Xiao Ling Zhao Lin Hai Han Hui Lu Concrete filled Tubular Members

Concrete-filled Tubular Members and Connections Concrete-filled Tubular Members and Connections Xiao-Ling Zhao, Lin-Hai Han and Hui Lu First published 2010 by Spon Press This edition published 2013 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN 711 Third Avenue, New York, NY 1001786$ Routledge is an imprint of the Taylor & Francis Group, an informa business © 2010 Xiao-Ling Zhao, Lin-Hai Han and Hui Lu Publisher’s note This book has been prepared from a camera-ready copy supplied by the authors All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. This publication presents material of a broad scope and applicability. Despite stringent efforts by all concerned in the publishing process, some typographical or editorial errors may occur, and readers are encouraged to bring these to our attention where they represent errors of substance. The publisher and author disclaim any liability, in whole or in part, arising from information contained in this publication. The reader is urged to consult with an appropriate licensed professional prior to taking any action or making any interpretation that is within the realm of a licensed professional practice. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Zhao, Xiao-Ling. Concrete-filled tubular members and connections / Xiao-Ling Zhao, Lin-Hai Han, and Hui Lu. p. cm. Includes bibliographical references and index. 1. Columns, Concrete. 2. Concrete-filled tubes. 3. Concrete-filled tubes--Joints. I. Han, Lin-Hai. II. Lu, Hui, 1963- III. Title. TA683.5.C7Z48 2010 624.1'83425--dc22 2009053651 ISBN13: 978-0-415-43500-0 (hbk) ISBN13: 978-0-203-84834-0 (ebk) Table of Contents Preface ix Notation xi Chapter 1: Introduction ………………………………………………………… 1.1 Applications of Concrete-Filled Steel Tubes ……………………………… 1.2 Advantages of Concrete-Filled Steel Tubes ……………………………….. 1.3 Current Knowledge on CFST Structures …………………………………... 1.3.1 Related Publications………………………………………………... 1.3.2 International Standards ……………………………………………. 1.4 Layout of the Book ………………………………………………………… 1.5 References …………………………………………………………………. 1 1 10 13 13 14 14 15 Chapter 2: Material Properties and Limit States Design ……………………... 2.1 Material Properties ………………………………………………………… 2.1.1 Steel Tubes ………………………………………………………… 2.1.2 Concrete …………………………………………………………… 2.2 Limit States Design ………………………………………………………... 2.2.1 Ultimate Strength Limit State ……………………………………... 2.2.2 Serviceability Limit State ………………………………………….. 2.3 References …………………………………………………………………. 19 19 19 24 26 26 28 29 Chapter 3: CFST Members Subjected to Bending ……………………………. 3.1 Introduction ………………………………………………………………... 3.2 Local Buckling and Section Capacity ……………………………………... 3.2.1 Local Buckling and Classification of Cross-Sections ……………... 3.2.2 Stress Distribution …………………………………………………. 3.2.3 Derivation of Plastic Moment Capacity …………………………… 3.2.4 Design Rules for Strength …………………………………………. 3.2.5 Comparison of Specifications ……………………………………... 3.2.6 Examples …………………………………………………………... 3.3 Member Capacity ………………………………………………………….. 3.3.1 Flexural-Torsional Buckling ………………………………………. 3.3.2 Effect of Concrete-Filling on Flexural-Torsional Buckling Capacity …………………………………………………………… 3.4 References …………………………………………………………………. 31 31 32 32 33 33 40 45 46 58 58 59 61 vi Concrete-Filled Tubular Members and Connections Chapter 4: CFST Members Subjected to Compression ……………………… 4.1 General …………………………………………………………………….. 4.2 Section Capacity …………………………………………………………… 4.2.1 Local Buckling in Compression …………………………………… 4.2.2 Confinement of Concrete ………………………………………….. 4.2.3 Design Section Capacity …………………………………………... 4.2.4 Examples ………………………………………………………....... 4.3 Member Capacity ………………………………………………………….. 4.3.1 Interaction of Local and Overall Buckling ………………………... 4.3.2 Column Curves ……………………………………………………. 4.3.3 Design Member Capacity …………………………………………. 4.3.4 Examples …………………………………………………………... 4.4 References …………………………………………………………………. 65 65 69 69 70 72 78 90 90 91 101 103 117 Chapter 5: CFST Members Subjected to Combined Actions ………………… 5.1 General …………………………………………………………………….. 5.2 Stress Distribution in CFST Members Subjected to Combined Bending and Compression …………………………………………………………... 5.3 Design Rules ……………………………………………………………….. 5.3.1 BS5400-5:2005 ……………………………………………………. 5.3.2 DBJ13-51 ………………………………………………………….. 5.3.3 Eurocode 4 ………………………………………………………... 5.3.4 Comparison of Codes ……………………………………………… 5.4 Examples …………………………………………………………………... 5.4.1 Example 1 CFST SHS ……………………………………………... 5.4.2 Example 2 CFST CHS …………………………………………….. 5.5 Combined Loads Involving Torsion or Shear ……………………………... 5.5.1 Compression and Torsion …………………………………………. 5.5.2 Bending and Torsion ………………………………………………. 5.5.3 Compression, Bending and Torsion ……………………………….. 5.5.4 Compression, Bending and Shear …………………………………. 5.5.5 Compression, Bending, Torsion and Shear ………………………... 5.6 References …………………………………………………………………. 123 123 125 128 128 131 134 135 137 137 146 156 156 157 157 159 159 160 Chapter 6: Seismic Performance of CFST Members …………………………. 6.1 General …………………………………………………………………….. 6.2 Influence of Cyclic Loading on Strength ………………………………….. 6.2.1 CFST Beams ………………………………………………………. 6.2.2 CFST Braces ………………………………………………………. 6.2.3 CFST Beam-Columns ……………………………………………... 6.3 Ductility ……………………………………………………………………. 6.3.1 Ductility Ratio (ȝ) …………………………………………………. 163 163 166 166 168 168 168 168 Table of Contents vii 6.3.2 Parameters Affecting the Ductility Ratio (ȝ) ……………………… 6.3.3 Some Measures to Ensure Sufficient Ductility ……………………. Parameters Affecting Hysteretic Behaviour ……………………………….. 6.4.1 Moment (M) versus Curvature (I) Responses ……………………. 6.4.2 Lateral Load (P) versus Lateral Deflection (ǻ) Responses ………... Simplified Hysteretic Models 6.5.1 Simplified Model of the Moment–Curvature Hysteretic Relationship ...................................................................................... 6.5.2 Simplified Model of the Load–Deflection Hysteretic Relationship …………………………………………………….… 6.5.3 Simplified Model of the Ductility Ratio (ȝ) …………………..…... References …………………………………………………………………. 184 185 Chapter 7: Fire Resistance of CFST Members ………………………………... 7.1 General …………………………………………………………………….. 7.2 Parameters Affecting Fire Resistance ……………………………………. 7.3 Fire Resistance Design …………………………………………………….. 7.3.1 Chinese Code DBJ13-51 …………………………………………... 7.3.2 CIDECT Design Guide No. 4 …………………………………… 7.3.3 Eurocode 4 Part 1.2 ………………………………………………... 7.3.4 North American Approach ………………………………………… 7.3.5 Comparison of Different Approaches ……………………………... 7.4 Examples …………………………………………………………………... 7.4.1 Column Design ……………………………………………………. 7.4.2 Real Projects ………………………………………………………. 7.5 Post-Fire Performance ……………………………………………………... 7.6 Repairing After Exposure to Fire ………………………………………….. 7.7 References …………………………………………………………………. 189 189 191 193 193 193 197 199 200 201 201 206 208 212 214 Chapter 8: CFST Connections ………………………………………………….. 8.1 General …………………………………………………………………….. 8.2 Classification of Connections ……………………………………………… 8.3 Typical CFST Connections ………………………………………………... 8.3.1 Simple Connections ………………………………………….......... 8.3.2 Semi-Rigid Connections …………………………………………... 8.3.3 Rigid Connections …………………………………………………. 8.4 Design Rules ……………………………………………………………….. 8.4.1 General …………………………………………………………….. 8.4.2 Design of Simple Connections …………………………………….. 8.4.3 Design of Rigid Connections ……………………………………… 8.4.4 Bond Strength ……………………………………………………... 8.5 Examples …………………………………………………………………... 219 219 219 221 221 221 223 225 225 225 227 231 233 6.4 6.5 6.6 170 170 173 173 175 178 178 182 viii Concrete-Filled Tubular Members and Connections 8.5.1 Example 1 Simple Connection …………………………………….. 8.5.2 Example 2 Rigid Connection ……………………………………… More Recent CFST Connections …………………………………………... 8.6.1 Blind Bolt Connections ……………………………………………. 8.6.2 Reduced Beam Section (RBS) Connections ………………………. 8.6.3 CFST Connections for Fatigue Application ……………………….. References ………………………………………………………………..... 233 236 239 239 239 240 241 Chapter 9: New Developments …………………………………………………. 9.1 Long-Term Load Effect ……………………………………………………. 9.2 Some Construction-Related Issues ………………………………………… 9.2.1 Effects of Local Compression ……………………………………... 9.2.2 Pre-Load Effect ……………………………………………………. 9.3 SCC (Self-Consolidating Concrete)-Filled Tubes …………………………. 9.4 Concrete-Filled Double Skin Tubes ……………………………………….. 9.4.1 General …………………………………………………………….. 9.4.2 CFDST Members Subjected to Static Loading ……………………. 9.4.3 CFDST Members Subjected to Dynamic Loading ………………... 9.4.4 CFDST Members Subjected to Fire ………………………………. 9.5 FRP (Fibre Reinforced Polymer) Confined CFST ………………………… 9.6 References …………………………………………………………………. 247 247 249 249 253 255 257 257 257 266 267 269 270 Index ……………………………………………………………………………… 277 8.6 8.7 Preface Concrete-filled steel tubes (CFSTs) have been used in many structural engineering applications, such as columns in high-rise buildings and bridge piers. CFSTs can be used in various fields ranging from civil and industrial construction through to the mining industry. A series of design guides on tubular structures have been produced by CIDECT (International Committee for the Development and Study of Tubular Structures) to assist practising engineers. The ones relevant to concrete-filled steel tubes are CIDECT Design Guides No. 4, No. 5, No. 7 and No. 9. There are a few books relevant to CFST members and connections. Some of the books are not focused on concrete-filled steel tubes. For those which do, explanations of failure mechanism and mechanics are not covered in detail. Most of the designs are based on Eurocode 4. There is a lack of comparison of different design standards. Seismic resistance has received only very little coverage. Worked examples are very limited. This book will fill these gaps. This book contains descriptions and explanation of some basic concepts. It not only summarises the research performed to date on concrete-filled tubular members and connections but also compares the design rules in various standards (Eurocode 4, BS5400 Part 5, AS5100 Part 6 and Chinese Standard DBJ13-51), and provides design examples. It also presents some recent developments in concretefilled tubular members and connections. It is suitable for structural engineers, researchers and university students who are interested in composite tubular structures. Chapter 1 outlines the application and advantages of concrete-filled steel tubes (CFSTs). Chapter 2 presents the material properties of steel tubes and concrete given in various standards. The limit states design method is described. The differences among the Australian, British, Chinese and European standards are pointed out to help the readers to interpret the design comparison later in the book. CFST members are covered in Chapter 3 (bending), Chapter 4 (compression) and Chapter 5 (combined actions). Chapter 6 and Chapter 7 present the performance and design methods of CFST structures under seismic loading and fire conditions. Steel or RC beam to CFST column connection details and designing approaches are covered in Chapter 8. Finally, Chapter 9 introduces some recent developments on concrete-filled steel tubular structures, e.g. the effect of long-term loading on the behaviour of CFST columns, the effect of axial local compression and preloads on the CFST column capacity, SCC (self-consolidating concrete)-filled tubular members, concrete-filled double skin tubes (CFDST) and FRP (Fibre Reinforced Polymer)-confined CFST columns. Comprehensive up-to-date references are given in the book. x Concrete-Filled Tubular Members and Connections We appreciated the comments from Dr. Mohamed Elchalakani at Higher Colleges of Technology, Dubai Mens College on Chapter 3, Dr. Ben Young at The University of Hong Kong on Chapter 4, Dr. Leroy Gardner at Imperial College, London, on Chapter 5, Prof. Amir Fam and Dr. Pedram Sadeghian at Queen’s University, Canada, on Chapter 6, Prof. Yong-Chang Wang at The University of Manchester on Chapter 7, Prof. Akihiko Kawano at Kyushu University on Chapter 8 and Dr. Zhong Tao at Fuzhou University on Chapter 9. We would like to thank Prof. Dennis Lam at The University of Leeds, UK, for providing necessary documents regarding BS5400 Part 5, Prof. Hanbin Ge at Meijo University, Japan, for obtaining some relevant Japanese documents and Prof. Peter Schaumann at The University of Hannover for discussions on fire design in Eurocode 4. We are very grateful to Mr. Robert Alexander at Monash University for preparing most of the diagrams and Ms. Dominique Thomson at Monash University for checking the English. We wish to thank Thyssen Krupp Steel for providing the front cover photo. We also wish to thank Simon Bates at Taylor & Francis for his advice on the format of the book. Finally, we wish to thank our families for their support and understanding during the many years that we have been undertaking research on composite tubular structures and during the preparation of this book. Xiao-Ling Zhao, Lin-Hai Han and Hui Lu January 2010 Notation The following notation is used in this book. Where non-dimensional ratios are involved, both the numerator and denominator are expressed in identical units. The dimensional units for length and stress in all expressions or equations are to be taken as millimetres and megapascals (N/mm2) respectively, unless specifically noted otherwise. When more than one meaning is assigned to one symbol, the correct one will be evident from the context in which it is used. Some symbols are not listed here because they are only used in one section and well defined in the local context. Aa Ac Aconcrete Ac,nominal Ag Ainner AL Ant Anv Aouter As Asr Asc B Bi Bo C C1, C2 and C3 D De Di Do Ɯ Ea Ec Ed Es elastic E sc G Ia Ib Area of a steel hollow section defined in EC4 Area of concrete in CFST Area of concrete in CFDST Nominal cross-sectional area of concrete in CFDST Gross cross-sectional area Area of inner steel hollow section in CFDST Localised load area on core concrete in CFST Net area in tension for block failure Net area in shear for block failure Area of outer steel hollow section in CFDST Area of steel in CFST Area of steel reinforcement Area of steel and concrete in CFST Overall width of an RHS Overall width of inner RHS in CFDST Overall width of outer RHS in CFDST Perimeter of CFST or carbonate aggregate Compressive forces in Figure 3.3 Overall depth of an RHS Outside diameter of a CHS in BS5400 Overall depth of inner RHS in CFDST Overall depth of outer RHS in CFDST Axial stiffness ratio of CFST Modulus of elasticity for CHS defined in EC4 Modulus of elasticity of concrete Design value of the effect of actions in EC4 Modulus of elasticity of steel Section modulus of a composite section Shear modulus of elasticity Second moment of area of CHS Second moment of area of beam xii Ic Is J K Ke Kj,ini K1 L Lb Le Lp Lw M Mc MCFDST Mmax Mo Mp Ms Mu,CFDST Mux Muy Mx My Myu N Nb Nc NCFDST Ncr NE No Np Ns Nu Nu,CFDST Nu,L Nu, nominal Nup Concrete-Filled Tubular Members and Connections Second moment of area of concrete Second moment of area of steel hollow section Torsion constant for a cross-section Effective length factor Flexural stiffness in the elastic stage of CFST Initial rotation stiffness of connections Member slenderness reduction factor given in Figure 4.6 Member length Span of beam Effective length of a member Length of shear plate Fillet weld length Bending moment Design moment at the beam end Ultimate moment capacity of CFDST Maximum moment for CFST under combined loads shown in Figure 5.1(d) Elastic flexural-tensional buckling moment Plastic moment capacity Nominal section moment capacity Section bending moment capacity of CFDST Design ultimate moment of resistance of CFST about the major axis Design ultimate moment of resistance of CFST about the minor axis Bending moment about major principal x-axis Bending moment about minor principal y-axis or yielding moment of CFST Ultimate moment of CFST under constant axial load Axial force Tensile force in an external diaphragm induced by the axial force in beam Design member capacity in compression Section capacity of CFDST in compression Critical buckling load of a compressive member Elastic buckling load Applied axial load on CFST Pre-load on steel tube Nominal section capacity of CFST Design axial section capacity or squash load of CFST Section capacity of CFDST in compression Ultimate load of CFST subjected to long-term sustained load Nominal axial capacity of CFST Ultimate load of CFST with pre-load on steel tube Notation Nus Nx Nxy Ny N* P Py Q R Rd Ru R* S S* T T1, T2 Tu V Vbolt Vmax Vu Vweld a b be bf bj bs d db di din xiii Ultimate strength of unfilled steel tubular column Design member capacity in compression under uniaxial bending about the major axis restrained from failure about the minor axis Design member capacity in compression under uniaxial bending about the major axis unrestrained from failure about the minor axis or under biaxial bending Design member capacity in compression under uniaxial bending about the minor axis, or yield capacity of external diaphragm connections Design axial tension load at beam end Cyclic lateral load defined in Figure 6.3 or applied load in fire Yield load of CFST or ultimate strength of CFST Shear force at beam end Ultimate resistance in DBJ13-51 or fire resistance Design resistance in EC4 Nominal capacity Design resistance Design action effects in DBJ13-51 or siliceous aggregate, or plastic section modulus of the steel section defined in BS5400 Design action effects Torsion, or shear stress Tensile forces in Figure 3.3 Torsion capacity of CFST Shear force Design shear capacity of a single bolt Maximum shear force in beam web Shear capacity of CFST Design shear capacity per unit length of fillet weld Thickness of fire protection for CFST Clear width of an RHS or the least lateral dimension of a column defined in BS5400 or effective width of diaphragm at critical section Effective width of tube wall to resist tensile force in a diaphragm connection Overall width of an RHS defined in BS5400 Total length of weld defined in Figure 8.6 Flange width of steel I beam or overall depth or width of an RHS in BS5400 Outside diameter of a CHS Bolt diameter Outside diameter of inner CHS in CFDST Hole diameter of the inner diaphragm xiv Concrete-Filled Tubular Members and Connections d1 dn Depth of web in steel I beam Distance of neutral axis to interior surface of the compressive flange of an RHS Overall height of steel I beam Load eccentricity Design bond strength between steel and concrete in CFST Ultimate strength of beam web Bond strength between steel and concrete in CFST Concrete compressive strength Design cylinder strength of concrete defined in EC4 Standard compressive strength of concrete (Chapter 2), or characteristic strength of concrete given in GB50010-2002 or characteristic cylinder strength of concrete at 28 days given in EC4 Mean value of the compressive strength of concrete at the relevant age Characteristic compressive cube strength of concrete at 28 days Ultimate strength of steel tube Yield strength of steel tube Characteristic compressive cylinder strength of concrete at 28 days Ultimate strength of shear plate Yield strength of shear plate Ultimate strength of shear plate Yield stress of steel diaphragm Standard tensile strength of concrete Tensile strength of concrete Ultimate tensile strength of steel Yield strength of beam web Ultimate strength of beam web Tensile yield stress of steel Design yield strength of RHS defined in EC4 Overall depth of an RHS without a round corner defined in EC3, or depth of concrete in BS5400 or overall depth of steel I beam Fillet weld leg length Distance defined in Figure 8.8 Reduction factor on concrete strength Member effective length factor Form factor Strength factor under fire Member length Effective length of CFST Length of a column for which Euler load equals the squash load Load level or fire load ratio doverall e fa fb,w,u fbond fc fcd fck fcm fcu fc,u fc,y fcc fp,u fp,y fp,u fs,y ftk ft fu fw,y fw,u fy fyd h hf hs kc ke kf kt l le lE n Notation xv nb pr r rc rext ri rint rm t tb,f tb,w tc tf ti t1 tp to ts Number of bolts Percentage of reinforcement in CFST Radius of gyration Diameter of core concrete in CFST External corner radius of an RHS Inner radius of a CHS Internal corner radius of an RHS Middle radius between inner and outer surfaces of a CHS Tube wall thickness or time Thickness of flange of steel I beam Thickness of web of steel I beam Tube wall thickness Wall thickness of an RHS defined in BS5400 Wall thickness of inner steel tube in CFDST Thickness of diaphragm Thickness of shear plate Wall thickness of outer steel tube in CFDST Thickness of steel beam flange D Steel ratio or angle between tensile force and critical section in external diaphragm connection Section constant of compression members Concrete contribution factor defined in BS5400, or member slenderness reduction factor defined in AS5100 Steel ratio Depth-to-width ratio for RHS or local compression area ratio Equivalent moment factor defined in GB50017 Ratio of smaller to larger bending moment at the ends of a member about major axis Ratio of smaller to larger bending moment at the ends of a member about minor axis Member slenderness reduction factor giver in Figure 4.9 Lateral deflection Lateral displacement corresponding to Py as defined in Figure 6.1 Lateral displacement defined in Figure 6.1 Yield displacement defined in Figure 6.1 Deflection of structures or steel contribution ratio defined in EC4 Deflection limit of structures Hogging of beams in the unloaded state Variation of the deflection of beams due to the permanent loads immediately after loading Db Dc Ds E Em Ex Ey Ȥ ǻ ǻp ǻu ǻy į įmax įo į1 xvi Concrete-Filled Tubular Members and Connections į2 Variation of the deflection of beams due to the variable loading plus the long-term deformation due to the permanent load Shrinkage strain of core concrete in CFSTs Resistance factor for yield of steel Resistance factor for failure associated with a connector Capacity factor or capacity factor for steel hollow section or curvature Capacity factor for concrete Curvature corresponding to the yield moment Slenderness reduction factor or stability factor Material property factor of concrete Coefficient of the building importance in DBJ13-51 Partial factor covering uncertainty in the resistance model plus geometric deviation in EC4 Material property factor of steel Curvature Non-dimensional slenderness Relative slenderness Slenderness ratio of a steel hollow section Plate element plasticity slenderness limit Plate element yield slenderness limit Modified compression member slenderness Relative slenderness of CFST defined in AS5100 Section slenderness Section plasticity slenderness limit Section yield slenderness limit Ȝe for the web in compression only Ȝey for the web in compression only Ȝ about major axis Ȝ about minor axis Ductility ratio or degree of utilisation in determining fire resistance Saturated surface-dry density of concrete in Chapter 2, or ratio of the average compressive stress in the concrete at failure to the design yield stress of the steel as defined in BS5400 Pre-stress in the steel tube Nominal constraining factor Design constraining factor Hsh ĭ1 ĭ3 I Ic Iy ĳ Jc Jo JRd Js N O CȜ Oe Oep Oey On Or Os Osp Osy Ȝw Ȝwy Ȝx Ȝy ȝ ȡ ı0 ȟ ȟo AIJ AISC Architectural Institute of Japan American Institute of Steel Construction or Australian Institute of Steel Construction Notation ASCCS ASI AS5100 BSI BS5400 CFST CFRP CFDST CHS CIDECT DBJ13-51 EC3 EC4 FR FRP IIW kN LSD MPa m mm PLR RHS RSI SCC SHS xvii Association for Steel-Concrete Composite Structures Australian Steel Institute Australian bridge design standard AS5100 British Standards Institution British bridge code BS5400 Concrete-filled steel tubes Carbon fibre reinforced polymer Concrete-filled double skin tubes Circular hollow section International Committee for the Development and Study of Tubular Structures Chinese code DBJ13-51 Eurocode 3 Eurocode 4 Fire resistance in minutes Fibre reinforced polymer International Institute of Welding Kilonewton Limit states design Megapascal (N/mm2) Metre Millimetre Pre-load ratio Rectangular hollow section Residual strength index Self-consolidating concrete Square hollow section CHAPTER ONE Introduction 1.1 APPLICATIONS OF CONCRETE-FILLED STEEL TUBES Using steel and concrete together utilises the beneficial material properties of both elements. Reinforced concrete (RC) sections are one example of this composite construction. This type of section primarily involves the use of a concrete section which is reinforced with steel rods in the tension regions. This book deals with another type of concrete–steel composite construction, namely concrete-filled steel tubes (CFSTs). The hollow steel tubes can be fabricated by welding steel plates together or by hot-rolled process, or by coldformed process. Figure 1.1 shows some typical CFST section shapes commonly found in practice, namely circular, square and rectangular. They are often called concrete-filled CHS (circular hollow section), SHS (square hollow section) and RHS (rectangular hollow section), respectively. Steel tube t Concrete Steel tube t Concrete d (a) B Circular hollow section (b) Steel tube Square hollow section Corner Steel tube rext t D t Concrete Concrete B (c) D B Rectangular hollow section without rounded corners (d) Rectangular hollow section with rounded corners Figure 1.1 Typical CFST sections 2 Concrete-Filled Tubular Members and Connections In Figure 1.1, d is the outer diameter of the circular section, B is the width of the square or the rectangular sections, D is the overall depth of the rectangular section and t is the steel wall thickness. SHS can be treated as a special case of RHS when D equals B. For cold-formed RHS, rounded corners exist (Zhao et al. 2005), as shown in Figure 1.1(d), where rext is the external corner radius. There is an increasing trend in using concrete-filled steel tubes in recent decades, such as in industrial buildings, structural frames and supports, electricity transmitting poles and spatial construction. In recent years, such composite columns are more and more popular in high-rise or super-high-rise buildings and bridge structures. A few examples are presented here to give an appreciation of the scale of such composite structures. Figure 1.2 shows the using of CFST columns in one workshop. It is well known that the columns in a subway may be subjected to very high axial compression. CFST is very suitable for supporting columns in subways. One subway under construction can be seen in Figure 1.3. Figure 1.4 shows an electricity transmitting pole with CFST legs. CFST columns have very high load-bearing capacity, which thus can be used in spacious construction. An example is given in Figure 1.5. Figure 1.6 shows the SEG Plaza in Shenzhen during construction. It is the tallest building in China using CFST columns. SEG Plaza is a 76-storey Grade A office block with a four-level basement, each basement floor having an area of 9653m2. The main structure is 291.6m high with an additional roof feature giving a total height of 361m (Wu and Hua 2000, Zhong 1999). The steel parts of the columns were shipped to the site in lengths of three storeys. After being mounted, they were connected to the I-beams by bolts and were brought into the exact position. Then, the steel tubes were filled with concrete, and the deck floors were constructed at the same time. In this way, up to two-and-a-half storeys could be built each week, demonstrating the efficiency of this technology. The diameter of the columns used in the building ranges from 900mm to 1600mm. Concrete was poured in from the top of the column. The concrete was vibrated to ensure the compaction. The SEG Plaza was the first application of circular concrete-filled steel tubes in super-high-rise buildings on such a large scale in China (Zhong 1999). This technology offers numerous new possibilities, such as new types of CFST column to steel beam connections, increased fire performance of CFST columns, etc. In recent years, CFST columns with square and rectangular sections are also becoming popular in high-rise buildings. Figure 1.7 presents a high-rise building during construction using square and rectangular CFST columns, i.e. Wuhan International Securities Building (WISB) in Wuhan, China. The main structure is 249.2m high, and was completed in 2004. The use of CFST in arch bridges reasonably exploits the advantages of such kind of structures (Han and Yang 2007, Zhou and Zhu 1997, Ding 2001). An important advantage of using CFST in arch bridges is that, during the stage of erection, the hollow steel tubes can serve as the formwork for casting the concrete, which can reduce construction cost. Furthermore, the composite arch can be Introduction 3 erected without the aid of a temporary bridge due to the good stability of the steel tubular structure. The steel tubes can be filled with concrete to convert the system into a composite structure and capable of bearing the service load. Since the weight of the hollow steel tubes is comparatively small, relatively simple construction technology can be used for the erection. The popular methods being used include cantilever launching methods, and either horizontal or vertical “swing” methods, whereby each half-arch can be rotated horizontally into position (Zhou and Zhu 1997). Figure 1.8 illustrates the process of an arch rib during construction. An elevation of the bridge after construction is shown in Figure 1.9. More than 100 bridges of this type have been constructed so far in China. There is much attention being paid both by researchers and the practising engineers to this kind of composite bridge. Figure 1.2 CFST used in a workshop (Han 2007) Figure 1.3 A subway station using CFST columns (under construction) 4 Concrete-Filled Tubular Members and Connections Figure 1.4 A transmitting pole with CFST legs (Han 2007) (a) During construction (b) After construction Figure 1.5 CFST in spacious construction (Han and Yang 2007) Introduction 5 (a) (b) Concrete-Filled Tubular Members and Connections 6 (c) (d) (e) Figure 1.6 SEG Plaza under construction (Han and Yang 2007) Introduction 7 (a) (b) (c) Figure 1.7 Wuhan International Securities Building under construction (Han and Yang 2004) 8 Concrete-Filled Tubular Members and Connections (a) (b) (c) Introduction 9 (d) Figure 1.8 Elevations of the arch rib during construction (Han 2007) Figure 1.9 Elevation of the arch after being constructed (Han and Yang 2004) 10 Concrete-Filled Tubular Members and Connections 1.2 ADVANTAGES OF CONCRETE-FILLED STEEL TUBES It is well known that tubular sections have many advantages over conventional open sections, such as excellent strength properties (compression, bending and torsion), lower drag coefficients, less painting area, aesthetic merits and potential of void filling (Wardenier 2002). Concrete-filled tubes involve the use of a steel tube that is then filled with concrete. This type of column has the advantage over other steel concrete composite columns, that during construction the steel tube provides permanent formwork to the concrete. The steel tube can also support a considerable amount of construction loads prior to the pumping of wet concrete, which results in quick and efficient construction. The steel tube provides confinement to the concrete core while the infill of concrete delays or eliminates local buckling of steel tubes. Compared with unfilled tubes, concrete-filled tubes demonstrate increased loadcarrying capacity, ductility, energy absorption during earthquakes as well as increased fire resistance. A simple comparison is given in Figure 1.10(a) for a column with an effective buckling length Le of 5m, mass of steel section of 60kg/m and concrete core strength of 40MPa. It can be seen from Figure 1.10(a) that the compression capacity increases significantly due to concrete-filling. Zhao and Grzebieta (1999) performed a series of tests on void-filled RHS subjected to pure bending. The increase in rotation angles at the ultimate moment due to the void filling was found to be 300%, as shown in Figure 1.10(b). A schematic view of interaction diagrams for beam-columns is shown in Figure 1.10(c). It is clear that less reduction in moment capacity is found for CFST members. This is due to the favourable stress distribution in CFST in bending. More discussion on CFST beam-columns will be given in Chapter 5. Zhao and Grzebieta (1999) also performed a series of tests on concrete-filled RHS subjected to large deformation cyclic bending. Typical failure modes are shown in Figure 1.10(d). For unfilled RHS beams, crack initiated at the corner and propagated across the section after several cycles. For concrete-filled RHS beams, either localised outward folding or uniform outward folding mechanism is formed without cracking. The fire resistance of unprotected RHS or CHS columns is normally found to be less than 30 minutes (Twilt et al. 1996). Figure 1.10(e) clearly shows that concrete-filling can significantly increase the fire resistance of tubular columns. Introduction 11 3000 2500 2000 1500 1000 500 0 Unfilled SHS Unfilled CHS Concrete-filled SHS Concrete-filled CHS Section type (a) For columns with Le of 5m, mass of steel section of 60kg/m and concrete cubic strength of 40MPa Increase in rotation angles at ultimate moment (%) 350 300 250 200 150 Low strength concrete 100 Light weight concrete 50 Normal concrete Polyurethane 0 0 20 40 60 80 Compressive strength of filler material (MPa) (b) Effect of concrete strength on ductility of CFST beams (adapted from Zhao and Grzebieta 1999) 1.2 1.0 Axial load ratio Compressive capacity (kN) 3500 0.8 0.6 CFST Steel tube 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Bending moment ratio (c) Comparison of interaction diagrams (schematic view) 12 Concrete-Filled Tubular Members and Connections (i) Unfilled RHS – local (single inward folding) failure mechanism with cracking (ii)RHS filled with low strength concrete – localised (single outward folding) mechanism without cracking (iii) RHS filled with normal concrete – uniform (multiple outward folding) mechanism without cracking (d) Comparison of cyclic behaviour (Zhao and Grzebieta 1999) Introduction 13 Fire resistance (minutes) 250 CHS 324x6.4 SHS 304.8x304.8x9.5 200 150 100 50 0 1 Unfilled Filled2 with plain concrete Filled with 3 steel fibre reinforced concrete (e) Comparison of fire resistance (column height is 3.81mm, both ends fixed; load ratio is 0.46) Figure 1.10 Advantage of CFST members 1.3 CURRENT KNOWLEDGE ON CFST STRUCTURES 1.3.1 Related Publications Extensive research projects on tubular structures were carried out in the last 30 years under the direction of CIDECT (International Committee for the Development and Study of Tubular Structures) and IIW (International Institute of Welding) Subcommission XV-E on Tubular Structures. Twelve international symposia on tubular structures have been held since 1984 (IIW 1984, Kurobane and Makino 1986, Niemi and Mäkeläinen 1989, Wardenier and Panjeh Shahi 1991, Coutie and Davies 1993, Grundy et al. 1994, Farkas and Jámai 1996, Choo and van der Vegte 1998, Puthli and Herion 2001, Jaurrieta et al. 2003, Packer and Willibald 2006, Shen et al. 2008). There have been several international conferences held through ASCCS (Association for Steel-Concrete Composite Structures) on steel-concrete composite structures since 1985. Many papers on concrete-filled tubes were presented at these conferences. Several state-of-the-art reports or papers were also published recently on concrete-filled steel tubular structures, such as Shams and Saadeghvaziri (1997), Schneider (1998), Shanmugam and Lakshmi (2001), Nishiyama et al. (2002), Han (2002) and Gourley et al. (2008). A series of design guides on tubular structures have been produced by CIDECT to assist practising engineers. The ones relevant to concrete-filled tubes are CIDECT Design Guides No. 4 (Twilt et al. 1996), No. 5 (Bergmann et al. 1995), No. 7 (Dutta et al. 1998) and No. 9 (Kurobane et al. 2005). Other relevant 14 Concrete-Filled Tubular Members and Connections books include Han and Zhong (1996), Wardenier (2002), Wang (2002), Nethercot (2003), Johnson and Anderson (2004), Zhao et al. (2005) and Han (2007). Some of the books listed above are not focused on concrete-filled tubes. For those that do, explanations of failure mechanism and mechanics are not covered in detail. Most of the designs are based on Eurocode 4. There is a lack of comparison of different design standards, seismic resistance has only received very little coverage and worked examples are very limited. This book will fill these gaps. 1.3.2 International Standards The application of CFST structures is supported by many well-known national codes, such as the Japanese code AIJ (1997), American code AISC (American Institute of Steel Construction 2005), British bridge code BS5400 (British Standards Institution 2005), Chinese code DBJ13-51 (2003) and Eurocode 4 (2004). For simplicity, these codes are to be referred to as “AIJ”, “AISC”, “BS5400”, “DBJ13-51” and “EC4” in the book. In 2004, a new version of the Australian bridge design standard AS5100 (Standards Australia 2004) for bridge design was issued, where design guidance for composite columns (including CFST columns) was incorporated. Tao et al. (2008) provided useful information for future possible revision of AS5100 for building construction. To fulfil this task, a wide range of experimental data (over 2000 test results) were used to evaluate whether AS5100 is applicable for calculating the strength of CFST members. Effects of different parameters on the accuracy of the strength predictions were discussed. In this book design examples using AS5100 are also given. 1.4 LAYOUT OF THE BOOK The following aspects of concrete-filled tubes have received little coverage in existing design standards, design guides or relevant books, but are addressed in this book: confinement, the effect of long-term loading, axial local compression and pre-loads on the performance of CFST columns, seismic behaviour and postfire behaviour, worked examples, mechanics models, concrete-filled double skin tubes, SCC (self-consolidating concrete)-filled tubes, and fibre reinforced polymer strengthening of concrete-filled tubes. This book contains descriptions and explanation of some basic concepts. It not only summarises the research performed to date on concrete-filled tubular members and connections but also compares the design rules in various standards (Eurocode 4, BS5400 Part 5 – 2005, AS5100 Part 6 – 2004 and Chinese Standard DBJ13-51 – 2003), and provides design examples. It also presents some recent developments in concrete-filled tubular members and connections. Comprehensive up-to-date references are given throughout the book. Introduction 15 Chapter 1 outlines the application and advantages of concrete-filled steel tubes (CFST). It also identifies the knowledge gap in CFST research and design. Chapter 2 presents the material properties of steel tubes and concrete given in various standards. The limit states design method is described. The differences among the Australian, British, Chinese and European standards are pointed out to help the readers to interpret the design comparison later in the book. CFST members are covered in Chapter 3 (bending), Chapter 4 (compression) and Chapter 5 (combined actions). Chapter 6 and Chapter 7 present the performance and design methods of CFST structures under seismic loading and fire conditions. Steel or RC beam to CFST column connection details and designing approaches are covered in Chapter 8. Some design examples are also presented using various codes. Finally, Chapter 9 introduces some recent developments on concrete-filled steel tubular structures. 1.5 REFERENCES 1. AIJ, 1997, Recommendations for design and construction of concrete filled steel tubular structures (Tokyo: Architectural Institute of Japan). 2. ANSI/AISC, 2005, Specification for structural steel buildings, ANSI/AISC 360-05 (Chicago: American Institute of Steel Construction). 3. Bergmann, R., Matsui, C., Meinsma, C. and Dutta, D., 1995, Design guide for concrete filled hollow section columns under static and seismic loading (Köln: TÜV-Verlag). 4. BSI, 2005, Steel, concrete and composite bridges, BS5400, Part 5: Code of practice for design of composite bridges (London: British Standards Institution). 5. Choo, S. and van der Vegte, G.J., 1998, Tubular structures VIII, Proceedings of 8th International Symposium on Tubular Structures (Rotterdam: Balkema). 6. Coutie, M.G. and Davies, G., 1993, Tubular structures V, Proceedings of 5th International Symposium on Tubular Structures (London: E & FN Spon). 7. DBJ13-51, 2003, Technical specification for concrete-filled steel tubular structures (Fuzhou: The Construction Department of Fujian Province). 8. Ding, D., 2001, Development of concrete-filled tubular arch bridges in China. Structural Engineering International, International Association for Bridge and Structural Engineering, 11(3), pp. 265-267. 9. Dutta, D., Wardenier, J., Yeomans, N., Sakae, K., Bucak, Ö. and Packer, J.A., 1998, Design guide for fabrication, assembly and erection of hollow section structures (Köln: TÜV-Verlag). 10. Eurocode 4, 2004, Design of composite steel and concrete structures – Part 1.1: General rules and rules for buildings. EN 1994-1-1:2004, December 2004 (Brussels: European Committee for Standardization). 11. Farkas, J. and Jámai, K., 1996, Tubular structures VII, Proceedings of 7th International Symposium on Tubular Structures (Rotterdam: Balkema). 12. Gourley, B.C., Tort, C., Denavit, M.D., Schiller, P.H. and Hajjar, J.F., 2008, A 16 Concrete-Filled Tubular Members and Connections synopsis of studies of the monotonic and cyclic behaviour of concrete-filled steel tube members, connections, and frames, Report No. NSEL-008, NSEL Report Series, Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, USA. 13. Grundy, P., Holgate, A. and Wong, B., 1994, Tubular structures VI, Proceedings of 6th International Symposium on Tubular Structures (Rotterdam: Balkema). 14. Han, L.H., 2002, Tests on stub columns of concrete-filled RHS sections. Journal of Constructional Steel Research, 58(3), pp. 353-372. 15. Han, L.H., 2007, Concrete-filled steel tubular structures – theory and practice, 2nd ed. (Beijing: China Science Press). 16. Han, L.H. and Yang, Y.F., 2004, Modern technology of concrete-filled steel tubular structures, 1st ed. (Beijing: China Architecture & Building Press). 17. Han, L.H. and Yang, Y.F., 2007, Modern technology of concrete-filled steel tubular structures, 2nd ed. (Beijing: China Architecture & Building Press). 18. Han, L.H. and Zhong, S.T., 1996, Mechanics of concrete filled steel tubes (Dalian: Dalian University of Technology Press). 19. IIW, 1984, Welding of tubular structures, Proceedings of 1st International Symposium on Tubular Structures (Oxford: Pergamon Press). 20. Jaurrieta, M.A., Alonso, A. and Chica, J.A., 2003, Tubular structures X, Proceedings of 10th International Symposium on Tubular Structures (Lisse: Balkema). 21. Johnson, R. and Anderson, D., 2004, Designers’ guide to EN1994-1-1 Eurocode 4: Design of composite steel and concrete structures, Part 1.1: General rules and rules for buildings (London: Thomas & Telford). 22. Kurobane, Y. and Makino, Y., 1986, Safety criteria in design of tubular structures, Proceedings of 2nd International Symposium on Tubular Structures (Tokyo: Architectural Institute of Japan). 23. Kurobane, Y., Packer, J.A., Wardenier, J. and Yeomans, N., 2005, Design guide for structural hollow section column connections (Köln: TÜV-Verlag). 24. Nethercot, D.A., 2003, Composite construction (London: Spon Press). 25. Niemi, E. and Mäkeläinen, P., 1989, Tubular structures III, Proceedings of 3rd International Symposium on Tubular Structures (London: Elsevier Applied Science). 26. Nishiyama, I., Morino, S., Sakino, K., Nakahara, H., Fujimoto, T., Mukai, A., Inai, E., Kai, M., Tokinoya, H., Fukumoto, T., Mori, K., Yoshika, K., Mori, O., Yonezawa, K., Mizuaki, U. and Hayashi, Y., 2002, Summary of research on concrete-filled structural steel tube column system carried out under the US – Japan cooperative research program on composite and hybrid structures, BRI Research Paper No.147 (Tokyo: Building Research Institute). 27. Packer, J.A. and Willibald, S., 2006, Tubular structures XI, Proceedings of 11th International Symposium on Tubular Structures (London: Taylor & Francis). 28. Puthli, R.S. and Herion, S., 2001, Tubular structures IX, Proceedings of 9th International Symposium on Tubular Structures (Lisse: Balkema). Introduction 17 29. Schneider, S.P., 1998, Axially loaded concrete-filled steel tubes. Journal of Structural Engineering, ASCE, 124(10), pp. 1125-1138. 30. Shams, M. and Saadeghvaziri, M.A., 1997, State of the art of concrete-filled steel tubular columns. ACI Structural Journal, 94(5), pp. 558-571. 31. Shanmugam, N.E. and Lakshmi, B., 2001, State of the art report on steel– concrete composite columns. Journal of Constructional Steel Research, 57(10), pp. 1041-1080. 32. Shen, Z.Y., Chen, Y.Y. and Zhao, X.Z., 2008, Tubular structures XII, Proceedings of 12th International Symposium on Tubular Structures (London: Taylor & Francis). 33. Standards Australia, 2004, Bridge design – Steel and composite construction, Australian Standard AS5100 (Sydney: Standards Australia). 34. Tao, Z., Uy, B., Han, L.H. and He, S.H., 2008, Design of concrete-filled steel tubular members according to Australian standard AS 5100. Australian Journal of Structural Engineering, 8(3), pp. 197-214. 35. Twilt, L., Hass, R., Klingsch, W., Edwards, M. and Dutta, D., 1996, Design guide for structural hollow section columns exposed to fire (Köln: TÜVVerlag). 36. Wang, Y.C., 2002, Steel and composite structures: Behaviour and design for fire safety (London: Taylor & Francis). 37. Wardenier, J., 2002, Hollow sections in structural applications (Rotterdam: Bouwen met Staal). 38. Wardenier, J. and Panjeh Shahi, E., 1991, Tubular structures IV, Proceedings of 4th International Symposium on Tubular Structures (Delft: Delft University Press). 39. Wu, G.L. and Hua, Y., 2000, Application of concrete filled steel tubular column in super high-rise building-SEG Plaza. In Proceedings of the 6th ASCCS International Conference on Steel–Concrete Composite Structures, Los Angeles, California, edited by Xiao, Y. and Mahin, S.A. (Los Angeles: Association for International Cooperation and Research in Steel–Concrete Composite Structures), pp. 77-84. 40. Zhao, X.L. and Grzebieta, R., 1999, Void-filled SHS beams subjected to large deformation cyclic bending. Journal of Structural Engineering, ASCE, 125(9), pp. 1020-1027. 41. Zhao, X.L., Wilkinson, T. and Hancock, G.J., 2005, Cold-formed tubular members and connections (Oxford: Elsevier). 42. Zhong, S.T., 1999, High-rise concrete-filled steel tubular structures, (Harbin: Heilongjiang Science & Technology Press). 43. Zhou, P. and Zhu, Z.Q., 1997, Concrete-filled tubular arch bridges in China. Structural Engineering International, International Association for Bridge and Structural Engineering, 7(3), pp. 161-166. Material Properties and Limit States Design 19 CHAPTER TWO Material Properties and Limit States Design 2.1 MATERIAL PROPERTIES Concrete-filled steel tube (CFST) consists of a steel tube and the concrete core. The hollow steel tubes can be fabricated by welding steel plates together or by hotrolled process, or by cold-formed process. The in-filled concrete can be normal concrete or self-consolidating concrete (SCC). Material properties of steel and concrete specified in AS5100 Part 6 (Standards Australia 2004), BS5400 Part 5 (BSI 2005), DBJ13-51 (2003), Eurocode 4 (2004) are summarised in this chapter. They will be used in the design examples later in the book. The unit MPa instead of N/mm2 is used in this chapter for the simplicity of writing. 2.1.1 Steel Tubes 2.1.1.1 AS5100 Part 6 This Standard does not cover the steelwork of the following structures, members and materials: (1) Bridges with orthotropic plate decks. (2) Cold-formed members other than those complying with AS1163 (Standards Australia 1991). (3) Steel members for which the value of yield stress (fy) used in design exceeds 450MPa. (4) Steel elements, other than packers, less than 3mm thick. The steel section shall be symmetrical, be fabricated from steel with a maximum yield stress of 350MPa, and have a wall thickness such that the plate element slenderness is less than the yield slenderness limit. 2.1.1.2 BS5400 Part 5 For BS5400 (2005), the sections of concrete-filled hollow steel can be either rectangular or circular and should either: (1) be a symmetrical box section fabricated from grade S275 or S355 steel complying with code EN10025 (2004); or Concrete-Filled Tubular Members and Connections 20 conform to code EN10210 (2006); and have a wall thickness of not less than bs(fy/3Es) for each wall in a rectangular hollow section (RHS) or De(fy/8Es) for circular hollow sections (CHS), where bs is the overall depth or width of the RHS, De is the outside diameter of the CHS, Es is the modulus of elasticity of steel and fy is the nominal yield strength of the steel. The surface of the steel member in contact with the concrete filling should be unpainted and free from deposits of oil, grease and loose scale or rust. (2) (3) 2.1.1.3 DBJ13-51 In DBJ13-51 (2003), the steel of CFST should comply with the Code for the design of steel structures (GB50017 2003). There are four grades: Q235, Q345, Q390 and Q420. 