ Lr
φbMn = Cb[φbMn − BF(Lb − Lp)]
= 1.0[33.0 − 2.03(4.0 − 3.1)]
= 33.0 − 1.8
= 31.2 kip-ft > 30 kip-ft req’d o.k.
Use: W8×10
Alternate
Solution
(Mp method):
Enter the Selection Table and note that in the column of φbMp values
for W8×10, Fy = 50 ksi, the value of φbMp is 33.0 kip-ft, which is
adequate. Also note, however, Lp = 3.1 ft is less than the bracing interval
Lb = 4.0 ft, and that BF is equal to 2.03 kips. Therefore:
φbMn = 1.0[33.0 − 2.03(4 − 3.1)]
= 31.2 kip-ft > 30 kip-ft req’d o.k.
Use: W8×10
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS
4 - 15
LOAD FACTOR DESIGN SELECTION TABLE
For shapes used as beams
φb = 0.90
Fy = 36 ksi
Zx
Fy = 50 ksi
BF
Lr
Lp
φbMr
φbMp
Zx
Kips
Ft
Ft
Kip-ft Kip-ft
in.3
φbMr
Lp
Lr
BF
Kip-ft Kip-ft
Ft
Ft
Kips
34.5
138.2
17.8
6180
10300
3830
W36×848a 14400
9510
15.1
90.5
64.3
34.1
130.1
17.7
5810
9639
3570
W36×798a 13400
8940
15.0
85.3
63.2
33.2
105.9
17.2
4720
7668
2840
W36×650a 10700
7260
14.6
70.0
61.1
41.9
84.8
15.9
4560
7450
2760
W40×593a 10400
7020
13.5
56.8
76.7
41.2
33.2
72.5
86.8
15.5
16.8
3860
3800
6210
6129
2300
2270
W40×503a
W36× 527a
8630
8510
5940
5850
13.2
14.2
49.5
58.3
73.9
60.4
46.9
58.2
11.3
3330
5540
2050
W40×466a
7690
5130
9.6
39.4
85.9
41.0
19.3
32.7
23.7
63.3
119.4
73.5
93.6
15.2
15.3
16.5
15.6
3300
3060
3160
2980
5270
5080
5022
4830
1950
1880
1860
1790
W40×431
W27× 539a
W36× 439a
W30× 477a
7310
7050
6980
6710
5070
4710
4860
4590
12.9
12.9
14.0
13.3
44.1
78.2
50.3
62.0
72.0
35.9
58.2
43.5
46.6
49.8
11.0
2810
4620
1710
W40×392a
6410
4320
9.3
34.3
83.7
39.9
32.5
56.6
67.2
15.0
16.3
2850
2830
4510
4482
1670
1660
W40×372
W36× 393a
6260
6230
4380
4350
12.7
13.8
40.3
46.7
68.4
57.0
48.6
15.3
18.9
32.5
48.0
123.3
99.2
62.4
14.6
14.2
14.9
16.1
2750
2520
2540
2570
4370
4190
4130
4077
1620
1550
1530
1510
W44×335
W24× 492a
W27× 448a
W36× 359a
6080
5810
5740
5660
4230
3870
3900
3960
12.4
12.1
12.6
13.7
35.5
80.5
65.3
44.0
79.7
28.4
34.9
56.2
46.2
22.9
29.4
43.2
77.5
64.4
10.7
15.3
15.6
2360
2440
2400
3860
3860
3830
1430
1430
1420
W40×331
W30× 391a
W33× 354a
5360
5360
5330
3630
3750
3690
9.1
13.0
13.2
30.5
52.1
44.7
80.9
41.2
51.9
46.1
38.4
32.2
38.4
45.3
51.2
58.5
48.9
14.6
14.8
16.0
14.8
2420
2440
2360
2280
3830
3830
3726
3590
1420
1420
1380
1330
W44×290
W40× 321
W36× 328a
W40× 297
5330
5330
5180
4990
3720
3750
3630
3510
12.4
12.6
13.6
12.5
34.0
37.2
41.7
35.9
74.1
63.9
54.9
63.2
43.4
28.9
31.6
14.7
37.3
19.0
44.2
23.4
31.0
28.2
43.7
43.1
59.3
55.1
103.0
47.9
82.0
38.2
66.6
53.0
55.7
37.0
14.4
15.5
16.0
13.9
14.9
14.5
10.5
15.0
15.9
15.4
10.5
2180
2160
2160
2070
2150
2070
1990
2010
2010
1970
1890
3430
3430
3402
3380
3380
3350
3210
3210
3159
3110
3050
1270
1270
1260
1250
1250
1240
1190
1190
1170
1150
1130
W44×262
W33× 318a
W36× 300
W24× 408a
W40× 277
W27× 368a
W40× 278
W30× 326a
W36× 280
W33× 291a
W40× 264
4760
4760
4730
4690
4690
4650
4460
4460
4390
4310
4240
3360
3330
3330
3180
3300
3180
3060
3090
3090
3030
2910
12.2
13.1
13.5
11.8
12.7
12.3
8.9
12.8
13.5
13.0
8.9
32.8
41.8
39.9
67.5
35.5
54.6
27.6
45.7
38.8
39.8
27.0
68.2
49.9
52.9
27.0
60.8
34.8
74.9
41.7
51.3
48.0
73.3
35.6
45.4
14.8
1930
3020
1120
W40×249
4200
2980
12.6
34.1
56.9
Shape
φbMp
aGroup 4 or Group 5 shape. See Notes in Table 1-2 (Part 1).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 16
BEAM AND GIRDER DESIGN
LOAD FACTOR DESIGN SELECTION TABLE
For shapes used as beams
φb = 0.90
Zx
Fy = 36 ksi
Fy = 50 ksi
BF
Lr
Lp
φbMr
φbMp
Zx
Kips
Ft
Ft
Kip-ft Kip-ft
in.3
φbMr
Lp
Lr
BF
Kip-ft Kip-ft
φbMp
Ft
Ft
Kips
40.1
30.3
23.1
37.0
27.7
15.0
18.7
41.8
29.6
41.2
50.6
60.5
39.7
52.0
84.5
69.4
35.1
48.8
14.3
15.8
14.9
11.0
15.3
13.5
14.3
10.6
15.6
1890
1860
1810
1750
1790
1680
1720
1700
1750
2970
2916
2860
2810
2810
2750
2750
2730
2727
1100
1080
1060
1040
1040
1020
1020
1010
1010
W44×230
W36×260
W30× 292a
W36×256
W33× 263a
W24× 335a
W27× 307a
W40×235
W36×245
4130
4050
3980
3900
3900
3830
3830
3790
3790
2910
2860
2780
2690
2750
2590
2650
2620
2690
12.1
13.4
12.7
9.4
12.9
11.4
12.1
9.0
13.3
31.7
37.5
42.1
28.8
37.8
55.8
46.9
26.0
36.4
62.0
49.4
40.4
62.7
46.3
27.8
33.7
68.6
47.7
33.1
28.7
22.8
27.0
36.1
42.7
47.3
55.4
49.2
37.2
14.8
15.5
14.8
15.1
10.9
1670
1630
1610
1620
1580
2600
2550
2540
2540
2530
963
943
941
939
936
W40×215
W36×230
W30×261
W33×241
W36×232
3610
3540
3530
3520
3510
2570
2510
2480
2490
2430
12.5
13.2
12.5
12.8
9.3
32.6
35.6
39.2
36.2
27.3
51.6
45.8
39.2
44.2
59.9
40.2
33.2
10.5
1530
2440
905
W40×211
3390
2360
8.9
24.9
64.7
31.6
26.0
18.6
22.4
14.7
34.9
41.1
46.9
59.6
51.6
71.2
35.0
14.4
15.0
14.0
14.7
13.2
10.8
1500
1480
1450
1450
1400
1400
2340
2310
2300
2280
2250
2250
868
855
850
845
835
833
W40×199
W33×221
W27×258
W30×235
W24× 279a
W36×210
3260
3210
3190
3170
3130
3120
2310
2270
2230
2240
2150
2160
12.2
12.7
11.9
12.4
11.2
9.1
31.6
35.0
41.1
37.1
47.6
26.1
48.8
41.9
32.9
37.7
26.9
56.8
37.4
25.0
18.5
34.0
8.40
21.8
14.7
31.2
44.8
55.0
33.5
109.5
47.9
64.3
10.4
14.8
13.9
10.7
12.3
14.5
13.1
1330
1330
1310
1290
1220
1290
1260
2110
2080
2080
2070
2030
2020
2010
781
772
769
767
753
749
744
W40×183
W33×201
W27×235
W36×194
W18× 311a
W30×211
W24× 250a
2930
2900
2880
2880
2820
2810
2790
2050
2050
2020
1990
1870
1990
1930
8.8
12.6
11.8
9.1
10.4
12.3
11.1
23.8
33.8
38.5
25.2
71.5
35.1
43.4
59.0
39.7
32.3
54.6
15.6
36.0
26.6
32.7
32.8
10.6
1210
1940
718
W36×182
2690
1870
9.0
24.9
52.0
b
Shape
27.5
18.2
38.4
52.0
13.6
13.8
1250
1220
1930
1910
715
708
W40×174
W27×217
2660
2660
1920
1870
12.0
11.7
29.9
36.8
41.3
31.3
35.6
8.29
14.7
21.0
31.5
28.3
17.8
29.7
99.6
59.3
45.4
31.9
32.6
48.0
10.0
12.1
13.0
14.4
10.5
10.4
13.7
1170
1100
1150
1170
1130
1070
1080
1870
1830
1830
1820
1800
1700
1700
692
676
676
673
668
629
628
W40×167
W18× 283a
W24×229
W30×191
W36×170
W33×169
W27×194
2600
2540
2540
2520
2510
2360
2360
1800
1690
1760
1790
1740
1650
1670
8.5
10.3
11.0
12.2
8.9
8.8
11.6
22.8
65.1
40.4
33.7
24.4
24.5
34.6
55.6
15.4
26.2
33.9
49.6
45.4
30.0
30.7
8.21
14.5
20.2
30.9
90.9
54.2
43.2
10.4
12.0
12.8
14.3
1060
1000
1040
1050
1680
1650
1640
1630
624
611
606
605
W36×160
W18× 258a
W24×207
W30×173
2340
2290
2270
2270
1630
1540
1590
1620
8.8
10.2
10.9
12.1
23.7
59.5
37.4
32.5
48.0
15.2
25.6
32.0
aGroup 4 or Group 5 shape. See Notes in Table 1-2 (Part 1).
bIndicates noncompact shape; F = 50 ksi
y
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS
4 - 17
LOAD FACTOR DESIGN SELECTION TABLE
For shapes used as beams
φb = 0.90
Fy = 36 ksi
Zx
Fy = 50 ksi
BF
Lr
Lp
φbMr
φbMp
Zx
Kips
Ft
Ft
Kip-ft Kip-ft
in.3
φbMr
Lp
Lr
BF
Kip-ft Kip-ft
Ft
Ft
Kips
32.8
29.4
17.5
26.8
14.3
8.09
11.0
28.2
30.2
45.2
31.2
51.3
82.8
60.8
9.5
10.3
13.6
10.3
12.8
11.9
12.6
998
983
979
950
957
909
899
1610
1570
1530
1510
1510
1480
1430
597
581
567
559
559
549
530
W40×149
W36× 150
W27× 178
W33× 152
W24× 192
W18× 234a
W21× 201
2240
2180
2130
2100
2100
2060
1990
1540
1510
1510
1460
1470
1400
1380
8.1
8.7
11.5
8.7
10.9
10.1
10.7
21.9
23.4
33.1
23.7
35.7
54.4
41.1
50.8
45.6
28.8
42.3
25.0
14.9
19.9
25.7
16.9
14.3
30.1
42.8
47.8
10.1
13.5
12.7
874
887
878
1390
1380
1380
514
512
511
W33×141
W27× 161
W24× 176
1930
1920
1920
1340
1370
1350
8.6
11.5
10.7
23.1
31.7
33.8
40.2
27.4
24.6
27.5
23.7
8.00
10.9
14.1
28.8
30.6
75.0
55.8
45.2
9.9
9.5
11.8
12.5
12.7
856
850
817
813
807
1370
1350
1320
1290
1260
509
500
490
476
468
W36×135
W30× 148
W18× 211a
W21× 182
W24× 162
1910
1880
1840
1790
1760
1320
1310
1260
1250
1240
8.4
8.1
10.0
10.6
10.8
22.4
22.8
49.5
38.1
32.4
42.2
38.6
14.7
19.4
23.8
24.5
16.2
7.98
22.4
10.8
13.8
29.1
40.7
68.3
29.0
51.7
42.0
10.0
13.4
11.6
9.4
12.4
12.5
792
801
741
741
741
723
1260
1240
1190
1180
1170
1130
467
461
442
437
432
418
W33×130
W27× 146
W18× 192
W30× 132
W21× 166
W24× 146
1750
1730
1660
1640
1620
1570
1220
1230
1140
1140
1140
1110
8.4
11.3
9.9
8.0
10.5
10.6
22.5
30.6
45.3
22.0
35.7
30.6
37.9
25.8
14.6
35.6
19.1
22.8
23.1
21.6
7.95
18.9
27.8
28.2
62.3
30.0
9.7
9.3
11.5
9.2
700
692
671
673
1120
1100
1070
1070
415
408
398
395
W33×118
W30× 124
W18× 175
W27× 129
1560
1530
1490
1480
1080
1070
1030
1040
8.2
7.9
9.8
7.8
21.7
21.5
41.5
22.3
35.5
34.1
14.5
30.9
21.1
10.7
13.3
7.87
27.1
46.4
39.3
56.7
9.1
12.3
12.4
11.4
642
642
642
605
1020
1010
999
961
378
373
370
356
W30×116
W21× 147
W24× 131
W18× 158
1420
1400
1390
1340
987
987
987
930
7.7
10.4
10.5
9.7
20.8
32.8
29.1
38.2
33.0
18.4
21.5
14.2
20.2
18.0
10.5
12.7
7.82
26.3
28.2
43.1
37.1
52.2
9.0
9.1
12.2
12.3
11.3
583
583
575
567
550
934
926
899
883
869
346
343
333
327
322
W30×108
W27× 114
W21× 132
W24× 117
W18× 143
1300
1290
1250
1230
1210
897
897
885
873
846
7.6
7.7
10.4
10.4
9.6
20.3
21.3
30.9
27.9
35.5
31.5
28.7
17.7
20.2
14.0
19.0
10.3
17.0
7.79
12.0
25.5
41.0
26.8
48.0
35.2
8.8
12.2
9.0
11.3
12.1
525
532
521
499
503
842
829
824
786
780
312
307
305
291
289
W30×99
W21× 122
W27× 102
W18× 130
W24× 104
1170
1150
1140
1090
1080
807
819
801
768
774
7.4
10.3
7.6
9.5
10.3
19.8
29.8
20.5
33.0
26.8
29.2
17.1
26.7
13.8
18.8
Shape
φbMp
aGroup 4 or Group 5 shape. See Notes in Table 1-2 (Part 1).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 18
BEAM AND GIRDER DESIGN
LOAD FACTOR DESIGN SELECTION TABLE
For shapes used as beams
φb = 0.90
Zx
Fy = 36 ksi
Fy = 50 ksi
BF
Lr
Lp
φbMr
φbMp
Zx
Kips
Ft
Ft
Kip-ft Kip-ft
in.3
φbMr
Lp
Lr
BF
Kip-ft Kip-ft
Ft
Ft
Kips
17.8
14.8
10.1
16.2
7.72
14.3
9.61
24.8
27.1
38.7
25.9
44.1
25.9
37.1
8.7
8.3
12.1
8.8
11.2
8.3
12.0
478
478
486
474
450
433
443
764
756
753
751
705
686
683
283
280
279
278
261
254
253
W30×90
W24×103
W21×111
W27× 94
W18×119
W24× 94
W21×101
1060
1050
1050
1040
979
953
949
735
735
747
729
693
666
681
7.4
7.0
10.3
7.5
9.5
7.0
10.2
19.4
20.1
28.5
19.9
30.8
19.4
27.6
27.1
24.1
16.4
25.2
13.4
23.0
15.4
15.0
3.87
7.62
24.9
73.6
40.4
8.6
15.7
11.1
415
408
398
659
632
621
244
234
230
W27×84
W14×132
W18×106
915
878
863
639
627
612
7.3
13.3
9.4
19.3
49.6
28.7
23.0
6.89
13.0
13.6
11.8
3.86
7.51
24.5
26.6
67.9
38.1
8.1
7.7
15.6
11.0
382
374
371
367
605
597
572
570
224
221
212
211
W24×84
W21× 93
W14×120
W18× 97
840
829
795
791
588
576
570
564
6.9
6.5
13.2
9.4
18.6
19.4
46.2
27.4
21.5
19.6
6.82
12.6
12.7
6.10
11.3
3.84
2.95
7.27
23.4
42.1
24.9
62.7
75.5
35.5
8.0
10.5
7.6
15.5
13.0
11.0
343
341
333
337
318
324
540
535
529
518
502
502
200
198
196
192
186
186
W24×76
W16×100
W21× 83
W14×109
W12×120
W18× 86
750
743
735
720
698
698
528
525
513
519
489
498
6.8
8.9
6.5
13.2
11.1
9.3
18.0
29.3
18.5
43.2
50.0
26.1
19.8
10.7
18.5
6.70
5.36
11.9
12.1
6.03
3.77
10.7
2.95
6.94
22.4
38.6
58.2
23.5
67.2
33.3
7.8
10.4
15.5
7.5
13.0
10.9
300
302
306
294
283
285
478
473
467
464
443
440
177
175
173
172
164
163
W24×68
W16× 89
W14× 99b
W21× 73
W12×106
W18× 76
664
656
647
645
615
611
462
465
471
453
435
438
6.6
8.8
13.4
6.4
11.0
9.2
17.4
27.3
40.6
17.7
44.9
24.8
18.7
10.3
6.46
17.0
5.32
11.1
10.4
3.75
22.8
54.1
7.5
15.4
273
279
432
424
160
157
W21×68
W14× 90b
600
587
420
429
6.4
15.0
17.3
38.4
16.5
6.31
13.8
5.85
2.01
2.91
8.29
17.2
34.9
86.4
61.4
24.4
5.8
10.3
11.2
12.9
7.1
255
261
246
255
248
413
405
397
397
392
153
150
147
147
145
W24×62
W16× 77
W10×112
W12× 96
W18× 71
574
563
551
551
544
393
402
378
393
381
4.9
8.7
9.5
10.9
6.0
13.3
25.2
56.5
41.3
17.8
21.4
9.75
3.68
5.20
13.8
9.84
4.15
21.7
43.0
7.4
10.3
248
240
389
375
144
139
W21×62
W14× 82
540
521
381
369
6.3
8.8
16.6
29.6
15.3
7.31
Shape
φbMp
bIndicates noncompact shape; F = 50 ksi.
y
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS
4 - 19
LOAD FACTOR DESIGN SELECTION TABLE
For shapes used as beams
φb = 0.90
Fy = 36 ksi
Zx
Fy = 50 ksi
BF
Lr
Lp
φbMr
φbMp
Zx
Kips
Ft
Ft
Kip-ft Kip-ft
in.3
φbMr
Lp
Lr
BF
Kip-ft Kip-ft
Ft
Ft
Kips
12.7
8.08
2.90
2.00
5.57
11.3
4.10
7.91
2.88
4.05
1.97
16.6
23.2
56.4
77.4
32.3
17.3
40.0
22.4
51.8
37.3
68.4
5.6
7.0
12.8
11.0
10.3
5.6
10.3
7.0
12.7
10.3
11.0
222
228
230
218
228
216
218
211
209
201
192
362
359
356
351
351
348
340
332
321
311
305
134
133
132
130
130
129
126
123
119
115
113
W24×55
W18× 65
W12× 87
W10× 100
W16× 67
W21× 57
W14× 74
W18× 60
W12× 79
W14× 68
W10× 88
503
499
495
488
488
484
473
461
446
431
424
342
351
354
336
351
333
336
324
321
309
296
4.7
6.0
10.9
9.4
8.7
4.8
8.8
6.0
10.8
8.7
9.3
12.9
17.1
38.4
50.8
23.8
13.1
28.0
16.7
35.7
26.4
45.1
19.6
13.3
5.12
3.66
9.02
18.0
7.12
12.8
5.03
6.91
3.58
7.65
21.4
7.0
192
302
112
W18×55
420
295
5.9
16.1
12.2
10.5
2.87
6.43
3.91
16.2
48.2
22.8
34.7
5.4
12.7
6.7
10.2
184
190
180
180
297
292
284
275
110
108
105
102
W21×50
W12× 72
W16× 57
W14× 61
413
405
394
383
284
292
277
277
4.6
10.7
5.7
8.7
12.5
33.6
16.6
24.9
16.4
4.93
10.7
6.51
7.31
1.95
2.80
20.5
60.1
44.7
6.9
10.8
12.6
173
168
171
273
264
261
101
97.6
96.8
W18×50
W10× 77
W12× 65b
379
366
358
267
258
264
5.8
9.2
11.8
15.6
39.9
31.7
11.5
3.53
4.72
9.68
6.18
8.13
4.17
2.91
1.93
5.91
15.4
21.3
16.6
28.0
38.4
53.7
20.2
5.3
6.6
5.4
8.0
10.5
10.8
6.5
159
158
154
152
152
148
142
258
248
245
235
233
230
222
95.4
92.0
90.7
87.1
86.4
85.3
82.3
W21×44
W16× 50
W18× 46
W14× 53
W12× 58
W10× 68
W16× 45
358
345
340
327
324
320
309
245
243
236
233
234
227
218
4.5
5.6
4.6
6.8
8.9
9.2
5.6
12.0
15.8
12.6
20.1
27.0
36.0
15.2
14.9
10.1
13.0
7.02
4.96
3.46
9.43
7.51
4.06
2.85
1.91
15.7
26.3
35.8
48.1
5.3
8.0
10.3
10.7
133
137
138
130
212
212
210
201
78.4
78.4
77.9
74.6
W18×40
W14× 48
W12× 53
W10× 60
294
294
292
280
205
211
212
200
4.5
6.8
8.8
9.1
12.1
19.2
25.6
32.6
11.7
6.70
4.77
3.38
5.54
3.06
1.30
3.91
1.89
19.3
30.8
64.0
24.7
43.9
6.5
8.2
8.8
7.9
10.7
126
126
118
122
117
197
195
190
188
180
72.9
72.4
70.2
69.6
66.6
W16×40
W12× 50
W8× 67
W14× 43
W10× 54
273
272
263
261
250
194
194
181
188
180
5.6
6.9
7.5
6.7
9.1
14.7
21.7
41.9
18.2
30.2
8.67
5.25
2.38
6.32
3.30
6.95
3.01
5.23
4.41
1.88
1.27
2.92
1.96
14.8
28.5
18.3
20.0
40.7
56.0
26.5
35.1
5.1
8.1
6.3
6.5
10.6
8.8
8.0
8.4
112
113
110
106
106
101
101
95.7
180
175
173
166
163
161
155
148
66.5
64.7
64.0
61.5
60.4
59.8
57.5
54.9
W18×35
W12× 45
W16× 36
W14× 38
W10× 49
W8× 58
W12× 40
W10× 45
249
243
240
231
227
224
216
206
173
174
170
164
164
156
156
147
4.3
6.9
5.4
5.5
9.0
7.4
6.8
7.1
11.5
20.3
14.1
14.9
28.3
36.8
19.3
24.1
10.7
5.07
8.08
7.07
3.25
2.32
4.82
3.45
Shape
φbMp
bIndicates noncompact shape; F = 50 ksi.
y
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 20
BEAM AND GIRDER DESIGN
LOAD FACTOR DESIGN SELECTION TABLE
For shapes used as beams
φb = 0.90
Zx
Fy = 36 ksi
Fy = 50 ksi
BF
Lr
Lp
φbMr
φbMp
Zx
Kips
Ft
Ft
Kip-ft Kip-ft
in.3
φbMr
Lp
Lr
BF
Kip-ft Kip-ft
Ft
Ft
Kips
4.18
19.0
6.4
94.8
147
54.6
W14×34
205
146
5.4
14.4
6.58
5.70
3.47
1.26
14.3
20.6
46.7
4.9
6.4
8.7
92.0
88.9
84.4
146
138
132
54.0
51.2
49.0
W16×31
W12× 35
W8×48
203
192
184
142
137
130
4.1
5.4
7.4
11.0
15.2
31.1
8.85
5.67
2.27
3.92
1.93
17.9
31.2
6.2
8.3
81.9
82.1
128
126
47.3
46.8
W14×30
W10× 39
177
176
126
126
5.3
7.0
13.7
21.8
6.06
3.32
5.15
3.22
13.3
19.1
4.7
6.3
74.9
75.3
119
116
44.2
43.1
W16×26
W12× 30
166
162
115
116
4.0
5.4
10.4
14.4
7.88
5.10
4.44
1.25
1.89
13.4
39.1
27.4
4.5
8.5
8.1
68.8
69.2
68.3
109
107
105
40.2
39.8
38.8
W14×26
W8×40
W10× 33
151
149
146
106
107
105
3.8
7.2
6.9
10.3
26.4
19.7
6.96
2.22
3.15
2.99
2.44
1.23
18.1
20.3
35.1
6.3
5.7
8.5
65.1
63.2
60.8
100
98.8
93.7
37.2
36.6
34.7
W12×26
W10× 30
W8×35
140
137
130
100
97.2
93.6
5.3
4.8
7.2
13.8
14.5
24.1
4.64
4.13
2.16
4.06
2.34
1.21
12.5
18.5
32.0
4.3
5.7
8.4
56.6
54.4
53.6
89.6
84.5
82.1
33.2
31.3
30.4
W14×22
W10× 26
W8×31
125
117
114
87.0
83.7
82.5
3.7
4.8
7.1
9.7
13.5
22.3
6.26
3.85
2.07
3.88
1.27
11.1
27.3
3.5
6.8
49.5
47.4
79.1
73.4
29.3
27.2
W12×22
W8×28
110
102
76.2
72.9
3.0
5.7
8.4
18.9
6.24
2.22
2.19
16.9
5.5
45.2
70.2
26.0
W10×22
97.5
69.6
4.7
12.7
3.50
3.61
1.24
10.4
24.4
3.4
6.7
41.5
40.8
66.7
62.6
24.7
23.2
W12×19
W8×24
92.6
87.0
63.9
62.7
2.9
5.7
7.9
17.2
5.70
2.11
2.60
1.46
12.0
18.6
3.6
5.3
36.7
35.5
58.3
55.1
21.6
20.4
W10×19
W8×21
81.0
76.5
56.4
54.6
3.1
4.5
8.9
13.3
4.26
2.47
3.30
0.741
2.46
9.6
31.3
11.2
3.2
6.3
3.5
33.3
32.6
31.6
54.3
51.0
50.5
20.1
18.9
18.7
W12×16
W6×25
W10× 17
75.4
70.9
70.1
51.3
50.1
48.6
2.7
5.4
3.0
7.4
21.0
8.4
5.12
1.33
3.97
2.97
1.40
2.34
0.728
9.2
16.7
10.3
25.6
3.1
5.1
3.4
6.3
29.1
29.6
26.9
26.1
47.0
45.9
43.2
40.2
17.4
17.0
16.0
14.9
W12×14
W8×18
W10× 15
W6×20
65.3
63.8
60.0
55.9
44.7
45.6
41.4
40.2
2.7
4.3
2.9
5.3
7.2
12.3
7.9
17.7
4.56
2.30
3.69
1.27
3.32
1.53
6.9
12.6
2.3
3.7
23.6
23.0
38.6
36.7
14.3
13.6
M12×11.8
W8×15
53.7
51.0
36.3
35.4
2.0
3.1
5.4
9.2
5.10
2.56
Shape
φbMp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
LOAD FACTOR DESIGN SELECTION TABLE FOR SHAPES USED AS BEAMS
4 - 21
LOAD FACTOR DESIGN SELECTION TABLE
For shapes used as beams
φb = 0.90
Fy = 36 ksi
Zx
Fy = 50 ksi
BF
Lr
Lp
φbMr
φbMp
Zx
Kips
Ft
Ft
Kip-ft Kip-ft
in.3
3.10
2.03
0.817
0.458
1.44
0.417
0.693
0.444
6.8
9.5
18.3
30.3
11.5
31.1
20.8
26.3
2.3
3.3
4.0
5.3
3.5
5.0
6.7
5.3
21.6
21.3
19.9
19.9
19.3
18.8
19.0
16.6
35.4
34.0
31.6
31.3
30.8
29.7
28.8
25.9
13.1
12.6
11.7
11.6
11.4
11.0
10.8
9.59
M12×10.8
W10× 12b
W6× 16
W5× 19
W8× 13
M5× 18.9
W6×15b,c
W5× 16
49.2
47.0
43.9
43.5
42.8
41.3
38.6
36.0
2.32
1.30
0.775
6.2
10.2
14.4
2.1
3.5
3.8
15.2
15.2
14.3
24.9
23.9
22.4
9.21
8.87
8.30
M10×9
W8× 10b
W6× 12
2.13
0.295
0.724
6.1
25.5
12.0
2.1
4.2
3.8
13.6
10.6
10.8
22.1
17.0
16.8
8.20
6.28
6.23
1.50
5.5
1.8
14.6
5.40
9.01
φbMr
Lp
Lr
BF
Kip-ft Kip-ft
Ft
Ft
Kips
33.3
32.7
30.6
30.6
29.7
28.9
29.2
25.5
2.0
2.9
3.4
4.5
3.0
4.2
6.8
4.5
5.3
7.4
12.5
20.1
8.5
20.5
15.0
17.6
4.74
3.13
1.46
0.830
2.35
0.758
1.16
0.795
34.5
33.0
31.1
23.5
23.4
21.9
1.8
3.1
3.2
4.9
7.8
10.2
3.59
2.03
1.33
M10×8
W4× 13
W6× 9
30.8
23.6
23.4
21.0
16.4
16.7
1.8
3.5
3.2
4.8
16.9
8.9
3.26
0.538
1.17
M8×6.5
20.2
13.9
1.6
4.3
2.35
Shape
φbMp
bIndicates noncompact shape; F = 50 ksi
y
cIndicates noncompact shape; F = 36 ksi
y
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 22
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
MOMENT OF INERTIA SELECTION TABLES FOR W AND M SHAPES
4 - 23
MOMENT OF INERTIA SELECTION TABLES FOR W AND M SHAPES
These two tables for moment of inertia (Ix and Iy) are provided to facilitate the selection
of beams and columns on the basis of their stiffness properties with respect to the X-X
axis or Y-Y axis, as applicable, where
Ix = moment of inertia, X-X axis, in.4
Iy = moment of inertia, Y-Y axis, in.4
In each table the shapes are listed in groups by descending order of moment of inertia
for all W and M shapes. The boldface type identifies the shapes that are the lightest in
weight in each group.
Enter the column headed Ix (or Iy) and find a value of Ix (or Iy) equal to or greater than
the moment of inertia required. The shape opposite this value, and all shapes above it,
have sufficient stiffness. Note that the member selected must also be checked for
compliance with specification provisions governing its specific application.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 24
Ix
Shape
BEAM AND GIRDER DESIGN
MOMENT OF INERTIA SELECTION TABLE
For W and M shapes
Ix
Shape
In.4
W36×848*
67400
W36×798*
62600
W40×593*
W36× 650*
50400
48900
W40×503*
W36× 527*
41700
38300
W40×466*
36300
W40×431
34800
W44×335
W36× 439*
W40× 392*
W40× 372
W36× 393*
31100
31000
29900
29600
27500
W44×290
W30× 477*
W27× 539*
W40× 321
W36× 359*
W40× 331
27100
26100
25500
25100
24800
24700
W44×262
W40× 297
W36× 328*
W40× 277
W33× 354*
24200
23200
22500
21900
21900
W44×230
W30× 391*
W40× 278
W27× 448*
W36× 300
W33× 318*
W40× 249
W40× 264
W24× 492*
W36× 280
W33× 291*
W40× 235
W36× 260
W30× 326*
W36× 256
20800
20700
20500
20400
20300
19500
19500
19400
19100
18900
17700
17400
17300
16800
16800
Ix
W40×215
W27× 368*
W36×245
W14× 808*
W33× 263*
16700
16100
16100
16000
15800
W40×211
W24× 408*
W36×230
W36×232
15500
15100
15000
15000
W40×199
W30× 292*
W14× 730*
W33×241
14900
14900
14300
14200
W40×183
W36×210
W27× 307*
W30×261
W33×221
W14× 665*
13300
13200
13100
13100
12800
12400
W40×174
W36×194
W24× 335*
W30×235
12200
12100
11900
11700
W40×167
W33×201
W36×182
W14× 605*
W27×258
W36×170
W30× 211
11600
11500
11300
10800
10800
10500
10300
W40×149
W36×160
W27×235
W24× 279*
W14× 550*
W33×169
W30×191
W36×150
W27×217
W24× 250*
W14× 500*
W30×173
W33×152
W27×194
9780
9750
9660
9600
9430
9290
9170
9040
8870
8490
8210
8200
8160
7820
Ix
Shape
In.4
Shape
In.4
W36×135
W24× 229
W33× 141
W14×455*
W27× 178
W18× 311*
W24× 207
7800
7650
7450
7190
6990
6960
6820
W33×130
W30× 148
W14×426*
W27× 161
W24× 192
W18×283*
W14×398*
6710
6680
6600
6280
6260
6160
6000
W33×118
W30× 132
W24× 176
W27× 146
W18×258*
W14×370*
W30× 124
W21× 201
W24× 162
5900
5770
5680
5630
5510
5440
5360
5310
5170
W30×116
W18×234*
W14×342*
W27× 129
W21× 182
W24× 146
4930
4900
4900
4760
4730
4580
W30×108
W18× 211*
W14× 311*
W21× 166
W27× 114
W12×336*
W24× 131
4470
4330
4330
4280
4090
4060
4020
*Group 4 or 5 shape. See Notes in Table 1-2 (Part 1).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Ix
In.4
W30×99
W18× 192
W14× 283*
W21× 147
3990
3870
3840
3630
W30×90
W27× 102
W12× 305*
W24× 117
W18× 175
W14× 257*
W27× 94
W21× 132
W12× 279*
W24× 104
W18× 158
W14× 233*
W24× 103
W21× 122
3620
3620
3550
3540
3450
3400
3270
3220
3110
3100
3060
3010
3000
2960
W27×84
W18× 143
W12× 252*
W24× 94
W21× 111
W14× 211
W18× 130
W12× 230*
W21× 101
W14× 193
2850
2750
2720
2700
2670
2660
2460
2420
2420
2400
W24×84
W18× 119
W14× 176
W12× 210*
2370
2190
2140
2140
W24×76
W21× 93
W18× 106
W14× 159
W12× 190
2100
2070
1910
1900
1890
MOMENT OF INERTIA SELECTION TABLE FOR W AND M SHAPES
4 - 25
MOMENT OF INERTIA SELECTION TABLE
For W and M shapes
Shape
Ix
Shape
In.4
W24×68
W21× 83
W18× 97
W14× 145
W12× 170
W21× 73
1830
1830
1750
1710
1650
1600
W24×62
W14× 132
W18× 86
W16× 100
W21× 68
W12× 152
W14× 120
1550
1530
1530
1490
1480
1430
1380
W24×55
W18× 76
W21× 62
W16× 89
W14× 109
W12× 136
W18× 71
W21× 57
W14× 99
W16× 77
W12× 120
W18× 65
W14× 90
W18× 60
1350
1330
1330
1300
1240
1240
1170
1170
1110
1110
1070
1070
999
984
W21×50
W16× 67
W12× 106
W18× 55
W14× 62
984
954
933
890
882
Ix
Shape
In.4
Ix
Shape
In.4
W21×44
W12× 96
W18× 50
W14× 74
W16× 57
W12× 87
W14× 68
W10× 112
W18× 46
W12× 79
W16× 50
W14× 61
W10× 100
843
833
800
796
758
740
723
716
712
662
659
640
623
W16×26
W14× 30
W12× 35
W8× 67
W10× 49
W10× 45
301
291
285
272
272
248
W14×26
W12× 30
W8× 58
W10× 39
245
238
228
209
W12×26
204
W18×40
W12× 72
W16× 45
W14× 53
W10× 88
W12× 65
612
597
586
541
534
533
W14×22
W8× 48
W10× 30
W10× 33
199
184
170
170
W16×40
518
W12×22
W8× 40
W10× 26
156
146
144
W18×35
W14× 48
W12× 58
W10× 77
W16× 36
W14× 43
W12× 53
W12× 50
W10× 68
W14× 38
510
485
475
455
448
428
425
394
394
385
W12×19
W8× 35
W10× 22
W8× 31
130
127
118
110
W12×16
W8× 28
W10× 19
103
98.0
96.3
W16×31
W12× 45
W10× 60
W14× 34
W12× 40
W10× 54
375
350
341
340
310
303
W12×14
W8× 24
W10× 17
W8× 21
88.6
82.8
81.9
75.3
M12×11.8
W10× 15
71.7
68.9
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Ix
Ix
In.4
M12×10.8
W8× 18
W10×12
W6× 25
W8× 15
W6× 20
W8× 13
65.8
61.9
53.8
53.4
48.0
41.4
39.6
M10×9
38.5
M10×8
W6× 16
W8× 10
W6× 15
W5× 19
M5× 18.9
W6× 12
W5× 16
34.3
32.1
30.8
29.1
26.2
24.1
22.1
21.3
M8×6.5
W6×9
W4× 13
18.1
16.4
11.3
4 - 26
Iy
Shape
BEAM AND GIRDER DESIGN
MOMENT OF INERTIA SELECTION TABLE
For W and M shapes
Iy
Shape
In.4
W14×808*
5510
W14×730*
W36× 848*
W36× 798*
4720
4550
4200
W14×665*
4170
W14×605*
3680
W14×550*
W36× 650*
W14×283*
W40×372
W36× 328*
W24× 408*
W27× 368*
W36×300
1440
1420
1420
1320
1310
1300
W14×257*
W33× 318*
W30× 326*
W36×280
W44×335
W12× 336*
W40×321
W33× 291*
1290
1290
1240
1200
1200
1190
1190
1160
3250
3230
W14×500*
2880
W14×455*
W40× 593*
W36× 527*
2560
2520
2490
W14×426*
2360
W14×398*
W27× 539*
W40× 503*
2170
2110
2050
W14×370*
W36× 439*
W30× 477*
1990
1990
1970
W14×342*
W36× 393*
W40× 431
W27× 448*
W24× 492*
1810
1750
1690
1670
1670
W14×311*
W36× 359*
W30× 391*
W33× 354*
Iy
1610
1570
1550
1460
W14×233*
W30× 292*
W40×297
W36×260
W44×290
W27× 307*
W12× 305*
W40×277
W33× 263*
W24× 335*
1150
1100
1090
1090
1050
1050
1050
1040
1030
1030
W14×211
W40× 466*
W36×245
W30×261
W36×230
W12× 279*
W33×241
1030
1010
1010
959
940
937
932
W14×193
W44×262
W40×249
W27×258
W30×235
W33×221
931
927
926
859
855
840
Iy
Shape
In.4
Shape
In.4
W14×176
W12×252*
W24×279*
W40×392*
W40× 215
W44× 230
W18× 311*
W27× 235
W30× 211
W33× 201
838
828
823
803
796
796
795
768
757
749
W14×159
W12×230*
W24×250*
W18×283*
W27× 217
W40× 199
748
742
724
704
704
695
W14×145
W30× 191
W12×210*
W24× 229
W40× 331
W18×258*
W27× 194
W30× 173
W12× 190
W24× 207
W18×234*
W27× 178
677
673
664
651
646
628
618
598
589
578
558
555
W14×132
W21× 201
W40× 174
W24× 192
W36× 256
W40× 278
W12× 170
W27× 161
548
542
541
530
528
521
517
497
*Group 4 or 5 shape. See Notes in Table 1-2 (Part 1).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Iy
In.4
W14×120
W40× 264
W18× 211*
W21× 182
W24× 176
W36× 232
W12× 152
495
493
493
483
479
468
454
W14×109
W40× 235
W24× 162
W27× 146
W18× 192
W21× 166
W36× 210
447
444
443
443
440
435
411
W14×99
W12× 136
W18× 175
W24× 146
W40× 211
W21× 147
W36× 194
402
398
391
391
390
376
375
W14×90
W36× 182
W18× 158
W12× 120
W24× 131
W40× 183
W21× 132
W36× 170
W18× 143
W33× 169
W21× 122
W12× 106
W24× 117
W36× 160
W40× 167
W18× 130
W21× 111
W33× 152
W36× 150
W12× 96
W24× 104
W18× 119
W21× 101
W33× 141
362
347
347
345
340
336
333
320
311
310
305
301
297
295
283
278
274
273
270
270
259
253
248
246
MOMENT OF INERTIA SELECTION TABLE FOR W AND M SHAPES
4 - 27
MOMENT OF INERTIA SELECTION TABLE
For W and M shapes
Shape
Iy
Shape
In.4
W12×87
W10× 112
W40× 149
W30× 148
W36× 135
W18× 106
W33× 130
241
236
229
227
225
220
218
W12×79
W10× 100
W18× 97
W30× 132
216
207
201
196
W12×72
W33× 118
W16× 100
W27× 129
W30× 124
W10× 88
W18× 86
195
187
186
184
181
179
175
W12×65
W30× 116
W16× 89
W27× 114
W10× 77
W18× 76
W14× 82
W30× 108
W27× 102
W16× 77
W10× 68
W14× 74
W30× 99
W27× 94
W14× 68
W24× 103
W16× 67
174
164
163
159
154
152
148
146
139
138
134
134
128
124
121
119
119
Iy
Shape
In.4
W10×60
W30× 90
W24× 94
116
115
109
W12×58
W14× 61
W27× 84
107
107
106
W10×54
103
W12×53
W24× 84
95.8
94.4
W10×49
W21× 93
W8× 67
W24× 76
W21× 83
W8× 58
W21× 73
W24× 68
W21× 68
93.4
92.9
88.6
82.5
81.4
75.1
70.6
70.4
64.7
W8×48
W18× 71
W14× 53
W21× 62
W12× 50
W18× 65
60.9
60.3
57.7
57.5
56.3
54.8
W10×45
W14× 48
W18× 60
53.4
51.4
50.1
W12×45
50.0
W8×40
W14× 43
49.1
45.2
Iy
Shape
In.4
W10×39
W18× 55
W12× 40
W16× 57
45.0
44.9
44.1
43.1
W8×35
W18× 50
W16× 50
42.6
40.1
37.2
W8×31
W10× 33
W24× 62
W16× 45
W21× 57
W24× 55
W16× 40
W14× 38
W21× 50
W12× 35
W16× 36
W14× 34
W18× 46
37.1
36.6
34.5
32.8
30.6
29.1
28.9
26.7
24.9
24.5
24.5
23.3
22.5
W8×28
W21× 44
W12× 30
W14× 30
W18× 40
21.7
20.7
20.3
19.6
19.1
W8×24
W12× 26
W6× 25
W10× 30
W18× 35
W10× 26
18.3
17.3
17.1
16.7
15.3
14.1
W6×20
W16× 31
W10× 22
W8× 21
W16× 26
13.3
12.4
11.4
9.77
9.59
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Iy
Iy
In.4
W6×15
W5× 19
W14×26
W8× 18
M5× 18.9
W5× 16
W14×22
W12×22
W6× 16
W10×19
9.32
9.13
8.91
7.97
7.86
7.51
7.00
4.66
4.43
4.29
W4×13
W12×19
W10×17
W8× 15
3.86
3.76
3.56
3.41
W6×12
W10×15
W12×16
W8× 13
W12×14
2.99
2.89
2.82
2.73
2.36
W6×9
W10×12
W8× 10
M12× 11.8
M12× 10.8
2.19
2.18
2.09
1.09
0.995
M10×9
0.673
M10×8
0.597
M8×6.5
0.371
4 - 28
BEAM AND GIRDER DESIGN
FACTORED UNIFORM LOAD TABLES
General Notes
The Tables of Factored Uniform Loads for W and S shapes and channels (C and MC)
used as simple laterally supported beams give the maximum uniformly distributed
factored loads in kips. The tables are based on the flexural design strengths specified in
Section F1 of the LRFD Specification. Separate tables are presented for Fy = 36 ksi and
Fy = 50 ksi. The tabulated loads include the weight of the beam, which should be deducted
in the calculation to determine the net load that the beam will support.
The tables are also applicable to laterally supported simple beams for concentrated
loading conditions. A method to determine the beam load capacity for several cases
is shown in this discussion.
It is assumed, in all cases, that the loads are applied normal to the X-X axis
(shown in the Tables of Properties of Shapes in Part 1 of this LRFD Manual) and
that the beam deflects vertically in the plane of bending. If the conditions of loading
involve forces outside this plane, design strengths must be determined from the
general theory of flexure and torsion.
Lateral Support of Beams
The flexural design strength of a beam is dependent upon lateral support of its compression flange in addition to its section properties. In these tables the notation Lp is used to
denote the maximum unbraced length of the compression flange, in feet, for the uniform
moment case (Cb = 1.0) and for which the design strengths for compact symmetrical
shapes are calculated with a flexural design strength of:
φbMn = φbMp = φbZxFy / 12
Noncompact shapes are calculated with a flexural design strength of:
 λ − λp 
φbMn′ = φbMp − φb(Mp − Mr) 