2.1.1.4 Eurocode 4 Properties should be obtained by reference to clauses 3.1 and 3.2 of Eurocode 3 Part 1.1 (2005), which apply to structural steel of nominal yield strength not more than 460MPa. 2.1.1.5 Yield stress and tensile strength The minimum values of yield stress (fy) and tensile strength (fu) specified in the above four codes are summarised in Table 2.1 for steel plates, Table 2.2 for hotrolled tubes and Table 2.3 for cold-formed tubes. It can be seen that the yield stress ranges from 200 to 460MPa while the tensile strength ranges from 300 to 720MPa. The ratio (fu/fy) ranges from 1.11 to 1.96. Typical stress-strain relationship of hot-rolled or fabricated mild steel tubes is shown in Figure 2.1(a) where an obvious yield plateau exists. A typical stress– strain relationship of cold-formed tubes is given in Figure 2.1(b) where 0.2% proof stress is adopted to define the yield stress. More discussions on cold-formed tubes can be found in Zhao et al. (2005). Material Properties and Limit States Design 21 Table 2.1 Minimum values of yield stress, tensile strength and tensile to yield ratio for steel plates (a) Grade AS/NZS 3678 (Standards Australia 1996) fy (MPa) >12 >20 d20 d32 N/A N/A 250 250 250 250 300 280 >32 d50 N/A 250 250 280 >50 d80 N/A 240 240 270 fu (MPa) fu/fy 300 410 410 430 1.50 1.46 to 1.71 1.46 to 1.71 1.34 to 1.59 340 450 1.25 to 1.32 360 360 480 1.20 to 1.33 420 400 N/A 1.11 to 1.30 340 340 N/A 520 500 450 t (mm) d8 200 250 250L15 300 300L15 350 350L15 400 400L15 450 450L15 WR350 WR350 L0 200 280 280 320 >8 d12 200 260 260 310 360 360 350 340 340 400 400 380 360 450 450 450 340 340 340 (b) Part Grade Part 2 S235 S275 S355 S450 S275N/NL S355N/NL S420N/NL S460N/NL S275M/ML S355M/ML S420M/ML S460M/ML S235 W S355 W S460Q/QL/QL1 Part 3 Part 4 Part 5 Part 6 Grade Q235 Q345 Q390 Q420 EN10025 (2004) fy (MPa) 40mm < t t d 40 mm d 80mm 235 215 275 255 355 335 440 410 275 255 355 335 420 390 460 430 275 255 355 335 420 390 460 430 235 215 355 225 460 440 (c) fy (MPa) 235 345 390 420 1.32 fu (MPa) 40mm < t t d 40 mm d 80mm 360 360 430 410 510 470 550 550 390 370 490 470 520 520 540 540 370 360 470 450 520 500 540 530 360 340 510 490 570 550 GB50017 (2003) fu (MPa) 372 to 461 470 to 630 490 to 650 520 to 680 fu/fy 1.53 to 1.67 1.56 to 1.61 1.44 to 1.40 1.25 to 1.34 1.42 to 1.45 1.38 to 1.32 1.24 to 1.33 1.17 to 1.26 1.35 to 1.41 1.32 to 1.34 1.24 to 1.28 1.17 to 1.23 1.53 to 1.58 1.44 to 1.46 1.24 to 1.25 fu/fy 1.58 to 1.96 1.36 to 1.83 1.26 to 1.67 1.24 to 1.62 Concrete-Filled Tubular Members and Connections 22 Table 2.2 Minimum values of yield stress, tensile strength and tensile to yield ratio for hot-rolled tubes Grade Q235 Q345 Q390 Q420 Grade S235H S275H S355H S275NH/NLH S355NH/NLH S420NH/NLH S460NH/NLH (a) GB50017 (2003) (b) EN10210 (2006) fy (MPa) 235 345 390 420 fu (MPa) 372 to 461 470 to 630 490 to 650 520 to 680 fy (MPa) 40 mm < t d 40 t d 80 mm mm 235 215 275 255 355 335 275 255 355 335 420 390 460 430 fu (MPa) 40 mm < t d 40 t d 80 mm mm 360 360 430 410 510 470 390 370 490 470 540 520 560 550 fu/fy 1.58 to 1.96 1.36 to 1.83 1.26 to 1.67 1.24to 1.62 fu/fy 1.53 to 1.67 1.56 to 1.61 1.44 to 1.40 1.42 to 1.45 1.38 to 1.40 1.29 to 1.33 1.22 to 1.28 Table 2.3 Minimum values of yield stress, tensile strength and tensile to yield ratio for cold-formed tubes (a) AS1163 (1991) (b) GB50018 (2002) Grade C250, C250L0 C350, C350L0 C450, C450L0 fy (MPa) 250 350 450 Grade Q235 Q345 Q390 Q420 fy (MPa) 235 345 390 420 fu (MPa) 320 430 500 fu (MPa) 372 to 461 470 to 630 490 to 650 520 to 680 fu/fy 1.28 1.23 1.11 fu/fy 1.58 to 1.96 1.36 to 1.83 1.26 to 1.67 1.25to 1.62 Material Properties and Limit States Design 23 Table 2.3 Minimum values of yield stress, tensile strength and tensile to yield ratio for cold-formed tubes (continued) Grade CHS S275NH S275NLH S355NH S355NLH S460NH S460NLH RHS/SHS S275NH S275NLH S355NH S355NLH S460NH S460NLH (c) EN 10219 (1992) t d 16 mm 275 fy (MPa) 16 mm < t d 40 mm 265 fu (MPa) t d 40 mm 370 – 510 1.35 to 1.92 355 345 470 – 630 1.33 to 1.83 460 440 550 – 720 1.20 to 1.63 t d 16mm 275 16mm < t d 24mm 265 t d 24mm 370 – 510 1.35 to 1.92 355 345 470 – 630 1.33 to 1.83 460 440 550 – 720 1.20 to 1.63 Stress fu fy Es Strain (a) Hot-rolled or fabricated mild steel tubes Stress fu fy 0.2% Proof stress Es 0.2% Strain (b) Cold-formed tubes Figure 2.1 Schematic view of stress–strain curves for steel tubes fu/fy 24 Concrete-Filled Tubular Members and Connections 2.1.2 Concrete 2.1.2.1 AS5100 (2004) In this code, concrete shall be of normal density and strength, meet the requirements of AS5100 Part 5, and have a maximum aggregate size of 20mm. Reinforcement is not normally required in concrete-filled hollow steel compression members, but if used it shall meet the requirements of AS5100 Part 5. The characteristic compressive cylinder strength at 28 days (fƍc) ranges from 25MPa to 65MPa with a saturated surface-dry density in the range of 2100kg/m3 to 2800 kg/m3. The modulus of elasticity of concrete can be estimated as U1.5 u 0.043fcm, where fcm is the mean value (in MPa) of the compressive strength of concrete at the relevant age. For concrete-filled steel tubes, the modulus of elasticity of concrete should be taken as one half of the material value. Consideration shall be given to the fact that the modulus of elasticity varies ±20%. 2.1.2.2 BS5400 (2005) The concrete in this code should be of normal density (not less than 2300kg/m3) with a characteristic 28-day cubic strength (fcu) of not less than 20N/mm2 for concrete-filled tubes. A nominal maximum aggregate size of 20mm is specified. The characteristic properties of concrete, reinforcement and pre-stressing steels should be determined in accordance with Part 4. For sustained loading, it should be sufficiently accurate to assume a modulus of elasticity of concrete equal to one half of the value used for short-term loading. 2.1.2.3 DBJ13-51 (2003) In code DBJ13-51-2003, the characteristic 28-day cubic strength (fcu) should not be less than 30MPa. The modulus of elasticity of concrete is given by Ec = 105/(2.2 + 34.7/fck), where fck is the standard compressive strength, in MPa. 2.1.2.4 Eurocode 4 (2004) It is regulated that unless otherwise given by Eurocode 4, properties should be obtained by reference to EN1992-1-1, clause 3.1, for normal concrete and to EN1992-1-1, clause 11.3, for lightweight concrete. This part of EN1994 does not cover the design of composite structures with concrete strength classes lower than C20/25 and LC20/22 or higher than C60/75 and LC60/66. In EN1992-1-1, the compressive strength of concrete (f’c) is denoted by concrete-strength classes which relate to the characteristic (5%) cylinder strength Material Properties and Limit States Design 25 or the cube strength in accordance with EN206-1 (2002). The strength classes in this code are based on the characteristic cylinder strength determined at 28 days. The modulus of elasticity of concrete is equal to Ec = 22,000 (fƍc/10)0.3. The unit of fƍc should be in MPa. 2.1.2.5 Concrete strength Concrete properties specified in the above-mentioned four codes are summarised in Table 2.4 where some values are rounded off to be consistent in presentation. The modulus of elasticity of concrete (Ec) is not given in Table 2.4 since it depends on the density and compressive strength of concrete. In general, Ec lies in the range of 20,000MPa to 40,000MPa, which is about 1/10 to 1/5 of Es (modulus of elasticity of steel). Table 2.4 Material properties of concrete Standard AS5100 BS5400 Characteristic compressive cylinder strength at 28 days fƍc (MPa) 25 32 40 50 65 N/A DBJ13-51 N/A Eurocode 4 20 25 30 40 50 60 Standard compressive strength fck (MPa) Design compressive strength fc (MPa) Standard tensile strength ftk (MPa) Tensile strength ft (MPa) N/A N/A N/A 20 25 30 40 50 60 20 27 32 39 45 50 13.3 16.7 20.0 26.7 33.3 40.0 14.3 19.1 23.1 27.5 31.8 35.9 13.3 16.7 20.0 26.7 33.3 40.0 2.0 2.3 2.5 2.8 3.2 N/A N/A 2.0 2.4 2.6 2.9 3.0 3.1 1.5 1.8 2.0 2.5 2.9 3.1 1.1 1.2 1.3 1.5 1.7 1.9 1.4 1.7 1.9 2.0 2.1 2.2 1.0 1.2 1.3 1.7 1.9 2.1 Concrete-Filled Tubular Members and Connections 26 A typical stress–strain relationship of high strength concrete and normal strength concrete is shown in Figure 2.2. Stress High strength concrete fc fc Normal strength concrete Ec Hc Hc Strain Figure 2.2 Schematic view of stress versus strain curves for concrete 2.2 LIMIT STATES DESIGN Limit states design (LSD) is a design method in which the performance of a structure is checked against various limiting conditions at appropriate load levels. The limiting conditions to be checked in structural steel design are ultimate limit state and serviceability limit state. Ultimate limit states are those states concerning safety, such as exceeding of load-carrying capacity, overturning, sliding and fracture due to fatigue or other causes. Serviceability limit states are those in which the behaviour of the structure is unsatisfactory, and include excessive deflection, excessive vibration and excessive permanent deformation. As mentioned in Chapter 1, design examples will be given in this book in accordance with BS5400 (2005), DBJ13-51 (2003), Eurocode 4 (2004) and AS5100 (Standards Australia 2004). A brief description of the limit states design is given in this section since all the standards adopt the LSD approach. 2.2.1 Ultimate strength limit state 2.2.1.1 AS5100 Part 6 For the strength limit state design, the structure is deemed to be satisfactory if its design load effect does not exceed its design resistance. In AS5100 this criterion is described as: S* d I R u (2.1) Material Properties and Limit States Design 27 where S* is the design action effects resulted from the design loads at the ultimate limit state, Ru is the nominal capacity and I is the capacity factor. For capacity in bending, I is taken as 0.9. For capacity in compression, I is taken as 0.9 for a steel component and 0.6 for a concrete component. Load factors are used in determining the design action effects (S*) as specified in AS/NZS1170.0 (Standards Australia 2002). For example, a load factor of 1.2 is given to the dead load and a load factor of 1.5 is given to the live load for static design. 2.2.1.2 BS5400 Part 5 For a satisfactory design the following relation should be satisfied in BS5400 (2005): S* d R * (2.2) where R* is the design resistance and S* is the design effects. R* = Function (fk)/(rm1 rm2), fk is the characteristic (or nominal) strength of the material; rm1 is intended to cover the possible reductions in the strength of the materials in the structure as a whole as compared with the characteristic value deduced from the control test specimen; rm2 is intended to cover possible weaknesses of the structure arising from any cause other than the reduction in the strength of the materials allowed for in rm1, including manufacturing tolerances. Material properties factors are used in determining the design resistance R*. A factor of 1.5 is used for concrete, whereas a factor of 1.05 is used for steel. S* = rf3 (effects of rf1 rf2 Qk), rf1 takes account of the possibility of unfavourable deviation of the loads from their nominal values; rf2 takes account of the reduced probability that various loadings acting together will all attain their nominal values simultaneously; rf3 is a factor that takes account of inaccurate assessment of the effects of loading, unforeseen stress distribution in the structure, and variations in dimensional accuracy achieved in construction. Load factors are used in determining the design action effects (S*) as specified in BS5400 Part 2 (BSI 2006). For example, a load factor of 1.2 is given to the dead load and a load factor of 1.5 is given to the live load for static design. 2.2.1.3 DBJ13-51 In DBJ13-51 (2003), the strength limit state criterion is expressed as: J oS d R (2.3) where S is the design action effect, R is the ultimate resistance and J0 is the coefficient of the building importance which varies from 0.9 to 1.1. The dead load factor is 1.2 and the live load factor is 1.4. The material property factor is 1.4 for concrete and about 1.12 for steel. Concrete-Filled Tubular Members and Connections 28 2.2.1.4 Eurocode 4 In Eurocode 4 (2004), the limit state design is in accordance with Eurocode 0 (2002), and this criterion is described as: 1 Ed d R d R X d, i ; a d (2.4) J Rd ^ ` where Ed is the design value of the effect of actions such as internal force, moment or a vector representing several internal forces or moments and Rd is the design value of the corresponding resistance. JRd is a partial factor covering uncertainty in the resistance model, plus geometric deviations if these are not modelled explicitly; Xd,i is the design value of material property i. Material property factors are used in determining the design resistance. Load factors are used in determining the design action effects (Ed) as specified in Eurocode 2 (2004) and Eurocode 3 (2005). Load factors, materials factors and capacity factors for the four standards mentioned above are summarised in Table 2.5. Table 2.5 Summary of load factors, material factors and capacity factors Standard Criterion Load factors Live AS5100 S* d I R u 1.5 Material property factors Dea d Jc 1.2 N/A Capacity factors Js 0.9 on capacity in bending N/A 0.9 on steel capacity in compression 0.6 on concrete capacity in ompression 1.5 1.2 1.5 1.05 N/A DBJ-13-51 S* d R * Jo S d R 1.4 1.2 1.4 1.12 N/A Eurocode 4 Ed d R d 1.5 1.1 1.5 1.00 N/A BS5400 2.2.2 Serviceability limit state For serviceability limit state, the deflection of the structure (G) should not exceed certain deformation limit (Gmax). For example, the serviceability limit states for the vertical deflection in a simply supported beam can be expressed as (Eurocode 3 Material Properties and Limit States Design 2004): G d G max 29 (2.5) where Gmax is the sagging in the final state relative to the straight line joining the supports. It contains three components as shown below: G max G1 G 2 G o (2.6) in which, Go is the hogging of the beam in the unloaded state, G1 is the variation of the deflection of the beam due to the permanent loads immediately after loading, and G2 is the variation of the deflection of the beam due to the variable loading plus the long-term deformations due to the permanent load. The load factors used to calculate the deflection (G) are taken as unity or smaller than those for ultimate strength limit states, e.g. 1.0 for the dead load and 0.7 for the live load in the Australian Standard AS1170.0 (2002). It should be noted that, for concrete-filled steel tubular structures, relevant stages in the sequence of construction shall be considered. 2.3 REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. BSI, 2006, Steel, concrete and composite bridges, BS5400, Part 2: Specification for loads (London: British Standards Institutions). BSI, 2005, Steel, concrete and composite bridges, BS5400, Part 5: Code of practice for design of composite bridges (London: British Standards Institution). DBJ13-51, 2003, Technical specification for concrete-filled steel tubular structures (Fuzhou: The Construction Department of Fujian Province). EN206, 2002, Concrete – Part 1: Specification, performance, production and conformity, EN206-1:2002 (Brussels: European Committee for Standardization). EN10025-1, 2004, Hot-rolled products of structural steels – Part 1: General technical delivery conditions, EN10025-1:2004, November 2004 (Brussels: European Committee for Standardization). EN10025-1, 2004, Hot-rolled products of structural steels – Part 2: Technical delivery conditions for non-alloy structural steels, EN10025-2:2004, November 2004 (Brussels: European Committee for Standardization). EN10025-1, 2004, Hot-rolled products of structural steels – Part 3: Technical delivery conditions for normalized/normalized rolled weldable fine grain structural steels, EN10025-3:2004, November 2004 (Brussels: European Committee for Standardization). EN10025-1, 2004, Hot-rolled products of structural steels – Part 4: Technical delivery conditions for thermomechanical rolled weldable fine grain structural steels, EN10025-4:2004, November 2004 (Brussels: European Committee for Standardization). EN10025-1, 2004, Hot-rolled products of structural steels – Part 5: Technical 30 Concrete-Filled Tubular Members and Connections delivery conditions for structural steels with improved atmospheric corrosion resistance, EN10025-5:2004, November 2004 (Brussels: European Committee for Standardization). 10. EN10025-1, 2004, Hot-rolled products of structural steels – Part 6: Technical delivery conditions for flat products of high yield strength structural steels in the quenched and tempered condition, EN10025-6:2004, November 2004 (Brussels: European Committee for Standardization). 11. EN10210-1, 2006, Hot finished structural hollow sections of non-alloy and fine grain steels – Part 1: Technical delivery requirements, EN102101:2006, May 2006 (Brussels: European Committee for Standardization). 12. EN10219-1, 2006, Cold formed welded structural hollow sections of non-alloy and fine grain steels – Part 1: Technical delivery requirements, EN102191:2006, May 2006 (Brussels: European Committee for Standardization). 13. Eurocode 0, 2002, Basis of structural design, EN1990:2002, July 2002 (Brussels: European Committee for Standardization). 14. Eurocode 2, 2004, Design of concrete structures – Part 1-1: General rules and rules for buildings, EN1992-1-1: 2004, December 2004 (Brussels: European Committee for Standardization). 15. Eurocode 3, 2005, Design of steel structures – Part 1.1: General rules and rules for buildings, EN1993-1-1:2005, May 2005 (Brussels: European Committee for Standardization). 16. Eurocode 4, 2004, Design of composite steel and concrete structures – Part 1.1: General rules and rules for buildings, EN1994-1-1:2004, December 2004 (Brussels: European Committee for Standardization). 17. GB50017, 2003, Code for design of steel structures, National Standard of P.R. China, GB50017-2003 (Beijing: China Architecture & Building Press). 18. GB50018, 2002, Technical code of cold-formed thin-wall steel structures, National Standard of P.R. China, GB50018-2002 (Beijing: China Architecture & Building Press). 19. Standards Australia, 1991, Structural steel hollow sections, Australian Standard AS1163 (Sydney: Standards Australia). 20. Standards Australia, 1996, Structural steel – Hot-rolled plates, floor plates and slabs, Australian/New Zealand Standard AS/NZS3678 (Sydney: Standards Australia). 21. Standards Australia, 2002, Structural design actions – Part 0: General principles, Australian/New Zealand Standard AS/NZS1170.0 (Sydney: Standards Australia). 22. Standards Australia, 2004, Bridge design – Steel and composite construction, Australian Standard AS5100, Part 6 (Sydney: Standards Australia). 23. Zhao, X.L., Wilkinson, T. and Hancock, G.J., 2005, Cold-formed tubular members and connections (Oxford: Elsevier). CHAPTER THREE CFST Members Subjected to Bending 3.1 INTRODUCTION CFST members are subjected to bending in applications such as horizontal beam and columns in portal frame structures. The behaviour of CFST beams is similar to that of unfilled tubular beams described in Zhao et al. (2005). A summary of experimental studies on CFST beams is given in Table 3.1. An increase in moment capacity due to concrete filling is obvious as shown in Figure 3.1 for CFST RHS where the percentage of increase depends on the strength of the filler material. For CFST CHS the measured increase was 21% for normal strength concrete with fc of 24MPa (Elchalakani et al. 2001). The increase in ductility because of infill concrete can be seen from Figure 1.10(b), which is independent of the filler material strength. Concrete-filled fibre reinforced polymer tubes in bending was recently studied by Fam and Rizkalla (2002), and Fam and Son (2008). This chapter presents the derivation of section moment capacity of CFST beams. It compares the design rules in AS5100 (2004), BS5400 (2005), DBJ13-51 (2003) and Eurocode 4 (2004). Examples are given for both CFST RHS and CHS. The effect of concrete-filling on flexural-torsional buckling capacity of CFST RHS is also examined. Table 3.1 Summary of experimental studies on CFST beams d/t or B/t Steel yield stress fy MPa 24-37.4 92.1 12-110 46.7-60 327-359 262 419 282-235 31.9 23.5-44.1 16-39.7 19.7-30.5 40-100 22-42 20-50 46.7-105 331 194-305 377-432 444-467 300 750 294-330 282-235 Concrete Number compressive of tests strength fc MPa CFST CHS 34.4-38.1 5 83 4 23.4 12 51.5-81.3 18 CFST RHS 35.5 1 23.5-30 4 71.8-79.3 12 5-60.4 7 39-59 5 36.7-39 3 27.3-40 16 51.5-81.3 18 Reference Pan (1990) Prion and Boehme (1994) Elchalakani et al. (2001) Han et al. (2006) Furlong (1967) Tomii and Sakino (1979) Lu and Kennedy (1994) Zhao and Grzebieta (1999) Uy (2000) Uy (2001) Han (2004) Han et al. (2006) Concrete-Filled Tubular Members and Connections Increase in Ultimate Moment Capacity (%) 32 40 35 30 25 20 15 10 5 0 12.4MPa 34.4MPa 60.4MPa Compressive Strength of Filler Material Figure 3.1 Effect of concrete strength on moment capacity for CFST RHS (adapted from Zhao and Grzebieta 1999) 3.2 LOCAL BUCKLING AND SECTION CAPACITY 3.2.1 Local Buckling and Classification of Cross-Sections For unfilled tubular sections local buckling occurs when the section slenderness is larger than a certain limit (Zhao et al. 2005). The local buckling is delayed or eliminated due to concrete-filling as shown in Figure 3.2. Three classification systems of steel sections exist in various design codes. Eurocode 3 (2004) classifies sections as Class 1, 2, 3 or 4. BS5950 Part 1 (2000) classifies sections as plastic, compact, semi-compact and slender. AS4100 (1998) and AISC-LRFD (1999) classify sections as compact, non-compact and slender. Which category a section belongs to depends on its cross-section geometry and certain limits on such geometry specified in the design code. The concrete-filling increases the plastic slenderness limit by about 50% (Elchalakani et al. 2001). (a) Unfilled CHS (b) Concrete-Filled CHS Figure 3.2 Comparison of failure mode (Elchalakani et al. 2001) CFST Members Subjected to Bending 33 3.2.2 Stress Distribution Stress distributions are needed in order to derive the plastic moment capacity of CFST sections. Typical stress distributions are shown in Figure 3.3 for CFST RHS without rounded corners, in Figure 3.4 for CFST RHS with rounded corners and in Figure 3.5 for CFST CHS. In these figures, neutral axis positions, compressive forces, tensile forces and associated distances are illustrated. B t f y (compression) C1 dn D T2 d T2 t C2 C3 d C2 dC 3 d C1 d T1 T1 f y (tension) Figure 3.3 Neutral axis and stress distribution for CFST RHS without rounded corners 3.2.3 Derivation of Plastic Moment Capacity 3.2.3.1 CFST RHS without rounded corners The effect of concrete filling on moment capacity of tubular sections can be studied by determining the new neutral axis based on assumed stress distributions in steel tube and in concrete. The assumed stress distributions are shown in Figure 3.3 for CFST RHS without rounded corners. The concrete below the neutral axis is in tension and is neglected in the analysis. The position of the neutral axis can be derived by using the equilibrium condition, i.e. compressive forces (C1, C2 and C3 in Figure 3.3) are equal to tensile forces (T1 and T2 in Figure 3.3) across the section. Once the neutral axis is determined the moment capacity can be determined using the sum of moments caused by the forces shown in Figure 3.3. The neutral axis position for CFST RHS without rounded corners can be derived from: C1 C2 C3 T1 T2 (3.1) in which C1 B t f y C2 2 dn t f y Concrete-Filled Tubular Members and Connections 34 B B - 2 J ext t Jext fy (compression) Jint dn dC2 dC1 C1 C2 C3 d C3 D D - 2t Neutral Axis d T3 T3 d T2 d T1 T2 T1 fy (tension) (a) RHS B - 2t B - 2 Jext J int J int f c (compression) Jint C4 C5 dC5 C6 dC6 dn d C4 Neutral Axis (b) Concrete Figure 3.4 Neutral axis and stress distribution for CFST RHS with rounded corners (adapted from Zhao and Grzebieta 1999) y r i cosJ fy Fsc dy d sc yo Jo d M Fcc d cc J d st ri t fc ro M x Fst fy Figure 3.5 Neutral axis and stress distribution for CFST CHS (adapted from Elchalakani et al. 2001) CFST Members Subjected to Bending C3 (B 2 t ) d n f c T1 2 (D 2 t d n ) t f y T2 B t fy 35 Hence dn § D 2t · ¸ FRHS ¨ © 2 ¹ where FRHS 1 1 f B 2 t 1 c 4 fy t (3.2) | 1 1 f B 1 c 4 fy t (3.3) It can be seen that when there is no concrete, i.e. fc = 0, FRHS becomes 1.0. This matches the neutral axis position of an unfilled RHS. The moment capacity can be determined using the sum of moments caused by the forces shown in Figure 3.3. M CFST, RHS C1 d C1 C 2 d C2 C3 d C3 T1 d T1 T2 d T 2 (3.4) in which d C1 d C2 d C3 d T1 dT2 dn t 2 dn 2 dn 2 (D 2 t d n ) 2 D 2 t dn t 2 Therefore 1 ª º f y t «B ( D t ) (D 2 t ) 2 » 2 ¬ ¼ 1 1 f y t (D 2 t ) 2 (1 FRHS ) 2 (B 2 t ) d 2n f c 2 2 M CFST, RHS (3.5) Concrete-Filled Tubular Members and Connections 36 The first term in Eq. (3.5) is the moment capacity for an unfilled RHS, i.e. MRHS. Equation (3.5) can be rewritten as: 1 1 M CFST, RHS M RHS f y t (D 2 t ) 2 (1 FRHS ) 2 (B 2 t ) d 2n f c (3.6) 2 2 The second and third terms in Eq. (3.6) are the increased bending moment capacity due to concrete infill. In order to assist designers the values of FRHS defined in Eq. (3.3) are plotted in Figure 3.6 against the B/t ratio for various fc/fy ratios. 3.2.3.2 CFST RHS with rounded corners Rounded corners exist in cold-formed RHS (Zhao et al. 2005). The derivation of moment capacity is similar to that described in Section 3.2.3.1 except that the stress distributions include the rounded corners. The assumed stress distributions are shown in Figure 3.4 for CFST RHS with rounded corners. The concrete below the neutral axis is in tension and is neglected in the analysis. The position of the neutral axis can be derived by using the equilibrium condition, i.e. compressive forces (C1 to C6 in Figure 3.4) are equal to tensile forces (T1, T2 and T3 in Figure 3.4) across the section. Once the neutral axis is determined the moment capacity can be determined using the sum of moments caused by the forces shown in Figure 3.4. 1.2 fc/fy = 0 0.02 0.04 0.06 0.08 0.10 0.15 0.2 0.3 0.4 1.1 1.0 0.9 FRHS 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 10 20 30 40 B/t Figure 3.6 Values of FRHS defined in Eq. (3.3) 50 60 CFST Members Subjected to Bending 37 The neutral axis position for CFST RHS with rounded corners can be derived from (Zhao and Grzebieta 1999): 6 ¦ Ci i 1 3 i 1 which gives (D 2 t ) dn (3.7) ¦ Ti S 1 f c rint § · ¨ 2 rext 2 t rint ¸ 2 fy t © 2 ¹ 2 1 fc § B 2 t · ¨ ¸ 2 fy © t ¹ (3.8) The external radius (rext) and internal radius (rint = rext – t) vary from section to section. It is commonly assumed that rext = 2.5t for sections with a thickness larger than 3mm, and rext = 2t for other thicknesses (Zhao et al. 2005). When rext = 2.5t, Eq. (3.8) can be simplified as dn f t f t 1 0.242 c 1 0.242 c fy D 2 t § D 2 t · fy D § D 2t · |¨ ¨ ¸ ¸ © 2 ¹ 1 1 fc B 2 t © 2 ¹ 1 1 fc B 4 fy t 4 fy t (3.9) When rext = 2t, Eq. (3.8) can be simplified as dn f t f t 1 0.108 c 1 0.108 c f D 2 t f § D 2t · § D 2t · y y D |¨ ¸ ¸ ¨ © 2 ¹ 1 1 fc B © 2 ¹ 1 1 fc B 2 t 4 fy t 4 fy t (3.10) The ultimate moment capacity (MCFST,cold-formedRHS) is the summation of moments caused by the forces shown in Figure 3.4, i.e. M CFST , cold formed RHS 3 6 i 1 i 1 ¦ Ti d Ti ¦ Ci d Ci (3.11) The expressions of Ti, Ci, dTi and dCi are given in Zhao and Grzebieta (1999). The moment capacities calculated using Eqs. (3.9), (3.10) and (3.11) are compared in Figure 3.7 with those calculated using Eqs. (3.2) and (3.5) for a wide range of cold-formed RHS sizes specified in ASI (1999). It can be seen that the two predictions are very close. Therefore Eqs. (3.2) and (3.5) can be used to predict the ultimate moment capacity of concrete-filled RHS with rounded corners. Concrete-Filled Tubular Members and Connections 38 350 MCFST,RHS (kNm) 300 250 200 fc = 30MPa fc = 50MPa 150 100 50 0 0 50 100 150 200 250 300 350 MCFST,cold-formed RHS (kNm) Figure 3.7 Comparisons of moment capacities 3.2.3.3 CFST CHS The derivation is similar to that described in Section 3.2.3.1 for CFST RHS beams. The assumed stress distributions are shown in Figure 3.5 for CFST CHS. The concrete below the neutral axis is in tension and is neglected in the analysis. The angular location of the plastic neutral axis (J0) can be derived by using the equilibrium condition, i.e. compressive forces (Fsc and Fcc in Figure 3.5) are equal to tensile force (Fst in Figure 3.5) across the section, i.e. Fsc Fcc Fst (3.12) in which Fsc Fcc Fst f y t rm (S 2 J 0 ) 1 §S · f c ri2 ¨ J 0 sin(2 J 0 ) ¸ 2 2 © ¹ f y t rm (S 2 J 0 ) dt 2 d 2t ri 2 An iterative procedure is required to determine J0. A closed-form solution for J0 can be obtained by assuming sinJ0 = J0. Hence S J0 FCHS (3.13) 2 rm CFST Members Subjected to Bending 39 1 fc d 1 fc d 2 t 8 fy t 8 fy t | 1 f d 1 f d 2t 1 c 1 c 4 fy t 4 fy t FCHS (3.14) It can be seen that when there is no concrete, i.e. fc = 0, FCHS becomes 0. This matches the neutral axis position of an unfilled CHS, i.e. J0 = 0. The moment capacity can be determined using the sum of moments (Msc, Mcc and Mst) caused by the forces shown in Figure 3.5. Msc, Mcc and Mst are the moments due to steel in compression, concrete in compression and steel in tension, respectively. They can be expressed as: 2 f y t rm2 cos J 0 M sc M st M cc 2 f c ri3 cos3 J 0 3 Therefore M CFST ,CHS 2 4 f y t rm2 cos J 0 f c ri3 cos3 J 0 3 (3.15) In order to assist designers the values of FCHS defined in Eq. (3.14) are plotted in Figure 3.8 against d/t ratio for various fc/fy ratios. 0.45 0.40 0.35 fc/fy = 0.4 0.3 0.2 0.15 0.10 0.08 0.06 0.04 0.02 0 FCHS 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0 10 20 30 40 d/t Figure 3.8 Values of FCHS defined in Eq. (3.14) 50 60 Concrete-Filled Tubular Members and Connections 40 3.2.4 Design Rules for Strength 3.2.4.1 AS5100 No design formulae are given in AS5100 for the moment capacity of concretefilled tubular beams. It is suggested that simple plastic theory be used to derive the ultimate moment capacity. Therefore the formulae derived in Section 3.2.3 of this book are adopted as an example for calculating the nominal moment capacity (Ms) of concrete-filled tubular beams. For RHS without rounded corners, Eq. (3.6) can be used. For RHS with rounded corners, Eq. (3.11) can be used. For CHS, Eq. (3.15) can be used. The design moment capacity is then determined by using the capacity factor I = 0.9 to give IMs. The above derivation is based on the assumption that no local buckling occurs in the RHS or CHS. A limit ratio of overall width to thickness (B/t) is given by Bergmann et al. (1995) for concrete-filled RHS to prevent local buckling, i.e. 235 B d 52 fy t (3.16) Equation (3.16) can be converted to the format used in the Australian Standard AS4100 as: fy fy 235 B 2t d 52 2 250 t 250 250 50.4 2 fy 250 (3.17) This limit ranges from 48.4 to 48.0 when the yield stress varies from 250MPa to 350MPa. It is slightly larger than the yield slenderness limit of 40 and 45 for unfilled cold-formed RHS and hot-rolled RHS subject to bending, respectively. A limit ratio of overall diameter to thickness (d/t) is given by Bergmann et al. (1995) for concrete-filled CHS in bending to prevent local buckling, i.e. d 235 d 90 t fy (3.18) Equation (3.18) can be converted to the format used in the Australian Standard AS5100 as: 235 d fy d 90 250 t 250 84.6 (3.19) CFST Members Subjected to Bending 41 This limit is larger than 50 specified in AS5100 to prevent local buckling for unfilled CHS. The ratio of slenderness limit for CFST CHS to unfilled CHS becomes 1.69 (=84.6/50). This is consistent with previous experimental testing by Elchalakani et al. (2001) that such a ratio is about 1.5 on average. 3.2.4.2 BS5400 The ultimate design moment capacity of concrete-filled tubular sections is given in Annex A.4. For concrete-filled RHS bending about the major axis: h dc º ª bf t f ( t f d c )» 0.95 f y «As (3.20) 2 ¼ ¬ in which h is the depth of concrete and dc is the distance between the neutral axis and the inner surface of the RHS, which is the same as dn defined in Figure 3.3. M CFST, RHS As 2 bf t f (3.21) b U 4 tf where As is the cross-sectional area of the RHS, bf is overall width of the RHS, tf is the thickness of the RHS and b is the clear width (= bf – 2t). The term U is the ratio of the average compressive stress in the concrete at failure to the design yield stress of the steel taken as 0.4 f cu U (3.22) 0.95 f y dc where fcu is the characteristic 28-day cube strength of concrete and fy is the yield stress of the steel hollow section. For concrete-filled CHS: M CFST,CHS 0.95 S f y (1 0.01 m) (3.23) in which the plastic section modulus of the steel section S, is given by: S §D · t 3 ¨ e 1¸ t © ¹ 2 (3.24) The parameter m represents the influence of concrete filling on the moment capacity. It is determined from Figure 3.9 where De is the outside diameter of the CHS, t is the wall thickness and U is the ratio defined in Eq. (3.22). Concrete-Filled Tubular Members and Connections 42 30 U = 0.20 28 U = 0.19 26 U = 0.18 24 0.15 0.14 0.13 U = 0.17 0.12 U = 0.16 22 value of U 0.11 0.10 20 0.09 0.08 18 0.07 16 m 0.06 14 0.05 12 0.04 10 0.03 8 0.02 6 4 0.01 2 U =0 0 0 5 10 15 20 25 30 35 40 45 50 55 60 De/t Figure 3.9 Chart to determine parameter m in Eq. (3.23) (adapted from Figure A.2 of BS5400 Part 5) The nominal moment capacity can be calculated from the above equations using fy to replace 0.95fy and using fcu to replace 0.4fcu. BS5400 Part 5 requires that concrete-filed RHS and CHS should have a wall thickness of not less than: t f t bs fy 3 Es for RHS (3.25) CFST Members Subjected to Bending t t De fy 8 Es 43 for CHS (3.26) Equation (3.25) can be rewritten in the format used in BS5950 Part 1 as: 3 Es bs 2 t f 3 Es d 2 H 2 275 tf fy (3.27) where H = (275/fy) and Es = 205,000MPa as defined in BS5950. The limit in Eq. (3.27) becomes (47.3H – 2). To prevent local buckling in concrete-filled RHS, the limiting width-tothickness ratio is about 20% to 70% larger than that (40H) of unfilled RHS (Matsui et al. 1997, Uy 2000 and Wright 1995), i.e. 48H to 68H. Therefore no local buckling needs to be considered for CFST RHS in bending if the thickness condition specified in Eq. (3.25) is satisfied. Equation (3.26) can be rewritten to the format used in BS5950 Part 1 as: De 8E s d t fy 8 E s f y § 275 · ¸ ¨ ¨ fy ¸ 275 ¹ © 8 Es f y 275 H2 (3.28) where H2 = (275/fy) and Es = 205,000MPa as defined in BS5950. When fy varies from 250MPa to 350MPa the ratio in Eq. (3.28) varies from 2 74H to 87H2. This limit is larger than 50H2 specified in BS5950 to prevent local buckling for Class 3 unfilled CHS. The ratio of slenderness limit for CFST CHS to unfilled CHS becomes 1.48 (=74/50) and 1.74 (=87/50) for grade 250 and 350 respectively. This is consistent with previous experimental testing by Elchalakani et al. (2001) that such a ratio is about 1.5 on average. 3.2.4.3 DBJ13-51 It was found (Han 2004, Han et al. 2006) that the moment versus curvature diagrams of CFST under bending have an initial elastic response followed by an inelastic behaviour with gradually decreasing stiffness until the ultimate moment is reached asymptotically (Han 2004, Han et al. 2006). The moment corresponding to the extreme fibre strain of 0.01 along the composite section is defined as the moment capacity (Mu). The ultimate design moment capacity of concrete-filled tubular sections is given by: M u J m Wsc f sc (3.29) For concrete-filled RHS: Jm 1.04 0.48 ln([ 0.1) (3.30a) Concrete-Filled Tubular Members and Connections 44 Wsc f sc B D2 6 (1.18 0.85 [0 ) f c For concrete-filled CHS: J m 1.1 0.48 ln([ 0.1) Wsc f sc S d3 32 (1.14 1.02 [0 ) f c (3.30b) (3.30c) (3.31a) (3.31b) (3.31c) in which [ is the nominal constraining factor and [0 is the design constraining factor, defined as: As f y [ (3.32) A c f ck [0 As f Ac fc (3.33) where B is the overall width of the RHS, D is the overall depth of the RHS (i.e. perpendicular to the neutral axis), d is the outside diameter of the CHS, As is the cross-sectional area of the RHS or CHS, Ac is the area of the concrete, fy is the tensile yield stress of the RHS or CHS, f is the design yield stress of the RHS or CHS given in GB50017 2003, fck is the characteristic strength of concrete given in GB50010 2002 and fc is the design compressive strength of concrete. The design yield stress f is approximately equal to fy/Js, whereas the design compressive concrete strength fc is approximately equal to fck/Jc. The value of material property factors (Js and Jc) is given in Table 2.5. The nominal moment capacity can be calculated from the above equations by adopting f = fy and fc = fck. A limit ratio of overall depth to thickness (D/t) is given in the standard for concrete-filled RHS to prevent local buckling, i.e. 235 (3.34) D / t d 60 fy A limit ratio of overall diameter to thickness (d/t) is given in the standard for concrete-filled CHS in bending to prevent local buckling, i.e. d 235 d 150 (3.35) t fy CFST Members Subjected to Bending 45 3.2.4.4 Eurocode 4 No design formulae are given in Eurocode 4 for the moment capacity of concretefilled tubular beams. It is suggested that rigid-plastic theory be used to derive the ultimate moment capacity. Therefore the formulae derived in Section 3.2.3 of this book are adopted as an example for calculating the nominal moment capacity (Ms) of concrete-filled tubular beams. For RHS without rounded corners, Eq. (3.6) can be used. For RHS with rounded corners, Eq. (3.11) can be used. For CHS, Eq. (3.15) can be used. The design moment capacity is determined using the same equations except that fy and fc are replaced by fy/Js and fc/Jc, respectively. The above derivation is based on the assumption that no local buckling occurs in the RHS or CHS. A limit ratio of overall depth to thickness (h/t) is given in Eurocode 4 for concrete-filled RHS to prevent local buckling, i.e. h 235 (3.36) d 52 52 H' t fy Equation (3.36) can be converted to the format used in the Eurocode 3 for unfilled RHS as: h 2t d 52 H'2 t (3.37) This limit ranges from 50 to 40 when the yield stress varies from 235MPa to 355MPa. It is slightly larger than the limit of 40Hc– 2 (i.e. 38 and 31 for fy of 235MPa and 355MPa, respectively) for unfilled RHS subject to bending. A limit ratio of overall diameter to thickness (d/t) is given in Eurocode 4 for concrete-filled CHS to prevent local buckling, i.e. d 235 d 90 90 H'2 (3.38) t fy This limit is larger than 70Hƍ2 specified in EC3 to prevent local buckling for Class 3 unfilled CHS. The ratio of slenderness limit for CFST CHS to CHS becomes 1.29 (=90/70). 3.2.5 Comparison of Specifications Rigid-plastic theory is adopted in AS5100 and Eurocode 4 with an assumed stress distribution. Neutral axis of the composite section is found followed by an integration to derive the plastic moment capacity. This is the case for both RHS and CHS. In BS5400 the same approach is adopted for RHS. The moment capacity Concrete-Filled Tubular Members and Connections 46 of CFST CHS is based on that of unfilled CHS with a correction factor to consider the influence of concrete filling. In the Chinese standard the CFST section is treated as one solid section described by the overall dimensions with a composite material property (fsc) and a correction factor obtained from regression analysis. The slenderness limits to prevent local buckling in CFST beams are compared in Table 3.2 for various codes. Table 3.2 Comparison of slenderness limits to prevent local buckling in CFST beams CFST CHS (d/t)limit Code 90Hc2 74H2 for Grade 250 87H2 for Grade 350 DBJ13-51 150Hc2 Eurocode 4 90Hc2 2 Note: H = 275/fy and Hc2 = 235/fy AS5100 BS5400 52Hc 38.6H CFST RHS (B/t)limit 60Hc 52Hc 3.2.6 Examples 3.2.6.1 Example 1 Determine the section moment capacity of a square hollow section (SHS 600 u 600 u 25 without rounded corners) filled with normal concrete for bending about the major axis. The nominal yield stress of the SHS is 345MPa. The compressive cylinder strength of concrete is 50 MPa and cubic strength is 60MPa. Solution according to AS 5100 1. Dimension and Properties D = 600mm B = 600mm t = 25mm fc = 50MPa fy = 345MPa 2. Section Slenderness Oe fy B 2t t 250 600 2 u 25 345 25 250 25.8 CFST Members Subjected to Bending 47 This is less than the limit given in Eq. (3.17), i.e. 50.4 – 2(345/250) = 48. Hence Eq. (3.6) can be used to determine the section moment capacity. 3. Moment Capacity B/t = 600/25 = 24 fc/fy = 50/345 = 0.145 From Figure 3.6, FRHS § 0.53 Using Eq. (3.2) dn § D 2t · ¸ FRHS ¨ © 2 ¹ § 600 2 u 25 · ¸ 0.53 | 146mm ¨ 2 ¹ © Using Eq. (3.5) the nominal moment capacity becomes: 1 1 ª º f y t «B (D t ) (D 2 t ) 2 » f y t (D 2 t ) 2 (1 FRHS ) 2 2 2 ¬ ¼ 1 (B 2 t ) d 2n f c 2 1 ª º 345 u 25 u «600 u (600 25) u (600 2 u 25) 2 » 2 ¬ ¼ 1 1 345 u 25 u u (600 2 u 25) 2 u (1 0.53) 2 u (600 2 u 25) u 146 2 u 50 2 2 M CFST, RHS 4280 u 10 6 288 u 10 6 293 u 10 6 The design moment capacity is given by: IM CFST, RHS 0.9 u 4861 4375kNm Solution according to BS5400 1. Dimension and Properties bs = bf = 600mm h 600 2 u 25 550mm tf = 25mm b b f 2 t f 600 2 u 25 550mm fcu = 60MPa fy = 345MPa Es = 205,000MPa 4861 u 10 6 Nmm 4861kNm Concrete-Filled Tubular Members and Connections 48 As b f (h 2 t f ) (b f 2 t f ) h 600 u (550 2 u 25) (600 2 u 25) u 550 57,500mm 2 2. Thickness Limit The thickness limit to prevent local buckling can be calculated using Eq. (3.25) as bs fy 3 Es 600 u 345 3 u 205000 14.2mm This condition is satisfied since tf is 25mm. 3. Moment Capacity From Eq. (3.22) U 0.4 f cu 0.95 f y 0.4 u 60 0.95 u 345 0.0732 From Eq. (3.21) dc As 2 bf t f b U 4 tf 57500 2 u 600 u 25 196mm 550 u 0.073 4 u 25 Using Eq. (3.20) the design moment capacity becomes M CFST , RHS h dc ª º b f t f ( t f d c )» 0.95 f y «A s 2 ¬ ¼ 550 196 ª º 0.95 u 345 u «57500 u 600 u 25 u (25 196)» 2 ¬ ¼ 4422 u 10 6 Nmm 4422kNm The nominal moment capacity can be calculated from the above equations using fy to replace 0.95fy and using fcu to replace 0.4fcu. Hence U f cu fy dc As 2 bf t f b U 4 tf 60 345 0.174 57500 2 u 600 u 25 141 mm 550 u 0.174 4 u 25 CFST Members Subjected to Bending M CFST , RHS 49 h dc ª º b f t f ( t f d c )» f y «A s 2 ¬ ¼ 550 141 ª º 345 u «57500 u 600 u 25 u (25 141)» 2 ¬ ¼ 4916 u 10 6 Nmm 4916kNm Solution according to DBJ13-51 1. Dimension and Properties B = 600mm D = 600mm t = 25mm fck = 38.5MPa (from GB50010 2002) fc = 27.5MPa (from Table 2.4) fy = 345MPa f = 295MPa (from GB50017 2003) Es = 206,000MPa (from GB50017 2003) A s B D (B 2 t ) (D 2 t ) 600 u 600 (600 2 u 25) u (600 2 u 25) 57,500mm 2 Ac (B 2 t ) (D 2 t ) (600 2 u 25) u (600 2 u 25) 302,500mm 2 2. Thickness Limit The thickness limit to prevent local buckling can be calculated using Eq. (3.34) as D / t d 60 235 fy 60 u 235 49.5mm 345 This condition is satisfied since t is 25mm. 3. Moment Capacity From Eq. (3.32) and Eq. (3.33) [ [0 As f y A c f ck 57,500 u 345 1.70 302,500 u 38.5 As f Ac fc 57,500 u 295 302,500 u 27.5 2.04 Concrete-Filled Tubular Members and Connections 50 Using Eq. (3.30) Jm Wsc f sc 1.04 0.48 ln([ 0.1) 1.04 0.48 u ln(1.70 0.1) 1.322 B D 2 600 u 600 2 36 u 10 6 mm3 6 6 (1.18 0.85 [ 0 ) f c (1.18 0.85 u 2.04) u 27.5 80.14MPa The ultimate design moment capacity of concrete-filled RHS is given by Eq. (3.29) as: Mu J m Wsc f sc 1.322 u 36 u 10 6 u 80.14 3814 u 10 6 Nmm 3814kNm The nominal moment capacity can be calculated from the above equations by adopting f = fy and fc = fck. Therefore [ [0 1.70 (as above) J m 1.322 (as above) Wsc 36 u 10 6 mm 3 (as above) f sc (1.18 0.85 [) f ck (1.18 0.85 u 1.70) u 38.5 101.06MPa The ultimate nominal moment capacity becomes: Mu J m Wsc f sc 1.322 u 36 u 10 6 u 101.06 4810 u 10 6 Nmm 4810kNm Solution according to Eurocode 4 1. Dimension and Properties h = 600mm b = 600mm t = 25mm fc = 50MPa fy = 345MPa 2. Overall Depth-to-Thickness Ratio The overall depth to thickness ratio (h/t) is 24 (=600/25) which is less than the limit given in Eq. (3.36) as 235 235 52 52 42.9 fy 345 CFST Members Subjected to Bending 51 Hence Eq. (3.6) can be used to determine the section moment capacity. 3. Moment Capacity The nominal capacity is determined using Eq. (3.6). The value is the same as that shown in the solution according to AS5100, i.e. M CFST , RHS 4861kNm The design moment capacity is determined using the same equations except that fy and fc are replaced by fy/Js and fc/Jc, respectively, where Js and Jc are given in Table 2.5. The symbols B and D in Section 3.2.3.1 are replaced by b and h in Eurocode 4 presentation. b/t = 600/25 = 24 fc / Jc f y / Js 50 / 1.5 345 / 1.0 0.097 | 0.1 From Figure 3.6, FRHS § 0.63 Using Eq. (3.2) dn § h 2t · ¨ ¸ FRHS © 2 ¹ § 600 2 u 25 · ¨ ¸ 0.63 | 173 mm 2 © ¹ The design moment capacity becomes: 1 ª º M CFST, RHS (f y / J s ) t «b (h t ) (h 2 t ) 2 » 2 ¬ ¼ 1 1 2 2 (f y / J s ) t (h 2 t ) (1 FRHS ) (b 2 t ) d 2n (f c / J c ) 2 2 1 ª º (345 / 1.0) u 25 u «600 u (600 25) u (600 2 u 25) 2 » 2 ¬ ¼ 1 (345 / 1.0) u 25 u u (600 2 u 25) 2 u (1 0.63) 2 2 1 u (600 2 u 25) u 1732 u (50 / 1.5) 2 4280 u 10 6 179 u 10 6 274 u 10 6 4733 u 10 6 Nmm 4733kNm Concrete-Filled Tubular Members and Connections 52 Comparison The moment capacities determined from the four different standards are compared in Table 3.3. The difference between the design moment capacities varies from 7% to 24% among the standards. This is mainly due to different material property factors or capacity factors being adopted in different standards, as shown in Table 2.5. However, the difference between the nominal moment capacities is less than 2.3%. This is because all the nominal moment capacity is based on simple plastic theory although slightly different stress distributions are adopted. Table 3.3 Comparison of moment capacities for CFST RHS Standard Design moment capacity (kNm) Nominal moment capacity (kNm) AS51002004 4375 BS54002005 4422 DBJ13-512003 3814 EC42004 4733 4861 4916 4810 4861 3.2.6.2 Example 2 Determine the section moment capacity of a circular hollow section (CHS 600 u 15) filled with normal concrete. The nominal yield stress of the CHS is 345MPa. The compressive cylinder strength of concrete is 50MPa and cubic strength is 60MPa. Solution according to AS5100 1. Dimension and Properties d = 600mm t = 15mm d t 600 15 rm 292.5mm 2 2 d 2 t 600 2 u 15 ri 285mm 2 2 fc = 50MPa fy = 345Mpa 2. Diameter-to-Thickness Ratio d fy 600 345 55.2 t 250 15 250 CFST Members Subjected to Bending 53 This is less than the limit of 84.6 given in Eq. (3.19). Hence Eq. (3.15) can be used to determine the section moment capacity. 3. Moment Capacity d/t = 600/15 = 40 fc/fy = 50/345 = 0.145 § 0.15 From Figure 3.8 FCHS § 0.30 Using Eq. (3.13) J0 S FCHS 2 S u 0.30 0.471 rad 2 Using Eq. (3.15) M CFST, CHS 2 f c ri3 cos 3 J 0 3 2 4 u 345 u 15 u 292.5 2 cos(0.471) u 50 u 2853 u cos 3 (0.471) 3 4 f y t rm2 cos J 0 1578 u 10 6 546 u 10 6 2124 u 10 6 Nmm 2124kNm The design moment capacity is given by: IM CFST, CHS 0.9 u 2124 1912kNm Solution according to BS 5400 1. Dimension and Properties De = 600mm t = 15mm fcu = 60MPa fy = 345MPa Es = 205,000MPa 2. Thickness Limit The thickness limit to prevent local buckling can be calculated using Eq. (3.26) as Concrete-Filled Tubular Members and Connections 54 De fy 8 Es 600 u 345 8 u 205000 8.7 mm This condition is satisfied since t is 15mm. 3. Moment Capacity From Eq. (3.24) §D · S t 3 ¨ e 1¸ © t ¹ 2 § 600 · 153 u ¨ 1¸ © 15 ¹ 2 5.133 u 10 6 mm3 From Eq. (3.22) U 0.4 f cu 0.95 f y 0.4 u 60 0.95 u 345 0.073 | 0.07 From Figure 3.9 with De/t of 40 and U of 0.07 m § 13.5 Using Eq. (3.23) the design moment capacity becomes: M CFST, CHS 0.95 S f y (1 0.01 m) 0.95 u 5.133 u 10 6 u 345 u (1 0.01u 13.5) 1910 u 10 6 Nmm 1910kNm The nominal moment capacity can be calculated from the above equations using fy to replace 0.95fy and using fcu to replace 0.4fcu. Hence U f cu fy 60 345 0.174 | 0.17 From Figure 3.9 with De/t of 40 and U of 0.17 m § 21.75 The nominal moment capacity becomes: M CFST, CHS S f y (1 0.01 m) 5.133 u 10 6 u 345 u (1 0.01u 21.75) 2156 u 10 6 Nmm 2156kNm CFST Members Subjected to Bending 55 Solution according to DBJ13-51 1. Dimension and Properties d = 600mm t = 15mm fck = 38.5MPa (from GB50010 2002) fc = 27.5MPa (from Table 2.4) fy = 345MPa f = 295MPa (from GB50017 2003) Es = 206,000MPa (from GB50017 2003) 1 1 As S d 2 S (d 2 t ) 2 4 4 1 1 u 3.142 u 600 2 u 3.142 u (600 2 u 15) 2 4 4 Ac 1 S (d 2 t ) 2 4 1 u 3.142 u (600 2 u 15) 2 4 27,568mm 2 255,176mm 2 2. Thickness Limit The thickness limit to prevent local buckling can be calculated using Eq. (3.35) as d 235 d 150 t fy 150 u 235 345 102 This condition is satisfied since d/t =40 < 102. 3. Moment Capacity From Eq. (3.32) and Eq. (3.33) [ [0 As f y A c f ck 27,568 u 345 255,176 u 38.5 As f Ac fc 27,568 u 295 1.159 255,176 u 27.5 0.968 Using Eq. (3.31) Jm Wsc f sc 1.1 0.48 ln([ 0.1) 1.1 0.48 u ln(0.968 0.1) 1.132 S d 3 3.142 u 6003 21.2 u 10 6 mm 3 32 32 (1.14 1.02 [ 0 ) f c (1.14 1.02 u 1.159) u 27.5 63.86MPa Concrete-Filled Tubular Members and Connections 56 The ultimate design moment capacity of concrete-filled CHS is given by Eq. (3.29) as: Mu J m Wsc f sc 1.132 u 21.2 u 10 6 u 63.86 1533 u 10 6 Nmm 1533kNm The nominal moment capacity can be calculated from the above equations by adopting f = fy and fc = fck. Therefore [ [0 0.968 (as above) J m 1.132 (as above) Wsc 21.2 u 10 6 mm3 (as above) f sc (1.14 1.02 [ 0 ) f ck (1.14 1.02 u 0.968) u 38.5 81.90MPa The ultimate nominal moment capacity becomes: Mu J m Wsc f sc 1.132 u 21.2 u 10 6 u 81.90 1966 u 10 6 Nmm 1966kNm Solution according to Eurocode 4 1. Dimension and Properties d = 600mm t = 15mm d t 600 15 rm 292.5mm 2 2 d 2 t 600 2 u 15 285mm ri 2 2 fc = 50MPa fy = 345MPa 2. Diameter-to-Thickness Ratio d t 600 15 40 The diameter-to-thickness ratio (d/t) is 40 (=600/15) which is less than the limit given in Eq. (3.38) as 235 235 90 u 90 u 61.3 fy 345 CFST Members Subjected to Bending 57 Hence Eq. (3.15) can be used to determine the section moment capacity. 3. Moment Capacity The nominal capacity is determined using Eq. (3.15). The value is the same as that shown in the solution according to AS5100, i.e. M CFST, CHS 2124 kNm The design moment capacity is determined using the same equations except that fy and fc are replaced by fy/Js and fc/Jc, respectively, where Js and Jc are given in Table 2.5. d/t = 600/15 = 40 fc / Jc f y / Js 50 / 1.5 345 / 1.0 0.097 | 0.1 From Figure 3.8, FCHS § 0.25 Using Eq. (3.13) J0 S FCHS 2 S u 0.25 2 0.393 rad Using Eq. (3.15), except that fy and fc are replaced by fy/Js and fc/Jc, the design moment capacity becomes: M CFST, CHS 2 (f c / J c ) ri3 cos 3 J 0 3 2 4 u (345 / 1.0) u 15 u 292.5 2 cos(0.393) u (50 / 1.5) u 2853 u cos 3 (0.393) 3 4 (f y / O s ) t rm2 cos J 0 1636 u 10 6 406 u 10 6 2042 u 10 6 Nmm 2042kNm Comparison The moment capacities determined from the four different standards are compared in Table 3.4. The difference between the design moment capacities varies from 7% to 33% among the standards. This is mainly due to different material property factors or capacity factors being adopted in different standards, as shown in Table 2.5. However, the difference between the nominal moment capacities is smaller (ranging from 1.5% to 9.6%). This is because all the nominal moment capacity is Concrete-Filled Tubular Members and Connections 58 based on simple plastic theory, although slightly different stress distributions are adopted. Table 3.4 Comparison of moment capacities for CFST CHS Standard Design moment capacity (kNm) Nominal moment capacity (kNm) AS51002004 1912 BS54002005 1910 DBJ13-512003 1533 EC42004 2042 2124 2156 1966 2124 3.3 MEMBER CAPACITY 3.3.1 Flexural-Torsional Buckling When a beam is being bent about its major axis, flexural-torsional buckling may occur. Flexural-torsional buckling is also called lateral buckling, lateral-torsional buckling, or out-of-plane buckling. There is no need to consider such buckling for RHS bending about the minor principal axis, SHS and CHS. Experimental investigations such as Zhao et al. (1995a) and analytical and finite element investigations (Pi and Trahair 1995, Zhao et al. 1995b) indicated that much higher lateral buckling strengths could be permitted for RHS beams. AISCLRFD (1999) does not even consider lateral buckling of RHS beams. This topic is covered extensively for unfilled steel sections in Trahair (1993) and Zhao et al. (2005). The lateral buckling capacity depends on the ratio of Ms/Mo, where Ms is the section moment capacity and Mo is the elastic buckling moment. For unfilled RHS without rounded corners (see Eq. (3.5) and Eq. (3.6)): 1 ª º Ms, RHS = f y t «B (D t ) (D 2 t ) 2 » 2 ¬ ¼ (3.39) For unfilled RHS (Zhao et al. 2005): M o, RHS = S 2 (G J ) ( E I y ) L2 where GJ is the torsion rigidity and EIy is the bending rigidity. The lower the ratio (Ms/Mo) is the less severe the lateral buckling is. (3.40) CFST Members Subjected to Bending 59 3.3.2 Effect of Concrete-Filling on Flexural-Torsional Buckling Capacity The increase in Ms due to concrete-filling depends on the concrete strength, as demonstrated in Zhao and Grzebieta (1999). An increase from 15% to 35% was obtained for a concrete strength from 10MPa to 60MPa, as shown in Figure 3.1. The increase in Ms due to concrete-filling can also be obtained by comparing MCFST,RHS given in Eq. (3.6) and MRHS given in Eq. (3.39). M CFST, RHS M RHS 2 | 1 (1 FRHS ) 2 0.25 (B / t ) (f c / f y ) FRHS 1 2 ( B / D) 1 2 ( B / D) (3.41) The elastic buckling moment Mo for CFST RHS can be approximately expressed in a similar way as Eq. (3.40) by using the composite torsion rigidity (GJ)composite and the composite bending rigidity (EI)composite. Mo = S 2 (G J ) composite (E I y ) composite (3.42) L2 in which G J composite (G J ) steel (G J ) concrete G steel J RHS G c J concrete (3.43) where Gsteel § 0.4Esteel and Gconcrete § 0.3Esteel, assuming no concrete cracks in the elastic range. The torsion constant can be found from Young and Budynas (2002). 4 (D t ) 2 (B t ) 2 t 2 (D t ) 2 (B t ) J RHS J concrete (3.44) E (D 2 t ) (B 2 t )3 | E (D t ) (B t )3 (3.45) where E = 0.196 to 0.263 for practical aspect ratio (D/B) ranging from 1.5 to 3. Therefore (GJ ) composite 1 G concrete J concrete G steel J RHS | 1 3E B § B· ¨1 ¸ 8 t © D¹ (GJ )steel E Iy composite 1 3 E Bt § Bt · ¨1 ¸ 4 2 t © Dt¹ E steel I y, RHS 0.6 E concrete I y, concrete (3.46) (3.47) Concrete-Filled Tubular Members and Connections 60 From Chapter 2 E concrete t E steel 8 From the geometry shown in Figure 3.3, the second moment area about the minor axis becomes: (D 2 t ) ( B 2 t ) 3 12 (3.48) D B3 (D 2 t ) (B 2 t )3 12 12 (3.49) I y, concrete I y, RHS The EI ratio can be expressed as: (EI y ) composite (EI y ) steel 1 0.6 E concrete I y, concrete E steel I y, RHS | 1 0.6 (D 2 t ) ( B 2 t ) 3 8 D B3 ( D 2 t ) ( B 2 t ) 3 1 0.6 (1 2 t / D) (1 2 t / B) 3 8 1 (1 2 t / D) (1 2 t / B) 3 (3.50) The ratio (Ms/Mo) for CFST RHS can be compared with that for unfilled RHS as § M s, CFST · ¨ ¸ ¨ M o, CFST ¸ © ¹ § M s, RHS · ¨ ¸ ¨ M o, RHS ¸ © ¹ § M s, CFST · ¨ ¸ ¨ M s, RHS ¸ © ¹ § M o, CFST · ¨ ¸ ¨ M o, RHS ¸ © ¹ § M s, CFST · ¨ ¸ ¨ M s, RHS ¸ © ¹ (GJ) composite (EI y ) composite (GJ) steel (EI y ) steel (3.51) where (Ms,CFST/Ms,RHS) is given by Eq. (3.41), (GJ)composite/(GJ)steel is given in Eq. (3.46) and (EIy)composite/(EIy)steel is given in Eq. (3.50). The ratio in Eq. (3.51) is plotted in Figure 3.10 for practical ranges of B/t, D/B and fc/fy. It can be seen that in general (Ms/Mo)CFST is much smaller than (Ms/Mo)RHS. Hence there is no need to consider the lateral buckling problem for CFST RHS beams. Ms/Mo Ratio (CFST/RHS) CFST Members Subjected to Bending 61 1.0 0.8 D/B = 3 0.6 fc/fy = 0.4 fc/fy = 0.3 0.4 fc/fy = 0.2 0.2 fc/fy = 0.1 fc/fy = 0.05 0.0 0 10 20 30 40 50 B/t Ms/Mo Ratio (CFST/RHS) (a) D/B = 3 1.0 0.8 D/B = 1.5 0.6 fc/fy = 0.4 fc/fy = 0.3 0.4 fc/fy = 0.2 0.2 fc/fy = 0.1 fc/fy = 0.05 0.0 0 10 20 30 40 50 B/t (b) D/B = 1.5 Figure 3.10 (Ms/Mo) ratio (CFST RHS versus unfilled RHS) 3.4 REFERENCES 1. 2. 3. 4. AISC–LRFD, 1999, Load and resistance factor design specification for structural steel buildings (Chicago: American Institute of Steel Construction). ASI, 1999, Design capacity tables for structural steel – Volume 2: Hollow sections (Sydney: Australian Steel Institute). Bergmann, R., Matsui, C., Meinsma, C. and Dutta, D., 1995, Design guide for concrete filled hollow section columns under static and seismic loading (Köln: TÜV-Verlag). BSI, 2000, Structural use of steelwork in building, BS5950, Part 1: General statement (London: British Standards Institution). 62 5. Concrete-Filled Tubular Members and Connections BSI, 2005, Steel, concrete and composite bridges, BS5400, Part 5: Code of practice for design of composite bridges (London: British Standards Institution). 6. DBJ13-51, 2003, Technical specification for concrete-filled steel tubular structures (Fuzhou: The Construction Department of Fujian Province). 7. Elchalakani, M., Zhao, X.L. and Grzebieta, R.H., 2001, Concrete filled circular steel tubes subjected to pure bending. Journal of Constructional Steel Research, 57(11), pp. 1141-1168. 8. Eurocode 3, 2005, Design of steel structures – Part 1.1: General rules and rules for buildings, EN1993-1-1:2005, May 2005 (Brussels: European Committee for Standardization). 9. Eurocode 4, 2004, Design of composite steel and concrete structures – Part 1.1: General rules and rules for buildings. EN1994-1-1:2004, December 2004 (Brussels: European Committee for Standardization). 10. Fam, A.Z. and Rizkalla, S.H., 2002, Flexural behaviour of concrete-filled fibre reinforced polymer circular tubes. Journal of Composites for Construction, ASCE, 6(2), pp. 23–32. 11. Fam, A.Z. and Son, J.K., 2008, Finite element modelling of hollow and concrete filled fibre composite tubes: Part 2 – Optimization of partial filling and a design method of poles. Engineering Structures, 30(10), pp. 2667–2676. 12. Furlong, R.W., 1967, Strength of steel-encased concrete beam-columns. Journal of Structural Division, ASCE, 93(ST5), pp. 113-124. 13. GB50010, 2002, Code for design of concrete structures, GB50010-2002 (Beijing: China Architecture & Building Press). 14. GB50017, 2003, Code for design of steel structures, National Standard of P.R. China, GB 50017-2003 (Beijing: China Architecture & Building Press). 15. Han, L.H., 2004, Flexural behaviour of concrete-filled steel tubes. Journal of Constructional Steel Research, 60(2), pp. 313–337. 16. Han, L.H., Lu, H., Yao, G.H. and Liao, F.Y., 2006, Further study on the flexural behaviour of concrete-filled steel tubes. Journal of Constructional Steel Research, 62(6), pp. 554–565. 17. Lu, Y. and Kennedy, D., 1994, Flexural behaviour of concrete-filled hollow structural sections. Canadian Journal of Civil Engineering, 21(1), pp. 111130. 18. Matsui, C., Mitani, I., Kawano, A. and Tsuda, K., 1997, AIJ design method for concrete filled steel tubular structures. In Proceedings of ASCCS Seminar on Concrete Filled Steel Tubes – A Comparison of International Codes and Practice, September, Innsbruck, Austria, pp. 93-116. 19. Pan, Y.G., 1990, Load carrying capacity of concrete-filled tubes subject to bending. Journal of Harbin University of Civil Engineering and Architecture, 2(1), pp. 41-49. 20. Pi, Y.L. and Trahair, N.S., 1995, Lateral buckling strengths of cold-formed rectangular hollow sections. Thin-Walled Structures, 22(2), pp. 71-95. CFST Members Subjected to Bending 63 21. Prion, H.G.L. and Boehme, J., 1994, Beam-column behaviour of steel tubes filled with high strength concrete. Canadian Journal of Civil Engineering, 21(2), pp. 207-218. 22. Standards Australia, 1998, Steel structures, Australian Standard AS4100 (Sydney: Standards Australia). 23. Standards Australia, 2004, Bridge design – Steel and composite construction, Australian Standard AS5100 Part 6 (Sydney: Standards Australia). 24. Tomii, M. and Sakino, K., 1979, Experimental studies on the ultimate moment of concrete filled square steel tubular beam-columns, Transactions of the Architectural Institute of Japan, 275(1), pp. 55-63. 25. Trahair N.S., 1993, Flexural torsional buckling of structures (London: E & FN Spon). 26. Uy, B., 2000, Strength of concrete filled steel box columns incorporating local buckling. Journal of Structural Engineering, ASCE, 126(3), pp. 341-352. 27. Uy, B., 2001, Strength of short concrete filled high strength steel box columns. Journal of Constructional Steel Research, 57(2), pp. 113-134. 28. Wright, H.D., 1995, Local stability of filled and encased steel sections. Journal of Structural Engineering, ASCE, 121(10), pp. 1382-1388. 29. Young, W.C. and Budynas, R.G., 2002, Roark's formulas for stress and strain, 7th ed. (New York: McGraw-Hill). 30. Zhao, X.L., Hancock, G.J. and Trahair, N.S., 1995a, Lateral buckling tests of cold-formed RHS beams. Journal of Structural Engineering, ASCE, 121(11), pp. 1565-1573. 31. Zhao, X.L., Hancock, G.J., Trahair, N.S. and Pi, Y.L., 1995b, Lateral buckling of RHS beams. In Proceedings of International Conference on Structural Stability and Design, Sydney, edited by Kitipornchai, S., Hancock, G.J. and Bradford, M. (Rotterdam: Balkema), pp. 55-60. 32. Zhao, X.L. and Grzebieta, R., 1999, Void-filled SHS beams subjected to large deformation cyclic bending. Journal of Structural Engineering, ASCE, 125(9), pp. 1020-1027. 33. Zhao, X.L., Wilkinson, T. and Hancock, G.J., 2005, Cold-formed tubular members and connections (Oxford: Elsevier). CHAPTER FOUR CFST Members Subjected to Compression 4.1 GENERAL Compression CFST members are commonly used as columns in building structures or bridge piers. The overall behaviour of CFST members in compression is similar to that of unfilled tubular columns described in Zhao et al. (2005). The strength of columns heavily depends on the member length (short, intermediate or long) and end-support conditions. The in-fill concrete delays or eliminates the local buckling of steel tubes, which leads to an increased section capacity and ductility. The bending stiffness of CFST columns increases due to the concrete filling, which results in an increased column capacity. A typical example is given in Figure 1.10(a). Large amounts of research have been carried out since the 1960s on CFST members subjected to compression. The experimental work reported in major journals is listed in Table 4.1 for stub columns and in Table 4.2 for columns subjected to static concentric loading. There are also many studies reported in conference papers and research reports, as listed in Shanmugam and Lakshmi (2001), and Gourley et al. (2008). It can be seen from Tables 4.1 and 4.2 that the experimental testing covered a wide range of parameters, i.e. d/t or B/t ranges from 10 to 150, fy varies from 200MPa to 800MPa, fc goes up to 140MPa, L/d or L/B ranges from 3 to 38. The work before 2001 was mainly focused on conventional mild steel and normal strength concrete. Recent research since 2001 covers various innovations, such as high strength steel tubes (Sakino et al. 2004, Liu and Gho 2005, Uy 2008), stainless steel tubes (Ellobody and Young 2006a, Young and Ellobody 2006, Lam and Gardner 2008, Dabaon et al. 2009a, 2009b), aluminium tubes (Zhou and Young 2008, 2009), elliptical hollow sections (Yang et al. 2008, Zhao and Packer 2009), high strength concrete (Ellobody et al. 2006, Yu et al. 2008), lightweight concrete (Mouli and Khelafi 2007), fibre reinforced concrete (Gopal and Manoharan 2006), recycled aggregate concrete (Yang and Han 2006a) and selfconsolidating concrete (Han and Yao 2004, Han et al. 2005). Apart from experimental testing, a large amount of research has been conducted on numerical analysis using the finite element method and on developing mechanics models and design formulae (for example, Han et al. 2001, Shanmugam et al. 2002, Bradford et al. 2002, Ellobody and Young 2006b, Liang et al. 2006). Performance-based design of CFST members is also under discussion in the literature (Liang 2009). Concrete-filled fibre reinforced polymer tubes in compression was reported by Fam and Rizkalla (2001), and Oehlers and Ozbakkaloglu (2008). Concrete-Filled Tubular Members and Connections 66 Section 4.2 deals with section capacity of CFST members in compression where failure modes, yield slenderness limits and concrete confinement are discussed. Section 4.3 deals with the interaction of local and overall buckling of columns in terms of column curves. Design rules in four different standards (AS5100, BS5450, DBJ13-51 and Eurocode 4) are presented in this chapter followed by examples on CFST CHS and CFST SHS. Comparisons are made among the design rules in the four standards. Table 4.1 Summary of experimental studies on CFST stub columns (a) CFST CHS Steel yield stress fy MPa Concrete compressive strength fc MPa Number of tests 29.5-48.5 363-633 21.2-41.9 14 33.8-64.6 92.1 35 226-324 270-328 303 18.2-37.3 73-85 37.4 11 6 4 28.3-42.3 338 24 2 40-150 266-342 27.15-31.15 3 22.9-30.5 343-365 25.1-83.9 13 25.4-55.5 33.3-66.7 39.7 16.7-152 45.4 30-134 13-46 52.1-76.6 38.95 45.8-60.7 72.7 72.8 52.6 34.8 35.7 9.7-59.7 310-483 304 340 279-823 318 282-404 271-358 336-350 360 350 363 363 404 300 370 217-268 61.4 46.8 51-79 25.4-85.1 55.2 68.2-72.0 46-53 23.9-34.2 17.8-32 34.1-61.8 59.4 59.4 97.3 37-108 53-110 44.8-106 21 12 4 36 1 26 8 15 24 12 16 8 4 3 4 31 d/t Reference Gardner and Jacobson (1967) Gardner (1968) Prion and Boehme (1994) Han (2000b) Campione and Scibilia (2002) Huang et al. (2002) Giakoumelis and Lam (2004) Han (2004) Han and Yao (2004) McAteer et al. (2004) Sakino et al. (2004) Wang et al. (2004) Han et al. (2005) Kang et al. (2005) Yang and Han (2006b) Gupta et al. (2007) Yu et al. (2007) Han et al. (2008a) Han et al. (2008b) Yu et al. (2008) Liew and Xiong (2009) Thayalan et al. (2009) Zhou and Young (2009) CFST Members Subjected to Compression 67 Table 4.1 Summary of experimental studies on CFST stub columns (continued) (b) B/t Steel yield stress fy MPa 16-20 44.5-73.9 21-55.6 15-24 40-100 42-102 20.5-36.5 31.5-41.0 22-42 33.3-40 15.8-47.2 40-150 45.3 45.3 66.7 10-25 24-54 18.4-73.9 30-134 17.2-34.5 13-43 20-35 26.3-100 19.9-47.4 51.5-53.6 25.8-54.2 25 50-131 16-20 62.5 52-105 76-100 52.6 8.2-50 40-80 100 33.3-50 340-363 266 317-767 300-439 300 300 321-330 228-294 750 338 194-228 266-342 340 340 304 289-400 761 262-835 282-404 300-495 284-372 495 234-311 255-347 330-388 448-536 465 280 346-350 363 258-363 270-342 404 115-280 285 338 324 Concrete compressive strength fc MPa 32.6-37.8 39.2-48.3 23.8-59.1 38.1-90.4 45-57 32-50 14.0-43.7 35.5-47.4 28-32 24 47.4 23.9-31.2 18.5 16.1-28.8 46.8 24.6-79.1 20.34 25.4-91.9 40.7-64.8 55-106 46-53 60-89 50.1-54.8 47.8-63.7 29.3-34.2 46.6-83.5 36.1 46 29.4-35.8 59.4 59.4-61.4 46.6-55.2 97.3 36.1-109 27.8-49.5 20.4-41.0 47.4 CFST RHS Number of tests Reference 13 4 26 13 10 8 20 16 6 2 24 14 3 4 6 15 4 48 24 26 8 22 15 50 15 14 1 12 8 16 28 36 4 32 10 12 16 Shakir-Khalil and Mouli (1990) Ge and Usami (1992) Kato (1996) Cederwall et al. (1997) Uy (1998) Uy (2000) Han et al. (2001) Han and Yang (2001) Uy (2001) Campione and Scibilia (2002) Han (2002) Huang et al. (2002) Han and Yao (2003a) Han and Yao (2003b) Han and Yao (2004) Lam and Williams (2004) Mursi and Uy (2004) Sakino et al. (2004) Han et al. (2005) Liu and Gho (2005) Kang et al. (2005) Liu (2005) Tao et al. (2005) Zhang et al. (2005) Yang and Han (2006b) Young and Ellobody (2006) Cai and Long (2007) Guo et al. (2007) Mouli and Khelafi (2007) Han et al. (2008a) Han et al. (2008b) Tao et al. (2008) Yu et al. (2008) Zhou and Young (2008) Dabaon et al. (2009a) Tao et al. (2009) Yang and Han (2009) Concrete-Filled Tubular Members and Connections 68 Table 4.2 Summary of experimental studies on CFST columns d/t or B/t L/d or L/B Steel yield stress fy MPa Concrete compressive strength fc MPa CFST CHS 21.4-35.6 21.2-34.9 18.3-37.3 41.5 20.7-61.0 39.9-58.5 23.8-28.2 25.5-37.5 37.4 64.5 8-26.7 41.6 46.8 35.5-40.6 17.8-32 97.3 44-139 CFST RHS 23.4-43.1 39.9 Number of tests 36-98.3 29.5-48.5 33.8-64.6 15.2-59 7.5-98.3 36.9-40.3 21-47 24 29.6 33.1 35.1-57.9 38 66.7 64.2 25.3-32.6 52.6 34.8 6-8 8-15 11-13 6-21 4-42 4-33 4 33-38 18.4 4 15-20 20 10 10 4-7 9-30 8-14 294-420 369-614 226-324 406-490 275-682 340-353 285-537 348 324 433 350-355 275 304 343 360 404 393-405 8 10 8 11 63 27 3 11 2 6 12 2 5 5 48 6 8 26.5-47.7 22.7 7-9 3-23 336-492 324 16 23 386.3 35.2 1 20 18.2 346.7 38.5 1 73 40.1 15 11.7-40.4 20.5-36.5 21.7-25 20.5-30.7 34.0-90.6 45.3 20-50 34.1-41.0 66.7 25-75 51 15-37.5 23.4-43.5 22.2 80 52.6 4 4-29 10 4-4.8 13-22 23-26 5-6 4-12 12 10-25 5-6 12 5 12 4 4-12 12 6-12 9-30 266 431 379 312-430 321-330 400-450 294 340 340 240-366 294 304 345-366 344 452-473 348-367 380 270 404 40.4-40.6 24-25.4 72 23.8-30.5 25.2-43.7 48.9-71.2 47.2 18.5 28.8 8-26.7 27.4 46.8 47.5 35.5-40.6 36.1 58.8 29-84 46.6-47.4 97.3 2 7 1 11 8 4 8 20 2 24 6 5 15 5 7 27 22 6 6 5 6 Reference Furlong (1967) Gardner and Jacobson (1967) Gardner (1968) Knowles and Park (1969) Task Group (1979) Kato (1996) Schneider (1998) Han (2000a) Han (2000b) Johansson and Gylltoft (2002) Ghannam et al. (2004) Gopal and Manoharan (2004) Han and Yao (2004) Yang and Han (2006a) Gupta et al. (2007) Yu et al. (2008) Liew and Xiong (2009) Furlong (1967) Knowles and Park (1969) Shakir-Khalil and Zeghiche (1989) Shakir-Khalil and Mouli (1990) Ge and Usami (1992) Nakamura (1994) Cederwall et al. (1997) Schneider (1998) Han et al. (2001) Vrcelj and Uy (2001) Han and Yang (2003a) Han and Yao (2003a) Han and Yao (2003b) Ghannam (2004) Han et al. (2004b) Han and Yao (2004) Cai and He (2006) Yang and Han (2006a) Cai and Long ( 2007) Lee (2007) Lue et al. ( 2007) Tao et al. (2007) Yu et al. (2008) CFST Members Subjected to Compression 69 4.2 SECTION CAPACITY 4.2.1 Local Buckling in Compression The local buckling of tubular sections in compression was well documented in Zhao et al. (2005). Typical inelastic local buckling modes are shown in Figure 4.1(a)(i) for unfilled SHS (so-called “roof mechanism”) and in Figure 4.1(b)(i) for unfilled CHS (so-called “elephant’s foot”). Concrete filling delays or eliminates local buckling of tubular sections. The typical failure modes of CFST sections are shown in Figure 4.1(a)(ii) for SHS and in Figure 4.1(b)(ii) for CHS. The failure mode is outward folding mechanism. Similar failure mode is also observed for concrete-filled double skin tubes (CFDST) as shown in Figures 4.1(a)(iii) and 4.1(b)(iii). (i) Unfilled SHS (ii) CFST SHS (iii) CFDST (a) Square Hollow Sections (i) Unfilled CHS (ii) CFST CHS (b) Circular Hollow Sections Figure 4.1 Comparison of failure mode (iii) CFDST 70 Concrete-Filled Tubular Members and Connections Local buckling occurs if the width-to-thickness ratio or diameter-to-thickness ratio of a tube exceeds a certain value, as given in Section 4.2.2 of Zhao et al. (2005). In general, concrete-filling increases the limiting width-to-thickness ratio or diameter-to-thickness ratio (Bergmann et al. 1995). For example, the limiting value in Eurocode 4 for CFST RHS sections is about 1.2 times that for unfilled RHS given in Eurocode 3. Research by Matsui et al. (1997), Uy (2000) and Wright (1995) showed that the increase in limiting value for CFST RHS sections is about 50%, while the actual value depends on the boundary conditions assumed in the analysis. However, the same limiting value is used in Eurocode 4 for CFST CHS in compression as that for unfilled CHS, whereas an increase of 70% is adopted in AIJ (1997). 4.2.2 Confinement of Concrete Some typical longitudinal stress versus strain curves of the concrete core in CFST sections are plotted in Figure 4.2(a) for CHS and in Figure 4.2(b) for SHS, where [ is the constraining factor defined in Eq. (3.32). It is clear that more confinement is achieved for CFST sections with a larger constraining factor. It is also obvious that more confinement is found in CFST CHS sections than that in CFST SHS sections. This explains why an increased concrete strength is normally considered in designing CFST CHS members. The confinement provided by a steel tube to concrete will reduce if the steel tube reaches its yield strength. For real, long concrete-filled columns, which will fail by overall flexural buckling, it can be expected that the steel tube may remain elastic and still provide significant confinement to the concrete core. A reduced steel capacity is considered in some codes such as Eurocode 4 and CSA-S16-09 because of hoop tension due to the outward expansion of the concrete. A typical stress–strain relationship of CFST sections in compression is plotted in Figure 4.3. The behaviour depends on the value of the constraining factor ([), i.e. three paths exist after yielding of the section. When [ is smaller than a certain value ([o) the stress starts to drop. When [ is larger than a certain value ([o) the stress continues to increase. For CFST CHS section [o is about 1.1 whereas for CFST RHS section [o is about 4.5. CFST Members Subjected to Compression 71 Stress (MPa) ȟ=0.4 ȟ=0.8 ȟ=1.0 ȟ=1.2 ȟ=1.6 ȟ=2.0 Strain (ȝİ) (a) Circular section Stress (MPa) ȟ=0.4 ȟ=0.8 ȟ=1.0 ȟ=1.2 ȟ=1.6 ȟ=2.0 Strain (ȝİ) (b) Square section Figure 4.2 Examples of concrete confinement Vsc [ > [o [ = [o [ < [o H sc Figure 4.3 Schematic view of stress–strain curves of CFST section in compression Concrete-Filled Tubular Members and Connections 72 4.2.3 Design Section Capacity 4.2.3.1 AS5100 CFST RHS The design section capacity for concrete-filled RHS is given by N u I A s f y Ic A c f c (4.1) The nominal capacity for concrete-filled RHS can be estimated by using Eq. (4.1) without the capacity factors I and Ic. (4.2) N u , no min al A s f y A c f c in which As is the cross-sectional area of the RHS, Ac is the area of concrete in the cross-section, fy is the yield stress of the RHS and fc is the characteristic compressive strength of concrete. The capacity factors I and Ic are taken as 0.9 and 0.6, respectively. CFST CHS The increase in concrete strength caused by the confinement of the steel circular tube may be taken into account if the following requirements are met: (a) The relative slenderness Ȝr, as defined in Eq. (4.3), is not greater than 0.5. (b) The eccentricity of loading (e) under the greatest design bending moment is not greater than d/10. Ns Or (4.3a) N cr Ns N cr As f y Ac fc (4.3b) S 2 (EI) e (4.3c) ( k e L) 2 in which As is the cross-sectional area of the CHS, Ac is the area of concrete in the cross-section, fy is the yield stress of the CHS and fc is the characteristic compressive strength of concrete. L is the column length, ke is the effective length factor and (EI)e is the effective elastic flexural stiffness. For members with idealised end restraints the values of the effective length factor (ke) are summarised in Table 4.3. For members in frames the effective length factor (ke) depends on the ratios of the compression member stiffness to the end restraint stiffness. Charts for the effective length factor (ke) are given in AS5100. CFST Members Subjected to Compression 73 Table 4.3 Effective length factors for members with idealised end restraints (adapted from Figure 4.3.2.2 of AS 5100 Part 6) Braced member ke = 0.7 ke = 0.85 Sway member ke = 1.0 ke = 1.2 ke = 2.2 The effective elastic flexural stiffness (EI)e is defined as (EI) e I E s Is Ic E c I c ke = 2.2 (4.4) where Es is the modulus of elasticity for the CHS, Ec is the modulus of elasticity for concrete given in Table 2.2, Is and Ic are the second moment of area of the CHS and concrete, respectively. The design section capacity for concrete-filled CHS is given by ª t fy º N u I A s K2 f y Ic A c f c «1 K1 » (4.5) d fc ¼ ¬ in which t is the thickness of the CHS, d is the outside diameter of the CHS and the other symbols (As, Ac, fy and fc) are defined as above. The capacity factors I and Ic are taken as 0.9 and 0.6, respectively. The nominal capacity for concrete-filled CHS can be estimated by using the above equations without the capacity factors I and Ic. N u , no min al ª t fy º A s K2 f y A c f c «1 K1 » d fc ¼ ¬ (4.6) The coefficients K1 and K2 for the case where eccentricity of loading (e) is zero are called K10 and K20. They are given by K10 K20 4.9 18.5 O r 17 O2r t 0 0.25 (3 2 O r ) d 1.0 (4.7a) (4.7b) Concrete-Filled Tubular Members and Connections 74 where Or is the relative slenderness defined as Eq. (4.3). If the eccentricity of loading (e) lies in the range 0 < e d d/10, K1 and K2 shall be calculated as follows: K1 § 10 e · K10 ¨1 ¸ d ¹ © K2 K20 (1 K20 ) (4.8a) 10 e d (4.8b) 4.2.3.2 BS5400 CFST RHS The design section capacity for concrete-filled RHS is given by N u 0.95 f y A s 0.45 f cu A c (4.9) in which As is the cross-sectional area of the RHS, Ac is the area of concrete in the cross-section, fy is the yield stress of the RHS and fcu is the characteristic cube compressive strength of concrete. BS5400 Part 5 requires that concrete-filled RHS should have a wall thickness of not less than the value given in Eq. (3.25). The concrete contribution factor (Dc) should satisfy the following condition. 0.45 A c f cu 0.1 D c 0.8 (4.10) Nu where Nu is given in Eq. (4.9). The nominal section capacity for concrete-filled RHS can be estimated from Eq. (4.9) using fy to replace 0.95fy and using fcu to replace 0.45fcu. CFST CHS The enhanced strength of triaxially constrained concrete may be taken into account to predict the section capacity of concrete-filled CHS. The design section capacity for concrete-filled RHS is given by Nu 0.95 f ' y A s 0.45 f cc A c (4.11) f cc f cu C1 t fy De (4.12) f 'y C2 f y (4.13) where t is the thickness of the CHS, De is the outside diameter of the CHS, C1 and C2 are constants given in Table 4.4 where le is the effective length of column. The values of C1 and C2 are also plotted in Figure 4.4 to assist the designers. CFST Members Subjected to Compression 75 Table 4.4 Values of constants C1 and C2 for axially loaded concrete-filled CHS (adapted from Table 3 of BS5400) C1 9.47 6.40 3.81 1.80 0.48 0 C1 le/De 0 5 10 15 20 25 C2 0.76 0.80 0.85 0.90 0.95 1.0 10 9 8 7 6 5 4 3 2 1 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 le/De (a) Constant C1 1 C2 0.9 0.8 0.7 0.6 0.5 0 2 4 6 8 10 12 14 16 18 20 22 24 26 le/De (b) Constant C2 Figure 4.4 Values of constants C1 and C2 BS5400 Part 5 requires that concrete-filled CHS should have a wall thickness of not less than that given in Eq. (3.26). Concrete-Filled Tubular Members and Connections 76 The concrete contribution factor (Dc) should satisfy the following condition. 0.45 A c f cc 0.8 (4.14) 0.1 D c Nu where fcc is given in Eq. (4.12) and Nu is given in Eq. (4.11). The nominal section capacity for concrete-filled CHS can be estimated from Eq. (4.11) using fy to replace 0.95fƍy and using fcu to replace 0.45fcc. 4.2.3.3 DBJ13-51 The design section capacity of concrete-filled RHS or CHS columns is given by N u f sc A sc (4.15) in which A sc As Ac (4.16) For concrete-filled RHS: f sc (1.18 0.85 [ 0 ) f c (4.17) For concrete-filled CHS: f sc (1.14 1.02 [ 0 ) f c (4.18) in which [0 is the design constraining factor, defined as: [0 As f Ac fc (4.19) As is the cross-sectional area of the RHS or CHS, Ac is the area of the concrete, f is the design yield stress of the RHS or CHS given in GB50017, 2003, fc is the design compressive strength of concrete. The design yield stress f is approximately equal to fy/Js, whereas the design compressive concrete strength fc is approximately equal to fck/Jc. fy is the tensile yield stress of the RHS or CHS, whereas fck is the characteristic strength of concrete given in GB50010, 2002. The value of material property factors (Js and Jc) is given in Table 2.5. The nominal section capacity can be calculated from the above equations by adopting f = fy and fc = fck. CFST Members Subjected to Compression 77 4.2.3.4 Eurocode 4 CFST RHS The design section capacity of concrete-filled RHS is given by Nu A a f yd A c f cd (4.20) in which Aa is the cross-sectional area of RHS and Ac is the cross-sectional area of concrete. fyd is the design value of the yield strength of the RHS which is defined as fy/Js. fcd is the design value of the cylinder compressive strength of concrete which is defined as fck/Jc. fy is the tensile yield stress of the RHS, whereas fck is the characteristic value of the cylinder compressive strength of concrete at 28 days. The value of material property factors (Js and Jc) is given in Table 2.5. The steel contribution ratio (į) should fulfil the following condition: A a f yd 0.2 d G d 0.9 (4.21) Nu where Nu is given in Eq. (4.20). The nominal section capacity can be calculated from Eq. (4.20) by adopting fyd = fy and fcd = fck. CFST CHS The increase in concrete strength caused by the confinement of the steel circular tube may be taken into account if the following requirements are met: (a) The relative slenderness CȜ, as defined in Eq. (4.22), is no greater than 0.5. (b) The ratio of load eccentricity to the CHS outside diameter (e/d) is no greater than 0.1. O N pl, Rk N pl, Rk N cr N cr A a f y A c f ck S 2 (EI) eff ( k e L) 2 (4.22a) (4.22b) (4.22c) in which Aa is the cross-sectional area of the CHS, Ac is the area of concrete in the cross-section, fy is the yield stress of the CHS and fck is the characteristic compressive strength of concrete. L is the column length, ke is the effective length factor and (EI)e is the effective elastic flexural stiffness. Concrete-Filled Tubular Members and Connections 78 For members with idealised end restraints the values of ke summarised in Table 4.3 can be adopted. For members in frames the effective buckling length (keL) is defined in Eurocode 3 (2005). The effective elastic flexural stiffness (EI)eff is defined as (EI) eff E a I a 0.6 E c I c (4.23) where Ea is the modulus of elasticity for the CHS, Ec is the modulus of elasticity for concrete given in Table 2.2, Ia and Ic are the second moment of area of the CHS and concrete, respectively. The design section capacity for concrete-filled CHS is given by ª t fy º N u A a Ka f yd A c f cd «1 Kc (4.24) » d f ck ¼ ¬ in which t is the thickness of the CHS, d is the outside diameter of the CHS and the other symbols (Aa, Ac, fyd and fcd) are defined as above. The nominal section capacity can be calculated from Eq. (4.24) by adopting fyd = fy and fcd = fck. The coefficients Kc and Ka for the case where eccentricity of loading (e) is zero are called Kc0 and Ka0. They are given by 2 Kc 0 4.9 18.5 O 17 O t 0 (4.25a) Ka 0 0.25 (3 2 O) d 1.0 (4.25b) whereCȜ is the relative slenderness defined as Eq. (4.22). If the ratio (e/d) lies in the range 0 < e/d d 0.1, Kc and Ka shall be calculated as follows: § 10 e · Kc Kc 0 ¨ 1 (4.26a) ¸ d ¹ © 10 e (4.26b) Ka Ka 0 (1 Ka 0 ) d For e/d >1.0, Kc = 0 and Ka = 1.0. 4.2.4 Examples 4.2.4.1 Example 1 Determine the section capacity of a square hollow section (SHS 600 u 600 u 25 without rounded corners) filled with normal concrete subjected to compression. The effective buckling length is 4570mm. The nominal yield stress of the SHS is 345MPa. The compressive cylinder strength of concrete is 50MPa and cubic strength is 60MPa. CFST Members Subjected to Compression 79 Solution according to AS5100 1. Dimension and Properties D = 600mm B = 600mm t = 25mm fc = 50MPa fy = 345MPa A s B D (B 2 t ) (D 2 t ) 57,500mm Ac 600 u 600 (600 2 u 25) u (600 2 u 25) 2 (B 2 t ) (D 2 t ) (600 2 u 25) u (600 2 u 25) 302,500mm 2 2. Section Capacity From Table 2.5, the capacity factors I and Ic are taken as 0.9 and 0.6. The design section capacity for concrete-filled RHS is given by Eq. (4.1): Nu I A s f y Ic A c f c 0.9 u 57500 u 345 0.6 u 302500 u 50 26,929 u 103 N 26,929kN The nominal capacity for concrete-filled RHS can be estimated by using Eq. (4.1) without the capacity factors I and Ic. N u , no min al As f y Ac fc 57500 u 345 302500 u 50 34963 u 103 N 34963 kN Solution according to BS5400 1. Dimension and Properties bs = bf = 600mm h 600 2 u 25 550mm tf = 25mm b b f 2 t f 600 2 u 25 550mm fcu = 60MPa fy = 345MPa Es = 205,000MPa A s b f (h 2 t f ) (b f 2 t f ) h 600 u (550 2 u 25) (600 2 u 25) u 550 57,500 mm 2 Ac (b f 2 t f ) h (600 2 u 25) u 550 302,500 mm 2 Concrete-Filled Tubular Members and Connections 80 2. Thickness Limit The thickness limit to prevent local buckling can be calculated using Eq. (3.25) as bs fy 3 Es 600 u 345 3 u 205000 14.2mm This condition is satisfied since tf is 25mm. 3. Section Capacity The design section capacity for concrete-filled RHS is given by Nu 0.95 f y A s 0.45 f cu A c 3 27013 u 10 N 0.95 u 345 u 57500 0.45 u 60 u 302500 27013 kN The nominal section capacity for concrete-filled RHS can be estimated from Eq. (4.9) using fy to replace 0.95fy and using fcu to replace 0.45fcu. N u , no min al f y A s f cu A c 37,988 u 103 N 345 u 57,500 60 u 302,500 37,988kN 4. Concrete Contribution Factor The concrete contribution factor (Dc) becomes 0.45 A c f cu 0.45 u 302,500 u 60 Dc 0.302 Nu 27,013 u 103 which satisfies the condition set in Eq. (4.10). Solution according to DBJ13-51 1. Dimension and Properties B = 600mm D = 600mm t = 25mm fck = 38.5MPa (from GB50010 (2002)) fc = 27.5MPa (from Table 2.2) fy = 345MPa f = 295MPa (from GB50017 (2003)) Es = 206,000MPa (from GB50017 (2003)) CFST Members Subjected to Compression As 81 B D (B 2 t ) (D 2 t ) 600 u 600 (600 2 u 25) u (600 2 u 25) 57,500mm 2 Ac (B 2 t ) (D 2 t ) (600 2 u 25) u (600 2 u 25) 302,500 mm 2 2. Properties of Composite Section From Eq. (4.16) the area becomes A sc As Ac 360,000mm 2 57,500 302,500 From Eq. (4.19) the design constraining factor becomes: As f 57,500 u 295 2.04 [0 A c f c 302,500 u 27.5 Using Eq. (4.17) the design compression strength becomes: f sc (1.18 0.85 [ 0 ) f c (1.18 0.85 u 2.04) u 27.5 80.14MPa 3. Section Capacity From Eq. (4.15) the design section capacity is given by Nu f sc A sc 80.14 u 360,000 28850 u 103 28850kN The nominal section capacity can be calculated from the above equations by adopting f = fy and fc = fck. Therefore As f y 57,500 u 345 302,500 u 38.5 [0 [ f sc (1.18 0.85 [) f ck A c f ck N u , no min al f sc A sc (1.18 0.85 u 1.70) u 38.5 101.06 MPa 101.06 u 360000 Solution according to Eurocode 4 1. Dimension and Properties h = 600mm b = 600mm t = 25mm fck = 50MPa fy = 345MPa fyd = 345/1.0 = 345 fcd = 50/1.5 = 33.33 1.70 36,382 u 103 N 36,382 kN Concrete-Filled Tubular Members and Connections 82 Aa h b (h 2 t ) (b 2 t ) 600 u 600 (600 2 u 25) u (600 2 u 25) 57,500mm 2 Ac (h 2 t ) (b 2 t ) (600 2 u 25) u (600 2 u 25) 302,500 mm 2 2. Section Capacity From Eq. (4.20) the design section capacity of concrete-filled RHS becomes: Nu A a f yd A c f cd 57,500 u 345 302,500 u 33.33 29,920 u 103 N 29,920kN The nominal section capacity can be calculated from Eq. (4.20) by adopting fyd = fy and fcd = fck. Therefore N u , no min al A a f y A c f ck 3 34,963 u 10 N 57,500 u 345 302,500 u 50 34,963kN 3. Steel Contribution Factor The steel contribution ratio (į) becomes: A a f yd 57,500 u 345 0.66 29,920 u 103 which satisfies the condition set in Eq. (4.21). G Nu Comparison The compressive section capacities determined from the four different standards are compared in Table 4.5. The difference between the design section capacities varies from 1% to 11% among the standards. This is mainly due to different material property factors or capacity factors being adopted in different standards, as shown in Table 2.5. The nominal section capacity predicted by BS5400 is higher than those from other standards. This is because that cube compressive strength of concrete (60MPa) is used in BS5400 rather than the cylinder strength (50MPa) used in other standards. The difference in nominal capacities among the other three standards is about 4%. Table 4.5 Comparison of compressive section capacities for CFST RHS Standard Design section capacity (kN) Nominal section capacity (kN) AS51002004 26,929 34,963 BS54002005 27,013 37,988 DBJ13-512003 28,850 36,382 EC42004 29,920 34,963 CFST Members Subjected to Compression 83 4.2.4.2 Example 2 Determine the section capacity of a circular hollow section (CHS 600 u 15) filled with normal concrete subjected to compression. The effective buckling length is 4570mm. The nominal yield stress of the CHS is 345MPa. The compressive cylinder strength of concrete is 50MPa and cubic strength is 60MPa. Solution according to AS5100 1. Dimension and Properties d = 600mm t = 15mm fc = 50MPa fy = 345MPa 1 1 S d 2 S (d 2 t ) 2 4 4 As Ac 27,568mm 2 1 S (d 2 t ) 2 4 1 1 u 3.1416 u 600 2 u 3.1416 u (600 2 u 15) 2 4 4 1 u 3.142 u (600 2 u 15) 2 4 255,176mm 2 Es = 200,000MPa (from AS4100) Ec = 0.5 (2400)1.5 0.043 (50) = 17,875 MPa (from Section 2.1.2.1 asuming concrete density of 2400kg/m3) Ic Is S (d 2 t ) 4 64 3.1416 u (600 2 u 15) 4 64 S d 4 S (d 2 t ) 4 64 64 5182 u 106 mm 4 3.1416 u 600 4 3.1416 u (600 2 u 15) 4 64 64 1180 u 106 mm 4 keL = 4570mm 2. Confinement Requirement Using Eq. (4.4) (EI) e I E s Is Ic E c I c 267,983 u 109 Nmm 2 From Eq. (4.3c) 0.9 u 200,000 u 1180 u 10 6 0.6 u 17,875 u 5182 u 10 6 Concrete-Filled Tubular Members and Connections 84 S 2 (EI) e N cr ( k e L) 2 3.1416 2 u 267,983 u 109 4570 2 126,642kN Using Eq. (4.3b) Ns As f y A c f c 27,568 u 345 255,176 u 50 22,270 u 103 N 22,270kN From Eq. (4.3a) Ns N cr Or 22,270 126,642 0.419 < 0.5 Therefore the requirement for confinement is satisfied. 3. Design Section Capacity Because there is no eccentricity of loading (e = 0) the coefficients K1 and K2 are determined using Eq. (4.7): K1 K10 4.9 18.5 O r 17 O2r K2 K20 0.25 (3 2 O r ) 4.9 18.5 u 0.419 17 u 0.419 2 0.25 u (3 2 u 0.419) 0.133 0.960 The design section capacity for concrete-filled CHS is given by Nu ª t fy º I A s K2 f y Ic A c f c «1 K1 » d fc ¼ ¬ 15 345 º ª 0.9 u 27,568 u 0.960 u 345 0.6 u 255,176 u 50 u «1 0.133 u u 600 50 »¼ ¬ 16,048 u 103 N 16,048kN 4. Nominal Section Capacity The nominal capacity for concrete-filled RHS can be estimated by using the above equations without the capacity factors I and Ic. Therefore (EI) e E s Is E c I c 200,000 u 1180 u 106 17,875 u 5182 u 106 328,633 u 109 Nmm 2 CFST Members Subjected to Compression N cr S 2 (EI) e ( k e L) 2 3.1416 2 u 328,633 u 109 4570 2 Ns 22,270kN (as above) Or Ns N cr 22,270 155,303 155,303kN 0.379 < 0.5 K1 K10 4.9 18.5 O r 17 O2r K2 K20 0.25 (3 2 O r ) N u , no min al 85 4.9 18.5 u 0.379 17 u 0.379 2 0.25 u (3 2 u 0.379) 0.330 0.940 ª t fy º A s K2 f y A c f c «1 K1 » d fc ¼ ¬ 15 345 º ª 27,568 u 0.940 u 345 255,176 u 50 u «1 0.330 u u 600 50 »¼ ¬ 22,425 u 103 N 22,425kN Solution according to BS 5400 1. Dimension and Properties De = 600mm t = 15mm le = 4570mm fcu = 60MPa fy = 345MPa Es = 205,000MPa 2. Thickness Limit The thickness limit to prevent local buckling can be calculated using Eq. (3.26) as De fy 8 Es 600 u 345 8 u 205000 8.7mm This condition is satisfied since t is 15mm. Concrete-Filled Tubular Members and Connections 86 3. Strength in CFST CHS Constants C1 and C2 depend on the ratio of effective column length to outside CHS diameter (le/De): le/De = 4570/600 = 7.6 From Figure 4.4 C1 § 5.0 C2 § 0.83 Using Eq. (4.12) f cc f cu C1 t fy De 60 5.0 u 15 u 345 103MPa 600 Using Eq. (4.13) f 'y C2 f y 0.83 u 345 286MPa 4. Section Capacity From Eq. (4.11) the design section capacity for concrete-filled RHS is given by Nu 0.95 f ' y A s 0.45 f cc A c 0.95 u 286 u 27,568 0.45 u 103 u 255,176 19,318 u 103 N 19,318kN The nominal section capacity for concrete-filled CHS can be estimated from Eq. (4.11) using fy to replace 0.95f’y and using fcu to replace 0.45fcc. N u , no min al f y A s f cu A c 24,822 u 103 N 345 u 27,568 60 u 255,176 24,822kN 5. Concrete Contribution Factor The concrete contribution factor (Dc) becomes Dc 0.45 A c f cc Nu 0.45 u 255,176 u 103 0.612 19,318 u 103 which satisfies the condition set in Eq. (4.14). CFST Members Subjected to Compression 87 Solution according to DBJ13-51 1. Dimension and Properties d = 600mm t = 15mm fck = 38.5MPa (from GB50010 (2002)) fc = 27.5MPa (from Table 2.2) fy = 345MPa f = 295MPa (from GB50017 (2003)) Es = 206,000MPa (from GB50017 (2003)) 1 1 1 1 As S d 2 S (d 2 t ) 2 u 3.142 u 600 2 u 3.142 u (600 2 u 15) 2 4 4 4 4 Ac 27,568mm 2 1 S (d 2 t ) 2 4 1 u 3.142 u (600 2 u 15) 2 4 255,176mm 2 2. Properties for the Composite Section From Eq. (4.19) the design constraining factor becomes: [0 As f Ac fc 27,568 u 295 255,176 u 27.5 1.159 Composite area is given by Eq. (4.16): A sc A s A c 27,568 255,176 282,744 mm 2 Composite strength for concrete-filled CHS is given by Eq. (4.18): f sc (1.14 1.02 [0 ) f c (1.14 1.02 u 1.159) u 27.5 63.9MPa 3. Design Section Capacity Using Eq. (4.15) the design section capacity of concrete-filled CHS becomes: Nu f sc A sc 282,744 u 63.9 18,067 u 103 N 18,067kN 4. Nominal Section Capacity The nominal section capacity can be calculated from the above equations by adopting f = fy and fc = fck. Therefore Concrete-Filled Tubular Members and Connections 88 As f y 27,568 u 345 255,176 u 38.5 [0 [ f sc (1.14 1.02 [0 ) f ck A c f ck N u , no min al f sc A sc 0.968 (1.14 1.02 u 0.968) u 38.5 81.90MPa 282,744 u 81.90 23,157 u 103 N 23,157kN Solution according to Eurocode 4 1. Dimension and Properties d = 600mm t = 15mm fck = 50MPa fy = 345MPa fyd = 345/1.0 = 345 fcd = 50/1.5 = 33.33 Ea = 210,000MPa (from Eurocode 3) Ec = 22000 (50/10)0.3 = 35,654MPa (from Section 2.1.2.4) Aa Ac Ic Ia 1 1 S d 2 S (d 2 t ) 2 4 4 27,568mm 2 1 S (d 2 t ) 2 4 1 1 u 3.142 u 600 2 u 3.142 u (600 2 u 15) 2 4 4 1 u 3.142 u (600 2 u 15) 2 4 255,176mm 2 S (d 2 t ) 4 3.1416 u (600 2 u 15) 4 5182 u 106 mm 4 64 64 S d 4 S (d 2 t ) 4 3.1416 u 600 4 3.1416 u (600 2 u 15) 4 64 64 64 64 1180 u 106 mm 4 keL = 4570mm 2. Confinement Requirement Using Eq. (4.23) (EI) eff E a I a 0.6 E c I c 358,662 u 109 Nmm 2 From Eq. (4.22c) 210,000 u 1180 u 106 0.6 u 35,654 u 5182 u 106 CFST Members Subjected to Compression S 2 (EI) e N cr 89 3.1416 2 u 358,662 u 109 ( k e L) 2 4570 2 169,494kN Using Eq. (4.22b) N pl, Rk A a f y A c f ck 27,568 u 345 255,176 u 50 22,270 u 103 N 22,270kN Using Eq. (4.22a) O N pl, Rk N cr 22,270 169,494 0.362 < 0.5 Therefore the requirement for confinement is satisfied. 3. Design Section Capacity Because there is no eccentricity of loading (e = 0) the coefficients Kc and Ka are determined using Eq. (4.25). The coefficients Kc and Ka for the case where eccentricity of loading (e) is zero are called Kc0 and Ka0. They are given by Kc Kc 0 4.9 18.5 O 17 O Ka Ka 0 0.25 (3 2 O) 2 4.9 18.5 u 0.362 17 u 0.362 2 0.25 u (3 2 u 0.362) 0.431 0.931 The design section capacity for concrete-filled CHS is given by Eq. (4.24): Nu ª t fy º A a Ka f yd A c f cd «1 Kc » d f ck ¼ ¬ 15 345 º ª u 27,568 u 0.931 u 345 255,176 u 33.33 u «1 0.431 u 600 50 »¼ ¬ 17,992 u 103 N 17,992 kN 4. Nominal Section Capacity The nominal section capacity can be calculated from Eq. (4.24) by adopting fyd = fy and fcd = fck. Concrete-Filled Tubular Members and Connections 90 ª t fy º A a Ka f y A c f ck «1 Kc » d f ck ¼ ¬ N u , no min al 15 345 º ª 27,568 u 0.931 u 345 255,176 u 50 u «1 0.431 u u 600 50 »¼ ¬ 22,562 u 103 N 22,562kN Comparison The compressive section capacities determined from the four different standards are compared in Table 4.6. The difference between the design section capacities varies from 5.8% to 20% among the standards. This is mainly due to different material property factors or capacity factors being adopted in different standards, as shown in Table 2.5. The nominal section capacity predicted by BS5400 is higher than those from other standards. This is because the cube compressive strength of concrete (60MPa) is used in BS5400 rather than the cylinder strength (50MPa) used in other standards. The difference in nominal capacities among the other three standards is less than 2.5%. Table 4.6 Comparison of compressive section capacities for CFST CHS Standard Design section capacity (kN) Nominal section capacity (kN) AS51002004 16,048 22,425 BS54002005 19,318 24,822 DBJ13-512003 18,067 23,157 EC42004 17,992 22,562 4.3 MEMBER CAPACITY 4.3.1 Interaction of Local and Overall Buckling Similar to unfilled steel columns, CFST columns can be classified as short, intermediate or long columns. For short (stub) columns the maximum strength becomes the section capacity as given in Section 4.2. For very long columns, the maximum strength is proportional to the bending stiffness of the section. Therefore, much larger elastic buckling column capacity is expected for CFST columns because of the increased bending stiffness. For immediate length the concept of interaction of local and overall buckling applies to CFST columns, although the local buckling is delayed or eliminated by the concrete filling, as explained in Section 4.2.1. The member capacity of CFST columns is treated in a similar manner as that for unfilled columns, i.e. member capacity is equal to a product of section capacity and a member slenderness reduction factor. The multiple column curves are adopted in design. In fact, the same column curves used for unfilled tubular columns are adopted in most standards for CFST members CFST Members Subjected to Compression 91 with a modified member slenderness taking into account the influence of concrete filling. 4.3.2 Column Curves 4.3.2.1 AS5100 Three column curves are used in AS5100 for CFST members, as shown in Figure 4.5. These curves are the same as those defined in AS4100 for steel columns except for the definition of the modified slenderness On. O n 90 O r (4.27) Ns N cr Or (4.28) where Ns is given in Eq. (4.1) for CFST RHS and Eq. (4.5) for CFST CHS, Ncr is given in Eq. (4.3c), but taking the values of I and Ic to be 1.0. 