 λr − λp 
as permitted in the LRFD Specification Appendix F1. The associated maximum unbraced
length for φbMn′ is tabulated as Lp. The notation Lr is the unbraced length of the
compression flange for which the flexural design strength for rolled shapes is:
φbMr = φbSx(Fy − 10) / 12
These tables are not applicable for beams with unbraced lengths greater than Lr. For such
cases, the beam charts should be used.
Flexural Design Strength and Tabulated Factored Uniform Loads
For symmetrical rolled shapes designated W and S the flexural design strengths and
resultant loads are based on the assumption that the compression flanges of the beams
are laterally supported at intervals not greater than Lp.
The Uniform Load Constant φbWc is obtained from the moment and stress relationship
of a simply supported, uniformly loaded beam. The relationship results in the formula:
φbWc = φb(2ZxFy / 3), kip-ft for compact shapes
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
4 - 29
The following expression may be used for calculating the tabulated uniformly distributed
factored load Wu on a simply supported beam or girder:
Wu = φbWc / L, kips
For compact shapes, the tabulated constant is based on the yield stress Fy = 36 ksi or
50 ksi and the plastic section modulus Zx. (See Section F1.1 of the LRFD Specification.)
For noncompact sections, the tabulated constant is based on the nominal resisting moment
as determined by Equation A-F1-3. (See LRFD Specification Appendix F1.)
Shear
For relatively short spans, the design strengths for beams and channels may be limited
by the shear strength of the web instead of the bending strength. This limit is indicated
in the tables by solid horizontal lines. Loads shown above these lines will produce the
design shear strength in the beam web.
End and Interior Bearing
For a discussion of end and interior bearing and use of the tabulated values φR1 through
φr R6 and φR, see Part 9 in Volume II of this LRFD Manual.
Vertical Deflection
For rolled shapes designated W, M, S, C, and MC, the maximum vertical deflection may
be calculated using the formula:
∆ = ML2 / (C1Ix)
where
M = maximum service load moment, kip-ft
L = span length, ft
Ix = moment of inertia, in.4
C1 = loading constant (see Figure 4-2)
∆ = maximum vertical deflection, in.
W
P
C1 = 161
P
C1 = 201
P
P
P
C1 = 158
C1= 170
Fig. 4-2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
P
4 - 30
BEAM AND GIRDER DESIGN
Table 4-2.
Recommended Span/Depth Ratios
Service Load Ratios
Maximum Span/Depth Ratios
Dead / Total
Dead / Live
Fy = 36 ksi
Fy = 50 ksi
0.2
0.3
0.4
0.5
0.6
0.25
0.43
0.67
1.00
1.50
20.0
22.2
25.0
29.0
—
14.0
16.0
18.0
21.0
26.0
Deflection can be controlled by limiting the span-depth ratio of a simply supported,
uniformly loaded beam as shown in Table 4-2. A live-load deflection limit of L / 360 is
assumed; i.e.,
∆LL ≤
Span Length
360
For large span/depth ratios, vibration may also be a consideration.
Use of Tables
Maximum factored uniform loads are tabulated for steels of Fy = 36 ksi and Fy = 50 ksi.
They are based on the design flexural strength determined from the LRFD Specification:
Equation F1-1 (in Section F1.1) for compact members, and Equation A-F1-3 (in Appendix F1) for noncompact members. The beams must be braced adequately and have an
axis of symmetry in the plane of loading. Factored loads may be read directly from the
tables when the distance between points of lateral support of the compression flange Lb
does not exceed Lp (tabulated earlier in the Load Factor Design Selection Table for
beams).
Loads above the heavy horizontal lines in the tables are governed by the design shear
strength, determined from Section F2 of the LRFD Specification.
EXAMPLE 4-4
Given:
A W16×45 floor beam of Fy = 50 ksi steel spans 20 feet. Determine the
maximum uniform load, end reaction, and total service load deflection.
The live load equals the dead load.
Solution:
Based on Section A4 of the LRFD Specification, the governing load
combination for a floor beam is 1.2 (dead load) + 1.6 (live load). As
the two loads are equal,
factored load = 1.4 (total load)
Enter the Factored Uniform Loads Table for Fy = 50 ksi and note that:
Maximum factored uniform load = Wu
= 124 kips, or 124/20 = 6.2 kips/ft
Factored end reaction = Wu / 2 = 124 / 2 = 61.8 kips
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
4 - 31
Service load moment =
124(20)
Wu L
=
8(1.4)
8(LF)
= 221 kip-ft
Deflection:
∆=
ML2 221(20)2
=
= 0.94 in.
C1Ix 161(586)
Live load deflection = 0.5 × 0.94 in. = 0.47 in. < (L / 360 = 20 ×
12 / 360 = 0.66 in.) o.k.
EXAMPLE 4-5
Given:
A W10×45 beam of Fy = 50 ksi steel spans 6 feet. Determine the
maximum load and corresponding end reaction.
Solution:
Enter the Factored Uniform Loads Table for Fy = 50 ksi and note that:
Maximum factored uniform load = Wu
= 191 kips, or 191/6 = 31.8 kips/ft
As Wu appears above the horizontal line, it is limited by shear in the
web.
Factored end reaction = Wu / 2 = 191 / 2 = 96 kips
EXAMPLE 4-6
Given:
Using Fy = 50 ksi steel, select an 18-in. deep beam to span 30 feet and
support two equal concentrated loads at the one-third and two-thirds
points of the span. The service load intensities are 10 kips dead load
and 24 kips live load. The beam is supported laterally at the points of
load application and the ends. Determine the beam size and service
live load deflection.
Solution:
Refer to the Table of Concentrated Load Equivalents on page 4-189
and note that:
Equivalent uniform load = 2.67Pu
1. Required factored uniform load:
Wu = 2.67Pu = 2.67[1.2(10) + 1.6(24)]
= 2.67(50.4)
= 135 kips
2. Enter the Factored Uniform Loads Table for Fy = 50 ksi and Wu ≥
135 kips
For W18×71: Wu = 145 kips > 135 kips; however, Lb = 10 ft > Lp =
6.0 ft.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 32
BEAM AND GIRDER DESIGN
For W18×76: Wu = 163 kips > 135 kips; however, Lb = 10 ft > Lp =
9.2 ft.
3. Since Lp < Lb < Lr, use the Load Factor Design Selection Table.
φbMn = Cb[φbMp − BF(Lb − Lp)]
For the central third of the span (uniform moment), Cb = 1.0.
Required flexural strength: Mu = Pu (L / 3) = 50.4(30 / 3) = 504 kip-ft
4. Try W18×71:
φbMn = 1.0[544 − 13.8(10 − 6)]
= 489 kip-ft < 504 kip-ft req’d. n.g.
5. Try W18×76:
φbMn = 1.0[611 − 11.1(10 − 9.2)]
= 602 kip-ft > 504 kip-ft req’d. o.k.
Use W18×76
6. Determine service live load deflection:
MLL = (PLL / Pu )Mu = (24 / 50.4)504 = 240 kip-ft
Maximum ∆ (at midspan) =
240(30)2
MLLL2
=
= 1.03 in.
C1Ix
158(1,330)
EXAMPLE 4-7
Given:
A W24×55 of 50 ksi steel spans 20 feet and is braced at 4-ft intervals.
Determine the maximum factored load and end reaction.
Solution:
1. Enter the Factored Uniform Load Table for Fy = 50 ksi and note that:
Maximum factored uniform load = Wu = 201 kips, or 201 / 20 =
10.1 kips/ft
This is true for Lb ≤ Lp : 4.0 ft < 4.7 ft o.k.
2. End reaction = R = Wu / 2 = 201 / 2 = 101 kips
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
4 - 33
Reference Notes on Tables
1. Maximum factored uniform loads, in kips, are given for beams with adequate lateral
support; i.e., Lb ≤ Lp for Cb = 1.0, Lb ≤ Lm for Cb > 1.0.
2. Loads below the heavy horizontal line are limited by design flexural strength, while
loads above the line are limited by design shear strength.
3. Factored loads are given for span lengths up to the smaller of L / d = 30 or 72 ft.
4. The end bearing values at the bottom of the tables are for use in solving LRFD
Specification Equations K1-3, K1-5a, and K1-5b. They are defined as follows:
φR1 = φ(2.5kFy tw)
φR2 = φ(Fy tw)
kips
kips/in.
Equation K1-3 becomes φRn = φR1 + N(φR2)