4.3.2.2 BS5400 Part 5 Four column curves are used in BS5400 Part 5 for CFST members, as shown in Figure 4.6. These curves are the same as those defined in BS5400 Part 3 for steel columns except for the definition of the non-dimensional slenderness O. The definition of O for CFST columns is given as le O (4.29) lE in which le is the effective length of the actual column defined in Table 4.7, where L is the length of the column between end restraints, lE is the length of column for which the Euler load equals the squash load, i.e. lE S 0.45 E c I c 0.95 E s Is Nu (4.30) where Es is the modulus of elasticity for the steel tube, Ec is the modulus of elasticity for the concrete taken as 450fcu, where fcu is the characteristic cube strength of the concrete, Ic and Is are the second moments of area of the concrete cross-section and steel tube, Nu is the squash load given in Eq. (4.9) for CFST RHS and Eq. (4.11) for CFST CHS. Concrete-Filled Tubular Members and Connections 92 Member Slenderness Reduction Factor D c 1.0 0.9 Db = -0.5 0.8 0.7 0.6 Db = -1.0 0.5 0.4 0.3 Db = 0 0.2 0.1 0.0 0 40 80 120 160 200 240 280 320 360 3.5 4.0 Modified Slenderness O n Figure 4.5 Column curves for CFST RHS and CHS given in AS5100 Member Slenderness Reduction Factor K1 1.0 Curve A 0.9 Curve B 0.8 0.7 0.6 0.5 Curve C 0.4 0.3 Curve D 0.2 0.1 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Non-dimensional Slenderness O Figure 4.6 Column curves for CFST RHS and CHS given in BS5400 CFST Members Subjected to Compression 93 Table 4.7 Effective length le for compression members (adapted from Table 10 of BS5400 Part 3) Restraint condition at each end Fixed – Fixed Fixed – Pinned Pinned – Pinned Fixed – Slide Fixed – Free or Pinned – Slide Effective length le 0.7L 0.85L L 1.5L 2.0L 4.3.2.3 DBJ13-51 The slenderness reduction factor (or called column stability factor M) in the Chinese code DBJ13-51 is a function of steel yield stress, concrete strength, steel ratio (Ds) and member slenderness (O). They are presented in Figure 4.7 for CFST CHS and in Figure 4.8 for CFST RHS. Only the combinations of steel grade and concrete grade recommended in DBJ13-51 are shown in Figures 4.7 and 4.8. Formulae are given in Han and Yang (2007) for general cases. The steel ratio (Ds) is defined as As Ds (4.31) Ac where As is the cross-sectional area of steel tube and Ac is the cross-sectional area of concrete. The definition of member slenderness (O) is given in Eq. (4.32). For CFST CHS member: L O 4 o (4.32a) d For CFST RHS member about the major axis: L O 2 3 o (4.32b) D For CFST RHS member about the minor axis: L O 2 3 o (4.32c) B in which d, D and B are defined in Figure 1.1, Lo is the calculated length of column given in Clause 5.3 of GB50017-2003. Concrete-Filled Tubular Members and Connections 94 Column Stability Factor M 1.0 Ds = 0.08 0.9 0.8 Ds = 0.2 0.7 0.6 0.5 Ds = 0.04 0.4 0.3 CFST CHS Steel Grade Q235 Concrete Grade C30 0.2 0.1 0.0 0 20 40 60 80 100 120 140 160 180 200 160 180 200 160 180 200 Member Slenderness O (a) Column Stability Factor M 1.0 Ds = 0.08 0.9 0.8 Ds = 0.2 0.7 0.6 0.5 Ds = 0.04 0.4 0.3 CFST CHS Steel Grade Q235 Concrete Grade C40 0.2 0.1 0.0 0 20 40 60 80 100 120 140 Member Slenderness O (b) Column Stability Factor M 1.0 Ds = 0.08 0.9 0.8 0.7 Ds = 0.2 0.6 0.5 Ds = 0.04 0.4 0.3 CFST CHS Steel Grade Q345 Concrete Grade C40 0.2 0.1 0.0 0 (c) 20 40 60 80 100 120 140 Member Slenderness O Figure 4.7 Column stability factor in DBJ13-51for CFST CHS CFST Members Subjected to Compression 95 Column Stability Factor M 1.0 0.9 Ds = 0.08 0.8 0.7 Ds = 0.2 0.6 0.5 Ds = 0.04 0.4 0.3 CFST CHS Steel Grade Q345 Concrete Grade C50 0.2 0.1 0.0 0 20 40 60 80 100 120 140 160 180 200 160 180 200 160 180 200 Member Slenderness O (d) Column Stability Factor M 1.0 0.9 Ds = 0.08 0.8 0.7 Ds = 0.2 0.6 0.5 Ds = 0.04 0.4 0.3 CFST CHS Steel Grade Q345 Concrete Grade C60 0.2 0.1 0.0 0 20 40 60 80 100 120 140 Member Slenderness O (e) Column Stability Factor M 1.0 0.9 Ds = 0.08 0.8 0.7 Ds = 0.2 0.6 0.5 Ds = 0.04 0.4 0.3 CFST CHS Steel Grade Q390 Concrete Grade C50 0.2 0.1 0.0 0 (f) 20 40 60 80 100 120 140 Member Slenderness O Figure 4.7 Column stability factor in DBJ13-51for CFST CHS (continued) Concrete-Filled Tubular Members and Connections 96 Column Stability Factor M 1.0 0.9 Ds = 0.08 0.8 0.7 Ds = 0.2 0.6 0.5 Ds = 0.04 0.4 0.3 CFST CHS Steel Grade Q390 Concrete Grade C60 0.2 0.1 0.0 0 20 40 60 80 100 120 140 160 180 200 160 180 200 160 180 200 Member Slenderness O (g) Column Stability Factor M 1.0 0.9 Ds = 0.08 0.8 0.7 Ds = 0.2 0.6 0.5 Ds = 0.04 0.4 0.3 CFST CHS Steel Grade Q420 Concrete Grade C50 0.2 0.1 0.0 0 20 40 60 80 100 120 140 Member Slenderness O (h) Column Stability Factor M 1.0 0.9 Ds = 0.08 0.8 0.7 Ds = 0.2 0.6 0.5 Ds = 0.04 0.4 0.3 CFST CHS Steel Grade Q420 Concrete Grade C60 0.2 0.1 0.0 0 (i) 20 40 60 80 100 120 140 Member Slenderness O Figure 4.7 Column stability factor in DBJ13-51for CFST CHS (continued) CFST Members Subjected to Compression 97 Column Stability Factor M 1.0 Ds = 0.08 0.9 0.8 Ds = 0.2 0.7 0.6 0.5 Ds = 0.04 0.4 0.3 CFST RHS Steel Grade Q235 Concrete Grade C30 0.2 0.1 0.0 0 20 40 60 80 100 120 140 160 180 200 160 180 200 160 180 200 Member Slenderness O (a) Column Stability Factor M 1.0 0.9 Ds = 0.08 0.8 0.7 Ds = 0.2 0.6 0.5 Ds = 0.04 0.4 0.3 CFST RHS Steel Grade Q235 Concrete Grade C40 0.2 0.1 0.0 0 20 40 60 80 100 120 140 Member Slenderness O (b) Column Stability Factor M 1.0 Ds = 0.08 0.9 0.8 0.7 Ds = 0.2 0.6 0.5 Ds = 0.04 0.4 0.3 CFST RHS Steel Grade Q345 Concrete Grade C40 0.2 0.1 0.0 0 (c) 20 40 60 80 100 120 140 Member Slenderness O Figure 4.8 Column stability factor in DBJ13-51 for CFST RHS Concrete-Filled Tubular Members and Connections 98 Column Stability Factor M 1.0 0.9 Ds = 0.08 0.8 0.7 Ds = 0.2 0.6 0.5 Ds = 0.04 0.4 0.3 CFST RHS Steel Grade Q345 Concrete Grade C50 0.2 0.1 0.0 0 20 40 60 80 100 120 140 160 180 200 160 180 200 160 180 200 Member Slenderness O (d) Column Stability Factor M 1.0 0.9 Ds = 0.08 0.8 0.7 Ds = 0.2 0.6 0.5 Ds = 0.04 0.4 0.3 CFST RHS Steel Grade Q345 Concrete Grade C60 0.2 0.1 0.0 0 20 40 60 80 100 120 140 Member Slenderness O (e) Column Stability Factor M 1.0 0.9 Ds = 0.08 0.8 0.7 Ds = 0.2 0.6 0.5 Ds = 0.04 0.4 0.3 CFST RHS Steel Grade Q390 Concrete Grade C50 0.2 0.1 0.0 0 (f) 20 40 60 80 100 120 140 Member Slenderness O Figure 4.8 Column stability factor in DBJ13-51 for CFST RHS (continued) CFST Members Subjected to Compression 99 Column Stability Factor M 1.0 0.9 Ds = 0.08 0.8 0.7 Ds = 0.2 0.6 0.5 Ds = 0.04 0.4 0.3 CFST RHS Steel Grade Q390 Concrete Grade C60 0.2 0.1 0.0 0 20 40 60 80 100 120 140 160 180 200 160 180 200 160 180 200 Member Slenderness O (g) Column Stability Factor M 1.0 0.9 Ds = 0.08 0.8 0.7 Ds = 0.2 0.6 0.5 Ds = 0.04 0.4 0.3 CFST RHS Steel Grade Q420 Concrete Grade C50 0.2 0.1 0.0 0 20 40 60 80 100 120 140 Member Slenderness O (h) Column Stability Factor M 1.0 0.9 Ds = 0.08 0.8 0.7 Ds = 0.2 0.6 0.5 Ds = 0.04 0.4 0.3 CFST RHS Steel Grade Q420 Concrete Grade C60 0.2 0.1 0.0 0 (i) 20 40 60 80 100 120 140 Member Slenderness O Figure 4.8 Column stability factor in DBJ13-51 for CFST RHS (continued) Concrete-Filled Tubular Members and Connections 100 4.3.2.4 Eurocode 4 Two column curves (curve a and curve b in EC3) are adopted for CFST members as shown in Figure 4.9. Curve a is for CFST members with Asr/Ac d 3% whereas curve b is for CFST members with 3% < Asr/Ac d 6% where Asr is the area of steel reinforcement. The non-dimensional slendernessCȜ is defined as N pl, Rk O (4.33) N cr N pl, Rk N cr (4.34) A a f y A c f ck S 2 (EI) eff (4.35) ( k e L) 2 (EI) eff (4.36) E a I a 0.6 E c I c in which Aa is the cross-sectional area of steel tube, Ac is the area of concrete in the cross-section, fy is the yield stress of the CHS and fck is the characteristic compressive strength of concrete. L is the column length and ke is the effective length factor. For members with idealised end restraints the values of ke summarised in Table 4.3 can be adopted. For members in frames the effective buckling length (keL) is defined in Eurocode 3 (2005). Ea is the modulus of elasticity for the steel tube, Ec is the modulus of elasticity for concrete given in Table 2.2, Ia and Ic are the second moment of area of the steel tube and concrete respectively. Member Slenderness Reduction Factor F 1.0 0.9 curve a 0.8 0.7 0.6 0.5 curve b 0.4 0.3 0.2 0.1 0.0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Non-dimensional Slenderness CO Figure 4.9 Column curves for CFST RHS and CHS given in Eurocode 4 2 CFST Members Subjected to Compression 101 4.3.3 Design Member Capacity 4.3.3.1 AS5100 The design member capacity according to AS5100 can be written as: N uc, design D c N us, design (4.37) where Nus,design is design section capacity given in Eq. (4.1) for CFST RHS and in Eq. (4.5) for CFST CHS, Dc is the member slenderness reduction factor given in Figure 4.5 or by Eq. (4.38). 2½ § 90 · ° ° ¸¸ ¾ D c [ ®1 1 ¨¨ (4.38a) © [O ¹ ° ° ¯ ¿ 2 [ § O · ¨ ¸ 1 K © 90 ¹ O O n Da D b (4.38c) K 0.00326 O 13.5 t 0 (4.38d) On 90 O r (4.38e) Da 2100 O n 13.5 2 O n 15.3 O n 2050 (4.38f) § O · 2¨ ¸ © 90 ¹ (4.38b) 2 in which Or is given in Eq. (4.28) and the compression member section constant (Db) is summarised in Table 4.8. Table 4.8 Compression member section constant (Db) for cold-formed tubes (adapted from Table 10.3.3 of AS5100 Part 6) Compression member section constant (Db) -1.0 -0.5 0 Section Description Hot-formed RHS and CHS with form factor (kf) of 1.0; Cold-formed (stress relieved) RHS and CHS with form factor (kf) of 1.0. Cold-formed (non-stress relieved) RHS and CHS with form factor of 1.0; Hot-formed RHS and CHS with form factor less than 1.0; Cold-formed RHS and CHS with form factor less than 1.0. Welded box sections Concrete-Filled Tubular Members and Connections 102 4.3.3.2 BS 5400 The design member capacity according to BS5400 Part 5 can be written as: N c 0.85 K1 N u (4.39) where Nu is design section capacity given in Eq. (4.9) for CFST RHS and in Eq. (4.11) for CFST CHS, K1 is the member slenderness reduction factor given in Figure 4.6 or by Eq. (4.40). ª º 2 1 K½ 1 K½ 4 K1 0.5«®1 2 ¾ ®1 2 ¾ 2 » (4.40) «¯ O ¿ O ¿ O » ¯ «¬ »¼ in which, O is given in Eq. (4.29) and K is determined as: K 0 if O d 0.2 (4.41a) K 75.5 D (O 0.2) if O > 0.2 (4.41b) Different D values are specified for the four curves (A to D) shown in Figure 4.6, i.e. D = 0.0025 for curve A D = 0.0045 for curve B D = 0.0062 for curve C D = 0.0083 for curve D The selection of curves depends on the value of r/y and method used to manufacture the box section. Details are given in Table 4.9 where r is the radius of gyration and y is the distance from the same axis to the extreme fibre of the section, i.e. d/2 for CHS or D/2 for RHS. Table 4.9 Selection of curves in Figure 4.6 (adapted from Note 1 of Figure 37 in BS5400 Part 3) All other members (including stress relieved welded members) Curve A Curve B Curve B Curve C Curve A Members fabricated by welding r/y 0.7 r/y = 0.6 r/y = 0.5 r/y d 0.45 Hot finished hollow sections Curve B Curve C Curve C Curve C For le/d or le/B exceeds 12, where le is defined in Table 4.7 and d and B are defined in Figure 1.1, more complicated formulae are required, as in clause 11.3.2.3 of BS5400 Part 5. CFST Members Subjected to Compression 103 4.3.3.3 DBJ13-51 The design member capacity of CFST RHS and CHS is given by Nc M Nu (4.42) where Nu is the design section capacity given in Eq. (4.15), M is the slenderness reduction factor (or called column stability factor) given in Figure 4.7 for CFST CHS and in Figure 4.8 for CFST RHS. The column stability factor depends on the steel yield stress, concrete strength, steel ratio (Ds) defined in Eq. (4.31) and member slenderness (O) defined in Eq. (4.32). 4.3.3.4 Eurocode 4 The design member capacity of CFST RHS and CHS is determined as Nc F Nu (4.43) where Nu is the design section capacity defined in Eq. (4.20) for CFST RHS and in Eq. (4.24) for CFST CHS, F is the member slenderness reduction factor given in Figure 4.9 where the non-dimensional slendernessCȜ is defined in Eq. (4.33). 4.3.4 Examples 4.3.4.1 Example 1 Determine the member capacity of a welded square hollow section (SHS 600 u 600 u 25 without rounded corners) filled with normal concrete subjected to compression. The effective buckling length is 4570mm. The nominal yield stress of the SHS is 345MPa. The compressive cylinder strength of concrete is 50MPa and cubic strength is 60MPa. Solution according to AS5100 1. Dimension and Properties D = 600mm B = 600mm t = 25mm Ic Is (B 2 t ) (D 2 t )3 12 (600 2 u 25) (600 2 u 25)3 12 B D3 (B 2 t ) (D 2 t )3 12 12 3175 u 10 6 mm 4 7626 u 106 mm 4 600 u 6003 (600 2 u 25) (600 2 u 25)3 12 12 Concrete-Filled Tubular Members and Connections 104 keL = 4570mm fc = 50MPa fy = 345Mpa Es = 200,000MPa (from AS4100) Ec = 0.5 (2400)1.5 0.043 (50) = 17,875MPa (from Section 2.1.2.1 assuming concrete density of 2400kg/m3) I = 0.9 Ic = 0.6 2. Section Capacity From the example in Section 4.2.4.1: Nominal capacity Nu,nominal = 34,963 kN Design capacity Nu = 26,929 kN 3. Modified Member Slenderness From Eq. (4.4), effective elastic flexural stiffness (EI) e I E s Is Ic E c I c 0.9 u 200,000 u 3175 u 106 0.6 u 17,875 u 7626 u 106 653,288 u 109 Nmm 2 From Eq. (4.3c) N cr S 2 (EI) e 3.1416 2 u 653,288 u 109 (k e L) 2 4570 2 From Eq. (4.28), the relative slenderness Or Ns N cr 34,963 308,727 0.337 From Eq. (4.38e) On 90 O r 90 u 0.337 30.3 308,727 kN CFST Members Subjected to Compression 105 4. Member Slenderness Reduction Factor From Table 4.8, section constant Db = 0 From Figure 4.5, Dc § 0.94 5. Member Capacity Nominal member capacity Nc,nominal = Dc Nu,nominal = 0.94 u 34,963 = 32,865kN Nc =Dc Nu = 0.94 u 26,929 = 25,313kN Therefore the nominal compressive member capacity is 32,865kN and the design compressive member capacity is 25,313kN. Solution according to BS5400 1. Dimension and Properties bf = 600mm tf = 25mm h D 2 tf 600 2 u 25 550mm fcu = 60MPa Es = 205,000MPa Ec = 450 fcu = 450 u 60 = 27,000MPa As b f (h 2 t f ) (b f 2 t f ) h 600 u (550 2 u 25) (600 2 u 25) u 550 57,500mm 2 Ic Is (b f 2 t f ) h 3 12 (600 2 u 25) (600 2 u 25)3 12 b f D3 (b f 2 t f ) h 3 12 12 3175 u 106 mm 4 le = 4570mm 7626 u 10 6 mm 4 600 u 6003 (600 2 u 25) (600 2 u 25)3 12 12 Concrete-Filled Tubular Members and Connections 106 2. Section Capacity From the example in Section 4.2.4.1: Nominal capacity Nu,nominal = 37,988kN Design capacity Nu = 27,013kN 3. Select Column Curve y= D/2 = 600/2 = 300mm r 3175 u 106 57,500 Is As 235mm r/y = 235/300 = 0.78 > 0.7 From Table 4.9 curve B should be used. 4. Member Slenderness Reduction Factor From Eq. (4.30) lE S 0.45 E c I c 0.95 E s Is Nu 3.1416 0.45 u 27,000 u 7626 u 106 0.95 u 2.05 u 105 u 3175 u 106 27,013 u 103 16,117mm From Eq. (4.29) O le lE 4570 16,117 0.284 From Figure 4.6, K1 § 0.97 5. Design Member Capacity From Eq. (4.39) N c 0.85 K1 N u 0.85 u 0.97 u 27,013 The nominal member capacity 22,272kN CFST Members Subjected to Compression N c, no min al 107 0.85 K1 N u , no min al 0.85 u 0.97 u 37,988 31,321 kN Solution according to DBJ13-51 1. Dimension and Properties B = 600mm D = 600mm t = 25mm A s B D (B 2 t ) (D 2 t ) 600 u 600 (600 2 u 25) u (600 2 u 25) 57,500mm 2 A c (B 2 t ) (D 2 t ) Lo = 4570 mm (600 2 u 25) u (600 2 u 25) 302,500 mm 2 Steel grade Q345 Concrete grade C60 2. Section Capacity From the example in Section 4.2.4.1: Nominal capacity Nu,nominal = 36,382kN Design capacity Nu = 28,850kN 3. Column Stability Factor From Eq. (4.31) the steel ratio becomes Ds As Ac 57,500 302,500 0.19 The member slenderness (O) is (Eq. (4.32b)) O L 2 3 o D 2 3 4570 600 26.4 From Figure 4.8(e) the column stability factor is approximately M § 0.92 4. Member Capacity From Eq. (4.42) the design member capacity Concrete-Filled Tubular Members and Connections 108 Nc M Nu 0.92 u 28,850 26,542kN The nominal member capacity N c, no min al M N u , no min al 0.92 u 36,382 33,471kN Solution according to Eurocode 4 1. Dimension and Properties h = 600mm b = 600mm t = 25mm fck = 50MPa fy = 345MPa A a h b (h 2 t ) (b 2 t ) 600 u 600 (600 2 u 25) u (600 2 u 25) 57,500mm 2 A c (h 2 t ) (b 2 t ) Asr = 0 (600 2 u 25) u (600 2 u 25) 302,500 mm 2 (b 2 t ) (h 2 t )3 12 (600 2 u 25) (600 2 u 25)3 12 7626 u 106 mm 4 Ic Ia b h 3 (b 2 t ) (h 2 t )3 12 12 600 u 6003 (600 2 u 25) (600 2 u 25)3 12 12 3175 u 106 mm 4 keL = 4570mm Ea = 210,000MPa (from Eurocode 3) Ec = 22,000 (50/10)0.3 = 35,654MPa (from Section 2.1.2.4) 2. Section Capacity From the example in Section 4.2.4.1: Nominal capacity Nu,nominal = 34,963 kN Design capacity Nu = 29,920 kN 3. Non-dimensional Slenderness From Eq. (4.34) CFST Members Subjected to Compression N pl, Rk A a f y A c f ck 109 57,500 u 345 302,500 u 50 34,963kN From Eq. (4.36) (EI) eff 210,000 u 3175 u 106 0.6 u 35,654 u 7626 u 106 E a I a 0.6 E c I c 829,888 u 109 Nmm2 From Eq. (4.35) N cr S 2 (EI) eff 3.1416 2 829,888 u 109 ( k e L) 2 4570 2 392183kN The non-dimensional slendernessCȜ is determined as O N pl, Rk N cr 34,963 392,183 0.298 4. Member Slenderness Reduction Factor Curve a in Figure 4.9 is selected because Asr/Ac < 3% where Asr is the area of steel reinforcement. From Figure 4.9 the member slenderness reduction factor is approximately F § 0.98 5. Member Capacity From Eq. (4.43) the design member capacity becomes Nc F Nu 0.98 u 29,920 29,322 kN The nominal member capacity N c, no min al F N u , no min al 0.98 u 34,963 34,264 kN Comparison The compressive member capacities determined from the four different standards are compared in Table 4.10. The reduction factor on section capacity for AS5100 is about 0.94, which is very close to that of 0.92 for DBJ13-51. The reduction factor on section capacity for Eurocode 4 is about 0.98, which is very close to that of 0.97 for BS5400. However, there is an extra reduction factor of 0.85 in the BS5400 Concrete-Filled Tubular Members and Connections 110 equation (see Eq. (4.39)). This makes the design member capacity obtained from BS5400 significantly lower (12% to 24%) than those from the other three standards. The nominal member capacity predicted from BS5400 is slightly less (5% to 8.5%) than that from the other three standards. The difference in the nominal member capacities is within 5% among the other three standards (AS5100, DBJ13-51 and Eurocode 4). Table 4.10 Comparison of compressive member capacities for CFST RHS Standard Design member capacity (kN) Nominal member capacity (kN) AS51002004 25,313 32,865 BS54002005 22,272 31,321 DBJ13-512003 26,542 33,471 EC42004 29,322 34,264 4.3.4.2 Example 2 Determine the member capacity of hot-formed circular hollow section (CHS 600 u 15) filled with normal concrete subjected to compression. The effective buckling length is 4570mm. The nominal yield stress of the CHS is 345MPa. The compressive cylinder strength of concrete is 50MPa and cubic strength is 60MPa. Solution according to AS 5100 1. Dimension and Properties d = 600mm t = 15mm Es = 200,000MPa (from AS4100) Ec = 0.5 (2400)1.5 0.043 (50) = 17,875 MPa (from Section 2.1.2.1 assuming concrete density of 2400kg/m3) Ic Is S (d 2 t ) 4 3.1416 u (600 2 u 15) 4 5182 u 106 mm 4 64 64 S d 4 S (d 2 t ) 4 3.1416 u 600 4 3.1416 u (600 2 u 15) 4 64 64 64 64 1180 u 10 6 mm 4 keL = 4570mm I = 0.9 Ic = 0.6 CFST Members Subjected to Compression 111 2. Section Capacity From the example in Section 4.2.4.2: Nominal capacity Nu,nominal = 22,425kN Design capacity Nu = 16,048kN 3. Modified Member Slenderness From Eq. (4.4), effective elastic flexural stiffness (EI) e I E s I s Ic E c I c 0.9 u 200,000 u 1180 u 106 0.6 u 17,875 u 5182 u 106 267,983 u 109 Nmm 2 From Eq. (4.3c) N cr S 2 (EI) e ( k e L) 2 3.1416 2 u 267,983 u 109 4570 2 126,642kN From Eq. (4.28), the relative slenderness Or Ns N cr 22,425 126,642 0.421 From Eq. (4.38e) On 90 O r 90 u 0.421 37.89 4. Member Slenderness Reduction Factor From Table 4.8, section constant Db = -1.0 From Figure 4.5, Dc § 0.98 5. Member Capacity Nominal member capacity Nc,nominal = Dc Nu,nominal = 0.98 u 22,425 = 21,977kN Nc = Dc Nu = 0.98 u 16,048 = 15,727kN Concrete-Filled Tubular Members and Connections 112 Therefore, the nominal compressive member capacity is 21,977 kN and the design compressive member capacity is 15,727 kN. Solution according to BS5400 1. Dimension and Properties De = 600mm t = 15mm le = 4570mm fcu = 60MPa Es = 205,000Mpa Ec = 450 fcu = 450 u 60 = 27,000MPa As 1 1 S D e2 S (D e 2 t ) 2 4 4 1 1 u 3.1416 u 600 2 u 3.1416 u (600 2 u 15) 2 4 4 27,568mm 2 Ic Is S (D e 2 t ) 4 3.1416 u (600 2 u 15) 4 5182 u 106 mm 4 64 64 S D e4 S (D e 2 t ) 4 3.1416 u 600 4 3.1416 u (600 2 u 15) 4 64 64 64 64 1180 u 106 mm 4 2. Section Capacity From the example in Section 4.2.4.2: Nominal capacity Nu,nominal = 24,822kN Design capacity Nu = 19,318kN 3. Select Column Curve y= De/2 = 600/2 = 300mm r Is As 1180 u 10 6 27,568 207mm r/y = 207/300 = 0.69 § 0.7 From Table 4.9 curve A should be used. CFST Members Subjected to Compression 113 4. Member Slenderness Reduction Factor From Eq. (4.30) lE S 0.45 E c I c 0.95 E s Is Nu 3.1416 0.45 u 27,000 u 5182 u 106 0.95 u 2.05 u 105 u 1180 u 106 19,318 u 103 12,230mm From Eq. (4.29) O le lE 4570 12,230 0.374 From Figure 4.6, K1 § 0.96 5. Design Member Capacity From Eq. (4.39) Nc 0.85 K1 N u 0.85 u 0.96 u 19,318 15,763 kN The nominal member capacity N c, no min al 0.85 K1 N u , no min al 0.85 u 0.96 u 24,822 20,255kN Solution according to DBJ13-51 1. Dimension and Properties d = 600mm t = 15mm 1 1 As S d 2 S (d 2 t ) 2 4 4 27,568mm 2 1 Ac S (d 2 t ) 2 4 Lo = 4570 mm Steel grade Q345 Concrete grade C60 1 1 u 3.142 u 600 2 u 3.142 u (600 2 u 15) 2 4 4 1 u 3.142 u (600 2 u 15) 2 4 255,176mm 2 Concrete-Filled Tubular Members and Connections 114 2. Section Capacity From the example in Section 4.2.4.2: Nominal capacity Nu,nominal = 23,157kN Design capacity Nu = 18,067kN 3. Column Stability Factor From Eq. (4.31) the steel ratio becomes Ds As Ac 27,568 255,176 0.108 The member slenderness (O) is (Eq. (4.32a)) O L 4 o d 4 4570 600 30.5 From Figure 4.7(e) the column stability factor is approximately M § 0.885 4. Member Capacity From Eq. (4.42) the design member capacity Nc M Nu 0.885 u 18,067 15,989kN The nominal member capacity N c, no min al M N u , no min al 0.885 u 23,157 20,494kN Solution according to Eurocode 4 1. Dimension and Properties d = 600mm t = 15mm fck = 50MPa fy = 345MPa Ea = 210,000MPa (from Eurocode 3) Ec = 22,000 (50/10)0.3 = 35,654MPa (from Section 2.1.2.4) CFST Members Subjected to Compression Aa Ac Ic Ia 1 1 S d 2 S (d 2 t ) 2 4 4 27,568mm 2 1 S (d 2 t ) 2 4 115 1 1 u 3.142 u 600 2 u 3.142 u (600 2 u 15) 2 4 4 1 u 3.142 u (600 2 u 15) 2 4 255,176mm 2 S (d 2 t ) 4 3.1416 u (600 2 u 15) 4 5182 u 106 mm 4 64 64 S d 4 S (d 2 t ) 4 3.1416 u 600 4 3.1416 u (600 2 u 15) 4 64 64 64 64 1180 u 10 6 mm 4 keL = 4570mm 2. Section Capacity From the example in Section 4.2.4.2: Nominal capacity Nu,nominal = 22,562kN Design capacity Nu = 17,992kN 3. Non-dimensional Slenderness From Eq. (4.34) N pl, Rk A a f y A c f ck 27,568 u 345 255,176 u 50 22,270kN From Eq. (4.36) (EI) eff 210,000 u 1180 u 106 0.6 u 35,654 u 5182 u 106 E a I a 0.6 E c I c 358,655 u 109 Nmm2 From Eq. (4.35) N cr S 2 (EI) eff ( k e L) 2 3.1416 2 358,655 u 109 4570 2 169,491kN The non-dimensional slendernessCȜ is determined as Concrete-Filled Tubular Members and Connections 116 O N pl, Rk N cr 22,270 169,491 0.362 4. Member Slenderness Reduction Factor Curve a in Figure 4.9 is selected because Asr/Ac < 3% where Asr is the area of steel reinforcement. From Figure 4.9 the member slenderness reduction factor is approximately F § 0.96 5. Member Capacity From Eq. (4.43) the design member capacity becomes Nc F Nu 0.96 u 17,992 17,272kN The nominal member capacity N c, no min al F N u , no min al 0.96 u 22,562 21,660kN Comparison The compressive member capacities determined from the four different standards are compared in Table 4.11. The reduction factor on section capacity for DBJ13-51 is 0.885. The reduction factor on section capacity for AS5100 is about 0.98, which is very close to that of 0.96 for BS5400 and for Eurocode 4. 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Liu, D. and Gho, W.M., 2005, Axial load behaviour of high-strength rectangular concrete-filled steel tubular stub columns. Thin-Walled Structures, 43(8), pp. 1131-1142. 60. Lue, D.M., Liu, J.L. and Yen, T., 2007, Experimental study on rectangular CFT columns with high-strength concrete. Journal of Constructional Steel Research, 61(7), pp. 902-911. 61. Matsui, C., Mitani, I., Kawano, A. and Tsuda, K., 1997, AIJ design method for concrete filled steel tubular structures. Proceedings of ASCCS Seminar on Concrete Filled Steel Tubes – A Comparison of International Codes and Practice, September, Innsbruck, Austria, pp. 93-116. 62. McAteer, P., Bonacci, J.F. and Lachemi, M., 2004, Composite response of high-strength concrete confined by circular steel tube. ACI Structural Journal, 101(4), pp. 466-474. 63. Mouli, M. and Khelafi, H., 2007, Strength of short composite rectangular hollow section columns filled with lightweight aggregate concrete. Engineering Structures, 29(8), pp. 1791-1797. 64. 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Zhao, X.L. and Packer, J.A., 2009, Tests and design of concrete-filled elliptical hollow section stub columns. Thin-Walled Structures, 47(6-7), pp. 617-628. 97. Zhao, X.L., Wilkinson, T. and Hancock, G.J., 2005. Cold-formed tubular members and connections (Oxford: Elsevier). 98. Zhou, F. and Young, B., 2008, Tests of concrete-filled aluminum stub columns. Thin-Walled Structures, 46(6), pp. 573-583. 99. Zhou, F. and Young, B., 2009, Concrete-filled aluminum circular hollow section column tests. Thin-Walled Structures, 47(11), pp. 1272-1280. CHAPTER FIVE CFST Members Subjected to Combined Actions 5.1 GENERAL Similar to unfilled tubular members CFST members are most likely to experience combined bending and compression in steel frame structures and trusses. Members subjected to combined bending and compression are often called “beam-columns”, representing the two types of design actions they are intended to resist. Extensive research has been conducted on the behaviour of CFST members subjected to combined bending and compression. A summary of the experimental work on CFST beam-columns is given in Table 5.1. Concrete-filled fibre reinforced polymer tubes in combined compression and bending was recently reported by Fam et al. (2003, 2005). Table 5.1 Summary of experimental studies on CFST beam-columns (a) CFST CHS d/t L/d e/d Steel yield stress fy MPa 14.4-78.4 9.6-22 0.05-0.28 193-312 Concrete compressive strength fc MPa 21.6-66.7 23.8-63.5 8-22.9 0.1-0.296 218 67.4 9 92.1 17 0.07-0.1 328 92 3 29.6-35 3-18.4 0.14-0.27 303-324 37.4 15 33.1 15.7 0.06 433 64.5 6 16.7-152 3 1.8-7.4 283-834 20-80 33 Number of tests 18 38 8.5-24 0.2-0.33 275 41.6 14 66.7 10 0.6 304 46.8 5 38 13-28 0.26 260 39.4-40 12 64.2 10 0.12-0.24 343 35.5-40.6 10 52.6 24-26.3 9-30 7-14 0.15-0.3 0.16-0.65 404 343-377 97.3 35.7-43.3 4 11 35.7 10.5 0.13-0.26 370 53-110 4 Reference Neogi et al. (1969) Rangan and Joyce (1992) Prion and Boehme (1994) Han (2000) Johansson and Gylltoft (2001) Fujimoto et al. (2004) Gopal and Manoharan (2004) Han and Yao (2004) Gopal and Manoharan (2006) Yang and Han (2006) Yu et al. (2008) Chang et al. (2009) Thayalan et al. (2009) Concrete-Filled Tubular Members and Connections 124 Table 5.1 Summary of experimental studies on CFST beam-columns (continued) (b) CFST RHS Concrete compressive strength fc MPa Number of tests B/t L/B e/B Steel yield stress fy MPa 22.7 11-19 0.1-0.33 324 39.9 4 16 23 0.2-0.5 343-386 32-36 6 16-20 18-23 0.06-0.6 340-363 38.3-40.5 8 12.7 20.5-36.5 22-42 33-50 13-22 2.9 0.46-1.38 0.13-0.43 0.12-0.31 370 321-330 750 55 22.7-43.3 30-32 8 21 7 49.1 4-12 0.11-0.24 340 18.5 12 45.3 3-12 0.12-0.26 340 28.8 13 18.7-73.7 3 0.19-8.3 262-834 20-80 32 66.7 11.55 0.6 304 46.8 5 19-36 6-14 0.2-0.75 542 60.8-72.1 12 24-54 11-25 0.08-0.09 761 20. 4 22.5-32.5 3-17 0.1-0.4 495 60 20 51 12 0.13-0.27 344 35.5-40.6 10 52.6 23.4-43.5 80 9-30 4-12 6-12 0.15-0.3 0.1-0.3 0.15-0.3 404 348-367 270 97.3 58.8 46.6-47.4 4 81 12 28.4-51.6 5-21 0.41 317-319 75.3 26 Reference Knowles and Park (1969) Shakir-Khalil and Zeghiche (1989) Shakir-Khalil and Mouli (1990) Wang (1999) Han et al. (2001) Uy (2001) Han and Yao (2003a) Han and Yao (2003b) Fujimoto et al. (2004) Han and Yao (2004) Liu (2004) Mursi and Uy (2004) Liu (2006) Yang and Han (2006) Yu et al. (2008) Lee (2007) Tao et al. (2007) Zhang and Guo (2007) The strength under the combined actions of bending and compression are related to the separate bending and compression strengths via an interaction formula. The capacities of CFST members under pure bending (see Chapter 3) and pure compression (see Chapter 4) will be utilised. Second-order effects which possibly magnify the bending moment should be considered in the structural analysis. The stress distribution in CFST members subjected to combined bending and compression is described in Section 5.2. The stress distribution can be used to derive the key points in an interaction diagram. Design rules in BS5400 (BSI2005), DBJ13-51 (2003) and Eurocode 4 (2004) are given in Section 5.3. The second- order effects are discussed in Section 5.3.4. The design rules in AS5100 (Standards Australia 2004) are not given since they are very similar to those in Eurocode 4. Examples are given in Section 5.4. Combined actions involving torsion or shear are presented in Section 5.5. CFST Members Subjected to Combined Actions 125 5.2 STRESS DISTRIBUTION IN CFST MEMBERS SUBJECTED TO COMBINED BENDING AND COMPRESSION The stress distribution in CFST members subjected to combined bending and compression is shown in Figure 5.1 for four typical cases. The location of the neutral axis in CFST beam-columns changes depending on the level of axial force versus the level of bending moment. The four cases (a, b, c and d) shown in Figure 5.1 correspond to the four key points (A, B, C and D) in the interaction diagrams defined in Eurocode 4 (see Figure 5.2(a)). For case (a) the CFST member is under pure compression. The compression capacity is given in Chapter 4. For case (b) the CFST member is under pure bending. The neutral axis is above the centroid of the section. The bending capacity is given in Chapter 3. For case (c) the CFST member is subject to combined bending and compression with axial force being fcAc. The neutral axis is below the centroid of the section. The bending capacity is the same as that for pure bending. For case (d) the CFST member is subject to combined bending and compression with axial force being 0.5fcAc. The neutral axis is at the centroid of the section. The bending capacity (Mmax) is larger than that for pure bending. The expression of Mmax can be derived from the stress distribution shown in Figure 5.1 (d). For CFST RHS shown in Figure 5.1(d): Similar to Section 3.2.3.1 and Figure 3.3 with dn = (D–2t)/2, Mmax is the same as MCFST,RHS in Eq. (3.6) except FRHS = 1, i.e. M max M RHS where M RHS 2 1 ªD 2 t º (B 2 t ) « » fc 2 ¬ 2 ¼ 1 ª º f y t «B (D t ) (D 2 t ) 2 » 2 ¬ ¼ (5.1) (5.2) For CFST CHS shown in Figure 5.1(d): Similar to Section 3.2.3.3 and Figure 3.5 with Jo = 0, Mmax is the same as MCFST,CHS in Eq. (3.15) except Jo = 0, i.e. M max rm ri 4 f y t rm2 dt 2 d 2t 2 2 f c ri3 3 (5.3) (5.4) (5.5) 126 Concrete-Filled Tubular Members and Connections fy fc Centroid (a) fy fc Neutral Axis Centroid fy (b) fy fc Centroid Neutral Axis fy (c) fy fc Neutral Axis at Centroid fy (d) Figure 5.1 Stress distribution of CFST members CFST Members Subjected to Combined Actions 127 N Nu A C A c fc 0.5 A c fc D B M p M max M (a) Eurocode 4 N A C A c fc B Mp M (b) BS5400 K( N ) Nu K( 1.0 A N ) MNu A C 2K 0 K0 M2K0 D B 1.0 (i) Section capacity C 2M2K0 ]0 D B E mM ] ( Mu ) 1.0 (ii) Member capacity (c) DBJ13-51 Figure 5.2 Interaction diagrams from various codes (schematic view) E mM ] ( d Mu ) 1+ M3 ]0 -1) m Concrete-Filled Tubular Members and Connections 128 5.3 DESIGN RULES 5.3.1 BS5400-5:2005 Four cases of axial force (N) and bending moment (M) combinations are specified in BS5400. The design interaction formulae are given below for each of them. 5.3.1.1 Column under uniaxial bending about the minor axis (i.e. N and My) 2 ª § My · º My » « ¨ ¸ N d N y N u K 1y (K 1y K 2 y 4K 3 ) 4K 3 « ¨ M uy ¸ » M uy © ¹ ¼» ¬« (5.6) It is required that My d Muy and My N u 0.03b, where b is the least lateral dimension of the column. Nu is the section capacity in compression given in Eq. (4.9) for CFST RHS and in Eq. (4.11) for CFST CHS. Muy is the design ultimate moment of resistance of the composite section about the minor axis. For CFST CHS, Muy can be taken as that in Eq. (3.23). For CFST RHS: M uy b dc º ª (h 2t f ) t f ( t f d c )» 0.95 f y «A s 2 ¼ ¬ (5.7) dc A s 2 (h 2t f ) t f h U 4 tf (5.8) U 0.4 f cu 0.95 f y (5.9) where As is the cross-sectional area of the RHS, tf is the thickness of the RHS and b is the clear width of the RHS, h is the depth of concrete, fcu is the characteristic 28day cube strength of concrete and fy is the yield stress of the steel hollow section. K1y can be determined using Eq. (4.40) using the parameters (radius of gyration and effective length) appropriate to the minor axis. For CFST CHS K2y is given by ª115 30(2E y 1) (1.8 D c ) 100O y º (5.10) K 2 y (0.9D c2 0.2) « » 50(2.1 E y ) ¬« ¼» For CFST RHS K2y is given by CFST Members Subjected to Combined Actions K 2y ª 90 25(2E y 1) (1.8 D c ) C 4 O y º (0.9D c2 0.2) « » 30(2.5 E y ) «¬ »¼ 129 (5.11) 0 d K2y d 0.75 For CFST CHS K3 is given by (0.5E y 0.4) (D c2 0.5) 0.15 O y K3 K 30 K 30 D 0.04 c t 0 15 1 O3y (5.12a) (5.12b) For CFST RHS K3 = 0. where Dc is given in Eq. (4.14) for CFST CHS and in Eq. (4.10) for CFST RHS, Oy is non-dimensional slenderness given in Eq. (4.29) using the effective length appropriate to the minor axis, for members subject to end bending moments only Ey is the ratio of the smaller to the larger of the two end moments about the minor axis, and Ey is positive for single curvature bending; for members with transverse loads Ey = 1.0 can be used as a conservative estimation. C4 is taken as 100, 120 and 140 for columns designed on the basis of curves A, B and C, respectively. The selection of curves can be made according to Table 4.9. 5.3.1.2 Column under uniaxial bending about the major axis (i.e. N and Mx) restrained from failure about the minor axis N d Nx 2 ª § M · º M N u «K 1x (K 1x K 2 x 4K 3 ) x 4K 3 ¨¨ x ¸¸ » « M ux © M ux ¹ »¼ ¬ (5.13) It is required that Mx d Mux and Mx N u 0.03b, where b is the least lateral dimension of the column. Nu is the section capacity in compression given in Eq. (4.9) for CFST RHS and in Eq. (4.11) for CFST CHS. Mux is the design ultimate moment of resistance of the composite section about the major axis. For CFST CHS, Mux can be taken as that in Eq. (3.23). For CFST RHS Mux can be taken as that in Eq. (3.20). K1x can be determined using Eq. (4.40). For CFST CHS K2x is given by Concrete-Filled Tubular Members and Connections 130 ª115 30(2E x 1) (1.8 D c ) 100O x º (0.9D c2 0.2) « » 50(2.1 E x ) ¼ ¬ For CFST RHS K2x is given by K 2x ª 90 25(2E x 1) (1.8 D c ) C 4 O x º (0.9D c2 0.2) « » 30(2.5 E x ) ¼ ¬ 0 d K2x d 0.75 K 2x (5.14) (5.15) For CFST CHS K3 is given by K3 K 30 K 30 0.04 (0.5E x 0.4) (D c2 0.5) 0.15 O x 1 O3x Dc t0 15 (5.16a) (5.16b) For CFST RHS K3 = 0. where Dc is given in Eq. (4.14) for CFST CHS and in Eq. (4.10) for CFST RHS, Ox is non-dimensional slenderness given in Eq. (4.29), for members subject to end bending moments only Ex is the ratio of the smaller to the larger of the two end moments about the minor axis, and Ex is positive for single curvature bending; for members with transverse loads Ex = 1.0 can be used as a conservative estimation. C4 is taken as 100, 120 and 140 for columns designed on the basis of curves A, B and C, respectively. The selection of curves can be made according to Table 4.9. 5.3.1.3 Column under uniaxial bending about the major axis (i.e. N and Mx) unrestrained against failure about the minor axis The column is likely to fail in a biaxial mode unless the axial load is very small. The column should be designed so that the requirement of Eq. (5.13) is satisfied and 1 N d N xy (5.17) 1 1 1 N x N y N ax in which Nx is given by Eq. (5.13), Ny is given by Eq. (5.6) taking My as equal to 0.03Nb, where b is the least lateral dimension of the column and N ax K 1x N u (5.18) CFST Members Subjected to Combined Actions 131 where K1x is given by Eq. (4.40) and Nu is given in Eq. (4.11) for CFST CHS and in Eq. (4.9) for CFST RHS. 5.3.1.4 Column under biaxial bending (i.e. N, Mx and My) It is required that Mx d Mux (5.19a) My d Muy (5.19b) Mx N u 0.03b (5.19c) My N u 0.03b (5.19d) 1 1 1 1 N x N y N ax N d N xy (5.19e) in which Nx is given by Eq. (5.13), Ny is given by Eq. (5.6), Nax is given by Eq. (5.18) and b is the least lateral dimension of the column. 5.3.2 DBJ13-51 5.3.2.1 Column under combined axial force (N) and uniaxial bending about the minor or major axis (My or Mx) – section capacity The schematic interaction diagram is shown in Figure 5.1 (c)(i). The interaction formulae are given below. N a Em M d 1.0 Nu Mu b N2 N 2u c N Em M d 1.0 Nu Mu if N/Nu 2Ko (5.20a) if N/Nu < 2Ko (5.20b) in which a 1 2 Ko (5.21a) Concrete-Filled Tubular Members and Connections 132 1 ] o b (5.21b) K o2 2 (] o 1) Ko c (5.21c) For CFST CHS: ]o 1 0.18 [ 1.15 (5.22a) Ko 0.5 0.2445 [ for [ d 0.4 ® 0.84 for [ ! 0.4 ¯0.1 0.14 [ (5.22b) For CFST RHS: ]o 1 0.14 [ 1.3 (5.23a) Ko 0.5 0.3175 [ for [ d 0.4 ® 0.81 for [ ! 0.4 ¯0.1 0.13 [ (5.23b) where Nu is the design section capacity given in Eq. (4.15), Mu is the ultimate design moment capacity given in Eq. (3.29), [ is the constraining factor defined in Eq. (3.32), Em is the equivalent moment factor specified in GB50017 (2003). For members subject to end bending moments only, M E m 0.65 0.35 2 (5.24) M1 M1 and M2 are end moments with |M1| |M2|. The ratio M2/M1 is positive for single curvature bending. For members with transverse loads, Em = 1.0 can be used as a conservative estimation. 5.3.2.2 Column under combined axial force (N) and uniaxial bending about the minor or major axis (My or Mx) – member capacity The schematic interaction diagram is shown in Figure 5.1(c)(ii). The interaction formulae are given below. a Em M N d 1.0 M Nu dm Mu b N2 N 2u in which c N Em M d 1.0 Nu dm Mu if N/Nu 2M3Ko (5.25a) if N/Nu < 2M3Ko (5.25b) CFST Members Subjected to Combined Actions 133 a 1 2 M 2 Ko (5.26a) b 1 ]o (5.26b) c M3 Ko2 2 (] o 1) Ko (5.26c) Nu is the design section capacity given in Eq. (4.15), Mu is the ultimate design moment capacity given in Eq. (3.29), M is the column stability factor given in Figures 4.7 and 4.8, Em is explained in Section 5.3.2.1, ]o and Ko are given in Eq. (5.22) for CFST CHS and in Eq. (5.23) for CFST RHS, dm is the factor related to the second-order effect which can be determined by N for CFST CHS (5.27a) d m 1 0.4 NE N for CFST RHS (5.27b) d m 1 0.25 NE where the elastic buckling load NE is given by NE S 2 E sc A sc O2 A sc A s A c O is given by Eq. (4.32) and Esc is determined by f scp E sc H scp For CFST CHS: ª º § fy · ¸ 0.488» f scy f scp «0.192 ¨¨ ¸ © 235 ¹ ¬« ¼» f scy (1.14 1.02 [) f c H scp 3.25 10 6 fy For CFST RHS: ª º § fy · 20 ¸ 0.365 0.104» f scy f scp «0.263 ¨¨ ¸ fc © 235 ¹ ¬« ¼» f scy (1.18 0.85 [) f c H scp 3.01 10 6 f y (5.28) (5.29) (5.30) (5.31a) (5.31b) (5.31c) (5.32a) (5.32b) (5.32c) Concrete-Filled Tubular Members and Connections 134 For CFST column under uniaxial bending about the major axis (i.e. N and Mx) unrestrained against failure about the minor axis, it is required to check the following condition: E M N d 1.0 m M N u 1.4 M u (5.33) 5.3.2.3 Column under biaxial bending (i.e. N, Mx and My) It is required that § Mx · ¨ ¸ ¨M ¸ © ux ¹ 1.8 § My · ¸ ¨ ¨ M uy ¸ ¹ © 1.8 d 1.0 (5.34) where Mx and My are the maximum bending moment in the column, Mux is the design ultimate moment of resistance of the composite section about the major axis given in Eq. (3.29), Muy is the design ultimate moment of resistance of the composite section about the minor axis given in Eq. (3.29) except that Wsc is given by Eq. (5.35) for CFST RHS. Wsc D B2 6 (5.35) 5.3.3 Eurocode 4 5.3.3.1 Combined compression (N) and uniaxial bending (Mx or My) The interaction curve in Eurocode 4 is simplified to be a polygonal diagram, i.e. the dashed lines in Figure 5.2(a). No explicit equations are given in Eurocode 4. The coordinates of the four key points (A, B, C and D) can be defined as: Point A (0, Nu) Point B (Mp, 0) Point C (Mp, Acfc) Point D (Mmax, 0.5Acfc) The interaction formulae can be written as If N Acfc CFST Members Subjected to Combined Actions Nu N Mp Nu Ac fc If 0.5Acfc < N < Acfc A f N M pl, N,Rd M p c c (M max M p ) 0.5 A c f c M pl, N,Rd If N d 0.5Acfc M pl, N,Rd Mp N (M max M p ) 0.5 A c f c 135 (5.36a) (5.36b) (5.36c) in which Nu is given in Eq. (4.20) for CFST RHS and in Eq. (4.24) for CFST CHS, the plastic moment capacity Mp is given by Eq. (3.6) for CFST RHS and in Eq. (3.15) for CFST CHS, Mmax can be determined using Eq. (5.1) for CFST RHS and Eq. (5.3) for CFST CHS. It is required that (5.37) M 2 nd d D m M pl, N,Rd where M2nd is the applied moment including the second-order effect given later in the chapter (see Table 5.2), Mpl,N,Rd is calculated from Eq. (5.36), Dm should be taken as 0.9 for steel grades between S235 and S355 inclusive, Dm should be taken as 0.8 for steel grades S420 and S460. 5.3.3.2 Combined compression (N) and biaxial bending (Mx and My) Similar check as in Section 5.3.3.1 should be made for both planes: M x ,2nd d D mx M pl, x , N,Rd (5.38a) M y,2nd d D my M pl, y, N,Rd (5.38b) M x ,2 nd M pl, x , N,Rd M y,2 nd M pl, y, N,Rd d 1.0 (5.39) 5.3.4 Comparison of Codes 5.3.4.1 Interaction diagrams It can be seen from Figure 5.2 that the interaction diagrams in Eurocode 4, BS5400 and DBJ13-51 are similar. The general shape of the interaction diagram corresponds to the stress distribution shown in Figure 5.1. Part CDB in the interaction diagram is unique for CFST members due to the contribution of concrete. The differences among various codes can be summarised as follows. 136 Concrete-Filled Tubular Members and Connections Three straight lines (AC, CD and DB) are adopted in Eurocode 4 to simplify the interaction diagram. In DBJ13-51, a combination of a straight line (AC) and a curve (CDB) is adopted. In BS5400 it is specified that the maximum bending moment should not exceed the ultimate moment capacity of CFST members subject to pure bending. Therefore the interaction diagram in BS5400 consists of only two parts (AC which is a straight line for CFST RHS and a curve for CFST CHS, and CB which is a vertical cut-off line). In the Eurocode 4 interaction diagram, section capacity in compression (Nu) is used for point A (see Figure 5.2(a)) instead of column member capacity (Nc). However, there is a requirement to check if the applied axial force (N) is less than the column member capacity in pure compression (Nc). In the BS5400 interaction diagram, column member capacity is directly used as point A in Figure 5.2(b). DBJ13-51 gives two separate interaction diagrams, one for section capacity and the other for member capacity in a non-dimensional format. In both Eurocode 4 and BS5400 the turning point C has a vertical coordinate of Acfc, whereas in DBJ13-51 a different value (2Ko or 2M2Ko) is used. The value of Acfc may be larger or smaller than 2Ko or 2M2Ko depending on the values of As/Ac, fy/fc and M. 5.3.4.2 Second-order effect It is necessary to consider the second-order effect for CFST columns, which magnifies the bending moment in the columns. The principle of the second-order effect for CFST columns is the same as that for unfilled tubular columns. Generally the second-order effect involves several aspects, such as moment amplification factor and imperfection in terms of load eccentricity. The moment amplification factor depends on the moment distribution and the ratio of axial load to the elastic buckling capacity. For example, in Eurocode 4 the second-order effect can be considered using equations given in Table 5.2. In DBJ13-51 the second-order effect is built in the interaction formulae (see Eqs. (5.20) and (5.25)) using the terms Em and dm. In BS5400 the second-order effect is also built in the interaction formulae by using factors K2 and K3 that are a function of Ex or Ey and member slenderness Ox or Oy. Similarly, Ex or Ey is related to moment distribution in the columns. The member slenderness Ox or Oy is used instead of the ratio of axial load to the elastic buckling capacity. The load eccentricity effect is indirectly considered by specifying a minimum value (N u 0.03b, where b is the least lateral dimension of the column) on Mx or My. CFST Members Subjected to Combined Actions 137 Table 5.2 Second-order effect in EC4 Secondorder effect Relative sway of the ends of a member Amplification factor Initial imperfection S 2 0.9 (E a I a 0.5 E c I c ) k2 N cr ,eff k1 M E t 1.0 1 N / N cr ,eff k1 N cr ,eff Moment including secondorder effect L2 1 1 N / N cr ,eff S 2 0.9 (E a I a 0.5 E c I c ) Combined L2 k 2 N eo eo = L/300 for Usd3% eo = L/200 for 3%<Usd6% M 2nd k1 M k 2 N e o Note: For members subject to end bending moments only, E = 0.66 + 0.44 (M2/M1) 0.44 where M1 and M2 are end moments with |M1| |M2|. The ratio M2/M1 is positive for single curvature bending. For members with transverse loads, E = 1.0 can be used as a conservative estimation. 5.4 EXAMPLES 5.4.1 Example 1 CFST SHS A beam-column is made of a welded square hollow section (SHS 600 u 600 u 25 without rounded corners) filled with normal concrete subjected to combined compression and bending about its major axis. The axial force (N) is 15,000kN while the bending moment (Mx) is 1500kNm. Transverse load exists on the column. Restraints are provided to prevent out-of-plain buckling about the minor axis. The column length is 5377mm and the effective column buckling length is 4570mm. The nominal yield stress of the SHS is 345MPa. The compressive cylinder strength of concrete is 50MPa and cubic strength is 60MPa. Determine if the composite column is sufficient to resist the combined loads. If the applied axial load is reduced 50%, what is the maximum allowed bending moment (Mx)? 5.4.1.1. Solution according to BS5400 1. Relevant Dimension and Properties b = 600mm = 0.6m N = 15,000kN Concrete-Filled Tubular Members and Connections 138 Mx = 1500kNm Ex = 1.0 (because transverse load exists) From Section 4.2.4.1: Dc = 0.302 From Section 4.3.4.1: Ox = 0.284 2. Capacities under Separate Loading From Table 3.3: Design moment capacity Mux = 4422kNm From Table 4.5: Design section capacity Nu = 27,013kN 3. Check Conditions Mx = 1500kNm < Mux = 4422kNm, satisfied. Mx = 1500kNm > N u 0.03b = 15,000 u 0.03u 0.6 = 270kNm, satisfied. 4. Determination of Factors Section 5.4.1.2 (column under uniaxial bending about the major axis (i.e. N and Mx) restrained from failure about the minor axis) should be used in this case. From Section 4.3.4.1: Curve B should be used and K1x = 0.970 From Eq. (5.15) where C4 = 120 corresponding to column design curve B: K 2x ª 90 25(2E x 1) (1.8 D c ) C 4 O x º (0.9D c2 0.2) « » 30(2.5 E x ) ¬ ¼ ª 90 25 ( 2 u 1 . 0 1 ) ( 1 . 8 0 . 302 ) 120 0.284 º (0.9 0.302 2 0.2) « » 30(2.5 1.0) ¬ ¼ 0.282 u 0.410 0.116 K3x = 0 for CFST RHS CFST Members Subjected to Combined Actions 139 5. Calculate Nx Mx/Mux = 1500/4422 = 0.339 From Eq. (5.13) Nx 2 ª § Mx · º Mx » « ¸ ¨ N u K1x (K1x K 2 x 4K 3 ) 4K 3 ¨ « M ux M ux ¸¹ » © ¬ ¼ 27,013 >0.970 (0.970 0.116 0) 0.339 0@ 27,013 u 0.681 18,396kN 6. Compare N and Nx N = 15,000kN < Nx =18,396kN Therefore the composite beam-column is sufficient to resist the applied loads. If the applied axial load is reduced 50%, i.e. Nx becomes 7500kN (= 0.5 u 15,000kN), the maximum allowed bending moment (Mx) can be calculated from Eq. (5.13) with the following parameters. Nu = 27,013kN Mux = 4422kNm K1x = 0.970 K2x = 0.116 K3x = 0 M º ª 7500 27,013 «0.970 (0.970 0.116) x » 4422 ¼ ¬ Mx = 3585kNm Nx Hence the maximum allowed bending moment (Mx) is about 3580kNm. 5.4.1.2 Solution according to DBJ13-51 1. Relevant Dimension and Properties fc = 27.5MPa (from Table 2.4) fy = 345MPa N = 15,000kN Mx = 1500kNm Concrete-Filled Tubular Members and Connections 140 From Section 3.2.6.1: [ = 1.70 From Eq. (5.24): Em = 1.0 (because transverse load exits) From Section 4.3.4.1: As = 57,500mm2 Ac = 302,500mm2 Member slenderness O = 26.4 Column stability factor M = 0.92 2. Capacities under Separate Loading From Table 3.3: Design moment capacity Mu = 3814kNm From Table 4.5: Design section capacity Nu = 28,850kN 3. Determination of Factors From Eq. (5.23): ]o 1 0.14 [ 1.3 1 0.14 u 1.70 1.3 Ko 0.1 0.13 [ 0.81 1.070 0.1 0.13 u 1.70 0.81 0.185 4. Section Capacity Check N/Nu = 15000/28850 = 0.520 > 2Ko = 2u0.185=0.37 According to Section 5.4.2.1, when N/Nu 2Ko Eq. (5.20a) applies. Constant a can be determined using Eq. (5.21a): a 1 2 Ko 1 2 u 0.185 Check Eq. (5.20a): 0.63 CFST Members Subjected to Combined Actions N a Em M Nu Mu 141 15,000 0.63 u 1.0 u 1500 28,850 3814 0.520 0.248 0.768 1.0 Section capacity is satisfactory. 5. Determination of Factors used in Member Capacity Check N/Nu = 15,000/28,850 = 0.520 > 2M3Ko = 2 u 0.923 u 0.185 = 0.288 According to Section 5.4.2.2, when N/Nu 2M3Ko Eq. (5.25a) applies. Constant a can be determined using Eq. (5.26a): a 1 2 M 2 Ko 1 2 u 0.92 2 u 0.185 0.687 Constant dm can be determined using Eq. (5.27b) with the following parameters defined in Section 5.3.2.2: H scp 3.01 10 6 f y f scy (1.18 0.85 [) f c (1.18 0.85 u 1.70) u 27.5 72.19MPa fy ª º 20 0.365 0.104» f scy «0.263 235 fc ¬ ¼ 345 20 º ª «0.263 235 0.365 27.5 0.104» 72.19 54.54 MPa ¼ ¬ f scp 54.54 52,493 MPa H scp 1.039 10 3 f scp E sc A sc As Ac 57,500 302,500 360,000 mm2 S 2 E sc A sc NE Hence dm 3.01 10 6 u 345 1.039 10 3 3.14159 2 u 52,493 u 360,000 O2 1 0.25 N NE 26.4 2 1 0.25 6. Member Capacity Check Check Eq. (5.25a): 15,000 267,606 0.986 2.676 u 108 N 267,606 kN Concrete-Filled Tubular Members and Connections 142 a Em M N M Nu dm Mu 15,000 0.687 u 1.0 u 1500 0.92 u 28,850 0.986 u 3814 0.565 0.274 0.839 1.0 Member capacity is satisfactory. If the applied axial load is reduced 50%, i.e. N becomes 7500kN (= 0.5 u 15,000kN), the maximum allowed bending moment (M) can be calculated from Eq. (5.25). N/Nu = 7500/28,850 = 0.26 < 2M3Ko = 2 u 0.923 u 0.185=0.288 According to Section 5.3.2.2, when N/Nu < 2M3Ko Eq. (5.25b) applies. The following parameters in Eq. (5.25b) are already available from above, i.e. Em = 1.0 NE = 267,606kN Nu = 28,850kN Mu = 3814kNm ]o = 1.070 Ko = 0.185 dm 1 0.25 N NE 1 0.25 7500 267,606 0.993 From Eq. (5.26b) b 1 ]o M 3 1 1.070 Ko2 0.92 3 u 0.185 2 2.627 From Eq. (5.26c) c 2 (] o 1) Ko b N2 N 2u 2 u (1.070 1) 0.185 c N Em M Nu dm Mu 0.757 2.627 u 7500 2 28,850 2 0.757 u 7500 1.0 u M d 1.0 28,850 0.993 u 3814 M d 3860kNm Hence the maximum allowed bending moment (M) is 3860kNm. CFST Members Subjected to Combined Actions 143 5.4.1.3 Solution according to Eurocode 4 1. Relevant Dimension and Properties fc = 50MPa L = 5377mm N = 15,000kN M = 1500kNm (without second-order effect) From Section 4.3.4.1: Ac = 302,500mm2 Ic = 7626 u 106mm4 Ia = 3175 u 106 mm4 Ea = 210,000MPa Ec = 35,654MPa 2. Capacities under Separate Loading From Table 3.3: Design moment capacity Mp = 4733kNm From Table 4.5: Design section capacity Nu = 29,920kN 3. Second-Order Effect The second-order effect in EC4 can be considered using Table 5.2. E = 1.0 (because transverse load exists) eo = L/300 (no reinforcement bars) N cr , eff S 2 0.9 (E a I a 0.5 E c I c ) L2 3.14159 2 u 0.9 u (210,000 u 3175 u 10 6 0.5 u 35,654 u 7626 u 10 6 ) 5377 2 246,612 u 10 3 N 246,612kN k1 E 1 N / N cr, eff 1.0 1 15,000 / 246,612 k2 1 1 N / N cr , eff 1 1.065 1 15,000 / 246,612 1.065 Concrete-Filled Tubular Members and Connections 144 Applied moment after considering the second-order effect becomes M 2nd k1 M k 2 N e o 1.065 u 1500 1.065 u 15,000 u (5377 / 300) / 1000 1884 kNm 4. Check Interaction Formula Acfc = 302,500 u 50 = 15,125 u 103 N = 15,125kN Since 0.5Acfc < N = 15000 kN < Acfc, Eq. (5.36b) applies. The maximum design moment capacity can be determined using Eq. (5.1) together with partial safety factors (Js = 1.0 for steel strength and Jc = 1.5 for concrete strength). M max 2 1 ª º 1 ªD 2 t º (f y / J s ) t « B ( D t ) ( D 2 t ) 2 » ( B 2 t ) « » (f c / J c ) 2 2 ¬ ¼ ¬ 2 ¼ 1 ª º (345 / 1.0) u 25 u «600 u (600 25) (600 2 u 25) 2 » 2 ¬ ¼ 2 1 ª 600 2 u 25 º (600 2 u 25) « » u (50 / 1.5) 2 2 ¬ ¼ 4280 u 10 6 693 u 10 6 M pl, N, Rd 4733 Mp 4973 u 10 6 Nmm 4973 kNm Ac fc N (M max M p ) 0.5 A c f c 15,125 15,000 (4973 4733) 0.5 u 15,125 4737 kNm Dm =0.9 (for steel grades between S235 and S355 inclusive) M 2 nd 1884 kNm D m M pl, N, Rd 0.9 u 4737 4263 kNm Therefore the composite beam-column is sufficient to resist the applied loads. If the applied axial load is reduced 50%, i.e. N becomes 7500kN (= 0.5 u 15,000kN), the maximum allowed bending moment (M) can be calculated as follows. 0.5Acfc = 0.5 u 302,500 mm2 u 50 MPa = 7563kN Mp = 4733kNm Ncr,eff = 246,612kN Because N < 0.5Acfc Eq. (5.36c) shall be used to obtain Mpl,N,Rd. CFST Members Subjected to Combined Actions M pl, N, Rd Mp 145 N (M max M p ) 0.5 A c f c 4733 7500 (4973 4733) 7563 4971kNm k1 E 1 N / N cr , eff 1.0 1 7500 / 246,612 k2 1 1 N / N cr, eff 1 1.031 1 7500 / 246,612 M 2nd k1 M k 2 N e o 1.031 1.031 u M 1.031 u 7500 u (5377 / 300) / 1000 1.031M 139 kNm From M 2nd 1.031M 139 D m M pl, N, Rd 0.9 u 4971 4474 kNm M < 4205 kNm The maximum allowed bending moment is about 4200kNm. 5.4.1.4 Comparison With the given conditions in the example all codes predict that the composite SHS beam-column is sufficient to resist the applied loads. It is difficult to have a direct comparison among the codes because they have slightly different approaches for design checking. BS5400 determines the allowed axial force (Nx) and compares it with the applied axial load (N). DBJ13-51 checks if the sum of the nondimensional (load/capacity) ratios is less than 1.0. Eurocode 4 determines the allowed bending moment (Mpl,N,Rd) and compares it with the applied moment including the second-order effect (M2nd). The value of Nx obtained by BS5400 is 18,396 kN which is larger than N of 15,000 kN. In order to have a clearer comparison among the three codes, the allowed axial force (Nx) in DBJ13-51 and Eurocode 4 is obtained. The allowed axial force (Nx) from DBJ13-51 can be determined using Eq. (5.25a) and Eq. (5.27b). The values of parameters in the equations are given in Section 5.4.1.2. Nx a Em M M Nu dm Mu dm 1 0.25 Nx NE Nx 0.687 u 1.0 u 1500 1.0 0.92 u 28,850 d m u 3814 1 0.25 Nx 267,606 Concrete-Filled Tubular Members and Connections 146 From the above two equations, Nx = 19249kN. The allowed axial force (Nx) from Eurocode 4 can be determined using the following relationship. The values of parameters in the equations are given in Section 5.4.1.3. M 2 nd D m M pl, N, Rd M 2nd k1 M k 2 N e o k1 1.0 1 N x / N cr , eff k2 k1 u 1500 k 2 u N x u (5377 / 300) / 1000 1.0 1 N x / 246,612 Based on the solutions from BS5400, it is expected that Nx is larger than Acfc of 15,125kN. Hence Eq. (5.36a) should be used to determine Mpl,N,Rd. M pl, N, Rd Nu N Mp Nu Ac fc 29,920 N x u 4733 29,920 15,125 From the above equations, Nx = 22,624 kN. It can be seen that all the Nx values are larger than the applied load N of 15,000 kN. The values given by BS5400 and DBJ13-51 are very close (within 5%). The value given by Eurocode 4 is slightly larger. However, when comparing the Nx value with the column design member capacity (Nc) given in Table 4.10, the ratio of Nx to Nc is reasonably close for the three codes, i.e. 83%, 73% and 77% for BS5400, DBJ13-51 and Eurocode 4, respectively. When the axial load is reduced 50%, the maximum allowed bending moment (Mx) is 3580kNm, 3860kNm and 4200kNm for BS5400, DBJ13-51 and Eurocode 4, respectively. The values given by BS5400 and DBJ13-51 are very close (within 8%). The value given by Eurocode 4 is slightly larger. The Mx value obtained by BS5400 is less than the design moment capacity (MCFST,RHS of 4422kNm given in Table 3.3). The Mx value from DBJ13-51 is slightly above MCFST,RHS of 3814kNm given in Table 3.3. The Mx from Eurocode 4 is less than MCFST,RHS of 4733kNm given in Table 3.3. However the value of Mpl,N,Rd from Eurocode 4 is 4737kNm which is slightly above MCFST,RHS. This is because that part CD in the interaction diagram is used (Figure 5.2(a) for Eurocode 4 and Figure 5.2(c) for DBJ13-51). 5.4.2 Example 2 CFST CHS A beam-column is made of hot-formed circular hollow section (CHS 600 u 15) filled with normal concrete subjected to combined compression and bending about its major axis. The axial force (N) is 10,000 kN while the bending moment (Mx) is 600kNm. Transverse load exists on the column. Restraints are provided to prevent out-of-plain buckling about the minor axis. The column length is 5377 mm and the CFST Members Subjected to Combined Actions 147 effective column buckling length is 4570mm. The nominal yield stress of the SHS is 345MPa. The compressive cylinder strength of concrete is 50MPa and cubic strength is 60MPa. Determine if the composite column is sufficient to resist the combined loads. If the applied axial load is reduced 50%, what is the maximum allowed bending moment (Mx)? 5.4.2.1 Solution according to BS5400 1. Relevant Dimension and Properties d = 600mm = 0.6m N = 10000kN Mx = 600kNm Ex = 1 (because transverse load exists) From Section 4.2.4.2: Dc = 0.612 From Section 4.3.4.2: Ox = 0.374 2. Capacities under Separate Loading From Table 3.4: Design moment capacity Mux = 1910kNm From Table 4.6: Design section capacity Nu = 19,318kN 3. Check conditions Mx = 600kNm < Mux = 1910kNm, satisfied. Mx = 600kNm > N u 0.03b = 10,000 u 0.03u 0.6 = 180kNm, satisfied. 4. Determination of Factors Section 5.4.1.2 (column under uniaxial bending about the major axis (i.e. N and Mx) restrained from failure about the minor axis) should be used in this case. From Section 4.3.4.2: Curve B should be used and K1x = 0.960 Concrete-Filled Tubular Members and Connections 148 From Eq. (5.14): K 2x ª115 30(2E x 1) (1.8 D c ) 100O x º (0.9D c2 0.2) « » 50(2.1 E x ) ¼ ¬ ª115 30 (2 u 1.0 1) (1.8 0.612) 100 u 0.374 º (0.9 u 0.612 2 0.2) « » 50 (2.1 1) ¼ ¬ 0.537 u 0.763 0.410 From Eq. (5.16): D K 30 0.04 c 0.04 0.612 / 15 15 Take the minimum value K30 = 0. K3 K 30 0 0.0008 (0.5E x 0.4) (D c2 0.5) 0.15 O x 1 O3x >(0.5 u1.0 0.4) (0.612 0.5) 0.15@ 0.374 2 1 0.3743 0.0122 5. Calculate Nx Mx/Mux = 600/1910 = 0.314 From Eq. (5.13) 2 ª § Mx · º Mx « » ¨ ¸ 4K 3 ¨ N x N u K1x (K1x K 2 x 4K 3 ) « M ux M ux ¸¹ » © ¬ ¼ > 19,318 0.960 (0.960 0.410 4 u 0.0122) 0.314 4 u 0.0122 u 0.314 2 19,318 u 0.798 15,415 kN @ 6. Compare N and Nx N = 10,000 kN < Nx =15,415 kN Therefore the composite beam-column is sufficient to resist the applied loads. If the applied axial load is reduced 50%, i.e. Nx becomes 5000kN (= 0.5 u 10000kN), the maximum allowed bending moment (Mx) can be calculated from Eq. (5.13) with the following parameters. CFST Members Subjected to Combined Actions 149 Nu = 19318kN Mux = 1910kNm K1x = 0.960 K2x = 0.410 K3x = 0.0122 N x 5000 2 ª M §M · º 19318 «0.960 (0.960 0.410 4 u 0.0122) x 4 u 0.0122 u ¨ x ¸ » 1910 «¬ © 1910 ¹ »¼ Mx = 2384 kNm However, the maximum moment should not exceed the ultimate moment capacity Mux of 1910kN. Hence the maximum allowed bending moment (Mx) is 1910kNm. 5.4.2.2 Solution according to DBJ13-51 1. Relevant Dimension and Properties fc = 27.5MPa (from Table 2.4) fy = 345MPa N = 10,000kN Mx = 600kNm From Section 3.2.6.2: [ = 0.968 From Eq. (5.24): Em = 1.0 (because transverse load exists) From Section 4.3.4.2: As = 27,568mm2 Ac = 255,176mm2 Member slenderness O = 30.5 Column stability factor M = 0.885 2. Capacities under Separate Loading From Table 3.4: Design moment capacity Mu = 1533kNm From Table 4.6: Concrete-Filled Tubular Members and Connections 150 Design section capacity Nu = 18067kN 3. Determination of Factors From Eq. (5.22): ]o 1 0.18 [ 1.15 Ko 0.1 0.14 [ 0.84 1 0.18 u 0.968 1.15 1.187 0.1 0.14 u 0.968 0.84 0.244 4. Section Capacity Check N/Nu = 10,000/18,067 = 0.553 > 2Ko = 2 u 0.244 = 0.488 According to Section 5.4.2.1, when N/Nu 2Ko Eq. (5.20a) applies. Constant a can be determined using Eq. (5.21a): a 1 2 Ko 1 2 u 0.244 0.512 Check Eq. (5.20a): N a Em M Nu Mu 10,000 0.512 u 1.0 u 600 18,067 1533 0.553 0.200 0.753 1.0 Section capacity is satisfactory. 5. Determination of Factors used in Member Capacity Check N/Nu = 10,000/18,067 = 0.553 > 2M3Ko = 2 u 0.8853 u 0.244 = 0.338 According to Section 5.4.2.2, when N/Nu 2M3Ko Eq. (5.25a) applies. Constant a can be determined using Eq. (5.26a): a 1 2 M 2 Ko 1 2 u 0.885 2 u 0.244 0.618 Constant dm can be determined using Eq. (5.27a) with the following parameters defined in Section 5.4.2.2: H scp 3.25 10 6 f y 3.25 u 10 6 u 345 1.121 u 10 3 f scy (1.14 1.02 [) f c (1.14 1.02 u 0.968) 27.5 58.50 MPa CFST Members Subjected to Combined Actions fy ª º 0.488» f scy «0.192 235 ¬ ¼ f scp E sc A sc NE 45.04 H scp 1.121 10 3 As Ac 345 ª º «0.192 235 0.488» 58.50 ¬ ¼ 27,568 255,176 282,744 mm2 3.14159 2 u 40,178 u 282,744 O 30.5 2 1 0.4 45.04 MPa 40,178 MPa S 2 E sc A sc Hence dm f scp 151 N NE 1 0.4 10,000 120,526 2 1.20526 u 108 N 120,526 kN 0.967 6. Member Capacity Check Check Eq. (5.25a): a Em M N M Nu dm Mu 10000 0.618 u 1.0 u 600 0.885 u 18,067 0.967 u 1533 0.625 0.250 0.875 1.0 Member capacity is satisfactory. If the applied axial load is reduced 50%, i.e. N becomes 5000kN (= 0.5 u 10000kN), the maximum allowed bending moment (M) can be calculated from Eq. (5.25). N/Nu = 5000/18,067 = 0.277 < 2M3Ko = 2 u 0.8853 u 0.244 = 0.338 According to Section 5.4.2.2, when N/Nu < 2M3Ko Eq. (5.25b) applies. The following parameters in Eq. (5.25b) are already available from above, i.e. Em = 1.0 NE = 120,526kN Nu = 18,067kN Mu = 1533kNm ]o = 1.187 Ko = 0.244 5000 N 0.983 1 0.4 d m 1 0.4 120,526 NE Concrete-Filled Tubular Members and Connections 152 From Eq. (5.26b) b 1 ]o M 3 1 1.187 Ko2 0.8853 u 0.244 2 4.531 From Eq. (5.26c) c 2 (] o 1) Ko b N2 N 2u 2(1.187 1) 0.244 c N Em M Nu dm Mu 1.533 4.531u 5000 2 18,067 2 1.533 u 5000 1.0 u M d 1.0 18,067 0.983 u 1533 M d 1623kNm Hence the maximum allowed bending moment (M) is about 1620kNm. 5.4.2.3 Solution according to Eurocode 4 1. Relevant Dimension and Properties fc = 50MPa L = 5377mm N = 10,000kN M = 600kNm (without second-order effect) From Section 4.3.4.2: Ac = 255,176mm2 Ic = 5182 x 106mm4 Ia = 1180 x 106mm4 Ea = 210,000MPa Ec = 35,654MPa 2. Capacities under Separate Loading From Table 3.4: Design moment capacity Mp = 2042kNm From Table 4.6: Design section capacity Nu = 17,992kN CFST Members Subjected to Combined Actions 153 3. Second-Order Effect The second-order effect in EC4 can be considered using Table 5.2. E = 1.0 (because transverse load exists) eo = L/300 (no reinforcement bars) N cr , eff S 2 0.9 (E a I a 0.5 E c I c ) L2 3.14159 2 u 0.9 u (210,000 u 1180 u 10 6 0.5 u 35,654 u 5182 u 10 6 ) 5377 2 104,513 u 10 3 N 104,513kN k1 E 1 N / N cr, eff 1.0 1.106 1 10,000 / 104,513 k2 1 1 N / N cr, eff 1 1.106 1 10,000 / 104,513 Applied moment after considering the second order effect becomes M 2nd k1 M k 2 N e o 1.106 u 600 1.106 u 10000 u (5377 / 300) / 1000 862 kNm 4. Check Interaction Formula Acfc = 255,176mm2 u 50MPa = 12,759kN Since 0.5Acfc < N = 10000 kN < Acfc, Eq. (5.36b) applies. The maximum design moment capacity can be determined using Eq. (5.3) together with partial safety factors (Js = 1.0 for steel strength and Jc = 1.5 for concrete strength). rm ri d t 600 15 292.50 mm 2 2 d 2 t 600 2 u 15 285 mm 2 2 Concrete-Filled Tubular Members and Connections 154 M max 2 (f c / J c ) ri3 3 2 4 u (345 / 1.0) u 15 u 292.50 2 u (50 / 1.5) u 2853 1771u 10 6 514 u 10 6 3 2 4 (f y / J s ) t rm 2285 u 10 6 Nmm 2285 kNm M pl, N, Rd Mp Ac fc N (M max M p ) 0.5 A c f c 2042 12,759 10,000 (2285 2042) 0.5 u 12,759 2147 kNm Dm = 0.9 (for steel grades between S235 and S355 inclusive) M 2 nd 862 kNm D m M pl, N , Rd 0.9 u 2147 1932 kNm Therefore the composite beam-column is sufficient to resist the applied loads. If the applied axial load is reduced 50%, i.e. N becomes 5000kN (= 0.5 u 10000kN), the maximum allowed bending moment (M) can be calculated as follows. 0.5Acfc = 0.5 u 255,176mm2 u 50MPa = 6379kN Mp = 2042kNm Ncr,eff = 104,513kN Because N < 0.5Acfc Eq. (5.36c) shall be used to obtain Mpl,N,Rd. N 5000 M pl, N, Rd M p (M max M p ) 2042 (2285 2042) 0.5 A c f c 6379 k1 2233 kNm E 1.0 1.050 1 N / N cr , eff 1 5000 / 104,513 k2 M 2nd 1 1 N / N cr , eff 1 1.050 1 5000 / 104,513 k1 M k 2 N e o 1.050 u M 1.050 u 5000 u (5377 / 300) / 1000 1.050M 94 kNm From M 2nd 1.050M 94 D m M pl, N, Rd 0.9 u 2233 2010 kNm M < 1825kNm The maximum allowed bending moment is about 1820kNm. CFST Members Subjected to Combined Actions 155 5.4.2.4 Comparison With the given conditions in the example all codes predict that the composite CHS beam-column is sufficient to resist the applied loads. It is difficult to have a direct comparison among the codes because they have slightly different approaches for design checking. BS5400 determines the allowed axial force (Nx) and compares it with the applied axial load (N). DBJ13-51 checks if the sum of the nondimensional (load/capacity) ratios is less than 1.0. Eurocode 4 determines the allowed bending moment (Mpl,N,Rd) and compares it with the applied moment including the second-order effect (M2nd). The value of Nx obtained by BS5400 is 15,415kN, which is larger than N of 10,000 kN. In order to have a clearer comparison among the three codes, the allowed axial force (Nx) in DBJ13-51 and Eurocode 4 is obtained. The allowed axial force (Nx) from DBJ13-51 can be determined using Eq. (5.25a) and Eq. (5.27a). The values of parameters in the equations are given in Section 5.4.2.2. Nx a Em M M Nu dm Mu Nx 0.618 u 1.0 u 600 1.0 0.885 u 18067 d m u 1533 Nx Nx 1 0.4 NE 120526 From the above two equations, Nx = 11,960kN. The allowed axial force (Nx) from Eurocode 4 can be determined using the following relationship. The values of parameters in the equations are given in Section 5.4.2.3. dm 1 0.4 M 2nd D m M pl, N, Rd M 2nd k1 M k 2 N e o k1 1.0 1 N x / N cr , eff k2 0.9 M pl, N, Rd k1 u 600 k 2 u N x u (5377 / 300) / 1000 1.0 1 N x / 104,513 Based on the solutions from BS5400, it is expected that Nx is larger than Acfc of 12,759kN. Hence Eq. (5.36a) should be used to determine Mpl,N,Rd. M pl, N, Rd Nu N Mp Nu Ac fc 17,992 N x u 2042 17,992 12,759 From the above equations, Nx = 15,114kN. Concrete-Filled Tubular Members and Connections 156 It can be seen that all the Nx values are larger than the applied load N of 10,000kN. The values given by BS5400 and Eurocode 4 are very close (within 2%). The value given by DBJ13-51 is slightly lower. When comparing the Nx value with the column design member capacity (Nc) given in Table 4.11, the ratio of Nx to Nc becomes 98%, 75% and 88% for BS5400, DBJ13-51 and Eurocode 4, respectively. When the axial load is reduced 50%, the maximum allowed bending moment (Mx) is 1910kNm, 1620kNm and 1820kNm for BS5400, DBJ13-51 and Eurocode 4, respectively. The values given by BS5400 and Eurocode 4 are very close (within 5%). The value given by DBJ13-51 is slightly lower. The Mx value obtained by BS5400 is limited by the design moment capacity (MCFST,RHS of 1910kNm given in Table 3.4). The Mx value from DBJ13-51 is slightly above MCFST,RHS of 1533kNm given in Table 3.4. The Mx from Eurocode 4 is less than MCFST,RHS of 2042kNm given in Table 3.4. However the value of Mpl,N,Rd from Eurocode 4 is 2233kNm which is slightly above MCFST,RHS. This is because of part CD in the interaction diagram is used (Figure 5.2(a) for Eurocode 4 and Figure 5.2(c) for DBJ13-51). 5.5 COMBINED LOADS INVOLVING TORSION OR SHEAR 5.5.1 Compression and Torsion Han et al. (2007b) derived the following formula to represent the interaction diagram of CFST members under combined compression force (N) and torsion (T). 2.4 2 § N · § T · ¨¨ ¸¸ ¨¨ ¸¸ d 1 (5.40) © M Nu ¹ © Tu ¹ in which Nu is the section capacity given in Eq. (4.15), M is the column stability factor given in Figures 4.7 and 4.8, and Tu is torsion capacity of the CFST members given as follows. Tu J t W scy Wsct (5.41) For CFST CHS members: Jt 1.294 0.267 ln([) (5.42a) Wscy (0.422 0.313D s2.33 ) [ 0.134 f scy (5.42b) Wsct S d 3 /16 (5.42c) For CFST RHS members: Jt 1.431 0.242 ln([) (5.43a) CFST Members Subjected to Combined Actions 157 W scy (0.455 0.313D s2.33 ) [ 0.25 f scy (5.43b) Wsct 0.208B3 (5.43c) where [ is given in Eq. (3.32), Ds is given in Eq. (4.31), fscy is given in Eq. (5.44) (Han et al. 2007a), d is the diameter of CHS and B is the flange width of SHS. For CFST CHS members: (5.44a) f scy (1.14 1.02[) f ck For CFST RHS members: f scy (1.18 0.85[) f ck (5.44b) 5.5.2 Bending and Torsion The interaction diagram of CFST members under combined bending moment (M) and torsion was derived by Han et al. (2007b), shown below. 2.4 2 § M · § T · ¨¨ ¸¸ ¨¨ ¸¸ d 1 © Mu ¹ © Tu ¹ where Mu is given in Eq. (3.29) and Tu is given in Eq. (5.41). (5.45) 5.5.3 Compression, Bending and Torsion Figure 5.3 shows a typical non-dimensional interaction diagram for CFST members subjected to combined compression (N), bending (M) and torsion (T), where (K is N/Nu, ] is M/Mu and E is T/Tu). The coordinates of the contraflexure point A(Ke, ]e, 0) in Figure 5.3 can be calculated as (Han et al. 2007b): Ke 2.4 1 E 2 Ko (5.46a) ]e 2.4 1 E 2 ] o (5.46b) in which Ko and ]o are defined in Eq. (5.22) for CFST CHS and in Eq. (5.23) for CFST RHS. For N / N u t 2M3 K0 2.4 1 (T / Tu ) 2 §1 N a M · ¸¸ ¨¨ © M Nu dm Mu ¹ 2.4 2 § T · ¸¸ d 1 ¨¨ © Tu ¹ (5.47a) Concrete-Filled Tubular Members and Connections 158 For N / N u 2M3 K0 2.4 1 (T / Tu ) 2 § N 2 N 1 M · ¨¨ b ( ¸ ) c( ) Nu Nu d m M u ¸¹ © 2.4 2 § T · ¸¸ d 1 ¨¨ © Tu ¹ (5.47b) in which a 1 2M 2 Ko (5.48a) 1 ]e (5.48b) b M3Ke 2 c 2 (] e 1) Ke (5.48c) dm § N · ¸¸ (CHS member) ° 1 0.4 ¨¨ ° © NE ¹ ® °1 0.25 §¨ N ·¸ (RHS member) ¨N ¸ ° © E¹ ¯ (5.48d) where M is the column stability factor given in Figures 4.7 and 4.8, and NE is determined by from Eq. (5.28). E (0,0,1) ( 2.4 2 1E ,0,E) (Ke ,0,E) (1,0,0) K (Ko,0,0) 0 2.4 2 (0, E ,E) (0,]e ,E) A(K e,]e,E) (0,1,0) (0,]o,0) (Ko,]o,0) ] Figure 5.3 Non-dimensional interaction diagram for CFST members subjected to combined compression, bending and torsion (adapted from Han et al. 2007b) CFST Members Subjected to Combined Actions 159 5.5.4 Compression, Bending and Shear Analysis done by Han et al. (2008) revealed that the load-bearing capacity for CFST members subjected to compression (N), bending (M) and shear (V) decreases with the increase of the V/Vu ratio, where Vu is the shear capacity of CFST members. However, the V/Vu ratio does not affect the shape of the N–M interaction curve. It was found that the interaction diagram N/Nu–M/Mu–V/Vu is similar to that given in Figure 5.3. The interaction relationship can be expressed as follows. For N / N u t 2M3 K0 2.4 1 (V / Vu ) 2 §1 N a M · ¨¨ ¸¸ M N d u m Mu ¹ © 2.4 2 § V · ¸¸ d 1 ¨¨ © Vu ¹ (5.49a) For N / N u 2M3 K0 2.4 1 (V / Vu ) 2 2 · § ¨ b §¨ N ·¸ c §¨ N ·¸ 1 M ¸ ¨N ¸ d ¨N ¸ ¸ ¨¨ m Mu ¸ © u¹ © u¹ ¹ © 2.4 2 § V · ¸¸ d 1 ¨¨ © Vu ¹ (5.49b) where, a, b, c, dm are defined in Eq. (5.48), M is the column stability factor given in Figures 4.7 and 4.8, Ko is defined in Eq. (5.22) for CFST CHS and in Eq. (5.23) for CFST RHS, Vu is defined below. (5.50) Vu J v A sc W scy For CFST CHS members: J v 0.97 0.2 ln([) (5.51a) For CFST RHS members: J v 0.954 0.162 ln([) (5.51b) where Asc is given in Eq. (4.16), Wscy is given in Eq. (5.42b) for CFST CHS and Eq. (5.43b) for CFST RHS. 5.5.5 Compression, Bending, Torsion and Shear For CFST members under combined compression (N), bending (M), torsion (T) and shear (V), the interaction relationship was obtained based on regression analysis (Han, 2007), i.e. 3 2 § T · § V · ¸ ¨ ¸ ¸ ¨ ¸ © Tu ¹ © Vu ¹ For N / N u t 2M K0 2.4 1 ¨¨ 2 Concrete-Filled Tubular Members and Connections 160 §1 N a M · ¸¸ ¨¨ N d M u m Mu ¹ © 2.4 2 2 § V · § T · ¸¸ d 1 ¸¸ ¨¨ ¨¨ © Vu ¹ © Tu ¹ 2 § T · § V · ¸¸ ¨¨ ¸¸ For N / N 2M3K0 2.4 1 ¨¨ © Tu ¹ © Vu ¹ 2 § · ¨ b §¨ N ·¸ c §¨ N ·¸ 1 M ¸ ¨N ¸ d ¨N ¸ ¸ ¨¨ m Mu ¸ © u¹ © u¹ ¹ © 2.4 (5.52a) 2 2 2 § V · § T · ¸¸ d 1 ¸¸ ¨¨ ¨¨ © Vu ¹ © Tu ¹ (5.52b) where, a, b, c, dm are defined in Eq. (5.48), M is the column stability factor given in Figures 4.7 and 4.8, Ko is defined in Eq. (5.22) for CFST CHS and in Eq. (5.23) for CFST RHS. The range of validity for Eq. (5.52) is D = 0.04 to 0.2, column slenderness O = 10 to 120, fy = 235 to 420MPa, fcu = 30 to 90MPa and [ = 0.2 to 5. 5.6 REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. BSI, 2005, Steel, concrete and composite bridges, BS5400, Part 5: Code of practice for design of composite bridges (London: British Standards Institution). Chang, X., Huang, C.K. and Chen, Y.-J., 2009, Mechanical performance of eccentrically loaded pre-stressing concrete filled circular steel tube columns by means of expansive cement. Engineering Structures, 31(11), pp. 2588-2597. DBJ13-51-2003, 2003, Technical specification for concrete-filled steel tubular structures (Fuzhou: The Construction Department of Fujian Province). Eurocode 4, 2004, Design of composite steel and concrete structures – Part 1.1: General rules and rules for buildings. EN1994-1-1:2004, December 2004 (Brussels: European Committee for Standardization). Fam, A.Z., Flisak, B. and Rizkalla, S., 2003, Experimental and analytical investigations of beam-column behavior of concrete-filled FRP tubes. ACI Structural Journal, 100(4), pp. 499-509. Fam, A.Z., Schnerch, D. and Rizkalla, S., 2005, Rectangular filament-wound glass fiber reinforced polymer tubes filled with concrete under flexural and axial loading: experimental investigation. Journal of Composites for Construction, ASCE, 9(1), pp. 25-33. Fujimoto, T., Mukai, A., Nishiyama, I. and Sakino, K., 2004, Behavior of eccentrically loaded concrete-filled steel tubular columns. Journal of Structural Engineering, ASCE, 130(2), pp. 203-212. GB50017, 2003, Code for design of steel structures, National Standard of P.R. China, GB 50017-2003 (Beijing: China Architecture & Building Press). CFST Members Subjected to Combined Actions 9. 161 Gopal, S.R. and Manoharan, P.D., 2004, Tests on fibre reinforced concrete filled steel tubular columns. Steel and Composite Structures, 4(1), pp. 37-48. 10. Gopal, S.R. and Manoharan, P.D., 2006, Experimental behaviour of eccentrically loaded slender circular hollow steel columns in-filled with fibre reinforced concrete. Journal of Constructional Steel Research, 62(5), pp. 513520. 11. Han, L.H., 2000, The influence of concrete compaction on the strength of concrete filled steel tubes. Advances in Structural Engineering – An International Journal, 3(2), pp. 131-137. 12. Han, L.H., 2007, Concrete-filled steel tubular structures – theory and practice, 2nd ed. (Beijing: China Science Press). 13. Han, L.H., Tao, Z. and Yao, G.H., 2008, Behaviour of concrete-filled steel tubular members subjected to shear and constant axial compression, ThinWalled Structures, 46(7-9), pp. 765-780. 14. Han, L.H. and Yao, G.H., 2003a, Influence of concrete compaction on the strength of concrete-filled steel RHS columns. Journal of Constructional Steel Research, 59(6), pp. 751-767. 15. Han, L.H. and Yao, G.H., 2003b, Behaviour of concrete-filled hollow structural steel (HSS) columns with pre-load on the steel tubes. Journal of Constructional Steel Research, 59(12), pp. 1455-1475. 16. Han, L.H. and Yao, G.H., 2004, Experimental behaviour of thin-walled hollow structural steel (HSS) columns filled with self-consolidating concrete (SCC). Thin-Walled Structures, 42(9), pp. 1357-1377. 17. Han, L.H., Yao, G.H. and Tao, Z., 2007a, Performance of concrete-filled thinwalled steel tubes under pure torsion. Thin-Walled Structures, 45(1), pp. 2436. 18. Han, L.H., Yao, G.H. and Tao, Z., 2007b, Behavior of concrete-filled steel tubular subjected to combined loading. Thin-Walled Structures, 45(6), pp. 600-619. 19. Han, L.H., Zhao, X.L. and Tao, Z., 2001, Tests and mechanics model for concrete-filled SHS stub columns, columns and beam-columns. Steel and Composite Structures, 1(1), pp. 51-74. 20. Johansson, M. and Gylltoft, K., 2001, Structural behaviour of slender circular steel–concrete composite columns under various means of load application. Steel and Composite Structures, 1(4), pp. 393-410. 21. Knowles, R.B. and Park, R., 1969, Strength of concrete filled steel tubular columns. Journal of Structural Division, ASCE, 95(ST12), pp. 2565-2587. 22. Lee, S.J., 2007, Capacity and the moment–curvature relationship of highstrength concrete filled steel tube columns under eccentric loads. Steel and Composite Structures, 7(2), pp. 135-160. 23. Liu, D.L., 2004, Behaviour of high strength rectangular concrete-filled steel hollow section columns under eccentric loading. Thin-walled Structures, 42(12), pp. 1631-1644. 24. Liu, D.L., 2006, Behaviour of eccentrically loaded high-strength rectangular concrete-filled steel tubular columns. Journal of Constructional Steel Research, 62(8), pp. 839-846. 162 Concrete-Filled Tubular Members and Connections 25. Mursi, M. and Uy, B., 2004, Strength of slender concrete filled high strength steel box columns. Journal of Constructional Steel Research, 60(12), pp. 1825-1848. 26. Neogi, P.K., Sen, H.K. and Chapman, J.C., 1969, Concrete filled tubular steel columns under eccentric loading. The Structural Engineer, 47(5), pp. 187-195. 27. Prion, H.G.L. and Boehme, J., 1994, Beam-column behaviour of steel tubes filled with high strength concrete. Canadian Journal of Civil Engineering, 21(2), pp. 207-218. 28. Rangan, B.V. and Joyce, M., 1992, Strength of eccentrically loaded slender steel tubular columns filled with high-strength concrete. ACI Structural Journal, 89(6), pp. 676-681. 29. Shakir-Khalil, H. and Mouli, M., 1990, Further tests on concrete-filled rectangular hollow-section columns. Structural Engineer, 68(20), pp. 405-413. 30. Shakir-Khalil, H. and Zeghiche, J., 1989, Experimental behaviour of concrete filled rolled rectangular hollow-section columns. Structural Engineer, 67(19), pp. 346-353. 31. Standards Australia, 2004, Bridge design – Steel and composite construction, Australian Standard AS 5100 (Sydney: Standards Australia). 32. Tao, Z., Han, L.H. and Wang, D.Y., 2007, Experimental behaviour of concrete-filled stiffened thin-walled steel tubular columns. Thin-Walled Structures, 45(5), pp. 517-527. 33. Thayalan, P., Aly, T. and Patnaikuni, I., 2009, Behaviour of concrete-filled steel tubes under static and variable repeated loading. Journal of Constructional Steel Research, 65(4), pp. 900-908. 34. Uy, B., 2000, Strength of concrete filled steel box columns incorporating local buckling. Journal of Structural Engineering, ASCE, 126(3), pp. 341-352. 35. Uy, B., 2001, Strength of short concrete filled high strength steel box columns. Journal of Constructional Steel Research, 57(2), pp. 113-134. 36. Wang, Y.C., 1999, Tests on slender composite columns. Journal of Constructional Steel Research, 49(1), pp. 25-41. 37. Yang, Y.F. and Han, L.H., 2006, Experimental behaviour of recycled aggregate concrete filled steel tubular columns. Journal of Constructional Steel Research, 62(12), pp. 1310-1324. 38. Yu, Q., Tao, Z. and Wu, Y.X., 2008, Experimental behavior of high performance concrete-filled steel tubular columns. Thin-Walled Structures, 46(4), pp. 362-370. 39. Zhang, S.M. and Guo, L.H., 2007, Behaviour of high strength concrete-filled slender RHS steel tubes. Advances in Structural Engineering – An International Journal, 10(4), pp. 337-351. CHAPTER SIX Seismic Performance of CFST Members 6.1 GENERAL It is well known that three important aspects in seismic design are strength, ductility and hysteretic behaviour. Strength and ductility can be seen from Figure 6.1(a), i.e. the yield load Py and the ductility ratio 'u/'y (to some extent represents ductility) which will be discussed in Section 6.3.1. Hysteretic behaviour can be demonstrated using Figure 6.1(b), where P and M are applied load and bending moment, and ' and I are displacement and curvature, respectively. General principles about seismic design can be found in AISC (2002) and Hajjar (2002). They are applicable to composite tubular members. Ductility ratio P = ' u ' y P P or M Py 85% Py Envelope curve ' or I 0 'y 'p 'u (a) Strength and ductility ' (b) Cyclic load response Figure 6.1 Load versus deformation relations (schematic view) It is important to choose tubular sections that have sufficient rotation capacity, to pay attention to connection detailing, to consider the favourable hingemechanism and to adopt the concept of strong-column/weak-beam. In frame structures, the formation of plastic hinges in the columns should be avoided. Other mechanisms, such as plastic hinges in the beams or plastic shear mechanisms in eccentric braced frames, mainly contribute to the overall energy dissipation. A comparison of undesirable and desirable mechanisms is shown in Figure 6.2. It can be seen from Figure 6.2(a) that the plastic hinges in the “weak” columns (or called soft-storey-mechanism) lead to poor energy dissipation. Figure 6.2(b) gives an example of building collapse due to soft-storey-mechanism during the Concrete-Filled Tubular Members and Connections 164 Sichuan earthquake on 12 May 2008. Figure 6.2(c) gives a desirable mechanism where many plastic hinges in the “weak” beams lead to excellent energy dissipation. Concrete eliminates or delays the local buckling of steel hollow sections, and significantly increases the ductility of the section, as shown in Chapters 3, 4 and 5. Connection details are discussed in Chapter 8. This chapter will focus on strength, ductility and hysteretic behaviour of CFST members. Joint without plastification Beam Beam Plastic hinge Column Joint without plastification Column Plastic hinge (a) Storey mechanism (undesirable) (b) Example of building collapse due to soft-storeymechanism Plane yielding in shear Beam Beam Column (c) Overall sway mechanism (desirable) Figure 6.2 Hinge mechanisms of frame structures (adapted from Kurobane et al.. 2004) No Cyclic loading P M No Cyclic loading P L1 ' ' L1 L1 No ' Cyclic loading P L1 L1 M L1 P No (a) No (b) No (c) Figure 6.3 Typical beam-columns Large amounts of experimental investigations were carried out on CFST columns subject to cyclic loading. Two types of loading conditions were often adopted. One is cyclic bending caused by a cyclic loading in the mid span as shown in Figure 6.3(a). The other is lateral cyclic loading applied at the end of the Seismic Performance of CFST Members 165 column as shown in Figures 6.3(b) and (c). In both cases a constant axial load (No) is also applied to the column. A summary of the existing experimental work is given in Table 6.1 for CFST beam-columns subjected to the first type of loading, and in Table 6.2 for CFST beam-columns subjected to the second type of loading. The axial load level (n) is defined as the ratio of the applied axial load (No) to the section capacity in compression. The existing experimental programme covered a wide range of parameters, e.g. diameter or width of tubes from 100 to 300mm, thickness from 2 to 10mm, yield stress from 275 to 835MPa, concrete strength from 20 to 120MPa. Most of the research on high strength concrete (fc > 100MPa) filled tubes and on high strength steel tubes (fy > 600MPa) happened from year 2000. Large amounts of theoretical analysis on CFST columns under cyclic loading have been carried out by many researchers, for example, Hajjar et al. (1997a, 1997b, 1998), Usami and Ge (1998), Liu et al. (2001), Susantha et al. (2001), Ge et al. (2003), Hsu and Yu (2003), Han et al. (2003), Han and Yang (2005), Thayalan et al. (2009) and Aly et al. (2010). Relevant to CFST columns, research has been conducted by Yogishita et al. (2000), Han et al. (2006) and Han et al. (2009) on concrete-filled double-skin tubes (CFDST) under cyclic loading, by Xiao et al. (2005) and Mao and Xiao (2006) on confined concrete-filled tubes, and by Han et al. (2005) on SCC (self-consolidating concrete)-filled tubular columns under cyclic loading. Table 6.1 Summary of experimental studies on CFST beam-columns under cyclic bending d or B (mm) t (mm) Steel yield stress fy (MPa) Concrete compressive strength fc (MPa) CFST CHS Axial load level n Number of tests 165–300 4.35–6.23 350–588 76.2 0.33– 0.82 7 152 1.7 328 102 0–0.64 3 160–241 4.5–9.1 338–806 43.1–104 152 3.12 347 70 100 1.9 282–404 325–336 3–6 303–312 Reference Ichinohe et al. (1991) Prion and Boehme (1994) Nishiyama et al. (2002) 2 Fam et al. (2004) 90.4–122 0.32– 0.49 0.44– 0.52 0.04–0.6 10 34.4–47.6 0.48–0.5 2 Han et al. (2005) Xiao et al. (2005) CFST RHS 200–250 4.5–6 350–367 32.4–55.5 178–211 4.5–9.5 323–837 47.8–105 203 4.4–9.2 378–411 53.4–109 100 1.9 282–404 90.4–122 0.26– 0.64 0.38– 0.53 0.14– 0.62 0.03–0.6 9 20 12 12 8 Shiiba and Harada (1994) Nishiyama et al. (2002) Hardika and Gardner (2004) Han et al. (2005) Concrete-Filled Tubular Members and Connections 166 Table 6.2 Summary of experimental studies on CFST beam-columns under lateral cyclic loading Concrete compressive strength fc (MPa) Axial load level n Number of tests CFST CHS 33.8 26.5–34.9 0.02–0.61 0.06–0.59 3 18 283–345 38.6–57.3 0.11–0.14 5 1.25–3 407–410 38.8–40.5 0.28–0.72 6 324 6.4–9.5 372 48.8–114 0.25–0.49 6 100 2 290 75 0–0.64 3 108–133 3–4.7 308–511 22–56.2 0–0.78 10 150 2.65–4.82 317–340 48.8–101 0.35–0.58 9 d or B (mm) t (mm) Steel yield stress fy (MPa) 108 108–165 5 2–5 328 267–359 203 1.9–2.8 96–100 CFST RHS 100 2.2–4.2 290–310 28.5–36.6 0.01–0.52 15 149 4.2–4.3 339–351 28.7–42.5 0.03–0.27 6 156–264 5.87 308 32.4–39.4 0.20 12 125 3.2–6 351–439 28.9–50.7 0–0.39 35 305 5.8–8.9 269–660 120 0.14–0.31 8 200 3–5 283–314 39.5–48.1 0.33–0.79 11 100–120 3.5 275 25.2 0.04–0.48 6 100–120 2.75–3 276–340 58–75 0–0.68 7 60–120 2.65–3.0 300–340 20.1–61.2 0.06–0.80 31 Reference Tu (1994) Zhong (1994) Boyd et al. (1995) Fujinaga et al. (1998) Elremaily and Azizinamini (2002) Tao and Yu (2006) Han (2007) Liu et al. (2008) Sakino and Tomii (1981) Morishita and Tomii (1982) Ge and Usami (1996) Kang et al. (1998) Varma et al. (2002) Lv et al. (2000) Tao (2001) Tao and Yu (2006) Han (2007) 6.2 INFLUENCE OF CYCLIC LOADING ON STRENGTH 6.2.1 CFST Beams Zhao and Grzebieta (1999) studied the influence of cyclic loading on the capacity of both CFST and unfilled SHS beams. It can be seen from Figure 6.4 that large deformation cyclic loading reduces the capacity of beams, especially for unfilled tubular beams. However, the strength reduction of the CFST members is about 10%. Seismic Performance of CFST Members 167 12 11 10 Moment (KNm) 9 8 7 6 5 Compact SHS filled with concrete 4 3 Non-compact SHS filled with concrete Slender SHS filled with concrete 2 Compact SHS (unfilled) Non-compact SHS (unfilled) 1 Slender SHS (unfilled) 0 0.5 1 1.5 2 2.5 3 3.5 4 Number of Cycles 4.5 5 5.5 6 Figure 6.4 Comparison of maximum bending moment reached in each cycle versus number of cycles (adapted from Zhao and Grzebieta 1999) 1.6 1.4 Lower bound (static) Mu /M ptH 1.2 1.0 O y = 60 [Elchalakani et al. 2002] 0.8 Compact 0.6 0.4 Static Tests [Elchalakani et al. 2001] SCCL Tests [Elchalakani et al. 2004] IICL Tests [Elchalakani and Zhao 2008] 0.2 0.0 Non-Compact 0 50 100 Slender O y = 140 [Elchalakani et al. 2002] 150 200 O s = (d/t) (f y /250) Figure 6.5 Effect of cyclic loading on bending strength of CFT (adapted from Elchalakani and Zhao 2008) For CFST beams, it was found (Elchalakani and Zhao 2008) that cyclic loading has a significant effect on the bending strength of those made of slender tubes, whereas it has little effect on those made of compact and non-compact tubes, as shown in Figure 6.5. The symbols in Figure 6.5 are defined as follows: d is the outer diameter of CHS, t is the wall thickness of CHS, Vy is the yield stress of CHS, Mu is the ultimate moment capacity of the CFST beam, MptH is the ultimate moment capacity of the unfilled CHS beam, Os is the section slenderness and Oy is the section slenderness limit. 168 Concrete-Filled Tubular Members and Connections 6.2.2 CFST Braces Zhao et al. (2002) studied the CFST braces subject to large deformation cyclic axial loading. Two loading schemes were used, namely the direct cyclic loading scheme and the incremental cyclic loading scheme. It was found that the reduction in strength due to cyclic loading depends on the number of cycles applied and the displacement at which the cyclic loading commences. One example is given in Figure 6.6 for the axial load versus axial displacement curves. The negative value shown in Figure 6.6 refers to compression. The reduction in strength is about 20% after 50 cycles when the displacement reached 10mm (see Figure 6.6(a)). For the incremental cyclic loading scheme shown in Figure 6.6(b), the cyclic load was applied (10 cycles) at five accumulative axial displacement increments. The corresponding strength reduction is 7.4%, 8.3%, 8.9%, 9.6% and 10.4%, respectively. 6.2.3 CFST Beam-Columns For an unfilled steel tubular beam, a reduction factor of 0.9 is assigned to the ultimate moment strength for the purpose of considering the effect of the cyclic loading. This value seems to be acceptable for a concrete-filled steel tubular beam. However, for CFST beam-columns, it may not be necessary to take into account the moment strength reduction due to the influence of the applied axial load (Han and Yang 2007). Research has been conducted (Han et al. 2003, Han and Yang 2005) on typical beam-columns shown in Figure 6.3. It was found that the interaction diagrams in various codes (e.g. Eurocode 4, DBJ13-51) developed for CFST beamcolumns subject to static loading can be adopted for CFST beam-columns subject to cyclic loading. 6.3 DUCTILITY As shown in Section 6.2 the cyclic loading has certain effects on the strength of CFST beams, braces and beam-columns. This section focuses on the effect of cyclic loading on ductility of CFST members. 6.3.1 Ductility Ratio (P P) Ductility is a key issue for the seismic design of concrete-filled steel tubular structures. For the convenience of design and analysis, the ductility ratio is used to quantify the ductility of concrete-filled steel tubular columns subjected to constant axial load and cyclic flexural loading. The ductility ratio (P) adopted in this chapter Seismic Performance of CFST Members 169 is defined by Han (2007), Han et al. (2003) and Han and Yang (2005). It is expressed as: 'u (6.1) P 'y where 'y is the yielding displacement and 'u is the displacement when the axial load falls to 85% of the ultimate strength (Py), as shown in the typical envelope curve of the cyclic lateral load (P) versus lateral deflection (') in Figure 6.1(a). Axial(kN) Load (kN) Axial Load -350 50 cycles -250 -150 -50 50 150 0 -2 -4 -6 -8 -10 -12 Displacement (mm) AxialAxial Deformation (mm) Axial Load (kN) Axial Load (kN) (a) Direct cyclic loading scheme -350 10 cycles each -250 -150 -50 50 150 0 -2 -4 -6 -8 -10 -12 Axial Displacement (mm) Axial Deformation (mm) (b) Incremental cyclic loading scheme Figure 6.6 CFST brace member subject to large deformation cyclic loading (adapted from Zhao et al. 2002) 170 Concrete-Filled Tubular Members and Connections It should be pointed out that a slightly different percentage on the unloading curve was adopted by other researchers (e.g. 95% in Susantha et al. 2008, 90% in Varma et al. 2002) in defining the ductility ratio. Different percentages adopted in the definition will affect the absolute values of P. However, the trend presented later in Figure 6.7 remains the same. Slightly different definitions of ductility ratio were adopted by other researchers, e.g. Zhao et al. (2002) where a ductility index (DI) was used. DI is defined as ('F – 'R)/'R, where 'R is a midspan lateral deflection on the rising load deflection curve when reaching to 90% of the ultimate load and 'F is a midspan lateral deflection on the falling load-deflection curve at 90% of the ultimate load level. The absolute value of the ductility index (DI) will be different compared with that of the ductility ratio (P). However, the larger the DI is, the larger the P is, and vice versa. 6.3.2 Parameters Affecting the Ductility Ratio (P P) It was found that the ductility ratio (P) depends on the axial load level (n), the member slenderness (O) defined in Eq. (4.32), the steel ratio (D) defined as the ratio of the steel cross-sectional area to that of concrete, and the strength of concrete (Han et al. 2003, Han and Yang 2005). The axial load level (n) is defined as No n (6.2) Nu where No is the axial load applied on the composite column and Nu is the axial compressive capacity of the composite section. Figure 6.7 shows typical examples of the ductility ratio (P) that is plotted against the axial load level (n) when other parameters, such as member slenderness (O), steel ratio (D) and the concrete cubic strength (fcu), vary. It can be seen from Figure 6.7 that the ductility ratio (P) decreases when the axial load level (n), the member slenderness (O) and the strength of concrete (fcu) increases. The ductility ratio (P) increases as the steel ratio (D) increases. It should be pointed out that the ductility of CFST columns decreases with the increase of concrete strength. More discussions on high strength concrete-filled tubes can be found in Lahlou el at. (1999), Varma et al. (2002), Elremaily and Azizinamini (2002), Nishyama et al. (2002), and Hardika and Gardner (2004). 6.3.3 Some Measures to Ensure Sufficient Ductility For the seismic design of concrete-filled steel tubular members, different researchers and different codes may choose to limit the value of some key parameters to ensure the desired member ductility. These parameters include axial load level, member slenderness, diameter or width-to-wall thickness ratio and constraining factor. Seismic Performance of CFST Members 171 60 D = 0.10 fsy= 345MPa, fcu= 60MPa 45 O= 30 40 P 30 60 80 15 0 100 0 0.2 0.4 n 0.6 0.8 (a) Member slenderness (O) 60 O= 40 fsy= 345MPa, fcu= 60MPa 45 P 30 D = 0.15 0.10 15 0 0.05 0 0.2 0.4 n 0.6 0.8 0.6 0.8 (b) Steel ratio (D) 60 D = 0.10, O= 40 fsy = 345MPa 45 f cu = 40MPa P 30 50MPa 60MPa 15 0 0 0.2 0.4 n (c) Concrete strength (fcu) Figure 6.7 Influence of different parameters on the ductility ratio Concrete-Filled Tubular Members and Connections 172 The axial load level (n) is a key parameter which was taken into account in all experimental work listed in Tables 6.1 and 6.2, ranging from 0 to 0.82. It was found that the ductility of CFST beam-columns decreases with the increasing of axial load level (see Figure 6.7). AIJ (1997) gives the following limiting value of axial compressive load level (n) in the composite columns under seismic horizontal loading. nd 1 2 § As f y · ¸ ¨ 3 3 ¨© A c f c ¸¹ § As f y · ¸ 1 ¨¨ ¸ A f c c ¹ © (6.3) where As and Ac are the area of steel tube and concrete, respectively, fs and fc are steel yield stress and concrete cylinder strength, respectively. Zhong et al. (2002) suggested that a limiting value on the member slenderness (O) rather than on the axial load level (n) be used for CFST columns under seismic loading to ensure a sufficient ductility ratio. The limiting value of O is about 33 to 44. Diameter or width-to-thickness ratio is often used to determine the section classification category (compact, non-compact or slender) by comparing the actual ratio with the limiting values. Plastic design (compact section) requires that plastic hinges be able to rotate for certain amounts. The required rotation capacity is three or four for plastic design subject to static loading (Eurocode 3 Editorial Group 1989, Hasan and Hancock 1988 and Zhao and Hancock 1991), whereas the required rotation capacity is about seven to nine for seismic loading (AISC LRFD 1999, Commentary to Clause B.5). It is well known that, in general, concretefilling increases the limiting diameter or width-to-thickness ratio, whereas the large-deformation cyclic loading decreases the limiting ratio (Bergmann et al. 1995). A simple rule was given in Zhao et al. (2005) that the limiting diameter or width-to-thickness ratios may increase or reduce by approximately 50% due to the combined effect of concrete-filling and large deformation cyclic loading depending on the ductility requirement and cyclic loading schemes. If the ductility requirement is low and the loading scheme is not severe, the limiting width-tothickness ratios are mainly influenced by the concrete-filling, i.e. they may increase up to 50%. If the ductility requirement is high and the loading scheme is severe, the limiting width-to-thickness ratios are mainly influenced by the cyclic loading, i.e. they may reduce up to 50%. The effect of diameter or width-tothickness ratio on the seismic behaviour of CFST columns was studied by many researchers (as listed in Tables 6.1 and 6.2) with the ratio ranging from 20 to 90. There is more increase in ductility and energy dissipation for slender members. However, when the diameter or width-to-thickness ratio is too large, the ductility and energy dissipation may not be sufficient due to more severe local buckling of steel tube and less confinement effect to concrete. CFST members have high ductility, and energy dissipation capacity due to the outer steel tube can provide effective confinement to core concrete. The Seismic Performance of CFST Members 173 confinement can delay the cracks in the core concrete, and thus lead to an increased ductility. A high level of confinement is very important to the seismic behaviour of the CFST columns. The confinement is represented to some extent by a constraining factor ([) defined in Eq. (3.32). It is specified in DBJ13-51 (2003) that the constraining factor ([) should not be lower than 0.6 for circular CFST columns and 1.0 for rectangular CFST columns when used in a seismic region. 