Fty tf 
φrR3 = φr 68t2w √

w
kips
1.5

 3  tw 
φrR4 = φr 68t2w    
 d  tf 


√Ft t 
y f
w

kips/in.
Equation K1-5a becomes φrRn = φrR3 + N(φrR4)
1.5


 tw 
φrR5 = φr 68t2w 1 − 0.2  

 tf 




1.5

 4   tw 
φrR6 = φr 68t2w    
 d   tf 


Fty tf 
√
w


√Fty t 
f
w

kips
kips/in.
Equation K1-5b becomes φrRn = φrR5 + N(φrR6)
where φ = 1.00, φr = 0.75, N = length of bearing (in.), and the other terms as defined
in the LRFD Specification, Section K1.
φR (N = 31⁄4) is defined as the design bearing strength for N = 31⁄4-in.
For N / d ≤ 0.2,
φR is the minimum of
φR1 + N(φR2)
φrR3 + N(φrR4)
For N / d > 0.2,
φR is the minimum of
φR1 + N(φR2)
φrR5 + N(φrR6)
For a complete explanation of end and interior bearing and use of the tabulated values,
see Part 9 in Volume II of this LRFD Manual.
5. The other terms at the bottom of the tables are:
Zx
= plastic section modulus for major axis bending, in.3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 34
BEAM AND GIRDER DESIGN
φvVn = design shear strength, kips
φbWc = uniform load constant
= φb(2ZxFy / 3) kip-ft for compact shapes;
per Equation A-F1-3 (LRFD Specification Appendix F1) for noncompact
shapes
6. Tabulated maximum factored uniformly distributed load for the given beam and span
is the minimum of
φbWc
and 2φvVn
L
See also Note 2 above.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 35
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 44
For beams laterally unsupported, see page 4-113
Designation
W 44
Span (ft)
Fy = 36 ksi
Wt./ft
335
290
262
230
20
21
22
23
24
25
1750
1670
1590
1520
1460
1400
1480
1460
1390
1330
1280
1230
1330
1310
1250
1190
1140
1100
1180
1130
1080
1030
990
950
26
27
28
29
30
31
1350
1300
1250
1210
1170
1130
1180
1140
1100
1060
1020
989
1060
1020
980
946
914
885
914
880
849
819
792
766
32
33
34
35
36
1090
1060
1030
1000
972
959
929
902
876
852
857
831
807
784
762
743
720
699
679
660
38
40
42
44
46
48
921
875
833
795
761
729
807
767
730
697
667
639
722
686
653
623
596
572
625
594
566
540
517
495
50
52
54
56
58
60
700
673
648
625
603
583
613
590
568
548
529
511
549
528
508
490
473
457
475
457
440
424
410
396
62
64
66
68
70
72
564
547
530
515
500
486
495
479
465
451
438
426
442
429
416
403
392
381
383
371
360
349
339
330
1270
27400
665
156
28.4
256
7.36
235
9.81
248
1100
23800
592
128
25.6
202
6.28
184
8.37
211
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1620
35000
873
235
36.7
419
12.5
383
16.7
355
1420
30700
738
186
31.3
312
8.77
287
11.7
288
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 36
BEAM AND GIRDER DESIGN
W 40
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
W 40
431
372
321
297
277
249
199
174
977
937
965
965
908
858
813
772
985
945
904
867
832
800
893
852
815
781
750
721
735
702
671
644
618
594
896
864
834
806
780
756
770
743
717
693
671
650
694
670
647
625
605
586
572
552
533
515
498
483
818
794
771
750
730
711
733
712
691
672
654
637
630
612
594
578
562
547
568
551
536
521
507
493
468
454
441
429
417
406
718
684
653
625
599
575
675
643
614
587
563
540
605
576
550
526
504
484
520
495
473
452
433
416
469
446
426
408
391
375
386
368
351
336
322
309
590
568
548
529
511
495
552
532
513
495
479
463
519
500
482
466
450
435
465
448
432
417
403
390
400
385
371
359
347
335
361
347
335
323
312
302
297
286
276
266
257
249
479
465
451
438
426
449
435
422
410
399
422
409
397
386
375
378
367
356
346
336
325
315
306
297
289
293
284
276
268
260
241
234
227
221
215
1120
24200
574
190
27.0
237
6.93
219
9.23
259
963
20800
493
154
23.4
177
5.30
163
7.07
194
868
18700
489
143
23.4
165
6.12
150
8.16
185
715
15400
483
117
23.4
146
7.95
126
10.6
172
1830
1800
1560
1530
1440
1440
21
22
23
24
25
26
2010
1910
1830
1760
1680
1620
1720
1640
1570
1500
1440
1390
1460
1390
1330
1280
1230
1180
1370
1310
1250
1200
1150
1100
1280
1230
1170
1130
1080
1040
1150
1100
1050
1010
968
930
27
28
29
30
31
32
1560
1500
1450
1400
1360
1320
1340
1290
1240
1200
1160
1130
1140
1100
1060
1020
989
959
1060
1030
991
958
927
898
1000
964
931
900
871
844
33
34
35
36
37
38
1280
1240
1200
1170
1140
1110
1090
1060
1030
1000
975
949
929
902
876
852
829
807
871
845
821
798
776
756
40
42
44
46
48
50
1050
1000
957
916
878
842
902
859
820
784
752
721
767
730
697
667
639
613
52
54
56
58
60
62
810
780
752
726
702
679
694
668
644
622
601
582
64
66
68
70
72
658
638
619
602
585
564
547
530
515
501
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1950
42100
1075
430
48.2
729
22.7
667
30.2
586
1670
36100
916
339
41.8
547
17.2
501
22.9
475
Span (ft)
2150
2110
Fy = 36 ksi
15
16
17
18
19
20
215
Properties and Reaction Values
1420
30700
779
264
36.0
407
12.9
373
17.3
381
1330
28700
720
256
33.5
353
11.2
323
15.0
365
1250
27000
640
224
29.9
290
8.40
268
11.2
318
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 37
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 40
For beams laterally unsupported, see page 4-113
Span (ft)
Fy = 36 ksi
Designation
Wt./ft
W 40
331
278
264
235
211
167
149
985
937
975
934
879
830
936
921
860
806
759
716
1030
977
931
889
850
815
888
843
803
767
733
703
787
747
712
679
650
623
679
645
614
586
561
537
873
839
808
779
752
727
782
752
724
698
674
652
675
649
625
602
582
562
598
575
554
534
515
498
516
496
478
461
445
430
787
763
740
718
697
678
704
682
661
642
623
606
631
611
592
575
559
543
544
527
511
496
482
469
482
467
453
440
427
415
416
403
391
379
368
358
695
676
643
612
584
559
660
642
610
581
555
531
590
574
545
519
496
474
528
514
489
465
444
425
456
444
422
402
383
367
404
393
374
356
340
325
349
339
322
307
293
280
644
618
594
572
552
533
536
514
494
476
459
443
509
488
469
452
436
421
455
436
420
404
390
376
407
391
376
362
349
337
351
337
324
312
301
291
311
299
287
277
267
258
269
258
248
239
230
222
60
62
64
66
68
70
515
498
483
468
454
441
428
415
402
389
378
367
407
394
381
370
359
349
364
352
341
331
321
312
326
315
305
296
287
279
281
272
264
256
248
241
249
241
234
226
220
214
215
208
201
195
190
184
72
429
357
339
303
272
234
208
179
781
16900
493
154
23.4
177
5.30
163
7.07
194
692
14900
488
143
23.4
162
6.37
146
8.50
183
597
12900
468
128
22.7
139
7.24
121
9.65
163
13
14
15
16
17
18
1930
1930
1820
1720
1590
1510
1430
1490
1440
1360
1280
1210
1150
1090
19
20
21
22
23
24
1630
1540
1470
1400
1340
1290
1350
1290
1220
1170
1120
1070
1280
1220
1160
1110
1060
1020
1150
1090
1040
992
949
909
25
26
27
28
29
30
1240
1190
1140
1100
1070
1030
1030
989
952
918
886
857
976
939
904
872
842
814
31
32
33
34
35
36
996
965
936
908
883
858
829
803
779
756
734
714
37
38
40
42
44
46
835
813
772
735
702
671
48
50
52
54
56
58
183
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1430
30900
967
364
43.9
602
19.2
550
25.6
506
1190
25700
796
275
36.7
424
13.4
388
17.9
395
1130
24400
746
254
34.6
379
11.7
347
15.6
366
1010
21800
640
205
29.9
290
8.40
268
11.2
303
905
19500
574
177
27.0
236
6.95
218
9.27
259
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 38
BEAM AND GIRDER DESIGN
W 36
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
W 36
Span (ft)
Fy = 36 ksi
Wt./ft
300
280
260
245
230
1120
1090
1040
992
949
909
1060
1020
970
926
886
849
19
20
21
22
23
24
1350
1300
1240
1180
1130
1260
1200
1150
1100
1050
1180
1170
1110
1060
1010
972
25
26
27
28
29
30
1090
1050
1010
972
938
907
1010
972
936
903
871
842
933
897
864
833
804
778
873
839
808
779
752
727
815
783
754
727
702
679
31
32
33
34
35
36
878
851
825
800
778
756
815
790
766
743
722
702
753
729
707
686
667
648
704
682
661
642
623
606
657
637
617
599
582
566
37
38
39
40
41
42
736
716
698
680
664
648
683
665
648
632
616
602
630
614
598
583
569
555
590
574
559
545
532
519
551
536
522
509
497
485
43
44
46
48
50
52
633
619
592
567
544
523
588
574
549
527
505
486
543
530
507
486
467
449
507
496
474
455
436
420
474
463
443
424
407
392
54
56
58
60
62
64
504
486
469
454
439
425
468
451
436
421
408
395
432
417
402
389
376
365
404
390
376
364
352
341
377
364
351
339
329
318
66
68
70
72
412
400
389
378
383
372
361
351
353
343
333
324
331
321
312
303
309
300
291
283
1010
21800
561
180
28.8
254
9.65
231
12.9
274
943
20400
530
162
27.4
228
8.91
206
11.9
251
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1260
27200
675
239
34.0
364
12.6
334
16.7
350
1170
25300
628
214
31.9
319
11.1
292
14.8
318
1080
23300
592
194
30.2
283
10.4
258
13.9
292
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 39
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 36
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
W 36
256
19
20
21
22
23
24
194
182
170
160
150
135
1260
1190
1120
1180
1120
1060
1000
1090
1040
975
920
1020
969
912
862
956
902
849
802
910
899
842
793
749
871
837
784
738
697
1180
1120
1070
1020
977
936
1060
1010
963
919
879
842
947
900
857
818
782
750
872
828
789
753
720
690
816
775
739
705
674
646
759
721
687
656
627
601
709
674
642
613
586
562
661
627
598
570
546
523
579
550
524
500
478
458
25
26
27
28
29
30
899
864
832
802
775
749
809
778
749
722
697
674
720
692
666
643
620
600
663
637
614
592
571
552
620
596
574
554
535
517
577
555
534
515
498
481
539
518
499
481
465
449
502
483
465
448
433
418
440
423
407
393
379
366
31
32
33
34
35
36
725
702
681
661
642
624
652
632
613
595
578
562
580
562
545
529
514
500
534
518
502
487
473
460
500
485
470
456
443
431
465
451
437
424
412
401
435
421
408
396
385
374
405
392
380
369
359
349
355
344
333
323
314
305
38
40
42
44
46
48
591
562
535
511
488
468
532
505
481
459
440
421
473
450
428
409
391
375
436
414
394
377
360
345
408
388
369
352
337
323
380
361
344
328
314
301
355
337
321
306
293
281
330
314
299
285
273
261
289
275
262
250
239
229
50
52
54
56
58
60
449
432
416
401
387
374
404
389
374
361
349
337
360
346
333
321
310
300
331
319
307
296
286
276
310
298
287
277
267
258
289
277
267
258
249
240
270
259
250
241
232
225
251
241
232
224
216
209
220
211
204
196
190
183
62
64
66
68
70
72
362
351
340
330
321
312
326
316
306
297
289
281
290
281
273
265
257
250
267
259
251
244
237
230
250
242
235
228
222
215
233
225
219
212
206
200
217
211
204
198
193
187
202
196
190
185
179
174
177
172
167
162
157
153
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1040
22500
699
227
34.6
379
12.5
347
16.7
339
936
20200
628
196
31.3
311
10.4
285
13.8
298
624
13500
455
113
23.4
162
6.86
145
9.15
184
581
12500
436
105
22.5
147
6.65
131
8.87
168
509
11000
415
91.1
21.6
126
7.06
110
9.41
149
Span (ft)
1400
1320
1250
210
829
785
733
687
647
611
Fy = 36 ksi
13
14
15
16
17
18
232
Properties and Reaction Values
833
18000
592
173
29.9
270
10.5
244
14.0
270
767
16600
543
151
27.5
230
8.94
208
11.9
240
718
15500
512
139
26.1
205
8.16
185
10.9
223
668
14400
478
122
24.5
180
7.25
162
9.67
202
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 40
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 33
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 33
241
221
W 33
201
169
152
141
130
118
755
710
671
635
604
575
694
653
617
584
555
529
630
593
560
531
504
480
560
527
498
472
448
427
16
17
18
19
20
21
1100
1070
1010
966
1020
972
923
879
936
926
878
834
794
849
799
755
715
679
647
22
23
24
25
26
27
922
882
845
811
780
751
839
803
770
739
710
684
758
725
695
667
641
618
618
591
566
543
523
503
549
525
503
483
464
447
505
483
463
444
427
411
459
439
420
403
388
374
407
390
374
359
345
332
28
29
30
31
32
33
724
699
676
654
634
615
660
637
616
596
577
560
596
575
556
538
521
505
485
468
453
438
425
412
431
416
402
389
377
366
397
383
370
358
347
336
360
348
336
325
315
306
320
309
299
289
280
272
34
35
36
37
38
40
597
579
563
548
534
507
543
528
513
499
486
462
490
476
463
451
439
417
400
388
377
367
358
340
355
345
335
326
318
302
327
317
308
300
292
278
297
288
280
273
265
252
264
256
249
242
236
224
42
44
46
48
50
52
483
461
441
423
406
390
440
420
401
385
369
355
397
379
363
347
334
321
323
309
295
283
272
261
287
274
262
252
241
232
264
252
241
231
222
214
240
229
219
210
202
194
213
204
195
187
179
172
54
56
58
60
62
64
376
362
350
338
327
317
342
330
318
308
298
289
309
298
288
278
269
261
252
243
234
226
219
212
224
216
208
201
195
189
206
198
191
185
179
173
187
180
174
168
163
158
166
160
155
149
145
140
66
68
70
72
307
298
290
282
280
272
264
257
253
245
238
232
206
200
194
189
183
178
172
168
168
163
159
154
153
148
144
140
136
132
128
125
514
11100
392
95.3
21.8
141
6.36
127
8.48
162
467
10100
373
88.1
20.9
125
6.33
111
8.44
146
415
8960
351
77.3
19.8
107
6.28
93.6
8.37
128
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
939
20300
552
163
29.9
274
11.0
249
14.6
261
855
18500
511
144
27.9
236
9.88
213
13.2
235
772
16700
468
125
25.7
198
8.66
179
11.6
208
629
13600
440
124
24.1
185
6.69
170
8.92
203
559
12100
413
107
22.9
159
6.65
144
8.87
181
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 41
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 30
For beams laterally unsupported, see page 4-113
Designation
W 30
Span (ft)
Fy = 36 ksi
Wt./ft
261
235
191
173
932
899
851
809
770
847
808
765
727
692
775
769
726
688
653
622
830
794
761
730
702
676
735
703
674
647
622
599
661
632
606
581
559
538
594
568
545
523
503
484
726
701
678
656
635
616
652
629
608
589
570
553
578
558
539
522
506
490
519
501
485
469
454
441
467
451
436
422
408
396
34
36
38
40
42
44
598
565
535
508
484
462
537
507
480
456
435
415
476
449
426
404
385
368
428
404
383
363
346
330
384
363
344
327
311
297
46
48
50
52
54
56
442
423
407
391
376
363
397
380
365
351
338
326
352
337
324
311
300
289
316
303
291
280
269
260
284
272
261
251
242
233
58
60
62
64
66
68
350
339
328
318
308
299
315
304
294
285
277
268
279
270
261
253
245
238
251
242
234
227
220
214
225
218
211
204
198
192
70
72
290
282
261
254
231
225
208
202
187
182
673
14500
423
124
25.6
199
9.04
181
12.0
207
605
13100
388
111
23.6
167
7.96
151
10.6
187
16
17
18
19
20
21
1140
1130
1070
1020
968
1010
961
913
869
22
23
24
25
26
27
924
884
847
813
782
753
28
29
30
31
32
33
211
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
941
20300
571
204
33.5
353
14.2
323
18.9
313
845
18300
505
168
29.9
283
11.2
260
14.9
265
749
16200
466
148
27.9
239
10.5
218
14.0
239
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 42
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 30
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 30
148
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
36
38
40
42
44
46
48
50
52
54
56
58
60
62
64
66
68
70
72
775
771
720
675
635
600
568
540
514
491
470
450
432
415
400
386
372
360
348
338
327
318
300
284
270
257
245
235
225
216
208
200
193
186
180
174
169
164
159
154
150
132
725
674
629
590
555
524
497
472
449
429
410
393
378
363
350
337
325
315
304
295
286
278
262
248
236
225
215
205
197
189
182
175
169
163
157
152
147
143
139
135
131
124
686
678
629
588
551
518
490
464
441
420
401
383
367
353
339
326
315
304
294
284
275
267
259
245
232
220
210
200
192
184
176
169
163
157
152
147
142
138
134
130
126
122
116
108
99
90
659
628
583
544
510
480
454
430
408
389
371
355
340
327
314
302
292
282
272
263
255
247
240
227
215
204
194
186
177
170
163
157
151
146
141
136
132
128
124
120
117
113
632
623
575
534
498
467
440
415
393
374
356
340
325
311
299
287
277
267
258
249
241
234
226
220
208
197
187
178
170
162
156
149
144
138
133
129
125
121
117
113
110
107
104
599
562
518
481
449
421
396
374
355
337
321
306
293
281
270
259
250
241
232
225
217
211
204
198
187
177
168
160
153
147
140
135
130
125
120
116
112
109
105
102
99
96
94
540
509
470
437
408
382
360
340
322
306
291
278
266
255
245
235
226
218
211
204
197
191
185
180
170
161
153
146
139
133
127
122
118
113
109
105
102
99
96
93
90
87
85
346
7470
316
76.6
19.6
107
6.55
94.3
8.74
129
312
6740
300
67.3
18.7
93.9
6.50
81.1
8.66
115
283
6110
270
55.5
16.9
77.0
5.29
66.6
7.05
94.2
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
500
10800
388
117
23.4
174
6.97
160
9.29
193
437
9440
362
96.9
22.1
148
7.05
133
9.39
169
408
8810
343
88.8
21.1
132
6.55
119
8.73
153
378
8160
330
82.6
20.3
120
6.49
107
8.65
141
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 43
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 27
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 27
258
235
194
178
161
146
917
900
850
805
765
820
798
754
714
678
784
765
720
680
645
612
708
691
651
614
582
553
644
622
586
553
524
498
791
755
722
692
664
639
728
695
665
637
612
588
646
617
590
565
543
522
583
557
532
510
490
471
527
503
481
461
442
425
474
453
433
415
398
383
680
656
633
612
592
574
615
593
573
554
536
519
566
546
527
510
493
478
502
484
468
452
438
424
454
437
422
408
395
383
410
395
381
369
357
346
369
356
343
332
321
311
33
34
35
36
37
38
556
540
525
510
496
483
503
489
475
461
449
437
463
450
437
425
413
402
411
399
388
377
367
357
371
360
350
340
331
322
335
325
316
307
299
291
302
293
285
277
269
262
40
42
44
46
48
50
459
437
417
399
383
367
415
395
378
361
346
332
382
364
348
332
319
306
339
323
308
295
283
271
306
292
278
266
255
245
276
263
251
240
230
221
249
237
226
216
207
199
52
54
56
58
60
62
353
340
328
317
306
296
319
308
297
286
277
268
294
283
273
264
255
247
261
251
242
234
226
219
236
227
219
211
204
198
213
205
197
191
184
178
191
184
178
172
166
161
64
66
287
278
260
252
239
232
212
206
191
186
173
168
156
151
567
12200
392
122
26.1
206
10.6
186
14.1
207
512
11100
354
108
23.8
171
8.86
154
11.8
185
461
9960
322
91.9
21.8
142
7.62
128
10.2
163
15
16
17
18
19
20
1100
1080
1020
966
918
1010
977
923
874
831
21
22
23
24
25
26
874
835
798
765
734
706
27
28
29
30
31
32
217
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
850
18400
552
221
35.3
395
16.8
362
22.5
335
769
16600
507
189
32.8
337
15.0
308
20.0
296
708
15300
459
163
29.9
283
12.3
260
16.4
261
628
13600
410
139
27.0
230
10.3
211
13.7
227
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 44
BEAM AND GIRDER DESIGN
W 27
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
W 27
Span (ft)
Fy = 36 ksi
Wt./ft
129
102
94
84
605
570
529
494
463
542
507
471
439
412
513
500
462
429
400
375
478
439
405
376
351
329
502
474
449
427
406
388
436
412
390
370
353
337
388
366
347
329
314
299
353
334
316
300
286
273
310
293
277
264
251
240
23
24
25
26
27
28
371
356
341
328
316
305
322
309
296
285
274
265
286
275
264
253
244
235
261
250
240
231
222
214
229
220
211
203
195
188
29
30
31
32
33
34
294
284
275
267
259
251
255
247
239
232
225
218
227
220
213
206
200
194
207
200
194
188
182
177
182
176
170
165
160
155
36
38
40
42
44
46
237
225
213
203
194
185
206
195
185
176
168
161
183
173
165
157
150
143
167
158
150
143
136
131
146
139
132
125
120
115
48
50
52
54
56
58
178
171
164
158
152
147
154
148
142
137
132
128
137
132
127
122
118
114
125
120
115
111
107
104
110
105
101
98
94
91
60
62
64
66
142
138
133
129
123
119
116
112
110
106
103
100
100
97
94
91
88
85
82
80
278
6000
256
63.4
17.6
90.6
5.39
80.9
7.18
108
244
5270
239
56.9
16.6
76.4
5.23
67.1
6.97
93.4
11
12
13
14
15
16
655
609
569
533
17
18
19
20
21
22
114
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
395
8530
328
99.5
22.0
153
6.86
140
9.14
171
343
7410
302
83.4
20.5
127
6.70
115
8.93
149
305
6590
271
72.4
18.5
103
5.58
93.0
7.44
121
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 45
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 24
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 24
229
207
192
176
146
131
117
104
685
674
632
595
562
625
602
564
531
502
576
571
533
500
470
444
519
505
471
441
415
392
468
446
416
390
367
347
581
552
526
502
480
460
532
505
481
459
440
421
475
451
430
410
393
376
421
400
381
363
347
333
372
353
336
321
307
294
329
312
297
284
271
260
483
464
447
431
416
402
442
425
409
394
381
368
404
389
374
361
349
337
361
347
334
322
311
301
320
307
296
285
276
266
283
272
262
252
244
235
250
240
231
223
215
208
422
409
397
385
374
364
389
377
366
355
345
335
356
345
334
325
315
307
326
316
306
297
289
281
291
282
274
266
258
251
258
250
242
235
228
222
228
221
214
208
202
196
201
195
189
184
178
173
384
365
348
332
317
304
344
327
312
297
285
273
318
302
287
274
262
252
290
276
263
251
240
230
266
253
241
230
220
211
238
226
215
205
196
188
210
200
190
182
174
167
186
177
168
161
154
147
164
156
149
142
136
130
292
281
270
261
252
243
262
252
242
234
226
218
241
232
224
216
208
201
221
212
204
197
190
184
202
194
187
181
174
168
181
174
167
161
156
150
160
154
148
143
138
133
141
136
131
126
122
118
125
120
116
111
108
104
676
14600
486
216
34.6
379
18.0
347
24.1
328
606
13100
435
186
31.3
311
15.0
285
20.0
288
370
7990
288
95.3
21.8
141
8.65
127
11.5
166
327
7060
259
80.4
19.8
115
7.41
103
9.88
139
289
6240
234
67.5
18.0
93.7
6.36
83.5
8.48
114
13
14
15
16
17
18
971
913
859
811
870
818
770
727
802
755
710
671
736
736
690
649
613
19
20
21
22
23
24
769
730
695
664
635
608
689
654
623
595
569
545
635
604
575
549
525
503
25
26
27
28
29
30
584
562
541
521
504
487
524
503
485
467
451
436
31
32
33
34
35
36
471
456
442
429
417
406
38
40
42
44
46
48
50
52
54
56
58
60
162
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
559
12100
401
164
29.2
270
13.1
247
17.5
259
511
11000
368
143
27.0
230
11.5
211
15.3
231
468
10100
343
127
25.4
200
10.5
182
14.1
209
418
9030
313
110
23.4
167
9.35
152
12.5
186
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 46
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 24
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 24
103
94
84
W 24
76
68
62
55
397
367
330
300
275
362
362
322
289
263
241
7
8
9
10
11
12
525
504
487
457
440
440
403
409
393
360
383
382
348
319
13
14
15
16
17
18
465
432
403
378
356
336
422
392
366
343
323
305
372
346
323
302
285
269
332
309
288
270
254
240
294
273
255
239
225
212
254
236
220
207
194
184
223
207
193
181
170
161
19
20
21
22
23
24
318
302
288
275
263
252
289
274
261
249
239
229
255
242
230
220
210
202
227
216
206
196
188
180
201
191
182
174
166
159
174
165
157
150
144
138
152
145
138
132
126
121
25
26
27
28
29
30
242
233
224
216
209
202
219
211
203
196
189
183
194
186
179
173
167
161
173
166
160
154
149
144
153
147
142
137
132
127
132
127
122
118
114
110
116
111
107
103
100
96
31
32
33
34
35
36
195
189
183
178
173
168
177
171
166
161
157
152
156
151
147
142
138
134
139
135
131
127
123
120
123
119
116
112
109
106
107
103
100
97
94
92
93
90
88
85
83
80
38
40
42
44
46
48
159
151
144
137
131
126
144
137
131
125
119
114
127
121
115
110
105
101
114
108
103
98
94
90
101
96
91
87
83
80
87
83
79
75
72
69
76
72
69
66
63
60
50
52
54
56
58
60
121
116
112
108
104
101
110
106
102
98
95
91
97
93
90
86
83
81
86
83
80
77
74
76
74
71
68
66
66
64
61
59
57
58
56
54
52
50
177
3820
191
51.4
14.9
62.6
4.73
55.1
6.30
77.9
153
3300
198
53.2
15.5
66.3
5.21
58.0
6.95
83.2
134
2890
181
46.7
14.2
54.0
4.75
46.5
6.34
69.4
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
280
6050
262
86.6
19.8
124
6.35
113
8.47
144
254
5490
243
75.3
18.5
106
5.89
96.2
7.86
125
224
4840
220
66.1
16.9
86.5
5.14
78.3
6.85
103
200
4320
205
56.9
15.8
73.6
4.81
66.0
6.41
89.3
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 47
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 21
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 21
201
182
166
147
132
122
111
101
552
514
480
450
423
400
506
474
442
414
390
368
460
430
402
377
354
335
415
390
364
342
321
304
13
14
15
16
17
18
815
763
716
673
636
733
685
643
605
571
656
622
583
549
518
618
575
537
504
474
448
19
20
21
22
23
24
603
572
545
520
498
477
541
514
490
467
447
428
491
467
444
424
406
389
424
403
384
366
350
336
379
360
343
327
313
300
349
332
316
301
288
276
317
301
287
274
262
251
288
273
260
248
238
228
25
26
27
28
29
30
458
440
424
409
395
382
411
395
381
367
355
343
373
359
346
333
322
311
322
310
298
288
278
269
288
277
266
257
248
240
265
255
246
237
229
221
241
232
223
215
208
201
219
210
202
195
188
182
31
32
33
34
35
36
369
358
347
337
327
318
332
321
312
302
294
286
301
292
283
274
267
259
260
252
244
237
230
224
232
225
218
212
206
200
214
207
201
195
189
184
194
188
183
177
172
167
176
171
166
161
156
152
38
40
42
44
46
48
301
286
273
260
249
239
271
257
245
234
224
214
246
233
222
212
203
194
212
201
192
183
175
168
189
180
171
163
156
150
175
166
158
151
144
138
159
151
143
137
131
126
144
137
130
124
119
114
50
52
229
220
206
198
187
179
161
155
144
138
133
128
121
116
109
105
307
6630
253
91.1
21.6
139
9.53
126
12.7
161
279
6030
230
80.4
19.8
117
8.11
105
10.8
143
253
5460
208
70.3
18.0
96.8
6.72
87.2
8.95
119
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
530
11400
407
195
32.8
339
18.4
311
24.6
301
476
10300
367
168
29.9
281
15.6
258
20.8
265
432
9330
328
143
27.0
232
12.7
213
16.9
231
373
8060
309
122
25.9
200
13.5
181
18.0
206
333
7190
276
106
23.4
163
11.2
147
14.9
182
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 48
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 21
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 21
93
83
73
W 21
68
62
57
50
44
281
258
229
206
187
172
7
8
9
10
11
12
488
477
434
398
429
423
385
353
376
372
338
310
353
346
314
288
326
311
283
259
332
310
279
253
232
308
297
264
238
216
198
13
14
15
16
17
18
367
341
318
298
281
265
326
302
282
265
249
235
286
265
248
232
219
206
266
247
230
216
203
192
239
222
207
194
183
173
214
199
186
174
164
155
183
170
158
149
140
132
159
147
137
129
121
114
19
20
21
22
23
24
251
239
227
217
208
199
223
212
202
192
184
176
196
186
177
169
162
155
182
173
165
157
150
144
164
156
148
141
135
130
147
139
133
127
121
116
125
119
113
108
103
99
108
103
98
94
90
86
25
26
27
28
29
30
191
184
177
170
165
159
169
163
157
151
146
141
149
143
138
133
128
124
138
133
128
123
119
115
124
120
115
111
107
104
111
107
103
100
96
93
95
91
88
85
82
79
82
79
76
74
71
69
31
32
33
34
35
36
154
149
145
140
136
133
137
132
128
125
121
118
120
116
113
109
106
103
111
108
105
102
99
96
100
97
94
91
89
86
90
87
84
82
80
77
77
74
72
70
68
66
66
64
62
61
59
57
38
40
42
44
46
48
126
119
114
108
104
99
111
106
101
96
92
88
98
93
88
84
81
77
91
86
82
79
75
72
82
78
74
71
68
65
73
70
66
63
61
58
63
59
57
54
52
50
54
52
49
47
45
43
50
52
95
92
85
81
74
71
69
66
62
60
56
54
48
46
41
129
2790
166
50.1
14.6
63.6
4.45
57.3
5.94
78.1
110
2380
154
44.9
13.7
52.4
4.52
46.2
6.03
67.1
95.4
2060
141
37.4
12.6
42.5
4.23
36.7
5.64
56.3
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
221
4770
244
88.1
20.9
130
8.91
118
11.9
156
196
4230
215
72.4
18.5
103
7.01
93.3
9.34
126
172
3720
188
61.4
16.4
80.8
5.50
73.0
7.34
98.7
160
3460
177
55.6
15.5
71.4
5.04
64.3
6.72
87.8
144
3110
163
49.5
14.4
60.7
4.55
54.3
6.07
75.5
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 49
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 18
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
W 18
192
175
158
W 18
143
130
119
106
97
86
76
430
414
382
355
331
311
387
380
351
326
304
285
343
335
309
287
268
251
301
293
271
251
235
220
693
661
614
573
537
621
592
549
513
481
553
535
497
464
435
501
484
449
419
393
17
18
19
20
21
22
562
530
502
477
455
434
506
478
452
430
409
391
452
427
405
384
366
350
409
386
366
348
331
316
370
349
331
314
299
286
332
313
297
282
268
256
292
276
261
248
237
226
268
253
240
228
217
207
236
223
211
201
191
183
207
196
185
176
168
160
23
24
25
26
27
28
415
398
382
367
354
341
374
358
344
331
318
307
334
320
308
296
285
275
302
290
278
268
258
248
273
262
251
242
233
224
245
235
226
217
209
201
216
207
199
191
184
177
198
190
182
175
169
163
175
167
161
155
149
143
153
147
141
135
130
126
29
30
31
32
33
34
329
318
308
298
289
281
296
287
277
269
261
253
265
256
248
240
233
226
240
232
224
217
211
205
217
210
203
196
190
185
194
188
182
176
171
166
171
166
160
155
151
146
157
152
147
142
138
134
139
134
130
126
122
118
121
117
114
110
107
104
35
36
37
38
39
40
273
265
258
251
245
239
246
239
232
226
220
215
220
214
208
202
197
192
199
193
188
183
178
174
180
175
170
165
161
157
161
157
152
148
145
141
142
138
134
131
127
124
130
127
123
120
117
114
115
112
109
106
103
100
101
98
95
93
90
88
42
44
227
217
205
195
183
175
166
158
150
143
134
128
118
113
109
104
96
91
84
80
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
442
9550
380
211
34.6
381
22.8
350
30.4
323
398
8600
347
180
32.0
324
20.3
297
27.1
284
230
4970
215
86.3
21.2
134
10.7
121
14.3
155
211
4560
193
75.2
19.3
112
8.69
101
11.6
138
186
4020
172
62.1
17.3
89.3
7.17
80.5
9.56
113
163
3520
150
52.6
15.3
69.9
5.69
63.0
7.59
88.4
Span (ft)
760
734
682
636
597
483
470
434
403
376
352
Fy = 36 ksi
11
12
13
14
15
16
Properties and Reaction Values
356
7690
311
155
29.2
268
17.2
245
22.9
250
322
6960
277
131
26.3
219
13.9
201
18.5
217
291
6290
251
113
24.1
184
12.0
168
15.9
191
261
5640
242
103
23.6
167
12.8
151
17.1
180
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 50
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 18
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 18
71
65
6
7
8
9
10
11
355
348
313
285
321
319
287
261
12
13
14
15
16
17
261
241
224
209
196
184
18
19
20
21
22
23
60
W 18
55
50
46
40
35
294
266
242
275
269
242
220
248
242
218
198
253
245
218
196
178
219
212
188
169
154
206
205
180
160
144
131
239
221
205
192
180
169
221
204
190
177
166
156
202
186
173
161
151
142
182
168
156
145
136
128
163
151
140
131
122
115
141
130
121
113
106
100
120
110
103
96
90
84
174
165
157
149
142
136
160
151
144
137
131
125
148
140
133
127
121
116
134
127
121
115
110
105
121
115
109
104
99
95
109
103
98
93
89
85
94
89
85
81
77
74
80
76
72
68
65
62
24
25
26
27
28
29
131
125
120
116
112
108
120
115
110
106
103
99
111
106
102
98
95
92
101
97
93
90
86
83
91
87
84
81
78
75
82
78
75
73
70
68
71
68
65
63
60
58
60
57
55
53
51
50
30
31
32
33
34
35
104
101
98
95
92
89
96
93
90
87
84
82
89
86
83
81
78
76
81
78
76
73
71
69
73
70
68
66
64
62
65
63
61
59
58
56
56
55
53
51
50
48
48
46
45
44
42
41
36
38
40
42
44
87
82
78
75
71
80
76
72
68
65
74
70
66
63
60
67
64
60
58
55
61
57
55
52
50
54
52
49
47
45
47
45
42
40
38
40
38
36
34
33
90.7
1960
126
40.5
13.0
51.4
3.92
46.7
5.23
64.2
78.4
1690
110
33.7
11.3
39.2
3.05
35.6
4.07
49.1
66.5
1440
103
30.4
10.8
32.8
3.29
28.9
4.39
43.5
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
145
3130
178
66.8
17.8
95.9
7.44
86.7
9.92
120
133
2870
161
58.2
16.2
80.0
6.08
72.6
8.10
99.8
123
2660
147
51.4
14.9
68.2
5.18
61.9
6.90
85.0
112
2420
137
46.1
14.0
59.2
4.77
53.4
6.36
74.7
101
2180
124
39.9
12.8
48.9
4.01
44.1
5.34
61.9
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 51
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 16
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 16
100
89
W 16
77
6
7
8
9
10
11
386
342
292
12
13
14
15
16
17
356
329
305
285
267
252
315
291
270
252
236
222
18
19
20
21
22
23
238
225
214
204
194
186
24
25
26
27
28
29
67
57
50
45
W 16
40
36
31
26
153
136
119
106
95
87
251
275
252
227
206
240
221
199
181
216
198
178
162
190
175
157
143
182
173
154
138
126
170
167
146
130
117
106
270
249
231
216
203
191
234
216
201
187
176
165
189
174
162
151
142
133
166
153
142
132
124
117
148
137
127
119
111
105
131
121
112
105
98
93
115
106
99
92
86
81
97
90
83
78
73
69
80
73
68
64
60
56
210
199
189
180
172
164
180
171
162
154
147
141
156
148
140
134
128
122
126
119
113
108
103
99
110
105
99
95
90
86
99
94
89
85
81
77
87
83
79
75
72
68
77
73
69
66
63
60
65
61
58
56
53
51
53
50
48
45
43
42
178
171
164
158
153
147
158
151
145
140
135
130
135
130
125
120
116
112
117
112
108
104
100
97
95
91
87
84
81
78
83
79
76
74
71
69
74
71
68
66
63
61
66
63
61
58
56
54
58
55
53
51
49
48
49
47
45
43
42
40
40
38
37
35
34
33
30
31
32
33
34
35
143
138
134
130
126
122
126
122
118
115
111
108
108
105
101
98
95
93
94
91
88
85
83
80
76
73
71
69
67
65
66
64
62
60
58
57
59
57
56
54
52
51
52
51
49
48
46
45
46
45
43
42
41
39
39
38
36
35
34
33
32
31
30
29
28
27
36
38
40
119
113
107
105
99
95
90
85
81
78
74
70
63
60
57
55
52
50
49
47
44
44
41
39
38
36
32
31
27
25
198
4280
193
88.8
21.1
136
11.0
123
14.7
157
175
3780
171
73.8
18.9
109
9.06
98.8
12.1
135
72.9
1570
94.9
32.6
11.0
36.6
3.22
33.2
4.30
47.1
64.0
1380
91.0
29.9
10.6
32.2
3.46
28.5
4.61
43.5
54.0
1170
84.9
27.8
9.90
29.3
2.73
26.4
3.64
38.2
44.2
955
76.3
23.9
9.00
22.5
2.65
19.7
3.53
31.2
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
150
3240
146
58.9
16.4
81.9
6.89
74.3
9.18
104
130
2810
125
48.9
14.2
61.9
5.21
56.3
6.95
78.9
105
2270
137
53.2
15.5
73.0
6.21
66.2
8.28
93.2
92.0
1990
120
44.9
13.7
56.9
4.92
51.6
6.56
72.9
82.3
1780
108
38.8
12.4
46.6
4.14
42.2
5.52
60.1
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 52
BEAM AND GIRDER DESIGN
W 14
Fy = 36 ksi
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
W 14
132
120
109
W 14
99
90
82
74
68
61
248
247
227
209
194
181
227
226
207
191
177
166
203
200
184
169
157
147
332
327
305
292
276
267
267
249
240
226
16
17
18
19
20
21
316
297
281
266
253
241
286
269
254
241
229
218
259
244
230
218
207
197
234
220
208
197
187
178
212
199
188
178
170
161
188
177
167
158
150
143
170
160
151
143
136
130
155
146
138
131
124
118
138
130
122
116
110
105
22
23
24
25
26
27
230
220
211
202
194
187
208
199
191
183
176
170
189
180
173
166
160
154
170
162
156
149
144
138
154
147
141
136
130
126
136
131
125
120
115
111
124
118
113
109
105
101
113
108
104
99
96
92
100
96
92
88
85
82
28
29
30
31
32
33
181
174
168
163
158
153
164
158
153
148
143
139
148
143
138
134
130
126
133
129
125
121
117
113
121
117
113
109
106
103
107
104
100
97
94
91
97
94
91
88
85
82
89
86
83
80
78
75
79
76
73
71
69
67
34
149
135
122
110
100
88
80
73
65
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
234
5050
184
98.0
23.2
161
16.3
145
21.8
173
212
4580
166
86.3
21.2
134
13.9
121
18.5
155
139
3000
142
74.6
18.4
103
9.95
93.6
13.3
134
126
2720
124
63.3
16.2
81.8
7.52
74.7
10.0
107
115
2480
113
56.0
14.9
69.4
6.49
63.3
8.65
91.5
102
2200
101
48.5
13.5
56.4
5.40
51.4
7.20
74.8
Span (ft)
368
361
337
284
273
250
231
214
200
Fy = 36 ksi
10
11
12
13
14
15
Properties and Reaction Values
192
4150
146
73.8
18.9
108
10.8
97.6
14.4
135
173
3740
134
62.7
17.5
91.3
9.48
82.3
12.6
119
157
3390
120
54.5
15.8
75.3
7.86
67.9
10.5
102
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 53
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 14
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 14
53
48
5
6
7
8
9
10
200
188
182
169
11
12
13
14
15
16
171
157
145
134
125
118
17
18
19
20
21
22
W 14
43
38
34
W 14
30
26
22
162
150
170
166
148
133
155
147
131
118
145
128
114
102
138
124
109
96
87
123
120
102
90
80
72
154
141
130
121
113
106
137
125
116
107
100
94
121
111
102
95
89
83
107
98
91
84
79
74
93
85
79
73
68
64
79
72
67
62
58
54
65
60
55
51
48
45
111
105
99
94
90
86
100
94
89
85
81
77
88
84
79
75
72
68
78
74
70
66
63
60
69
66
62
59
56
54
60
57
54
51
49
46
51
48
46
43
41
39
42
40
38
36
34
33
23
24
25
26
27
28
82
78
75
72
70
67
74
71
68
65
63
60
65
63
60
58
56
54
58
55
53
51
49
47
51
49
47
45
44
42
44
43
41
39
38
36
38
36
35
33
32
31
31
30
29
28
27
26
29
30
31
32
33
34
65
63
61
59
57
55
58
56
55
53
51
50
52
50
48
47
46
44
46
44
43
42
40
39
41
39
38
37
36
35
35
34
33
32
31
30
30
29
28
27
26
26
25
24
23
22
22
21
47.3
1020
72.6
22.8
9.72
26.6
3.39
23.5
4.52
38.2
40.2
868
69.0
21.5
9.18
25.5
2.61
23.1
3.47
34.4
33.2
717
61.4
18.1
8.28
19.5
2.43
17.3
3.24
27.8
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
87.1
1880
100
47.9
13.3
55.9
5.06
51.3
6.75
73.2
78.4
1690
91.1
42.1
12.2
46.8
4.40
42.8
5.86
61.8
69.6
1500
81.0
36.0
11.0
37.5
3.60
34.2
4.80
49.8
61.5
1330
85.0
29.6
11.2
37.9
3.77
34.4
5.02
50.7
54.6
1180
77.5
25.7
10.3
31.4
3.34
28.3
4.45
42.8
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 54
BEAM AND GIRDER DESIGN
W 12
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
W 12
120
106
96
87
W 12
79
72
65
58
53
162
153
140
129
120
112
306
295
272
253
236
272
265
244
227
212
251
238
219
204
190
226
214
198
184
171
205
194
179
167
156
184
174
161
149
139
16
17
18
19
20
21
251
236
223
211
201
191
221
208
197
186
177
169
198
187
176
167
159
151
178
168
158
150
143
136
161
151
143
135
129
122
146
137
130
123
117
111
131
123
116
110
105
100
117
110
104
98
93
89
105
99
93
89
84
80
22
23
24
25
26
27
183
175
167
161
155
149
161
154
148
142
136
131
144
138
132
127
122
118
130
124
119
114
110
106
117
112
107
103
99
95
106
101
97
93
90
86
95
91
87
84
80
77
85
81
78
75
72
69
76
73
70
67
65
62
28
29
30
143
139
134
127
122
118
113
109
106
102
98
95
92
89
86
83
80
78
75
72
70
67
64
62
60
58
56
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
186
4020
181
116
25.6
192
22.7
173
30.2
199
164
3540
153
92.6
22.0
145
16.3
131
21.8
164
108
2330
102
53.2
15.5
70.6
8.89
63.4
11.9
102
96.8
2090
91.9
46.1
14.0
58.0
7.43
52.0
9.90
84.1
86.4
1870
85.3
44.6
13.0
52.9
5.49
48.4
7.32
72.2
77.9
1680
80.9
38.8
12.4
47.0
5.44
42.6
7.25
66.2
Span (ft)
362
335
309
287
268
171
170
156
144
133
124
Fy = 36 ksi
10
11
12
13
14
15
Properties and Reaction Values
147
3180
136
80.4
19.8
118
13.4
107
17.8
145
132
2850
125
69.5
18.5
102
12.4
91.5
16.5
130
119
2570
113
60.8
16.9
84.5
10.5
75.9
14.0
116
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 55
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 12
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 12
50
45
W 12
40
4
5
6
7
8
9
175
174
157
155
10
11
12
13
14
15
156
142
130
120
112
104
16
17
18
19
20
21
35
30
W 12
26
22
19
16
14
111
107
89
76
67
59
103
87
72
62
54
48
93
75
63
54
47
42
137
146
138
123
125
116
103
109
100
89
124
105
90
79
70
140
127
116
108
100
93
124
113
104
96
89
83
111
101
92
85
79
74
93
85
78
72
66
62
80
73
67
62
57
54
63
58
53
49
45
42
53
49
44
41
38
36
43
39
36
33
31
29
38
34
31
29
27
25
98
92
87
82
78
74
87
82
78
74
70
67
78
73
69
65
62
59
69
65
61
58
55
53
58
55
52
49
47
44
50
47
45
42
40
38
40
37
35
33
32
30
33
31
30
28
27
25
27
26
24
23
22
21
23
22
21
20
19
18
22
23
24
25
26
27
71
68
65
63
60
58
64
61
58
56
54
52
56
54
52
50
48
46
50
48
46
44
43
41
42
40
39
37
36
34
37
35
33
32
31
30
29
28
26
25
24
23
24
23
22
21
21
20
20
19
18
17
17
16
17
16
16
15
14
14
28
29
30
56
54
52
50
48
47
44
43
37
39
38
31
33
32
27
29
28
21
23
22
18
19
18
16
15
13
13
72.4
1560
87.7
45.8
13.3
55.1
5.96
50.3
7.95
76.1
64.7
1400
78.5
37.7
12.1
45.0
4.98
41.0
6.64
62.6
29.3
633
62.2
20.5
9.36
26.4
3.08
23.9
4.11
37.3
24.7
534
55.6
17.2
8.46
20.6
2.80
18.4
3.73
30.5
20.1
434
51.3
14.9
7.92
16.3
3.08
13.8
4.10
27.1
17.4
376
46.3
12.4
7.20
13.0
2.74
10.8
3.65
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
57.5
1240
68.5
33.2
10.6
35.2
3.83
32.1
5.11
48.7
51.2
1110
72.9
27.0
10.8
36.3
3.81
33.1
5.08
49.6
43.1
931
62.4
21.9
9.36
26.9
2.97
24.5
3.96
37.3
37.2
804
54.6
18.1
8.28
20.8
2.41
18.8
3.21
29.3
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
22.7
4 - 56
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 10
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
W 10
112
100
88
77
68
60
54
49
9
10
11
12
13
14
333
318
289
265
244
227
293
281
255
234
216
201
255
244
222
203
188
174
218
211
192
176
162
151
190
184
167
154
142
132
167
161
146
134
124
115
145
144
131
120
111
103
132
130
119
109
100
93
15
16
17
18
19
20
212
198
187
176
167
159
187
176
165
156
148
140
163
153
144
136
128
122
141
132
124
117
111
105
123
115
108
102
97
92
107
101
95
90
85
81
96
90
85
80
76
72
87
82
77
72
69
65
21
22
23
24
151
144
138
132
134
128
122
117
116
111
106
102
100
96
92
88
88
84
80
77
77
73
70
67
69
65
63
60
62
59
57
54
74.6
1610
83.4
49.6
15.1
68.7
9.79
62.0
13.0
98.8
66.6
1440
72.6
41.6
13.3
54.0
7.49
49.0
9.99
81.4
60.4
1300
66.0
36.3
12.2
45.4
6.46
41.1
8.61
69.1
Span (ft)
Fy = 36 ksi
Wt./ft
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
147
3180
167
127
27.2
224
27.8
203
37.1
216
130
2810
147
107
24.5
182
23.2
164
31.0
187
113
2440
127
88.5
21.8
143
18.9
130
25.3
159
97.6
2110
109
71.5
19.1
110
14.8
99.7
19.8
134
85.3
1840
95.0
58.2
16.9
86.5
11.9
78.3
15.9
113
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 57
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 10
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
W 10
45
3
4
5
6
7
8
137
9
10
11
12
13
14
39
W 10
33
30
26
W 10
22
19
17
15
12
73
68
54
45
39
34
100
93
78
67
58
94
81
67
58
50
89
86
69
58
49
43
121
110
105
122
113
99
104
97
85
95
94
80
70
132
119
108
99
91
85
112
101
92
84
78
72
93
84
76
70
64
60
88
79
72
66
61
56
75
68
61
56
52
48
62
56
51
47
43
40
52
47
42
39
36
33
45
40
37
34
31
29
38
35
31
29
27
25
30
27
25
23
21
19
15
16
17
18
19
20
79
74
70
66
62
59
67
63
59
56
53
51
56
52
49
47
44
42
53
49
47
44
42
40
45
42
40
38
36
34
37
35
33
31
30
28
31
29
27
26
25
23
27
25
24
22
21
20
23
22
20
19
18
17
18
17
16
15
14
14
21
22
23
24
56
54
52
49
48
46
44
42
40
38
36
35
38
36
34
33
32
31
29
28
27
26
24
23
22
21
20
19
19
18
18
17
16
16
15
14
13
12
12
11
54.9
1190
68.7
39.4
12.6
49.9
6.29
45.7
8.38
72.9
46.8
1010
60.7
31.9
11.3
39.4
5.46
35.8
7.28
59.4
21.6
467
49.8
18.3
9.00
24.0
3.55
21.6
4.73
37.0
18.7
404
47.2
16.2
8.64
20.7
3.80
18.1
5.07
34.6
16.0
346
44.7
14.2
8.28
17.5
4.14
14.8
5.52
32.7
12.6
272
36.5
10.7
6.84
11.6
3.04
9.61
4.05
22.8
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
38.8
838
54.9
27.7
10.4
31.5
5.29
28.1
7.05
51.0
36.6
791
61.1
25.3
10.8
35.9
4.64
32.7
6.19
52.8
31.3
676
52.2
20.5
9.36
26.9
3.55
24.5
4.73
39.8
26.0
562
47.4
16.2
8.64
21.6
3.47
19.2
4.62
34.3
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 58
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W8
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
W8
67
58
48
7
8
9
10
11
12
199
190
168
152
138
126
40
35
31
174
161
144
129
117
108
132
118
106
96
88
115
107
96
86
78
72
98
94
83
75
68
62
89
82
73
66
60
55
13
14
15
16
17
18
117
108
101
95
89
84
99
92
86
81
76
72
81
76
71
66
62
59
66
61
57
54
51
48
58
54
50
47
44
42
51
47
44
41
39
36
19
20
80
76
68
65
56
53
45
43
39
37
35
33
39.8
860
57.7
34.4
13.0
49.5
9.27
44.4
12.4
76.5
34.7
750
48.9
27.9
11.2
37.2
6.80
33.5
9.07
63.0
30.4
657
44.3
24.0
10.3
30.7
6.11
27.4
8.14
53.9
Span (ft)
Fy = 36 ksi
Wt./ft
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
70.2
1520
99.7
73.7
20.5
127
20.2
115
26.9
140
59.8
1290
86.8
60.2
18.4
100
17.2
90.3
22.9
120
49.0
1060
66.1
42.8
14.4
64.1
10.1
58.4
13.5
89.6
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 59
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W8
For beams laterally unsupported, see page 4-113
Designation
W8
Span (ft)
Fy = 36 ksi
Wt./ft
28
W8
24
21
W8
18
15
13
10
71
62
49
41
35
31
52
48
38
32
27
24
3
4
5
6
7
8
89
84
73
76
72
63
80
73
63
55
73
61
52
46
77
73
59
49
42
37
9
10
11
12
13
14
65
59
53
49
45
42
56
50
46
42
39
36
49
44
40
37
34
31
41
37
33
31
28
26
33
29
27
24
23
21
27
25
22
21
19
18
21
19
17
16
15
14
15
16
17
18
19
20
39
37
35
33
31
29
33
31
29
28
26
22
29
28
26
24
23
18
24
23
22
20
19
15
20
18
17
16
15
16
15
14
14
13
13
12
11
11
10
13.6
294
38.6
16.5
8.82
20.8
5.28
18.0
7.05
40.9
11.4
246
35.7
14.2
8.28
17.0
5.48
14.1
7.31
37.9
8.87
192
26.1
9.56
6.12
9.71
2.79
8.24
3.72
20.3
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
27.2
588
44.7
24.0
10.3
31.7
5.67
28.7
7.56
53.3
23.2
501
37.8
19.3
8.82
23.5
4.26
21.2
5.67
39.7
20.4
441
40.2
18.3
9.00
24.2
4.33
21.8
5.77
40.6
17.0
367
36.4
15.5
8.28
19.4
4.16
17.1
5.54
35.2
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 60
BEAM AND GIRDER DESIGN
W 6–5–4
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
W6
25
2
3
4
5
6
7
79
68
58
8
9
10
11
12
13
14
20
W6
15*
16
W5
12
9
63
54
46
54
46
38
33
63
63
51
42
36
54
45
36
30
26
39
34
27
22
19
51
45
41
37
34
31
40
36
32
29
27
25
29
26
23
21
19
18
32
28
25
23
21
19
22
20
18
16
15
14
17
15
13
12
11
10
29
23
16
18
13
18.9
408
39.7
23.4
11.5
37.4
10.4
33.0
13.8
60.8
14.9
322
31.3
17.5
9.36
24.5
7.13
21.6
9.51
48.0
19
W4
16
13
54
50
42
36
47
41
35
30
45
45
34
27
23
19
31
28
25
23
21
26
23
21
19
17
17
15
14
11.6
251
27.0
19.7
9.72
28.2
8.16
25.4
10.9
51.3
9.59
207
23.4
16.2
8.64
21.6
7.04
19.2
9.38
44.3
6.28
136
22.6
17.3
10.1
26.6
14.0
22.7
18.7
50.1
9.6
Span (ft)
Fy = 36 ksi
Wt./ft
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
10.8
230
26.8
12.9
8.28
17.2
7.17
14.3
9.56
39.8
11.7
253
31.7
17.5
9.36
25.8
6.34
23.2
8.46
48.0
8.30
179
27.0
12.9
8.28
17.9
6.62
15.2
8.82
39.8
6.23
135
19.5
8.61
6.12
9.95
3.56
8.55
4.74
24.0
*Indicates noncompact shape.
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 61
BEAMS
S Shapes
Maximum factored uniform loads in kips
for beams laterally supported
S 24–20
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
S 24
121
12
13
14
15
16
17
90
S 20
80
96
S 20
86
75
66
521
494
439
395
359
494
472
413
367
330
300
393
378
336
302
275
591
548
695
648
576
518
471
583
533
480
436
467
441
401
551
508
472
441
413
389
502
464
430
402
377
354
432
399
370
346
324
305
400
369
343
320
300
282
367
339
315
294
275
259
356
329
305
285
267
252
329
304
282
264
247
233
275
254
236
220
207
194
252
233
216
202
189
178
18
19
20
21
22
23
367
348
330
315
300
287
335
317
301
287
274
262
288
273
259
247
236
225
266
252
240
228
218
208
245
232
220
210
200
192
238
225
214
204
194
186
220
208
198
188
180
172
184
174
165
157
150
144
168
159
151
144
137
131
24
25
26
27
28
29
275
264
254
245
236
228
251
241
232
223
215
208
216
207
199
192
185
179
200
192
184
178
171
165
184
176
169
163
157
152
178
171
164
158
153
147
165
158
152
146
141
136
138
132
127
122
118
114
126
121
116
112
108
104
30
32
34
36
38
40
220
207
194
184
174
165
201
188
177
167
159
151
173
162
152
144
136
130
160
150
141
133
126
120
147
138
130
122
116
110
143
134
126
119
113
107
132
124
116
110
104
99
110
103
97
92
87
83
101
95
89
84
80
76
42
44
46
48
50
52
157
150
144
138
132
127
143
137
131
126
121
116
123
118
113
108
104
100
114
109
104
100
96
92
105
100
96
92
88
85
102
97
93
89
86
94
90
86
82
79
79
75
72
69
66
72
69
66
63
60
54
56
58
60
122
118
114
110
112
108
104
100
96
93
89
86
89
86
83
80
82
79
76
73
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
306
6610
381
144
28.8
229
17.6
200
23.5
238
279
6030
295
112
22.3
156
8.19
143
10.9
183
183
3950
260
104
23.8
157
14.1
138
18.8
181
153
3300
247
92.9
22.9
138
14.8
118
19.7
167
140
3020
196
73.9
18.2
97.9
7.44
88.0
9.91
122
Span (ft)
762
734
661
601
100
631
611
535
475
428
389
Fy = 36 ksi
6
7
8
9
10
11
S 24
106
Properties and Reaction Values
240
5180
348
117
26.8
184
18.2
154
24.2
205
222
4800
292
98.4
22.5
141
10.7
124
14.3
172
204
4410
233
78.8
18.0
101
5.50
92.1
7.33
119
198
4280
316
126
28.8
210
25.2
176
33.6
220
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 62
BEAM AND GIRDER DESIGN
S 18–15–12–10
BEAMS
S Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
S 18
70
3
4
5
6
7
8
498
450
386
338
9
10
11
12
13
14
S 15
54.7
50
S 12
42.9
50
S 12
40.8
35
S 10
31.8
35
25.4
121
102
88
77
240
214
187
321
264
220
189
165
216
191
164
143
200
194
161
138
121
163
151
130
113
231
191
153
127
109
96
185
167
151
139
128
119
166
150
136
125
115
107
147
132
120
110
102
94
127
115
104
96
88
82
108
97
88
81
74
69
101
91
82
76
70
65
85
76
70
64
59
55
68
61
56
51
47
44
151
142
133
126
119
113
111
104
98
93
88
83
100
94
88
83
79
75
88
83
78
73
70
66
76
72
67
64
60
57
65
60
57
54
51
48
60
57
53
50
48
45
51
48
45
42
40
38
41
38
36
34
32
31
129
123
117
113
108
104
108
103
99
95
91
87
79
76
72
69
67
64
71
68
65
62
60
58
63
60
57
55
53
51
55
52
50
48
46
44
46
44
42
40
39
37
43
41
39
38
36
35
36
35
33
32
31
29
28
27
26
25
27
28
29
30
31
32
100
96
93
90
87
84
84
81
78
76
73
71
62
59
57
56
54
52
55
53
52
50
48
47
49
47
46
44
42
41
40
38
36
35
33
32
34
32
31
30
33
34
35
36
37
38
82
79
77
75
73
71
69
67
65
63
61
60
50
49
48
46
45
45
44
43
42
40
40
42
44
68
64
61
57
54
52
125
2700
249
96.0
25.6
152
26.5
121
35.4
179
105
2270
161
62.2
16.6
79.6
7.23
70.9
9.64
103
44.8
968
99.8
45.7
15.4
63.2
11.0
54.4
14.7
95.8
42.0
907
81.6
37.4
12.6
46.7
6.03
41.9
8.04
68.0
35.4
765
115
60.1
21.4
98.2
39.2
72.0
52.2
130
28.4
613
60.5
31.5
11.2
37.2
5.62
33.4
7.50
57.8
323
284
321
278
238
208
300
270
245
225
208
193
252
227
206
189
174
162
15
16
17
18
19
20
180
169
159
150
142
135
21
22
23
24
25
26
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
77.1
1670
160
68.1
19.8
98.4
16.4
82.1
21.8
132
69.3
1500
120
50.9
14.8
63.6
6.83
56.8
9.11
86.4
61.2
1320
160
88.9
24.7
141
37.6
111
50.2
169
53.1
1150
108
59.8
16.6
78.0
11.4
68.8
15.3
114
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 63
BEAMS
S 8–6–5–4–3
S Shapes
Maximum factored uniform loads in kips
for beams laterally supported
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
S8
23
1
2
3
4
5
6
137
104
83
69
7
8
9
10
11
12
S6
18.4
17.25
S5
12.5
10
42
41
31
24
20
60
52
46
42
38
35
51
45
40
36
32
30
33
29
25
23
21
19
26
23
20
18
17
15
17
15
14
12
11
10
13
32
27
18
14
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
19.3
417
68.6
39.7
15.9
58.5
23.1
46.2
30.8
91.3
16.5
356
42.1
24.4
9.76
28.2
5.36
25.3
7.15
48.5
S3
7.7
7.5
5.7
41
25
17
13
10
8.50
20
14
11
8.42
7.02
51
44
29
22
17
15
30
25
19
15
13
12
11
9.70
8.73
11
9.48
8.42
7.58
7.28
6.02
3.51
75.8
15.0
13.0
6.95
14.0
5.63
12.5
7.51
35.6
2.36
51.0
20.4
21.6
12.6
32.2
50.0
22.2
66.7
62.4
1.95
42.1
9.91
10.5
6.12
10.9
5.78
9.78
7.71
30.4
Span (ft)
54
46
37
30
Fy = 36 ksi
84
71
59
108
76
57
46
38
S4
9.5
Properties and Reaction Values
10.6
229
54.2
36.6
16.7
58.1
42.9
41.0
57.1
91.0
8.47
183
27.1
18.3
8.35
20.5
5.32
18.4
7.10
41.4
5.67
122
20.8
15.6
7.70
17.3
5.52
15.5
7.36
39.4
4.04
87.3
25.3
22.0
11.7
30.8
27.1
23.6
36.2
60.1
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 64
BEAM AND GIRDER DESIGN
MC,C 18–15
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
MC 18
Span (ft)
Fy = 36 ksi
Wt./ft
58
51.9
C 15
45.8
42.7
50
40
33.9
303
247
206
177
154
233
218
181
156
136
3
4
5
6
7
8
490
409
341
292
255
420
374
311
267
234
350
339
282
242
212
315
268
230
201
418
368
295
246
210
184
9
10
11
12
13
14
227
204
186
170
157
146
208
187
170
156
144
133
188
169
154
141
130
121
179
161
146
134
124
115
164
147
134
123
113
105
137
124
112
103
95
88
121
109
99
91
84
78
15
16
17
18
19
20
136
128
120
114
108
102
125
117
110
104
98
93
113
106
100
94
89
85
107
100
95
89
85
80
98
92
87
82
78
74
82
77
73
69
65
62
73
68
64
60
57
54
21
22
23
24
25
26
97
93
89
85
82
79
89
85
81
78
75
72
81
77
74
71
68
65
77
73
70
67
64
62
70
67
64
61
59
57
59
56
54
51
49
48
52
49
47
45
44
42
28
30
32
34
36
38
73
68
64
60
57
54
67
62
58
55
52
49
60
56
53
50
47
45
57
54
50
47
45
42
53
49
46
43
41
44
41
39
36
34
39
36
34
32
30
40
42
44
51
49
46
47
44
42
42
40
38
40
38
37
68.2
1470
209
92.6
25.8
149
34.6
115
46.1
176
57.2
1240
152
67.3
18.7
92.5
13.2
79.3
17.7
128
50.4
1090
117
51.8
14.4
62.4
6.03
56.4
8.03
82.5
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
94.6
2040
245
86.6
25.2
142
28.0
108
37.3
169
86.5
1870
210
74.3
21.6
112
17.6
91.3
23.5
144
78.4
1690
175
61.9
18.0
85.5
10.2
73.3
13.6
119
74.4
1610
157
55.7
16.2
73.0
7.44
64.1
9.91
97.2
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 65
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
MC 13
For beams laterally unsupported, see page 4-113
Designation
MC 13
Span (ft)
Fy = 36 ksi
Wt./ft
50
40
35
31.8
3
4
5
6
7
8
398
327
261
218
187
163
283
275
220
183
157
137
226
200
166
143
125
190
186
155
133
116
9
10
11
12
13
14
145
131
119
109
101
93
122
110
100
92
85
79
111
100
91
83
77
71
103
93
85
78
72
66
15
16
17
18
19
20
87
82
77
73
69
65
73
69
65
61
58
55
67
62
59
55
53
50
62
58
55
52
49
47
21
22
23
24
25
26
62
59
57
54
52
50
52
50
48
46
44
42
48
45
43
42
40
38
44
42
40
39
37
36
27
28
29
30
31
32
48
47
45
44
42
41
41
39
38
37
35
34
37
36
34
33
32
31
34
33
32
31
30
29
46.2
998
113
55.3
16.1
71.4
10.3
62.5
13.8
107
43.1
931
94.8
46.4
13.5
54.9
6.10
49.6
8.14
76.0
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
60.5
1310
199
97.4
28.3
167
56.4
118
75.2
189
50.9
1100
142
69.3
20.2
100
20.3
82.5
27.1
135
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 66
BEAM AND GIRDER DESIGN
C, MC 12
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
Wt./ft
C 12
30
25
MC 12
20.7
50
45
40
MC 12
35
31
10.6
181
158
126
105
90
132
110
91
78
390
303
242
202
173
332
279
223
186
160
275
255
204
170
146
218
185
154
132
173
170
141
121
8
9
10
11
12
13
91
81
73
66
60
56
79
70
63
57
53
49
69
61
55
50
46
42
151
135
121
110
101
93
140
124
112
102
93
86
128
114
102
93
85
79
116
103
92
84
77
71
106
94
85
77
71
65
31
28
25
23
21
19
14
15
16
17
18
19
52
48
45
43
40
38
45
42
39
37
35
33
39
37
34
32
30
29
87
81
76
71
67
64
80
74
70
66
62
59
73
68
64
60
57
54
66
62
58
54
51
49
61
57
53
50
47
45
18
17
16
15
14
13
20
21
22
23
24
25
36
35
33
32
30
29
32
30
29
27
26
25
27
26
25
24
23
22
61
58
55
53
50
48
56
53
51
49
47
45
51
49
46
44
43
41
46
44
42
40
39
37
42
40
39
37
35
34
13
12
11
11
10
10
26
27
28
29
30
28
27
26
25
24
24
23
23
22
21
21
20
20
19
18
47
45
43
42
40
43
41
40
39
37
39
38
36
35
34
36
34
33
32
31
33
31
30
29
28
9.64
9.28
8.95
8.64
8.35
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
33.6
726
119
51.6
18.4
78.9
20.3
62.7
27.0
111
29.2
631
90.3
39.2
13.9
52.1
8.85
45.1
11.8
83.4
47.3
1020
138
69.7
21.2
116
22.4
98.1
29.9
139
42.8
924
109
55.2
16.8
81.7
11.1
72.8
14.8
110
39.3
849
86.3
43.7
13.3
57.6
5.54
53.2
7.38
77.2
11.6
251
44.3
11.8
6.84
14.1
1.70
12.7
2.26
20.1
Span (ft)
238
181
145
121
104
89
84
63
50
42
36
Fy = 36 ksi
2
3
4
5
6
7
Properties and Reaction Values
25.4
549
65.8
28.6
10.2
32.4
3.42
29.7
4.57
44.5
56.1
1210
195
98.6
30.1
195
63.6
144
84.8
196
51.7
1120
166
84.1
25.6
154
39.4
122
52.6
167
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 67
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C, MC 10
For beams laterally unsupported, see page 4-113
Designation
Span (ft)
Fy = 36 ksi
Wt./ft
C 10
MC 10
30
25
20
2
3
4
5
6
7
262
192
144
115
96
82
205
166
124
99
83
71
8
9
10
11
12
13
72
64
57
52
48
44
14
15
16
17
18
19
20
21
22
23
24
33.6
MC 10
28.5
25
MC 10
15.3
41.1
22
147
139
104
83
69
60
93
85
68
57
49
309
280
210
168
140
120
224
180
144
120
103
165
160
128
107
91
148
139
111
93
80
113
102
85
73
66
57
42
34
28
24
8.4
62
55
50
45
41
38
52
46
42
38
35
32
43
38
34
31
28
26
105
93
84
76
70
65
90
80
72
66
60
55
80
71
64
58
53
49
70
62
56
51
46
43
64
57
51
46
42
39
21
19
17
15
14
13
41
38
36
34
32
30
35
33
31
29
28
26
30
28
26
25
23
22
24
23
21
20
19
18
60
56
53
49
47
44
52
48
45
42
40
38
46
43
40
38
36
34
40
37
35
33
31
29
36
34
32
30
28
27
12
11
11
10
9.4
8.9
29
27
26
25
24
25
24
23
22
21
21
20
19
18
17
17
16
16
15
14
42
40
38
37
35
36
34
33
31
30
32
30
29
28
27
28
27
25
24
23
25
24
23
22
21
8.5
8.1
7.7
7.4
7.1
26.6
575
131
60.6
24.2
112
64.2
68.8
85.6
139
23.0
497
102
47.3
18.9
77.1
30.6
56.7
40.9
109
29.6
639
82.6
47.8
15.3
64.3
12.3
56.1
16.3
97.5
25.8
557
73.9
42.8
13.7
54.4
8.76
48.5
11.7
86.5
23.6
510
56.4
32.6
10.4
36.2
3.89
33.6
5.19
50.5
7.86
170
33.0
10.5
6.12
11.3
1.61
10.3
2.15
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
19.3
417
73.7
34.1
13.6
47.1
11.5
39.5
15.3
78.5
15.8
341
46.7
21.6
8.64
23.8
2.91
21.8
3.88
34.4
38.9
840
155
89.6
28.7
165
80.5
111
107
183
33.4
721
112
64.7
20.7
101
30.4
80.9
40.5
132
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
17.3
4 - 68
BEAM AND GIRDER DESIGN
C, MC 9
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
C9
Span (ft)
Fy = 36 ksi
Wt./ft
MC 9
20
15
13.4
25.4
23.9
2
3
4
5
6
7
157
121
91
73
60
52
100
97
73
58
49
42
82
68
54
45
39
157
125
100
84
72
140
120
96
80
69
8
9
10
11
12
13
45
40
36
33
30
28
36
32
29
27
24
22
34
30
27
25
23
21
63
56
50
46
42
39
60
53
48
44
40
37
14
15
16
17
18
19
26
24
23
21
20
19
21
19
18
17
16
15
19
18
17
16
15
14
36
33
31
29
28
26
34
32
30
28
27
25
20
21
22
18
17
16
15
14
13
14
13
12
25
24
23
24
23
22
23.2
501
78.7
48.1
16.2
68.5
16.9
58.4
22.5
101
22.2
480
70.0
42.8
14.4
57.4
11.9
50.3
15.8
89.6
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
16.8
363
78.4
37.8
16.1
59.0
22.2
45.6
29.6
90.2
13.5
292
49.9
24.0
10.3
29.9
5.72
26.5
7.62
51.3
12.5
270
40.8
19.7
8.39
22.1
3.12
20.2
4.17
33.8
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 69
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C, MC 8
For beams laterally unsupported, see page 4-113
Designation
C8
Span (ft)
Fy = 36 ksi
Wt./ft
MC 8
MC 8
MC 8
18.75
13.75
11.5
22.8
21.4
20
18.7
1
2
3
4
5
6
151
149
99
75
60
50
8.5
94
78
59
47
39
68
52
41
34
133
102
81
68
117
97
78
65
124
117
87
70
58
110
83
67
55
56
50
37
30
25
7
8
9
10
11
12
43
37
33
30
27
25
34
29
26
24
21
20
29
26
23
21
19
17
58
51
45
41
37
34
56
49
43
39
35
32
50
44
39
35
32
29
48
42
37
33
30
28
21
19
17
15
14
12
13
14
15
16
17
18
23
21
20
19
18
17
18
17
16
15
14
13
16
15
14
13
12
11
31
29
27
25
24
23
30
28
26
24
23
22
27
25
23
22
21
19
26
24
22
21
20
18
11
11
10
9.3
8.8
8.3
19
20
16
15
12
12
11
10
21
20
20
19
18
17
18
17
7.9
7.5
16.2
350
62.2
40.5
14.4
54.7
14.7
46.9
19.6
87.3,
15.4
333
54.9
35.7
12.7
45.4
10.1
40.0
13.5
77.0
6.91
149
27.8
12.1
6.44
12.9
2.12
11.8
2.82
21.0
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
13.8
298
75.7
41.1
17.5
64.9
34.0
46.8
45.3
98.1
10.9
235
47.1
25.6
10.9
31.9
8.18
27.5
10.9
61.0
9.55
206
34.2
18.6
7.92
19.7
3.13
18.0
4.18
31.6
18.8
406
66.4
45.6
15.4
61.9
17.0
52.8
22.7
95.6
18.0
389
58.3
40.1
13.5
50.9
11.5
44.8
15.4
84.0
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 70
BEAM AND GIRDER DESIGN
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C, MC 7–6
Fy = 36 ksi
For beams laterally unsupported, see page 4-113
Designation
C7
12.25
MC 7
9.8
22.7
C6
19.1
13
10.5
73
66
44
33
27
22
1
2
3
4
5
6
85
60
45
36
30
57
51
38
31
26
137
117
87
70
58
96
77
62
51
102
78
52
39
31
26
7
8
9
10
11
12
26
23
20
18
16
15
22
19
17
15
14
13
50
44
39
35
32
29
44
39
34
31
28
26
22
20
17
16
14
13
19
17
15
13
12
11
13
14
15
16
14
13
12
11
12
11
10
9.61
27
25
23
22
24
22
21
19
12
11
10
10
9.49
8.86
8.40
181
42.7
24.7
11.3
32.6
11.1
27.4
14.8
61.5
7.12
154
28.6
16.5
7.56
17.8
3.32
16.3
4.42
30.6
MC 6
8.2
MC 6
MC 6
18
16.3
15.1
12
47
37
28
22
18
88
83
62
50
41
87
73
55
44
37
74
70
52
42
35
72
53
40
32
27
16
14
12
11
10
9.23
35
31
28
25
23
21
31
28
24
22
20
18
30
26
23
21
19
17
23
20
18
16
14
13
8.52
7.91
7.39
19
18
17
17
16
15
16
15
14
12
11
11
11.5
248
44.2
36.2
13.6
49.2
17.5
42.2
23.4
80.6
10.2
220
43.7
35.9
13.5
48.4
17.0
41.6
22.6
79.7
9.69
209
36.9
30.2
11.4
37.5
10.2
33.4
13.6
67.2
7.38
159
36.2
22.7
11.2
32.3
12.2
27.5
16.2
58.9
Span (ft)
Fy = 36 ksi
Wt./ft
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
16.2
350
68.4
50.9
18.1
77.2
33.4
61.6
44.5
110
14.3
309
47.9
35.6
12.7
45.2
11.4
39.8
15.3
76.8
7.26
157
51.0
32.0
15.7
51.8
37.2
36.9
49.6
83.1
6.15
133
36.6
23.0
11.3
31.5
13.8
26.0
18.4
59.7
5.13
111
23.3
14.6
7.20
16.0
3.57
14.6
4.76
30.1
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 36 ksi
4 - 71
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C 5–4–3
For beams laterally unsupported, see page 4-113
Designation
C5
Wt./ft
9
1
2
3
4
5
6
C3
7.25
5.4
6
5
4.1
63
47
31
24
19
16
37
25
19
15
13
50
30
20
15
12
10
29
24
16
12
9.8
8.1
37
19
12
9.3
7.4
6.2
30
16
11
8.1
6.5
5.4
20
14
9.4
7.0
5.6
4.7
13
12
10
9.4
8.6
7.9
11
9.5
8.4
7.6
6.9
6.3
7.0
6.1
5.4
4.9
5.3
4.6
4.0
1.72
37.2
20.8
22.0
12.8
34.0
50.6
23.8
67.4
63.7
1.50
32.4
15.0
16.0
9.29
21.0
19.2
17.1
25.7
46.1
1.30
28.1
9.91
10.5
6.12
11.2
5.51
10.1
7.34
30.4
8.7
7.6
6.7
6.1
Span (ft)
Fy = 36 ksi
7
8
9
10
11
12
C4
6.7
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
4.36
94.2
31.6
21.9
11.7
32.1
19.7
25.5
26.3
60.0
3.51
75.8
18.5
12.8
6.84
14.3
3.94
13.0
5.25
30.1
2.81
60.7
25.0
19.9
11.6
30.3
25.6
23.4
34.2
57.4
2.26
48.8
14.3
11.4
6.62
13.1
4.83
11.9
6.44
32.8
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 72
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 44
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
W 44
Span (ft)
Fy = 50 ksi
Wt./ft
335
290
262
230
20
21
22
23
24
25
2420
2310
2210
2110
2030
1940
2050
2030
1940
1850
1780
1700
1850
1810
1730
1660
1590
1520
1650
1570
1500
1430
1380
1320
26
27
28
29
30
31
1870
1800
1740
1680
1620
1570
1640
1580
1520
1470
1420
1370
1470
1410
1360
1310
1270
1230
1270
1220
1180
1140
1100
1060
32
33
34
35
36
38
1520
1470
1430
1390
1350
1280
1330
1290
1250
1220
1180
1120
1190
1150
1120
1090
1060
1000
1030
1000
971
943
917
868
40
42
44
46
48
50
1220
1160
1100
1060
1010
972
1070
1010
968
926
888
852
953
907
866
828
794
762
825
786
750
717
688
660
52
54
56
58
60
62
935
900
868
838
810
784
819
789
761
734
710
687
733
706
680
657
635
615
635
611
589
569
550
532
64
66
68
70
72
759
736
715
694
675
666
645
626
609
592
595
577
560
544
529
516
500
485
471
458
1270
38100
924
216
39.5
302