6.4 PARAMETERS AFFECTING HYSTERETIC BEHAVIOUR 6.4.1 Moment (M) versus Curvature (I I) Responses The important parameters that influence the moment (M) versus curvature (I) responses of CFST components include: axial load level (n), steel ratio (D), strength of steel (fsy) and concrete (fcu), and depth-to-width ratio (E) for RHS defined in Eq. (6.4). D E (6.4) B where D and B are the depth and width for rectangular sections. CFST members with rectangular sections are used here to illustrate the effects of the above parameters. Figure 6.8 shows typical theoretical examples of the composite beam columns bending about the major (x–x) axis. More details can be found in Han and Yang (2005). It is worth noting that the moment (M) versus curvature (I) responses shown in Figure 6.8 are expressed in terms of envelop curves, which can be obtained by connecting the peak point of each cycle on the hysteretic curves, as shown in Figure 6.1 (b). It can be found from Figure 6.8 that, in general, the stiffness of the moment (M) versus curvature (I) curves in the elastic stage increases as the steel ratio (D) and the depth-to-width ratio (E) increase. However, the axial load level (n), the steel yield stress (fsy) and the concrete strength (fcu) have moderate influence on the stiffness in the elastic stage. Figure 6.8(a) indicates that the ultimate moment increases with the axial load level (n) when n is less than 0.3 or so; however, the ultimate moment decreases with the axial load level (n) when n is greater than 0.3. The yielding moment increases with the increase of either the steel ratio (D), the steel yield stress (fsy), the concrete strength (fcu) or the depth-to-width ratio (E). If different values of the parameters were used, the absolute values of the curves would be different. However, the trend presented in Figure 6.8 would still be valid. Concrete-Filled Tubular Members and Connections 174 3000 0.1 M (kN.m) 2400 n=0 0.3 0.2 0.4 1800 0.5 1200 0.6 600 0 0.7 0.9 0 0.01 0.8 0.02 0.03 I (1/m) 0.04 0.05 (a) Axial load level n (D × B = 600 × 400mm, L = 4000mm, fsy = 345MPa, D = 0.1, fcu = 60MPa) 3000 D = 0.15 2400 M (kN.m) 0.10 1800 0.05 1200 600 0 0 0.01 0.02 0.03 I (1/m) 0.04 0.05 (b) Steel ratio D (D × B = 600 × 400mm, L = 4000mm, n = 0.4, fsy = 345MPa, fcu = 60MPa) 3000 f sy = 390MPa M (kN.m) 2400 f sy = 345MPa 1800 f sy = 235MPa 1200 600 0 0 0.01 0.02 0.03 I (1/m) 0.04 0.05 (c) Steel strength fsy (D × B = 600 × 400mm, L = 4000mm, n = 0.4, fcu = 60MPa, D = 0.1) Seismic Performance of CFST Members 175 3000 M (kN.m) 2400 f cu = 60MPa 1800 f cu = 50MPa f cu = 40MPa 1200 600 0 0 0.01 0.02 0.03 I (1/m) 0.04 0.05 (d) Concrete strength f cu (D × B = 600 × 400mm, L = 4000mm, n = 0.4, fsy = 345MPa, D = 0.1) 3000 E = 1.75 M (kN.m) 2400 1.5 1800 1.25 1200 1.0 600 0 0 0.01 0.02 0.03 I (1/m) 0.04 0.05 (e) Depth-to-width ratio E (B = 400mm, L = 4000mm, n = 0.4, fsy = 345MPa, fcu = 60MPa, D = 0.1) Figure 6.8 Influence of different parameters on moment (M) versus curvature (I ) envelope curves (adapted from Han and Yang 2005) 6.4.2 Lateral Load (P) versus Lateral Deflection (' ') Responses Theoretical models were developed by Han et al. (2003) for the influence of the axial load level (n), steel ratio (D), steel yield stress (fsy), concrete strength (fcu), member slenderness (O) and depth-to-width ratio (E) on the lateral load (P) versus lateral deflection (' defined in Figure 6.3) response in terms of the envelope curve. Figure 6.9 shows typical examples of the composite beam-columns buckling about the major (x–x) axis. Concrete-Filled Tubular Members and Connections 176 1500 P (kN) 1200 0.1 n=0 0.2 900 0.3 0.4 600 0.5 300 0 0.8 0.6 0.7 0.9 0 20 40 60 ' (mm) 80 100 (a) Axial load level (n) (D × B = 600 × 400mm, L = 4000mm, fsy = 345MPa, fcu = 60MPa, D = 0.1) 1500 D = 0.15 P (kN) 1200 0.10 900 0.05 600 300 0 0 20 40 60 ' (mm) 80 100 (b) Steel ratio (D) (D × B = 600 × 400mm, L = 4000mm, n = 0.4, fsy = 345MPa, fcu = 60MPa) 1500 P (kN) 1200 f sy = 390MPa f sy = 345MPa 900 f sy = 235MPa 600 300 0 0 20 40 60 ' (mm) 80 100 (c) Steel strength (f sy) (D × B = 600 × 400mm, L = 4000mmҏ, n = 0.4, fcu = 60MPa, D = 0.1) Seismic Performance of CFST Members 177 1500 P (kN) 1200 f cu= 60MPa f cu= 50MPa 900 f cu= 40MPa 600 300 0 0 20 40 60 ' (mm) 80 100 (d) Concrete strength (fcu) (D × B = 600 × 400mm, L = 4000mm, n = 0.4, fsy = 345MPa, D = 0.1) 1500 O = 20 P (kN) 1200 900 30 600 40 60 300 0 80 100 0 20 40 60 ' (mm) 80 100 (e) slenderness ratio (O) (D × B = 600 × 400mm, n = 0.4, fsy = 345MPa, fcu = 60MPa, D = 0.1) 1500 E = 1.75 P (kN) 1200 E = 1.5 900 E = 1.25 600 E = 1.0 300 0 0 20 40 60 ' (mm) 80 100 (f) depth-to-width ratio (E) (D × B = 600 × 400mm, L = 4000mm, n = 0.4, fsy = 345MPa, fcu = 60MPa, D = 0.1) Figure 6.9 Influence of different parameters on lateral load (P) versus lateral deflection (') envelope curves (adapted from Han and Yang 2005) 178 Concrete-Filled Tubular Members and Connections It can be found from Figure 6.9 that, in general, the stiffness of the curves in the elastic range increases as the steel ratio (D) and the depth-to-width ratio (E) increase, or the member slenderness (O) decreases. However, other parameters, such as the axial load level (n), the steel yield stress (fsy) and concrete strength (fcu) have moderate influence on the stiffness in the elastic stage. This is consistent with the observation for moment versus curvature response described in Section 6.4.1. Figure 6.9(a) indicates that the ultimate lateral load increases with the axial load level (n) when n is less than 0.3 or so; however, the ultimate lateral load decreases with the axial load level (n) when n is greater than 0.3. The ultimate lateral load increases with the increase of the steel ratio (D), the steel yield stress (fsy) and concrete strength (fcu) and the depth-to-width ratio (E). This is again consistent with the observation for moment versus curvature response. 6.5 SIMPLIFIED HYSTERETIC MODELS Detailed analysis was conducted by Han et al. 2003 and Han and Yang 2005 on moment versus curvature and load versus deflection hysteretic models. The theoretical predictions showed good agreement with test results (within 12% difference). Simplified models were proposed for cyclic load response and ductility ratio based on parametric studies that included the key parameters: axial load level, member slenderness, steel ratio and strength of materials. 6.5.1 Simplified Model of the Moment–Curvature Hysteretic Relationship Figure 6.10 gives a schematic view of the moment (M) versus curvature (I) relationship, for both circular and rectangular CFSTs, respectively. 6.5.1.1 Circular CFST member The parameters (Ke, My, Ms, Iy and Kp) that define the curve in Figure 6.10(a) are given as follows: (1) The stiffness in the elastic stage (Ke) for circular CFST is given by Ke Es Is 0.6Ec Ic 6.5) in which Es and Ec are modulus of elasticity for steel and concrete, Is and Ic are moments of inertia for the hollow steel cross-section and the core concrete crosssection, respectively. (2) Yielding moment (My) The yielding moment (My) can be calculated by f A 1 cu B1 60 My M yu ( A 1 B1 ) ( p n q ) (6.6) Seismic Performance of CFST Members 179 M My D Ms 5' B 3 4 1 C Kp A 2' Ke Iy O 2 I 5 A' 3' 1' C' 4' D' B' (a) Circular CFST member M A My 1 MB 0.2 My 4' B 3 IB -0.2 My I C 2' Ke O 2 C' 3' B' 1' 4 A' (b) Rectangular CFST member Figure 6.10 A schematic view of moment (M) versus curvature ( I) relationship (adapted from Han et al. 2003) where A1 0.137 ® ¯0.118 b 0.255 (b d 1) B1 ° 0.468 b 2 0.8 b 0.874 ® °̄1.306 0.1 b p 0.566 0.789 b ® ¯ 0.11 b 0.113 (b ! 1) ( b d 1) ( b ! 1) (b d 1) (b ! 1) Concrete-Filled Tubular Members and Connections 180 q 1.195 0.34 b ® ¯1.025 ( b d 0.5) ( b ! 0.5) b =D /0.1 and the unit for fcu is MPa. in which Myu is the ultimate moment of the composite beam-columns under constant axial load level (n), and can be determined by using the axial load versus the bending moment interaction curve given in Chapter 5. (3) Bending moment (Ms) corresponding to point A Ms (6.7) 0.6M y (4) Curvature corresponding to yielding moment §f · 0.0135 ¨ cu 1¸ (1.51 n ) © 60 ¹ Iy (6.8) (5) Stiffness (Kp) Kp (6.9) D do K e where Ddo = Dd /1000, Dd can be determined as: If [ ! 1.1 , Dd 2.2 [ 7.9 ® ¯ (7.7 [ 11.9) n 0.88 [ 3.14 ( n d 0.4) ( n ! 0. 4) (6.10a) If [ d 1.1 , Dd A n B ® ¯C n D (n d n o ) (n ! n o ) in which, no §f · (0.245 [ 0.203) ¨ cu ¸ © 60 ¹ 0.513 f A 12.8 cu (ln [ 1) 5.4 ln [ 11.5 60 B f cu (0.6 1.1 ln [) 0.7 ln [ 10.3 60 (6.10b) Seismic Performance of CFST Members C 181 f (68.5 ln [ 32.6) ln cu 46.8 [ 67.3 60 f D 7.8 [ 0.8078 ln cu 10.2 [ 20 60 6.5.1.2 Rectangular CFST member The parameters (Ke, My, MB and IB) that defined the curve in Figure 6.10(b) are given below. (1) The stiffness in the elastic stage (Ke) for rectangular CFST is given by K e E s I s 0.2E c I c (6.11) in which Es and Ec are the moduli of elasticity for steel and concrete, Is and Ic are moments of inertia for the hollow steel cross-section and the core concrete crosssection, respectively. (2) Yielding moment (My) corresponding to point A The yielding moment (My) corresponding to point A in Figure 6.10(b) can be calculated by: (6.12) M y M yu where Myu is the ultimate moment of the composite beam-columns under constant axial load level (n), and can be determined by using the axial load versus bending moment interaction curve shown in Chapter 5. (3) Bending moment (MB) and curvature (IB) corresponding to point B Simplified models are established based on regression analysis, i.e. MB M y (1 n ) k o (6.13) IB 20 I e (2 n ) (6.14) where ko Ie [ 2.5 0.544 f y /( E s D) (about the major axis) or Ie 0.544 f y /( E s B) (about the minor axis). The simplified model shown in Figure 6.10 is suitable for predicting the moment–curvature hysteretic responses of the composite beam-columns about both major (x–x) axis and minor (y–y) axis. The range of validity for the simplified model is given as follows: n = 0 to 0.8, D = 0.04 to 0.2, fsy = 200 to 500MPa, fcu = 30 to 80MPa and E = 1 to 2. Concrete-Filled Tubular Members and Connections 182 6.5.2 Simplified Model of the Load–Deflection Hysteretic Relationship A schematic view of the P–' hysteretic relationship is shown in Figure 6.11. The parameters (Ka, PA, Py, 'p and Kd) that define the curve are given as follows: P B Py P1 P4 3 4 1 A Kd 2' 5' C Ka O 2 'p 5 ' A' C' 4' B' 1' 3' Figure 6.11 A schematic view of lateral load (P) versus lateral deflection (') relationship (adapted from Han et al. 2003) (1) Stiffness in the elastic stage (Ka), is given by Ka 24K e L3 (6.15) where L is the column length, Ke is given by Eq. (6.5) for CFST CHS and Eq. (6.11) for CFST RHS. (2) Strength (PA) corresponding to point A PA 0.6Py (6.16) (3) Ultimate strength (Py) and corresponding displacement ('p) For circular CFST: Py 2.1 a M y / L (1 [ d 4) ® a ( 0 . 4 1 . 7 ) M / L [ (0.2 d [ d 1) y ¯ (6.17a) Seismic Performance of CFST Members 183 where 0.96 0.002 [ ® ¯(1.4 0.34 [) n 0.1 [ 0.54 and My can be determined using Eq. (6.6). (0 d n d 0.3) (0.3 n 1) a For rectangular CFST: °(2.5n 2 0.75n 1) M y / L Py ® °̄(0.63n 0.848) M y / L for 0 d n d 0 .4 for 0 .4 n 1 (6.17b) where My can be determined using Eq. (6.12). For circular CFST: ª§ O · 2 º O 3.33» f1 ( n ) 6.74 «¨ ln ¸ 1.08 ln 40 «¬© 40 ¹ »¼ Py 'p (8.7 f sy /345) Ka (6.18a) where the unit for fsy is MPa, O is given in Eq. (4.32). °1.336 n 2 0.044 n 0.804 (0 d n d 0.5) f1 (n ) ® °̄1.126 0.02 n (0.5 n 1) For rectangular CFST: (1.7 n 0.5[) Py 'p Ka (6.18b) (4) Stiffness of the descending stage (Kd) is given by For circular CFST: Kd where 0.03 f 2 (n ) f (f sy , D) °§ f · 2 ½° f cu ¸ 3.39 cu 5.41¾ ®¨ 60 °̄© 60 ¹ °¿ f 2 (n ) 3.043 n 0.21 ® ¯ 0.5 n 1.57 f (f sy , D) ( 0 d n d 0. 7 ) (0.7 n 1) (8 D 8.6) (f sy / 345) 6 D 0.9 ® ¯(15 D 13.8) (f sy / 345) 6.1 D For rectangular CFST: (6.19a) Ka (f sy d 345 MPa ) (f sy ! 345 MPa ) Concrete-Filled Tubular Members and Connections 184 Kd 9.83 n1.2 O0.75 f sy Es [ Ka (6.19b) where O is given in Eq. (4.32). The lateral loads at point 2 and point 2ƍ (shown in Figure 6.11) are taken as –0.2P1 and 0.2P1, respectively. The lateral loads at point 5 and point 5ƍ (see Figure 6.11) are taken as –0.2P4 and 0.2P4, respectively. The simplified model shown in Figure 6.11 is suitable for predicting the P–' hysteretic responses of the composite beam-columns for both major axis (x–x) and minor (y–y) axis bending. The validity range for this simplified model is given as follows: n = 0 to 0.8, D = 0.04 to 0.2, O = 10 to 100, fsy = 200 to 500MPa, fcu = 20 to 80MPa and E = 1 to 2. 6.5.3 Simplified Model of the Ductility Ratio (P) For the convenience of analysis, the ductility ratio (P) is used to quantify the ductility of concrete-filled tubular columns subjected to constant axial load and cyclic flexural loading. It is defined in Eq. (6.1) where 'y is the yielding displacement and 'u is the displacement when the axial load falls to 85% of the ultimate strength (Py), as shown in Figure 6.12. P B Py 0.85P y A Kd C Ka O 'y 'p 'u ' Figure 6.12 Envelope of cyclic lateral load (P) versus lateral deflection (') response The displacements of 'y and 'u can be calculated by Eqs. 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Mao, X.Y. and Xiao, Y., 2006, Seismic behaviour of confined square CFT columns. Engineering Structures, 28(10), pp. 1378-1386. 41. Morishita, Y. and Tomii, M., 1982, Experimental studies on bond strength between square steel tube and encased concrete core under cyclic shearing force and constant axial force. Transactions of Japan Concrete Institute, 4, pp. 363-370. 42. Nishiyama, I., Morino, S., Sakino, K., Nakahara, H., Fujimoto, T., Mukai, A., Inai, E., Kai, M., Tokinoya, H., Fukumoto, T., Mori, K., Yoshika, K., Mori, O., Yonezawa, K., Mizuaki, U. and Hayashi, Y., 2002, Summary of research on concrete-filled structural steel tube column system carried out under the US–Japan cooperative research program on composite and hybrid structures, BRI Research Paper No.147 (Tokyo: Building Research Institute). 43. Prion, H.G.L. and Boehme, J., 1994, Beam-column behaviour of steel tubes filled with high strength concrete. Canadian Journal of Civil Engineering, 21(2), pp. 207-218. 44. Sakino, K. and Tomii, M., 1981, Hysteretic behavior of concrete filled square steel tubular beam-columns failed in flexure. Transactions of the Japan Concrete Institute, 3, pp. 439-446. 45. Shiiba, K. and Harada, N., 1994, An experiment study on concrete-filled square steel tubular columns. Proceedings of the 4th International Conference 188 Concrete-Filled Tubular Members and Connections on Steel–Concrete Composite Structures, Slovakia, pp. 103-106. 46. Susantha, K.A.S., Aoki, T. and Hattori, M., 2008, Seismic performance improvement of circular steel columns using pre-compressed concrete-filled steel tube. Journal of Constructional Steel Research, 64(1), pp. 30–36. 47. Susantha, K.A.S., Ge, H.B. and Usami, T., 2001, Uniaxial stress–strain relationship of concrete confined by various shaped steel tubes. Engineering Structures, 23(10), pp. 1331-1347. 48. Tao, Z., 2001, Several key issues for the behaviour of concrete filled square steel tubular members. PhD Thesis, Harbin Institute of Technology, Harbin, P.R. China. 49. Tao, Z. and Yu, Q., 2006, New types of composite columns–experiments, theory and methodology (Beijing: China Science Press). 50. Thayalan, P., Aly, T. and Patnaikuni, I., 2009, Behaviour of concrete-filled steel tubes under static and variable repeated loading. Journal of Constructional Steel Research, 65(4), pp. 900-908. 51. Tu, Y.Q., 1994, Research on hysteretic characters of concrete filled steel tubular beam-columns. PhD Thesis, Harbin Institute of Technology, Harbin, P.R. China. 52. Usami, T. and Ge, H.B., 1998, Cyclic behaviour of thin-walled steel structures – Numerical analysis. Thin-Walled Structures, 32(1-3), pp. 41-80. 53. Varma, A.H., Ricles, J.M., Sause, R. and Lu, L.W., 2002, Seismic behavior and modeling of high-strength composite concrete-filled steel tube (CFT) beam-columns. Journal of Constructional Steel Research, 58(5-8), pp. 725758. 54. Xiao, Y., He, W. and Choi, K., 2005, Confined concrete-filled tubular columns. Journal of Structural Engineering, ASCE, 131(3), pp. 488-497. 55. Yogishita, F., Kitoh, H., Sugimoto, M., Tanihira, T. and Sonoda, K., 2000, Double-skin composite tubular columns subjected cyclic horizontal force and constant axial force. Proceedings of 6th ASCCS International Conference on Steel–Concrete Composite Structures, Los Angeles, USA, pp. 497-503. 56. Zhao, X.L. and Grzebieta, R., 1999, Void-filled SHS beams subjected to large deformation cyclic bending. Journal of Structural Engineering, ASCE, 125(9), pp. 1020-1027. 57. Zhao, X.L., Grzebieta, R.H. and Lee, C., 2002, Void-filled cold-formed rectangular hollow section braces subjected to large deformation cyclic axial loading, Journal of Structural Engineering, ASCE, 128(6), pp. 746-753. 58. Zhao, X.L. and Hancock, G.J., 1991, Tests to determine plate slenderness limits for cold-formed rectangular hollow sections of grade C450. Steel Construction, Australian Institute of Steel Construction, 25(4), pp. 2-16. 59. Zhao, X.L., Wilkinson, T. and Hancock, G.J., 2005, Cold-formed tubular members and connections (Oxford: Elsevier). 60. Zhong, S.T., 1994, The concrete-filled steel tubular structures (Harbin: Heilongjiang Science and Technology Press). 61. Zhong, S.T., Zhang, W.F. and Tu, Y.Q., 2002, The research of seismic behaviours for concrete-filled steel tubular (CFST) structures. Progress in Steel Building Structures, 4(2), pp. 3-15. CHAPTER SEVEN Fire Resistance of CFST Members 7.1 GENERAL An important criterion for the design of CFST structures, besides the serviceability and load-bearing capacity, is fire resistance. The required fire resistance depends on the type of building (e.g. less than three storeys or high rise), which varies from less than 30 minutes to three hours. The fire resistance of unprotected rectangular hollow section (RHS) or circular hollow section (CHS) columns is normally found to be less than 30 minutes. There are several methods to increase the fire resistance of tubular columns, such as applying external insulation, concrete-filling and water-filling (Twilt et al. 1995). The increase in fire resistance due to concretefilling is demonstrated in Figure 1.10(e). The concrete and steel tube help each other under fire conditions. The temperature in the steel tube of a CFST column increases much slower when compared with that in a bare steel tube because part of the heat is absorbed by the core concrete. The steel tube provides confinement to the concrete and prevents spalling of concrete at elevated temperatures. A typical behaviour of CFST columns under fire is shown in Figure 7.1, where the axial load is maintained at a constant level. Three stages (I, II and III) can be identified during fire exposure. In stage I the steel carries most of the load because the steel section expands more rapidly than the concrete core. The column experiences tensile deformation at this stage. In stage II the steel section gradually yields as its strength decreases at elevated temperatures. The core concrete starts to carry more of the load and the column experiences compressive deformation. In stage III the strength of steel and concrete significantly decreases with time leading to the failure of the column through local compression or overall buckling (see Figure 7.2). The fire resistance is defined as the total fire exposure time of the three stages. Axial deformation A 0 B C I II III Time Figure 7.1 Typical behaviour of CFST columns under fire (schematic view) Concrete-Filled Tubular Members and Connections 190 (i) Local compression (ii) Overall buckling (a) CFST circular columns (Han et al. 2003a) (i) Local compression (ii) Overall buckling (b) CFST square columns (Han et al. 2003b) (c) Concrete core (Lu et al. 2009) Figure 7.2 Typical failure modes of CFST columns Fire Resistance of CFST Members 191 A large amount of experimental work has been conducted by many researchers on fire resistance of CFST columns, as summarised in Table 7.1. They covered a wide range of parameters such as the outside diameter or width of steel tubes (from 140mm to 478mm), fire load ratio or degree of utilization (defined as the ratio of applied load in fire to load-carrying capacity at ambient temperature, ranging from 0.1 to 0.8), type of concrete (plain, bar-reinforced, fibre-reinforced and self-consolidating concrete) and fire resistance (FR) ranging from 7 to 294 minutes. Different kinds of theoretical analysis of fire performance of CFST columns were also reported in the literature, e.g. equivalent time approach (Wang 1997), reduced squash load and rigidity approach (Wang 2000), interaction model (Tan and Tang 2004), residual strength index approach (Han and Huo 2003, Han et al. 2005), Green’s function method for temperature analysis (Wang and Tan 2007), realistic modelling considering the air gap and slip at the steel/concrete interface, concrete tensile behaviour and column initial imperfections (Ding and Wang 2008), and non-linear finite element analysis (Zha 2003, Yin et al. 2006, Chung et al. 2008, Hong and Varma 2009). In addition to CFST columns, research on CFST connections and frames were carried out by many researchers such as Wang (1999), Wang and Davies (2003), Ding and Wang (2007), Han et al. (2007), and Jones and Wang (2010). This chapter focuses on the design of CFST columns in terms of standard fire resistance. Post-fire performance of CFST columns and repairing after exposure to fire are also discussed. Real fire exposure, connections and frames under fire, and fire-induced structural collapse are not covered in this chapter. More research is needed to fully address these aspects. 7.2 PARAMETERS AFFECTING FIRE RESISTANCE The following factors influence the fire resistance of CFST columns. x Fire load ratio or degree of utilisation, defined as the ratio of axial force in the fire situation to the design resistance at ambient temperature x Column size x Effective buckling length x External protection which improves fire resistance x Reinforcement of concrete using steel bars or fibres x Material strength x Bending moments and eccentricity Different codes have different ways to consider the above parameters in design, as will be described later in Section 7.3.5. The most important parameters that influence the fire resistance of a concrete-filled steel tubular column are degree of utilisation, the column size, the member slenderness and fire protection. Concrete-Filled Tubular Members and Connections 192 Table 7.1 Experimental studies on fire resistance of CFST columns d or D (mm) t (mm) Length (m) Fire load ratio Type of concrete CHS steel bar reinforced concrete External protection FR (min) Number of specimens References No 96–188 2 Chabot and Lie (1992) No 33–294 38 Lie and Chabot (1992) No 65–227 6 Kodur and Lie (1995) No 71–134 3 Yes 7–196 13 No 43–259 6 Kodur and Latour (2005) No 39–212 6 Chabot and Lie (1992) 273 6.35 3.81 0.37–0.67 141–406 4.8– 12.7 3.81 0.09–0.47 324–406 6.35 3.81 0.32–0.67 219 3.6 3.60 0.20–0.60 150–478 4.6–8 3.81 0.77 219–406 6.35 3.81 0.24–0.52 203–305 6.35 3.81 0.22–0.82 152–305 6.35 3.81 0.2–0.34 plain concrete No 63–131 6 300 9.0 3.5 0.2–0.33 plain concrete Yes 16–194 18 160–300 3.6– 7.0 3.6 0.27–0.60 No 48–192 3 219–350 5.3– 7.7 3.81 0.77 Yes 109– 169 3 300–350 9 3.5 0.34–0.47 No 28–160 7 203 6.35 3.81 0.32–0.43 No 89–128 2 150–200 5.0– 6.0 0.76 0.17–0.44 No 26–90 6 300 7.96 3.81 0.77 Yes 16–146 8 plain concrete steel fibre reinforced concrete steel bar reinforced concrete plain concrete plain, fibre or bar reinforced concrete SHS steel bar reinforced concrete steel bar reinforced concrete plain concrete plain concrete fibre or bar reinforced concrete high strength SCC RHS plain concrete Lie and Kodur (1996) Han et al. (2003a) Lie and Chabot (1992) Sakumoto et al. (1994) Lie and Kodur (1996) Han et al. (2003b) Kim et al. (2005) Kodur and Latour (2005) Lu et al. (2009) Han et al. (2003b) Fire Resistance of CFST Members 193 7.3 FIRE RESISTANCE DESIGN 7.3.1 Chinese Code DBJ13-51 The preferred solution in China to achieve sufficient fire resistance is to use plain concrete-filled tubes with external fire protection rather than using steel bar or fibre-reinforced concrete. The formulae in DBJ13-51 to calculate the thickness (a) of fire protection materials are based on the research by Han et al. (2003a, 2003b) where the fire load ratio (n) of 0.77 was used. The formulae in DBJ13-51 also consider the cases for other fire load ratios by introducing a modification factor (kLR). For CFST circular columns a k LR (19.2R 9.6) C (0.28 0.0019O ) t 7mm For CFST rectangular columns 5 (7.1) 2 a k LR (149.6R 22) C ( 0.42 0.0017 O 2u10 O ) t 7 mm k LR ( n k t ) / 0.77 k t ) for k t d n 0.77 k LR 1 /(3.695 3.5 n ) for n t 0.77 and k t 0.77 k LR Z (n k t ) /(1 k t ) for n t 0.77 and k t t 0.77 (7.2) (7.3a) (7.3b) (7.3c) where R is the fire resistance in hours, C is the perimeter of the column in mm, Ȝ is the member slenderness defined in Eq. (4.32), Z = 7.2R for CFST circular column and Z = 10R for CFST rectangular column. The strength factor under fire (kt) depends on the value of Ȝ, C and R, as given in Table 7.2 for CFST circular columns and in Table 7.3 for CFST rectangular columns. The validity range of parameters is given as follows: d = 200 to 2000mm, B = 200 to 2000mm, O = 10 to 80, R d 3 hours, fy = 235 to 420MPa, fck = 20 to 60MPa. The fire protection material has the following parameters: the thermal conductivity of 0.116W/m·K, the specific heat of 1.047 × 103J/kg·K and the density of 400 ± 20kg/m3 as specified in CECS24 (1990). 7.3.2 CIDECT Design Guide No. 4 Three levels of assessment on fire resistance of unprotected CFST columns were presented in CIDECT Design Guide No. 4 (Twilt et al. 1995). Level 1 assessment utilises a simple design table to determine the minimum cross-sectional dimensions, reinforcement ratios and location of reinforcement bars to satisfy certain degree of utilisation (P) and fire resistance (R30 minutes to R180 minutes). This table is reproduced as Table 7.4 for the convenience of readers. The tube thickness should not exceed 1/25 of B or d. Concrete-Filled Tubular Members and Connections 194 Table 7.2 Strength factor under fire (kt) for CFST circular columns (adapted from DBJ13-51) O 20 40 60 80 C (mm) 628 785 942 1884 2826 3768 4710 628 785 942 1884 2826 3768 4710 628 785 942 1884 2826 3768 4710 628 785 942 1884 2826 3768 4710 0.25 0.96 0.92 0.90 0.91 0.92 0.93 0.95 0.85 0.85 0.85 0.87 0.89 0.90 0.92 0.78 0.78 0.79 0.81 0.83 0.85 0.88 0.71 0.71 0.72 0.74 0.77 0.80 0.83 0.5 0.59 0.60 0.61 0.64 0.67 0.71 0.75 0.44 0.46 0.47 0.52 0.57 0.61 0.66 0.29 0.31 0.33 0.39 0.43 0.47 0.52 0.27 0.29 0.31 0.39 0.43 0.46 0.47 0.75 0.43 0.45 0.46 0.51 0.55 0.58 0.61 0.28 0.30 0.32 0.39 0.43 0.46 0.47 0.23 0.26 0.28 0.36 0.42 0.44 0.46 0.21 0.23 0.26 0.36 0.42 0.45 0.47 1 0.36 0.38 0.40 0.47 0.50 0.52 0.53 0.24 0.26 0.28 0.37 0.42 0.45 0.46 0.18 0.20 0.23 0.34 0.40 0.44 0.45 0.14 0.17 0.20 0.33 0.40 0.44 0.46 1.25 0.36 0.38 0.38 0.45 0.50 0.52 0.53 0.20 0.22 0.25 0.35 0.41 0.45 0.46 0.12 0.15 0.18 0.31 0.39 0.43 0.45 0.07 0.11 0.15 0.30 0.39 0.44 0.46 1.5 0.32 0.34 0.36 0.44 0.49 0.52 0.53 0.15 0.18 0.21 0.33 0.40 0.44 0.46 0.06 0.10 0.14 0.29 0.38 0.43 0.44 0 0.05 0.09 0.27 0.37 0.43 0.45 R (hour) 1.75 0.29 0.32 0.34 0.43 0.49 0.52 0.53 0.11 0.15 0.18 0.31 0.39 0.44 0.45 0 0 0.09 0.26 0.36 0.42 0.44 0 0 0.04 0.24 0.36 0.42 0.45 2 0.27 0.29 0.32 0.42 0.48 0.51 0.53 0.07 0.11 0.14 0.29 0.38 0.43 0.45 0 0 0.04 0.24 0.35 0.41 0.44 0 0 0 0.21 0.34 0.41 0.44 2.25 0.24 0.27 0.30 0.41 0.48 0.51 0.52 0.03 0.07 0.11 0.27 0.37 0.43 0.45 0 0 0 0.21 0.34 0.41 0.43 0 0 0 0.18 0.33 0.41 0.44 2.5 0.22 0.25 0.28 0.40 0.47 0.51 0.52 0 0.03 0.07 0.25 0.36 0.42 0.44 0 0 0 0.18 0.33 0.40 0.43 0 0 0 0.15 0.31 0.40 0.43 2.75 0.19 0.23 0.26 0.39 0.46 0.50 0.52 0 0 0.03 0.23 0.35 0.42 0.44 0 0 0 0.16 0.31 0.39 0.42 0 0 0 0.12 0.30 0.39 0.43 3 0.17 0.20 0.24 0.38 0.46 0.50 0.52 0 0 0 0.21 0.34 0.41 0.44 0 0 0 0.13 0.30 0.39 0.42 0 0 0 0.09 0.28 0.38 0.42 Table 7.3 Strength factor under fire (kt) for CFST rectangular columns (adapted from DBJ13-51) O 20 40 60 80 C (mm) 800 1000 1200 2400 3600 4800 6000 800 1000 1200 2400 3600 4800 6000 800 1000 1200 2400 3600 4800 6000 800 1000 1200 2400 3600 4800 6000 0.25 0.74 0.75 0.75 0.78 0.81 0.84 0.87 0.74 0.75 0.75 0.78 0.81 0.84 0.87 0.76 0.76 0.77 0.79 0.82 0.85 0.88 0.78 0.78 0.78 0.81 0.83 0.86 0.89 0.5 0.42 0.43 0.43 0.47 0.51 0.56 0.62 0.42 0.43 0.43 0.47 0.51 0.56 0.62 0.44 0.44 0.45 0.49 0.53 0.58 0.64 0.39 0.40 0.40 0.42 0.45 0.49 0.53 0.75 0.29 0.29 0.30 0.32 0.35 0.39 0.45 0.27 0.27 0.28 0.30 0.32 0.36 0.40 0.23 0.23 0.23 0.24 0.26 0.28 0.31 0.18 0.19 0.17 0.18 0.20 0.21 0.22 1 0.22 0.22 0.23 0.24 0.26 0.29 0.33 0.18 0.19 0.19 0.22 0.24 0.26 0.26 0.15 0.15 0.16 0.19 0.21 0.22 0.22 0.12 0.12 0.13 0.16 0.17 0.18 0.18 1.25 0.19 0.19 0.20 0.23 0.26 0.27 0.27 0.16 0.17 0.17 0.21 0.23 0.24 0.24 0.13 0.13 0.14 0.17 0.19 0.19 0.19 0.09 0.10 0.10 0.13 0.15 0.15 0.15 1.5 0.18 0.19 0.19 0.23 0.25 0.27 0.27 0.15 0.16 0.16 0.19 0.22 0.23 0.23 0.10 0.11 0.11 0.14 0.17 0.17 0.17 0.06 0.07 0.07 0.10 0.12 0.12 0.12 R (hour) 1.75 0.18 0.19 0.19 0.22 0.25 0.27 0.27 0.14 0.14 0.15 0.18 0.20 0.21 0.21 0.08 0.09 0.19 0.12 0.14 0.15 0.15 0.03 0.04 0.04 0.07 0.09 0.09 0.09 2 0.18 0.18 0.19 0.22 0.25 0.26 0.27 0.12 0.13 0.13 0.16 0.19 0.20 0.20 0.06 0.06 0.07 0.10 0.12 0.13 0.13 0 0 0.01 0.04 0.06 0.06 0.06 2.25 0.18 0.18 0.19 0.22 0.25 0.26 0.26 0.11 0.11 0.12 0.15 0.17 0.19 0.19 0.04 0.04 0.05 0.08 0.10 0.10 0.11 0 0 0 0.01 0.03 0.03 0.03 2.5 0.17 0.18 0.18 0.22 0.24 0.26 0.26 0.09 0.10 0.11 0.14 0.16 0.17 0.17 0.01 0.02 0.02 0.05 0.08 0.08 0.08 0 0 0 0 0 0 0 2.75 0.17 0.18 0.18 0.21 0.24 0.26 0.26 0.08 0.09 0.09 0.12 0.15 0.16 0.16 0 0 0 0.03 0.05 0.06 0.06 0 0 0 0 0 0 0 3 0.17 0.17 0.18 0.21 0.24 0.25 0.26 0.07 0.07 0.08 0.11 0.13 0.15 0.15 0 0 0 0.01 0.03 0.04 0.05 0 0 0 0 0 0 0 Fire Resistance of CFST Members 195 Table 7.4 Minimum cross-sectional dimensions, reinforcement ratios and axis distances of the re-bars for fire resistance classification for various degrees of utilization ȝ (adapted from Twilt et al. 1995) Fire Resistance Class Reinforcing bars Concrete D R30 dr t B R90 R120 R180 260 6.0 50 400 6.0 60 450 6.0 50 500 6.0 60 - - dr dr t R60 d Minimum cross-sectional dimensions for ȝ = 0.3 Minimum width (B) or diameter (d) 160 200 220 Minimum % of reinforcement (pr) 0 1.5 3.0 Minimum depth of re-bar centre (dr) 30 40 Minimum cross-sectional dimensions for ȝ = 0.5 Minimum width (B) or diameter (d) 260 260 400 Minimum % of reinforcement (pr) 0 3.0 6.0 Minimum depth of re-bar centre (dr) 30 40 Minimum cross-sectional dimensions for ȝ = 0.7 Minimum width (B) or diameter (d) 260 450 500 Minimum % of reinforcement (pr) 3.0 6.0 6.0 Minimum depth of re-bar centre (dr) 25 30 40 Level 2 assessment utilises the concept of buckling curve for CFST columns at different fire classes. It recommends a buckling curve for given values of tube size, steel grade, fire class, concrete grade and the amount of reinforcement. The effective buckling length factor of columns in braced frames is between 0.5 and 0.7 depending on the boundary conditions (Twilt et al. 1995). A conservative value of 0.7 may be used for estimating the buckling length of columns on the top floor and for the columns at the edge of a building with only one adjacent beam. The lower value of 0.5 may be used for all the other columns. Design charts were given in Twilt et al. (1995). Typical examples are given in Figure 7.3 for CFST circular columns and in Figure 7.4 for CFST square columns. The validity range of level 2 assessment can be summarised as follows: fire classes are R60, R90 and R120, concrete grades C20, C30 and C40, CHS diameter d = 219 to 406mm and thickness t = 4.5 to 6.3mm, SHS width B = 180 to 400mm and thickness t = 6.3 to 10mm. Level 3 assessment or general calculation procedure includes a complete thermal and mechanical analysis with real boundary conditions. This is the most sophisticated level. It requires expert knowledge and time in handling necessary computer programs. Concrete-Filled Tubular Members and Connections 196 CHS244. 5 x 5.0 Fire class R90 9000 9 Axial Buckling Load (kN) 8000 6 8 3 5 7 7000 6000 2 4 5000 4000 1 Concrete pr% grade 3000 1 2 3 4 5 2000 1000 0 Steel grade Fe 360 Reinforcing bars S 400 C20 C20 C20 C30 C30 0 1.0 2.5 4.0 1.0 2.5 1 6 7 8 9 C30 C40 C40 C40 2 4.0 1.0 2.5 4.0 3 Buckling Length (m) 4 Figure 7.3 Typical example of design graph for unprotected CFST circular columns (adapted from Twilt et al. 1995) SHS 220 x 220 x 6.3 Steel grade Fe 360 Fire class R90 Reinforcing bars S 400 7000 9 8 6 7 5 3 4 2 Axial Buckling Load (kN) 6000 5000 4000 1 3000 Concrete pr% grade 2000 1 2 3 4 5 1000 0 0 C20 C20 C20 C30 C30 1.0 2.5 4.0 1.0 2.5 1 6 7 8 9 2 C30 C40 C40 C40 4.0 1.0 2.5 4.0 3 4 Buckling Length (m) Figure 7.4 Typical example of design graph for unprotected CFST square columns (adapted from Twilt et al. 1995) Fire Resistance of CFST Members 197 7.3.3 Eurocode 4 Part 1.2 In the main text of Eurocode 4 Part 1.2, three methods are introduced, i.e. the tabulated method, the simple calculation method and the general calculation method, as in the CIDECT Design Guide No. 4. The tabulated method is limited in scope. The simplified method deals with axial force only. The general method is suitable for every situation but is rather complicated. Wang (2000) proposed a simple design method based on the principle of EC4 for calculating the fire resistance of concrete-filled CHS columns. EC4 also has the Annex H method which is described in this section. Annex H presents a simple calculation model for concrete-filled hollow sections exposed to fire all around the column according to the standard temperature–time curve. The method consists of two steps. The first step is to determine the temperature distribution in the composite column after a given duration of exposure to the ISO-834 standard fire (ISO 1975). The second step is to calculate the design axial buckling load for the field of temperature previously obtained. In the first step, numerical method should be utilised to calculate the temperature field because of the non-uniform temperature distribution. EC4 gives general principles for this calculation, namely, the thermal response model should consider the relevant thermal actions specified in Eurocode 1 Part 1.2 (2002). The thermal properties of the materials specified in EC4 should be used. In the second step, mechanical properties of the materials at elevated temperatures are used. The design axial buckling load Nfi,Rd can be obtained from: (7.4) N fi,Rd N fi,cr N fi,pl,Rd where Nfi,cr is the elastic Euler buckling load and Nfi,pl,Rd is the design value of the plastic resistance to axial compression of the total cross-section. The axial strain of the steel tube, concrete and reinforcing steel is assumed to be the same. The normal procedure is to increase the strain in steps. As the strain increases, Nfi,cr decreases and Nfi,pl,Rd increases. The level of strain can be found where Nfi,cr is equal to Nfi,pl,Rd.. Because EC4 Annex H only provides general heat transfer equations for calculating the non-uniform temperature field in the composite cross-section and the iterative procedure to find the strain satisfying Eq. (7.4) is not easy, this method appears to be difficult to implement by practising engineers. Two design graphs are given in EC4 for fire resistance design of CFST columns, as shown in Figures 7.5 and 7.6. When there is a load eccentricity a correction factor is given in EC4 to determine the equivalent axial load to be used in connection with the axial load graphs in the fire situation. There are some concerns in Europe about the Annex H method. Wang and Orten (2008) pointed out that this method is rather antiquated. An alternative method was developed by Wang and Orten (2008) based on the well-established code design method for composite columns in the main part of Eurocode 4 Part 1.1 (EN1994-1-1). A design package named “Firesoft” is now available to assist designers, which has been verified by Wang and Orten (2008). Concrete-Filled Tubular Members and Connections Design curve 1 2 3 4 5 6 Circular section 219.1u4.5 329.9u5.6 406.4u6.3 219.1u4.5 329.9u5.6 406.4u6.3 pr (%) 1.0 1.0 1.0 4.0 4.0 4.0 Reinforcing bars Concrete Fire resistance: R60 Structural steel grade: S355 Concrete grade: C30/C35 Reinforcing bars: S500 Reinforcement axis distance dr; 40mm 5000 Axial Buckling Load (kN) 198 CFST CHS 6 4000 3 3000 2000 5 2 1000 t 0 dr 4 1 0 1 2 3 4 4.5 Buckling Length (m) d Figure 7.5 Design graph for CFST circular columns (adapted from Eurocode 4 2005) Circular section 200u6.3 300u7.1 400u10 200u6.3 300u7.1 400u10 pr (%) 1.0 1.0 1.0 4.0 4.0 4.0 Concrete Reinforcing bars D Fire resistance: R90 Structural steel grade: S355 Concrete grade: C30/C35 Reinforcing bars: S500 Reinforcement axis distance dr; 40mm 5000 Axial Buckling Load (kN) Design curve 1 2 3 4 5 6 CFST RHS 6 4000 3 3000 2000 5 2 1000 t dr 0 B 4 1 0 1 2 3 4 4.5 Buckling Length (m) Figure 7.6 Design graph for CFST square columns (adapted from Eurocode 4 2005) Fire Resistance of CFST Members 199 7.3.4 North American Approach An extensive experimental programme was carried out in North America on CFST circular and square columns under fire. The programme consisted of fire tests on about 80 full-scale unprotected CSFT columns, with three types of concrete-filling, namely plain concrete, steel bar-reinforced concrete and steel fibre-reinforced concrete (Lie and Chabot 1992, Chabot and Lie 1992 and Kodur and Lie 1995). Standard fire exposure according to ASTM E-119 (2001) was used, which is very similar to that specified in ISO-834 (1975). Numerical simulation and mathematical models were developed to predict the behaviour of square and circular CFST columns under fire conditions (Lie and Chabot 1990, Kodur and Lie 1996). After parametric studies (Lie and Stringer 1994, Kodur and Lie 1996 and Kodur 1998) a formula was proposed (Lie and Stringer 1994, Kodur 1999) to calculate the fire resistance of CFST columns. R (f 'c 20) D D2 P (KL 1000) f (7.5) where R is fire resistance in minutes, fƍc is the specified 28-day cylinder concrete strength in MPa, D is the outside diameter or width of the column in mm, P is the applied axial load in kN, K is the effective length factor, L is the column length in mm and f is a parameter that depends on the type of concrete filling (plain, barreinforced or fibre-reinforced), the cross-sectional shape (circular or square), the type of aggregate (carbonate or siliceous), the percentage of steel reinforcement (pr) and the thickness of concrete cover. Values of the parameter f can be obtained from Table 7.5 derived by Kodur (2007). The symbol S in Table 7.5 refers siliceous aggregate while the symbol C refers to carbonate aggregate. Table 7.5 Values of the parameter f in Eq. (7.5) (adapted from Kodur 2007) Filling type Aggregate type Plain concrete S pr (%) Thickness of concrete cover Circular CFST Square CFST C S N/A C < 3% N/A Fibre-reinforced concrete Bar-reinforced concrete 3% < 3% 3% <25 25 <25 25 <25 25 <25 25 S C 1.75% 1.75% N/A 0.07 0.08 0.075 0.08 0.08 0.085 0.085 0.09 0.09 0.095 0.075 0.085 0.06 0.07 0.065 0.07 0.07 0.075 0.075 0.08 0.08 0.085 0.065 0.075 Concrete-Filled Tubular Members and Connections 200 The validity range of parameters for using Eq. (7.5) is described for each type of concrete filling below. (a) For plain concrete filled tubes: R d 120 minutes, KL = 2 to 4m, fƍc= 20 to 40MPa, d = 140 to 410mm, B = 140 to 305mm and P d Cƍr where Cƍr is the factored compressive resistance of the concrete core given in Kodur and Mackinnon (2000). C' r 0.85Ic A c f 'c Oc2 ª« 1 0.25Oc4 0.5Oc2 º» ¬ ¼ (7.6) in which I c = 0.60 fƍc= compressive strength of concrete A c = cross-sectional area of the concrete core Oc KL rc f 'c S2 E c rc = radius of gyration of the concrete area and Ec is the elastic modulus of concrete which can be taken as 4500 f 'c for normal density concrete. (b) For steel bar-reinforced concrete filling: R d 180 minutes, KL = 2 to 4.5m, fc’ = 20 to 55MPa, d = 165 to 410mm, B = 175 to 305mm, pr = 1.5 to 5%, concrete cover = 20 to 50mm and P d 1.7Cƍr. (c) For steel fibre-reinforced concrete filling: R d 180 minutes, KL = 2 to 4.5m, fƍc = 20 to 55MPa, d = 140 to 410mm, B = 100 to 305mm, pr = 1.75% and P d 1.1Cƍr. For all three types of concrete filling d/t or (B–4t)/t ratio should not exceed the limiting value for Class 3 section defined in CAN/CSA-S16.1-M94 (1994), i.e. 23,000/fy for CHS and 670/fy for RHS. 7.3.5 Comparison of Different Approaches Different design codes adopt different approaches to deal with the important factors listed in Section 7.2. The comparison is made in the same sequence as that in Section 7.2. Fire load ratio (n) or degree of utilisation (P): Most of the research for developing DBJ13-51 was conducted for n of 0.77. A modification factor, as a function of n, is used to take into account the influence of the fire load ratio. Level one design in CIDECT Design Guide No. 4 and EC4 provides minimum requirement for three specific P values (0.3, 0.5 and 0.7), whereas level two design considers the buckling load directly instead of P. In the North America method the applied load is explicitly included in the fire-resistance formula. Column size: The perimeter of the column is explicitly included in the formula for protection thickness in DBJ13-51. The column diameter or width is also explicitly Fire Resistance of CFST Members 201 used in the fire-resistance formula in North America method. Some specific column sizes are recommended as the minimum values in level one design of CIDECT Design Guide No. 4 and EC4 while the design charts in level two are also given for specific column sizes. Effective buckling length: In all design codes, except level one of CIDECT Design Guide No. 4 and EC4, the effective buckling length is explicitly used in calculating fire protection thickness and fire resistance. External protection: Only DBJ13-51 calculates the fire protection thickness. Reinforcement of concrete: No reinforcement is used in DBJ13-51. Steel barreinforced concrete is used in CIDECT Design Guide No. 4 and EC4, whereas both bar and fibre-reinforced concrete is used in the North America method. Material strength: Material strength is not explicitly used in DBJ13-51 formulae although regression analysis was conducted for a wide range of material strength. Design charts in CIDECT Design Guide No. 4 and EC4 are for CFST columns with specific steel grades. Concrete strength is explicitly used in North America method. Bending moment and eccentricity: They are not explicitly shown in equations or charts although load eccentricity was included in most of the research work listed in Table 7.1. 7.4 EXAMPLES 7.4.1 Column Design Design a concrete-filled tubular column (4286mm in length) in a braced frame for a building to achieve a fire resistance of 90 minutes. The column is axially loaded with an effective length factor of 0.7. The applied axial load is 1500kN. The solutions from CIDECT Design Guide No. 4 and Eurocode 4 are described first since they are based on simple design charts. 7.4.1.1 Solutions according to CIDECT Design Guide No. 4 Level 1 design From Table 7.4 the possible tube size (d or B) for fire class R90 is 220mm with a degree of utilisation of 0.3 or 400mm with a degree of utilisation of 0.5. The corresponding minimum reinforcement is 3% or 6%. Select S355 steel tubes (355MPa yield stress) and C30 concrete (compressive cylinder strength of 30MPa). The actual degree of utilisation can be calculated as the ratio of the applied load (1500kN) to the column design capacity (Nu) which can be determined according to Chapter 4. 202 Concrete-Filled Tubular Members and Connections For the case of CHS 220mm in diameter, the tube thickness should not exceed 1/ 25 of d, i.e. 220/25 = 8.8mm. Choose section CHS 220 u 8mm. From the equations in Chapter 4 the corresponding column design capacity is 2274kN. This leads to a degree of utilisation of about 0.66 (= 1500/2274) which is larger than 0.3. Hence CHS 220 u 8 mm is not suitable. For the case of CHS 400mm in diameter, the tube thickness should not exceed 1/ 25 of d, i.e. 400/25 = 16mm. Choose section CHS 400 u 10 mm. From the equations in Chapter 4 the corresponding column design capacity is 9633kN. This leads to a degree of utilisation of about 0.16 (= 1500/9633) which is less than 0.5. Hence CHS 400 u 10mm is suitable although it is conservative. A final size could be between CHS 220 u 8mm and CHS 400 u 10mm, e.g. CHS 300 u 10mm. For the case of SHS 220mm in width, the tube thickness should not exceed 1/ 25 of B, i.e. 220/25 = 8.8mm. Choose section SHS 220 u 220 u 8mm. From the equations in Chapter 4 the corresponding column design capacity is 2995kN. This leads to a degree of utilisation of about 0.50 (= 1500/2995) which is larger than 0.3. Hence SHS 220 u 220 u 8 mm is not suitable. For the case of SHS 400mm in width, the tube thickness should not exceed 1/ 25 of B, i.e. 400/25 = 16mm. Choose section SHS 400 u 400 u 10mm. From the equations in Chapter 4 the corresponding column design capacity is 8276kN. This leads to a degree of utilization of about 0.18 (= 1500/8276) which is less than 0.5. Hence SHS 400 u 400 u 10mm is suitable although it is conservative. A final size could be between SHS 220 u 220 u 8mm and SHS 400 u 400 u 10mm, e.g. SHS 300 u 300 u 10mm. Level 2 design Effective buckling length is 3000mm (i.e. 0.7 u 4286mm). Form Figure 7.3 a suitable design could be: Fe360 CHS 244.5u5.0mm filled with bar-reinforced (pr of 1%) C20 concrete. Alternatively from Figure 7.4 select Fe360 SHS 220 u 220 u 6.3mm filled with bar-reinforced (pr of 1%) C20 concrete. 7.4.1.2 Solutions according to Eurocode 4 Part 1.2 For quick design see “Level 1 design” described in Section 7.4.1.1. For the calculation method specified in Annex H, no graphs are given in Eurocode 4 Part 1.2 for CFST circular columns with a fire resistance of 90 minutes. From Figure 7.6 curve 5 should be selected based on the effective length of 3m and applied load of 1500kN. Hence the suitable design is as follow: S355 SHS 300 u 300 u 7.1 mm filled with bar-reinforced (pr of 4%) C30 concrete. Fire Resistance of CFST Members 203 7.4.1.3 Solutions according to DBJ13-51 Use CFST CHS column Try Q345 CHS 250 u 5mm filled with C40 plain concrete with the following parameters: steel yield stress fy = 345MPa standard concrete strength fck = 26.8MPa d = 250mm KL = 0.7 u 4286mm = 3000mm C = Sd = 785mm P = 1500kN R = 90 minutes = 1.5 hours The above parameters are within the validity range given in Section 7.3.1. Using equations in Chapter 4: O = 48 Ds = 0.085 M = 0.83 Nc = 2464kN n = P/Nc = 1500/2464 = 0.608 From Table 7.2 kt = 0.15. Since kt < n < 0.77 Eq. (7.3a) should be used. k LR (n k t ) /(0.77 k t ) (0.608 0.15) /(0.77 0.15) 0.74 From Eq. (7.1) a k LR (19.2R 9.6) C(0.28 0.0019O ) 0.74 u (19.2 u 1.5 9.6) u 785 (0.28 0.0019u48) 8.1 mm Adopt a thickness of 9mm. Use CFST SHS column Try Q345 SHS 220 u 220 u 6mm filled with C40 plain concrete with the following parameters: steel yield stress fy = 345MPa standard concrete strength fck = 26.8MPa B = 220mm KL = 0.7 u 4286mm = 3000mm C = 4B = 880mm Concrete-Filled Tubular Members and Connections 204 P = 1500kN R = 90 minutes = 1.5 hours The above parameters are within the validity range given in Section 7.3.1. Using equations in Chapter 4: O = 47.2 Ds = 0.119 M = 0.87 Nc = 2798kN n = P/Nc = 1500/2798 = 0.536 From Table 7.2, using linear interpolation, kt | 0.14 Since kt < n < 0.77 Eq. (7.3a) should be used. k LR (n k t ) /(0.77 k t ) (0.536 0.14) /(0.77 0.14) 0.63 From Eq. (7.1) a k LR (19.2R 9.6) C(0.28 0.0019O ) 0.63 u (19.2 u 1.5 9.6) u 880 (0.28 0.0019u47.2) 7.1 mm Adopt a thickness of 8mm. 7.4.1.4 Solutions according to the North American approach Use CFST CHS column Try CHS 273 u 6.4mm filled with bar-reinforced concrete with the following parameters: steel yield stress fy = 350MPa concrete cylinder strength fƍc = 40MPa type of aggregate = carbonate pr = 3% thickness of concrete cover = 25mm KL = 0.7 u 4286mm = 3000mm D = 273mm P = 1500kN The above parameters are within the validity range given in Section 7.3.4. It is required to check the design conditions regarding section slenderness (d/t < 23,000/fy) and applied load (P < 1.7Cƍr). Fire Resistance of CFST Members 205 d/t = 273/6.4 = 42.7 < 23,000/fy = 23,000/350 = 65.7, satisfied. Based on the above dimensions and material properties Ac = 53,175mm2 rc = 65mm Oc = 0.55 0.85Ic A cf 'c Oc2 ª« 1 0.25Oc4 0.5Oc2 º» ¼ ¬ C' r 0.85 u 0.60 u 53175 u 40 u 0.55 2 ª« 1 0.25 u 0.55 4 0.5 u 0.55 2 º» ¼ ¬ | 1000kN P = 1500 < 1.7Cƍr = 1.7 u 1000 = 1700kN, satisfied. From Table 7.5, the value of f = 0.095 and the fire resistance is given by: R f (f 'c 20) D D2 (KL 1000) P 0.095 (40 20) 273 2732 (3000 1000) 1500 91 minutes This meets the requirement of 90 minutes. Use CFST SHS column Try SHS 254 u 254 u 6.4mm filled with bar-reinforced concrete with the following parameters: steel yield stress fy = 350MPa concrete cylinder strength f’c = 40MPa type of aggregate = carbonate pr = 3% thickness of concrete cover = 25mm KL = 0.7 u 4286mm = 3000mm D = 254mm P = 1500kN The above parameters are within the validity range given in Section 7.3.4. It is required to check the design conditions regarding section slenderness ((B–4t)/t < 670/fy) and applied load (P < 1.7Cƍr). (B–4t)/t = (254 – 4 u 6.4)/6.4 = 35.7 < 670/fy = 670/350 = 35.8, satisfied. Based on the above dimensions and material properties Concrete-Filled Tubular Members and Connections 206 Ac = 58,177mm2 rc = 70mm Oc = 0.51 C' r 0.85Ic A c f 'c Oc2 ª« 1 0.25Oc4 0.5Oc2 º» ¼ ¬ 0.85 u 0.60 u 58177 u 40 u 0.51 2 ª« 1 0.25 u 0.51 4 0.5 u 0.51 2 º» ¬ ¼ | 1114kN P = 1500 < 1.7Cƍr = 1.7 u 1114 = 1894kN, satisfied. From Table 7.5, the value of f = 0.085 and the fire resistance is given by: (f 'c 20) D (40 20) 254 68 minutes R f D2 0.085 254 2 1500 (KL 1000) P (3000 1000) This does not meet the requirement of 90 minutes. Select the next size up in the CISC Structural Section Tables (CISC 2009), i.e. SHS 305 u 305 u 8mm. Similar calculations can be made to give: (B–4t)/t = (305 – 4 u 8)/8 = 34 < 670/fy = 670/350 = 35.8, satisfied. Cƍr = 1650kN P = 1500 < 1.7Cƍr = 1.7 u 1650 = 2805kN, satisfied. From Table 7.5, the value of f = 0.085 and the fire resistance is given by: (f 'c 20) D (40 20) 305 R f D2 0.085 3052 107 minutes (KL 1000) P (3000 1000) 1500 This meets the requirement of 90 minutes. It can be proven that a smaller size SHS 285 u 285 u 8mm can achieve a fire resistance of 90 minutes although it is not listed in the CISC Structural Section Tables. 7.4.2 Real Projects 7.4.2.1 Composite column without external protection Many building projects were described in Twilt et al. (1995) where CFST columns without external protection were used. Three examples are mentioned here where three different approaches were adopted, i.e. plain concrete, steel bar-reinforced concrete and steel fibre-reinforced concrete. Fire Resistance of CFST Members 207 Nakanoshima Intes is a 22-storey office building located in Osaka City, Japan. The structure frame consists of CFST columns and steel beams. Square columns (600-850mm in width) and circular columns (700-800mm in diameter) are filled with plain concrete. No external protection was applied to columns from the 10th floor up to the 22nd floor, for which the fire resistance requirement is 60 to 120 minutes. The Tecnocent building is located in Oulu, Finland. Both circular (219 mm in diameter) and square (200mm × 200mm) CFST columns are used in this building which has a fire resistance requirement of 60 minutes. The fire endurance is fulfilled by filling the hollow section with bar-reinforced concrete without any external protection. The Rochdale bus station in Lancashire, UK, adopted square (150mm u 150mm) CFST columns filled with steel fibre-reinforced concrete to provide 60minute fire resistance. Again no external fire protection was applied to the columns. It can be seen that a much smaller size of tube filled with fibre-reinforced concrete can achieve the same fire resistance (e.g. 60 minutes) as that achieved by a much larger size of tube filled with plain concrete. A number of other buildings, such as The Museum of Flight building in Seattle, WA, and the school buildings in Hamilton, Canada, also adopted CFST columns without external protection (Kodur and Mackinnon 2000). 7.4.2.2 Composite column with external protection The research work in China on external fire protection was applied to some highrise buildings, such as SEG Plaza (291.6m in height; see Figure 1.6) in Shenzhen, Ruifeng International Trading Centre (89.7m tall) in Hangzhou, and Wuhan International Stock Centre (242.9m in height; see Figure 1.7) in Wuhan. Figure 7.7 shows an example of applying external fire protection materials to CFST columns in SEG Plaza. The columns of the three tall buildings were required to have a minimum fire resistance rating of 180 minutes under full design loads according to Chinese code (GB50045-95 2001). The fire protection material has the following parameters: thermal conductivity of 0.116W/m·K, specific heat of 1.047 × 103J/kg·K and density of 400 ± 20kg/m3. The required protection thickness should be 50mm according to the conventional code (GB50045-95 2001) for fire protection of steel columns. The actual protection thicknesses applied to the CFST columns in SEG Plaza, Ruifeng Centre and Wuhan International Stock Centre is shown in Figure 7.8, which is significantly less than 50mm. ENICOM Computer Centre is a six storey building in Tokyo with a required fire resistance of two hours. Plain concrete-filled steel square (600mm in width) tubes were adopted. By using fire-resistant steel the thickness of the fire protection (a ceramics-type sprayed material) was reduced to 5mm, which is significantly lower than that (30mm) for conventional steel (Twilt et al. 1995). Concrete-Filled Tubular Members and Connections 208 (a) Spraying of protection material (b) Spraying of protection material (c) Sprayed protection material (d) After spraying the protection material Thickness of Fire Protection Material (mm) Figure 7.7 Applying external fire protection materials to CFST columns in SEG Plaza (Han 2001) 60 50 40 30 20 10 0 GB50045-95 SEG Plaza Ruifeng Centre Wuhan International Stock Centre Code and Real Projects Figure 7.8 Comparison of fire protection thickness of CFST columns (adapted from Han and Yang 2007) 7.5 POST-FIRE PERFORMANCE The residual strength (capacity) of a composite column may be used to assess damage caused by fire and to establish an approach for minimising post-fire repair. Han et al. (2002a) reported 26 tests on CFST stub columns with rectangular sections after being exposed to high temperatures up to 900oC in the steel tube. It was found that the load versus axial strain relationships of the test specimens Fire Resistance of CFST Members 209 subjected to elevated temperatures showed strain hardening or an elastic-perfectly plastic behaviour. Twelve tests were conducted on CFST columns with or without fire protection after exposure to the ISO-834 standard fire (Han et al. 2002b). A mechanics model was developed for CFST columns after exposure to the ISO-834 Standard Fire (Han and Huo, 2003). The predicted load versus mid-span deflection relationship for the composite columns is in good agreement with test results (within 12% difference). A residual strength index (RSI) was proposed to measure the level of capacity remaining after the fire. The RSI is defined as N u (t) RSI (7.7) Nu where Nu(t) is the residual strength (capacity) corresponding to the standard fire exposure duration time (t) of the composite columns, and Nu is the ultimate strength of the composite columns at ambient temperatures. It was found that, in general, the member slenderness, sectional dimensions and the fire duration time had a significant influence on the residual strength index (RSI). However, the steel ratio, the load eccentricity ratio and the strength of the materials had only moderate influence on RSI. Formulae for RSI were developed by Han and Huo (2003) in terms of the following three parameters: to = t/100, Do = d/600 or B/600, Oo = O/40, where t is the fire exposure time in minutes, d is the diameter (in mm) of circular tube, B is the width (in mm) of square tube and O is the member slenderness defined in Eq. (4.32). They are reproduced in a table format in this chapter to assist designers; see Table 7.6 for CFST CHS and Table 7.7 for CFST SHS columns. Three fire exposure durations (1 hour, 2 hours and 3 hours) are chosen as examples. The most severe reduction occurs for a combination of the largest member slenderness, the smallest tube size and the longest fire exposure duration. The RSI formulae are valid when the parameters are within the following range: t d 180 minutes, d or B = 200 to 2000mm, O = 15 to 80, steel ratio D = 0.04 to 0.2, load eccentricity e = 0 to 0.15d or 0.15B, fsy = 200 to 500MPa and fck = 20 to 60MPa. A similar study was carried out by Han et al. (2005) on the post-fire performance of CFST beams. The residual strength index (RSI) for bending is defined as the ratio of Mu(t) to Mu, where Mu(t) is the residual bending moment after exposure to fire duration (t) and Mu is the moment capacity at the ambient temperature. Formulae for RSI were given in Han et al. (2005). Examples of RSI are given in Figure 7.9(a) for CFST CHS and in Figure 7.9(b) for CFST SHS beams. The reduction is less than 40% if t does not exceed 1 hour or Do is larger than 0.5. Huo et al. (2009) studied the effect of sustained axial load and cooling phase on post-fire behaviour of CFST columns. The effect of pre-load in columns and the fire cooling phase had no significant effects on the residual strength of firedamaged composite columns. However, the effects of preload in columns and the fire cooling phase on the residual deformation and axial compressive stiffness of composite columns should be taken into consideration in assessing the firedamaged CFST columns. More research is needed to understand the effect of Concrete-Filled Tubular Members and Connections 210 different cooling regimes on the mechanical properties of fire-damaged CFST columns in order to establish confident assessment of such columns. Han and Lin (2004) studied the seismic behaviour of CFST columns after exposure to fire up to 90 minutes. The columns were under constant axial load (with the load level n up to 0.45) and cyclic lateral bending. It was found that the energy dissipation of CFST circular columns was much higher than that of CFST square columns if other conditions were similar. For example, Figure 7.10 compares the performance of these two types of CFST columns. Fire exposure time is 90 minutes and load level is 0.45. The circular column has a diameter of 133mm and a thickness of 4.7mm (As is 1894mm2, Ac is 11,999mm2, perimeter is 418mm), whereas the square column has a width of 120mm with a thickness of 2.9mm (As is 1358mm2, Ac is 13,042mm2, perimeter is 480mm). Table 7.6 Residual strength index (RSI) for CFST circular columns after exposure to fire to = 0.6 Oo 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Oo 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Oo 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.4 0.73 0.72 0.71 0.70 0.69 0.68 0.67 0.66 0.67 0.6 0.79 0.78 0.77 0.76 0.75 0.74 0.73 0.72 0.72 0.8 0.82 0.81 0.80 0.79 0.78 0.77 0.76 0.75 0.75 1.0 0.83 0.82 0.81 0.80 0.79 0.78 0.77 0.76 0.77 to = 1.2 0.4 0.53 0.51 0.50 0.49 0.48 0.47 0.46 0.45 0.43 0.6 0.64 0.62 0.61 0.60 0.58 0.57 0.55 0.54 0.52 0.8 0.70 0.69 0.67 0.66 0.64 0.63 0.61 0.60 0.58 1.0 0.72 0.70 0.69 0.67 0.66 0.64 0.63 0.61 0.59 to = 1.8 0.4 0.39 0.38 0.37 0.36 0.35 0.34 0.34 0.33 0.29 0.6 0.54 0.53 0.52 0.51 0.49 0.48 0.47 0.46 0.40 0.8 0.63 0.62 0.60 0.59 0.58 0.56 0.55 0.53 0.47 1.0 0.66 0.64 0.63 0.61 0.60 0.58 0.57 0.55 0.49 Do Do Do 1.5 0.87 0.86 0.84 0.83 0.82 0.81 0.80 0.79 0.79 2.0 0.90 0.88 0.87 0.86 0.85 0.84 0.83 0.82 0.82 2.5 0.92 0.91 0.90 0.89 0.88 0.87 0.85 0.84 0.85 3.0 0.95 0.94 0.93 0.92 0.91 0.89 0.88 0.87 0.87 1.5 0.76 0.74 0.72 0.71 0.69 0.68 0.66 0.64 0.62 2.0 0.79 0.77 0.76 0.74 0.72 0.71 0.69 0.67 0.65 2.5 0.83 0.81 0.79 0.77 0.76 0.74 0.72 0.70 0.68 3.0 0.86 0.84 0.82 0.81 0.79 0.77 0.75 0.73 0.71 1.5 0.70 0.68 0.67 0.65 0.63 0.62 0.60 0.59 0.51 2.0 0.74 0.72 0.70 0.68 0.67 0.65 0.63 0.62 0.54 2.5 0.77 0.76 0.74 0.72 0.70 0.68 0.67 0.65 0.57 3.0 0.81 0.79 0.77 0.75 0.74 0.72 0.70 0.68 0.60 Fire Resistance of CFST Members 211 Table 7.7 Residual strength index (RSI) for CFST square columns after exposure to fire to = 0.6 Oo 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Oo 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Oo 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.4 0.69 0.69 0.68 0.67 0.66 0.65 0.64 0.63 0.64 0.6 0.75 0.74 0.73 0.72 0.71 0.70 0.69 0.68 0.69 0.8 0.79 0.78 0.77 0.76 0.75 0.74 0.73 0.72 0.72 1.0 0.80 0.79 0.78 0.77 0.76 0.75 0.74 0.73 0.73 to = 1.2 0.4 0.48 0.47 0.46 0.45 0.44 0.43 0.42 0.41 0.40 0.6 0.59 0.57 0.56 0.55 0.54 0.52 0.51 0.50 0.48 0.8 0.65 0.63 0.62 0.60 0.59 0.58 0.56 0.55 0.53 1.0 0.66 0.65 0.63 0.62 0.61 0.59 0.58 0.56 0.55 to = 1.8 0.4 0.35 0.35 0.34 0.33 0.32 0.31 0.31 0.30 0.26 0.6 0.50 0.48 0.47 0.46 0.45 0.44 0.43 0.42 0.36 0.8 0.58 0.56 0.55 0.54 0.52 0.51 0.50 0.48 0.42 1.0 0.60 0.59 0.57 0.56 0.54 0.53 0.52 0.50 0.44 Do Do 1.2 1.2 1.0 1.0 RSI (to=0.6) 0.6 RSI (to=1.2) 0.4 RSI (to=1.8) 0.2 0.0 1.5 0.83 0.82 0.81 0.80 0.79 0.78 0.76 0.75 0.76 2.0 0.86 0.84 0.83 0.82 0.81 0.80 0.79 0.78 0.78 2.5 0.88 0.87 0.86 0.85 0.84 0.83 0.82 0.81 0.81 3.0 0.91 0.90 0.89 0.88 0.87 0.85 0.84 0.83 0.84 1.5 0.70 0.68 0.67 0.65 0.64 0.62 0.61 0.59 0.57 2.0 0.73 0.71 0.70 0.68 0.67 0.65 0.64 0.62 0.60 2.5 0.76 0.75 0.73 0.71 0.70 0.68 0.67 0.65 0.63 3.0 0.79 0.78 0.76 0.74 0.73 0.71 0.69 0.68 0.65 1.5 0.64 0.62 0.61 0.59 0.58 0.56 0.55 0.53 0.47 2.0 0.67 0.65 0.64 0.62 0.61 0.59 0.58 0.56 0.49 2.5 0.70 0.69 0.67 0.65 0.64 0.62 0.61 0.59 0.52 3.0 0.74 0.72 0.70 0.69 0.67 0.65 0.64 0.62 0.54 0.8 RSI 0.8 RSI Do RSI (to=0.6) RSI (to=1.2) RSI (to=1.8) 0.6 0.4 0.2 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Do (a) CFST circular beams 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Do (b) CFST square beams Figure 7.9 Residual strength index (RSI) for CFST beams after exposure to fire Concrete-Filled Tubular Members and Connections 212 90 Lateral load, P(kN) 45 0 -45 -90 -70 -35 0 35 Lateral displacement, 䦲 (mm) 70 (a) Circular sections (n = 0.45) Lateral load, P (kN) 90 45 0 -45 -90 -70 -35 0 35 Lateral displacement, 䦲 (mm) 70 (b) Square columns (n = 0.45) Figure 7.10 Cyclic load (P) versus lateral displacement (ǻ) curves of tested specimens (adapted from Han and Lin 2004) 7.6 REPAIRING AFTER EXPOSURE TO FIRE Han et al. (2006) proposed a method to repair CFST columns after exposure to fire, i.e. by wrapping concrete and thin-walled steel tubes around the fire-damaged columns (see Figure 7.11). The benefit of repairing is demonstrated in Figure 7.12 by comparing the lateral load (P) versus lateral displacement (ǻ) envelope curves. It can be seen from Figure 7.12 that the ultimate capacity of the repaired column is about 7.5 times that before repairing. The initial stiffness increases more than three times. The energy absorption of CFST columns is compared in Figure 7.13, where the non-dimensional energy (E/Eoriginal) is plotted against the lateral displacement ratio ('/'y), and Eoriginal is the energy absorption of the original CFST column before exposure to fire. The increase in energy absorption due to repairing is more than 2.5 times. Fire Resistance of CFST Members New CHS 213 New SHS or RHS CFST column CFST column Fresh concrete Fresh concrete (a) Circular cross-section (b) Square or rectangular cross-section Lateral Load P (kN) Figure 7.11 Schematic view of repairing CFST columns after exposure to fire (adapted from Han et al. 2006) -80 100 after 80 repairing 60 before fire 40 exposure 20 0 -40 -20 -20 0 20 40 60 80 -40 after fire -60 exposure -80 -100 Lateral Displacement ' (mm) -60 Energy Ratio (normalised to that before fire exposure) Figure 7.12 Comparison of lateral load (P) versus lateral displacement (') envelope curves (adapted from Han et al. 2006) 4.0 3.5 3.0 2.5 2.0 after repairing 1.5 before fire exposure 1.0 after fire exposure 0.5 0.0 0 2 4 6 8 10 ' /' 'y Figure 7.13 Comparison of cumulative energy absorption (adapted from Han et al. 2006) 214 Concrete-Filled Tubular Members and Connections 7.7 REFERENCES 1. 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Journal of Structural Engineering, ASCE, 130(9), pp. 1405-1413. Fire Resistance of CFST Members 217 46. Twilt, L., Hass, R., Klingsch, W., Edwards, M. and Dutta, D., 1995, Design guide for structural hollow section columns exposed to fire (Köln: TÜVVerlag). 47. Wang, Y.C., 1997, Some considerations in the design of unprotected concretefilled steel tubular columns under fire conditions. Journal of Constructional Steel Research, 44(3), pp. 203-223. 48. Wang, Y.C., 1999, The effects of structural continuity on the fire resistance of concrete filled columns in non-sway frames. Journal of Constructional Steel Research, 50(2), pp. 177-197. 49. Wang, Y.C., 2000, A simple method for calculating the fire resistance of concrete-filled CHS columns. Journal of Constructional Steel Research, 54(3), pp. 365-386. 50. Wang, Y.C. and Davies, J.M., 2003, An experimental study of the fire performance of non-sway loaded concrete-filled steel tubular column assemblies with extended end plate connections. Journal of Constructional Steel Research, 59(7), pp. 819-838. 51. Wang, Y.C. and Orten, A.H., 2008, Fire resistance design of concrete filled tubular steel columns. The Structural Engineer, 7 (October), pp. 40-45. 52. Wang, Z.H. and Tan, K.H., 2007, Temperature prediction of concrete-filled rectangular hollow sections in fire using Green’s function method. Journal of Engineering Mechanics, ASCE, 133(6), pp. 688-700. 53. Yin, J., Zha, X.X. and Li, L.Y., 2006, Fire resistance of axially loaded concrete filled steel tube columns. Journal of Constructional Steel Research, 62(7), pp. 723-729. 54. Zha, X.X., 2003, FE analysis of the fire resistance of concrete filled CHS columns. Journal of Constructional Steel Research, 59(6), pp. 769-779. CHAPTER EIGHT CFST Connections 8.1 GENERAL CFST connections are similar to unfilled tubular connections described, for example, in Syam and Chapman (1996), Packer and Henderson (1997) and Kurobane et al. (2004). The differences caused by concrete-filling in connection design include increased strength, stiffness and ductility of CFST members which may lead to the change of certain failure modes, bond between steel and concrete. Extensive research has been conducted on CFST connections, especially those connecting steel beams to CFST columns subjected to seismic loading. The special characteristics include using external diaphragm, through diaphragm, internal diaphragm (e.g. Choi et al. 1995, Alostaz and Schneider 1996, Fu et al. 1998, Schneider and Alostaz 1998, Cheng et al. 2000, Beutel et al. 2002, Azizinamini and Schneider 2004, Nishiyama et al. 2004, Park et al. 2005, Choi et al. 2006), wider flange beam (Ricles et al. 2004), external T-stiffners (Lee et al. 1993), blind bolts (Gardner and Goldsworthy 2005, Loh et al. 2006a, 2006b, Yao et al. 2008, Wang et al. 2009a, 2009b), and reduced beam section connection (Park et al. 2008, Wang et al. 2008). Besides investigation in the connection itself, research has also been carried out to study CFST connections in frames or substructures subject to seismic loading (e.g. Matsui 1985, Nie et al. 2006, Herrera et al. 2006, 2008, Du et al. 2008, Han et al. 2008a, 2008b, 2009, Wang et al. 2009). This chapter focuses on CFST connections used in buildings. It begins with general classification of connection types (simple, semi-rigid and rigid connections). Typical examples of each type of connections are illustrated. Design rules are described for simple shear connection and rigid connection with external diaphragms followed by design examples. Brief discussions are made on CFST connections utilising blind bolts and reduced beam section. CFST connections for fatigue application are also introduced. 8.2 CLASSIFICATION OF CONNECTIONS The classification of connections for steel structures is generally applicable for CFST connections. The connections can be classified according to the behaviour in terms of moment versus rotation relationship. Three types of connections are normally adopted, i.e. simple connection, semi-rigid connection and rigid connection, as illustrated in Figure 8.1. The general definition is given as follows (Eurocode 3 2005). (1) Simple connection: Able to transmit internal forces but unable to transmit bending moments. Concrete-Filled Tubular Members and Connections 220 Moment Rigid connection Semi-rigid connection Simple connection Rotation Figure 8.1 Typical moment–rotation relation for connections in buildings (schematic view) (2) Semi-rigid connection: Not enough stiffness for the connection to maintain angles between connected members unchanged. The connection can transfer internal forces and moments while rotation between connected members cannot be neglected. The moment–rotation response should generally be established by analytical or experimental methods. (3) Rigid connection: Sufficient stiffness to keep angles between connected members unchanged when subjected to internal forces and moments. Three types of connections can be further quantitatively defined by the initial rotational stiffness (Kj,ini) in the moment–rotation relation (Eurocode 3, 2005). For braced frames, the connection is defined as: Simple connection, if Kj,ini < 0.5EIb/Lb Rigid connection, if Kj,ini 8EIb/Lb Semi-rigid, if 0.5EIb/Lb d Kj,ini < 8EIb/Lb (8.1a) (8.1b) (8.1c) For unbraced frames, the connection is defined as: Simple connection, if Kj,ini < 0.5EIb/Lb Rigid connection, if Kj,ini 25EIb/Lb Semi-rigid, if 0.5EIb/Lb d Kj,ini < 25EIb/Lb (8.2a) (8.2b) (8.2c) where E is the elastic modulus of steel, Ib is the second moment of area of beam and Lb is the beam span. Connections can also be classified according to their strength, as pinned, partial strength and full strength connections. Full strength connections can achieve the full plastic moment capacity of the connected elements. If the design moment capacity of a connection is not greater than 25% of the moment capacity required for a full strength connection, it can be classified as pinned connection. Partial strength connections are those with design moment capacity between the above limits. During the concept design of structures, connections can be primarily selected by their classification in rotation stiffness and/or strength based on the anticipated performance of the connections. Three connection models are given in Eurocode 3 (2005); namely, simple, semi-continuous and continuous. Connections CFST Connections 221 can be further classified according to the types of connection model and global structural analysis method. 8.3 TYPICAL CFST CONNECTIONS 8.3.1 Simple Connections As mentioned before, simple CFST connections only transmit shear force or axial force. Various kinds of attachments are utilised to transmit the forces. Typical examples are shown in Figure 8.2. The simplest one is by welding one single plate to the column face and by bolting the plate to the steel beam web (see Figure 8.2(a)). A variation of this type is to use a T-connection rather than a single plate, as shown in Figure 8.2(b), or to use a single angle or double angle to replace the single plate. A “through plate” can be used (see Figure 8.2(c)) to help transfer the beam reactions into the core concrete during a fire (Kodur and Mackinnon 2000). The single shear plate and single angle connections are the cheapest to manufacture. The “through plate” connection is more expensive than the fillet-welded Tconnection type. If the beam is a square hollow section rather than an I-section, similar connection details can be used except that the plates are welded to both webs or the beam is welded to an end plate (see Figure 8.2(d)). Unstiffened or stiffened seat connection (see Figure 8.2(e)) is another type of simple connection commonly used for light loads and for open web steel joints. The seat is assumed to carry the entire end reaction of the supported beam. The angle must be placed in a certain location to ensure satisfactory performance and stability. The fin plate connection shown in Figure 8.2(f) is commonly used at the end of a diagonal bracing member. More details can be found in Kurobane et al. (2004). 8.3.2 Semi-Rigid Connections Four types of semi-rigid connections were described in Kurobane et al. (2004). They are (1) Unreinforced welded tube-to-tube connection (Makino et al. 2001, Packer and Fear 1991, Packer and Kenedi 1993), (2) Bolted tube-to-tube connection made using flange plates, gusset plates, angle cleats or cut-outs of open sections, (3) Unreinforced welded I-section beam to tube connection (Morita 1994, Lu 1997, de Winkel 1998), and (4) Bolted I-section beam to tube connection shown in Figure 8.3 (Lu 1997, de Winkel 1998, France et al. 1999). The tube can be either a circular hollow section (CHS) or a rectangular hollow section (RHS). Concrete-Filled Tubular Members and Connections 222 CFST Column CFST Column Steel beam A A A A Single plate T-section Beam web Beam web Section A-A Concrete Concrete (a) Shear plate connection Section A-A (b) T-connection Steel hollow section beam CFST Column Steel beam A Steel beam Angle A Concrete CFST Column Through plate Beam web Section A-A Concrete (c) “Through-plate” connection (d) Hollow section to hollow section connection CFST Column Steel beam Fin plate Angle Steel tube T-section Concrete (e) Stiffened seat connection (f) Fin plate connection Figure 8.2 Typical simple connections for CFST columns (adapted from Kurobane et al. 2004) CFST Connections 223 The first type may occur in frames or Vierendeel girders where concrete filling of the column or chord is generally only used for repair purposes. The second type is not significantly affected by concrete filling. The last two types with I-section beams are the most commonly used ones. These two types behave in a similar manner. Increased ultimate capacity due to concrete filling was observed by de Winkel (1998) for I-beam-to-CHS CFST column connections. It was suggested that the strength of bolted I-beam-to-CFST column connections can be determined by the yield capacity for the compressive side of the connection and punching shear capacity for the tensile side of the connection. More details can be found in Kurobane et al. (2004). CFST Column Concrete slab Steel beam Steel tube Concrete (a) CHS CFST column (adapted from de Winkel 1998) CFST Column Concrete slab Steel beam Steel tube (b) Concrete RHS CFST column (adapted from Lu 1997) Figure 8.3 Typical semi-rigid connections for steel I-beam-to-CFST column 8.3.3 Rigid Connections Various methods exist to increase the stiffness of a connection to satisfy the condition of a rigid connection. Kurobane et al. (2004) gave some examples by utilising diaphragms, e.g. using a welded through diaphragm (Kurobane 1998), bolted through diaphragm (Ochi et al. 1998, Kurobane 2002), internal diaphragm (Engelhardt and Sabol 1994), combined internal and through diaphragm (Kurobane et al. 2001, Miura et al. 2002) and external diaphragm (Kamba et al. 1983, Tabuchi et al. 1985). Design of rigid connections with external diaphragms is Concrete-Filled Tubular Members and Connections 224 given later in Section 8.4.3. Han and Yang (2007) summarised many examples of other options for rigid connections. In principle there are two categories. One is to provide strengthening from outside the tubular column, e.g. using variable width RC beams with seats at the bottom of the beam (see Figure 8.4(a)), using RC ring beam (see Figure 8.4(b)). The other category is to provide strengthening inside the tubular column, e.g. using anchor stiffeners in critical locations (see Figure 8.4(c)). Concrete Stirrup Concrete RC ring beam CHS (a) Connection with variable width RC beam (b) Connection with RC ring Concrete Steel beam A RC beam RC beam Rebar CHS Transverse plate A CFST column Section A-A Vertical plate Section A-A (c) Connection with anchor stiffeners Figure 8.4 Some rigid connections for CFST columns (adapted from DBJ13-51) Advantages of using the external diaphragm are efficient in load transfer, less stress concentration in the connection zone, high stiffness and capacity, and good plastic deformation behaviour. The main disadvantage is that the external diaphragm may cause unfavourable architecture effect on the building façade, especially when the dimension of the CFST column is relatively small, whereas the size of the external diaphragm is relatively large. The variable width RC beam connection (see Figure 8.4(a)) has a continuous RC beam, while the beam-tocolumn connection is pinned. The beam reaction force transfers to the column through the bracket beneath the beam. The load transfer through the connection is efficient, but the construction procedure is relatively complicated. The RC ring beam connection (see Figure 8.4(b)) is efficient in load transfer. It meets the general seismic design principles for connections, i.e. strong in column and weak in beam, and strong in shear and weak in flexural capacity. However, the fabrication is also complicated. Connection with anchor stiffeners (see Figure 8.4(e)) requires enough space for fabricating the anchor stiffeners inside the steel tube. CFST Connections 225 8.4 DESIGN RULES 8.4.1 General Chapters 3, 4 and 5 described the design of CFST members subjected to bending, axial forces and combined actions. Chapter 6 clearly showed that CFST columns have excellent load-bearing capacity and ductility to resist large deformation cyclic loading. Design of CFST connections becomes a key issue in the seismic design of CFST structures. Rigid connections are often adopted for CFST structures in the seismic zone due to its high strength, ductility and energy absorption. Chapter 7 demonstrated the advantage of CFST columns in fire conditions. Detailed design methods were given in Chapter 7 to calculate the fire resistance of CFST columns. However, limited research has been conducted on the fire resistance of CFST connections (Wang and Davies 2003, Ding and Wang 2007, Han et al. 2007). CFST column to I-section beam connections were studied by Wang and Davies (2003) and Ding and Wang (2007). Most of the connections in the testing programme were simple and semi-rigid connections. It is found that the reverse channel connection has the best desired features, i.e. moderate construction cost, ability to develop catenary action and high ductility (Ding and Wang 2007). Han et al. (2007) studied CFST connections with an external ring exposed to fire. There are no design guidelines for fire resistance of CFST connections. Full or partial external fire protection is generally applied to such connections to ensure sufficient fire resistance. This section will only focus on the design rules for simple connections and rigid connections at ambient temperature. The design of semi-rigid CFST connections is similar to that of unfilled tubular semi-rigid connections. It should be noted that some semi-rigid connections for unfilled tubular columns may change into rigid connections after concrete filling. Changes in stiffness and capacity also lead to changes in failure modes, e.g. the column face plastification failure mode for unfilled tubular connections may change to the punching shear failure mode for CFST connections. More details can be found in Kurobane et al. (2004). The design procedure for CFST connections generally starts from selecting the type of connection based on the structural performance requirement. The capacity of the connection is checked against the applied actions corresponding to each failure mode. The bond strength between steel and concrete interface also needs to be checked to ensure sufficient composite action. 8.4.2 Design of Simple Connections Design of simple CFST connections is similar to that of unfilled tubular connections described in Syam and Chapman (1996), CSA (2003), Kurobane et al. (2004) and AISC (2005). Possible failure modes are steel tube buckling, bolt shear failure, weld shear failure, pushing shear failure, yielding of steel tube, shear failure of steel beam, bearing failure of shear plate or beam web, fracture failure of Concrete-Filled Tubular Members and Connections 226 shear plate or coped beam web, yielding of shear plate and shear failure of steel tube adjacent to a beam web. Slightly different equations are given in various codes for the above failure modes. The equations summarised below mainly come from Kurobane et al. (2004). The geometric dimensions are defined in Figure 8.5 and Figure 8.6. (1) Slenderness requirement of steel tubes to avoid local buckling (B 4 t c ) / t c 1.4 d/t c 0.114 E f c, y (for RHS) (8.3a) (for CHS) (8.3b) E f c, y (2) Bolt shear failure V n b Vbolt (3) Weld shear failure V L w Vweld (4) Punch shear failure t p (f c, u /f p, y ) t c (8.4) (8.5) (8.6) (5) Shear yield of steel tube V 2)1L p t c (0.6 f c, y ) (8.7) (6) Shear failure of steel beam V )1d1t b, w (0.6 f w, y ) (8.8) (7) Bearing failure of shear plate or beam web V 3) 3 t p n b d b f p, u (8.9a) or V 3) 3 t b, w n b d b f b, w, u (8.9b) (8) Fracture failure of shear plate V 0.85 )1 (A nv 0.6 f p, u A nt f p, u ) (8.10) (9) Yielding of shear plate V 0.85 )1A g f p, y (8.11) (10) Shear failure of steel tube adjacent to a beam web § 2r · V W 0.6 max log¨ c ¸ d 0.6f p, y ¨ bj ¸ Lp t c © ¹ (8.12) where B is the width of RHS, d is the outer diameter of CHS, tc, tp and tb,w are the thickness of tubular column, shear plate and beam web, respectively, Lp is the length of the shear plate, Lw is the total length of fillet welds, db is the bolt diameter, nb is the number of bolts, Ag is gross area of the shear plate to resist shear force (Ag = Lptp), Anv is net area in shear for block failure, Ant is the net area in tension for block failure, E is the elastic modulus of steel, fc,y, fp,y and fw,y are the yield stress CFST Connections 227 of steel tube, shear plate and beam web, respectively, fc,u, fp,u and fb,w,u are the ultimate strength of steel tube, shear plate and beam web, respectively, V is the design shear force, Vbolt is the design shear capacity of a single bolt, Vweld is the design shear capacity per unit length of a fillet weld, Vmax is the maximum shear force in beam web, Ɏ1 is the resistance factor for yielding of steel (taken as 0.9), Ɏ3 is the resistance factor used for failure associated with a connector (taken as 0.67), rc is the dimension for core concrete in CFST, i.e. rc = d/2 – tc for CHS CFST and rc = B/2 – tc for RHS CFST, and bj is the total length of the weld given by bj = tb,w + 2hf, where hf is fillet weld leg length. The bond strength is described later in Section 8.4.4 since it applies to both simple and rigid connections. B or d A tc Steel beam t b,w d1 d overall Lp t b,f tp Shear plate Shear plate Steel tube bb,f A Section A-A Figure 8.5 Geometric dimensions of a simple connection bj Lp bj Lp Vmax tc rc Vmax tc rc Figure 8.6 Geometric dimensions for shear capacity calculation 8.4.3 Design of Rigid Connections 8.4.3.1 Load action and critical location Only the design of CFST connections with external or through diaphragms, as shown in Figure 8.7 and Figure 8.8, is covered in this section. The applied design Concrete-Filled Tubular Members and Connections 228 action (N*) is the axial tensile load at the beam end, which can be calculated as follows (Han and Yang 2007). M (8.13) N* Nb h V d M Mc ˈand M t 0.7 M c (for CHS CFST) (8.14a) 3 VB M Mc ˈand M t 0.7 M c (for RHS CFST) (8.14b) 3 where Nb is tensile force in an external diaphragm induced by the axial force in beam, h is the overall depth of steel I-beam, Mc is design moment at the beam support, V is the shear force at the beam end corresponding to Mc, d is outer diameter of CHS and B is the width of RHS. The failure mode of such rigid connections is the yielding of the external diaphragm under tensile force transmitted from the flange of steel I-beam. The critical location, or the maximum stress location, in the external diaphragm depends on the connection type shown in Figures 8.7 and 8.8. The critical location for CHS CFST connection is A-A section as shown in Figure 8.7. The critical location for type I and type II RHS CFST connections is B-B section, while the critical location is C-C and D-D for type III shown in Figure 8.8. 8.4.3.2 CHS CFST connections Design equations in terms of yield capacity (Ny) are given in AIJ (1997) for the four types of CHS CFST connections shown in Figure 8.7. The critical section for CHS columns is assumed to be a T-section which consists of a cross-section of the diaphragm with the height b and a portion of the column wall with the effective width be (see Figure 8.9). The yield capacity is given as follows. For Type I and Type II connections: N y 1.24 f1 (Į) b t1 f s, y 2.16 f 2 (Į) b e t f c, y (8.15) For Type III and Type IV connections: N y 1.77 b t1 f s, y 1.53 b e t f c, y (8.16) in which f1 (Į) 2sin 2 Į 1 f 2 (Į ) sin Į be b · § ¨ 0.63 0.88 s ¸ d t t1 d ¹ © (8.17) (8.18) (8.19) where Į = angle between tensile force and critical section (Į = 45o for Type III and Type IV connections) b = effective width of diaphragm at critical section CFST Connections 229 be = effective width of tube wall to resist tensile force together with the diaphragm bs = flange width of steel I-beam d = outside diameter of CHS t = thickness of steel tube t1 = thickness of diaphragm fs,y = yield stress of steel diaphragm fc,y = yield stress of steel tube The validity range for Eq. (8.15) and Eq. (8.16) is: 20 d d/t d 50, b/d d 0.3 and 0.25 d bs/d d 0.75. It should be pointed out that the ultimate capacity equations are adopted in Kurobane et al. (2004) instead of the yield capacity given in Eq. (8.15) and Eq. (8.16). The ultimate capacity equals the yield capacity times a factor of 1.43 (=1/0.7). In DBJ13-51-2003 (2003), the yield capacity equations in AIJ (1997) are rewritten to determine the width of the diaphragm. N N A D A D A b t A b t r > 10mm r > 10mm N bs d (a) Type I N bs d (b) Type II N1 N1 A D=45 <30 N2 A N2 t b N1 bs d (c) Type III A D=45 N2 A N2 t b N1 bs d (d) Type IV Figure 8.7 External diaphragm rigid connections for CHS CFST (adapted from AIJ 1997) Concrete-Filled Tubular Members and Connections 230 N N hs <30 hs B hs B D hs 45 hs C hs B B t t r > 10mm N r > 10mm N bs B (a) Type I r > 10mm N bs B d in t Inner diaphragm N bs B (c) Type III (b) Type II Figure 8.8 External diaphragm rigid connections for RHS CFST (adapted from AIJ 1997) Tube wall t1 be Diaphragm t b Figure 8.9 Effective width for CHS CFST (adapted from AIJ 1997) 8.4.3.3 RHS CFST connections For Type I connection two design equations are given. 2/3 Ny Ny 2/3 § t · § t · § t h s · 2 f s, y 2.62¨ ¸ ¨¨ 1 ¸¸ ¨ ¸B 0.58 © B ¹ © t hs ¹ © B ¹ 4 h s t1 f s, y 2(4t t1 ) t f c, y 3 (8.20a) (8.20b) The first equation is based on the yield capacity for connections to unfilled columns with a slightly larger resistance factor due to concrete-filling. The second equation is based on a lower bound solution of plastic theory following the same procedure as that used for connections to CHS columns described in Section 8.4.3.2. The larger capacity from the above two equations are taken as the yield capacity of the connection since both equations were proven to be conservative (Matsui 1981). CFST Connections 231 For Type II connection Eq. (8.20b) can be used. For Type III connection Ny (B 2h s d in ) 2 b s t1 2 d in f s, y (8.21) where B = width of RHS section bs = flange width of beam din = hole diameter of the inner diaphragm hs = distance shown in Figure 8.8 t = thickness of steel tube t1 = thickness of diaphragm ts = thickness of steel beam flange fs,y = yield stress of steel diaphragm fc,y = yield stress of steel tube The validity range for the above equations is: 20 d B/t d 50, 0.75 d t1 /t d 2, t1 ts, hs/B 0.1ts/t1 for Type I and hs/B 0.15ts/t1 for Type II. It should be pointed out that the ultimate capacity equations are adopted in Kurobane et al. (2004) instead of the yield capacity given in Eq. (8.20) and Eq. (8.21). The ultimate capacity equals the yield capacity times a factor of 1.43 (=1/0.7). In DBJ13-51-2003 (2003), the yield capacity equations in AIJ (1997) are rewritten to determine the width of the diaphragm. 8.4.4 Bond Strength Performance of CFST members and connections relies on composite action between the steel hollow section and concrete. The bending moment is transmitted from the beam flange through the external diaphragm to the CFST column by tensile or compressive forces. These forces do not significantly affect the composite action in the CFST column. However, the shear force transmitted to the steel tube may induce slipping between the steel tube and concrete at the interface. In order to ensure that the shear force can effectively transmitted from the steel tube to the core concrete, the bond strength between steel and concrete should reach a certain level. The load transfer from the beam to CFST column induces axial force increments in both steel and concrete, i.e., ǻNs and ǻNc, as shown in Figure 8.10. It is assumed that bond stress is uniform in the range of middle height (l) of the CFST column above and below the connection, as shown in Figure 8.10. The bond strength (fbond) between steel and concrete can be calculated by the following equation (AIJ, 1997): ǻN ic f bond d fa (8.22) Ȍl where < is the inner perimeter of the steel tube and fa is the design bond strength. The design bond strength between steel and concrete in CFST columns is specified Concrete-Filled Tubular Members and Connections 232 in design codes, e.g. 0.225MPa for CHS and 0.15MPa for RHS in AIJ (1997) and DBJ13-61-2004 (2004), 0.55MPa for CHS, 0.4MPa for RHS in Eurocode 4 (2004) and 0.4MPa in BS5400 (2005). 'Nic is the axial force taken by concrete transmitted from beams at the ith floor, which can be determined as follows. If the total shear force at the beam end is set as ǻNi and the axial force applied on the CFST column is called Ni, then: (1) When Ni 0.85fcAc, the shear force at the beam end is totally resisted by the steel tube. It is not necessary to calculate the bond strength between steel and concrete. (2) When Ni < 0.85fcAc and Ni + 'Ni > 0.85fcAc, 'N ic 0.85 f c A c N i (3) When Ni + 'Ni < 0.85fcAc, 'N ic 'N i When the bond strength cannot meet the requirement in Eq. (8.22), internal diaphragms or studs are needed to ensure effective shear force transmission. N=Ns +Nc Ns Nc Ns 'N=6Q Q Q Nc +'Nc Ns +'N s N+'N Beam 1 l 'N1c 'N1 =6Q1 l Beam 2 'N2c 'N2 =6Q2 Figure 8.10 Load transfer mechanism (adapted from AIJ 1997) CFST Connections 233 8.5 EXAMPLES 8.5.1 Example 1 Simple Connection A steel I-beam (Grade 300 PLUS universal beam 460UB82.1) is connected to a cold-formed CHS (Grade C350 CHS 508 u 12.7) CFST column via a single plate (Grade 250) simple connection to transmit a shear force of 600kN. Concrete strength is 40MPa. The height of the CFST column between floors is l = 4000mm. The axial load on the top of the column is 4000kN. Check if the connection is adequate. (1) Dimensions and material properties. Steel tube (from AISC 1999): d = 508mm tc = 12.7mm fc,y = 350MPa fc,u = 430MPa Concrete: fc = 40MPa Steel I beam (from BHP 1994): doverall = 460mm d1 = 428mm bs = 191mm tb,f = 16mm tb,w = 9.9mm fw,y = 320MPa fw,u = 440MPa Shear plate (from AS3678, Standards Australia 1996): fp,y = 260MPa fp,u = 410MPa (2) Slenderness requirement From Eq. (8.3b) d/t c 508/12.7 40 0.114E/f c, y 0.114 u 200,000/350 65 , satisfied. (3) Number of bolts Adopt M24 high strength 8.8/S bolt, the design shear capacity of a single bolt (Vbolt) is 186kN (Syam and Chapman 1996). From Eq. (8.4) nb = V/Vbolt = 600/186 = 3.2 Choose four M24 bolts. The bolt hole diameter is 26mm (= 24 + 2). Concrete-Filled Tubular Members and Connections 234 (4) Weld shear failure check From Eq. (8.5) Vweld V / L w V /( 2d1 ) 600 /( 2 u 428) 0.7 kN / mm From Syam and Chapman (1996) a weld size (weld leg length hf) of 6mm is sufficient if the SP (Structural Purpose) weld is used. (5) Shear plate thickness From Eq. (8.6) t p (f c, u /f p, y ) t c (430 / 260) u 12.7 21mm A plate thickness of 16mm is selected. (6) Shear plate length From Eq. (8.7) Lp ! Vmax 2)1 t c (0.6 f c, y ) 600 u 103 125mm 2 u 0.9 u 12.7 u 0.6 u 350 Adopt Lp = 400 mm which is less than d1 of 428mm. (7) Check shear failure of steel beam From Eq. (8.8) )1d1t b, w (0.6 f w, y ) 0.9 u 428 u 9.9 u 0.6 u 320 732 u 103 N !V 732 kN 600kN, satisfied. (8) Bearing failure of shear plate or beam web From Eq. (8.9a) 3 u 0.67 u 16 u 4 u 26 u 410 1371u 103 N 1371 kN 3) 3 t p n b d b f p, u !V 600kN, satisfied. From Eq. (8.9b) 3) 3 t b, w n b d b f w, u 3 u 0.67 u 4 u 9.9 u 26 u 440 911 u 103 N 911 kN !V 600kN, satisfied. (9) Fracture failure of shear plate Two possible failure paths are as shown in Figure 8.11. For failure path shown in Figure 8.11(a), i.e. shear fracture alone, from Eq. (8.10), CFST Connections 235 0.85 )1 (A nv 0.6 f p, u ) 0.85 u 0.9 u (400 4 u 26) u 16 u 0.6 u 410 891 u 103 N 891 kN ! V 600kN, satisfied. For failure path shown in Figure 8.11(b), i.e. shear fracture and tensile failure combined, from Eq. (8.10), 0.85 )1 (A nv 0.6 f p, u A nt f p, u ) 0.85 u 0.9 u [(400 80 3 u 26 0.5 u 26) u 0.6 (60 0.5 u 26)] u 16 u 410 925 u 103 N 925 kN ! V 600 kN, satisfied. Shear plate Shear plate Tensile rapture 80 80 80 400 80 Shear rapture (a) 80 400 Shear rapture 80 80 80 80 60 (b) Figure 8.11 Failure paths of the shear plate (10) Yielding of shear plate From Eq. (8.11) 0.85 )1 A g f p, y 0.85 u 0.9 u 400 u 16 u 260 1273 u 103 N 1273 kN ! V 600 kN (11) Shear failure of steel tube adjacent to a beam web rc = d/2 - tc = 508/2 – 12.7 = 241.30mm bj = tb,w + 2hf = 9.9 + 2u6 = 21.9mm Vmax = 600kN § 2r · V 600 u 103 § 2 u 241.30 · log¨ W 0.6 max log¨ c ¸ 0.6 u ¸ ¨ bj ¸ u Lp t c 400 12.7 © 21.9 ¹ ¹ © 95.2 MPa d 0.6f p, y 0.6 u 260 156 MPa , satisfied. (12) Bond strength between concrete and steel tube Given l = 4000mm, Ni = 1500kN 80 60 Concrete-Filled Tubular Members and Connections 236 The load transfer from beam to the column is 'Ni = 2V = 2 u 600 = 1200 kN The ultimate strength of concrete, N u, c 0.85f c A c 0.85 u 40 u ʌ u (508 12.7 u 2) 2 / 4 6220 u 103 N 6220 kN Axial load on the bottom of the column, N i ǻN i 4000 1200 5200 kN Since N i ǻN i N u, c , ǻN ic f bond ǻN ic < l ǻN i 1200 kN . From Eq. (8.22) 1200 u 103 ʌ u (508 - 12.7 u 2) u 4000 0.198 MPa which is less than the design bond strength given in design code, e.g. 0.225MPa in AIJ (1997). Hence the connection is adequate to resist the shear force of 600kN. 8.5.2 Example 2 Rigid Connection A steel I-beam (Grade 300 PLUS universal beam 460UB82.1) is connected to a hot-rolled SHS (Grade S355 SHS 400 u 400 u 16) CFST column via a diaphragm (Grade 300 plate) rigid connection. Concrete strength is 40MPa. The diameter of the inner diaphragm din is 250mm (for Type III). The tensile force transmitted from beam flange to the diaphragm is 1000kN. The height of the CFST column between floors is l = 4000mm. The axial load on the top of the column is 4000kN. The vertical load transfer from beam to the column is 1200kN. Check if the connection is adequate. (1) Dimensions and material property Steel tube: B = 400mm t =16mm fc,y = 355MPa (from Table 2.2) Concrete: fc = 40MPa Steel I-beam (from BHP 1994): bs = 191mm ts = 16mm Diaphragm (from AS3678, Standards Australia 1996): fp,y = 300MPa fp,u = 430MPa din = 250mm (for Type III connection) CFST Connections 237 (2) Determine the minimum thickness of diaphragm t1 N f s, y b s 1000 u 103 300 u 191 17.5 mm Choose t1 = 18mm. (3) Type I diaphragm connection (a) Check validity range B/t = 400/16 = 25 which satisfies 20 d B/t d 50 t1/t = 18/16 = 1.125 which satisfies 0.75 d t1 /t d 2 t1 = 18 mm > ts = 16 mm, satisfied (b) Determine the minimum value of hs From condition hs/B 0.1ts/t1 hs 0.1B u ts/t1 = 0.1 u 400 u 16/18 = 36mm Choose hs = 50mm (c) Determine yield capacity From Eq. (8.20a) Ny §t· 2.62¨ ¸ ©B¹ 2/3 § t1 · ¨ ¸ ¨th ¸ s¹ © § 16 · 2.62 u ¨ ¸ © 400 ¹ 2/3 2/3 § t h s · 2 f s, y ¨ ¸B 0.58 © B ¹ § 18 · u¨ ¸ © 16 50 ¹ 2/3 300 § 16 50 · u¨ ¸ u 400 2 u 0.58 © 400 ¹ 1760 u 103 N 1760 kN From Eq. (8.20b) 4 h s t1 f s, y 2(4t t1 ) t f c, y Ny 3 4 u 50 u 18 u 300 2 u (4 u 16 18) u 16 u 355 3 1555 u 103 N 1555 kN The yield capacity Ny = max{1760, 1555} = 1760kN. The connection is adequate since Ny of 1760kN is greater than N of 1000kN. (4) Type II diaphragm connection (a) Check validity range B/t = 400/16 = 25 which satisfies 20 d B/t d 50 t1/t = 18/16 = 1.125 which satisfies 0.75 d t1 /t d 2 t1 = 18 mm > ts = 16 mm, satisfied Concrete-Filled Tubular Members and Connections 238 (b) Determine the minimum value of hs From condition hs/B 0.15ts/t1 hs 0.15B u ts/t1 = 0.15 u 400 u 16/18 = 53mm Choose hs= 60mm (c) Determine yield capacity From Eq. (8.20b) 4 Ny h s t1 f s, y 2(4t t1 ) t f c, y 3 4 u 60 u 18 u 300 2 u (4 u 16 18) u 16 u 355 3 1680 u 103 N 1680 kN The connection is adequate since Ny of 1680kN is greater than N of 1000kN. (5) Type III diaphragm connection (a) Check validity range B/t = 400/16 = 25 which satisfies 20 d B/t d 50 t1/t = 18/16 = 1.125 which satisfies 0.75 d t1 /t d 2 t1 = 18mm > ts = 16mm, satisfied (b) Determine the minimum value of hs By rearranging Eq. (8.21) hs 1 2 2 N y d in 1 (B d in ) bs t1f s, y 2 1 1000 u 103 u 250 2 1 u u (500 300) 2 191u 18 u 300 2 Choose hs = 30mm. Hence the connection is adequate with hs of 30mm. (6) Bond strength Given l = 4000mm, Ni = 1500kN The load transfer from beam to the column is 'Ni = 1200kN The ultimate strength of concrete, N u, c 0.85f c A c 0.85 u 40 u (400 16 u 2) 2 4604 u 103 N Axial load on the bottom of the column, N i ǻN i 4000 1200 5200 kN Since Ni < 0.85fcAc and Ni + 'Ni > 0.85fcAc, 'N ic 0.85 f c A c N i 4604 4000 604 kN 4604 kN 23 mm CFST Connections 239 From Eq. (8.22) f bond ǻNic < l 604 u 103 (400 16 u 2) 2 u 4000 0.001MPa which is less than the design bond strength given in design code, e.g. 0.225MPa in AIJ (1997). Hence the connection is adequate. 8.6 MORE RECENT CFST CONNECTIONS 8.6.1 Blind Bolt Connections Blind bolts are needed to connect beams to tubular columns because of a lack of access to the inside of tubes. Examples are given in Kurobane et al. (2004) for steel I-beam to RHS column connections through blind bolts. Flush end plates are welded to the end of the beams, then bolted to column faces by MUTF (Metric Ultra Twist Fastener) blind bolts (Huck 1994). The column walls are partially thickened over the area where the end plates are attached to prevent local distortion of the column walls and to achieve a full strength connection (Tanaka et al. 1996). In a similar manner, steel I-beam to CFST column connections were developed by Gardner and Goldsworthy (2005) and Yao et al. (2008) where T-stubs bolted to the beam end were adopted. Wang et al. (2009a, 2009b) studied the same type of connections using flush end plates welded to the beam end. Both details end up as typical semi-rigid connections. The common failure mode of such a connection is the loss of anchorage of the bolts in the core concrete, which leads to the pull-out of the steel tube. The tube wall thickness and end plate thickness are two key parameters influencing the behaviour. Blind bolts with a cogged extension were used by Gardner and Goldsworthy (2005) to increase the anchor length in the concrete, which resulted in improved connection strength and stiffness. Loh et al. (2006a, 2006b) developed a steel–concrete composite beam to a CFST tubular column connection where flush end plates are welded to the beam end to form a semi-rigid, partial strength connection. It was found that the current restriction of providing full shear connection design within hogging moment regions of continuous and semi-continuous structures could be relaxed. 