8.67
277
11.6
330
1100
33000
823
178
35.5
238
7.40
217
9.86
262
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1620
48600
1212
327
51.0
494
14.7
451
19.6
492
1420
42600
1025
258
43.5
368
10.3
338
13.8
400
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 73
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 40
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
W 40
431
372
321
297
277
249
199
174*
1360
1300
1340
1330
1250
1180
1120
1070
1370
1310
1260
1200
1160
1110
1240
1180
1130
1090
1040
1000
1010
969
927
888
852
820
1240
1200
1160
1120
1080
1050
1070
1030
996
963
932
903
964
930
898
868
840
814
789
761
735
710
687
666
1140
1100
1070
1040
987
938
1020
988
960
933
884
840
875
850
825
803
760
722
789
766
744
723
685
651
646
627
609
592
561
533
950
907
867
831
798
767
893
852
815
781
750
721
800
764
730
700
672
646
688
657
628
602
578
556
620
592
566
543
521
501
507
484
463
444
426
410
789
761
734
710
687
666
739
713
688
665
644
623
694
670
647
625
605
586
622
600
579
560
542
525
535
516
498
482
466
451
482
465
449
434
420
407
395
381
367
355
344
333
645
626
609
592
605
587
570
554
568
551
536
521
509
494
480
467
438
425
413
401
395
383
372
362
323
313
304
296
1120
33600
797
264
37.5
279
8.16
258
10.9
306
963
28900
684
213
32.5
209
6.25
193
8.33
229
868
26000
679
198
32.5
195
7.21
176
9.62
218
715
21300
670
163
32.5
172
9.37
148
12.5
203
2550
2510
2160
2130
2000
2000
21
22
23
24
25
26
2790
2660
2540
2440
2340
2250
2390
2280
2180
2090
2000
1930
2030
1940
1850
1780
1700
1640
1900
1810
1730
1660
1600
1530
1780
1700
1630
1560
1500
1440
1590
1530
1460
1400
1340
1290
27
28
29
30
31
32
2170
2090
2020
1950
1890
1830
1860
1790
1730
1670
1620
1570
1580
1520
1470
1420
1370
1330
1480
1430
1380
1330
1290
1250
1390
1340
1290
1250
1210
1170
33
34
35
36
38
40
1770
1720
1670
1630
1540
1460
1520
1470
1430
1390
1320
1250
1290
1250
1220
1180
1120
1070
1210
1170
1140
1110
1050
998
42
44
46
48
50
52
1390
1330
1270
1220
1170
1130
1190
1140
1090
1040
1000
963
1010
968
926
888
852
819
54
56
58
60
62
64
1080
1040
1010
975
944
914
928
895
864
835
808
783
66
68
70
72
886
860
836
813
759
737
716
696
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1950
58500
1493
597
67.0
859
26.7
786
35.6
814
1670
50100
1273
471
58.0
645
20.3
590
27.0
660
Span (ft)
2990
2930
Fy = 50 ksi
15
16
17
18
19
20
215
Properties and Reaction Values
1420
42600
1082
367
50.0
480
15.3
439
20.3
529
1330
39900
1000
356
46.5
415
13.2
380
17.7
458
1250
37500
889
311
41.5
342
9.90
316
13.2
374
*Noncompact shape; Fy = 50 ksi.
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 74
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 40
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 40
331
278
264
235
211
167
149
1370
1300
1350
1300
1220
1150
1300
1280
1190
1120
1050
995
1430
1360
1290
1230
1180
1130
1230
1170
1120
1070
1020
976
1090
1040
989
944
903
865
943
896
853
814
779
746
1210
1170
1120
1080
1040
1010
1090
1040
1010
970
936
905
937
901
868
837
808
781
830
798
769
741
716
692
716
689
663
640
618
597
1090
1060
1030
997
969
942
977
947
918
891
866
842
876
848
823
799
776
754
756
732
710
689
669
651
670
649
629
611
593
577
578
560
543
527
512
498
939
893
850
811
776
744
892
848
807
770
737
706
797
758
721
689
659
631
714
679
646
617
590
566
617
586
558
533
509
488
546
519
494
472
451
433
471
448
426
407
389
373
858
825
794
766
740
715
714
687
661
638
616
595
678
652
628
605
584
565
606
583
561
541
522
505
543
522
503
485
468
453
469
451
434
418
404
391
415
399
384
371
358
346
358
344
332
320
309
299
692
670
650
631
613
596
576
558
541
525
510
496
547
530
514
499
484
471
489
473
459
446
433
421
438
424
411
399
388
377
378
366
355
345
335
325
335
324
315
305
297
288
289
280
271
263
256
249
781
23400
684
213
32.5
209
6.25
193
8.33
229
692
20800
677
198
32.5
191
7.51
172
10.0
216
597
17900
650
177
31.5
164
8.53
143
11.4
192
13
14
15
16
17
18
2690
2680
2520
2380
2210
2100
1980
2070
1990
1880
1780
1680
1590
1510
19
20
21
22
23
24
2260
2150
2040
1950
1870
1790
1880
1790
1700
1620
1550
1490
1780
1700
1610
1540
1470
1410
1590
1520
1440
1380
1320
1260
25
26
27
28
29
30
1720
1650
1590
1530
1480
1430
1430
1370
1320
1280
1230
1190
1360
1300
1260
1210
1170
1130
31
32
33
34
35
36
1380
1340
1300
1260
1230
1190
1150
1120
1080
1050
1020
992
38
40
42
44
46
48
1130
1070
1020
975
933
894
50
52
54
56
58
60
62
64
66
68
70
72
183
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1430
42900
1344
505
61.0
709
22.6
648
30.1
703
1190
35700
1106
383
51.0
500
15.8
458
21.1
548
1130
33900
1037
353
48.0
446
13.8
409
18.4
491
1010
30300
889
285
41.5
342
9.90
316
13.2
374
905
27200
797
246
37.5
279
8.19
257
10.9
305
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 75
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 36
For beams laterally unsupported, see page 4-139
Designation
W 36
Span (ft)
Fy = 50 ksi
Wt./ft
300
280
260
245
230
1560
1520
1440
1380
1320
1260
1470
1410
1350
1290
1230
1180
19
20
21
22
23
24
1870
1800
1720
1640
1580
1750
1670
1600
1530
1460
1640
1620
1540
1470
1410
1350
25
26
27
28
29
30
1510
1450
1400
1350
1300
1260
1400
1350
1300
1250
1210
1170
1300
1250
1200
1160
1120
1080
1210
1170
1120
1080
1040
1010
1130
1090
1050
1010
976
943
31
32
33
34
35
36
1220
1180
1150
1110
1080
1050
1130
1100
1060
1030
1000
975
1050
1010
982
953
926
900
977
947
918
891
866
842
913
884
857
832
808
786
38
40
42
44
46
48
995
945
900
859
822
788
924
878
836
798
763
731
853
810
771
736
704
675
797
758
721
689
659
631
744
707
674
643
615
589
50
52
54
56
58
60
756
727
700
675
652
630
702
675
650
627
605
585
648
623
600
579
559
540
606
583
561
541
522
505
566
544
524
505
488
472
62
64
66
68
70
72
610
591
573
556
540
525
566
548
532
516
501
488
523
506
491
476
463
450
489
473
459
446
433
421
456
442
429
416
404
393
1010
30300
779
250
40.0
300
11.4
272
15.2
337
943
28300
737
226
38.0
268
10.5
243
14.0
302
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1260
37800
937
332
47.3
429
14.8
393
19.7
477
1170
35100
873
297
44.3
376
13.1
344
17.4
419
1080
32400
822
269
42.0
333
12.3
303
16.4
373
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 76
BEAM AND GIRDER DESIGN
W 36
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
W 36
256
19
20
21
22
23
24
194
182
170
160
150
135
1740
1650
1560
1640
1560
1470
1390
1510
1440
1350
1280
1420
1350
1270
1200
1330
1250
1180
1110
1260
1250
1170
1100
1040
1210
1160
1090
1030
968
1640
1560
1490
1420
1360
1300
1480
1400
1340
1280
1220
1170
1320
1250
1190
1140
1090
1040
1210
1150
1100
1050
1000
959
1130
1080
1030
979
937
898
1050
1000
954
911
871
835
985
936
891
851
814
780
917
872
830
792
758
726
804
764
727
694
664
636
25
26
27
28
29
30
1250
1200
1160
1110
1080
1040
1120
1080
1040
1000
968
936
1000
961
926
893
862
833
920
885
852
822
793
767
862
828
798
769
743
718
802
771
742
716
691
668
749
720
693
669
646
624
697
670
646
623
601
581
611
587
566
545
527
509
31
32
33
34
35
36
1010
975
945
918
891
867
906
878
851
826
802
780
806
781
757
735
714
694
742
719
697
677
657
639
695
673
653
634
615
598
646
626
607
589
573
557
604
585
567
551
535
520
562
545
528
513
498
484
493
477
463
449
436
424
38
40
42
44
46
48
821
780
743
709
678
650
739
702
669
638
610
585
658
625
595
568
543
521
606
575
548
523
500
479
567
539
513
490
468
449
527
501
477
455
436
418
493
468
446
425
407
390
459
436
415
396
379
363
402
382
364
347
332
318
50
52
54
56
58
60
624
600
578
557
538
520
562
540
520
501
484
468
500
481
463
446
431
417
460
443
426
411
397
384
431
414
399
385
371
359
401
385
371
358
346
334
374
360
347
334
323
312
349
335
323
311
301
291
305
294
283
273
263
255
62
64
66
68
70
72
503
488
473
459
446
433
453
439
425
413
401
390
403
390
379
368
357
347
371
360
349
338
329
320
347
337
326
317
308
299
323
313
304
295
286
278
302
293
284
275
267
260
281
272
264
256
249
242
246
239
231
225
218
212
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
1040
31200
970
315
48.0
446
14.8
409
19.7
471
936
28100
872
272
43.5
367
12.2
336
16.3
406
668
20000
664
170
34.0
212
8.55
191
11.4
240
624
18700
632
157
32.5
191
8.09
171
10.8
217
581
17400
605
146
31.3
173
7.84
154
10.5
198
509
15300
576
127
30.0
149
8.32
129
11.1
176
Span (ft)
1940
1840
1730
210
1150
1090
1020
954
898
848
Fy = 50 ksi
13
14
15
16
17
18
232
Properties and Reaction Values
833
25000
822
240
41.5
318
12.4
288
16.5
358
767
23000
754
209
38.3
271
10.5
245
14.0
305
718
21500
711
193
36.3
242
9.62
219
12.8
273
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 77
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 33
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 33
241
221
W 33
201
169
152
141
130
118
1050
986
932
883
839
799
964
907
857
812
771
734
876
824
778
737
701
667
778
732
692
655
623
593
16
17
18
19
20
21
1530
1480
1410
1340
1420
1350
1280
1220
1300
1290
1220
1160
1100
1180
1110
1050
993
944
899
22
23
24
25
26
27
1280
1220
1170
1130
1080
1040
1170
1120
1070
1030
987
950
1050
1010
965
926
891
858
858
820
786
755
726
699
762
729
699
671
645
621
701
670
643
617
593
571
637
609
584
560
539
519
566
541
519
498
479
461
28
29
30
31
32
33
1010
971
939
909
880
854
916
884
855
827
802
777
827
799
772
747
724
702
674
651
629
609
590
572
599
578
559
541
524
508
551
532
514
497
482
467
500
483
467
452
438
425
445
429
415
402
389
377
34
35
36
37
38
40
829
805
783
761
741
704
754
733
713
693
675
641
681
662
643
626
609
579
555
539
524
510
497
472
493
479
466
453
441
419
454
441
428
417
406
386
412
400
389
379
369
350
366
356
346
336
328
311
42
44
46
48
50
52
671
640
612
587
563
542
611
583
558
534
513
493
551
526
503
483
463
445
449
429
410
393
377
363
399
381
365
349
335
323
367
350
335
321
308
297
334
318
305
292
280
269
296
283
271
259
249
239
54
56
58
60
62
64
522
503
486
470
454
440
475
458
442
428
414
401
429
414
399
386
374
362
349
337
325
315
304
295
311
299
289
280
270
262
286
275
266
257
249
241
259
250
242
234
226
219
231
222
215
208
201
195
66
68
70
72
427
414
402
391
389
377
366
356
351
341
331
322
286
278
270
262
254
247
240
233
234
227
220
214
212
206
200
195
189
183
178
173
514
15400
544
132
30.3
166
7.49
150
9.99
191
467
14000
518
122
29.0
147
7.46
131
9.95
172
415
12500
488
107
27.5
127
7.40
110
9.87
151
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
939
28200
766
227
41.5
323
12.9
293
17.2
362
855
25700
710
200
38.8
278
11.6
251
15.5
316
772
23200
650
173
35.8
234
10.2
211
13.6
267
629
18900
612
173
33.5
218
7.89
201
10.5
244
559
16800
574
149
31.8
187
7.84
170
10.5
213
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 78
BEAM AND GIRDER DESIGN
W 30
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
W 30
Span (ft)
Fy = 50 ksi
Wt./ft
261
235
191
173
1290
1250
1180
1120
1070
1180
1120
1060
1010
961
1080
1070
1010
955
908
864
1150
1100
1060
1010
975
939
1020
977
936
899
864
832
918
878
841
808
777
748
825
789
756
726
698
672
1010
973
941
911
882
855
905
874
845
818
792
768
803
775
749
725
702
681
721
696
673
651
631
612
648
626
605
585
567
550
34
36
38
40
42
44
830
784
743
706
672
642
746
704
667
634
604
576
661
624
591
562
535
511
594
561
531
505
481
459
534
504
478
454
432
413
46
48
50
52
54
56
614
588
565
543
523
504
551
528
507
488
469
453
488
468
449
432
416
401
439
421
404
388
374
361
395
378
363
349
336
324
58
60
62
64
66
68
487
471
455
441
428
415
437
423
409
396
384
373
387
375
362
351
340
330
348
337
326
315
306
297
313
303
293
284
275
267
70
72
403
392
362
352
321
312
288
280
259
252
673
20200
588
172
35.5
235
10.7
213
14.2
269
605
18200
538
154
32.8
197
9.38
178
12.5
228
16
17
18
19
20
21
1590
1570
1490
1410
1340
1400
1330
1270
1210
22
23
24
25
26
27
1280
1230
1180
1130
1090
1050
28
29
30
31
32
33
211
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
941
28200
794
283
46.5
415
16.7
380
22.2
434
845
25400
701
233
41.5
334
13.2
306
17.6
368
749
22500
647
206
38.8
282
12.4
257
16.5
322
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 79
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 30
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 30
148
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
36
38
40
42
44
46
48
50
52
54
56
58
60
62
64
66
68
70
72
1080
1070
1000
938
882
833
789
750
714
682
652
625
600
577
556
536
517
500
484
469
455
441
417
395
375
357
341
326
313
300
288
278
268
259
250
242
234
227
221
214
208
132
1010
936
874
819
771
728
690
656
624
596
570
546
524
504
486
468
452
437
423
410
397
386
364
345
328
312
298
285
273
262
252
243
234
226
219
211
205
199
193
187
182
124
953
942
874
816
765
720
680
644
612
583
556
532
510
490
471
453
437
422
408
395
383
371
360
340
322
306
291
278
266
255
245
235
227
219
211
204
197
191
185
180
175
170
116
108
99
90
916
872
810
756
709
667
630
597
567
540
515
493
473
454
436
420
405
391
378
366
354
344
334
315
298
284
270
258
247
236
227
218
210
203
196
189
183
177
172
167
162
158
878
865
798
741
692
649
611
577
546
519
494
472
451
433
415
399
384
371
358
346
335
324
315
305
288
273
260
247
236
226
216
208
200
192
185
179
173
167
162
157
153
148
144
833
780
720
669
624
585
551
520
493
468
446
425
407
390
374
360
347
334
323
312
302
293
284
275
260
246
234
223
213
203
195
187
180
173
167
161
156
151
146
142
138
134
130
749
708
653
606
566
531
499
472
447
425
404
386
369
354
340
327
314
303
293
283
274
265
257
250
236
223
212
202
193
185
177
170
163
157
152
146
142
137
133
129
125
121
118
346
10400
439
106
27.3
126
7.73
111
10.3
152
312
9360
416
93.4
26.0
111
7.66
95.6
10.2
136
283
8490
375
77.1
23.5
90.8
6.24
78.5
8.31
111
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
500
15000
538
163
32.5
205
8.21
189
10.9
232
437
13100
503
135
30.8
174
8.30
157
11.1
201
408
12200
477
123
29.2
156
7.72
140
10.3
181
378
11300
458
115
28.3
141
7.65
126
10.2
166
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 80
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 27
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 27
258
235
194
178
161
146
1270
1250
1180
1120
1060
1140
1110
1050
992
942
1090
1060
1000
945
895
851
983
960
904
853
808
768
895
864
814
768
728
692
1100
1050
1000
961
923
887
1010
965
923
885
850
817
897
856
819
785
754
725
810
773
740
709
680
654
731
698
668
640
614
591
659
629
601
576
553
532
944
911
879
850
823
797
854
824
796
769
744
721
787
759
732
708
685
664
698
673
650
628
608
589
630
608
587
567
549
532
569
549
530
512
495
480
512
494
477
461
446
432
33
34
35
36
37
38
773
750
729
708
689
671
699
679
659
641
624
607
644
625
607
590
574
559
571
554
538
523
509
496
515
500
486
473
460
448
465
452
439
427
415
404
419
407
395
384
374
364
40
42
44
46
48
50
638
607
580
554
531
510
577
549
524
502
481
461
531
506
483
462
443
425
471
449
428
410
393
377
425
405
387
370
354
340
384
366
349
334
320
307
346
329
314
301
288
277
52
54
56
58
60
62
490
472
455
440
425
411
444
427
412
398
385
372
408
393
379
366
354
343
362
349
336
325
314
304
327
315
304
293
284
274
295
284
274
265
256
248
266
256
247
238
231
223
64
66
398
386
360
350
332
322
294
285
266
258
240
233
216
210
567
17000
544
170
36.3
243
12.5
220
16.6
283
512
15400
492
150
33.0
201
10.4
182
13.9
235
461
13800
447
128
30.3
168
8.97
151
12.0
197
15
16
17
18
19
20
1530
1500
1420
1340
1280
1410
1360
1280
1210
1150
21
22
23
24
25
26
1210
1160
1110
1060
1020
981
27
28
29
30
31
32
217
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
850
25500
767
306
49.0
465
19.9
427
26.5
466
769
23100
704
263
45.5
397
17.7
363
23.6
411
708
21200
637
227
41.5
334
14.5
306
19.3
362
628
18800
569
193
37.5
271
12.1
248
16.2
311
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 81
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 27
For beams laterally unsupported, see page 4-139
Designation
W 27
Span (ft)
Fy = 50 ksi
Wt./ft
129
102
94
84
840
792
735
686
643
753
704
654
610
572
712
695
642
596
556
521
663
610
563
523
488
458
697
658
624
593
564
539
605
572
542
515
490
468
538
508
482
458
436
416
491
463
439
417
397
379
431
407
385
366
349
333
23
24
25
26
27
28
515
494
474
456
439
423
447
429
412
396
381
368
398
381
366
352
339
327
363
348
334
321
309
298
318
305
293
282
271
261
29
30
31
32
33
34
409
395
382
370
359
349
355
343
332
322
312
303
316
305
295
286
277
269
288
278
269
261
253
245
252
244
236
229
222
215
36
38
40
42
44
46
329
312
296
282
269
258
286
271
257
245
234
224
254
241
229
218
208
199
232
219
209
199
190
181
203
193
183
174
166
159
48
50
52
54
56
58
247
237
228
219
212
204
214
206
198
191
184
177
191
183
176
169
163
158
174
167
160
154
149
144
153
146
141
136
131
126
60
62
64
66
198
191
185
180
172
166
161
156
153
148
143
139
139
135
130
126
122
118
114
111
278
8340
356
88.0
24.5
107
6.35
95.4
8.46
127
244
7320
332
79.1
23.0
90.0
6.16
79.0
8.21
110
11
12
13
14
15
16
910
846
790
741
17
18
19
20
21
22
114
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
395
11900
455
138
30.5
180
8.08
165
10.8
206
343
10300
420
116
28.5
150
7.89
135
10.5
175
305
9150
377
101
25.8
121
6.57
110
8.76
143
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 82
BEAM AND GIRDER DESIGN
W 24
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
W 24
131
117
104
952
936
878
826
780
868
836
784
738
697
800
793
740
694
653
617
721
701
654
613
577
545
650
619
578
542
510
482
807
767
730
697
667
639
739
702
669
638
610
585
660
627
597
570
545
523
584
555
529
505
483
463
516
491
467
446
427
409
456
434
413
394
377
361
671
645
621
599
578
559
613
590
568
548
529
511
562
540
520
501
484
468
502
482
464
448
432
418
444
427
411
396
383
370
392
377
363
350
338
327
347
333
321
310
299
289
586
568
551
535
519
505
541
524
508
493
479
466
495
479
465
451
438
426
453
439
425
413
401
390
405
392
380
369
358
348
358
347
336
326
317
308
316
307
297
289
280
273
280
271
263
255
248
241
534
507
483
461
441
423
478
455
433
413
395
379
441
419
399
381
365
349
403
383
365
348
333
319
369
351
334
319
305
293
330
314
299
285
273
261
292
278
264
252
241
231
258
245
234
223
213
204
228
217
206
197
188
181
50
52
54
56
58
60
406
390
376
362
350
338
364
350
337
325
313
303
335
323
311
299
289
280
307
295
284
274
264
256
281
270
260
251
242
234
251
241
232
224
216
209
222
213
206
198
191
185
196
189
182
175
169
164
173
167
161
155
149
145
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
676
20300
674
300
48.0
446
21.3
409
28.4
456
606
18200
604
258
43.5
367
17.6
336
23.5
400
370
11100
400
132
30.3
166
10.2
150
13.6
199
327
9810
360
112
27.5
136
8.73
121
11.6
164
289
8670
325
93.8
25.0
110
7.49
98.4
9.99
135
Span (ft)
146
Fy = 50 ksi
229
207
192
176
13
14
15
16
17
18
1350
1270
1190
1130
1210
1140
1070
1010
1110
1050
986
932
1020
1020
958
902
852
19
20
21
22
23
24
1070
1010
966
922
882
845
957
909
866
826
790
758
883
839
799
762
729
699
25
26
27
28
29
30
811
780
751
724
699
676
727
699
673
649
627
606
31
32
33
34
35
36
654
634
615
596
579
563
38
40
42
44
46
48
162
Properties and Reaction Values
559
16800
557
228
40.5
318
15.5
291
20.6
359
511
15300
511
199
37.5
271
13.5
248
18.0
315
468
14000
476
176
35.3
236
12.4
215
16.6
276
418
12500
434
152
32.5
197
11.0
179
14.7
233
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 83
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 24
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 24
103
94
84
W 24
76
68
62
55
551
510
459
417
383
503
503
447
402
365
335
7
8
9
10
11
12
729
700
676
635
612
611
560
568
545
500
532
531
483
443
13
14
15
16
17
18
646
600
560
525
494
467
586
544
508
476
448
423
517
480
448
420
395
373
462
429
400
375
353
333
408
379
354
332
312
295
353
328
306
287
270
255
309
287
268
251
236
223
19
20
21
22
23
24
442
420
400
382
365
350
401
381
363
346
331
318
354
336
320
305
292
280
316
300
286
273
261
250
279
266
253
241
231
221
242
230
219
209
200
191
212
201
191
183
175
168
25
26
27
28
29
30
336
323
311
300
290
280
305
293
282
272
263
254
269
258
249
240
232
224
240
231
222
214
207
200
212
204
197
190
183
177
184
177
170
164
158
153
161
155
149
144
139
134
31
32
33
34
35
36
271
263
255
247
240
233
246
238
231
224
218
212
217
210
204
198
192
187
194
188
182
176
171
167
171
166
161
156
152
148
148
143
139
135
131
128
130
126
122
118
115
112
38
40
42
44
46
48
221
210
200
191
183
175
201
191
181
173
166
159
177
168
160
153
146
140
158
150
143
136
130
125
140
133
126
121
115
111
121
115
109
104
100
96
106
101
96
91
87
84
50
52
54
56
58
60
168
162
156
150
145
140
152
147
141
136
131
127
134
129
124
120
116
112
120
115
111
107
103
106
102
98
95
92
92
88
85
82
79
80
77
74
72
69
177
5310
266
71.3
20.8
73.7
5.57
64.9
7.43
91.8
153
4590
276
73.9
21.5
78.1
6.14
68.4
8.19
98.1
134
4020
251
64.8
19.8
63.6
5.60
54.8
7.47
81.8
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
280
8400
364
120
27.5
146
7.49
133
9.98
170
254
7620
338
105
25.8
125
6.95
113
9.26
147
224
6720
306
91.8
23.5
102
6.05
92.2
8.07
122
200
6000
284
79.1
22.0
86.8
5.67
77.8
7.55
105
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 84
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 21
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 21
201
182
166
147
132
122
111
101
766
714
666
624
588
555
702
658
614
576
542
512
639
598
558
523
492
465
577
542
506
474
446
422
13
14
15
16
17
18
1130
1060
994
935
883
1020
952
893
840
793
910
864
810
762
720
858
799
746
699
658
622
19
20
21
22
23
24
837
795
757
723
691
663
752
714
680
649
621
595
682
648
617
589
563
540
589
560
533
509
487
466
526
500
476
454
434
416
485
461
439
419
400
384
441
419
399
380
364
349
399
380
361
345
330
316
25
26
27
28
29
30
636
612
589
568
548
530
571
549
529
510
492
476
518
498
480
463
447
432
448
430
414
400
386
373
400
384
370
357
344
333
368
354
341
329
318
307
335
322
310
299
289
279
304
292
281
271
262
253
31
32
33
34
35
36
513
497
482
468
454
442
461
446
433
420
408
397
418
405
393
381
370
360
361
350
339
329
320
311
322
312
303
294
285
278
297
288
279
271
263
256
270
262
254
246
239
233
245
237
230
223
217
211
38
40
42
44
46
48
418
398
379
361
346
331
376
357
340
325
310
298
341
324
309
295
282
270
294
280
266
254
243
233
263
250
238
227
217
208
242
230
219
209
200
192
220
209
199
190
182
174
200
190
181
173
165
158
50
52
318
306
286
275
259
249
224
215
200
192
184
177
167
161
152
146
307
9210
351
127
30.0
164
11.2
148
15.0
201
279
8370
319
112
27.5
138
9.56
124
12.8
169
253
7590
288
97.7
25.0
114
7.91
103
10.6
140
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
530
15900
566
270
45.5
400
21.7
366
29.0
418
476
14300
509
233
41.5
332
18.4
304
24.5
368
432
13000
455
199
37.5
273
14.9
251
19.9
321
373
11200
429
169
36.0
236
15.9
213
21.2
286
333
9990
383
147
32.5
192
13.1
173
17.5
235
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 85
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 21
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 21
93
83
73
W 21
68
62
57
50
44
390
358
318
286
260
239
7
8
9
10
11
12
677
663
603
553
596
588
535
490
522
516
469
430
491
480
436
400
453
432
393
360
461
430
387
352
323
427
413
367
330
300
275
13
14
15
16
17
18
510
474
442
414
390
368
452
420
392
368
346
327
397
369
344
323
304
287
369
343
320
300
282
267
332
309
288
270
254
240
298
276
258
242
228
215
254
236
220
206
194
183
220
204
191
179
168
159
19
20
21
22
23
24
349
332
316
301
288
276
309
294
280
267
256
245
272
258
246
235
224
215
253
240
229
218
209
200
227
216
206
196
188
180
204
194
184
176
168
161
174
165
157
150
143
138
151
143
136
130
124
119
25
26
27
28
29
30
265
255
246
237
229
221
235
226
218
210
203
196
206
198
191
184
178
172
192
185
178
171
166
160
173
166
160
154
149
144
155
149
143
138
133
129
132
127
122
118
114
110
114
110
106
102
99
95
31
32
33
34
35
36
214
207
201
195
189
184
190
184
178
173
168
163
166
161
156
152
147
143
155
150
145
141
137
133
139
135
131
127
123
120
125
121
117
114
111
108
106
103
100
97
94
92
92
89
87
84
82
80
38
40
42
44
46
48
174
166
158
151
144
138
155
147
140
134
128
123
136
129
123
117
112
108
126
120
114
109
104
100
114
108
103
98
94
90
102
97
92
88
84
81
87
83
79
75
72
69
75
72
68
65
62
60
50
52
133
128
118
113
103
99
96
92
86
83
77
74
66
63
57
129
3870
230
69.6
20.3
74.9
5.25
67.6
7.00
92.0
110
3300
214
62.3
19.0
61.8
5.33
54.4
7.10
79.1
95.4
2860
195
52.0
17.5
50.1
4.99
43.2
6.65
66.3
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
221
6630
339
122
29.0
154
10.5
138
14.0
188
196
5880
298
101
25.8
122
8.26
110
11.0
149
172
5160
261
85.3
22.8
95.2
6.48
86.0
8.64
116
160
4800
245
77.3
21.5
84.2
5.94
75.8
7.92
103
144
4320
227
68.8
20.0
71.5
5.36
64.0
7.15
89.0
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 86
BEAM AND GIRDER DESIGN
W 18
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 18
192
175
158
W 18
143
130
119
106
97
86
76
597
575
531
493
460
431
537
528
487
452
422
396
477
465
429
399
372
349
418
408
376
349
326
306
11
12
13
14
15
16
1050
1020
947
884
829
963
918
853
796
746
863
822
763
712
668
768
743
690
644
604
696
672
624
582
546
671
653
602
559
522
489
17
18
19
20
21
22
780
737
698
663
631
603
702
663
628
597
569
543
628
593
562
534
509
485
568
537
508
483
460
439
514
485
459
437
416
397
461
435
412
392
373
356
406
383
363
345
329
314
372
352
333
317
301
288
328
310
294
279
266
254
288
272
257
245
233
222
23
24
25
26
27
28
577
553
530
510
491
474
519
498
478
459
442
426
464
445
427
411
396
381
420
403
386
372
358
345
380
364
349
336
323
312
340
326
313
301
290
280
300
288
276
265
256
246
275
264
253
243
234
226
243
233
223
215
207
199
213
204
196
188
181
175
29
30
31
32
33
34
457
442
428
414
402
390
412
398
385
373
362
351
368
356
345
334
324
314
333
322
312
302
293
284
301
291
282
273
265
257
270
261
253
245
237
230
238
230
223
216
209
203
218
211
204
198
192
186
192
186
180
174
169
164
169
163
158
153
148
144
35
36
37
38
39
40
379
368
358
349
340
332
341
332
323
314
306
299
305
297
289
281
274
267
276
268
261
254
248
242
249
243
236
230
224
218
224
218
212
206
201
196
197
192
186
182
177
173
181
176
171
167
162
158
159
155
151
147
143
140
140
136
132
129
125
122
42
44
316
301
284
271
254
243
230
220
208
198
186
178
164
157
151
144
133
127
116
111
442
13300
527
293
48.0
449
26.9
412
35.8
449
398
11900
482
250
44.5
382
23.9
350
31.9
395
230
6900
298
120
29.5
158
12.6
143
16.8
199
211
6330
269
104
26.8
132
10.2
119
13.7
165
186
5580
238
86.3
24.0
105
8.45
94.9
11.3
133
163
4890
209
73.0
21.3
82.4
6.71
74.3
8.94
104
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
356
10700
431
215
40.5
315
20.2
289
27.0
347
322
9660
384
183
36.5
258
16.4
237
21.8
301
291
8730
348
157
33.5
217
14.1
199
18.8
262
261
7830
335
143
32.8
197
15.1
178
20.2
246
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 87
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 18
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 18
71
65
6
7
8
9
10
11
494
483
435
395
446
443
399
363
12
13
14
15
16
17
363
335
311
290
272
256
18
19
20
21
22
23
60
W 18
55
50
46
40
35
409
369
335
381
373
336
305
345
337
303
275
351
340
302
272
247
304
294
261
235
214
287
285
249
222
200
181
333
307
285
266
249
235
308
284
264
246
231
217
280
258
240
224
210
198
253
233
216
202
189
178
227
209
194
181
170
160
196
181
168
157
147
138
166
153
143
133
125
117
242
229
218
207
198
189
222
210
200
190
181
173
205
194
185
176
168
160
187
177
168
160
153
146
168
159
152
144
138
132
151
143
136
130
124
118
131
124
118
112
107
102
111
105
100
95
91
87
24
25
26
27
28
29
181
174
167
161
155
150
166
160
153
148
143
138
154
148
142
137
132
127
140
134
129
124
120
116
126
121
117
112
108
104
113
109
105
101
97
94
98
94
90
87
84
81
83
80
77
74
71
69
30
31
32
33
34
35
145
140
136
132
128
124
133
129
125
121
117
114
123
119
115
112
109
105
112
108
105
102
99
96
101
98
95
92
89
87
91
88
85
82
80
78
78
76
74
71
69
67
67
64
62
60
59
57
36
38
40
42
44
121
114
109
104
99
111
105
100
95
91
103
97
92
88
84
93
88
84
80
76
84
80
76
72
69
76
72
68
65
62
65
62
59
56
53
55
53
50
48
45
90.7
2720
176
56.3
18.0
60.6
4.62
55.0
6.16
75.6
78.4
2350
152
46.8
15.8
46.2
3.60
41.9
4.80
57.9
66.5
2000
143
42.2
15.0
38.6
3.88
34.0
5.18
51.3
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
145
4350
247
92.8
24.8
113
8.77
102
11.7
142
133
3990
223
80.9
22.5
94.3
7.16
85.5
9.55
118
123
3690
204
71.3
20.8
80.4
6.10
73.0
8.13
100
112
3360
191
64.0
19.5
69.7
5.62
62.9
7.50
88.0
101
3030
172
55.5
17.8
57.6
4.72
51.9
6.29
72.9
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 88
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 16
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 16
100
89
77
6
7
8
9
10
11
536
475
406
12
13
14
15
16
17
495
457
424
396
371
349
438
404
375
350
328
309
18
19
20
21
22
23
330
313
297
283
270
258
24
25
26
27
28
29
W 16
67
57
50
45
W 16
40
36
31
26
212
189
166
147
133
121
348
382
350
315
286
334
307
276
251
301
274
247
224
264
243
219
199
253
240
213
192
175
236
231
203
180
162
147
375
346
321
300
281
265
325
300
279
260
244
229
263
242
225
210
197
185
230
212
197
184
173
162
206
190
176
165
154
145
182
168
156
146
137
129
160
148
137
128
120
113
135
125
116
108
101
95
111
102
95
88
83
78
292
276
263
250
239
228
250
237
225
214
205
196
217
205
195
186
177
170
175
166
158
150
143
137
153
145
138
131
125
120
137
130
123
118
112
107
122
115
109
104
99
95
107
101
96
91
87
83
90
85
81
77
74
70
74
70
66
63
60
58
248
238
228
220
212
205
219
210
202
194
188
181
188
180
173
167
161
155
163
156
150
144
139
134
131
126
121
117
113
109
115
110
106
102
99
95
103
99
95
91
88
85
91
87
84
81
78
75
80
77
74
71
69
66
68
65
62
60
58
56
55
53
51
49
47
46
30
31
32
33
34
35
198
192
186
180
175
170
175
169
164
159
154
150
150
145
141
136
132
129
130
126
122
118
115
111
105
102
98
95
93
90
92
89
86
84
81
79
82
80
77
75
73
71
73
71
68
66
64
62
64
62
60
58
56
55
54
52
51
49
48
46
44
43
41
40
39
38
36
38
40
165
156
149
146
138
131
125
118
113
108
103
98
88
83
79
77
73
69
69
65
62
61
58
55
53
51
45
43
37
35
198
5940
268
123
29.2
160
13.0
145
17.3
202
175
5250
237
103
26.2
128
10.7
116
14.2
163
72.9
2190
132
45.3
15.3
43.2
3.80
39.1
5.06
55.6
64.0
1920
126
41.5
14.7
37.9
4.07
33.6
5.43
51.2
54.0
1620
118
38.7
13.8
34.5
3.22
31.1
4.29
45.0
44.2
1330
106
33.2
12.5
26.5
3.12
23.2
4.16
36.7
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
150
4500
203
81.8
22.8
96.5
8.12
87.5
10.8
123
130
3900
174
67.9
19.8
73.0
6.14
66.3
8.19
93.0
105
3150
191
73.9
21.5
86.0
7.32
78.0
9.76
110
92.0
2760
167
62.3
19.0
67.1
5.80
60.8
7.73
85.9
82.3
2470
150
53.9
17.3
54.9
4.87
49.7
6.50
70.8
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 89
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 14
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
W 14
132
120
109
W 14
99*
90*
82
74
68
61
344
344
315
291
270
252
315
314
288
265
246
230
281
278
255
235
219
204
461
454
424
406
384
371
370
345
333
329
307
16
17
18
19
20
21
439
413
390
369
351
334
398
374
353
335
318
303
360
339
320
303
288
274
323
304
287
272
259
246
288
271
256
243
230
219
261
245
232
219
209
199
236
222
210
199
189
180
216
203
192
182
173
164
191
180
170
161
153
146
22
23
24
25
26
27
319
305
293
281
270
260
289
277
265
254
245
236
262
250
240
230
222
213
235
225
216
207
199
192
210
200
192
184
177
171
190
181
174
167
160
154
172
164
158
151
145
140
157
150
144
138
133
128
139
133
128
122
118
113
28
29
30
31
32
33
251
242
234
226
219
213
227
219
212
205
199
193
206
199
192
186
180
175
185
178
172
167
162
157
165
159
154
149
144
140
149
144
139
135
130
126
135
130
126
122
118
115
123
119
115
111
108
105
109
106
102
99
96
93
34
206
187
169
152
136
123
111
101
90
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
234
7020
255
136
32.3
190
19.2
171
25.6
241
212
6360
231
120
29.5
158
16.3
143
21.8
213
126
3780
172
87.9
22.5
96.5
8.86
88.1
11.8
126
115
3450
157
77.8
20.8
81.8
7.65
74.6
10.2
108
102
3060
141
67.4
18.8
66.5
6.37
60.6
8.49
88.2
Span (ft)
511
501
468
394
379
348
321
298
278
Fy = 50 ksi
10
11
12
13
14
15
Properties and Reaction Values
192
5760
203
103
26.2
127
12.7
115
16.9
170
173
5170
185
87.1
24.3
108
11.2
97.0
14.9
145
157
4610
167
75.6
22.0
88.7
9.26
80.0
12.3
120
139
4170
197
104
25.5
121
11.7
110
15.6
161
*Noncompact shape; Fy = 50 ksi.
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 90
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 14
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 14
53
48
5
6
7
8
9
10
278
261
253
235
11
12
13
14
15
16
238
218
201
187
174
163
17
18
19
20
21
22
W 14
43
38
34
W 14
30
26
22
225
209
236
231
205
185
215
205
182
164
202
177
158
142
192
172
151
134
121
171
166
142
125
111
100
214
196
181
168
157
147
190
174
161
149
139
131
168
154
142
132
123
115
149
137
126
117
109
102
129
118
109
101
95
89
110
101
93
86
80
75
91
83
77
71
66
62
154
145
138
131
124
119
138
131
124
118
112
107
123
116
110
104
99
95
109
103
97
92
88
84
96
91
86
82
78
74
83
79
75
71
68
65
71
67
63
60
57
55
59
55
52
50
47
45
23
24
25
26
27
28
114
109
105
101
97
93
102
98
94
90
87
84
91
87
84
80
77
75
80
77
74
71
68
66
71
68
66
63
61
59
62
59
57
55
53
51
52
50
48
46
45
43
43
42
40
38
37
36
29
30
31
32
33
34
90
87
84
82
79
77
81
78
76
74
71
69
72
70
67
65
63
61
64
62
60
58
56
54
56
55
53
51
50
48
49
47
46
44
43
42
42
40
39
38
37
35
34
33
32
31
30
29
47.3
1420
101
31.6
13.5
31.4
4.00
27.7
5.33
45.0
40.2
1210
95.8
29.9
12.8
30.1
3.07
27.2
4.09
40.6
33.2
996
85.3
25.2
11.5
23.0
2.86
20.4
3.81
32.8
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
87.1
2610
139
66.5
18.5
65.9
5.96
60.4
7.95
86.2
78.4
2350
127
58.4
17.0
55.1
5.18
50.4
6.91
72.8
69.6
2090
112
50.0
15.3
44.2
4.24
40.4
5.65
58.7
61.5
1850
118
41.2
15.5
44.7
4.44
40.5
5.92
59.7
54.6
1640
108
35.6
14.3
37.0
3.94
33.3
5.25
50.4
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 91
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 12
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
W 12
120
106
96
87
W 12
79
72
65*
58
53
225
212
195
180
167
156
425
410
378
351
328
377
368
339
315
294
348
330
305
283
264
314
298
275
255
238
284
270
249
231
216
255
238
220
204
191
16
17
18
19
20
21
349
328
310
294
279
266
308
289
273
259
246
234
276
259
245
232
221
210
248
233
220
208
198
189
223
210
198
188
179
170
203
191
180
171
162
154
179
168
159
151
143
136
162
152
144
136
130
123
146
137
130
123
117
111
22
23
24
25
26
27
254
243
233
223
215
207
224
214
205
197
189
182
200
192
184
176
170
163
180
172
165
158
152
147
162
155
149
143
137
132
147
141
135
130
125
120
130
124
119
114
110
106
118
113
108
104
100
96
106
102
97
93
90
87
28
29
30
199
192
186
176
170
164
158
152
147
141
137
132
128
123
119
116
112
108
102
99
95
93
89
86
83
81
78
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
186
5580
252
161
35.5
227
26.7
203
35.6
276
164
4920
212
129
30.5
171
19.2
154
25.7
228
96.8
2860
128
64.0
19.5
68.3
8.75
61.2
11.7
99.2
86.4
2590
118
61.9
18.0
62.3
6.47
57.1
8.63
85.1
77.9
2340
112
53.9
17.3
55.4
6.41
50.3
8.54
78.0
Span (ft)
503
465
429
399
372
237
236
216
199
185
173
Fy = 50 ksi
10
11
12
13
14
15
Properties and Reaction Values
147
4410
189
112
27.5
140
15.7
126
21.0
194
132
3960
174
96.6
25.8
120
14.6
108
19.4
171
119
3570
157
84.5
23.5
99.6
12.3
89.4
16.5
143
108
3240
142
73.9
21.5
83.2
10.5
74.7
14.0
120
*Indicates noncompact shape; Fy = 50 ksi.
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 92
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 12
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 12
50
45
4
5
6
7
8
9
244
241
218
216
10
11
12
13
14
15
217
197
181
167
155
145
16
17
18
19
20
21
W 12
40
35
30
W 12
26
22
19
16
14
154
148
124
106
93
82
142
121
101
86
75
67
129
104
87
75
65
58
190
203
192
171
173
162
144
152
140
124
173
147
126
110
98
194
176
162
149
139
129
173
157
144
133
123
115
154
140
128
118
110
102
129
118
108
99
92
86
112
101
93
86
80
74
88
80
73
68
63
59
74
67
62
57
53
49
60
55
50
46
43
40
52
47
44
40
37
35
136
128
121
114
109
103
121
114
108
102
97
92
108
101
96
91
86
82
96
90
85
81
77
73
81
76
72
68
65
62
70
66
62
59
56
53
55
52
49
46
44
42
46
44
41
39
37
35
38
35
34
32
30
29
33
31
29
27
26
25
22
23
24
25
26
27
99
94
91
87
84
80
88
84
81
78
75
72
78
75
72
69
66
64
70
67
64
61
59
57
59
56
54
52
50
48
51
49
47
45
43
41
40
38
37
35
34
33
34
32
31
30
29
27
27
26
25
24
23
22
24
23
22
21
20
19
28
29
30
78
75
72
69
67
65
62
59
51
55
53
43
46
45
37
40
38
29
31
30
25
26
26
22
21
19
18
72.4
2170
122
63.6
18.5
64.9
7.02
59.2
9.37
89.7
64.7
1940
109
52.3
16.8
53.0
5.87
48.3
7.82
73.7
29.3
879
86.4
28.4
13.0
31.2
3.63
28.2
4.85
43.9
24.7
741
77.2
23.9
11.8
24.3
3.30
21.6
4.40
35.9
20.1
603
71.2
20.6
11.0
19.2
3.63
16.3
4.83
32.0
17.4
522
64.3
17.2
10.0
15.3
3.23
12.7
4.31
26.7
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
57.5
1730
95.1
46.1
14.7
41.5
4.52
37.9
6.02
57.4
51.2
1540
101
37.5
15.0
42.7
4.49
39.0
5.99
58.5
43.1
1290
86.6
30.5
13.0
31.7
3.50
28.8
4.67
44.0
37.2
1120
75.9
25.2
11.5
24.5
2.83
22.2
3.78
34.5
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 93
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 10
For beams laterally unsupported, see page 4-139
Designation
W 10
112
100
88
77
68
60
54
49
9
10
11
12
13
14
463
441
401
368
339
315
408
390
355
325
300
279
354
339
308
283
261
242
303
293
266
244
225
209
264
256
233
213
197
183
232
224
203
187
172
160
202
200
182
167
154
143
183
181
165
151
139
129
15
16
17
18
19
20
294
276
259
245
232
221
260
244
229
217
205
195
226
212
199
188
178
170
195
183
172
163
154
146
171
160
151
142
135
128
149
140
132
124
118
112
133
125
118
111
105
100
121
113
107
101
95
91
21
22
23
24
210
200
192
184
186
177
170
163
161
154
147
141
139
133
127
122
122
116
111
107
107
102
97
93
95
91
87
83
86
82
79
76
74.6
2240
116
68.9
21.0
80.9
11.5
73.1
15.4
123
66.6
2000
101
57.8
18.5
63.6
8.83
57.7
11.8
96.0
60.4
1810
91.6
50.5
17.0
53.5
7.61
48.4
10.1
81.4
Span (ft)
Fy = 50 ksi
Wt./ft
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
147
4410
232
177
37.8
265
32.8
240
43.7
300
130
3900
204
149
34.0
214
27.4
194
36.5
259
113
3390
177
123
30.3
169
22.3
153
29.8
221
97.6
2930
152
99.4
26.5
130
17.5
117
23.3
185
85.3
2560
132
80.8
23.5
102
14.0
92.2
18.7
153
Load above heavy line is limited by design shear strength.
Values of φR (N = 31⁄4) in boldface exceed maximum web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 94
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 10
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
W 10
45
3
4
5
6
7
8
191
9
10
11
12
13
14
39
W 10
33
30
26
W 10
22
19
17
15
12*
101
94
75
63
54
47
138
130
108
93
81
131
112
94
80
70
124
120
96
80
69
60
169
152
146
170
157
137
145
134
117
132
130
111
98
183
165
150
137
127
118
156
140
128
117
108
100
129
116
106
97
90
83
122
110
100
91
84
78
104
94
85
78
72
67
87
78
71
65
60
56
72
65
59
54
50
46
62
56
51
47
43
40
53
48
44
40
37
34
42
38
34
31
29
27
15
16
17
18
19
20
110
103
97
92
87
82
94
88
83
78
74
70
78
73
68
65
61
58
73
69
65
61
58
55
63
59
55
52
49
47
52
49
46
43
41
39
43
41
38
36
34
32
37
35
33
31
30
28
32
30
28
27
25
24
25
23
22
21
20
19
21
22
23
24
78
75
72
69
67
64
61
59
55
53
51
49
52
50
48
46
45
43
41
39
37
35
34
33
31
29
28
27
27
26
24
23
23
22
21
20
18
17
16
16
54.9
1650
95.4
54.7
17.5
58.8
7.41
53.8
9.88
85.9
46.8
1400
84.4
44.3
15.8
46.4
6.43
42.2
8.58
70.0
21.6
648
69.1
25.4
12.5
28.3
4.18
25.5
5.57
43.6
18.7
561
65.5
22.5
12.0
24.4
4.48
21.3
5.98
40.8
16.0
480
62.0
19.8
11.5
20.7
4.88
17.4
6.51
38.6
12.6
376
50.6
14.8
9.50
13.7
3.58
11.3
4.77
26.8
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
38.8
1160
76.2
38.5
14.5
37.1
6.23
33.1
8.31
60.1
36.6
1100
84.8
35.2
15.0
42.3
5.47
38.5
7.29
62.2
31.3
939
72.5
28.4
13.0
31.7
4.18
28.8
5.58
47.0
26.0
780
65.9
22.5
12.0
25.4
4.08
22.7
5.45
40.4
*Indicates noncompact shape; Fy = 50 ksi.
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 95
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W8
For beams laterally unsupported, see page 4-139
Designation
W8
67
58
48
7
8
9
10
11
12
277
263
234
211
191
175
40
35
31
241
224
199
179
163
150
184
163
147
134
123
160
149
133
119
109
100
136
130
116
104
95
87
123
114
101
91
83
76
13
14
15
16
17
18
162
150
140
132
124
117
138
128
120
112
106
100
113
105
98
92
86
82
92
85
80
75
70
66
80
74
69
65
61
58
70
65
61
57
54
51
19
20
111
105
94
90
77
74
63
60
55
52
48
46
39.8
1190
80.2
47.8
18.0
58.3
10.9
52.3
14.6
99.6
34.7
1040
68.0
38.8
15.5
43.8
8.02
39.5
10.7
74.2
30.4
912
61.6
33.4
14.3
36.2
7.20
32.3
9.60
63.5
Span (ft)
Fy = 50 ksi
Wt./ft
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
70.2
2110
139
102
28.5
150
23.8
136
31.7
195
59.8
1790
120
83.7
25.5
118
20.2
106
27.0
167
49.0
1470
91.8
59.4
20.0
75.5
11.9
68.8
15.9
120
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 96
BEAM AND GIRDER DESIGN
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W8
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
W8
Span (ft)
Fy = 50 ksi
Wt./ft
28
W8
24
21
W8
18
15
13
10*
99
86
68
57
49
43
72
66
53
44
38
33
3
4
5
6
7
8
124
117
102
105
99
87
112
102
87
77
101
85
73
64
107
102
82
68
58
51
9
10
11
12
13
14
91
82
74
68
63
58
77
70
63
58
54
50
68
61
56
51
47
44
57
51
46
43
39
36
45
41
37
34
31
29
38
34
31
29
26
24
29
26
24
22
20
19
15
16
17
18
19
20
54
51
48
45
43
41
46
44
41
39
37
31
41
38
36
34
32
26
34
32
30
28
27
20
27
26
24
23
21
23
21
20
19
18
18
16
16
15
14
13.6
408
53.6
23.0
12.3
24.5
6.23
21.2
8.30
48.2
11.4
342
49.6
19.8
11.5
20.1
6.46
16.6
8.61
44.6
8.87
264
36.2
13.3
8.50
11.4
3.29
9.72
4.38
24.0
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
27.2
816
62.0
33.4
14.3
37.4
6.68
33.8
8.91
62.8
23.2
696
52.5
26.8
12.3
27.7
5.02
25.0
6.69
46.7
20.4
612
55.9
25.4
12.5
28.5
5.10
25.7
6.81
47.8
17.0
510
50.5
21.6
11.5
22.9
4.90
20.2
6.53
41.4
*Indicates noncompact shape; Fy = 50 ksi.
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 97
BEAMS
W Shapes
Maximum factored uniform loads in kips
for beams laterally supported
W 6–5–4
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
W6
25
2
3
4
5
6
7
110
95
81
8
9
10
11
12
13
20
W6
15*
16
W5
12
9
75
62
50
42
36
54
47
37
31
27
71
63
57
52
47
44
56
50
45
41
37
34
38
34
31
28
26
24
44
39
35
32
29
27
31
28
25
23
21
19
23
21
19
17
16
14
14
41
32
22
25
18
13
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
18.9
567
55.1
32.5
16.0
44.0
12.2
38.8
16.3
84.5
14.9
447
43.5
24.4
13.0
28.9
8.40
25.4
11.2
61.8
W4
16
13
75
70
58
50
65
58
48
41
63
63
47
38
31
27
44
39
35
32
29
36
32
29
26
24
24
21
19
11.6
348
37.5
27.4
13.5
33.2
9.62
29.9
12.8
71.3
9.59
288
32.5
22.5
12.0
25.4
8.29
22.7
11.1
58.6
6.28
188
31.4
24.1
14.0
31.4
16.5
26.8
22.1
69.6
Span (ft)
88
88
70
59
50
Fy = 50 ksi
87
75
64
74
62
51
44
19
Properties and Reaction Values
10.8
308
37.2
18.0
11.5
20.3
8.45
16.9
11.3
53.5
11.7
351
44.1
24.4
13.0
30.4
7.48
27.3
9.97
59.7
8.30
249
37.4
18.0
11.5
21.0
7.80
17.9
10.4
51.7
6.23
187
27.1
12.0
8.50
11.7
4.19
10.1
5.59
28.2
*Indicates noncompact shape; Fy = 50 ksi.
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 98
BEAM AND GIRDER DESIGN
S 24–20
BEAMS
S Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
S 24
121
12
13
14
15
16
17
90
S 20
80
96
S 20
86
75
66
723
686
610
549
499
686
656
574
510
459
417
545
525
467
420
382
820
761
966
900
800
720
655
810
740
666
605
648
612
556
765
706
656
612
574
540
698
644
598
558
523
492
600
554
514
480
450
424
555
512
476
444
416
392
510
471
437
408
383
360
495
457
424
396
371
349
458
422
392
366
343
323
383
353
328
306
287
270
350
323
300
280
263
247
18
19
20
21
22
23
510
483
459
437
417
399
465
441
419
399
380
364
400
379
360
343
327
313
370
351
333
317
303
290
340
322
306
291
278
266
330
313
297
283
270
258
305
289
275
261
250
239
255
242
230
219
209
200
233
221
210
200
191
183
24
25
26
27
28
29
383
367
353
340
328
317
349
335
322
310
299
289
300
288
277
267
257
248
278
266
256
247
238
230
255
245
235
227
219
211
248
238
228
220
212
205
229
220
211
203
196
189
191
184
177
170
164
158
175
168
162
156
150
145
30
32
34
36
38
40
306
287
270
255
242
230
279
262
246
233
220
209
240
225
212
200
189
180
222
208
196
185
175
167
204
191
180
170
161
153
198
186
175
165
156
149
183
172
161
153
144
137
153
143
135
128
121
115
140
131
124
117
111
105
42
44
46
48
50
52
219
209
200
191
184
177
199
190
182
174
167
161
171
164
157
150
144
138
159
151
145
139
133
128
146
139
133
128
122
118
141
135
129
124
119
131
125
119
114
110
109
104
100
96
92
100
95
91
88
84
54
56
58
60
170
164
158
153
155
149
144
140
133
129
124
120
123
119
115
111
113
109
106
102
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
306
9180
529
200
40.0
269
20.7
236
27.7
330
279
8370
410
155
31.0
184
9.66
168
12.9
215
183
5490
362
144
33.0
185
16.7
163
22.2
240
153
4590
343
129
31.8
163
17.4
139
23.2
219
140
4200
273
103
25.3
115
8.76
104
11.7
144
Span (ft)
1060
1020
918
835
100
877
849
743
660
594
540
Fy = 50 ksi
6
7
8
9
10
11
S 24
106
Properties and Reaction Values
240
7200
483
163
37.3
216
21.4
182
28.6
284
222
6660
405
137
31.3
166
12.6
146
16.9
207
204
6120
324
109
25.0
119
6.48
109
8.64
140
198
5940
438
175
40.0
248
29.7
207
39.5
305
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 99
BEAMS
S 18–15–12–10
S Shapes
Maximum factored uniform loads in kips
for beams laterally supported
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
S 18
70
3
4
5
6
7
8
691
625
536
469
9
10
11
12
13
14
S 15
54.7
50
S 12
42.9
50
S 12
40.8
35
S 10
31.8
35
25.4
168
142
122
107
333
297
260
445
367
306
262
230
299
266
228
199
277
269
224
192
168
227
210
180
158
321
266
212
177
152
133
257
231
210
193
178
165
231
208
189
173
160
149
204
184
167
153
141
131
177
159
145
133
123
114
149
134
122
112
103
96
140
126
115
105
97
90
118
106
97
89
82
76
95
85
77
71
66
61
210
197
185
175
166
158
154
145
136
129
122
116
139
130
122
116
109
104
122
115
108
102
97
92
106
100
94
89
84
80
90
84
79
75
71
67
84
79
74
70
66
63
71
66
62
59
56
53
57
53
50
47
45
43
179
170
163
156
150
144
150
143
137
131
126
121
110
105
101
96
93
89
99
95
90
87
83
80
87
83
80
77
73
71
76
72
69
66
64
61
64
61
58
56
54
52
60
57
55
53
50
48
51
48
46
44
42
41
39
37
36
34
27
28
29
30
31
32
139
134
129
125
121
117
117
113
109
105
102
98
86
83
80
77
75
72
77
74
72
69
67
65
68
66
63
61
59
57
55
53
50
48
46
45
47
45
43
42
33
34
35
36
37
38
114
110
107
104
101
99
95
93
90
88
85
83
70
68
66
64
63
63
61
59
58
56
40
42
44
94
89
85
79
75
72
125
3750
346
133
35.6
180
31.3
142
41.7
249
105
3150
224
86.4
23.1
93.8
8.52
83.6
11.4
122
44.8
1340
139
63.5
21.4
74.5
13.0
64.1
17.3
120
42.0
1260
113
52.0
17.5
55.1
7.11
49.4
9.47
80.2
35.4
1060
160
83.5
29.7
116
46.2
84.9
61.6
180
28.4
852
84.0
43.7
15.5
43.8
6.63
39.4
8.84
68.1
448
394
446
386
330
289
417
375
341
313
288
268
350
315
286
263
242
225
15
16
17
18
19
20
250
234
221
208
197
188
21
22
23
24
25
26
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
77.1
2310
223
94.5
27.5
116
19.3
96.7
25.7
180
69.3
2080
166
70.6
20.6
74.9
8.05
66.9
10.7
102
61.2
1840
223
123
34.3
167
44.4
131
59.1
235
53.1
1590
150
83.0
23.1
91.9
13.5
81.1
18.0
140
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 100
BEAM AND GIRDER DESIGN
S 8–6–5–4–3
BEAMS
S Shapes
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
S8
23
1
2
3
4
5
6
191
145
116
96
7
8
9
10
11
12
S6
18.4
17.25
S5
12.5
9.5
75
64
51
42
58
57
43
34
28
83
72
64
58
53
48
71
62
55
50
45
41
45
40
35
32
29
27
36
32
28
25
23
21
24
21
19
17
15
14
13
45
38
24
20
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
19.3
579
95.3
55.1
22.1
68.9
27.2
54.4
36.3
127
16.5
495
58.5
33.9
13.6
33.2
6.32
29.8
8.42
57.2
S3
7.7
7.5
5.7
70
61
40
30
24
20
42
35
26
21
18
57
35
24
18
14
12
28
20
15
12
9.75
17
15
13
12
15
13
12
11
10
8.36
4.04
121
35.2
30.6
16.3
36.3
32.0
27.8
42.6
83.5
3.51
105
20.8
18.1
9.65
16.6
6.64
14.8
8.85
43.5
2.36
70.8
28.3
30.0
17.5
37.9
59.0
26.1
78.6
86.7
1.95
58.5
13.8
14.6
8.50
12.9
6.81
11.5
9.09
41.1
Span (ft)
117
99
83
151
106
80
64
53
Fy = 50 ksi
S4
10
Properties and Reaction Values
10.6
318
75.3
50.9
23.3
68.5
50.5
48.3
67.3
126
8.47
254
37.6
25.4
11.6
24.1
6.27
21.6
8.36
48.8
5.67
170
28.9
21.7
10.7
20.4
6.50
18.2
8.67
46.4
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 101
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
MC,C 18–15
For beams laterally unsupported, see page 4-139
Designation
MC 18
Span (ft)
Fy = 50 ksi
Wt./ft
58
51.9
C 15
45.8
42.7
50
40
33.9
421
343
286
245
215
324
302
252
216
189
3
4
5
6
7
8
680
568
473
405
355
583
519
433
371
324
486
470
392
336
294
437
372
319
279
580
511
409
341
292
256
9
10
11
12
13
14
315
284
258
237
218
203
288
260
236
216
200
185
261
235
214
196
181
168
248
223
203
186
172
159
227
205
186
170
157
146
191
172
156
143
132
123
168
151
137
126
116
108
15
16
17
18
19
20
189
177
167
158
149
142
173
162
153
144
137
130
157
147
138
131
124
118
149
140
131
124
117
112
136
128
120
114
108
102
114
107
101
95
90
86
101
95
89
84
80
76
21
22
23
24
25
26
135
129
123
118
114
109
124
118
113
108
104
100
112
107
102
98
94
90
106
101
97
93
89
86
97
93
89
85
82
79
82
78
75
72
69
66
72
69
66
63
60
58
28
30
32
34
36
38
101
95
89
83
79
75
93
87
81
76
72
68
84
78
74
69
65
62
80
74
70
66
62
59
73
68
64
60
57
61
57
54
50
48
54
50
47
44
42
40
42
44
71
68
65
65
62
59
59
56
53
56
53
51
68.2
2050
290
129
35.8
176
40.7
135
54.3
245
57.2
1720
211
93.4
26.0
109
15.6
93.4
20.8
161
50.4
1510
162
71.9
20.0
73.6
7.10
66.5
9.47
97.2
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
94.6
2840
340
120
35.0
167
33.0
127
44.0
234
86.5
2600
292
103
30.0
133
20.8
108
27.7
200
78.4
2350
243
85.9
25.0
101
12.0
86.4
16.0
140
74.4
2230
219
77.3
22.5
86.1
8.76
75.5
11.7
115
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 102
BEAM AND GIRDER DESIGN
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
MC 13
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
MC 13
Span (ft)
Fy = 50 ksi
Wt./ft
50
40
35
31.8
3
4
5
6
7
8
552
454
363
303
259
227
393
382
305
255
218
191
314
277
231
198
173
263
259
216
185
162
9
10
11
12
13
14
202
182
165
151
140
130
170
153
139
127
117
109
154
139
126
116
107
99
144
129
118
108
99
92
15
16
17
18
19
20
121
113
107
101
96
91
102
95
90
85
80
76
92
87
82
77
73
69
86
81
76
72
68
65
21
22
23
24
25
26
86
83
79
76
73
70
73
69
66
64
61
59
66
63
60
58
55
53
62
59
56
54
52
50
27
28
29
30
31
32
67
65
63
61
59
57
57
55
53
51
49
48
51
50
48
46
45
43
48
46
45
43
42
40
46.2
1390
157
76.8
22.4
84.2
12.2
73.6
16.2
126
43.1
1290
132
64.5
18.8
64.7
7.19
58.4
9.59
89.6
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
60.5
1820
276
135
39.3
197
66.5
139
88.7
263
50.9
1530
197
96.3
28.0
118
24.0
97.3
31.9
187
Load above heavy line is limited by design shear strength.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 103
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C,MC 12
For beams laterally unsupported, see page 4-139
Designation
Wt./ft
C 12
50
45
40
251
219
175
146
125
183
152
127
109
541
421
337
281
240
461
388
310
259
222
382
355
284
237
203
126
112
101
92
84
78
110
97
88
80
73
67
95
85
76
69
64
59
210
187
168
153
140
129
194
172
155
141
129
119
14
15
16
17
18
19
72
67
63
59
56
53
63
58
55
52
49
46
54
51
48
45
42
40
120
112
105
99
94
89
20
21
22
23
24
25
50
48
46
44
42
40
44
42
40
38
37
35
38
36
35
33
32
30
26
27
28
29
30
39
37
36
35
34
34
32
31
30
29
29
28
27
26
25
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
33.6
1010
165
71.7
25.5
93.0
23.9
73.9
31.8
155
29.2
876
125
54.4
19.4
61.5
10.4
53.1
13.9
98.3
Span (ft)
25
2
3
4
5
6
7
330
252
202
168
144
8
9
10
11
12
13
MC 12
20.7
Fy = 50 ksi
30
MC 12
35
31
10.6
303
257
214
183
240
236
197
168
123
116
87
70
58
50
177
158
142
129
118
109
161
143
128
117
107
99
147
131
118
107
98
91
44
39
35
32
29
27
111
103
97
91
86
82
101
95
89
83
79
75
92
86
80
76
71
68
84
79
74
69
66
62
25
23
22
20
19
18
84
80
77
73
70
67
78
74
71
67
65
62
71
68
65
62
59
57
64
61
58
56
54
51
59
56
54
51
49
47
17
17
16
15
15
14
65
62
60
58
56
60
57
55
53
52
55
53
51
49
47
49
48
46
44
43
45
44
42
41
39
13
13
12
12
12
47.3
1420
191
96.8
29.5
137
26.5
116
35.3
193
42.8
1280
151
76.6
23.4
96.3
13.1
85.8
17.5
143
39.3
1180
120
60.7
18.5
67.9
6.52
62.7
8.70
91.0
11.6
348
61.6
16.3
9.50
16.6
2.00
15.0
2.67
23.7
Properties and Reaction Values
25.4
762
91.4
39.7
14.1
38.2
4.04
35.0
5.38
52.5
56.1
1680
271
137
41.8
230
75.0
170
100.0
273
51.7
1550
231
117
35.6
181
46.5
144
62.0
233
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 104
BEAM AND GIRDER DESIGN
C,MC 10
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
Span (ft)
Fy = 50 ksi
Wt./ft
C 10
MC 10
30
25
20
2
3
4
5
6
7
363
266
200
160
133
114
284
230
173
138
115
99
8
9
10
11
12
13
100
89
80
73
67
61
14
15
16
17
18
19
20
21
22
23
24
33.6
MC 10
28.5
25
MC 10
15.3
41.1
22
205
193
145
116
96
83
130
119
95
79
68
430
389
292
233
195
167
311
251
200
167
143
230
222
178
148
127
205
194
155
129
111
157
142
118
101
92
79
59
47
39
34
8.4
86
77
69
63
58
53
72
64
58
53
48
45
59
53
47
43
40
36
146
130
117
106
97
90
125
111
100
91
84
77
111
99
89
81
74
68
97
86
77
70
65
60
89
79
71
64
59
54
29
26
24
21
20
18
57
53
50
47
44
42
49
46
43
41
38
36
41
39
36
34
32
30
34
32
30
28
26
25
83
78
73
69
65
61
72
67
63
59
56
53
63
59
56
52
49
47
55
52
48
46
43
41
51
47
44
42
39
37
17
16
15
14
13
12
40
38
36
35
33
35
33
31
30
29
29
28
26
25
24
24
23
22
21
20
58
56
53
51
49
50
48
46
44
42
44
42
40
39
37
39
37
35
34
32
35
34
32
31
30
12
11
11
10
9.83
26.6
798
182
84.1
33.6
131
75.6
81.0
101
193
23.0
690
142
65.8
26.3
90.8
36.1
66.8
48.1
151
29.6
888
115
66.4
21.3
75.8
14.4
66.1
19.3
129
25.8
774
103
59.4
19.0
64.1
10.3
57.2
13.8
102
23.6
708
78.3
45.3
14.5
42.7
4.59
39.6
6.12
59.5
7.86
236
45.9
14.6
8.50
13.4
1.90
12.1
2.53
20.3
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
19.3
579
102
47.4
19.0
55.6
13.5
46.6
18.0
105
15.8
474
64.8
30.0
12.0
28.0
3.43
25.7
4.57
40.6
38.9
1170
215
124
39.8
194
94.9
131
127
254
33.4
1000
155
89.8
28.8
119
35.8
95.4
47.7
183
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 105
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C,MC 9
For beams laterally unsupported, see page 4-139
Designation
C9
Span (ft)
Fy = 50 ksi
Wt./ft
MC 9
20
15
13.4
25.4
23.9
2
3
4
5
6
7
218
168
126
101
84
72
139
135
101
81
68
58
113
94
75
63
54
219
174
139
116
99
194
167
133
111
95
8
9
10
11
12
13
63
56
50
46
42
39
51
45
41
37
34
31
47
42
38
34
31
29
87
77
70
63
58
54
83
74
67
61
56
51
14
15
16
17
18
19
36
34
31
30
28
27
29
27
25
24
23
21
27
25
23
22
21
20
50
46
44
41
39
37
48
44
42
39
37
35
20
21
22
25
24
23
20
19
18
19
18
17
35
33
32
33
32
30
23.2
696
109
66.8
22.5
80.7
19.9
68.8
26.6
140
22.2
666
97.2
59.4
20.0
67.7
14.0
59.3
18.7
120
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
16.8
504
109
52.5
22.4
69.5
26.2
53.8
34.9
125
13.5
405
69.3
33.4
14.3
35.3
6.74
31.2
8.98
60.4
12.5
375
56.6
27.3
11.7
26.1
3.68
23.9
4.91
39.8
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 106
BEAM AND GIRDER DESIGN
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C,MC 8
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
C8
Span (ft)
Fy = 50 ksi
Wt./ft
MC 8
MC 8
MC 8
18.75
13.75
11.5
22.8
21.4
20
18.7
8.5
1
2
3
4
5
6
210
207
138
104
83
69
131
109
82
65
55
95
72
57
48
184
141
113
94
162
135
108
90
173
162
122
97
81
152
116
92
77
77
69
52
41
35
7
8
9
10
11
12
59
52
46
41
38
35
47
41
36
33
30
27
41
36
32
29
26
24
81
70
63
56
51
47
77
68
60
54
49
45
69
61
54
49
44
41
66
58
51
46
42
39
30
26
23
21
19
17
13
14
15
16
17
18
32
30
28
26
24
23
25
23
22
20
19
18
22
20
19
18
17
16
43
40
38
35
33
31
42
39
36
34
32
30
37
35
32
30
29
27
36
33
31
29
27
26
16
15
14
13
12
12
19
20
22
21
17
16
15
14
30
28
28
27
26
24
24
23
11
10
16.2
486
86.4
56.3
20.0
64.5
17.3
55.3
23.1
121
15.4
462
76.2
49.6
17.7
53.5
11.9
47.1
15.9
98.7
6.91
207
38.7
16.8
8.95
15.2
2.49
13.9
3.33
24.7
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
13.8
414
105
57.1
24.3
76.5
40.1
55.2
53.4
136
10.9
327
65.4
35.5
15.2
37.6
9.65
32.4
12.9
74.2
9.55
287
47.5
25.8
11.0
23.2
3.69
21.3
4.92
37.3
18.8
564
92.2
63.4
21.3
72.9
20.1
62.2
26.7
133
18.0
540
81.0
55.7
18.8
60.0
13.6
52.8
18.1
112
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
FACTORED UNIFORM LOAD TABLES
Fy = 50 ksi
4 - 107
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C,MC 7–6
For beams laterally unsupported, see page 4-139
Designation
C7
12.25
MC 7
9.8
22.7
C6
MC 6
MC 6
MC 6
19.1
13
10.5
8.2
18
16.3
15.1
12
102
92
62
46
37
31
65
51
38
31
26
123
115
86
69
58
122
102
77
61
51
102
97
73
58
48
100
74
55
44
37
1
2
3
4
5
6
119
84
63
50
42
79
71
53
43
36
190
162
122
97
81
133
107
86
72
142
109
73
54
44
36
7
8
9
10
11
12
36
31
28
25
23
21
31
27
24
21
19
18
69
61
54
49
44
41
61
54
48
43
39
36
31
27
24
22
20
18
26
23
21
18
17
15
22
19
17
15
14
13
49
43
38
35
31
29
44
38
34
31
28
26
42
36
32
29
26
24
32
28
25
22
20
18
13
14
15
16
19
18
17
16
16
15
14
13
37
35
32
30
33
31
29
27
17
16
15
14
13
12
12
11
10
27
25
23
24
22
20
22
21
19
17
16
15
8.40
252
59.3
34.3
15.7
38.4
13.1
32.3
17.4
85.4
7.12
214
39.7
23.0
10.5
21.0
3.91
19.2
5.21
36.1
11.5
345
61.4
50.3
19.0
58.0
20.7
49.7
27.6
112
10.2
306
60.8
49.8
18.8
57.1
20.0
49.1
26.7
111
9.69
291
51.2
42.0
15.8
44.2
12.0
39.4
16.0
91.3
7.38
221
50.2
31.5
15.5
38.1
14.3
32.4
19.1
81.9
Span (ft)
Fy = 50 ksi
Wt./ft
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
16.2
486
95.1
70.7
25.2
91.0
39.3
72.6
52.5
152
14.3
429
66.5
49.5
17.6
53.3
13.5
47.0
18.0
105
7.26
218
70.8
44.4
21.9
61.0
43.9
43.5
58.5
115
6.15
185
50.9
31.9
15.7
37.2
16.3
30.7
21.7
82.9
5.13
154
32.4
20.3
10.0
18.9
4.21
17.2
5.61
35.4
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 108
BEAM AND GIRDER DESIGN
BEAMS
Channels
Maximum factored uniform loads in kips
for beams laterally supported
C 5–4–3
Fy = 50 ksi
For beams laterally unsupported, see page 4-139
Designation
C5
9
C4
C3
6.7
7.25
5.4
69
42
28
21
17
14
40
34
23
17
14
11
1
2
3
4
5
6
88
65
44
33
26
22
51
35
26
21
18
7
8
9
10
11
12
19
16
15
13
12
11
15
13
12
11
9.6
8.8
12
11
9.4
8.4
9.7
8.5
7.5
6.8
6
5
4.1
52
26
17
13
10
8.6
42
23
15
11
9.0
7.5
28
20
13
9.8
7.8
6.5
7.4
6.4
5.6
1.72
51.6
28.8
30.6
17.8
40.0
59.6
28.1
79.5
88.4
1.50
45.0
20.9
22.2
12.9
24.7
22.7
20.2
30.2
64.1
1.30
39.0
13.8
14.6
8.50
13.2
6.49
11.9
8.65
40.0
Span (ft)
Fy = 50 ksi
Wt./ft
Properties and Reaction Values
Zx in.3
φbWc kip-ft
φvVn kips
φR1 kips
φR2 kips/in.
φr R3 kips
φr R4 kips/in.
φr R5 kips
φr R6 kips/in.
φR (N = 31⁄4) kips
4.36
131
43.9
30.5
16.3
37.8
23.2
30.1
30.9
83.3
3.51
105
25.7
17.8
9.50
16.9
4.64
15.3
6.18
35.4
2.81
84.3
34.7
27.6
16.1
35.7
30.2
27.6
40.3
79.7
2.26
67.8
19.9
15.8
9.20
15.5
5.69
14.0
7.59
38.6
Load above heavy line is limited by design shear strength.
Values of R in bold face exceed maximum design web shear φvVn.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 109
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH
GREATER THAN Lp
General Notes
Spacing of lateral bracing at distances greater than Lp creates a problem in which the
designer is confronted with a given laterally unbraced length (usually less than the total
span) along the compression flange, and a calculated required bending moment. The
beam cannot be selected from its plastic section modulus alone, since depth, flange
proportions, and other properties have an influence on its bending strength.
The following charts show the design moment φbMn for W and M shapes of Fy = 36 ksi
and Fy = 50 ksi steels, used as beams, with respect to the maximum unbraced length for
which this moment is permissible. In bending, φb of 0.9 is given in Section F1.2 of the
LRFD Specification. The charts extend over varying unbraced lengths, depending upon
the flexural strengths of the beams represented. In general, they extend beyond most
unbraced lengths frequently encountered in design practice. The design moment φbMn,
kip-ft, is plotted with respect to the unbraced length with no consideration of the moment
due to weight of the beam. Design moments are shown for unbraced lengths in feet,
starting at spans less than Lp, for spans between Lp and Lr and for spans beyond Lr.
The unbraced length Lp, in feet, with the limit indicated by a solid symbol, , is the
maximum unbraced length of the compression flange, with Cb = 1.0, for which the design
moment is given by φbMp,
where
Fy
Lp = 300ry / √
Mp = ZxFy
(F1-4)
For those noncompact rolled shapes, which meet the requirements of compact sections
Fy , but is less than 141 / √

Fy −Fr , the design moment is
except that bf / 2tf exceeds 65 / √
obtained from Equation A-F1-3 in Appendix F1 of the LRFD Specification. This criterion
applies to one W shape when Fy is equal to 36 ksi and to seven W shapes when Fy is equal
to 50 ksi. (Noncompact W shapes are given on p. 4-7.)
For the case Cb = 1.0 and noncompact shapes:
 λ − λp 
Mn′ = Mp − (Mp − Mr) 

 λr − λp 
(A-F1-3)
 Mp − Mn′ 
Lp′ = Lp + (Lr − Lp) 

 Mp − Mr 
λ = bf / 2tf
λp = 65 / √
Fy
λr = 141 / √

Fy −Fr
Lr =
ryX1

√
1+√

1 + X2(Fy − Fr)2
Fy − Fr
X1 =
π
Sx

√
EGJA
2
(F1-6)
(F1-8)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 110
BEAM AND GIRDER DESIGN
4Cw
X2 =
Iy
 Sx 
 
 GJ 
2
(F1-9)
Mr = (Fy − Fr )Sx
Mp = ZxFy
Fr = 10 ksi for rolled shapes
(F1-7)
The unbraced length in the charts may be either the total span or any part of the total
span between braced points. The plots shown in these charts were computed for beams
for which Cb = 1.0. When a moment gradient exists between points of bracing, Cb may
be larger than unity. (See Table 4-1.) Using this larger value of Cb may provide a more
liberal flexural strength for the section chosen if the unbraced length is greater than Lp.
In these cases, the design moment can be determined using the provisions of Section
F1.2a of the LRFD Specification.
 Lb − Lp 

φbMn = φbCb Mp − (Mp − Mr) 
 ≤ φbMp
 Lr − Lp 

The unbraced length Lr, ft, with the limit indicated by an open symbol , is the
maximum unbraced length of the compression flange beyond which the design moment
is governed by Specification Section F1.2b. For unbraced lengths greater than Lr:
φbMn = φbMcr = φbCb
π
Lb

√
2
 πE 
EIyGJ +   IyCw ≤ φbCbMr and φbMp
 Lb 
In computing the points for the curves, Cb in the above formulas was taken as unity,
E = 29,000 ksi and G = 11,200 ksi. The properties of the beams are taken from the Tables
of Dimensions and Properties in Part 1 of this LRFD Manual. The beam strengths have
been reduced by multiplying the nominal flexural strength Mn by 0.9, the resistance factor
φb for flexure.
Over a limited range of length, a given beam is the lightest available for various
combinations of unbraced length and design moment. The charts are designed to assist
in selection of the lightest available beam for the given combination.
The solid portion of each curve indicates the most economical section by weight. The
dashed portion of each curve indicates ranges in which a lighter weight beam will satisfy
the loading conditions.
The curves are plotted without regard to shear strength and deflection criteria, therefore
due care must be exercised in their use. The curves do not extend beyond an arbitrary
span/depth limit of 30.
The following examples illustrate the use of the charts.
EXAMPLE 4-8
Given:
Using Fy = 50 ksi steel, determine the size of a “simple” framed girder
with a span of 35 feet, which supports two equal concentrated loads.
The factored loads produce a required moment of 440 kip-ft in the
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 111
center 15-ft section between the loads. The load points are laterally
braced.
Solution:
For this loading condition, Cb = 1.0 due to nearly uniform moment
across the central portion of the span.
Center section of 15 feet is longest unbraced length.
With total span equal to 35 feet and Mn = 440 kip-ft, assume approximate weight of beam at 70 lbs/ft (equal to 0.07 kips/ft).
 0.07 × (35)2

× 1.2 = 453 kip-ft
Total Mu = 440 + 
8


Entering chart, with unbraced length equal to 15 feet on the bottom
scale (abscissa), proceed upward to meet the horizontal line corresponding to a design moment equal to 453 kip-ft on the left hand scale
(ordinate). Any beam listed above and to the right of the point so
located satisfies the design moment requirement. In this case, the
lightest section satisfying this criterion is a W21×68, for which the total
design moment with an unbraced length of 15 feet is 457 kip-ft.
Use: W21×68
Note: If depth is limited, a W14×82 could be selected, provided
deflection conditions are not critical.
EXAMPLE 4-9
Given:
A “fixed end” girder with a span of 60 feet supports a concentrated
load at the center. The compression flange is laterally supported at the
concentrated load point and at the inflection points. The factored load
produces a maximum calculated moment of 440 kip-ft at the load point
and the supports. Determine the size of the beam using Fy = 50 ksi steel.
Solution:
For this loading condition, Cb = 1.67 (by comparison with Table 4-1),
with an unbraced length of 15 feet. With the total span equal to 60 feet
and Mu = 440 kip-ft, assume approximate weight of beam at 60 lbs/ft
(0.06 kips/ft).
 0.06 × (60)2

Total Mu = 440 + 
×1.2
24


= 451 kip-ft at the centerline and 462 at the supports
Compute Mequiv by dividing the required design moment by Cb
Mequiv = 462 / 1.67 = 277 kip-ft
Enter charts with unbraced length equal to 15 feet and proceed upward
to 277 kip-ft. Any beam listed above and to the right of the point
satisfies the design moment.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 112
BEAM AND GIRDER DESIGN
The lightest section satisfying the criteria of a design moment of
277 kip-ft at an unbraced length of 15 feet and φbMp greater than 462
kip-ft is a W21×62. The design moment for a W21×62 with an
unbraced length of 15 feet is 406 kip-ft and φbMp is 540 kip-ft.
Since (φbMn = 406 kip-ft) > (Mequiv = 277 kip-ft) and (φbMp = 540
kip-ft) > (Mu = 462 kip-ft), a W21×62 is o.k.
A 21-in. nominal depth beam spanning 60 feet should be checked for
deflection since the span/depth ratio exceeds 30.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 113
4 - 114
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 115
4 - 116
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 117
BEAM AND GIRDER DESIGN
4 - 118
W3
x3
18
30
3x3
W
97
26
0x2
31
W4
0x3
W44
x26
2
0x2
W
24
W4
49
x3
x2
77
35
0x2
30
W4
61
0x2
78
W4
4x2
30
W
11
35
x2
x2
30
27
W
67
W4
79
x2
0x1
0x2
15
W
24
x2
50
W4
0x
4
24
99
W
0x1
49
W4
17
0x1
x2
07
W
92
30
x1
W
24
x1
91
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
0
92
W4
W
35
11
94
W4
W21x201
28
x2
6x
30
07
4
35
x2
0x2
6x1
W4
8
25
8x
W1
W18x234
W
x3
x26
0x2
30
W4
W3
W27x178
29
x2
24
W
W
24
3
28
8x
W1
1
31
8x
W1
W3
27
W40
W4
W
W40x183
W4
W
W40x199
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 119
W
24
x4
08
W4
0x2
97
W
27
x3
68
W
30
x3
26
W
W
27
30
x3
x2
07
92
W
24
x3
35
30
W3
W
91
61
3x2
x2
W
24
W
x2
27
79
x2
58
W1
W
24
x2
50
W
W1
8x
27
28
3
x2
35
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8x
31
1
4 - 120
BEAM AND GIRDER DESIGN
W
W3
11
W2
4
4x
9
x169
22
W33
x183
01
W18x211
x17
8
x2
34
W40
17
21
x2
W40
7x
W
18
0x2
W2
W
18
W40x
W
24
167
x1
W21x182
92
W
24
x2
07
W36
x170
W2
7x
19
18
4
W
x1
92
W40
x149
W3
0x1
16
W
18
x1
W
58
18
x1
75
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
x2
58
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 121
W2
79
35
W36
7x2
4x2
W2
x245
W
18
x2
83
W2
4x
25
0
W3
0x1
91
W2
4x
22
W
9
W36
x210
W
24
x2
07
W
21
x2
01
W
18
x2
34
W
24
x1
92
W
18
x1
92
W
x1
7x1
21
W2
W
18
x2
11
94
82
W
24
x1
76
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
18
x2
58
4 - 122
BEAM AND GIRDER DESIGN
W30x1
32
W1
15
W1
8x
8x
8
17
5
W 3 3 x1 3
0
W30x90
W24x103
W27
x94
W 36 x1 60
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 123
W21
x20
1
W1
W 36 x1 70
8x
21
1
W1
8x1
W 33 x1 69
92
W1
8x1
75
W21
x18
2
W1
8x1
58
W 36 x1 60
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 124
BEAM AND GIRDER DESIGN
W14x132
W
14
x1
32
W30
x90
W27
x90
x94
W30
W12x120
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 125
W1
8x
78
5
17 W27x1
W1
8x
15
8
W
W24x
14
x1
32
117
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 126
BEAM AND GIRDER DESIGN
W
x1
20
W30x9
12
0
W12x106
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DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 127
W
14
x1
32
W
12
x1
20
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BEAM AND GIRDER DESIGN
W12x96
W
12
x9
6
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DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
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W
12
x1
20
W
12
x1
06
W
10
x1
12
W
12
x9
6
W
10
x1
00
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BEAM AND GIRDER DESIGN
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DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
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W
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
10
x1
00
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BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
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W
10
x6
8
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BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 135
W
8x
48
W1
0x4
5
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BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
M12x1
0 .8
M10
x8
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4 - 138
BEAM AND GIRDER DESIGN
M10
x8
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DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
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BEAM AND GIRDER DESIGN
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DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
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BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BEAM AND GIRDER DESIGN
W24x250
0x2
61
x3
0x2
18
W4
x183
W
W27x217
W3
x235
4
W40
x19
x211
W40
W40
W36
W40x174
15
11
W40x167
W
24
x2
79
W2
7x2
21
58
3x2
5
83
W3
23
x2
7x
18
W2
W
W4
W
x2
0x1
24
99
29
W4
0x1
74
W18x258
0x
W33x
W3
W40x149
3
241
17
W
07
3x2
x2
W3
24
01
W24x192
W18x234
W21x201
W18x211
W21x182
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
30
92
7x
0x2
W2
W3
7
W
24
x3
35
W3
0x
26
1
W2
7x
25
8
W
18
x3
11
W
24
x2
79
W
50 235
x
x2
24 W27
W1 8x 28 3
W
18
x2
83
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4 - 146
BEAM AND GIRDER DESIGN
W
x2
W
7
11
20
x2
4x
34
18
W2
18
W21x182
W2
1x
20
1
W18x192
W2
4x1
x149
W18x158
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92
W40
W18x175
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 147
W2
07
29
4x2
4x2
W2
W
18
x2
58
W
18
x2
34
W2
4x
19
2
W
18
x2
11
W
21
x2
01
W
21
x1
82
W
18
x1
92
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BEAM AND GIRDER DESIGN
W
18
x1
75
W
18
x1
58
W30x90
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DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
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W
W2
18
1x
x2
2
11
18
W
18
x1
92
W
18
x1
75
W
18
x1
58
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BEAM AND GIRDER DESIGN
W30
x90
W 27 x9 4
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DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
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BEAM AND GIRDER DESIGN
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DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
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W
14
x1
32
W
12
x1
20
W
12
x1
06
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BEAM AND GIRDER DESIGN
W1
2x
96
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
W1
2x
10
6
W1
2x
96
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4 - 156
BEAM AND GIRDER DESIGN
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DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
4 - 157
W
12
x9
6
W
10
x1
00
W1
2x
72
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BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
W
10
x7
7
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4 - 160
BEAM AND GIRDER DESIGN
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DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
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W
8x
67
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BEAM AND GIRDER DESIGN
W8
x48
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DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
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4 - 164
BEAM AND GIRDER DESIGN
M12x10
.8
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
DESIGN FLEXURAL STRENGTH OF BEAMS WITH UNBRACED LENGTH > Lp
M12x1
0 .8
M10x
8
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BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
PLATE GIRDER DESIGN
4 - 167
PLATE GIRDER DESIGN
General Notes
The distinction between a beam and a plate girder, according to Chapter G of the LRFD
Specification, must be made before the design can be undertaken. A beam can be a rolled
or welded shape, but its web width-thickness ratio h / tw must be less than or equal to
970 / √
Fyf. For doubly symmetric plate girders h / tw is greater than 970 / √
Fyf.
The limit states that must be considered in plate girder design include: flexural strength,
bearing under concentrated loads, shear strength, and flexure-shear interaction (for
tension field action only). From these checks, the adequacy of the design and the need
for stiffeners can be determined. This section contains design examples to explain these
items from the LRFD Specification. A flowchart covering plate girder design has been
published (Zahn, 1987).
Flexural and Shear Strength
General
In the design of welded girders, the flexural strength of the trial section must be
determined to ensure that an adequate section modulus is provided. Although there are
preliminary steps, flexural strength, using elastic design, is determined from LRFD
Specification Section F1 if the section is compact. For sections with more slender webs,
either LRFD Specification Appendix F1 or Appendix G2 is used, depending on the
section’s classification as a beam or plate girder.
A shear strength calculation is required to ascertain if there is a need for intermediate
stiffeners. The applicable formulas are found in LRFD Specification Section F2, or
Appendix G3 if tension field action is implemented. Note, however, that Appendix G
cannot be used if h / tw exceeds the limits given in Appendix G1.
Table of Dimensions and Properties of Built-up Wide Flange sections
This table serves as a guide for selecting welded built-up I sections of economical
proportions. It provides dimensions and properties for a wide range of sections with
nominal depths from 45 to 92 inches. No preference is intended for the tabulated flange
plate dimensions, as compared to other flange plates having the same area. Substitution
of wider but thinner flange plates, without a change in flange area, will result in a slight
reduction in section modulus.
In analyzing overall economy, weight savings must be balanced against higher fabrication costs incurred in splicing the flanges. In some cases, it may prove economical to
reduce the size of flange plates at one or more points near the girder ends, where the
bending moment is substantially less. Economy through reduction of flange plate sizes
is most likely to be realized with long girders, where flanges must be spliced in any case.
Only one thickness of web plate is given for each depth of girder. When the design is
dominated by shear in the web, rather than flexural strength, overall economy may dictate
selection of a thicker web plate. The resultant increase in elastic section modulus can be
obtained by multiplying the value S′, given in the table, by the number of sixteenths of
an inch increase in web thickness, and adding the value obtained to the section modulus
value S for the girder profile shown in the table. The increase in plastic section modulus
Z can be calculated in the same way with Z′.
Overall economy may often be obtained by using a web plate of such thickness that
intermediate stiffeners are not required. This is not always the case, however. The girder
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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BEAM AND GIRDER DESIGN
section listed in the table will provide a “balanced” design with respect to bending
moment and web shear without excessive use of intermediate stiffeners.
The maximum design end shear strength without transverse stiffeners is given in the
table column labeled φvVn. These values come from the equation,
φvVn = 0.6φvAwFywCv
where
Cv =
44,000k
with k = 5.0
(h / tw)2Fyw
It is evident from this formula that a thicker web plate increases the design shear strength.
Design Examples
Design of a plate girder should begin with a preliminary design or selection of a trial
section. The initial choice may require one or more adjustments before arriving at a final
cross section that satisfies all the provisions of the LRFD Specification with maximum
economy. In the following design examples, applicable provisions of the LRFD Specification are indicated at the left of each page.
In addition, references to Tables 9 and 10 in the LRFD Specification are listed. These
tables may be used in place of the equations for φvVn. Values for φvVn / Aw are given in ksi
for plate girders. Tables 9-36 and 9-50 do not include the tension field action equation
and, therefore, are based on LRFD Specification Section F2. For design with tension field
action, Tables 10-36 and 10-50, based on Appendix G3, are applicable. Table 10 also
includes the required gross area of pairs of stiffeners, as a percent of (h × tw), from LRFD
Specification Formula A-G4-1.
Example 4-10 illustrates a recommended procedure for designing a welded plate girder
of constant depth. The selection of a suitable trial cross section is obtained by the flange
area method, and then checked by the moment of inertia method.
Example 4-11 shows a recommended procedure for designing a welded hybrid girder
of constant depth.
Example 4-12 illustrates use of the Table of Dimensions and Properties of Built-up
Wide-Flange Sections to obtain an efficient trial profile. The 52-in. depth specified for
this example demonstrates how tabular data may be used for girder depths intermediate
to those listed. Another design requirement in this example is the omission of intermediate
web stiffeners.
EXAMPLE 4-10 Design a welded plate girder to support a factored uniform load of
7 kips per foot and two concentrated factored loads of 150 kips located
17 feet from each end. The compression flange of the girder will be
laterally supported only at points of concentrated load. (See Figure 4-3.)
Given:
Maximum bending moment: 4,566 kip-ft
Maximum vertical shear: 318 kips
Span: 48 feet
Maximum depth: 72 inches
Steel: Fy = 50 ksi
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
PLATE GIRDER DESIGN
Solution:
LRFD
Specification
Reference
Section B5 &
Table B5.1
4 - 169
A. Preliminary web design:
1. Assume web depth, h = 70 inches. For noncompact web,
640 / √
Fy < h / tw ≤ 970 / √
Fy = 137
Corresponding thickness of web = 70 / 137 = 0.51 in.
(A-G1-2)
2. Assuming a / h > 1.5, minimum thickness of web = 70 / 243 =
0.29 in.
Choose thinnest web.
Try web plate 5⁄16×70:
Aw = 21.9 in.2
h / tw = 70 / 0.313 = 224
Since 0.31 < 0.51 in. as calculated above, expect RPG to be less than
1.0
B. Preliminary flange design:
1. Required flange area:
An approximate formula for the area of one flange is:
Af ≈
Mu 4,566(12)
=
= 15.7 in.2
Fy h
50(70)
Try 1×16 plate. Af = 16 in.2
150 kips
150 kips
7 kips/ft
17 ft.
14 ft.
17 ft.
318 kips
318 kips
199 kips
318 kips
49 kips
318 kips
M max = 4566 kip-ft
M1 = 4395 kip-ft
M1 = 4395 kip-ft
Figure 4-3
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
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Table B5.1
BEAM AND GIRDER DESIGN
2. Check for compactness for no reduction in critical stress:
bf
16
=
= 8 ≤ 65 / √
50
 = 9.2 o.k.
2tf 2(1)
C. Trial girder section:
Web 5⁄16×70; two flange plates 1×16
1. Find section modulus by moment of inertia method:
Section
A in.2
1 web 5⁄16×70
21.9
1 flange 1×16
1 flange 1×16
16
16
y in.
35.5
ΣA2y in.4
Io in.4
Igr in.4
8,932
8,932
3
40,331
40,328
Moment of inertia
49,263
Section modulus furnished: 49,263 / 36.0 = 1,368 in.3
Section F1 &
Appendix G2
2. Check flexural strength using elastic design:
Fyf, Appendix G2 applies.
Since h / tw > 970 / √
Moment of inertia of flange plus 1⁄6 web about Y-Y axis:
Ioy = 1 × (16)3 / 12 = 341 in.4
Af + 1⁄6Aw = 16.0 + 1⁄6(21.9) = 19.65 in.2
rT = √

341 / 19.65
 = 4.17 in.
a. Check limitations of Appendix G:
Assume a / h ≤ 1.5
(A-G1-1)
(h / tw) max =
2,000
= 283 > 224 o.k.
Fyf
√
b. Check strength of 14-ft panel: Mu = 4,566 kip-ft
The moment in the 14-ft unbraced segment is nearly constant.
Section F1.2a
Therefore, Cb ≈ 1.0
Appendix G2
For the limit state of lateral-torsional buckling:
(A-G2-7)
λ=
(A-G2-8)
λp = 300 / √
Fyf = 42.4
(A-G2-9)
λr = 756 / √
Fyf = 106.9
(A-G2-4)
Since λ ≤ λp, Fcr = Fyf = 50 ksi
Lb 14 × 12
=
= 36.0
4.67
rT
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
PLATE GIRDER DESIGN
4 - 171
For the limit state of flange local buckling:
(A-G2-11)
λ = bf / 2tf = 16 / (2 × 1.0) = 8.0
(A-G2-12)
λp = 65 / √
Fyf = 9.2
(A-G2-13)
λr =
(A-G2-4)
Since λ ≤ λp, Fcr = Fyf = 50 ksi
230

√
Fyf / kc
Design flexural strength:
ar
(A-G2-3)
= 21.9 / 16 = 1.37
RPG = 1 −
1.37
1,200 + 300(1.37)
 70
970 
 = 0.927
 0.313 −
√50
 

With Fcr = 50 ksi use Equation A-G2-1 or A-G2-2 as applicable:
(A-G2-1) or
(A-G2-2)
Mn = 1,368(1 / 12)(0.927)(1.0)(50) = 5,284 kip-ft
Therefore, φMn = 0.90(5,284) = 4,756 kip-ft > 4,566 kip-ft req’d
o.k.
c. Check strength of 17-ft panels:
Mu = 4,395 kip-ft
Appendix G2
and (F1-3)
For moment increasing approximately linearly from zero at one end
of the unbraced segment to a maximum value at the other end,
Cb ≈ 1.67.
For the limit state of lateral-torsional buckling:
(A-G2-7)
λ =
(A-G2-8)
λp = 300 / √
Fyf = 42.4
(A-G2-9)
λr = 756 / √
Fyf = 106.9
(A-G2-5)
Lb 17(12)
=
= 48.9
4.17
rT

1  λ − λp  
Since λp ≤ λ ≤ λr, Fcr = CbFyf 1 − 
 ≤F
2  λr − λp   yf


As the middle term exceeds Fyf, Fcr = Fyf = 50.0 ksi.
For the limit state of flange local buckling:
(A-G2-4)
Fcr = Fyf = 50 ksi (as for the 14-ft panel)
(A-G2-3)
RPG = 0.927 (as for the 14-ft panel)
Again, with Fcr = 50 ksi use Equation A-G2-1 or A-G2-2 as
applicable:
Mn = 5,284 kip-ft (see Step C.2a)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 172
(A-G2-1) or
(A-G2-2)
BEAM AND GIRDER DESIGN
φbMn = 0.90 × 5,284 = 4,756 kip-ft > 4,395 kip-ft req’d. o.k.
Use: Web: One plate 5⁄16×70
Use: Flanges: Two plates 7⁄8×18
D. Stiffener requirements:
1. Bearing stiffeners:
Section K1
a. Check bearing at end reactions:
Assume point bearing (N = 0) and 5⁄16-in. web-to-flange welds.
Check local web yielding:
(K1-2)
Rn = (5k + N)Fywtw; k = 7⁄8 + 5⁄16 = 1.188 in.
φRn = 1.0[5(1.188) + 0](50)(5⁄16)
= 92.8 kips < 318 n.g.
Therefore, provide bearing stiffeners at unframed girder ends.
(Note: If local web yielding criteria are satisfied, criteria set forth in
Section K1.4 and K1.5 should also be checked.)
b. Bearing stiffeners are also required at concentrated load points since
92.8 < 150 n.g.
2. Intermediate stiffeners:
Appendix G3
a. Check shear strength in unstiffened end panel:
h / tw = 224 > 418 / √
Fyw = 59.1
a / h = 17 × 12 / 70 = 2.9
Vu / Aw = 318 / 21.9 = 14.5 ksi
Appendix G3
Tension field action is not permitted for end panels, or when a / h >
3.0 or [260 / (h / tw)]2. Here, 2.9 > (260 / 224)2 = 1.35. In either of
these cases, Equations A-G3-3 and F2-3 are both applicable, as they
are equivalent formulas.
Section F2.2
Using Equation F2-3,
(F2-3) or
(A-G3-3) or
Table 9-50
φvVn 0.9(132,000)
=
= 2.4 < 14.5 ksi
Aw
(224)2
Therefore, provide intermediate stiffeners.
b. End panel stiffener spacing
(F2-3) or
(A-G3-3) or
Table 9-50
Let
φvVn
= 14.5 ksi and solve for a / h.
Aw
Result: a / h = 0.45
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
PLATE GIRDER DESIGN
4 - 173
a ≤ (0.45)(70) = 31.5 in.
Use: 30 in.
c. Check for additional stiffeners:
Shear at first intermediate stiffener:
Vu = 318 − [7(30 / 12)] = 301 kips
Vu
301
=
= 13.7 ksi
Aw 21.9
Distance between first intermediate stiffener and concentrated load:
a
(A-G3-4)
= (17)(12) − 30 = 174 in.
a / h = 174 / 70 = 2.5
Then k = 5.8, and the shear strength is inadequate.
Therefore, provide intermediate stiffeners spaced at 174 / 2 = 87 in.
a / h = 87 / 70 = 1.24
Appendix G3
Maximum a / h for tension field action:
2
2
 260  =  260  = 1.35 > 1.24
 (h / t )   224 

w
 

Design for tension field action:
For a / h = 1.24 and h / tw = 224,
(A-G3-4)
Appendix G3
(A-G3-6)
(A-G3-2) or
Table 10-50
k
=5+
5
= 8.2
(1.24)2
h / tw = 224 > 234 √

8.2 / 50
 = 95
Cv
=
44,000(8.2)
= 0.14
(224)2(50)
1 − 0.14

φvVn

= (0.9)(0.6)(50) 0.14 +
2
Aw
1.15√

1 + (1.24) 

= 16.5 ksi > 13.7 ksi o.k.
d. Check center 14-ft panel:
h / tw = 224
a / h = (14)(12) / 70 = 2.4 > 1.35
k
= 5.0
Cv = 0.12
(A-G3-3) or
Table 9-50
φvVn
= 2.4 ksi
Aw
Vu
49
=
= 2.2 ksi < 2.4 ksi o.k.
21.9
Aw
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 174
BEAM AND GIRDER DESIGN
3. Flexure-shear interaction:
Appendix G5
Check Vu / φVn and Mu / φMn at intermediate stiffener and concentrated load locations in tension field panel:
Location
Vu
φVn
Vu / φVn
Mu
φMn
Mu / φMn
2.5 ft
9.75 ft
17.0 ft
301
250
199
318
361
361
0.95
0.69
0.55
744
2769
4395
4756
4756
4756
0.16
0.58
0.92
Vu
Mu
≤ 1.0 and 0.75 ≤
≤ 1.0 (with φ = 0.9 for both
φVn
φMn
shear and bending) do not occur simultaneously at 2.5 ft, 9.75 ft, and
17.0 ft, Interaction Equation A-G5-1 need not be checked.
Since 0.6 ≤
Summary: space stiffeners as shown in Figure 4-4:
E. Stiffener design: Let stiffener Fyst = 36 ksi.
1. For intermediate stiffeners:
a. Area required (single plate stiffener):
Vu
< 1, use Equation A-G4-2
For a single plate stiffener, or when
φVn
instead of Table 10.
Fyw 
Vu

0.15Dhtw(1 − Cv)
− 18t2w ≥ 0
Fyst 
φV
n


where
(A-G4-1)
Ast =
h = 70 in.
tw = 0.3125 in.
D = 2.4
Cv = 0.14
Vu = 250 kips
φVn = 361 kips
 250 
50 

0.15(2.4)(70)(0.3125)(10.14) 
 − 18(0.3125)2
36 
 361 

= 4.07 in.2
Ast =
Try one bar 5⁄8×7
2 ′-6
′
2@7 -3
14 ′-0
′
2@7 -3
Figure 4-4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2 ′-6
PLATE GIRDER DESIGN
4 - 175
Ast = 4.38 in.2 > 4.07 in.2 req’d. o.k.
b. Check width-thickness ratio:
Table B5.1
7 / 0.625 = 11.2 < 95 / √
Fy = 15.8 o.k.
c. Check moment of inertia:
Appendix F2.3
Ireq’d = at3wj
(A-F2-4)
2.5
− 2 = −0.4 < 0.5; take j = 0.5
(1.24)2
Ireq’d = 87(5⁄16)3(0.5) = 1.33 in.4
Ifurn = 1⁄3(0.625)(7)3 = 71.5 in.4
j
=
71.5 in.4 > 1.33 in.4 o.k.
d. Minimum length required:
Section F3
It is suggested that intermediate stiffeners be stopped short of the
tension flange and the weld by which they are attached to the web
not closer than four times nor more than six times the web thickness
from the near toe of the web-to-flange weld.*
70 − 5⁄16 − (4)(5⁄16) = 68.4 in.
70 − 5⁄16 − (6)(5⁄16) = 67.8 in.
Use for intermediate stiffeners:
One plate 5⁄8×7×5′-8, fillet-welded to the compression flange and
web.
2. For bearing stiffeners:
At end of girder, design for end reaction.
Try two 5⁄8×8-in. bars (see Figure 4-5).
a. Check width-thickness ratio (local buckling check):
Table B5.1
8 / 0.625 = 12.8 < 95 / √
Fy = 15.8 o.k.
b. Check compressive strength:
(16.31)3
= 226 in.4
12
Aeff = (2)(8)(5⁄8) + [(12)(5⁄16)2] = 11.17 in.2
I
= (5⁄8)
r
=

√
226
= 4.50 in.
11.17
*When single stiffeners are used, they shall be attached to the compression flange, if it consists of a rectangular plate, to
resist any uplift tendency due to torsion in the plate. When lateral bracing is attached to a stiffener, or a pair of stiffeners, these,
in turn, shall be connected to the compression flange to transmit one percent of the total flange stress, unless the flange is
composed only of angles.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 176
BEAM AND GIRDER DESIGN
Section K1.9
KL = 0.75h = (0.75)70 = 52.5 in.
Kl 52.5
=
= 11.7
r
4.50
λc = 0.13
(E2-2) or
Table 3-36
Design stress: φFcr = 30.38
Design strength:
φPn = φFcr Ag= (30.38)11.17 = 339 kips
339 kips > 318 kips req’d o.k.
Section J8
c. Check bearing criterion
Design strength:
φRn = (0.75)1.8Fy Apb
Apb = 2(16 − 0.5)(5⁄8) = 19.4 in.2
(The 0.5 accounts for cutout for welds.)
φRn = 943 kips > 318 kips req’d. o.k.
Use for bearing stiffeners: Two plates 5⁄8×8×5′-93⁄4 with close bearing
on flange receiving reaction or concentrated loads.
Use same size stiffeners for bearing under concentrated loads.*
EXAMPLE 4-11 Design a hybrid girder to support a factored uniform load of three kips
per foot and three concentrated factored loads of 300 kips located at
the quarter points. The girder depth must be limited to five feet. The
compression flange will be laterally supported throughout its length.
(See Figure 4-6.)
Given:
Maximum bending moment: 14,400 kip-ft
*In this example, bearing stiffeners were designed for end bearing; however, 25tw may be used in determining effective area
of web for bearing stiffeners under concentrated loads at interior panels (Section K1-9).
5/
8 x8
End bearing
stiffeners
tw
12t w
Web
5/
8 x8
Figure 4-5
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
PLATE GIRDER DESIGN
4 - 177
Maximum vertical shear: 570 kips
Span: 80 ft
Maximum depth: 60 in.
Steel: Flanges: Fy = 50 ksi
Steel: Web: Fy = 36 ksi
Solution:
A. Preliminary web design:
LRFD
Specification
Reference
Assume web depth, h = 54 in.
(A-G1-2)
For a / h > 1.5 minimum thickness of web: 54 / 243 = 0.22 in.
(A-G2-3)
For RPG = 1.0, h / tw ≤ 970 / √
Fyf = 137
(F2-1) or
Table 9-36
Corresponding web thickness = 54 / 137 = 0.39
φvVn
Minimum tw required for maximum
of 19.4 ksi:
Aw
tw
=
Vn
570
=
= 0.54 in.
19.4h 19.4 × 54
Try web plate 5⁄8×54; Aw = 33.75 in.2
Vu
Aw
Table B5.1
= 570 / 33.75 = 16.9 ksi < 19.4 ksi o.k.
h / tw = 54 / 0.625 = 86.4 < (640 / √
Fyf = 90.5) o.k.
Web is compact.
300 kips 300 kips
300 kips
3 kips/ft
20 ft.
20 ft.
20 ft.
20 ft.
80 ft.
570 kips
570 kips
510 kips
570 kips
210 kips
150 kips
230 kips
14400 kip-ft
10800 kip-ft
10800 kip-ft
Figure 4-6
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 178
BEAM AND GIRDER DESIGN
B. Preliminary flange design:
1. An approximate formula for the area of one flange is:
Af ≈
Mu 14,400(12)
=
= 64.0 in.2
Fyf h
(50)(54)
2. Check adequacy against local buckling:
Table B5.1
bf / 2tf = 24 / (2)(2.625) = 4.6 < (65 / √
Fy = 9.2) o.k.
Flange is compact.
C. Trial girder section:
Web 5⁄8×54; two flange plates 25⁄8×24
1. Determine plastic section moduli:
 54 2.625 
3
Zf = 2 (2.625)(24)  +
 = 3.567 in.
2
2



 54   54 
Zw = 2 (5⁄8)     = 456 in.3
 2   4 

2. Check flexural strength:
Compression flange is supported laterally for its full length and the
section is compact.
Appendix F1
Mn = Mp = Fyf Zf + FywZw
Mn = [(50)(3,567) + (36)(456)] 1 / 12 = 16,230 kip-ft
φbMn = (0.90)16,230 = 14,610 kip-ft > 14,400 kip-ft o.k.
Use: Web: One plate 5⁄8×54 (Fy = 36 ksi)
Use: Flanges: Two plates 25⁄8×24 (Fy = 50 ksi)
D. Stiffener requirements:
1. Bearing stiffeners
Section K1
a. Check bearing at end reactions:
Assume point bearing (N = 0) and 5⁄16-in. web-to-flange welds.
Check local web yielding:
(K1-2)
Rn = (5k + N)Fywtw; k = 25⁄8 + 5⁄16 = 215⁄16-in.
φRn = 1.0[(5)(215⁄16) + 0](36)(5⁄8) = 330 kips
330 kips < 570 kips n.g.
Note: If local web yielding criteria are satisfied, applicable criteria
set for in Sections K1.4 and K1.5 should also be checked.
b. Bearing stiffeners at points of concentrated loads are also required.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
PLATE GIRDER DESIGN
4 - 179
2. Intermediate stiffeners:
The LRFD Specification does not permit design of hybrid girders
on the basis of tension field action. Therefore, determine the need
for intermediate stiffeners by use of Equations F2-1, F2-2, F2-3,
Table 9-36.
a. Check shear strength without intermediate stiffeners:
Section F2
h / tw = 86.4, a / h exceeds 3.0
Therefore, k = 5.0
Vu
570
=
= 16.9 ksi
Aw 33.75
Since h / tw = 86.4 > 523 / √
36
 = 87, but h / tw = 86.4 < 418 / √
36
 =
70, use Equation F2-2:
(F2-2) or
Table 9-36
φvVn
Vu
= 15.5 ksi <
= 16.9 ksi
Aw
Aw
Therefore, intermediate stiffeners required.
b. End panel stiffener spacing
(F2-2) or
Table 9-36
φvVn
= 16.9 ksi
Aw
Therefore, a / h = 2.5 for h / tw = 86.4.
Max. a1 = 2.5(54) = 135 in. (Use 10 ft = 120 in.)
c. Check need for stiffeners between concentrated loads:
h / tw = 86.4, a / h is over 3, k = 5
Vu
Aw
(F2-3) or
Table 9-36
=
210
= 6.2 ksi
33.75
φvVn
= 15.5 ksi > 6.2 ksi o.k.
Aw
Therefore, intermediate stiffeners not required between the concentrated loads.
Summary (see Figure 4-7):
E. Stiffener design:
1. Bearing stiffeners:
See Step E.2, Example 4-10, for design procedure.
Use for bearing stiffeners: Two plates 3⁄4×11×4′-53⁄4 with close
bearing on flange receiving reaction or concentrated loads.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 180
BEAM AND GIRDER DESIGN
2. Intermediate stiffeners:
Assume 5⁄16×4 in., Fy = 36 ksi, on each side of web.
a. Check width-thickness ratio:
4 / 0.313 = 12.8 < 95 / √
Fy = 15.8 o.k.
Table B5.1
b. Check moment of inertia:
Ireq’d = 120(5⁄8)3(0.5) = 14.6 in.4
Ifurn = 1⁄12(0.313)(8.63)3 = 16.8 in.4
16.8 in.4 > 14.6 in.4 o.k.
Appendix F2.3
c. Length required (see Step E.1.d. Example 4-10):
54 − 5⁄16 − (6)(9⁄16) = 505⁄16
54 − 5⁄16 − (4)(9⁄16) = 517⁄16 (use 51 in.)
Use for intermediate stiffeners: Two plates 5⁄16×4×4′-3, fillet-welded
to the compression flange and web, one on each side of the web.
EXAMPLE 4-12 Design the section of a nominal 52-in. deep welded girder with no
intermediate stiffeners to support a factored uniform load of 5.0 kips
per linear foot on an 85-ft span. The girder will be framed between
columns and its compression flange will be laterally supported for its
entire length.
Required bending moment: 4,516 kip-ft
Required vertical shear: 213 kips
Span: 85 ft
Nominal depth: 52 in.
Steel: Fy = 50 ksi
Given:
For compact web and flange, Mn = Fy Z
Solution:
20 ′-0
20 ′-0
Bearing stiffener
Bearing stiffeners
4 ′-9
5 ′-1
5 ′-1
Intermediate stiffeners
5 ′-1
40 ′-0
Figure 4-7
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Sym.
about cL
PLATE GIRDER DESIGN
LRFD
Specification
Reference
4 - 181
Design for a compact web and flange:
Design for plastic moment, Fy Z:
Required plastic section modulus:
Zreq’d =
Mu 4,516 × 12
=
= 1,204 in.3
φFy 0.90 × 50
Enter Table of Built-up Wide-Flange Sections, Dimensions and
Properties:
For girder having 3⁄8×48 web with 11⁄4×16 flange plates:
Z = 1,200 in.3 < 1,204 in.3
For girder having 3⁄8×52 web with 11⁄4×18 flange plates:
Z = 1,450 in.3 > 1,204 in.3
A. Determine web required:
Table B5.1
For compact web, h / tw ≤ 640 / √
Fyf = 91
Assume h = 50 in.
Minimum tw = 50 / 91 = 0.55 in.
Try: web = 9⁄16×50; Aw = 28.1 in.2
h / tw = 50 / 0.56 = 89 < 91
The web is compact.
Intermediate stiffeners can be avoided if the design shear strength
Fyf,
of the web is adequate. (For plate girders with h / tw > 970 / √
refer to Appendix G4 of the LRFD Specification.)
(F2-3)
φvVn = φv(132,000Aw) / (h / tw)2
= 0.9(132,000 × 28.1) / (89)2
= 421 kips > 213 kips req’d. o.k.
Therefore, no intermediate stiffeners are necessary.
B. Determine flange required.
Af ≈
(4,516)(12)
= 21.7 in.2
50 × 50
Try 1×18 plate: Af = 18.0 in.2
Table B5.1
bf / 2tf = 18 / (2)(1.0) = 9.0 < 65 / √
Fy = 9.2 o.k.
Flange is compact.
C. Check plastic section modulus:
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 182
BEAM AND GIRDER DESIGN
 51.0   9   50   50  
Zx = 2 (18)(1.0) 
 +        = 1,270 in.3
2

  16   2   4  

3
3
1,270 in. > 1,204 in. req’d. o.k.
Use: Web: One plate 9⁄16×50
Use: Flanges:* Two plates 1×18
Section K1.8
Note: Because this girder will be framed between columns, the usual
end bearing stiffeners are not required.
*Because this girder is longer than 60 feet, some economy may be gained by decreasing the flange size in areas of smaller
moment, i.e., near ends of girder.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
PLATE GIRDER DESIGN
4 - 183
bf
tf
Nominal
Size
(h / tw)
Wt.
per
Ft
Area Depth
In.
Lb.
In.2
92× 30
(131)
823
721
619
568
517
466
415
86× 28
(134)
80× 26
(125)
74× 24
(128)
68× 22
(132)
d
Flange
Web
In.
In.
In.
In.
242
212
182
167
152
137
122
96.00
95.00
94.00
93.50
93.00
92.50
92.00
30
30
30
30
30
30
30
3
21⁄2
2
13⁄4
11⁄2
11⁄4
1
90
90
90
90
90
90
90
11⁄
16
11⁄
16
11⁄
16
11⁄
16
11⁄
16
11⁄
16
11⁄
16
750
654
559
512
464
416
369
220
192
164
150
136
122
108
90.00
89.00
88.00
87.50
87.00
86.50
86.00
28
28
28
28
28
28
28
3
21⁄2
2
13⁄4
11⁄2
11⁄4
1
84
84
84
84
84
84
84
5⁄
8
5⁄
8
5⁄
8
5⁄
8
5⁄
8
5⁄
8
5⁄
8
696
609
519
475
431
387
343
320
205
179
153
140
127
114
101
94.2
84.00
83.00
82.00
81.50
81.00
80.50
80.00
79.75
26
26
26
26
26
26
26
26
3
21⁄2
2
13⁄4
11⁄2
11⁄4
1
78
78
78
78
78
78
78
78
5⁄
8
5⁄
8
5⁄
8
5⁄
8
5⁄
8
5⁄
8
5⁄
8
5⁄
8
627
546
464
423
382
342
301
280
184
160
136
124
112
100
88.5
82.5
78.00
77.00
76.00
75.50
75.00
74.50
74.00
73.75
24
24
24
24
24
24
24
24
3
21⁄2
2
13⁄4
11⁄2
11⁄4
1
72
72
72
72
72
72
72
72
9⁄
16
9⁄
16
9⁄
16
9⁄
16
9⁄
16
9⁄
16
9⁄
16
9⁄
16
561
486
411
374
337
299
262
243
224
165
143
121
110
99.0
88.0
77.0
71.5
66.0
72.00
71.00
70.00
69.50
69.00
68.50
68.00
67.75
67.50
22
22
22
22
22
22
22
22
22
3
21⁄2
2
13⁄4
11⁄2
11⁄4
1
66
66
66
66
66
66
66
66
66
1⁄
2
1⁄
2
1⁄
2
1⁄
2
1⁄
2
1⁄
2
1⁄
2
1⁄
2
1⁄
2
7⁄
8
8
7⁄
8
3⁄
4
X
X
h
tw
f
Axis X-X
Width Thick Depth Thick
bf
tf
h
tw
7⁄
d=h+2t f
BUILT-UP WIDE-FLANGE SECTIONS
Dimensions and properties
In.
Z
In.3
In.3
In.3
431000
363000
296000
263000
230000
198000
166000
8980
7640
6290
5620
4950
4280
3610
79.1
79.9
80.8
81.2
81.7
82.1
82.5
9760
8330
6910
6210
5510
4810
4120
127
127
127
127
127
127
127
428.9
428.9
428.9
428.9
428.9
428.9
428.9
349000
293000
238000
211000
184000
158000
132000
7750
6580
5410
4820
4240
3650
3070
68.6
69.4
70.2
70.6
71.0
71.4
71.8
8410
7160
5920
5300
4690
4090
3480
110
110
110
110
110
110
110
345.3
345.3
345.3
345.3
345.3
345.3
345.3
281000
235000
191000
169000
148000
127000
106000
95500
6680
5670
4660
4160
3650
3150
2650
2390
58.8
59.6
60.3
60.7
61.0
61.4
61.8
62.0
7270
6180
5110
4580
4050
3530
3000
2750
95.1
95.1
95.1
95.1
95.1
95.1
95.1
95.1
371.8
371.8
371.8
371.8
371.8
371.8
371.8
371.8
220000
184000
149000
132000
115000
98000
81400
73300
5640
4780
3920
3490
3060
2630
2200
1990
49.8
50.5
51.2
51.5
51.8
52.2
52.5
52.7
6130
5200
4280
3830
3380
2930
2480
2260
81.0
81.0
81.0
81.0
81.0
81.0
81.0
81.0
293.7
293.7
293.7
293.7
293.7
293.7
293.7
293.7
169000
141000
114000
100000
87000
74000
61000
55000
49000
4700
3970
3250
2890
2530
2170
1800
1620
1440
41.6
42.2
42.8
43.1
43.4
43.7
44.0
44.2
44.4
5100
4310
3540
3150
2770
2390
2020
1830
1650
68.1
68.1
68.1
68.1
68.1
68.1
68.1
68.1
68.1
225.0
225.0
225.0
225.0
225.0
225.0
225.0
225.0
225.0
S
In.4
a
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Z′
φvVn
S′
I
b
c
In.3
Kips
4 - 184
BEAM AND GIRDER DESIGN
bf
d=h+2t f
tf
X
X
h
tw
f
BUILT-UP WIDE-FLANGE SECTIONS
Dimensions and properties
Flange
Web
Axis X-X
Nominal
Size
(h / tw)
Wt.
per
Ft
Area Depth
In.
Lb.
In.2
In.
In.
In.
In.
In.
61× 20
(137)
429
361
327
293
259
225
208
191
126
106
96.2
86.2
76.2
66.2
61.2
56.2
65.00
64.00
63.50
63.00
62.50
62.00
61.75
61.50
20
20
20
20
20
20
20
20
21⁄2
2
13⁄4
11⁄2
11⁄4
1
60
60
60
60
60
60
60
60
7⁄
16
7⁄
16
7⁄
16
7⁄
16
7⁄
16
7⁄
16
7⁄
16
7⁄
16
389
328
298
267
236
206
190
175
160
115
96.5
87.5
78.5
69.5
60.5
56.0
51.5
47.0
61.00
60.00
59.50
59.00
58.50
58.00
57.75
57.50
57.25
18
18
18
18
18
18
18
18
18
21⁄2
2
13⁄4
11⁄2
11⁄4
1
56
56
56
56
56
56
56
56
56
7⁄
16
7⁄
16
7⁄
16
7⁄
16
7⁄
16
7⁄
16
7⁄
16
7⁄
16
7⁄
16
342
311
280
250
219
189
173
158
143
100
91.5
82.5
73.5
64.5
55.5
51.0
46.5
42.0
56.50
56.00
55.50
55.00
54.50
54.00
53.75
53.50
53.25
18
18
18
18
18
18
18
18
18
21⁄4
2
13⁄4
11⁄2
11⁄4
1
52
52
52
52
52
52
52
52
52
3⁄
8
3⁄
8
3⁄
8
3⁄
8
3⁄
8
3⁄
8
3⁄
8
3⁄
8
3⁄
8
306
279
252
224
197
170
156
143
129
90.0
82.0
74.0
66.0
58.0
50.0
46.0
42.0
38.0
52.50
52.00
51.50
51.00
50.50
50.00
49.75
49.50
49.25
16
16
16
16
16
16
16
16
16
21⁄4
2
13⁄4
11⁄2
11⁄4
1
48
48
48
48
48
48
48
48
48
3⁄
8
3⁄
8
3⁄
8
3⁄
8
3⁄
8
3⁄
8
3⁄
8
3⁄
8
3⁄
8
237
210
183
69.8
61.8
53.8
47.50
47.00
46.50
16
16
16
13⁄4
11⁄2
11⁄4
44
44
44
5⁄
16
5⁄
16
5⁄
16
57× 18
(128)
53× 18
(138)
49× 16
(128)
45× 16
(141)
d
Width Thick Depth Thick
bf
tf
h
tw
7⁄
8
3⁄
4
7⁄
8
3⁄
4
5⁄
8
7⁄
8
3⁄
4
5⁄
8
7⁄
8
3⁄
4
5⁄
8
S′
Z
In.3
In.3
106000
84800
74600
64600
54800
45100
40300
35600
3250
2650
2350
2050
1750
1450
1310
1160
83500
67000
58900
51000
43300
35600
31900
28100
24400
Z′
φvVn
b
c
In.3
In.3
Kips
34.6
35.2
35.4
35.7
36.0
36.3
36.4
36.6
3520
2870
2560
2240
1930
1610
1460
1310
56.3
56.3
56.3
56.3
56.3
56.3
56.3
56.3
165.8
165.8
165.8
165.8
165.8
165.8
165.8
165.8
2740
2230
1980
1730
1480
1230
1100
979
854
30.0
30.5
30.7
31.0
31.3
31.5
31.7
31.8
32.0
2980
2430
2160
1900
1630
1370
1240
1110
980
49.0
49.0
49.0
49.0
49.0
49.0
49.0
49.0
49.0
177.6
177.6
177.6
177.6
177.6
177.6
177.6
177.6
177.6
64000
56900
49900
43000
36300
29700
26400
23200
20000
2270
2030
1800
1570
1330
1100
983
866
750
25.9
26.2
26.4
26.6
26.9
27.1
27.2
27.4
27.5
2450
2200
1950
1700
1450
1210
1090
966
846
42.3
42.3
42.3
42.3
42.3
42.3
42.3
42.3
42.3
120.5
120.5
120.5
120.5
120.5
120.5
120.5
120.5
120.5
48900
43500
38100
32900
27700
22700
20200
17700
15300
1860
1670
1480
1290
1100
910
811
716
620
21.9
22.2
22.4
22.6
22.8
23.0
23.2
23.3
23.4
2030
1820
1610
1400
1200
1000
900
801
702
36.0
36.0
36.0
36.0
36.0
36.0
36.0
36.0
36.0
130.5
130.5
130.5
130.5
130.5
130.5
130.5
130.5
130.5
31500
27100
22700
1330
1150
976
18.7
18.9
19.1
1430
1240
1060
30.3
30.3
30.3
82.4
82.4
82.4
I
S
In.4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
a
PLATE GIRDER DESIGN
4 - 185
bf
tf
Flange
Nominal
Size
(h / tw)
Wt.
per
Ft
Area Depth
In.
Lb.
In.2
In.
In.
45× 16
(141)
156
142
129
116
45.8
41.8
37.8
33.8
46.00
45.75
45.50
45.25
16
16
16
16
d
Web
In.
In.
In.
1
44
44
44
44
5⁄
16
5⁄
16
5⁄
16
5⁄
16
8
3⁄
4
5⁄
8
X
X
h
tw
f
Axis X-X
Width Thick Depth Thick
bf
tf
h
tw
7⁄
d=h+2t f
BUILT-UP WIDE-FLANGE SECTIONS
Dimensions and properties
S′
Z
In.3
In.3
801
713
626
538
19.3
19.4
19.5
19.6
I
S
In.4
18400
16300
14200
12200
a
Z′
φvVn
b
c
In.3
In.3
Kips
871
780
688
598
30.3
30.3
30.3
30.3
82.4
82.4
82.4
82.4
a S′
= Additional section modulus corresponding to 1⁄16″ increase in web thickness.
b Z′
= Additional plastic section modulus corresponding to 1⁄16″ increase in web thickness.
c φvVn = Maximum design end shear strength permissible without transverse stiffeners for tabulated web plate
(LRFD Specification Section F2). φv = 0.90.
Notes:
Based on their width-thickness ratios the girders in this table are noncompact shapes in accordance with
LRFD Specification Section B5 for Fy = 36 ksi steel. For steels of higher yield strengths, check
flanges for compliance with this section.
This table does not consider local effects on the web due to concentrated loads. (See LRFD Specification
Section K1.)
See LRFD Specification Appendix G4 for design of stiffeners.
Welds are not included in the tabulated weight per foot.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 186
BEAM AND GIRDER DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BEAM DIAGRAMS AND FORMULAS
4 - 187
BEAM DIAGRAMS AND FORMULAS
Nomenclature
E
= modulus of elasticity of steel at 29,000 ksi
I
= moment of inertia of beam (in.4)
L
= total length of beam between reaction points (ft)
Mmax = maximum moment (kip-in.)
M1 = maximum moment in left section of beam (kip-in.)
M2 = maximum moment in right section of beam (kip-in.)
M3 = maximum positive moment in beam with combined end moment conditions
(kip-in.)
Mx = moment at distance x from end of beam (kip-in.)
P
= concentrated load (kips)
P1 = concentrated load nearest left reaction (kips)
P2 = concentrated load nearest right reaction, and of different magnitude than P1
(kips)
R
= end beam reaction for any condition of symmetrical loading (kips)
R1 = left end beam reaction (kips)
R2 = right end or intermediate beam reaction (kips)
R3 = right end beam reaction (kips)
V
= maximum vertical shear for any condition of symmetrical loading (kips)
V1 = maximum vertical shear in left section of beam (kips)
V2 = vertical shear at right reaction point, or to left of intermediate reaction point
of beam (kips)
V3 = vertical shear at right reaction point, or to right of intermediate reaction point
of beam (kips)
Vx = vertical shear at distance x from end of beam (kips)
W = total load on beam (kips)
a
= measured distance along beam (in.)
b
= measured distance along beam which may be greater or less than a (in.)
l
= total length of beam between reaction points (in.)
w = uniformly distributed load per unit of length (kips per in.)
w1 = uniformly distributed load per unit of length nearest left reaction (kips per in.)
w2 = uniformly distributed load per unit of length nearest right reaction, and of
different magnitude than w1 (kips per in.)
x
= any distance measured along beam from left reaction (in.)
x1 = any distance measured along overhang section of beam from nearest reaction
point (in.)
∆max = maximum deflection (in.)
∆a
= deflection at point of load (in.)
∆x
= deflection at any point x distance from left reaction (in.)
∆x1 = deflection of overhang section of beam at any distance from nearest reaction
point (in.)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 188
BEAM AND GIRDER DESIGN
BEAM DIAGRAMS AND FORMULAS
Frequently Used Formulas
The formulas given below are frequently required in structural designing. They are
included herein for the convenience of those engineers who have infrequent use for such
formulas and hence may find reference necessary. Variation from the standard nomenclature on page 4-187 is noted.
BEAMS
Flexural stress at extreme fiber:
f = Mc / I = M / S
Flexural stress at any fiber:
f = My / I
y = distance from neutral axis to fiber
Average vertical shear (for maximum see below):
v = V / A = V / dt (for beams and girders)
Horizontal shearing stress at any section A-A:
v = VQ / Ib
Q = statical moment about the neutral axis of that portion
of the cross section lying outside of section A-A
b = width at section A-A
(Intensity of vertical shear is equal to that of horizontal shear acting normal to it at the
same point and both are usually a maximum at mid-height of beam.)
Shear and deflection at any point:
x and y are abscissa and ordinate respectively of a point on the neutral
d 2y
EI 2 = M
axis, referred to axes of rectangular coordinates through a selected
dx
point of support.
(First integration gives slopes; second integration gives deflections. Constants of integration must be determined.)
CONTINUOUS BEAMS (the theorem of three moments)
Uniform load:
 w1l31 w2l32 
 l1 l2 
l1
l2

Ma + 2Mb  +  + Mc = − 1⁄4 
+
I1
I2
I2 
 I1
 I1 I2 
Concentrated loads:
 l1 l2 
l1
l2
P1a1b1 
a1  p2a2b2 
b2 
Ma + 2Mb  +  + Mc = −
1 +  −
1 + 
I1
I2
I1 
l1 
I2 
I2 
 I1 I2 
Considering any two consecutive spans in any continuous structure:
Ma, Mb, Mc = moments at left, center, and right supports respectively, of any pair of
adjacent spans
= length of left and right spans, respectively, of the pair
l1 and l2
= moment of inertia of left and right spans, respectively
I1 and I2
w1 and w2 = load per unit of length on left and right spans, respectively
= concentrated loads on left and right spans, respectively
P1 and P2
a1 and a2
= distance of concentrated loads from left support, in left and right spans,
respectively
= distance of concentrated loads from right support, in left and right spans,
b1 and b2
respectively
The above equations are for beam with moment of inertia constant in each span but
differing in different spans, continuous over three or more supports. By writing such an
equation for each successive pair of spans and introducing the known values (usually
zero) of end moments, all other moments can be found.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BEAM DIAGRAMS AND FORMULAS
4 - 189
BEAM DIAGRAMS AND FORMULAS
Table of Concentrated Load Equivalents
n
Loading
P
2
P
3
P
4
P
P
P
5
P
P
P
Beam Fixed One
End, Supported
at Other
Beam Fixed
Both Ends
a
b
c
d
e
f
g
0.125
—
0.500
—
0.013
1.000
1.000
0.070
0.125
0.375
0.625
0.005
1.000
0.415
0.042
0.083
—
0.500
0.003
0.667
0.300
a
b
c
d
e
f
g
0.250
—
0.500
—
0.021
2.000
0.800
0.156
0.188
0.313
0.688
0.009
1.500
0.477
0.125
0.125
—
0.500
0.005
1.000
0.400
a
b
c
d
e
f
g
0.333
—
1.000
—
0.036
2.667
1.022
0.222
0.333
0.667
1.333
0.015
2.667
0.438
0.111
0.222
—
1.000
0.008
1.778
0.333
a
b
c
d
e
f
g
0.500
—
1.500
—
0.050
4.000
0.950
0.266
0.469
1.031
1.969
0.021
3.750
0.428
0.188
0.313
—
1.500
0.010
2.500
0.320
a
b
c
d
e
f
g
0.600
—
2.000
—
0.063
4.800
1.008
0.360
0.600
1.400
2.600
0.027
4.800
0.424
0.200
0.400
—
2.000
0.013
3.200
0.312
Coeff.
∞
P
Simple
Beam
P
Maximum positive moment (kip-ft): aPL
Maximum negative moment (kip-ft): bPL
Pinned end reaction (kips): cP
Fixed end reaction (kips): dP
Maximum deflection (in): ePl3 / EI
Equivalent simple span uniform load (kips): f P
Deflection coefficient for equivalent simple span uniform load: g
Number of equal load spaces: n
Span of beam (ft): L
Span of beam (in): l
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 190
BEAM AND GIRDER DESIGN
BEAM DIAGRAMS AND FORMULAS
For Various Static Loading Conditions
For meaning of symbols, see page 4-187
1. SIMPLE BEAM—UNIFORMLY DISTRIBUTED LOAD
Total Equiv. Uniform Load . . . . . . = wl
l
wl
x
R
R
l
2
l
2
V
. . . . . . . . . . . . . . . . . =
Vx
. . . . . . . . . . . . . . . . . = w  − x
M max
Shear
V
Mx
l
2
∆x
Moment


wl 2
(at center) . . . . . . . . . . . . =
8
wx
. . . . . . . . . . . . . . . . . =
(l − x)
2
∆ max (at center) . . . . . . . . . . . .
Mmax
wl
2
R=V
. . . . . . . . . . . . . . . . .
5wl 4
384 EI
wx
=
(l2 − 2lx 2 + x3 )
24EI
=
2. SIMPLE BEAM—LOAD INCREASING UNIFORMLY TO ONE END
Total Equiv. Uniform Load . . . . . . =
l
x
R 1 = V1 . . . . . . . . . . . . . . . . .
W
R2
R1
V1
Shear
V2
max
Vx
. . . . . . . . . . . . . . . . . =
. . . . . . . . . . . . . . .
M max (at x =
Mx
M max
l
= .5774 l) . . . . . . .
√3


√
158
√
∆x
W Wx 2
− 2
3
l
2Wl
=
= .1283 Wl
9√
3
. . . . . . . . . . . . . . . . . =
∆ max (at x = l 1 −
Moment
W
3
2W
=
3
=
R 2 = V2
.5774 l
= .5193 l) . .
16W
= 1.0264W
9√
3
Wx
3l2
(l2 − x2 )
= 0.1304
. . . . . . . . . . . . . . . . . =
Wl 3
EI
Wx
180 EIl2
(3x4 − 10l2 x2 + 7l4 )
3. SIMPLE BEAM—LOAD INCREASING UNIFORMLY TO CENTER
4W
3
W
=
2
W
Total Equiv. Uniform Load . . . . . . =
l
x
W
R
R=V
R
l
2
Vx
l
2
V
. . . . . . . . . . . . . . . . .
l
2
(when x < ) . . . . . . . . . . =
M max (at center) . . . . . . . . . . . .
Shear
V
Mx
M max
∆x
(l2 − 4x2)
1
l
2
(when x < ) . . . . . . . . . . = Wx  −
∆ max (at center) . . . . . . . . . . . .
Moment
2l2
Wl
=
6
l
2
2
=
(when x < ) . . . . . . . . . . =
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Wl 3
60EI
Wx
480 EIl2
2x 2 

3l2 
(5l2 − 4x2 )2
BEAM DIAGRAMS AND FORMULAS
4 - 191
BEAM DIAGRAMS AND FORMULAS
For Various Static Loading Conditions
For meaning of symbols, see page 4-187
4. SIMPLE BEAM—UNIFORMLY LOAD PARTIALLY DISTRIBUTED
l
b
wb
a
R
1
R2
x
V1
wb
(2c + b)
2l
wb
(2a + b)
R 2 = V2 (max. when a > c) . . . . . . . =
2l
R 1 = V1 (max. when a < c) . . . . . . . =
c
Vx
(when x > a and < (a + b)) . . . = R 1 − w(x − a)
M max
Mx

R1 
R1 

at x = a + w  . . . . . . . . = R 1 a + 2w 




(when x < a) . . . . . . . . . = R 1x
Mx
(when x > a and < (a + b)) . . . = R 1x −
Mx
(when x > (a + b)) . . . . . . . = R 2(l − x)
Shear
V2
R1
a+ w
M max
Moment
w
(x − a)2
2
5. SIMPLE BEAM—UNIFORM LOAD PARTIALLY DISTRIBUTED AT ONE END
R 1 = V1
max
. . . . . . . . . . . . . . .=
l
a
wa
R 2 = V2
R
1
R2
x
V1
R1
w
M max
wa 2
2l
Vx
(when x < a) . . . . . . . . . = R 1 − wx
M max

R 
at x = 1 
w

Mx
(when x < a) . . . . . . . . . = R 1x −
Mx
(when x > a) . . . . . . . . . = R 2 (l − x)
∆x
(when x < a) . . . . . . . . . =
wx
(a 2 (2l − a)2 − 2ax 2 (2l − a) + lx 3 )
24EIl
∆x
(when x > a) . . . . . . . . . =
wa 2 (l − x)
(4xl − 2x2 − a 2 )
24EIl
V2
Shear
. . . . . . . . . . . . . . . .=
wa
(2l − a)
2l
. . . . . . . . . .=
Moment
R 21
2w
wx 2
2
6. SIMPLE BEAM—UNIFORM LOAD PARTIALLY DISTRIBUTED AT EACH END
l
a
w1 a
R1
b
c
w2 c
R2
x
R 1 = V1
. . . . . . . . . . . . . . . .=
w 1a(2l − a) + w 2 c2
2l
R 2 = V2
. . . . . . . . . . . . . . . .=
w 2c(2l − c) + w 1 a2
2l
Vx
(when x < a) . . . . . . . . . = R 1 − w 1x
Vx
(when x > a and < (a + b))
Vx
(when x > (a + b)) . . . . . . . = R 2 − w 2 (l − x)
= R 1 − w 1a
R1
R1


=
at x = w when R 1 < w 1a 
2w 1
1


R 22
R1


at x = l − w when R 2 < w 2 c = 2w
2
2


2
V1
Shear
R1
w1
V2
M max
M max
M max
Mx
Moment
Mx
Mx
w 1x2
2
w1a
(when x > a and < (a + b)) . . . = R 1x −
(2x − a)
2
(when x < a) . . . . . . . . . = R 1x −
(when x > (a + b)) . . . . . . . = R 2(l − x) −
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
w 2(l − x)2
2
4 - 192
BEAM AND GIRDER DESIGN
BEAM DIAGRAMS AND FORMULAS
For Various Static Loading Conditions
For meaning of symbols, see page 4-187
7. SIMPLE BEAM—CONCENTRATED LOAD AT CENTER
Total Equiv. Uniform Load . . . . . . . . . . = 2P
l
P
x
R
l
2
R=V
. . . . . . . . . . . . . . . . . . . . =
P
2
M max
(at point of load) . . . . . . . . . . . =
Pl
4
Mx

Px
1
when x <  . . . . . . . . . . . . . =
2
2

∆ max
(at point of load) . . . . . . . . . . . =
∆x

1
Px
(3l2 − 4x2 )
when x <  . . . . . . . . . . . . . =
2
48EI

R
l
2
V
Shear
V
M max
Moment
Pl 3
48EI
8. SIMPLE BEAM—CONCENTRATED LOAD AT ANY POINT
Total Equiv. Uniform Load . . . . . . . . . . =
l
x
P
R
1
a
Pb
l
R 2 = V2 (max when a > b ) . . . . . . . . . . . =
Pa
l
M max
(at point of load) . . . . . . . . . . . =
Pab
l
Mx
(when x < a ) . . . . . . . . . . . . . . =
Pbx
l
∆ max

at x =

Pab (a + 2b)√

3a(a + 2b)
27EIl
∆a
(at point of load) . . . . . . . . . . . =
Pa 2b 2
3EIl
∆x
(when x < a ) . . . . . . . . . . . . . . =
Pbx 2
(l − b 2 − x2 )
6EIl
V1
V2
Shear
M max
Moment
l2
R 1 = V1 (max when a < b ) . . . . . . . . . . . =
R2
b
8Pab

a(a + 2b)
√

 when a > b
3
. . . =
9. SIMPLE BEAM—TWO EQUAL CONCENTRATED LOADS SYMMETRICALLY PLACED
Total Equiv. Uniform Load . . . . . . . . . . =
l
x
P
P
R
R
a
a
V
Shear
V
M max
Moment
8Pa
l
R=V
. . . . . . . . . . . . . . . . . . . . =P
M max
(between loads) . . . . . . . . . . . . = Pa
Mx
(when x < a ) . . . . . . . . . . . . . . = Px
∆ max
(at center) . . . . . . . . . . . . . . . =
Pa
(3l2 − 4a2 )
24EI
∆x
(when x < a ) . . . . . . . . . . . . . . =
Px
(3la − 3a 2 − x2 )
6EI
∆x
(when x > a and < (l − a)) . . . . . . . =
Pa
(3lx − 3x2 − a 2)
6EI
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BEAM DIAGRAMS AND FORMULAS
4 - 193
BEAM DIAGRAMS AND FORMULAS
For Various Static Loading Conditions
For meaning of symbols, see page 4-187
10. SIMPLE BEAM—TWO EQUAL CONCENTRATED LOADS UNSYMMETRICALLY
PLACED
l
P
x
P
R
1
a
b
R2
V1
V2
Shear
M2
M1
Moment
R 1 = V1
(max. when a < b ) . . . . . . . . . =
P
(l − a + b)
l
R 2 = V2
(max. when a > b ) . . . . . . . . . =
P
(l − b + a)
l
Vx
(when x > a and < (l − b)) . . . . . =
P
(b − a)
l
M1
(max. when a > b ) . . . . . . . . . = R 1 a
M2
(max. when a < b ) . . . . . . . . . = R 2 b
Mx
(when x < a ) . . . . . . . . . . . . = R 1 x
Mx
(when x > a and < (l − b)) . . . . . = R 1 x − P(x − a)
11. SIMPLE BEAM—TWO UNEQUAL CONCENTRATED LOADS UNSYMMETRICALLY
PLACED
l
x
P1
P2
R
1
a
b
R2
V1
V2
Shear
M2
M1
Moment
R 1 = V1
. . . . . . . . . . . . . . . . . . =
P1 (l − a) + P2 b
l
R 2 = V2
. . . . . . . . . . . . . . . . . . =
P1 a + P2 (l − b)
l
Vx
(when x > a and < (l − b)) . . . . . = R 1 − P1
M1
(max. when R 1 < P1) . . . . . . . . = R 1 a
M2
(max. when R 2 < P2) . . . . . . . . = R 2 b
Mx
(when x < a ) . . . . . . . . . . . . = R 1 x
Mx
(when x > a and < (l − b)) . . . . . = R 1 x − P(x − a)
12. BEAM FIXED AT ONE END, SUPPORTED AT OTHER—UNIFORMLY DISTRIBUTED
LOAD
Total Equiv. Uniform Load . . . . . . . . . . = wl
R 1 = V1
. . . . . . . . . . . . . . . . . . =
3wl
8
R 2 = V2 max
. . . . . . . . . . . . . . . . . . =
5wl
8
Vx
. . . . . . . . . . . . . . . . . . = R 1 − wx
M max
. . . . . . . . . . . . . . . . . . =
l
wl
R
1
R2
x
V1
Shear
V2
3
l
8
l
4
M1
Moment
M max
wl 2
8
Mx

9
3
wl 2
at x = l . . . . . . . . . . . . . =
128
8

Mx
. . . . . . . . . . . . . . . . . . = R1x −
∆ max
∆x
wx 2
2


l
wl 4
33
 ) = .4215 l . . . =
at x = (1 + √
16
185 EI


. . . . . . . . . . . . . . . . . .
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
wx 3
(l − 3lx + 2x3 )
48EI
4 - 194
BEAM AND GIRDER DESIGN
BEAM DIAGRAMS AND FORMULAS
For Various Static Loading Conditions
For meaning of symbols, see page 4-187
13. BEAM FIXED AT ONE END, SUPPORTED AT OTHER—CONCENTRATED LOAD AT
CENTER
l
l
2
1
3P
2
R 1 = V1 . . . . . . . . . . . . . . . . . . =
5P
15
R 2 = V2 max . . . . . . . . . . . . . . . . =
11P
16
M max (at fixed end) . . . . . . . . . . . =
3Pl
16
(at point of load) . . . . . . . . . . =
5Pl
32
P
x
R
Total Equiv. Uniform Load . . . . . . . =
l
2
R
2
M1
V1
Shear
V2
Mx
Mx
M1
∆ max
Moment
M max
3
11 l
∆x
∆x
∆x

l
5Px
when x <  . . . . . . . . . . . . =
2
16


 l 11x 
l
when x >  . . . . . . . . . . . . = P  −

2

 2 16 
3
3


at x = l√
 15 = .4472 l . . . . . . . = Pl = .009317 PlEI

48EI√
5
(at point of load) . . . . . . . . . . =
7PL 3
768 EI

Px
l
(3l2 − 5x2 )
when x <  . . . . . . . . . . . . =
96EI
2


l
P
(x − l)2(11x − 2l)
when x >  . . . . . . . . . . . . =
2
96EI

14. BEAM FIXED AT ONE END, SUPPORTED AT OTHER—CONCENTRATED LOAD AT
ANY POINT
R 1 = V1 . . . . . . . . . . . . . . . . . . =
R 2 = V2 . . . . . . . . . . . . . . . . . . =
l
P
x
R
1
a
b
R2
V1
Shear
Pa
2l3
(a + 2l)
(3l2 − a2 )
(at point of load) . . . . . . . . . . = R 1 a
M2
(at fixed end) . . . . . . . . . . . =
Mx
(when x < a ) . . . . . . . . . . . . = R 1 x
Mx
(when x > a ) . . . . . . . . . . . . = R 1 x − P(x − a)

∆ max when a < .414 l at x = l


∆ max when a > .414 l at x = l
Moment
Pa
R2
2l3
M
V2
M1
Pb 2

M2
∆a
Pab
2l2
(a + l)
Pa(l2 + a2 )3
(l2 + a 2) 
 =
2
2
(3l − a ) 
3EI(3l2 − a2 )2

.......... 
√
2l + a 
a
=
(at point of load) . . . . . . . . . . =
∆
(when x < a ) . . . . . . . . . . . . =
∆x
(when x > a ) . . . . . . . . . . . . =
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
Pab 2
6EI
2l+ a
√
Pa 2 b3
12EIl3
2
Pb x
12EIl3
Pa
12EIl2
a
(3l + a)
(3al 2 − 2lx 2 − ax 2)
(l − x)2 (3l2 x − a 3 x − 2a 2l)
BEAM DIAGRAMS AND FORMULAS
4 - 195
BEAM DIAGRAMS AND FORMULAS
For Various Static Loading Conditions
For meaning of symbols, see page 4-187
15. BEAM FIXED AT BOTH ENDS—UNIFORMLY DISTRIBUTED LOADS
2wl
3
wl
. . . . . . . . . . . . . . . . . . =
2
Total Equiv. Uniform Load . . . . . . . . =
l
x
R=V
wl
R
R
l
2
l
2
V
V
Shear
.2113 l
M1
Moment
M max
M max
Vx
M max
(at ends) . . . . . . . . . . . . . =
M1
(at center) . . . . . . . . . . . . . =
Mx
. . . . . . . . . . . . . . . . . . =
∆ max
∆x
l

2

wl 2
12
wl 2
24
w
(6lx − l2 − 6x2 )
12
wl 4
384 EI
wx 2
(l − x)2
24EI
. . . . . . . . . . . . . . . . . . = w  − x
(at center) . . . . . . . . . . . . . =
. . . . . . . . . . . . . . . . . . =
16. BEAM FIXED AT BOTH ENDS—CONCENTRATED LOAD AT CENTER
l
R
Total Equiv. Uniform Load . . . . . . . . = P
P
x
l
2
R=V
R
l
2
V
V
Shear
M max
Mx
∆ max
l
4
M max
Moment
M max
M max
∆x
P
2
Pl
(at center and ends) . . . . . . . . =
8
. . . . . . . . . . . . . . . . . . =

when x <

P
l
 . . . . . . . . . . . = (4x − l)
8
2
Pl 3
(at center) . . . . . . . . . . . . . =
192 EI

when x <

l
Px 2
(3l − 4x)
 . . . . . . . . . . . =
2
48EI
17. BEAM FIXED AT BOTH ENDS—CONCENTRATED LOAD AT ANY POINT
R 1 = V1 (max. when a < b ) . . . . . . . . =
R 2 = V2 (max. when a > b ) . . . . . . . . =
l
P
x
R1
b
a
R2
V1
Ma
M1
Moment
M2
l3
Pa 2
(3a + b)
(a + 3b)
l3
Pab 2
M1
(max. when a < b ) . . . . . . . . =
M2
(max. when a > b ) . . . . . . . . =
Ma
(at point of load) . . . . . . . . . =
Mx
(when x < a ) . . . . . . . . . . . = R 1 x −
∆ max

2Pa 3b 2
2al 
 . . . . =
when a > b at x =
3a + b 
3EI(3a + b)2

∆a
(at point of load) . . . . . . . . . =
∆x
(when x < a ) . . . . . . . . . . . =
V2
Shear
Pb 2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
l2
Pa 2 b
l2
2Pa 2b 2
l3
Pab 2
l2
Pa 3 b3
3EIl3
Pb 2 x2
6EIl2
(3al − 3ax − bx)
4 - 196
BEAM AND GIRDER DESIGN
BEAM DIAGRAMS AND FORMULAS
For Various Static Loading Conditions
For meaning of symbols, see page 4-187
18. CANTILEVER BEAM—LOAD INCREASING UNIFORMLY TO FIXED END
8
3
Total Equiv. Uniform Load . . . . . . . . = W
l
R=V . . . . . . . . . . . . . . . . . . . =W
W
Vx
R
x2
. . . . . . . . . . . . . . . . . . . =W
l2
x
M max (at fixed end) . . . . . . . . . . . . =
V
Shear
Mx
M max
Moment
. . . . . . . . . . . . . . . . . . . =
∆ max (at free end) . . . . . . . . . . . . . =
∆x
. . . . . . . . . . . . . . . . . . . =
Wl
3
Wx 3
3l2
Wl 3
15EI
W
60EIl2
(x5 − 5l4 x + 4l5 )
19. CANTILEVER BEAM—UNIFORMLY DISTRIBUTED LOAD
Total Equiv. Uniform Load . . . . . . . . = 4wl
l
R = V . . . . . . . . . . . . . . . . . . . = wl
wl
Vx
R
x
V
M max
Moment
M max (at fixed end) . . . . . . . . . . . . =
wl 2
2
. . . . . . . . . . . . . . . . . . . =
wx 2
2
∆ max (at free end) . . . . . . . . . . . . . =
wl 4
8EI
∆x
w
(x 4 − 4l3 x + 3l4 )
24EI
Mx
Shear
. . . . . . . . . . . . . . . . . . . = wx
. . . . . . . . . . . . . . . . . . . =
20. BEAM FIXED AT ONE END, FREE TO DEFLECT VERTICALLY BUT NOT ROTATE
AT OTHER—UNIFORMLY DISTRIBUTED LOAD
Total Equiv. Uniform Load . . . . . . . . =
l
R = V . . . . . . . . . . . . . . . . . . . = wl
wl
M
R
Vx
. . . . . . . . . . . . . . . . . . . = wx
x
M max (at fixed end) . . . . . . . . . . . . =
V
Shear
Mx
. . . . . . . . . . . . . . . . . . . =
.4227 l
M1
Moment
8
wl
3
wl 2
3
w 2
(l − 3x2 )
6
∆ max (at deflected end) . . . . . . . . . . =
wl 4
24EI
∆x
w(l2 − x2 )2
24EI
M max
. . . . . . . . . . . . . . . . . . . =
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BEAM DIAGRAMS AND FORMULAS
4 - 197
BEAM DIAGRAMS AND FORMULAS
For Various Static Loading Conditions
For meaning of symbols, see page 4-187
21. CANTILEVER BEAM—CONCENTRATED LOAD AT ANY POINT
Total Equiv. Uniform Load . . . . . . . . =
R=V
8Pb
l
. . . . . . . . . . . . . . . . . . . =P
l
M max (at fixed end) . . . . . . . . . . . . = Pb
P
x
a
(when x > a) . . . . . . . . . . . . = P(x − a)
R
Mx
V
∆ max (at free end) . . . . . . . . . . . . . =
Pb 2
(3l − b)
6EI
∆a
(at point of load) . . . . . . . . . . =
Pb 3
3EI
∆x
(when x < a) . . . . . . . . . . . . =
Pb 2
(3l − 3x − b)
6EI
∆x
(when x > a) . . . . . . . . . . . . =
P(l − x)2
(3b − l + x)
6EI
b
Shear
Mmax
Moment
22. CANTILEVER BEAM—CONCENTRATED LOAD AT FREE END
l
Total Equiv. Uniform Load . . . . . . . . = 8P
P
R=V
. . . . . . . . . . . . . . . . . . . =P
R
x
M max (at fixed end) . . . . . . . . . . . . = Pl
Mx
V
Shear
M max
Moment
. . . . . . . . . . . . . . . . . . . = Px
∆ max (at free end) . . . . . . . . . . . . . =
Pl 3
3EI
∆x
P
(2l3 − 3l2x + x3 )
6EI
. . . . . . . . . . . . . . . . . . . =
23. BEAM FIXED AT ONE END, FREE TO DEFLECT VERTICALLY BUT NOT ROTATE
AT OTHER—CONCENTRATED LOAD AT DEFLECTED END
Total Equiv. Uniform Load . . . . . . . . = 4P
l
R=V
P
M
x
. . . . . . . . . . . . . . . . . . . =P
R
M max (at both ends) . . . . . . . . . . . . =
V
Mx
l
2
l
2
Moment
M max

. . . . . . . . . . . . . . . . . . . = P  − x
Shear
M max
Pl
2

3
∆ max (at deflected end) . . . . . . . . . . =
pl
12EI
∆x
P(l − x)2
(l + 2x)
12EI
. . . . . . . . . . . . . . . . . . . =
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 198
BEAM AND GIRDER DESIGN
BEAM DIAGRAMS AND FORMULAS
For Various Static Loading Conditions
For meaning of symbols, see page 4-187
24. BEAM OVERHANGING ONE SUPPORT—UNIFORMLY DISTRIBUTED LOAD
l
x
R1
w(l +a)
a2
l
1 – 2)
2 (
l
a
x1
R 2 = V2 + V3 . . . . . . . . . . . =
w
(l + a)2
2l
V2
. . . . . . . . . . . . . . . = wa
V3
. . . . . . . . . . . . . . . =
V3
Moment
(between supports) . . . . . = R 1 − wx

M2
a 2 
w
l 
2
2
1 − 2  . . . . . = 2 (l + a) (l − a)
2
l 
8l


wa 2
(at R 2) . . . . . . . . . . . . =
2
M 1 at x =
M2
M1
a2
l (1 – 2 )
l
w 2
(l + a2 )
2l
Vx 1 (for overhang) . . . . . . . = w(a − x 1)
V2
Shear
w 2
(l − a2 )
2l
Vx
R2
V1
R 1 = V1 . . . . . . . . . . . . . . =
M x (between supports) . . . . . =
wx 2
(l − a 2 − xl)
2l
M x1 (for overhang) . . . . . . . =
w
(a − x1 )2
2
∆x
wx
(l4 − 2l2 x2 + lx 3 − 2a 2l2 + 2a 2x 2)
24EIl
(between supports) . . . . . =
∆ x 1 (for overhang) . . . . . . . =
wx 1
(4a2 l − l3 + 6a 2 x1 − 4ax 21 + x31 )
24EI
25. BEAM OVERHANGING ONE SUPPORT—UNIFORMLY DISTRIBUTED LOAD ON
OVERHANG
R 1 = V1 . . . . . . . . . . . . . . =
R2
V1 + V2 . . . . . . . . . . . . =
x
a
x1
Vx 1 (for overhang) . . . . . . . = w(a − x 1)
wa
R1
R2
M max (at R 2) . . . . . . . . . . . =
wa 2
2
M x (between supports) . . . . . =
wa 2 x
2l
M x1 (for overhang) . . . . . . . =
w
(a − x 1)2
2
V2
V1
Shear

∆ max between supports at x =
Moment
wa
(2l + a)
2l
. . . . . . . . . . . . . . . = wa
V2
l
wa 2
2l

M max
wa 2 l2
l 
wa 2 l2
= 0.03208
 =
EI
18√
3 EI
√3 

∆ max (for overhang at x1 = a ) . . . =
wa 3
(4l + 3a)
24EI
∆x
wa 2x 2
(l − x 2)
12EIl
(between supports) . . . . . =
∆ x 1 (for overhang) . . . . . . . =
wx 1
(4a2 l + 6a 2x 1 − 4ax 21 + x31)
24EI
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BEAM DIAGRAMS AND FORMULAS
4 - 199
BEAM DIAGRAMS AND FORMULAS
For Various Static Loading Conditions
For meaning of symbols, see page 4-187
26. BEAM OVERHANGING ONE SUPPORT—CONCENTRATED LOAD AT END OF OVERHANG
Pa
l
P
= (l + a)
l
=P
= Pa
Pax
=
l
= P(a − x 1)
R 1 = V1 . . . . . . . . . . . . . . . . . . . . . =
a
x1
l
x
R 2 = V1 + V2 . . . . . . . . . . . . . . . . . . .
P
R2
R1
V2
V2
M max
. . . . . . . . . . . . . . . . . . . . .
(at R 2) . . . . . . . . . . . . . . . . .
Mx
(between supports) . . . . . . . . . .
M x1
(for overhang) . . . . . . . . . . . . .

l 
Pal 2
Pal 2
= .06415
 . . . . . =
between supports at x =
EI
√3 

9√
3 EI

∆ max
V1
Shear
∆ max
M max
Moment
∆x
∆ x1
Pa 2
(l + a)
3EI
Pax 2
(between supports) . . . . . . . . . . =
(l − x2)
6EIl
Px 1
(for overhang) . . . . . . . . . . . . . =
(2al + 3ax 1 − x21 )
6EI
(for overhang at x1 = a) . . . . . . . . =
27. BEAM OVERHANGING ONE SUPPORT—UNIFORMLY DISTRIBUTED LOAD
BETWEEN SUPPORTS
Total Equiv. Uniform Load . . . . . . . . . . = wl
a
l
x
R
l
2
. . . . . . . . . . . . . . . . . . . . . =
Vx
. . . . . . . . . . . . . . . . . . . . . = w  − x
x1
wl
l
2
R
M max
Mx
V
V
Shear
M max
wl
2
R=V
∆ max
(at center) . . . . . . . . . . . . . . . =
. . . . . . . . . . . . . . . . . . . . . =
(at center) . . . . . . . . . . . . . . . =
∆x
. . . . . . . . . . . . . . . . . . . . . =
∆ x1
. . . . . . . . . . . . . . . . . . . . . =
Moment
l

2

wl 2
8
wx
(l − x)
2
5wl 4
384 EI
wx 2
(l − 2lx 2 + x3)
24EI
3
wl x1
24EI
28. BEAM OVERHANGING ONE SUPPORT—CONCENTRATED LOAD AT ANY POINT
BETWEEN SUPPORTS
Total Equiv. Uniform Load . . . . . . . . . . =
R 1 = V1 (max. when a < b ) . . . . . . . . . . . =
l
x
R1
R 2 = V2 (max. when a > b ) . . . . . . . . . . . =
x1
P
R2
a
b
V1
V2
Shear
M max
Moment
M max
(at point of load) . . . . . . . . . . . . =
Mx
(when x < a ) . . . . . . . . . . . . . . =
∆ max

at x =

∆a
(at point of load) . . . . . . . . . . . . =
∆x
(when x < a ) . . . . . . . . . . . . . . =
∆x
(when x > a ) . . . . . . . . . . . . . . =
∆ x1
. . . . . . . . . . . . . . . . . . . . . =

a(a + 2b)
√

 when a > b
3
. . . =
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
8Pab
l2
Pb
l
Pa
l
Pab
l
Pbx
l
Pab (a + 2b)√

3a(a + 2b)
27EIl
Pa 2b 2
3EIl
Pbx 2
(l − b 2 − x2 )
6EIl
Pa(l − x)
(2lx − x 2 − a2 )
6EIl
Pabx1
(l + a)
6EIl
4 - 200
BEAM AND GIRDER DESIGN
BEAM DIAGRAMS AND FORMULAS
For Various Static Loading Conditions
For meaning of symbols, see page 4-187
29. CONTINUOUS BEAM—TWO EQUAL SPANS—UNIFORM LOAD ON ONE SPAN
x
Total Equiv. Uniform Load
=
49
wl
64
R 1 = V1 . . . . . . . . . . .
=
7
wl
16
R 2 = V2 + V3 . . . . . . . . .
=
5
wl
8
R 3 = V3 . . . . . . . . . . .
=−
wl
R1
R2
l
R3
l
V1
V3
V2
7l
16
Shear
V2
. . . . . . . . . . . . =

M max at x =

M max
M1
7 
l
16 
. . . . . =
1
wl
16
9
wl
16
49
wl 2
512
M1
(at support R 2) . . . . =
1
wl 2
16
Mx
(when x < l) . . . . . =
wx
(7l − 8x)
16
Moment
∆ max (at 0.472 l from R 1 ) . .
= .0092 wl 4 / EI
30. CONTINUOUS BEAM—TWO EQUAL SPANS—CONCENTRATED LOAD AT CENTER
OF ONE SPAN
P
l
2
l
2
R2
R1
l
R3
Total Equiv. Uniform Load
=
13
P
8
R 1 = V1 . . . . . . . . . . .
=
13
P
32
R 2 = V2 + V3 . . . . . . . . .
=
11
P
16
R 3 = V3 . . . . . . . . . . .
=−
l
V1
V3
Shear
V2
V2
. . . . . . . . . . . . =
M1
M1
Moment
19
P
32
=
13
Pl
64
(at support R 2) . . . . =
3
Pl
32
M max (at point of load) . . .
M max
3
P
32
∆ max (at 0.480 l from R 1 ) . .
= .015 Pl 3 / EI
31. CONTINUOUS BEAM—TWO EQUAL SPANS—CONCENTRATED LOAD AT ANY POINT
P
a
R1
b
R2
l
R3
l
V1
Shear
V2
M max
=
R 2 = V2 + V3 . . . . . . . . .
=
R 3 = V3 . . . . . . . . . . .
=−
V3
V2
. . . . . . . . . . . . =
M max (at point of load) . . .
M1
Moment
Pb
R 1 = V1 . . . . . . . . . . .
M1
=
(at support R 2) . . . . =
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4l3
Pa
2l3
(4l2 − a(l + a))
(2l2 + b(l + a))
Pab
4l3
Pa
4l3
(4l2 + b(l + a))
Pab
4l3
Pab
4l2
(l + a)
(4l2 − a(l + a))
(l + a)
BEAM DIAGRAMS AND FORMULAS
4 - 201
BEAM DIAGRAMS AND FORMULAS
For Various Static Loading Conditions
For meaning of symbols, see page 4-187
32. BEAM—UNIFORMLY DISTRIBUTED LOAD AND VARIABLE END MOMENTS
R 1 = V1
. . . . . . . . . . .
=
wl M 1 − M 2
+
2
l
R 2 = V2
. . . . . . . . . . .
=
wl M 1 − M 2
−
2
l
l
x
M1
wl
M
1
l
2
R2
2
V
1
Shear
V2

l M 1 − M 2 
M 3 at x = +
. .
wl 
2

=
M3
M2
M1
b

. . . . . . . . . . . . . = w  − x +
Vx
M >M
R1
2
. . . . . . . . . . . . . =
Mx

M1 − M2
l
2
wl 2 M 1 + M 2 (M 1 − M 2)
−
+
8
2
2wl 2
wx
(l − x) +
2
M − M 
2
 1
 x − M1
l


b
Moment
M + M  M − M 
l
√
−

+
4 
w
  wl 
2
b
(to locate inflection points) =
∆x =
wx
24EI
1
2
1
2
2
8M 1l 4M 2l 
4M 1 4M 2  2 12M 1
 3 
2
 x −  2l + wl − wl  x + w x + l − w − w 




33. BEAM—CONCENTRATED LOAD AT CENTER AND VARIABLE END MOMENTS
M1
l
P
x
R
1
l
2
M1 >M
2
M2
l
R 1 = V1
. . . . . . . . . . . =
P M1 − M2
+
2
l
R 2 = V2
. . . . . . . . . . . =
P M1 − M2
−
2
l
R2
2
Pl M 1 + M 2
−
4
2
M 3 (at center) . . . . . . . .
=

l
M x when x <  . . . . . .
2

P M1 − M2 
 x − M1
= +
l
2


l
M x when x >  . . . . . .
2

=
V
1
V2
Shear
M3
Moment
M1
M2
(M 1 − M 2)x
P
(l − x) +
− M1
2
l


8(l − x)
l
Px  2
 3l − 4x2 −
∆ x when x <  =
[M 1 (2l − x) + M 2 (l + x)]
2
48EI
Pl




AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 202
BEAM AND GIRDER DESIGN
BEAM DIAGRAMS AND FORMULAS
For Various Static Loading Conditions
For meaning of symbols, see page 4-187
34. CONTINUOUS BEAM—THREE EQUAL SPANS—ONE END SPAN UNLOADED
wl
A
wl
B
l
RA = 0.383 w l
C
l
0.583 w l
0.383 w l
D
l
RC = 0.450 w l
RB = 1.20 w l
RD = –0.033 w l
0.033 w l
0.617 w l
Shear
0.033 w l
0.417 w l
–0.1167 w l 2
+0.0735 w l 2
–0.0333 wl 2
+0.0534 w l 2
Moment
0.383 l
0.583 l
∆max (0.430 l from A) = 0.0059 wl 4/ El
35. CONTINUOUS BEAM—THREE EQUAL SPANS—END SPANS LOADED
wl
A
wl
B
l
RA = 0.450 w l
C
l
RB = 0.550 wl
D
l
RC = 0.550 w l
RD = 0.450 w l
0.550 wl
0.450 wl
0.450 w l
0.550 w l
Shear
–0.050 w l 2
+0.1013 w l 2
+0.1013 w l 2
Moment
0.450 l
0.450 l
∆max (0.479 l from A or D) = 0.0099 wl 4/ El
36. CONTINUOUS BEAM—THREE EQUAL SPANS—ALL SPANS LOADED
wl
A
wl
B
l
wl
C
l
RB = 1.10 w l
RA = 0.400 w l
0.500 w l
0.400 w l
0.400 w l
0.500 w l
–0.100 w l 2
–0.100 w l 2
+0.080 w l 2
RD = 0.400 w l
0.600 w l
0.600 w l
Shear
D
l
R C = 1.10 w l
+0.080 w l 2
+0.025w l 2
Moment
0.400 l
0.500 l
0.500 l
0.400 l
∆max (0.446 l from A or D) = 0.0069 w / El
l4
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BEAM DIAGRAMS AND FORMULAS
4 - 203
BEAM DIAGRAMS AND FORMULAS
For Various Static Loading Conditions
For meaning of symbols, see page 4-187
37. CONTINUOUS BEAM—FOUR EQUAL SPANS—THIRD SPAN UNLOADED
wl
wl
A
B
l
RA = 0.380 w l
wl
C
l
RE = 0.442 w l
0.558 w l
0.620 w l
Shear
0.442 w l
0.040 w l
0.397 w l
–0.058 w l 2
–0.0179 w l 2
–0.1205 w l 2
+0.0977 w l 2
+0.0611 w l 2
2
+0.072 w l
E
l
R D = 0.598 w l
0.603 w l
0.380 w l
D
l
RC = 0.357 w l
RB = 1.223 w l
Moment
0.603 l
0.442 l
0.380 l
∆ max (0.475 l from E) = 0.0094 wl 4/ El
38. CONTINUOUS BEAM—FOUR EQUAL SPANS—LOAD FIRST AND THIRD SPANS
wl
wl
A
B
l
RA = 0.446 w l
C
l
RC = 0.464 w l
RB = 0.572 w l
RE = –0.054 w l
0.054 w l
0.518 w l
–0.0536 w l 2
–0.0357 w l 2
–0.0536 w l 2
+0.0996 w l
E
0.054 w l
0.554 w l
Shear
l
R D = 0.572 w l
0.482 w l
0.018 w l
0.446 w l
D
l
+0.0805 w l 2
2
Moment
0.518 l
0.446 l
∆ max (0.477 l from A) = 0.0097 wl 4/ El
39. CONTINUOUS BEAM—FOUR EQUAL SPANS—ALL SPANS LOADED
wl
wl
A
B
l
0.607 w l
Shear
+0.0772
D
l
l
RD = 1.143 w l
+0.0364 w l 2
0.393 w l
0.536 w l
–0.1071 w l 2
+0.0364 w l 2
+0.0772 w l 2
Moment
0.536 l
E
RE = 0.393 w l
0.607 w l
0.464 w l
–0.0714 w l 2
–0.1071 w l 2
wl 2
wl
RC = 0.928 w l
0.464 w l
0.536 w l
0.393 w l
C
l
RB = 1.143 w l
RA = 0.393 w l
wl
0.536 l
0.393 l
0.393 l
∆ max (0.440 l from A and D) = 0.0065 w l 4/ El
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 204
BEAM AND GIRDER DESIGN
BEAM DIAGRAMS AND FORMULAS
For Various Static Loading Conditions
For meaning of symbols, see page 4-187
40. SIMPLE BEAM—ONE CONCENTRATED MOVING LOAD
x
P
R2
R1
l
R 1 max = V1 max (at x = 0) . . . . . . . . . . .
=P

1
M max at point of load, when x =  . . . . .
2

=
Pl
4
41. SIMPLE BEAM—TWO EQUAL CONCENTRATED MOVING LOADS
R 1 max = V1 max (at x = 0) . . . . . . . . . . .

a
l
= P 2 − 

when a <, (2 − √
2 ) l . . . . . = .586 l
x
a
P
R1
under load 1 at x
P
R2
2
1
M max
1
l −
2
a
. .
2
=
P 
l −
2l 
a

2
2
when a > (2 − √
2 )l . . . . . = .586 l
l
with one load at center of span =
Pl
4
(Case 40)
42. SIMPLE BEAM—TWO UNEQUAL CONCENTRATED MOVING LOADS
R 1 max = V1 max (at x = 0) . . . . . . . . . . .
under P1 , at x =
P1 > P2
x
a
P1
R1
P2
R2
M max
P 2a 
1
l−
2  P1 + P2


= P1 + P2
l−a
l
= (P1 + P2 )
x2
l
M max may occur with larger
load at center of span and other
l
load off span (Case 40) . . . =
P1 l
4
GENERAL RULES FOR SIMPLE BEAMS CARRYING MOVING CONCENTRATED LOADS
l
P1
a
C.G.
R1
P2
R2
x
b
l
2
M
Moment
The maximum shear due to moving concentrated loads occurs at
one support when one of the loads is at that support. With several
moving loads, the location that will produce maximum shear must be
determined by trial.
The maximum bending moment produced by moving concentrated
loads occurs under one of the loads when that load is as far from one
support as the center of gravity of all the moving loads on the beam is
from the other support.
In the accompanying diagram, the maximum bending moment
occurs under load P1 when x = b . It should also be noted that this
condition occurs when the centerline of the span is midway between
the center of gravity of loads and the nearest concentrated load.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
BEAM DIAGRAMS AND FORMULAS
4 - 205
BEAM DIAGRAMS AND FORMULAS
Design properties of cantilevered beams
Equal loads, equally spaced
No. Spans
System
a
2
M1
M1
M1
A
B
3
A
b
b
M3
M3
M2
M2
M3
C
D
c
c
C
D
M1
M1
M1
M1
M4
A
E
4
A
E
d
M1
M1
b
D
M1
D
M1
M1
A
F
H
f
f
H
M3
C
M1
M5
H
G
3
F
A
4
P
2
P
P
5
P
P
2
P
2
P
P
P
P
Moments
P
P
2
M1
M2
M3
M4
M5
0.086PL
0.096PL
0.063PL
0.039PL
0.051PL
0.167PL
0.188PL
0.125PL
0.083PL
0.104PL
0.250PL
0.278PL
0.167PL
0.083PL
0.139PL
0.333PL
0.375PL
0.250PL
0.167PL
0.208PL
0.429PL
0.480PL
0.300PL
0.171PL
0.249PL
Reactions
P
D
M1
M3
H
M2
d
e
A
B
C
D
E
F
G
H
0.414P
1.172P
0.438P
1.063P
1.086P
1.109P
0.977P
1.000P
0.833P
2.333P
0.875P
2.125P
2.167P
2.208P
1.958P
2.000P
1.250P
3.500P
1.333P
3.167P
3.250P
3.333P
2.917P
3.000P
1.667P
4.667P
1.750P
4.250P
4.333P
4.417P
3.917P
4.000P
2.071P
5.857P
2.200P
5.300P
5.429P
5.557P
4.871P
5.000P
Cantilever
Dimensions
P
H
M3
P
2
M3
M3
M3
M3
P
2
b
M3
M3
M3
2
P
2
P
C
f
M3
M3
G
∞
D
f
M3
M5
M2
H
M3
H
e
M3
d
M3
M3
f
M3
M3
b
M3
M3
H
f
M3
A
f
f
M3
G
b
C
M1
F
M3
F
D
M1
G
M5
M2
d
M5
e
M3
M1
C
e
M3
G
d
Typical Span
Loading
H
M3
F
M2
M3
H
e
M3
d
M5
A
b
M3
M3
M3
M1
A
C
f
M3
M3
M1
n
D
f
M3
M2
C
M2
G
F
5
≥7
(odd)
M3
M3
M5
A
≥6
(even)
b
e
M3
a
b
c
d
e
f
0.172L
0.125L
0.220L
0.204L
0.157L
0.147L
0.250L
0.200L
0.333L
0.308L
0.273L
0.250L
0.200L
0.143L
0.250L
0.231L
0.182L
0.167L
0.182L
0.143L
0.222L
0.211L
0.176L
0.167L
0.176L
0.130L
0.229L
0.203L
0.160L
0.150L
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
P
2
4 - 206
BEAM AND GIRDER DESIGN
BEAM DIAGRAMS AND FORMULAS
CONTINUOUS BEAMS
MOMENT AND SHEAR COEFFICIENTS
EQUAL SPANS, EQUALLY LOADED
MOMENT
in terms of wl2
UNIFORM LOAD
SHEAR
in terms of wl
+.07
+.07
–.125
+.08
+.025
0 3
8
+.08
–.10
–.10
–.073
–.105
0 15
38
+.078
+.078
–.106
–.077
–.077
–.086
–.106
0 41
104
+.078
+.078
–.106
–.077
–.085
–.085
–.077
–.106
0 36
142
MOMENT
in terms of Pl
+.156
23 20
38
63 55
104
86 75
142
18 19
38
67 70
142
4 0
10
15 17
28
19 18
38
53 53
104
72 71
142
CONCENTRATED LOADS
at center
+.156
5 6
10
13 13
28
43 51
104
0
8
6 5
10
17 15
28
0 11
28
+.078
–.073
3
5
8
0 4
10
+.077
+.036
+.036
+.077
–.107
–.071
–.107
+.078
–.105
5
11 0
28
20 23
38
51 49
104
71 72
142
P
15 0
38
55 63
104
70 67
142
41 0
104
75 86
142
36 0
142
SHEAR
in terms of P
P
+.157
.31
+.178
+.10
P
+.175
–.15
+.13
+.11
–.119
–.119
+.222
+.111
+.111
.65
P
+.171
P
.50
.50
P
.65
.35
P
P
P
–.158
.34
MOMENT
in terms of Pl
.31
–.15
+.11
–.138
.69
P
.35
+.171
.69
+.222
.66
.54
.46
.50
.50
.46
.54
CONCENTRATED LOADS
at 1⁄3 points
.66
.34
SHEAR
in terms of P
P
P
P
P
–.333
.67
+.156
+.244
+.066
–.267
+.066 +.156
–.267
+.244
P
.73
+.24
+.146
+.076
–.281
+.099 +.122
–.211
+.122 +.099
–.211
+.076 +.146
–.281
+.24
P
.72
MOMENT
in terms of Pl
+.258
+.267
+.267
+.022 +.022
+.258
-.465
P
1.28
P
P
1.0
1.0
+.155
+.303
+.204
+.155
+.303
+.079 +.006
+.054 +.079
+.079 +.054
+.277
+.006 +.079
-.394
-.296
-.296
-.394
1.97
P P P
P P P
1.11
1.89
P
P
.93
.73
1.07
P
P
1.28
.72
1.87
1.40
P P P
1.97
P P P
1.50
P P P
1.60
P
SHEAR
in terms of P
P P P
+.314
+.128
+.314
+.097 +.003 +.003 +.097 +.282
-.372
-.372
P
1.27
CONCENTRATED LOADS
at 1⁄4 points
1.13
+.277
1.0
P
.93
.67
P
1.0
P
1.03
+.282
1.33
P
1.27
P
1.07
1.33
1.50
P P P
1.50
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
1.50
1.03
P P P
1.87
1.13
P P P
1.40
1.60
P P P
1.89
1.11
FLOOR DEFLECTIONS AND VIBRATIONS
4 - 207
FLOOR DEFLECTIONS AND VIBRATIONS
Serviceability
Serviceability checks are necessary in design to provide for the satisfactory performance
of structures. Chapter L of the LRFD Specification and Commentary contains general
guidelines on serviceability. In contrast with the factored forces used to determine the
required strength, the (unfactored) working loads are used in serviceability calculations.
The primary concern regarding the serviceability of floor beams is the prevention of
excessive deflections and vibrations. The use of higher strength steels and composite
construction has resulted in shallower and lighter beams. Serviceability has become a
more important consideration than in the past, as the design of more beams is governed
by deflection and vibration criteria.
Deflections and Camber
Criteria for acceptable vertical deflections have traditionally been set by the design
engineer, based on the intended use of the given structure. What is appropriate for an
office building, for example, may not be satisfactory for a hospital. An illustration of
deflection criteria is the following:
1. Live load deflections shall not exceed a specified fraction of the span (e.g., 1⁄360) nor a
specific quantity (e.g., one inch). A deeper and/or heavier beam shall be selected, if
necessary, to meet these requirements.
2. Under dead load, plus a given portion of the design live load (say, 10 psf), the floor
shall be theoretically level. Where feasible and necessary, upward camber of the beam
shall be specified.
Regarding camber, the engineer is cautioned that:
1. It is unrealistic to expect precision in cambering. The limits and tolerances given in
Part 1 of of this Manual for cambering of rolled beams are typical for mill camber.
Kloiber (1989) states that camber tolerances are dependent on the method used (hot
or cold cambering) and whether done at the mill or the fabrication shop. According to
the AISC Code of Standard Practice, Section 6.4.5: “When members are specified on
the contract documents as requiring camber, the shop fabrication tolerance shall be
−0 / +1⁄2 in. for members 50 ft and less in length, or −0 / + (1⁄2 in. + 1⁄8 in. for each 10 ft
or fraction thereof in excess of 50 ft in length) for members over 50 ft. Members
received from the rolling mill with 75 percent of the specified camber require no further
cambering. For purposes of inspection, camber must be measured in the fabricator’s
shop in the unstressed condition.” Some of the camber may be lost in transportation
prior to placement of the beam, due to vibration.
2. There are two methods for erection of floors: uniform slab thickness and level floor.
As a consequence of possible overcamber, the latter may result in a thinner concrete
slab for composite action and fire protection at midspan, and may cause the shear studs
to protrude above the slab.
3. Due to end restraint at the connections, actual beam deflections are often less than the
calculated values.
4. The deflections of a composite beam (under live load for shored construction, and
under dead and live loads for unshored) cannot be determined as easily and accurately
as the deflections of a bare steel beam. Equation C-I3-6 in Section I3.2 of the
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 208
BEAM AND GIRDER DESIGN
Commentary on the LRFD Specification provides an approximate effective moment
of inertia for partially composite beams.
5. Cambers of less than 3⁄4-in. should not be specified, and beams less than 24 ft in length
should not be cambered (Kloiber, 1989).
Vibrations
Annoying floor motion may be caused by the normal activities of the occupants.
Remedial action is usually very difficult and expensive and not always effective. The
prevention of excessive and objectionable floor vibration should be part of the design
process.
Several researchers have developed procedures to enable structural engineers to
predict occupant acceptability of proposed floor systems. Based on field measurement
of approximately 100 floor systems, Murray (1991) developed the following acceptability criterion:
D > 35Ao f + 2.5
(4-1)
where
D = damping in percent of critical
Ao = maximum initial amplitude of the floor system due to a heel-drop excitation, in.
f = first natural frequency of the floor system, hz
Damping in a completed floor system can be estimated from the following ranges:
Bare Floor: 1–3 percent
Lower limit for thin slab of lightweight concrete; upper limit for thick slab of normal
weight concrete.
Ceiling: 1–3 percent
Lower limit for hung ceiling; upper limit for sheetrock on furring attached to beams or
joists.
Ductwork and Mechanical: 1–10 percent
Depends on amount and attachment.
Partitions: 10–20 percent
If attached to the floor system and not spaced more than every five floor beams or the
effective joist floor width.
Note: The above values are based on observation only.
Beam or girder frequency can be estimated from
1⁄2
 gEIt 
f = K  3
 WL 
where
f = first natural frequency, hz
K = 1.57 for simply supported beams
= 0.56 for cantilevered beams
= from Figure 4-8 for overhanging beams
g = acceleration of gravity = 386 in./sec2
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(4-2)
FLOOR DEFLECTIONS AND VIBRATIONS
4 - 209
E = modulus of elasticity, psi
It = transformed moment of inertia of the tee-beam model, Figure 4-9, in.4 (to be
used for both composite and noncomposite construction)
W= total weight supported by the tee beam, dead load plus 10–25 percent of design
live load, lbs
L = tee-beam span, in.
System frequency is estimated using
1 1 1
= +
fs2 fb2 fg2
1.6
1.4
L
Frequency Coefficient, K
1.2
H
1.0
.8
gElt
f=K
WL3
.6
.4
.2
0
.2
.4
.6
.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
Cantilever - Backspan Ratio, H / L
Fig. 4-8. Frequency coefficients for overhanging beams.
Beam spacing S
Beam spacing S
Slab
Deck
de
Actual
Model
Fig. 4-9. Tee-beam model for computing transformed moment of inertia.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
2.4
4 - 210
BEAM AND GIRDER DESIGN
where
fs = system frequency, hz
fb = beam or joist frequency, hz
fg = girder frequency, hz
Amplitude from a heel-drop impact can be estimated from
Ao =
Aot
Neff
(4-3)
where
Ao = initial amplitude of the floor system due to a heel-drop impact, in.
Neff = number of effective tee beams
Aot = initial amplitude of a single tee beam due to a heel-drop impact, in.
= (DLF)maxds
(4-4)
where
(DLF)max = maximum dynamic load factor, Table 4-2
ds
= static deflection caused by a 600 lbs force, in.
See (Murray, 1975) for equations for (DLF)max and ds
For girders, Neff = 1.0.
For beams:
1. S < 2.5ft, usual steel joist-concrete slab floor systems.

πx 
 for x ≤ xo
Neff = 1 + 2Σ cos
2xo 

where
x = distance from the center joist to the joist under consideration, in.
xo = distance from the center joist to the edge of the effective floor, in.
= 1.06εL
L = joist span, in.
ε = (Dx / Dy)0.25
Dx = flexural stiffness perpendicular to the joists
= Ect3 / 12
Dy = flexural stiffness parallel to the joists
= EIt / S
Ec = modulus of elasticity of concrete, psi
E = modulus of elasticity of steel, psi
t = slab thickness, in.
It = transformed moment of inertia of the tee beam, in.4
S = joist spacing, in.
2. S > 2.5 ft, usual steel beam-concrete slab floor systems.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
(4-5)
BEAMS: OTHER SUBJECTS
4 - 211
Neff = 2.97 −
S
L4
+
17.3de 135EIT
(4-6)
where E is defined above and
S = beam spacing, in.
de = effective slab depth, in.
L = beam span, in.
Limitations:
15 ≤ (S / de) < 40; 1 × 106 ≤ (L4 / IT) ≤ 50 × 106
The amplitude of a two-way system can be estimated from
Aos = Aob + Aog / 2
where
Aos = system amplitude
Aob = Aot for beam
Aog = Aot for girder
Additional information on building floor vibrations can be obtained from the abovereferenced paper by Murray (1991) and the references cited therein.
BEAMS: OTHER SUBJECTS
Other topics related to the design of flexural members covered elsewhere in this Manual
include:
Beam Bearing Plates, in Part 11 (Volume II);
Beam Web Penetrations, in Part 12 (Volume II).
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
4 - 212
BEAM AND GIRDER DESIGN
Table 4-2.
Dynamic Load Factors for Heel-Drop Impact
f, hz
DLF
F, hz
DLF
F, hz
DLF
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
2.10
2.20
2.30
2.40
2.50
2.60
2.70
2.80
2.90
3.00
3.10
3.20
3.30
3.40
3.50
3.60
3.70
3.80
3.90
4.00
4.10
4.20
4.30
4.40
4.50
4.60
4.70
4.80
4.90
5.00
5.10
5.20
5.30
5.40
0.1541
0.1695
0.1847
0.2000
0.2152
0.2304
0.2456
0.2607
0.2758
0.2908
0.3058
0.3207
0.3356
0.3504
0.3651
0.3798
0.3945
0.4091
0.4236
0.4380
0.4524
0.4667
0.4809
0.4950
0.5091
0.5231
0.5369
0.5507
0.5645
0.5781
0.5916
0.6050
0.6184
0.6316
0.6448
0.6578
0.6707
0.6835
0.6962
0.7088
0.7213
0.7337
0.7459
0.7580
0.7700
5.50
5.60
5.70
5.80
5.90
6.00
6.10
6.20
6.30
6.40
6.50
6.60
6.70
6.80
6.90
7.00
7.10
7.20
7.30
7.40
7.50
7.60
7.70
7.80
7.90
8.00
8.10
8.20
8.30
8.40
8.50
8.60
8.70
8.80
8.90
9.00
9.10
9.20
9.30
9.40
9.50
9.60
9.70
9.80
9.90
0.7819
0.7937
0.8053
0.8168
0.8282
0.8394
0.8505
0.8615
0.8723
0.8830
0.8936
0.9040
0.9143
0.9244
0.9344
0.9443
0.9540
0.9635
0.9729
0.9821
0.9912
1.0002
1.0090
1.0176
1.0261
1.0345
1.0428
1.0509
1.0588
1.0667
1.0744
1.0820
1.0895
1.0969
1.1041
1.1113
1.1183
1.1252
1.1321
1.1388
1.1434
1.1519
1.1583
1.1647
1.1709
10.00
10.10
10.20
10.30
10.40
10.50
10.60
10.70
10.80
10.90
11.00
11.10
11.20
11.30
11.40
11.50
11.60
11.70
11.80
11.90
12.00
12.10
12.20
12.30
12.40
12.50
12.60
12.70
12.80
12.90
13.00
13.10
13.20
13.30
13.40
13.50
13.60
13.70
13.80
13.90
14.00
14.10
14.20
14.30
14.40
1.1770
1.1831
1.1891
1.1949
1.2007
1.2065
1.2121
1.2177
1.2231
1.2285
1.2339
1.2391
1.2443
1.2494
1.2545
1.2594
1.2643
1.2692
1.2740
1.2787
1.2834
1.2879
1.2925
1.2970
1.3014
1.3058
1.3101
1.3143
1.3185
1.3227
1.3268
1.3308
1.3348
1.3388
1.3427
1.3466
1.3504
1.3541
1.3579
1.3615
1.3652
1.3688
1.3723
1.3758
1.3793
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
REFERENCES
4 - 213
REFERENCES
Allison, H., 1991, Low- and Medium-Rise Steel Buildings, AISC Steel Design Guide
Series No. 5, American Institute of Steel Construction, Chicago, IL.
American Institute of Steel Construction, 1983, Torsional Analysis of Steel Members,
AISC, Chicago.
Fisher, J. M. and M. A. West, 1990, Serviceability Design Considerations for Low-Rise
Buildings, AISC Steel Design Guide Series No. 3, AISC, Chicago.
Kloiber, L. A., 1989, “Cambering of Steel Beams,” Steel Structures: Proceedings of
Structures Congress ’89, American Society of Civil Engineers (ASCE), New York.
Murray, T. M., 1991, “Building Floor Vibrations,” Proceedings of the 1991 National Steel
Construction Conference, AISC, Chicago.
Zahn, C. J., 1987, “Plate Girder Design Using LRFD,” Engineering Journal, 1st Qtr.,
AISC, Chicago.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5-1
PART 5
COMPOSITE DESIGN
OVERVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-3
COMPOSITE BEAMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-5
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-5
Design Flexural Strength (Positive) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-5
Concrete Flange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-7
Shear Connectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-8
Strength During Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-8
Lateral Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-9
Design Shear Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-9
Lower Bound Moment of Inertia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-9
Composite Beam Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-10
Preliminary Section Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-11
Floor Deflections and Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-12
Selection Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-18
Lower Bound Elastic Moment of Inertia Tables . . . . . . . . . . . . . . . . . . . . . . 5-50
COMPOSITE COLUMNS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-67
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-67
Combined Axial Compression and Bending (Interaction) . . . . . . . . . . . . . . . . . 5-69
COMPOSITE COLUMNS—W SHAPES ENCASED IN CONCRETE . . . . . . . . . . 5-73
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-73
Tables: fc′ = 3.5 ksi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-74
Tables: fc′ = 5 ksi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-86
Tables: fc′ = 8 ksi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-98
COMPOSITE COLUMNS—CONCRETE-FILLED STEEL PIPE AND
STRUCTURAL TUBING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-110
General Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-110
Steel Pipe Filled with Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-110
Structural Tubing Filled with Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-110
Tables: Steel Pipe (fc′ = 3.5 ksi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-111
Tables: Steel Pipe (fc′ = 5 ksi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-113
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5-2
COMPOSITE DESIGN
Tables: Square Structural Tubing (fc′ = 3.5 ksi) . . . . . . . . . . . . . . . . . . . . . 5-115
Tables: Square Structural Tubing (fc′ = 5 ksi) . . . . . . . . . . . . . . . . . . . . . . . 5-122
Tables: Rectangular Structural Tubing (fc′ = 3.5 ksi) . . . . . . . . . . . . . . . . . . . 5-129
Tables: Rectangular Structural Tubing (fc′ = 5 ksi) . . . . . . . . . . . . . . . . . . . . 5-136
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-143
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
OVERVIEW
5-3
OVERVIEW
Tables are given for the design of composite beams and columns.
Composite Beam tables are located as follows:
Selection Tables, Fy = 36 ksi, begin on . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-18
Selection Tables, Fy = 50 ksi, begin on . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-34
Lower Bound Elastic Moment of Inertia Tables begin on . . . . . . . . . . . . . . . . . 5-50
Composite Column tables are located as follows:
W Shapes Encased in Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-74
Concrete-Filled Steel Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-111
Concrete-Filled Structural Tubing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-115
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5-4
COMPOSITE DESIGN
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5-5
COMPOSITE BEAMS
General Notes
The Composite Beam Tables can be used for the design and analysis of simple composite
steel beams. Values for the design flexural strength φMn for rolled I-shaped beams with
yield strengths of 36 ksi and 50 ksi are tabulated, as well as lower bound moments of
inertia. The values tabulated are independent of the concrete flange properties. The
strength evaluation of the concrete flange portion of the composite section is left to the
design engineer. The preparation of these tables is based upon the fact that the location
of the plastic neutral axis (PNA) is uniquely determined by the horizontal shear force
ΣQn at the interface between the steel section and the concrete slab. With the knowledge
of the location of the PNA and the distance to the centroid of the concrete flange force
ΣQn, the design flexural strengths φMn for the rolled section can be computed.
Design Flexural Strength (Positive)
The design flexural strength of simple steel beams with composite concrete flanges is
computed from the equilibrium of internal forces using the plastic stress distribution as
shown in Figure 5-1:
φMn = φTTot y = φCToty
where
φ = 0.85
TTot = sum of tensile forces = Fy × (tensile force beam area)
CTot = sum of compressive forces = concrete flange force + Fy × (compressive force
beam area)
y = moment arm between centroid of tensile force and the resultant compressive
force
The model used in the calculation of the design strengths tabulated herein is given in
Figure 5-2. A summary of the model properties follows:
As = area of steel cross section, in.2
Af = flange area = bf × tf, in.2
Aw = web area = (d − 2k)tw, in.2
0.85fc ′
b
Cconc
a
Cstl
PNA
Fy
TTot = Tstl
Fy
Fig. 5-1. Plastic stress distribution.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
C Tot = Cconc + Cstl
y
5-6
COMPOSITE DESIGN
Kdep = k − tf, in.
Karea = (As − 2Af − Aw) / 2, in.2
Limitations for the tabulated values include the following:
Fy
(d − 2k) / tw ≤ 640 / √
and
ΣQn (min.) = 0.25AsFy
The limitation of ΣQn (min.) is not required by the Specification, but is deemed to be
a practical minimum value. Design strength moment values are tabulated for plastic
neutral axis (PNA) locations at the top and intermediate quarter points through the
thickness of the steel beam top flange. In addition, PNA locations are computed at the
point where ΣQn equals 0.25AsFy, and the point where ΣQn is the average of the minimum
value of (0.25AsFy) and the value of ΣQn when the PNA is at the bottom of the top flange
(see Figure 5-3).
To use the tables, select a valid value of ΣQn, determine the appropriate value of Y2
and read the design flexural strength moment φMn directly. Values for Y1 are also
tabulated for convenience. The parameters Y1 and Y2 are defined as follows:
Y1 = distance from PNA to beam top flange
Y2 = distance from concrete flange force to beam top flange
Valid values for ΣQn are the smaller of the following three expressions (LRFD
Specification Section I5):
0.85fc′Ac
AsFy
nQn
bf
tf
K dep
k
K area
K dep
tw
d
d – 2k
K dep
tf
k
Fig. 5-2. Composite beam model.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5-7
where
fc′
Ac
As
Fv
n
= specified compressive strength of concrete, ksi
= area of concrete slab within effective width, in.2
= area of steel cross section, in.2
= specified minimum yield stress, ksi
= number of shear connectors between the point of maximum positive moment
and the point of zero moment to either side
Qn = shear capacity of single shear connector, kips
Concrete Flange
According to LRFD Specification Section I3.1 the effective width of the concrete slab
on each side of the beam centerline shall not exceed:
a. one-eighth of the beam span, center to center, of supports;
b. one-half the distance to the centerline of the adjacent beams; or
c. the distance to the edge of the slab.
The maximum concrete flange force is equal to 0.85 fc′Ac where Ac is based on the
actual slab thickness, tc. However, often the maximum concrete flange force exceeds the
maximum capacity of the specified steel beam. In that case, the effective concrete flange
force is determined from a value of ΣQn, which will be the smaller of AsFy or nQn. The
effective concrete flange force is:
b
Ycon
Location of
effective concrete
flange force (∑Qn)
a/
2
a
Y2
TFL (pt. 1)
BFL (pt. 5)
6
7
Y1 (varies—see figure below)
Y1 = Distance from top of steel flange to any
of the seven tabulated PNA locations
∑ Qn (@ pt. 5) + ∑Q n (@ pt. 7)
∑ Qn (@ point
6 )=
∑ Qn (@ point
7 ) = .25A sFy
Beam
top flange
2
4 Equal
spaces
1
2
3
4
5
PNA FLANGE LOCATIONS
Fig. 5-3. Composite beam table parameters.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
TFL
tf
BFL
5-8
COMPOSITE DESIGN
ΣQn = Cconc = 0.85fc′ba
where
Cconc = effective concrete flange force, kips
b
= effective concrete flange width, in.
a
= effective concrete flange thickness, in.
The basis of the design of most composite beams will be the relationship:
a=
ΣQn
0.85fc′b
From this relationship, the value of Y2 can be computed as:
Y2 = Ycon − a / 2
where
Ycon = distance from top of steel beam to top of concrete, in.
Shear Connectors
Shear connectors must be headed steel studs, not less than four stud diameters in length
after installation, or hot-rolled steel channels. Shear connectors must be embedded in
concrete slabs made with ASTM C33 aggregate or with rotary kiln produced aggregates
conforming to ASTM C330, with concrete unit weight not less than 90 pcf.
The nominal strength of one stud shear connector embedded in a solid concrete slab is:
Qn = 0.5Asc √

fc′Ec ≤ AscFu
(I5-1)
where
Asc = cross-sectional area of a stud shear connector, in.2
fc′ = specified concrete compressive strength, ksi
Fu = minimum specified tensile strength of stud, ksi
Ec = modulus of elasticity of concrete, ksi
= (w1.5)√
fc ′
w = unit weight of concrete, lb/cu ft
The nominal shear strengths of 3⁄4-in. headed studs embedded in concrete slabs are
listed in Table 5-1.
Note the effective shear strengths of studs used in conjunction with composite or
non-composite metal forms may be affected by the shape of the deck and spacing of the
studs. See LRFD Specification Sections I3.5 and I5.6.
Strength During Construction
When temporary shores are not used during construction, the steel section must have
sufficient strength to support the applied loads prior to the concrete attaining 75 percent
of the specified concrete strength fc′ (LRFD Specification Section I3.4). The effect of
deflection on unshored steel beams during construction should be considered.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5-9
Table 5-1.
Nominal Stud Shear Strength Qn (kips) for 3⁄4-in Headed Studs
fc′
(ksi)
w
(lbs/cu. ft)
Qn
(kips)
3.0
3.0
3.5
3.5
4.0
4.0
115
145
115
145
115
145
17.7
21.0
19.8
23.6
21.9
26.1
Lateral Support
Adequate lateral support for the compression flange of the steel section will be provided
by the concrete slab after hardening. During construction, however, lateral support must
be provided, or the design strength must be reduced in accordance with Section F1 of the
LRFD Specification. Steel deck with adequate attachment to the compression flange will
usually provide the necessary lateral support. For construction using fully encased beams,
particular attention should be given to lateral support during construction.
Design Shear Strength
The design shear strength of composite beams is determined by the strength of the steel
web, in accordance with the requirements of Section F2 of the LRFD Specification.
Lower Bound Moment of Inertia
With regard to serviceability, a table of lower bound moments of inertia of composite
sections is included to assist in the evaluation of deflection. If calculated deflections using
the lower bound moment of inertia are acceptable, a complete elastic analysis of the
composite section can be avoided.
The lower bound moment of inertia is based on the area of the beam and an equivalent
concrete area of ΣQn / Fy. The analysis includes only the horizontal shear force transferred
by the shear connectors supplied; and, thus, neglects the contribution of the concrete
flange not considered in the plastic distribution of forces (see Figure 5-4). The lower
bound moment of inertia, therefore, is the moment of inertia of the section at the factored
(ultimate) load. This is smaller than the moment of inertia at service loads where
deflection is calculated. The value for the lower bound moment of inertia can be
calculated as follows:
ILB = Ix + As YENA −

2
d   ΣQn 
+
(d + Y2 − YENA)2
2   Fy 
where
YENA = distance from bottom of beam to elastic neutral axis (ENA)
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 10
COMPOSITE DESIGN
=
 Asd  ΣQn 

 2 +  F  (d + Y2)
 y 


 ΣQn 

As +  F 
 y 

Composite Beam Reactions
Design reactions for symmetrically loaded composite beams may be computed using the
Composite Beam Tables. Two situations will be considered. First, an upper bound value
for a beam reaction may be computed neglecting the composite concrete flange properties
other than concrete strength. Second, a more refined value for a beam reaction can be
computed if the properties of the composite concrete flange are determined initially.
When the properties of the composite concrete flange have not been computed, a
conservative value for the maximum horizontal shear between the composite concrete
slab and the steel section (ΣQn) may be taken as the smaller of AsFs or nQn. Here, n is the
number of headed studs between the reaction point and point of maximum moment. The
value of Qn may be taken from Table 5-1 or determined from LRFD Specification Section
I5. A value for φMn of the composite section may be obtained from the Composite Beam
Tables using the sum of horizontal shear ΣQn as described above. In this case, Y2 is defined
as the distance from the top of the steel beam to the top of the concrete slab. The design
reaction may be determined from the value of φMn as discussed in the following
paragraph.
When the properties of the concrete flange have been computed (effective width and
depth), a slightly different method is used to find φMn. The stud efficiency can be
determined in accordance with Section I5 of the LRFD Specification, or Table 5-1 can
be used for 3⁄4-in. diameter stud shear connectors. The value for the sum of the horizontal
shear force ΣQn can be taken as the smaller of nQn, AsFy, or 0.85fc′Ac, where fc′ is the
concrete cylinder strength (ksi) and Ac is the maximum permitted concrete flange area
(LRFD Specification Section I5.2). The distance Y2 is the distance from the top of the
steel beam to the top of the concrete slab less [ΣQn / (0.85fc′b)] / 2. Using these values
for ΣQn and Y2, the value for φMn can be selected from the Composite Beam Tables.
Equivalent concrete area =
∑Qn
Fy
Y2
d + Y2 – YENA
ENA
d
YENA
Fig. 5-4. Moment of inertia.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 11
The design beam reaction for a symmetrically loaded composite beam may be
computed from known values of φMn and the span length as:
R = CcφMn / L
where
R = design beam reaction, kips
Cc = coefficient from Figure 5-5
φMn = composite beam flexural design strength, kip-ft
L = span length, ft
Preliminary Section Selection
When using the Composite Beam Tables, the approximate beam weight per unit length
required for several different beam depths may be calculated as follows:
Mu(12)


Beam weight (lb/ft) = 
 3.4
(d
/
2
+
Y
−
a
/
2
)φ
F
con
y


where
Mu = required flexural strength, kip-ft
d = nominal beam depth, in.
Ycon = distance from top of steel beam to top of concrete slab, in.
a = effective concrete slab thickness, in.
Fy = steel yield stress, ksi
φ = 0.85
3.4 = ratio of the weight of a beam to its area, lb/in.2
For convenience in the preliminary selection phase the nominal depth may be used. A
value for a/2 must also be selected. For relatively light sections and loads, this value can
be assumed to be one inch. With the PNA at the top of the steel beam, i.e., ΣQn = AsFy,
the flexural design strength is:
φMn = φAsFy (d / 2 + Ycon − a / 2) / 12
where
φMn = flexural design strength, kip-ft
As = steel beam cross-sectional area, in.2
Uniform
load
R
Pu
R
Cc = 4
R
Pu
R
Pu
R
Cc = 2
Pu Pu Pu
R
Cc = 3
R=
Cc φM n
L
Fig. 5-5. Beam reaction coeficients.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
R
R
Cc = 3
5 - 12
COMPOSITE DESIGN
Floor Deflections and Vibrations
Refer to the discussion of Floor Deflections and Vibrations at the end of Part 4 of this
LRFD Manual.
EXAMPLE 5-1
Given:
Determine the beam, with Fy = 50 ksi, required to support a service live
load of 1.3 kips/ft and a service dead load of 0.9 kips/ft. The beam span
is 30 ft and the beam spacing 10 ft. The slab is 31⁄4-in. 1ight weight
concrete (fc′ = 3.5 ksi, 115 pcf) supported by a 3-in. deep composite
metal deck with an average rib width of six inches. The ribs are oriented
perpendicular to the beam. Shored construction is specified. Also,
determine the number of 3⁄4-in. diameter headed studs required and the
service live load deflection.
Solution:
A. Load tabulation:
LL
DL
Total
Service load
(kips/ft)
1.3
0.9
2.2
(L.F.)
(1.6)
(1.2)
Factored load
(kips/ft)
2.1
1.1
3.2
B. Flexural design strength:
Beam moments
Mu = 3.2(30)2/8 = 360 kip-ft
MLL = 1.3(30)2/8 = 146 kip-ft
C. Select section and determine properties:
At this point, go directly to the Composite Beam Tables and select
a section or compute a preliminary trial section size using the
formula:

Mu(12)

Beam weight = 
 3.4
(d
/
2
+
Y
−
a
/2)φF
con
y

where
Ycon = 3 + 3.25 = 6.25 in.
a / 2= 1 in. (estimate)
φ = 0.85
Fy = 50 ksi
Mu(12)(3.4)
d/2
φFy
16
346
8
d
18
346
9
(Ycon − a / 2)
Beam Weight
5.25
26
5.25
24
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 13
From the results above, a W16×26 would be the most appropriate
selection.
Let ΣQn = AsFy = 7.68(50) = 384 kips.
The effective width of the concrete flange is

≤ 2 × L / 8 = 2 × 30 ft / 8 = 7.5 ft = 90 in. (gover ns)
10 ft spacing
ΣQn
384
areq’d =
=
= 1.43 in.
0.85fc′b 0.85(3.5)(90)
Y2 = 6.25 − 1.43 / 2 = 5.53 in.
b
By interpolation from the Composite Beam Tables for a W16×26
and a value of Y2 equal to 5.53 in.,
φMn = 363 + (0.03 / 0.50)(377 − 363)
= 364 kip-ft > 360 kip-ft req’d o.k.
The selected section is adequate for Y2 = 5.5 in. and Y1 = 0.0 in.,
for which φMn = 363 kip-ft
D. Compute number of studs required:
The stud reduction is calculated to be:
Reduction factor =
0.85
(wr / hr)(Hs / hr − 1.0) ≤ 1.0
Nr
√
Reductionfactor=
0.85
(6 / 3)(5.5 / 3 − 1.0) = 1.0
2
√
(I3-1)
where
Nr = number of stud connectors in one rib; not to exceed three
in computations, although more than three may be installed
wr = average width of rib, in.
hr = nominal rib height, in.
Hs = length of stud connector after welding, in.; not to exceed
the value (hr + 3) in computations, although actual length
may be greater. Also must not be less than four stud
diameters
The value for Hs = 5.5 was selected to ensure the stud capacity
reduction factor is 1.0.
The number of studs required is:
with Qn = 19.8 kips (Table 5-1)
2(ΣQn) / Qn = 2(384) / 19.8 = 38.8, say 40 studs
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 14
COMPOSITE DESIGN
E. Check deflection:
For the selected section, a W16×26, Fy = 50 ksi, Y2 = 5.5 in. and
Y1 = 0.0 in.; from the Elastic Moment of Inertia Tables one can find
the lower bound moment of inertia is 985 in.4 Thus, the service live
load deflection can be calculated as follows (see LRFD Manual
Part 4):
∆LL =
MLLL2 146(30)2
L
L
=
= 0.83 in. =
<
o.k.
434 360
161ILB 161(985)
F. Shear check:
Vu = 3.2(15) = 48 kips
φVn = φ0.6FywAw
= (0.9)(0.6)(50)(15.69 × 0.250)
= 106 kips > 48 kips req’d o.k.
EXAMPLE 5-2
Given:
Determine the beam, with Fy = 50 ksi, required to support a service live
load of 250 psf and a service dead load of 90 psf. The beam span is
40 ft and the beam spacing is 10 ft. Assume 3 in. metal deck is used
with a 4.5 in. slab of 4 ksi normal weight concrete (145 pcf). The stud
reduction factor is 1.0. Unshored construction is specified. Determine
the beam size and service dead and live load deflections. Also select a
non-composite section (no shear connectors).
Solution:
A. Load tabulation:
LL
DL
Total
Service load
(kips/ft)
2.5
0.9
3.4
(L.F.)
(1.6)
(1.2)
Factored load
(kips/ft)
4.0
1.1
5.1
B. Beam moments:
Mu = 5.1(40)2 / 8 = 1,020 kip-ft
MLL = 2.5(40)2 / 8 = 500 kip-ft
MDL = 0.9(40)2 / 8 = 180 kip-ft
C. Select section and determine properties:
Assume a = 2 in.; therefore, take Y2 = 7.5 − 2 / 2 = 6.5 in. From the
Composite Beam Tables, for Fy = 50 ksi and Y2 = 6.5 in., W21×62,
W24×55, and W24×62 are possible sizes.
Try a W24×55:
Fy = 50 ksi
Y2 = 6.5 in.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 15
Y1 = 0.0 in.
Qn = 810 kips
φMn = 1,050 kip-ft
Compute Y2 for ΣQn = 810 kips:
2 × L / 8 = 2 × 40 ft / 8 = 10 ft
b ≤
10 ft spacing
= 120 in.
ΣQn
810
=
= 1.99
a =
0.85fc′b 0.85(4)(120)
Y2 = 7.5 − 1.99 / 2 = 6.5 in.
D. Compute the number of studs required:
Qn = 26.1 kips (Table 5-1)
Number of studs = (2)ΣQn / Qn = 2(810) / 26.1 = 62.1, say 64 studs
E. Construction phase strength check:
A construction live load of 20 psf will be assumed. From the LRFD
Specification (Section A4.1), the relevant load combinations are
1.4D
= 1.4 × 0.9 = 1.26 k/ft
1.2D + 1.6L = 1.2 × 0.9 + 1.6 × 0.2 = 1.40 k/ft
= 1.40 × (40)2 / 8 = 280 kip-ft
Mu
From the Composite Beam Tables for a W24×55 with Fy = 50 ksi,
and assuming adequate lateral support is provided by the attachment
of the steel deck to the compression flange,
φMn = φMp = 503 kip-ft > 280 kip-ft
F. Service load deflections:
Assume that the wet concrete load moment is equal to the service
dead load moment. With Ix = 1,350 in.4 for a W24×55,
∆DL =
180(40)2
= 1.33 in.
161(1,350)
For the W24×55 with Y2 = 6.5 in. and Y1 = 0.0 in., the lower bound
moment of inertia can be found in the Lower Bound Elastic Moment
of Inertia Tables; ILB = 4,060 in.4
500(40)2
= 1.22 in.
161(4,060)
L
L
<
o.k.
=
∆LL =
393
360
Specify a beam camber of 11⁄4-in. to overcome the dead load
deflection.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 16
COMPOSITE DESIGN
G. Check shear:
Vu = 5.1(40) / 2 = 102 kips
φV = φ(0.6)FywAw
= (0.9)(0.6)(50)(23.57 × 0.395)
= 251 kips > 102 kips o.k.
H. Final section selection:
Use: W24×55, Fy = 50 ksi, camber 11⁄4-in., 64 studs, 3⁄4-in. diameter
(32 each side of midspan)
I. Noncomposite section:
Considering the given problem without shear connectors (i.e., noncomposite), a steel section can be selected from the φMp values
tabulated under each section in either the Composite Beam Tables
or the Load Factor Design Selection Tables.
For Mu = 1,020 kip-ft, select a W27×94, Fy = 50 ksi, with a φMp
flexural design strength equal to 1,040 kip-ft.
∆DL =
180(40)2
= 0.55 in.
161(3,270)
∆LL =
500(40)2
= 1.52 in. > L / 360
161(3,270)
For ∆ = L / 360 = 1.33 in.
Ireq’d =
500(40)2
= 3,736 in.4
161(1.33)
Use: W30×99, Fy = 50 ksi, φMn = φbMp = 1,170 kip-ft
EXAMPLE 5-3
Given:
A W21×44, Fy = 50 ksi, steel girder spans 30 feet and supports
intermediate beams at the third points. A total of fifty 3⁄4-in. diameter
headed studs are applied to the beam as follows: 24 between each
support and the beams at the one-third points, and two between the
intermediate beams. The slab consists of 31⁄4-in. light-weight concrete
(115 pcf) with a specified design strength of 3.5 ksi over a 3-in. deep
composite metal deck with an average rib width of six inches. The ribs
are oriented parallel to the beam centerline. Determine the design beam
reactions.
Solutions:
For studs in a single row the spacing between the support and first
intermediate beam would be 10(12) / 24 = 5.0 in. which is greater than
the specified minimum of six stud diameters (LRFD Specification
Section I5.6). Since wr / hr = 6 / 3 = 2 is greater than 1.5, the stud
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 17
reduction factor is not necessary (LRFD Specification I3.5c). Therefore, from Table 5.1, the stud shear strength is:
ΣQn = nQn = 24(19.8) = 475 kips
For ΣQn = 475 kips, the required effective concrete flange thickness
can be calculated to be:
a =
475
= 1.77 in.
0.85(3.5)(7.5)(12)
Y2 = 3 + 3.25 − 1.77 / 2 = 5.36 in.
Beam reaction:
From the Composite Beam Selection Table, for a W21×44, Fy = 50 ksi,
ΣQn = 475 kips places the PNA at Y1 = 0.27 in.
For Y2 = 5.36 in. and Y1 = 0.27 in., φMn = 655 kip-ft
R = CcφMn / L
= 3(655) / 30
= 65.5 kips
where
R = design reaction, kips
Cc = coefficient from Figure 5-5
φMn = flexural design strength of beam, kip-ft
L = span length, ft
Note: The beam weight was neglected in this example.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 18
COMPOSITE DESIGN
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
Kip-ft
W40×297
3590
W 40 X 278 3210
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
0.00
0.41
0.83
1.24
1.65
4.59
8.17
3150
2680
2210
1740
1270
1030
787
4890
4810
4720
4620
4510
4420
4280
5000
4910
4800
4690
4550
4460
4310
5110
5000
4880
4750
4600
4500
4340
5220
5100
4960
4810
4640
4540
4370
5330
5190
5040
4870
4690
4570
4390
5440
5290
5120
4930
4730
4610
4420
5550
5380
5190
4990
4780
4640
4450
5670
5480
5270
5050
4820
4680
4480
5780
5570
5350
5120
4870
4720
4500
5890
5660
5430
5180
4910
4750
4530
6000
5760
5510
5240
4960
4790
4560
TFL 0.00
2
0.45
3
0.91
4
1.36
BFL 1.81
6
5.64
7 10.06
2940
2550
2160
1770
1380
1060
736
4610
4540
4470
4380
4280
4160
3930
4710
4630
4550
4450
4330
4190
3960
4810
4730
4620
4510
4380
4230
3980
4920
4820
4700
4570
4430
4270
4010
5020
4910
4780
4640
4480
4310
4040
5130
5000
4850
4700
4530
4340
4060
5230
5090
4930
4760
4580
4380
4090
5340
5180
5010
4820
4630
4420
4110
5440
5270
5080
4890
4680
4460
4140
5540
5360
5160
4950
4730
4490
4170
5650
5450
5240
5010
4780
4530
4190
TFL
2
3
4
BFL
6
7
W40×277
3380
TFL
2
3
4
BFL
6
7
0.00
0.39
0.79
1.18
1.58
4.25
7.60
2930
2480
2030
1580
1130
932
732
4530
4460
4380
4280
4170
4110
3990
4630
4550
4450
4340
4210
4140
4020
4740
4630
4520
4390
4250
4170
4050
4840
4720
4590
4450
4290
4210
4070
4940
4810
4660
4510
4330
4240
4100
5050
4900
4740
4560
4370
4270
4120
5150
4990
4810
4620
4410
4300
4150
5250
5070
4880
4670
4450
4340
4180
5360
5160
4950
4730
4490
4370
4200
5460
5250
5020
4790
4540
4400
4230
5570
5340
5100
4840
4580
4440
4250
W40×264
3050
TFL
2
3
4
BFL
6
7
0.00
0.43
0.87
1.30
1.73
5.49
9.90
2790
2420
2050
1680
1310
1000
698
4350
4300
4230
4140
4050
3930
3730
4450
4380
4300
4200
4100
3970
3750
4550
4470
4370
4260
4140
4000
3780
4650
4550
4440
4320
4190
4040
3800
4750
4640
4520
4380
4240
4070
3820
4850
4720
4590
4440
4280
4110
3850
4950
4810
4660
4500
4330
4150
3870
5050
4900
4730
4560
4380
4180
3900
5140
4980
4810
4620
4420
4220
3920
5240
5070
4880
4680
4470
4250
3950
5340
5150
4950
4740
4510
4290
3970
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 19
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W40×249
Kip-ft
3020
TFL
2
3
4
BFL
6
7
0.00
0.36
0.71
1.07
1.42
4.06
7.47
2640
2240
1830
1430
1030
844
660
4050
3990
3920
3840
3750
3690
3580
4150
4070
3980
3890
3780
3720
3610
4240
4150
4050
3940
3820
3750
3630
4330
4230
4110
3990
3850
3770
3650
4430
4310
4180
4040
3890
3800
3680
4520
4390
4240
4090
3930
3830
3700
4610
4470
4310
4140
3960
3860
3720
4710
4550
4370
4190
4000
3890
3750
4800
4630
4440
4240
4040
3920
3770
4900
4700
4500
4290
4070
3950
3790
4990
4780
4570
4340
4110
3980
3820
W40×235
2730
TFL
2
3
4
BFL
6
7
0.00
0.39
0.79
1.18
1.58
5.18
9.47
2480
2140
1810
1470
1130
876
620
3840
3790
3720
3650
3570
3480
3310
3930
3860
3790
3700
3610
3510
3330
4010
3940
3850
3760
3650
3540
3350
4100
4010
3920
3810
3690
3570
3370
4190
4090
3980
3860
3730
3600
3400
4280
4170
4040
3910
3770
3630
3420
4370
4240
4110
3960
3810
3660
3440
4450
4320
4170
4020
3850
3690
3460
4540
4390
4240
4070
3890
3730
3480
4630
4470
4300
4120
3930
3760
3510
4720
4540
4360
4170
3970
3790
3530
W40×215
2600
TFL
2
3
4
BFL
6
7
0.00
0.31
0.61
0.92
1.22
3.84
7.32
2280
1930
1590
1240
895
733
570
3470
3420
3360
3290
3210
3160
3080
3550
3480
3410
3330
3240
3190
3100
3630
3550
3470
3380
3280
3210
3120
3710
3620
3520
3420
3310
3240
3140
3790
3690
3580
3460
3340
3270
3160
3870
3760
3640
3510
3370
3290
3180
3950
3830
3690
3550
3400
3320
3200
4030
3900
3750
3600
3440
3340
3220
4110
3960
3810
3640
3470
3370
3240
4200
4030
3860
3680
3500
3400
3260
4280
4100
3920
3730
3530
3420
3280
W40×211
2440
TFL
2
3
4
BFL
6
7
0.00
0.35
0.71
1.06
1.42
4.99
9.35
2230
1930
1630
1330
1030
793
558
3430
3380
3330
3270
3200
3110
2960
3510
3450
3390
3310
3230
3140
2980
3590
3520
3440
3360
3270
3170
3000
3670
3590
3500
3410
3310
3200
3020
3740
3660
3560
3460
3340
3230
3040
3820
3720
3620
3500
3380
3250
3060
3900
3790
3670
3550
3420
3280
3080
3980
3860
3730
3600
3450
3310
3100
4060
3930
3790
3640
3490
3340
3120
4140
4000
3850
3690
3530
3370
3140
4220
4070
3910
3740
3560
3400
3160
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 20
COMPOSITE DESIGN
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W40×199
Kip-ft
2340
TFL
2
3
4
BFL
6
7
0.00
0.27
0.53
0.80
1.07
4.16
8.10
2100
1800
1500
1200
895
710
526
3180
3130
3080
3020
2960
2900
2800
3250
3200
3130
3070
2990
2930
2820
3330
3260
3190
3110
3020
2950
2830
3400
3320
3240
3150
3060
2980
2850
3480
3390
3290
3190
3090
3000
2870
3550
3450
3350
3240
3120
3030
2890
3620
3510
3400
3280
3150
3050
2910
3700
3580
3450
3320
3180
3080
2930
3770
3640
3500
3360
3210
3100
2950
3850
3710
3560
3400
3250
3130
2960
3920
3770
3610
3450
3280
3150
2980
W40×183
2110
TFL
2
3
4
BFL
6
7
0.00
0.31
0.61
0.92
1.22
4.76
9.16
1930
1670
1410
1160
896
690
483
2940
2900
2860
2810
2750
2680
2550
3010
2960
2910
2850
2780
2710
2570
3080
3020
2960
2890
2810
2730
2580
3150
3080
3010
2930
2850
2750
2600
3220
3140
3060
2970
2880
2780
2620
3290
3200
3110
3010
2910
2800
2640
3350
3260
3160
3050
2940
2830
2650
3420
3320
3210
3090
2970
2850
2670
3490
3380
3260
3130
3000
2880
2690
3560
3440
3310
3180
3040
2900
2700
3630
3500
3360
3220
3070
2930
2720
W40×174
1930
TFL
2
3
4
BFL
6
7
0.00
0.21
0.42
0.62
0.83
4.59
9.27
1840
1600
1370
1130
898
679
460
2750
2710
2680
2630
2590
2520
2380
2810
2770
2720
2670
2620
2540
2400
2880
2830
2770
2710
2650
2570
2410
2940
2880
2820
2750
2680
2590
2430
3010
2940
2870
2790
2720
2620
2450
3080
3000
2920
2830
2750
2640
2460
3140
3060
2970
2870
2780
2660
2480
3210
3110
3020
2910
2810
2690
2490
3270
3170
3060
2960
2840
2710
2510
3340
3230
3110
3000
2870
2740
2530
3400
3280
3160
3040
2910
2760
2540
W40×167
1870
TFL
2
3
4
BFL
6
7
0.00
0.26
0.51
0.77
1.03
5.00
9.85
1770
1550
1330
1110
896
669
442
2670
2630
2600
2560
2510
2430
2280
2730
2690
2640
2600
2540
2460
2300
2790
2740
2690
2630
2570
2480
2310
2850
2800
2740
2670
2610
2510
2330
2920
2850
2790
2710
2640
2530
2350
2980
2910
2830
2750
2670
2550
2360
3040
2960
2880
2790
2700
2580
2380
3100
3020
2930
2830
2730
2600
2390
3170
3070
2970
2870
2760
2620
2410
3230
3130
3020
2910
2800
2650
2420
3290
3180
3070
2950
2830
2670
2440
W40×149
1610
TFL 0.00
2
0.21
3
0.42
4
0.62
BFL 0.83
6
5.15
7 10.41
1580
1400
1220
1050
871
633
394
2360
2330
2300
2270
2240
2160
1990
2410
2380
2340
2310
2270
2180
2010
2470
2430
2390
2340
2300
2200
2020
2520
2480
2430
2380
2330
2220
2030
2580
2530
2470
2420
2360
2250
2050
2640
2580
2520
2460
2390
2270
2060
2690
2630
2560
2490
2420
2290
2070
2750
2680
2600
2530
2450
2310
2090
2800
2730
2650
2570
2480
2340
2100
2860
2780
2690
2600
2510
2360
2120
2920
2830
2730
2640
2540
2380
2130
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 21
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 36×300
Kip-ft
3400
TFL
2
3
4
BFL
6
7
0.00
0.42
0.84
1.26
1.68
3.97
6.69
3180
2680
2170
1670
1160
979
795
4590
4510
4410
4310
4180
4120
4020
4700
4600
4490
4360
4220
4150
4050
4810
4700
4570
4420
4260
4190
4080
4920
4790
4640
4480
4310
4220
4110
5040
4890
4720
4540
4350
4260
4140
5150
4980
4800
4600
4390
4290
4160
5260
5080
4880
4660
4430
4330
4190
5370
5170
4950
4720
4470
4360
4220
5490
5270
5030
4780
4510
4400
4250
5600
5360
5110
4840
4550
4430
4280
5710
5460
5180
4900
4590
4470
4300
W 36×280
3160
TFL
2
3
4
BFL
6
7
0.00
0.39
0.79
1.18
1.57
3.88
6.62
2970
2500
2030
1560
1090
916
742
4260
4180
4100
4000
3890
3830
3740
4360
4270
4170
4050
3930
3860
3770
4470
4360
4240
4110
3960
3890
3790
4570
4450
4310
4160
4000
3930
3820
4680
4540
4390
4220
4040
3960
3850
4780
4630
4460
4280
4080
3990
3870
4890
4710
4530
4330
4120
4020
3900
4990
4800
4600
4390
4160
4060
3920
5100
4890
4670
4440
4200
4090
3950
5200
4980
4740
4500
4230
4120
3980
5310
5070
4820
4550
4270
4150
4000
W 36×260
2920
TFL
2
3
4
BFL
6
7
0.00
0.36
0.72
1.08
1.44
3.86
6.75
2750
2330
1900
1470
1040
863
689
3930
3860
3780
3700
3600
3540
3450
4020
3940
3850
3750
3630
3570
3470
4120
4030
3920
3800
3670
3600
3500
4220
4110
3980
3850
3710
3630
3520
4320
4190
4050
3900
3740
3660
3550
4410
4270
4120
3960
3780
3690
3570
4510
4350
4190
4010
3820
3720
3600
4610
4440
4250
4060
3850
3750
3620
4710
4520
4320
4110
3890
3780
3640
4800
4600
4390
4160
3930
3820
3670
4900
4680
4450
4210
3960
3850
3690
W 36×245
2730
TFL
2
3
4
BFL
6
7
0.00
0.34
0.68
1.01
1.35
3.81
6.77
2600
2190
1790
1390
991
820
649
3680
3620
3550
3470
3380
3330
3240
3780
3700
3620
3520
3420
3360
3260
3870
3780
3680
3570
3450
3380
3280
3960
3860
3740
3620
3490
3410
3310
4050
3930
3810
3670
3520
3440
3330
4140
4010
3870
3720
3560
3470
3350
4240
4090
3930
3770
3590
3500
3380
4330
4170
4000
3820
3630
3530
3400
4420
4240
4060
3870
3660
3560
3420
4510
4320
4120
3910
3700
3590
3440
4600
4400
4190
3960
3730
3620
3470
W 36×230
2550
TFL
2
3
4
BFL
6
7
0.00
0.32
0.63
0.95
1.26
3.81
6.83
2430
2060
1690
1310
939
774
608
3440
3380
3320
3240
3160
3110
3020
3530
3450
3380
3290
3190
3140
3040
3610
3530
3440
3340
3230
3160
3070
3700
3600
3500
3380
3260
3190
3090
3780
3670
3560
3430
3290
3220
3110
3870
3750
3620
3480
3330
3250
3130
3960
3820
3670
3520
3360
3270
3150
4040
3890
3730
3570
3390
3300
3170
4130
3970
3790
3610
3430
3330
3200
4210
4040
3850
3660
3460
3360
3220
4300
4110
3910
3710
3490
3380
3240
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 22
COMPOSITE DESIGN
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 36×210
Kip-ft
2250
TFL
2
3
4
BFL
6
7
0.00
0.34
0.68
1.02
1.36
5.06
9.04
2220
1930
1630
1330
1030
794
556
3210
3160
3110
3050
2980
2890
2740
3280
3230
3170
3090
3020
2920
2760
3360
3300
3220
3140
3050
2950
2780
3440
3370
3280
3190
3090
2980
2800
3520
3430
3340
3240
3130
3010
2820
3600
3500
3400
3280
3160
3030
2840
3680
3570
3450
3330
3200
3060
2860
3760
3640
3510
3380
3240
3090
2880
3840
3710
3570
3420
3270
3120
2900
3920
3770
3630
3470
3310
3150
2920
3990
3840
3680
3520
3350
3170
2940
W 36×194
2070
TFL
2
3
4
BFL
6
7
0.00
0.32
0.63
0.95
1.26
4.94
8.93
2050
1780
1500
1230
953
733
513
2940
2900
2850
2800
2740
2660
2520
3020
2960
2910
2840
2770
2690
2540
3090
3030
2960
2890
2810
2710
2560
3160
3090
3010
2930
2840
2740
2580
3230
3150
3070
2970
2870
2760
2590
3310
3220
3120
3020
2910
2790
2610
3380
3280
3170
3060
2940
2820
2630
3450
3340
3220
3100
2970
2840
2650
3520
3400
3280
3150
3010
2870
2670
3600
3470
3330
3190
3040
2890
2680
3670
3530
3380
3230
3080
2920
2700
W 36×182
1940
TFL
2
3
4
BFL
6
7
0.00
0.29
0.59
0.89
1.18
4.89
8.92
1930
1670
1420
1160
904
693
482
2760
2720
2670
2620
2570
2490
2360
2820
2780
2720
2660
2600
2520
2380
2890
2840
2770
2710
2630
2540
2400
2960
2890
2820
2750
2660
2570
2410
3030
2950
2870
2790
2700
2590
2430
3100
3010
2920
2830
2730
2620
2450
3170
3070
2970
2870
2760
2640
2460
3230
3130
3020
2910
2790
2670
2480
3300
3190
3070
2950
2820
2690
2500
3370
3250
3120
2990
2860
2720
2520
3440
3310
3170
3030
2890
2740
2530
W 36×170
1800
TFL
2
3
4
BFL
6
7
0.00
0.28
0.55
0.83
1.10
4.84
8.89
1800
1560
1320
1090
847
649
450
2560
2520
2480
2440
2390
2320
2200
2620
2580
2530
2480
2420
2340
2210
2690
2640
2580
2520
2450
2370
2230
2750
2690
2620
2550
2480
2390
2240
2820
2750
2670
2590
2510
2410
2260
2880
2800
2720
2630
2540
2440
2280
2940
2860
2770
2670
2570
2460
2290
3010
2910
2810
2710
2600
2480
2310
3070
2970
2860
2750
2630
2500
2320
3130
3020
2910
2780
2660
2530
2340
3200
3080
2950
2820
2690
2550
2360
W 36×160
1680
TFL
2
3
4
BFL
6
7
0.00
0.26
0.51
0.77
1.02
4.82
8.97
1690
1470
1250
1030
811
617
423
2400
2360
2330
2290
2240
2170
2050
2460
2420
2370
2320
2270
2200
2070
2520
2470
2420
2360
2300
2220
2080
2580
2520
2460
2400
2330
2240
2100
2640
2570
2500
2430
2360
2260
2110
2700
2630
2550
2470
2380
2280
2130
2760
2680
2590
2510
2410
2310
2140
2820
2730
2640
2540
2440
2330
2160
2880
2780
2680
2580
2470
2350
2170
2940
2830
2730
2610
2500
2370
2190
3000
2890
2770
2650
2530
2390
2200
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 23
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
5
5.5
6
6.5
7
W 36×150
Kip-ft
1570
TFL
2
3
4
BFL
6
7
0.00 1590 2250 2300 2360 2410 2470 2530
0.24 1390 2220 2260 2310 2360 2410 2460
0.47 1190 2180 2220 2270 2310 2350 2390
0.71 983 2140 2180 2210 2250 2280 2320
0.94 781 2100 2130 2160 2190 2210 2240
4.83 589 2040 2060 2080 2100 2120 2140
9.08 398 1920 1930 1950 1960 1970 1990
In.
Kips
2
2.5
3
3.5
4
4.5
2580
2510
2430
2350
2270
2160
2000
2640
2560
2480
2390
2300
2190
2020
2700
2610
2520
2420
2330
2210
2030
2750
2660
2560
2460
2350
2230
2040
2810
2710
2600
2490
2380
2250
2060
W 36×135
1370
TFL
2
3
4
BFL
6
7
0.00 1430 2000 2050 2100 2150 2200 2260
0.20 1260 1980 2020 2070 2110 2160 2200
0.40 1090 1950 1990 2030 2060 2100 2140
0.59 919 1920 1950 1980 2020 2050 2080
0.79 749 1890 1910 1940 1970 1990 2020
4.96 553 1820 1840 1860 1880 1900 1920
9.50 357 1690 1710 1720 1730 1740 1760
2310
2240
2180
2110
2050
1940
1770
2360
2290
2220
2150
2070
1960
1780
2410
2330
2260
2180
2100
1980
1790
2460
2380
2300
2210
2130
2000
1810
2510
2420
2330
2240
2150
2020
1820
W 33×221
2310
TFL
2
3
4
BFL
6
7
0.00
0.32
0.64
0.96
1.28
3.76
6.48
2340
1980
1610
1250
889
737
585
3140
3090
3020
2950
2870
2820
2750
3230
3160
3080
3000
2900
2850
2770
3310
3230
3140
3040
2940
2880
2790
3390
3300
3200
3090
2970
2900
2810
3470
3370
3250
3130
3000
2930
2830
3560
3440
3310
3170
3030
2960
2850
3640
3510
3370
3220
3060
2980
2870
3720
3580
3420
3260
3090
3010
2890
3810
3650
3480
3310
3120
3030
2910
3890
3720
3540
3350
3160
3060
2930
3970
3790
3600
3400
3190
3090
2960
W 33×201
2080
TFL
2
3
4
BFL
6
7
0.00
0.29
0.58
0.86
1.15
3.67
6.51
2130
1800
1480
1150
824
678
532
2840
2790
2730
2670
2600
2560
2480
2910
2850
2790
2710
2630
2580
2500
2990
2920
2840
2750
2660
2600
2520
3070
2980
2890
2790
2690
2630
2540
3140
3050
2940
2830
2720
2650
2560
3220
3110
2990
2870
2750
2680
2580
3290
3170
3050
2920
2780
2700
2600
3370
3240
3100
2960
2810
2720
2620
3440
3300
3150
3000
2830
2750
2630
3520
3360
3200
3040
2860
2770
2650
3590
3430
3260
3080
2890
2800
2670
W 33×141
1390
TFL
2
3
4
BFL
6
7
0.00 1500 1980 2030 2080 2140 2190 2240
0.24 1300 1950 1990 2040 2090 2130 2180
0.48 1100 1920 1950 1990 2030 2070 2110
0.72 900 1880 1910 1940 1970 2010 2040
0.96 700 1840 1860 1890 1910 1940 1960
4.31 537 1790 1810 1820 1840 1860 1880
8.05 374 1690 1710 1720 1730 1740 1760
2300
2220
2150
2070
1990
1900
1770
2350
2270
2190
2100
2010
1920
1780
2400
2320
2230
2130
2040
1940
1800
2460
2360
2270
2170
2060
1960
1810
2510
2410
2300
2200
2090
1980
1820
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 24
COMPOSITE DESIGN
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
5
5.5
6
6.5
7
W 33×130
Kip-ft
1260
TFL
2
3
4
BFL
6
7
0.00 1380 1810 1860 1910 1960 2010 2060
0.21 1200 1780 1830 1870 1910 1950 2000
0.43 1020 1760 1790 1830 1860 1900 1940
0.64 847 1720 1750 1780 1810 1840 1870
0.86 670 1690 1710 1740 1760 1780 1810
4.39 507 1640 1660 1670 1690 1710 1730
8.29 345 1540 1550 1570 1580 1590 1600
In.
Kips
2
2.5
3
3.5
4
4.5
2100
2040
1970
1900
1830
1750
1610
2150
2080
2010
1930
1860
1760
1630
2200
2130
2050
1960
1880
1780
1640
2250
2170
2080
1990
1900
1800
1650
2300
2210
2120
2020
1930
1820
1660
W 33×118
1120
TFL
2
3
4
BFL
6
7
0.00 1250 1630 1680 1720 1760 1810 1850
0.19 1100 1610 1650 1690 1720 1760 1800
0.37 943 1580 1620 1650 1680 1720 1750
0.56 790 1560 1580 1610 1640 1670 1700
0.74 638 1530 1550 1570 1600 1620 1640
4.44 475 1480 1490 1510 1530 1540 1560
8.54 312 1380 1390 1400 1410 1420 1430
1900
1840
1780
1720
1660
1580
1450
1940
1880
1820
1750
1690
1590
1460
1980
1920
1850
1780
1710
1610
1470
2030
1960
1880
1810
1730
1630
1480
2070
2000
1920
1840
1750
1650
1490
W 30×116
1020
TFL
2
3
4
BFL
6
7
0.00 1230 1480 1530 1570 1610 1660 1700
0.21 1070 1460 1500 1530 1570 1610 1650
0.43 910 1430 1460 1500 1530 1560 1590
0.64 749 1400 1430 1460 1480 1510 1540
0.85 589 1370 1390 1410 1440 1460 1480
3.98 448 1330 1350 1360 1380 1390 1410
7.44 308 1250 1260 1270 1290 1300 1310
1740
1690
1630
1560
1500
1430
1320
1790
1720
1660
1590
1520
1440
1330
1830
1760
1690
1620
1540
1460
1340
1880
1800
1720
1640
1560
1470
1350
1920
1840
1750
1670
1580
1490
1360
W 30×108
934
TFL
2
3
4
BFL
6
7
0.00 1140 1370 1410 1450 1490 1530 1570
0.19 998 1350 1380 1420 1450 1490 1520
0.38 855 1320 1350 1380 1410 1440 1470
0.57 711 1300 1320 1350 1370 1400 1420
0.76 568 1270 1290 1310 1330 1350 1370
4.04 427 1230 1240 1260 1270 1290 1300
7.64 285 1150 1160 1170 1180 1190 1200
1610
1560
1500
1450
1390
1320
1210
1650
1590
1530
1470
1410
1330
1220
1690
1630
1570
1500
1430
1350
1230
1730
1660
1600
1520
1450
1360
1240
1770
1700
1630
1550
1470
1380
1250
W 30×99
842
TFL
2
3
4
BFL
6
7
0.00 1050 1250 1290 1320 1360 1400 1430
0.17 922 1230 1260 1300 1330 1360 1390
0.34 796 1210 1240 1270 1290 1320 1350
0.50 670 1190 1210 1240 1260 1280 1310
0.67 543 1170 1180 1200 1220 1240 1260
4.07 403 1120 1140 1150 1170 1180 1190
7.83 262 1040 1050 1060 1070 1080 1090
1470
1430
1380
1330
1280
1210
1100
1510
1460
1410
1350
1300
1220
1110
1550
1490
1440
1380
1320
1240
1120
1580
1520
1460
1400
1340
1250
1130
1620
1560
1490
1430
1360
1270
1140
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 25
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
5
5.5
6
6.5
7
W 27×102
Kip-ft
824
TFL
2
3
4
BFL
6
7
0.00 1080 1190 1230 1270 1300 1340 1380
0.21 930 1170 1200 1230 1270 1300 1330
0.42 781 1140 1170 1200 1230 1250 1280
0.62 631 1120 1140 1160 1180 1210 1230
0.83 482 1090 1100 1120 1140 1160 1170
3.41 376 1060 1070 1080 1100 1110 1120
6.26 270 1010 1010 1020 1030 1040 1050
In.
Kips
2
1420
1360
1310
1250
1190
1140
1060
1460
1400
1340
1270
1210
1150
1070
1500
1430
1360
1290
1220
1160
1080
1530
1460
1390
1320
1240
1180
1090
1570
1500
1420
1340
1260
1190
1100
W 27×94
751
TFL
2
3
4
BFL
6
7
0.00
0.19
0.37
0.56
0.75
3.39
6.39
997
863
729
595
461
355
249
1300
1260
1210
1150
1100
1050
974
1340
1290
1230
1170
1120
1060
982
1370
1320
1260
1200
1130
1070
991
1410
1350
1280
1220
1150
1090
1000
1450
1380
1310
1240
1170
1100
1010
W 27×84
659
TFL
2
3
4
BFL
6
7
0.00
0.16
0.32
0.48
0.64
3.44
6.62
893
778
663
549
434
329
223
971 1000 1030 1070 1100 1130 1160 1190 1220
954 982 1010 1040 1060 1090 1120 1150 1170
936 959 983 1010 1030 1050 1080 1100 1120
916 936 955 975 994 1010 1030 1050 1070
896 911 926 942 957 972 988 1000 1020
866 878 890 901 913 925 936 948 960
814 822 830 838 846 854 861 869 877
1260
1200
1150
1090
1030
971
885
1290
1230
1170
1110
1050
983
893
W 24×76
540
TFL
2
3
4
BFL
6
7
0.00
0.17
0.34
0.51
0.68
3.00
5.60
806
696
586
476
366
284
202
797
781
764
745
724
703
666
826
806
784
762
737
713
673
855
830
805
778
750
723
680
883
855
826
795
763
733
687
912
880
847
812
776
743
694
940
904
867
829
789
753
702
969
929
888
846
802
763
709
997 1030 1050 1080
954 978 1000 1030
909 930 950 971
863 880 896 913
815 828 841 854
773 783 793 803
716 723 730 737
W 24×68
478
TFL
2
3
4
BFL
6
7
0.00
0.15
0.29
0.44
0.59
3.05
5.81
724
629
535
440
346
263
181
711
697
682
666
649
628
590
736
719
701
682
662
637
596
762
741
720
697
674
646
603
788
764
739
713
686
656
609
813
786
758
729
698
665
616
839
808
777
744
711
674
622
864
830
796
760
723
684
628
890
853
815
775
735
693
635
1090
1070
1050
1030
1000
972
921
2.5
1130
1100
1080
1050
1020
985
929
3
1160
1130
1100
1070
1030
997
938
3.5
1200
1160
1130
1090
1050
1010
947
4
1230
1190
1150
1110
1070
1020
956
4.5
1270
1230
1180
1130
1080
1040
965
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
916
875
833
791
747
702
641
941
897
852
807
760
712
648
967
920
871
822
772
721
654
5 - 26
COMPOSITE DESIGN
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 24×62
Kip-ft
413
TFL
2
3
4
BFL
6
7
0.00
0.15
0.29
0.44
0.59
3.47
6.58
655
580
506
431
356
260
164
644
633
621
608
595
568
520
667
653
639
624
608
577
526
690
674
657
639
620
587
532
713
694
675
654
633
596
538
737
715
693
669
646
605
543
760
736
711
685
658
614
549
783
756
728
700
671
623
555
806
777
746
715
683
633
561
829
797
764
731
696
642
567
853
818
782
746
709
651
572
876
838
800
761
721
660
578
W 24×55
362
TFL
2
3
4
BFL
6
7
0.00
0.13
0.25
0.38
0.51
3.45
6.66
583
520
456
392
328
237
146
569
560
550
540
529
504
458
590
579
566
554
540
512
463
611
597
583
568
552
520
468
631
615
599
582
564
529
474
652
634
615
595
575
537
479
673
652
631
609
587
546
484
693
671
647
623
599
554
489
714
689
663
637
610
562
494
735
707
679
651
622
571
499
755
726
696
665
634
579
505
776
744
712
679
645
588
510
W 21×62
389
TFL
2
3
4
BFL
6
7
0.00
0.15
0.31
0.46
0.62
2.53
4.78
659
568
476
385
294
229
165
583
570
555
540
523
507
482
606
590
572
553
534
516
487
630
610
589
567
544
524
493
653
630
606
581
555
532
499
676
650
623
594
565
540
505
700
670
640
608
575
548
511
723
690
656
622
586
556
517
746
710
673
635
596
564
522
770
730
690
649
607
572
528
793
751
707
663
617
581
534
816
771
724
676
628
589
540
W 21×57
348
TFL
2
3
4
BFL
6
7
0.00
0.16
0.33
0.49
0.65
2.90
5.38
601
525
448
371
294
222
150
534
522
510
497
483
464
433
555
541
526
510
493
472
438
576
559
542
523
504
480
443
597
578
558
536
514
488
449
619
597
574
550
525
496
454
640
615
589
563
535
504
459
661
634
605
576
546
511
465
683
652
621
589
556
519
470
704
671
637
602
566
527
475
725
689
653
615
577
535
481
747
708
669
628
587
543
486
W 21×50
297
TFL
2
3
4
BFL
6
7
0.00
0.13
0.27
0.40
0.54
2.92
5.58
529
466
403
341
278
205
132
465
456
446
436
425
406
374
484
473
461
448
435
413
379
503
489
475
460
445
421
383
522
506
489
472
454
428
388
540
522
504
484
464
435
393
559
539
518
496
474
442
397
578
555
532
508
484
450
402
597
572
546
520
494
457
407
615
588
561
532
504
464
411
634
605
575
545
513
472
416
653
621
589
557
523
479
421
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 27
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 21×44
Kip-ft
258
TFL
2
3
4
BFL
6
7
0.00
0.11
0.23
0.34
0.45
2.90
5.69
468
415
363
310
257
187
117
409
401
393
384
376
358
326
425
416
406
395
385
364
331
442
430
419
406
394
371
335
458
445
432
417
403
378
339
475
460
444
428
412
384
343
492
475
457
439
421
391
347
508
489
470
450
430
398
351
525
504
483
461
439
404
355
541
519
496
472
448
411
360
558
533
509
483
458
417
364
574
548
521
494
467
424
368
W 18×60
332
TFL
2
3
4
BFL
6
7
0.00
0.17
0.35
0.52
0.70
2.19
3.82
634
539
445
350
256
207
158
499
485
470
454
436
424
407
522
504
486
466
445
432
413
544
523
501
478
454
439
418
566
542
517
491
463
446
424
589
561
533
503
472
454
430
611
581
549
516
481
461
435
634
600
564
528
491
468
441
656
619
580
540
500
476
447
679
638
596
553
509
483
452
701
657
612
565
518
490
458
723
676
627
578
527
498
463
W 18×55
302
TFL
2
3
4
BFL
6
7
0.00
0.16
0.32
0.47
0.63
2.16
3.86
583
498
412
327
242
194
146
457
444
431
416
401
389
372
477
462
445
428
409
396
377
498
479
460
439
418
403
383
519
497
474
451
426
410
388
539
515
489
462
435
417
393
560
532
504
474
443
424
398
581
550
518
486
452
430
403
601
568
533
497
461
437
408
622
585
547
509
469
444
414
643
603
562
520
478
451
419
663
620
577
532
486
458
424
W 18×50
273
TFL
2
3
4
BFL
6
7
0.00
0.14
0.29
0.43
0.57
2.07
3.82
529
452
375
299
222
177
132
412
401
389
376
362
352
336
431
417
402
387
370
358
341
450
433
415
397
378
365
346
468
449
429
408
386
371
350
487
465
442
418
394
377
355
506
481
455
429
402
383
360
525
497
469
439
409
390
365
543
513
482
450
417
396
369
562
529
495
461
425
402
374
581
545
508
471
433
408
379
600
561
522
482
441
415
383
W 18×46
245
TFL
2
3
4
BFL
6
7
0.00
0.15
0.30
0.45
0.61
2.40
4.34
486
420
354
288
222
172
122
380
370
360
348
337
324
305
397
385
372
359
345
330
310
414
400
385
369
352
336
314
431
415
397
379
360
343
318
449
430
410
389
368
349
322
466
444
422
399
376
355
327
483
459
435
410
384
361
331
500
474
447
420
392
367
335
517
489
460
430
400
373
340
535
504
472
440
407
379
344
552
519
485
450
415
385
348
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
5 - 28
COMPOSITE DESIGN
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 18×40
Kip-ft
212
TFL
2
3
4
BFL
6
7
0.00
0.13
0.26
0.39
0.53
2.26
4.27
425
368
311
254
197
152
106
329
321
312
303
293
282
265
345
334
323
312
300
288
269
360
347
334
321
307
293
273
375
360
345
330
314
298
277
390
373
356
339
321
304
280
405
386
367
348
328
309
284
420
399
378
357
335
315
288
435
412
389
366
342
320
292
450
425
400
375
349
325
295
465
438
411
384
356
331
299
480
451
423
393
363
336
303
W 18×35
180
TFL
2
3
4
BFL
6
7
0.00
0.11
0.21
0.32
0.43
2.37
4.56
371
325
279
233
187
140
92.7
285
278
271
264
256
245
227
298
290
281
272
263
250
230
311
301
291
280
269
255
233
324
313
301
289
276
260
237
338
324
311
297
283
265
240
351
336
321
305
289
270
243
364
347
331
313
296
275
246
377
359
340
322
303
280
250
390
370
350
330
309
285
253
403
382
360
338
316
290
256
416
393
370
346
323
295
260
W 16×36
173
TFL
2
3
4
BFL
6
7
0.00
0.11
0.22
0.32
0.43
1.79
3.44
382
328
273
219
165
130
95.4
268
261
252
244
234
227
215
282
272
262
251
240
232
219
295
284
272
259
246
236
222
309
295
281
267
252
241
226
322
307
291
275
258
245
229
336
319
301
282
264
250
232
349
330
310
290
270
255
236
363
342
320
298
275
259
239
377
353
330
306
281
264
243
390
365
339
314
287
268
246
404
377
349
321
293
273
249
W 16×31
146
TFL
2
3
4
BFL
6
7
0.00
0.11
0.22
0.33
0.44
2.00
3.79
328
285
241
197
153
118
82.1
231
225
218
211
204
196
183
243
235
227
218
209
200
186
254
245
235
225
214
204
189
266
255
244
232
220
208
192
278
265
252
239
225
212
195
289
275
261
246
231
217
198
301
285
269
253
236
221
201
313
295
278
260
242
225
204
324
305
286
267
247
229
207
336
315
295
274
253
233
209
347
326
303
281
258
237
212
W 16×26
119
TFL
2
3
4
BFL
6
7
0.00
0.09
0.17
0.26
0.35
2.04
4.01
276
242
208
174
140
104
69.1
193
188
183
177
172
164
151
203
196
190
184
177
168
154
212
205
197
190
182
171
156
222
214
205
196
187
175
159
232
222
212
202
192
179
161
242
231
220
208
197
182
164
252
239
227
214
202
186
166
261
248
234
220
206
190
169
271
257
242
227
211
194
171
281
265
249
233
216
197
173
291
274
256
239
221
201
176
aY1 = distance from top of the steel beam to plastic neutral axis.
bY2 = distance from top of the steel beam to concrete flange force.
cSee Figure 5-3 for PNA locations.
AMERICAN INSTITUTE OF STEEL CONSTRUCTION
COMPOSITE BEAMS
5 - 29
Fy = 36 ksi
COMPOSITE DESIGN
COMPOSITE BEAM SELECTION TABLE
W Shapes
φ = 0.85
φb = 0.90
Shape
φb M p PNAc Y1a
ΣQ n
φM n (kip-ft)
Y2b (in.)
In.
Kips
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
W 14×38
Kip-ft
166
TFL
2
3
4
BFL
6
7
0.00
0.13
0.26
0.39
0.52
1.38
2.53
403
340
278
215
152
126
101
258
249
240
229
218
213
206
273
261
249
237
224
218
209
287
273
259
244
229
222
213
301
285
269
252
234
226
217
316
298
279
260
240
231
220
330
310
289
267
245
235
224
344
322
299
275
251
240
227
358
334
308
283
256
244
231
373
346
318
290
261
249
234
387
358
328
298
267
253
238
401
370
338
305
272
258
242
W 14×34
147
TFL
2
3
4
BFL
6
7
0.00
0.11
0.23
0.34
0.46
1.41
2.60
360
305
250
194
139
115
90.0
229
221
213
204
194
189
182
242
232
222
211
199
193
186
255
243
230
218
204
197
189
267
254
239
224
209
202
192
280
264
248
231
214
206
195
293
275
257
238
219
210
198
306
286
266
245
224
214
202
318
297
275
252
229
218
205
331
308
283
259
234
222
208
344
318
292
266
239
226
211
357
329
301
273
244
230
214
W 14×30
128
TFL
2
3
4
BFL
6
7
0.00
0.10
0.19