8.6.2 Reduced Beam Section (RBS) Connections After Kobe and Northridge earthquakes lots of research was conducted (AIJ Kinki 1997, FEMA 2000) on reduced beam section (RBS) connections to avoid failure in beam-column connections and to deliberately move the maximum bending moment away from the beam ends. This can be achieved by utilising cuts or drilled Concrete-Filled Tubular Members and Connections 240 holes in both the top and bottom flanges to reduce the flange area over a certain length. The same concept was applied recently to steel-concrete composite beam to CFST square column connections (Park et al. 2008) and steel beam to CFST circular column connections (Wang et al. 2008). Typical reduced beams are shown in Figure 8.12. The reduced beam shown in Figure 8.12(a) only applies to the bottom beam flange. For this connection, failure did not occur at the reduced beam section but at the anchors inside the steel tube. To achieve the ductile failure of the reduced beam section, the capacity of the anchors inside the beam must be increased. This was proven to be impossible in a partially restrained connection. Hence the reduced beam section was found to be unsuitable for such a connection (Park et al. 2008). The reduced beam connection shown in Figure 8.12(b) failed in the RBS. Such a connection exhibited good seismic performance and ductility although the ultimate load reduced slightly (Wang et al. 2008). Anchors Concrete 150 Bottom flange of steel beam 375 50 SHS 400 x 400 x 12 (a) Steel–concrete composite beam to CFST column (adapted from Park et al. 2008) External ring Reduced section Concrete CHS 140 x 2.13 15 Steel beam 70 50 100 140 100 50 340 (b) Steel beam to CFST column (adapted from Wang et al. 2008) Figure 8.12 Typical reduced beams 8.6.3 CFST Connections for Fatigue Application Stress concentration is a major issue for welded tubular connections subject to fatigue loading (Zhao et al. 2001). One method to reduce the stress concentration of tubular connections is to fill the chord member with concrete. Udomworarat et CFST Connections 241 al. (2000) and Tong et al. (2008) studied the fatigue of concrete-filled tubular Kjoints, whereas Gu et al. (2008) and Mashiri and Zhao (2009) studied the fatigue of concrete-filled T-joints. It was found by Tong et al. (2008) that the hot-spot stress reduces about 30% due to concrete filling. Mashiri and Zhao (2009) found that on average the reduction of stress concentration factor is 40% and the fatigue life increases 1.7 times. 8.7 REFERENCES 1. AIJ Kinki, 1997, Full-scale test on plastic rotation capacity of steel wide flange beams connected with square steel tube columns, Committee of Steel Building Structures (Osaka: Kinki Branch of Architectural Institute of Japan). 2. AIJ, 1997, Recommendations for design and construction of concrete filled steel tubular structures (Tokyo: Architectural Institute of Japan). 3. AISC, 1999, Design capacity tables for structural steel hollow sections, 1st ed. (Sydney: Australian Institute of Steel Construction). 4. AISC, 2005, Specification for structural steel buildings, ANSI/AISC 360-05 (Chicago: American Institute of Steel Construction). 5. 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Eurocode 3, 2005, Design of Steel Structures – Part 8: Design of joints, BS EN1993-1-8:2005 (Brussels: European Committee for Standardization). 21. Eurocode 4, 2004, Design of steel and concrete structures–Part 1-1: General rules and rules for building, EN1994-1-1 (Brussels: European Committee for Standardization). 22. Eurocode 4, 2005, Design of composite steel and concrete structures, Part 1-2: General rules–structural fire design, EN1994-1-2:2005 (Brussels: European Committee for Standardization). 23. FEMA, 2000, Recommended seismic design criteria for new steel moment frame buildings, SAC Joint Venture, FEMA-350 (Washington DC: Federal Emergency Management). 24. France, J.E., Davison, J.B. and Kirby, P.A., 1999, Strength and rotational stiffness of simple connections to tubular columns using flowdrill connectors. Journal of Constructional Steel Research, 50(1), pp. 15-34. 25. Fu, G., Morita, K. and Ebato, K., 1998, Structural behaviour of beam-tocolumn connection of concrete filled circular tube column and H-beam space subassemblage. Journal of Structural Engineering, 508(1), pp. 157-164. 26. Gardner, A.P. and Goldsworthy, H.M., 2005, Experimental investigation of the stiffness of critical components in a moment-resisting composite connection. Journal of Constructional Steel Research, 61(5), pp. 1709-1726. 27. Gu, M., Tong, L.W., Zhao, X.L. and Lin, X.G., 2008, Stress intensity factors of surface cracks in welded T-joints between CHS brace and concrete-filled chord. In Proceedings of 12th International Symposium on Tubular Structures, Shanghai, China, pp. 359-366. 28. Han, L.H, Huo, J.S. and Wang, Y.C., 2007, Behaviour of steel beam to concrete-filled tubular column connections after exposure to fire. Journal of Structural Engineering, ASCE, 133(6), pp. 800-814. 29. Han, L.H., Li, W. and Uy, B., 2009, Seismic behaviour of concrete-filled steel tubular frame to RC shear wall high-rise mixture structures. Journal of Constructional Steel Research, 65(5), pp. 1249-1260. 30. Han, L.H., Qu, H., Tao, Z. and Wang, Z.F., 2008a, Experimental behaviour of CFST Connections 243 thin-walled steel tube confined concrete column to RC beam joints under cyclic loading. Thin-Walled Structures, 47(8-9), pp. 847-857. 31. Han, L.H., Wang, W.D. and Zhao, X.L., 2008b, Behaviour of steel beam to concrete-filled SHS column frames: Finite element model and verifications. Engineering Structures, 30(6), pp. 1647-1658. 32. Han, L.H. and Yang, Y.F., 2007, Modern technology of concrete-filled steel tubular structures, 2nd ed. (Beijing: China Architecture & Building Press). 33. Herrera, R., Ricles, J. and Sause, R., 2006, Experimental study of a large-scale composite MRF system with CFT columns under seismic loading. In Proceedings of the 8th U.S. National Conference on Earthquake Engineering, San Francisco, pp. 18-22. 34. Herrera, R.A., Ricles, J.M. and Sause, R., 2008, Seismic performance evaluation of a large-scale composite MRF using pseudodynamic testing. Journal of Structural Engineering, ASCE, 134(2), pp. 279-288. 35. Huck, 1994, The ultra-twist fastening system (Irvine, CA: Huck International Inc.). 36. Jones, M.H. and Wang, Y.C., 2010, Typing behavior of fin-plate connection to concrete-filled rectangular steel tubular column – Development of a simplified calculation method. Journal of Constructional Steel Research, 66(1), pp. 1-10. 37. Kamba, T., Kanatani, H., Fujiwara, Y. and Tabuchi, M., 1983, Empirical formulae for strength of steel tubular column to H-beam connections: Part 2 – A study on the tubular to beam connections. Transactions of Architectural Institute of Japan, 325, pp. 67-73. 38. Kodur, V.K.R. and Mackinnon, D.H., 2000, Design of concrete-filled hollow structural steel columns for fire endurance. Engineering Journal, AISC, 37(1), pp. 13-24. 39. Kurobane, Y., 1998, Improvement of I-beam to RHS column moment connections for avoidance of brittle fracture. In Proceedings of the 8th International Symposium on Tubular Structures, Singapore, pp. 3-17. 40. Kurobane, Y., 2002, Connections in tubular structures. Progress in Structural Engineering and Materials, 4(1), pp. 35-45. 41. Kurobane, Y., Makino, Y., Miura, K., Tokutome, Y. and Tanaka, M., 2001, Testing of new RHS column to beam connections with U-shaped welded connections. In Proceedings of the 9th International Symposium on Tubular Structures, Düsseldorf, Germany, pp. 493-502. 42. Kurobane, Y., Packer, J.A., Wardenier, J. and Yeomans, N., 2004, Design guide for structural hollow section column connections (Köln: Verlag TÜV). 43. Lee, S.L., Ting, L.C. and Shanmugam, N.E., 1993, Use of external T-stiffeners in box-column to beam connections. Journal of Constructional Steel Research, 26(2-3), pp. 77–98. 44. Loh, H.Y., Uy, B. and Bradford, M.A., 2006a, The effect of partial shear connection in composite flush end plate joints. Part 1 – Experimental study. Journal of Constructional Steel Research, 62(4), pp. 378-390. 45. Loh, H.Y., Uy, B. and Bradford, M.A., 2006b, The effects of partial shear connection in composite flush end plate joints. Part II – analytical study and design appraisal. Journal Constructional Steel Research, 62(4), pp. 391-412. 244 Concrete-Filled Tubular Members and Connections 46. Lu, L.H., 1997, The static strength of I-beam to rectangular hollow section column connections. PhD Thesis, Delft University of Technology, Delft, The Netherlands. 47. Makino, Y., Kurobane, Y., Fukushima, A. and Katgayama, M., 2001, Experimental study on concrete filled tubular joints under axial loads. In Proceedings of the 9th International Symposium on Tubular Structures, Düsseldorf, Germany, pp. 535-541. 48. Mashiri, F.R. and Zhao, X.L., 2009, Square hollow section (SHS) T-joints with concrete-filled chords subjected to in-plane fatigue loading in the brace. ThinWalled Structures, in press, Available online 8 October 2009. 49. Matsui, C., 1981, Design of connections in concrete filled steel square tubular structures, Research Report No. 5, Architectural Institute of Japan, ChugokuKyushu Division, Kyushu. 50. Matsui, C., 1985, Strength and behaviour of frames with concrete filled square steel tubular columns under earthquake loading. In Proceeding of 1st International Speciality Conference on Concrete Filled Steel Tubular Structures, Harbin, China, pp. 104-111. 51. Miura, K., Makino, Y., Kurobane, Y., Tanaka, M., Tokutome, K. and van der Vegte, G.J., 2002, Testing of beam-to-RHS column connections without weld access holes. International Journal of Offshore and Polar Engineering, 12(3), pp. 229-235. 52. Morita, K., 1994, Structural behavior of semi-rigid composite joint. In Proceedings of the 6th International Symposium on Tubular Structures, Melbourne, Australia, pp. 349-356. 53. Nie, J.G., Qin, K. and Xiao, Y., 2006, Push-over analysis of the seismic behavior of a concrete-filled rectangular tubular frame structure. Tsinghua Science and Technology, 11(1), pp. 124-130. 54. Nishiyama, I., Fujimoto, T., Fukumoto, T. and Yoshioka, K., 2004, Inelastic force-deformation response of joint shear panels in beam-column moment connections to concrete-filled tubes. Journal of Structural Engineering, ASCE, 130(2), pp. 244-252. 55. Ochi, K., Yamashita, Y., Kurobane, Y., Tokutome, K. and Tanaka, M., 1998, New bolted connections between RHS columns and I-section beams. In Proceedings of the 5th Pacific Structural Steel Conference, Seoul, Korea, pp. 753-758. 56. Packer, J.A. and Fear, C.E., 1991, Concrete-filled rectangular hollow section X and T connections. In Proceedings of the 4th International Symposium on Tubular Structures, Delft, The Netherlands, pp. 382-391. 57. Packer, J.A. and Henderson, J.E., 1997, Hollow structural section connections and trusses – A design guide, 2nd ed. (Toronto: Canadian Institute of Steel Construction). 58. Packer, J.A. and Kenedi, W.W., 1993, Concrete-filled rectangular hollow section K connections. In Proceedings of the 5th International Symposium on Tubular Structures, Nottingham, UK, pp. 220-227. 59. Park, S., Choi, S., Park, Y., Kim, Y. and Kim, J., 2008, Ductility characteristics of partially restrained beam-to-column composite connections CFST Connections 245 in concrete filled square tubes. Advanced in Structural Engineering, 11(5), pp. 565-575. 60. Park, J.M., Kang, S.M. and Yang, S.C., 2005, Experimental studies of wide flange beam to square concrete-filled tube column joints with stiffening plates around the column. Journal of Structural Engineering, ASCE, 131(12), pp. 1866-1876. 61. Ricles, J.M., Peng, S.W. and Lu, L.W., 2004, Seismic behavior of composite concrete filled steel tube column-wide flange beam moment connections. Journal of Structural Engineering, ASCE, 130 (2), pp. 223-232. 62. Schneider, S.P. and Alostaz, Y.M., 1998, Experimental behaviour of connections to concrete-filled steel tubes. Journal of Constructional Steel Research, 45(3), pp. 321–352. 63. Standards Australia, 1996, Structural steel – Hot-rolled plates, floorplates and slabs, Australia Standard AS/NZS 3678 (Sydney: Standards Australia). 64. Syam, A.A. and Chapman, B.G., 1996, Design of structural steel hollow section connections,1st ed. (Sydney: Australian Institute of Structural Steel). 65. Tabuchi, M., Kanatani, H. and Kamba, T., 1985, Empirical formulae for local strength of welded RHS column to H-beam connections: Part 2 – An experimental study on the welded RHS column to beam connections. Transactions of Architectural Institute of Japan, 352, pp. 79-89. 66. Tanaka, T., Tabuchi, M., Furumi, K., Morita, T., Usami, K., Murayama, M. and Matsubara, Y., 1996, Experimental study on end-plate to SHS column connections reinforced by increasing wall. In Proceedings of the 7th International Symposium on Tubular Structures, Miskolc, Hungary, pp. 253262. 67. Tong, L.W., Sun, C.Q., Chen, Y.Y, Zhao, X.L., Shen, B. and Liu, C.B., 2008, Experimental comparison in hot spot stress between CFCHS and CHS Kjoints with gap. In Proceedings of 12th International Symposium on Tubular Structures, Shanghai, China, pp. 389-395. 68. Udomworarat, P., Miki, C., Ichikawa, A., Sasaki, E., Sakamoto, T., Mitsuki K. and Hasaka, T., 2000, Fatigue and ultimate strengths of concrete filled tubular K-joints on truss girder. Journal of Structural Engineering, Japan Society of Civil Engineers, 46A (March), pp. 1627-1635. 69. Wang, J.F., Han, L.H. and Uy, B., 2009a, Behaviour of flush end plate joints to concrete-filled steel tubular columns. Journal of Constructional Steel Research, 65(4), pp. 925-939. 70. Wang, J.F., Han, L.H. and Uy, B., 2009b, Hysteretic behaviour of flush end plate joints to concrete-filled steel tubular columns. Journal of Constructional Steel Research, 65(8-9), pp. 1644-1663. 71. Wang, W.D., Han, L.H. and Uy, B., 2008, Experimental behaviour of steel reduced beam section to concrete filled circular hollow section column connections. Journal of Constructional Steel Research, 64(5), pp. 493-504. 72. Wang, W.D., Han, L.H. and Zhao, X.L., 2009, Analytical behaviour of frames with steel beams to concrete-filled steel tubular column. Journal of Constructional Steel Research, 65(3), pp. 497-508. 246 Concrete-Filled Tubular Members and Connections 73. Wang, Y.C. and Davies, J.M., 2003, An experimental study of the fire performance of non-sway loaded concrete-filled steel tubular column assemblies with extended end plate connections. Journal of Constructional Steel Research, 59(7), pp. 819-838. 74. Winkel, G.D. de, 1998, The static strength of I-beam to circular hollow section column connections. PhD Thesis, Delft University of Technology, Delft, The Netherlands. 75. Yao, H., Goldsworthy, H. and Gad, E., 2008, Experimental and numerical investigation of the tensile behaviour of blind-bolted T-stub connections to concrete-filled circular columns. Journal of Structural Engineering, ASCE, 134(2), pp. 198-208. 76. Zhao, X.L., Herion, S., Packer, J.A., Puthli, R., Sedlacek, G., Wardenier, J., Weynand, K., van Wingerde, A. and Yeomans, N., 2001, Design guide for circular and rectangular hollow section joints under fatigue loading (Köln: Verlag TÜV). CHAPTER NINE New Developments This chapter addresses some of the issues related to the application and construction of concrete-filled tubular structures, e.g. the effect of long-term loading on the behaviour of CFST columns, the effect of axial local compression and pre-loads on the CFST column capacity. This chapter also presents some innovative concepts in concrete-filled tubular structures, e.g. SCC (selfconsolidating concrete) filled tubular members, concrete-filled double skin tubes (CFDST) and FRP (fibre reinforced polymer) confined CFST columns. 9.1 LONG-TERM LOAD EFFECT CFST columns are susceptible to behaviours under long-term load, a common phenomenon in concrete structures. Such a problem has not been addressed satisfactorily by the existing design codes. The temperature field during cement hydration, and the shrinkage of the concrete core in self-consolidating concrete (SCC)-filled steel tubes are experimentally studied by Han et al. (2005a). The main parameters are sectional dimensions and sectional types. It was found that the characteristics of the temperature field in CFST specimens are similar to those of normal concrete (NC) members during cement hydration. The shrinkage value of the concrete core in CFST specimens is significantly smaller than that of NC alone. Figure 9.1(a) gives a comparison of the measured shrinkage of NC and concrete core in CFST specimens for similar overall dimensions. The sectional type has only a minor influence on the shrinkage. The sectional size of the column has a significant influence on the shrinkage of the specimen. The shrinkage in a specimen decreases with the increased sectional size, as shown in Figure 9.1(b). Based on the measured results, shrinkage model proposed by ACI 209 (1992) specifications for normal concrete was modified to predict the shrinkage of the concrete core in CFSTs. The shrinkage value of core concrete in CFSTs can be expressed as: (9.1) (H sh ) t - CFST §¨ t ·¸ (H sh ) max - CFST © 35 t ¹ where t is time (in day), (Hsh)max-CFST is the ultimate shrinkage strain of core concrete in CFSTs given as: (H sh ) max - CFST Eu E u Hsh max 0.0002 D size 0.63 (9.2a) (9.2b) Concrete-Filled Tubular Members and Connections 248 400 CFST 300 İ sh (ȝİ) NC 200 100 0 50 250 450 t (day) 700 900 (a) Normal concrete (NC) alone and concrete core in CFST 300 200mm in diameter 1000mm in diameter 240 İ sh (ȝİ) 180 120 60 0 50 250 450 t (day) 700 900 (b) Sectional dimensions for CFST specimens Figure 9.1 Effect of different parameters on concrete shrinkage in which (Hsh)max is the ultimate shrinkage strain of normal concrete (ACI 209 1992), Eu is a factor reflecting the restraint against the core concrete shrinkage provided by the outer steel tubes, and Dsize is the overall dimension of the steel tube (in mm). The validity range of Dsize is between 100mm and 1200mm. Strength index kcr can be used to quantify the influence of long-term sustained load on the concrete-filled HSS columns. It is expressed as: N uL k cr (9.3) Nu where NuL is the ultimate load of the composite columns subjected to long-term sustained loads, and Nu is the ultimate load under short-term loading condition. The research conducted by Han et al. (2004a) and Han and Yang (2003) revealed that kcr depends on three parameters, namely the constraining factor ([), the column slenderness ratio (O) and load eccentricity ratio (e/r), where e is the New Developments 249 load eccentricity, r is d/2 for CHS and B/2 for SHS. Some typical values of kcr are given in Table 9.1 for concrete-filled circular columns. It was found that the maximum strength reduction of the composite columns due to long-term load effects could be expected to be roughly 20% of their strength under short-term loading. Table 9.1 Some typical values of kcr for concrete-filled circular columns O 20 40 80 100 120 e/r = 0 0.928 0.872 0.808 0.800 0.808 [=1 e/r = 0.5 0.959 0.930 0.849 0.834 0.837 e/r = 1 0.970 0.950 0.863 0.846 0.847 e/r = 0 0.944 0.903 0.836 0.828 0.836 [=2 e/r = 0.5 0.976 0.963 0.879 0.864 0.867 e/r = 1 0.987 0.984 0.893 0.876 0.877 e/r = 0 0.954 0.921 0.854 0.845 0.854 [=3 e/r = 0.5 0.986 0.983 0.897 0.881 0.884 e/r = 1 0.997 1.000 0.912 0.894 0.895 9.2 SOME CONSTRUCTION-RELATED ISSUES 9.2.1 Effects of Local Compression 9.2.1.1 General In practice, CFST columns are often subject to axial local compression, in situations such as the pier of a girder bridge, the underneath-bearing members of rigid frame, reticulate frame and arch structures. Figure 9.2 illustrates a schematic view of the CFST columns under axial local compression, where AC is the crosssectional area of concrete and AL is the local compression area. In recent years, studies were carried out on the behaviour of steel tube confined concrete and CFST columns under axial local compression (Han et al. 2008a, 2008b). It was found that, compared with unconfined concrete, the distribution of the cracks around the local compression zone is more uniform for CFSTs. Detailed parametric studies were also conducted to investigate the influences of the following factors on the section capacity of CFST columns subjected to axial local compression: sectional type, local compression area ratio, steel ratio, steel and concrete strength and endplate thickness. The parametric studies provide information for the development of formulae for the calculation of the sectional capacity of the composite columns under such conditions. The main findings are summarised in this section. 9.2.1.2 Load-deformation curve Figure 9.3 schematically shows the typical curves of axial load (N) versus axial deformation (') for CFSTs subjected to axial local compression. Concrete-Filled Tubular Members and Connections 250 N N Bearing plate Bearing plate Top end plate Top end plate Circular hollow section Square hollow section Concrete Concrete AL AL Ac Ac Figure 9.2 CFST columns subjected to axially local compression N BC A [![ o or E!9) D D [ ~ [o and E9) or [[o and E ~ 9) [[ o and E9) D 0 ' Figure 9.3 Typical N–' relationships (schematic view) It was found that the curves are a function of the confinement factor ([) and the local compression area ratio (E) defined as: Ac E (9.4) AL It can be seen from Figure 9.3 that, in general, with the increase of [ and E, the descending branch of the N–' curve becomes less steep. There is no descending branch when [ is greater than [o or E is greater than nine. It was found that the values of [o for concrete-filled CHS (circular hollow section) and SHS (square New Developments 251 hollow section) can be given by 1.1 and 4.5, respectively (Han 2007). Furthermore, the descending branch of CFSTs with square sections appears earlier and is steeper than that of CFSTs with circular sections. There are three or four stages in N–' curves, as shown in Figure 9.4: (1) Stage 1: Elastic stage (from point 0 to point A). During this stage, steel and concrete are in the elastic state, and there is no confined stress between them. The proportional stress (about 75% of fy) of steel occurs at point A. (2) Stage 2: Elastic-plastic stage (from point A to point B). During this stage, concrete is confined by the steel tube because the Poisson ratio of the concrete is larger than that of steel. The confinement enhances as the longitudinal deformation increases. At point B, the steel tube near the top of the composite column enters into a plastic state, and the maximum longitudinal stress of concrete is attained. (3) Stage 3: Strain hardening stage (from point B to point C or from point B to point D). During this stage, N–' curves tend to go upwards. The shape of the curve depends on the value of confinement factor ([) and local compression area ratio (E). If [ is larger than [o or E is greater than nine the curve goes up steadily to points C and D. When [o and E are relatively small, the curve starts to go down after a short increase to point C. The smaller the confinement factor and local compression area ratio, the earlier the curve starts to descend. (4) Stage 4: Falling stage (from point C to point D). This occurs only when the confinement factor ([) is less than [o, and the local compression area ratio (E) is less than nine. The smaller the confinement factor and the local compression area ratio, the steeper the falling stage. 9.2.1.3 Sectional capacities It was found (Han 2007) that the possible parameters that influence the sectional capacities of CFST under axial local compression are local compression area ratio (E , steel ratio (D steel and concrete strength and the top endplate thickness (ta). For convenience of analysis, strength index (KLC) is used to quantify the effects of the above parameters on the sectional capacity of CFST columns: N uL K LC (9.5) Nu where NuL is the axial compressive capacity of locally loaded CFST and Nu is the axial compressive capacity of fully loaded CFST. In order to further clarify the influence of endplate rigidity, the relative rigidity radius of the endplate (nr) was defined (Han 2007) as for concrete-filled circular sections: 1 nr 1 § · 4 § E s t 3a · 4 4 ¸ ¨ ¸ ¨ ¨ 3(1 P 2 ) ¸ ¨ E d 3 ¸ s ¹ © ¹ © (9.6) Concrete-Filled Tubular Members and Connections 252 where Ɯ is the axial stiffness ratio defined as Ɯ = (Es u As + Ec u Ac)/Asc, Asc (= As + Ac) is the cross-sectional area of the composite section, Ps is the Poisson ratio of steel and d is the outside diameter of the CHS. For CFSTs with square sections, d should be replaced by B in Eq. (9.6). Examples are given below to show the influence of E, D and nr on the strength index (KLC) for a composite column with d or B of 400mm and length of 1200mm. Figure 9.4 shows the influences of the local compression area ratio (E) and steel ratio (D) on KLC. The calculating conditions for the examples are CHS CFST: fy = 345MPa, fcu= 60MPa, ta = 0.1mm, E = 1 to 25 and D = 0.04 to 0.2. 1.2 D = 0.05 D = 0.1 D = 0.15 K LC 0.8 0.4 0 1 7 13 E 19 25 Figure 9.4 Influence of local compression area ratio (E) and steel ratio (D) on the strength index (KLC) It can be seen that KLC decreases with the increase of E. For concrete-filled CHS, KLC decreases slowly with the increase of E For concrete-filled SHS, however, KLC decreases quickly when E is relatively small (i.e. E d 9). It can also be found from Figure 9.4 that, for concrete-filled CHS, KLC increases with the increase of D Such an increase in KLC is not observed for concrete-filled SHS. This matches the fact that the confinement of the circular steel tube to its core concrete is better than that provided by the square steel tube. Figure 9.5 indicates the influences of the relative rigidity radius of the endplate (nr) on KLC. The calculating conditions are CHS CFST with D = 0.1, fy = 345MPa, fcu = 60MPa and E = 1 to 25. It can be seen from Figure 9.5 that KLC increases with the increase of nr. KLC increases quickly when nr is relatively small and increases slowly when KLC is close to unity. At the same value of nr and E, KLC of circular CFST is higher than that of square CFST. This again reflects the fact that the confinement of circular steel tubes to its concrete core is better than that provided by square steel tubes. It was found that, in general, KLC slightly decreases with the increase of the steel yielding strength and the increase of concrete strength. New Developments 253 1.2 K LC 0.8 0.4 0 E = 1.21 E=9 E = 25 0 0.2 0.4 nr 0.6 0.8 1 Figure 9.5 Influences of relative rigidity radius of the endplate on KLC 9.2.2 Pre-Load Effect One of the advantages of using concrete-filled steel CHS or SHS columns is that steel tubes can provide permanent and integral formwork for the concrete infill. The bare steel tubular columns are designed to resist the gravity loads and the construction loads. Figure 9.6 illustrates a concrete-filled steel tubular column during construction (Han and Yao, 2003; Uy and Das, 1997). It is obvious that the steel tube will be subjected to pre-load due to the axial loads and hydrostatic loads imposed on a steel tubular column during construction and wet concrete pumping operations. Unfilled steel tube Concrete is pumped up Second floor Wet concrete First floor Steel beam Composite slab Concrete pump Ground Figure 9.6 A concrete-filled steel tube during construction The CFST columns are thus susceptible to the effects of pre-load on the steel tubes during construction. An attempt to predict the load-deformation behaviour of CFST beam-columns was reported by Han and Yao (2003). A comparison of results calculated using this model showed good agreement with test results (within an 8% difference). Concrete-Filled Tubular Members and Connections 254 Strength index (kp) is defined in Eq. (9.7) to quantify the influence of preload on the steel tubes on the concrete-filled composite columns (Han and Yao 2003). N up (9.7) kp Nu where Nup and Nu are the ultimate loads of the composite columns with or without pre-load on the steel tubes, respectively. The strength index (kp) can be expressed in terms of slenderness ratio (O), load eccentricity ratio (e/r) and the pre-load ratio (PLR). kp 1 f (O o ) f (e / r ) PLR (9.8) where f(Oo) is the function for accounting the influence of the slenderness ratio (O) and can be expressed as: For concrete-filled steel SHS columns: 0.14O o 0.02 f (O o ) ® 2 ¯ 0.15O o 0.42O o 0.11 For concrete-filled steel CHS columns: 0.17O o 0.02 f (O o ) ® 2 ¯ 0.13O o 0.35O o 0.07 (O o d 1) (O o ! 1) (O o d 1) (O o ! 1) in which Oo = O/80. The function of f(e/r) in Eq. (9.8) takes into account the influence of the load eccentricity ratio (e/r), where e is the load eccentricity, r is d/2 for CHS and B/2 for SHS. The function can be expressed as: For concrete-filled steel SHS: °1.35(e/r ) 2 0.04(e/r ) 0.8 f (e/r ) ® °̄ 0.2(e/r ) 1.08 For concrete-filled steel CHS: ° 0.75(e/r ) 2 0.05(e/r ) 0.9 f (e/r ) ® °̄ 0.15(e/r ) 1.06 The pre-load ratio PLR is defined as: Vo NP PLR N us M f y (e/r d 0.4) (e/r ! 0.4) (e/r d 0.4) (e/r ! 0.4) (9.9) where Np (= VoAs) is the pre-load on steel tubes, Nus is the ultimate strength of the unfilled steel tubular column (Nus = MfyAs), Vo is the pre-stress in the steel tube, fy is the yield stress of the steel tube, As is the cross-sectional area of the steel tube and M is the stability ratio of the unfilled steel tubular column. New Developments 255 9.3 SCC (SELF-CONSOLIDATING CONCRETE)-FILLED TUBES Self-consolidating concrete (SCC) is a new technology in concrete which originated in Japan in 1980s (Okamura and Ouchi 2003). SCC can fill every part of the mould or framework by its own weight without the external mechanical aid for compaction. The use of SCC can increase the workability of the concrete, reduce noise impact on environment, and speed up the construction. Due to its good performance, SCC has been more and more widely accepted and applied in Japan, the USA, Europe and other countries (Ouchi et al. 2003). SCC has a great potential in CFST columns because of the difficulty in compacting concrete in steel tubes by vibration. The use of SCC in CFST can improve the construction quality of concrete, thus ensuring the performance of CFST. Due to the workability requirement of SCC in a fresh state, the mixture of SCC is obviously different to that of conventional concrete. Use of superplasticiser and a low water/binder ratio are the typical characteristics in the SCC mixture. On the other hand, it is not difficult to obtain high-strength SCC by the mixture. A case study conducted by Domone (2006) showed that 20% of SCC used in 46 projects in Japan, the USA and Europe had concrete compressive strength over 60MPa. Table 9.2 lists one typical mixture proportion of self-consolidating concrete prepared at Monash University. Slump flow tests or L-box tests (see Figure 9.7) can be used to determine the workability of the SCC. Table 9.3 lists the commonly used workability for the SCC. Table 9.2 Mixture proportion of self-consolidating concrete (kg/m3) Water Cement Fly ash Sand 178 380 170 776 Coarse aggregate 831 Superplasticiser 11 Table 9.3 Workability of the self-consolidating concrete Slump (mm) Slump flow (mm) T50 (s) T40 (s) H1 (mm) H2 (mm) Flow speed (mm/s) 273 694–740 3.1 3.6 530 60 111 256 Concrete-Filled Tubular Members and Connections (a) Slump flow test of SCC (b) Test of SCC in an L-box Figure 9.7 Tests to determine the workability of SCC Despite differences between SCC and conventional concrete in a fresh state, the material properties of SCC are generally similar to those of conventional concrete (ACI 237R-07 2007). Research on the structural behaviour of SCC-filled CFST columns and beams under ambient temperature found that the behaviour of an SCC-filled CFST is also similar to that filled with conventional concrete (Han and Yao 2004, Han et al. 2005b, 2006a). Comparisons are made with predicted section capacity using the existing codes, such as ACI (1999), AIJ (1997), AISCLRFD (1999), BS5400 (BSI 2005) and EC4 (2004). It seems that the conclusion regarding predictions using existing design codes made for normal concrete (NC) filled steel tubular columns remains the same for SCC-filled tubular columns. It was also found that the features of SCC-filled columns under a constant axial load and cyclically increasing flexural loading are similar to those of normal concretefilled steel tubular columns. Studies on SCC-filled tubular sections under elevated temperatures were recently carried out (Lu et al. 2006) where the strength of SCC reached 100MPa. New Developments 257 9.4 CONCRETE-FILLED DOUBLE SKIN TUBES 9.4.1 General Double skin composite construction (Wright et al. 1991a, 1991b) and “Bisteel” (Corus 2006) consist of an inner and outer steel skin with the annulus between the skins filled with concrete. This type of steel–concrete–steel sandwich (SCSS) double skin system was originally used as tube tunnels (Montague 1975, Roberts et al. 1995, Shakir-Khalil 1991, McKinley and Boswell 2002). The sandwich cross- section was shown to have high bending stiffness that avoids instability under external pressure. The perceived advantages of the system are that the external steel plates act as both primary reinforcement and permanent formwork, and also as impermeable, impact and blast-resistant membranes. The full depth and overlapping stud connectors transfer normal and shearing forces between the concrete and steel plates, and also act as transverse shear reinforcement (Roberts et al. 1996). It is therefore understandable why steel–concrete–steel sandwich panels have been alternatively suggested for their use in: submerged tube tunnels, blast resistant structures, and nuclear containment, liquid and gas-retaining structures. Investigations undertaken by Lan et al. (2005) and El-Badawy et al. (2003) concluded that the steel–concrete–steel formation significantly increases blast resistance. A novel double skin sandwich composite system has been proposed by Liew and Wang (2005), which adopted various forms of shear connectors. In recent years, a concept called concrete-filled double skin tubes (CFDST) was developed (Zhao and Han 2006). The idea was from steel–concrete–steel sandwich (SCSS) and concrete-filled steel tubes (CFST). There may be a potential for concrete-filled double skin tubes to be used as columns in building structures, bridge piers and composite piles in offshore applications. There are four combinations of square hollow section (SHS) and circular hollow section (CHS) as outer and inner tubes. The dimensions are defined in Figure 9.8. The behaviour of such members subjected to static and dynamic loads and fire condition are described in this section. 9.4.2 CFDST Members Subjected to Static Loading 9.4.2.1 Axial compressive capacity A series of tests were conducted by Zhao and Grzebieta (2002), Zhao et al. (2002a, 2002b, 2010) and Elchalakani et al. (2002) on concrete-filled double skin tubular stub columns with four combinations of the outer tube and the inner tube. It was found that the outer tube of CFDST behaves like the steel tube in CFST whereas the inner tube of CFDST behaves similarly to that of an unfilled tube. A comparison of typical failure modes is given in Figure 9.9. Concrete-Filled Tubular Members and Connections 258 outer tube t0 t0 Jext 0 Jint 0 ti Jext i Jint i inner tube outer tube Di ti D0 di d0 concrete Bi concrete inner tube B0 (a) SHS + SHS t0 (b) CHS + CHS outer tube outer tube t0 Jext 0 Jint 0 ti inner tube di D0 ti Jext i Jint i inner tube Di Bi concrete concrete d0 B0 (c) SHS + CHS (d) CHS + SHS Figure 9.8 Dimensions of CFDST (adapted from Zhao and Han 2006) CHS outer alone with D/t of 55 CFSDT with D/t of 55 CHS outer alone with D/t of 96 CFSDT with D/t of 96 Figure 9.9 Comparison of typical failure modes at axial deformation of 100mm (outer CHS alone versus CFDST (CHS+CHS); Zhao et al. 2010) New Developments 259 Axial Load (kN) CFDST (CHS Outer + CHS Inner) CHS Outer Axial Shortening (mm) (a) Specimen with D/t of 55 Axial Load (kN) CFDST (CHS Outer + CHS Inner) CHS Outer Axial Shortening (mm) (b) Specimen with D/t of 96 Figure 9.10 Typical behaviour of CFDST versus that of outer steel tube (adapted from Zhao et al. 2010) Typical behaviour of CFDST stub columns is compared in Figure 9.10 with that of the relevant outer steel tube. It can be seen that there is a significant increase in the ultimate load-carrying capacity and ductility. The energy absorption (defined as the area under an axial load-shortening curve) is compared in Figure 9.11 where an increase up to 14 times is obtained. It seems that more increase in ductility and energy absorption has been observed for concrete-filled double skin tubes having slender outer tubes with larger diameter-to-thickness ratio. The section capacity of concrete-filled double skin tubes in compression can be estimated using the superposition method, i.e. a sum of capacities of the outer tube, inner tube and the concrete. N CFDST N outer N concrete N inner (9.10) The formulae for Nouter, Ninner and Nconcrete can be simplified as follows, if the corner radii (rext and rint) are ignored. (9.11a) N outer f yo A outer N inner N concrete f yi A inner k c f c A concrete (9.11b) (9.11c) Concrete-Filled Tubular Members and Connections 260 16 14 Energy Ratio (CFDST/Outer Tube) 12 SHS Outer + SHS Inner (Zhao and Grzebieta 2002) 10 CHS Outer + CHS Inner (Zhao et al. 2002a, 2008) 8 SHS outer & CHS Inner (Zhao et al. 2002b) CHS Outer + SHS Inner (Elchalakani et al. 2002) 6 4 2 0 0 20 40 60 80 100 120 Outer Tube Width-to-Thickness or Diameter-to-Thickness Ratio Figure 9.11 Energy absorption of CFDST versus that of outer steel tube where fyo is the yield stress of the outer tube, fyi is the yield stress of the inner tube, fc is the compressive strength of concrete. The simplified expression of the crosssectional area is given in Table 9.4 where dimensions are defined in Figure 9.8. The term kc is the reduction factor on the concrete strength as that defined in AS3600 (Standards Australia 2001). For CFDST the value of kc is taken as 0.85 for all the combinations except for that with circular hollow section (CHS) as both outer and inner tubes. This reflects, to some extent, better confinement provided by the combination of CHS outer and CHS inner. The collapse behaviour of concrete-filled double skin tubular stub columns can be estimated using the plastic mechanism analysis (Zhao 2003). Details were given in Zhao et al. (2002c) to predict the unloading curves for concrete-filled double skin tubes with square hollow section (SHS) as both outer and inner tubes. New Developments 261 Table 9.4 Simplified expression of cross-sectional area Combination Aouter Ainner Aconcrete SHS outer and SHS inner SHS outer and CHS inner Do Bo ( Do 2t o ) ( Bo 2t o ) Do Bo ( Do 2t o ) ( Bo 2t o ) S ( Di ti ) ti Di Bi ( Di 2ti ) ( Bi 2ti ) ( Do 2t o ) ( Bo 2t o ) Di Bi ( Do 2t o ) ( Bo 2t o ) S 4 d i2 Combination Aouter CHS outer and CHS inner S ( Do to ) to CHS outer and SHS inner S ( Do to ) to Ainner S ( Di ti ) ti Di Bi ( Di 2ti ) ( Bi 2ti ) Aconcrete S 4 ( Do 2to ) 2 S 4 di2 S 4 ( Do 2to ) 2 Di Bi 9.4.2.2 Bending capacity Four-point bending tests were conducted on concrete-filled double skin tubular beams (Zhao and Grzebieta 2002, Han et al. 2004b). The failure modes of outer and inner tubes are shown in Figure 9.12. Similar to concrete-filled double skin tubes in compression, it can be concluded that the outer tube behaves in the same way as a concrete-filled tube, whereas the inner tube behaves in a similar way as an unfilled tube. Based on this experimental observation, the ultimate moment capacity of CFDST (MCFDST) can be estimated using the sum of the section capacity of an inner tube and that of an outer tube filled with concrete, i.e. M CFDST M inner M outer - with - concrete (9.12) where Minner is the ultimate moment capacity of the unfilled inner tube, Mouter-withconcrete is the ultimate moment capacity of the outer steel tube together with the infilled concrete, which can be derived in a similar way as that described in Chapter 3 for fully filled tubes. The expression of Minner is similar to that given in Eq. (3.5), i.e. 1 ª º M inner f yi t i «B i ( D i t i ) ( D i 2 t i ) 2 » (9.13) 2 ¬ ¼ Derivations of Mouter-with-concrete were given in Zhao and Grzebieta (2002) for CFDST with cold-formed RHS as both outer and inner tubes, based on a full plastic stress distribution in the outer steel tube. It should be noted that two cases need to be considered for the neutral axis position, i.e. above or below the top surface of the inner tube (see Figure 9.13). Concrete-Filled Tubular Members and Connections 262 Outward mechanism of outer tube Inward mechanism of inner tube (a) SHS Outer and SHS Inner CFDST beam (Zhao and Grzebieta 2002) (b) SHS outer and CHS inner CFDST beam (Han et al. 2004b) Figure 9.12 Failure modes of CFDST beams I J L K Neutral axis above the top surface of the inner tube Neutral axis below the top surface of the inner tube Concrete Outer tube Inner tube Figure 9.13 Neutral axis positions in the CFDST beam New Developments 263 When the neutral axis is above the top surface of the inner tube, the moment capacity becomes the same as that for fully filled tubes. When the neutral axis is below the top surface of the inner tube, the moment capacity contributed by the concrete block IJKL (see Figure 9.13), as in the fully filled case, should not be included. The calculations of Mouter-with-concrete can be simplified to the following steps. Step 1: calculate dn according to Eq. (3.2) and Eq. (3.3) by using the dimensions and material properties of the outer tube, i.e. § D 2 to · (9.14a) d n ¨¨ o ¸¸ FRHS 2 © ¹ where FRHS | 1 1 f c Bo 1 4 f yo t o (9.14b) Step 2: check if the neutral axis is above the top surface of the inner tube, i.e. check if § D 2 t o Di · d n ¨¨ o (9.15) ¸¸ 2 © ¹ Step 3a: if the condition in Eq. (9.15) is true, calculate Mouter-with-concrete according to Eq. (3.5) with the dimensions and material properties of the outer tube, i.e. M outer - with - concrete 1 º ª f yo t o «Bo (D o t o ) (D o 2 t o ) 2 » 2 ¼ ¬ 1 1 f y o t o (D o 2 t o ) 2 (1 FRHS ) 2 (Bo 2 t o ) d 2n f c 2 2 (9.16) where dn is given by Eq. (9.14) Step 3b: if the condition in Eq. (9.15) is not true, recalculate dn using the following equation: § Do 2 t o · ¨¨ ¸¸ FRHS 2 © ¹ 1 FRHS | 1 f c B o 2 t o Bi 1 4 f yo to dn (9.17a) (9.17b) Concrete-Filled Tubular Members and Connections 264 then calculate Mouter-with-concrete according to Eq. (3.5) with a deduction of the extra moment capacity due to concrete block IJKL (see Figure 9.13), i.e. (9.18a) M outer - with - concrete M CFST, RHS M extra M CFST, RHS 1 ª º f yo t o «Bo (D o t o ) (D o 2 t o ) 2 » 2 ¬ ¼ 1 1 f y o t o (D o 2 t o ) 2 (1 FRHS ) 2 (Bo 2 t o ) d 2n f c 2 2 (9.18b) 2 D 2 t o Di º ª 1 B i «d n o » fc 2 2 ¼ ¬ M extra (9.18c) where dn is given by Eq. (9.17) The moment capacity formulae for other combinations shown in Figure 9.8 are given in Zhao and Choi (2010). 9.4.2.3 Capacity under combined compression and bending Tests on concrete-filled double skin tubular beam-columns were carried out by Han et al. (2004b) and Tao et al. (2004). The main parameters varied in the testing programme are: (1) hollow section ratio (i.e. diameter or width of the inner tube to that of the outer tube), (2) outer tube diameter or width to thickness ratio, (3) column slenderness and (4) load eccentricity. Mechanics models were developed to predict the behaviour of concrete-filled double skin tubular stub columns, beams, columns and beam-columns. The unified theory (Han et al. 2001) was adopted in the derivation, where a confinement factor was introduced to describe the composite action between the steel tube and the sandwiched concrete. The interaction formulae for concrete-filled double skin tubes are similar to those given by Han et al. (2001) for concrete-filled beam-columns. They can be expressed as: K 1 9 M for K t 2K'o (9.19a) K'o N 1 0.25 1 2 NE M 2 9 1 0.25 in which K N NE N N u , CFDST § K· §K· a ¨¨ ¸¸ b ¨¨ ¸¸ 1 ©M¹ ©M¹ for K 2K'o (9.19b) New Developments 9 NE a 265 M M u , CFDST elastic S 2 E sc (A outer A concrete ) O2 1 9 'o K'o2 b 2K'o (1 9'o ) M K'o K'o M3 Ko M is the stability reduction factor for composite slender columns given as 1 if O d Oo °° if O o O d O p M ®C1 O2 C 2 O C 3 ° C 4 / (O 35) 2 if O ! Op °¯ where Nu,CFDST is the section capacity of concrete-filled double skin tubes in compression, Mu,CFDST is the section bending moment capacity of concrete-filled double skin tubes, Aouter is the cross-sectional area of the outer tube, Aconcrete is the elastic cross-sectional area of concrete, E sc is the section modulus of the composite sections in elastic stage and O is the slenderness ratio of the composite columns. The rest of the symbols are defined as follows: Ko §f · 0.2 ¨ ck ¸ © 20 ¹ 0.65 § 235 · ¸ ¨ ¨ f yo ¸ © ¹ 0.38 § 0.1 · ¨ ¸ © D ¹ 0.45 9'o 1 M5 (9 o 1) 9o C1 1.46 (O p O o ) 2 C2 C 5 2 C1 O p C3 1 C1 O2o C 2 O o C5 1.65 § 235 · ¸ ¨ ¨ f yo ¸ © ¹ 1 (35 2 O p O o ) C 5 §f · 1 0.11 ¨ ck ¸ © 20 ¹ C 4 (O p 35) 3 1.4 § 0.1 · ¨ ¸ © D ¹ Concrete-Filled Tubular Members and Connections 266 C4 C4 0.3 0.05 § § ·· ¨13,000 4657 ln¨ 235 ¸ ¸ §¨ 25 ·¸ §¨ D ·¸ for circular hollow section ¨ f yo ¸ ¸ ¨© f ck 5 ¸¹ ¨ © 0.1 ¹ © ¹¹ © 0.3 0.05 § ·· § ¨13,500 4810 ln¨ 235 ¸ ¸ §¨ 25 ·¸ §¨ D ·¸ for square hollow section ¨ f yo ¸ ¸ ¨© f ck 5 ¸¹ ¨ © 0.1 ¹ ¹¹ © © D A outer A c,nominal A c, nominal is the nominal cross-sectional area of concrete defined as A c, nominal (B o 2t o ) (D o 2t o ) for square hollow section (SHS) outer tube and S (d o 2 t o ) 2 4 for circular hollow section (CHS) outer tube. °1743 f y for CHS Op ® °̄1811 f y for SHS A c, nominal Oo ° S (420[ 550) [(1.02[ 1.14) f ck ] for CHS ® °̄S (220[ 450) [(0.85[ 1.18) f ck ] for SHS [ D f yo f ck where the units for fyo and fck (characteristic concrete strength) are N/mm2. 9.4.3 CFDST Members Subjected to Dynamic Loading 9.4.3.1 Cyclic loading Three stub columns, three beams and nine beam-column tests on concrete-filled double skin tubes were reported by Lin and Tsai (2005). The main experimental parameters are the thickness of the outer tube and the magnitude of the axial load. The test results have shown that the CFDST beam-columns can effectively provide strength and deformation capacity, even with a large diameter-to-thickness ratio (100–150 for the outer tubes, and 90 for the inner tubes). Cyclic tests were performed on four concrete-filled double skin tubular beam-columns and two concrete-filled tubular specimens by Yagishita et al. (2000). The CFDST beam-columns showed satisfactory ultimate strengths and New Developments 267 restoring force characteristics. However, no theoretical model or formula was given to predict the load-carrying capacities of concrete-filled double skin tubular beam-columns. Nakanishi et al. (1999) studied several short CFDST column specimens with steel box cross-sections subject to cyclic loading. They explored the method of inserting an additional steel tube to the inside of a steel bridge pier to form a concrete-filled double skin tubular member. Their tests involved examining the seismic behaviour of square hollow section (SHS) members, SHS concrete-filled tubular members and concrete-filled double skin tubular members (SHS outer and CHS inner). Results from these tests concluded that the CFDST members showed the best performance under cyclic loading. Han et al. (2006b) conducted 28 concrete-filled double skin tubular beamcolumn tests under constant axial load and cyclical flexural loading. Sixteen specimens had a combination of SHS outer and CHS inner, whereas the rest of them had CHS as both outer and inner members. The CFDST beam-columns were found to have a significant increase in strength, ductility and dissipated energy over the outer jackets. In general, the ductility and dissipated energy ability of specimens with CHS outer skin are higher than those of the specimens with SHS outer skin. The mechanics model developed for concrete-filled tubular beamcolumns subjected to constant axial load and cyclical flexural loading (Han et al. 2003, Han and Yang 2005) was used to analyse the behaviour of concrete-filled double skin tubular beam-columns. It was found that the predicted cyclic responses for the composite beam-columns are generally in reasonable agreement with test results. 9.4.3.2 Impact loading Corbett et al. (1990) found that concrete-filled double skin tubes are not capable of withstanding localised quasi-static loading to any great degree without partial failure. From their investigations it was reported that to overcome this, the minimum infill material thickness must exceed 38mm in order to see a three-fold increase in the energy required to penetrate the column. The concrete filler is most effective in withstanding projectile impact when the inner skin is not deformed. It is therefore recommended that sandwich tubes with 1mm-thick steel skins require a filler thickness five times greater than the thickness of the steel tubes. For thicker steel tubes the required filler thickness would probably be less due to the transition to a less favourable shear-dominated mechanism in the steel tube. 9.4.4 CFDST Members Subjected to Fire Lu et al. (2010) conducted an experimental investigation on fire resistance of SCC- filled CFDST columns under standard fire. Typical failure mode of specimen was overall buckling which is shown in Figure 9.14. It was found that the eccentrically loaded specimen had much more lateral deflection than the Concrete-Filled Tubular Members and Connections 268 concentrically loaded ones. There were obvious local outward bulges in specimens with square outer tubes, whereas only minor local outward bulges were observed in specimens with circular outer tubes. After the test, the outer steel tubes were removed to observe the failure mode of the concrete. It was found that the concrete was crushed at positions corresponding to severe local outward bulges of the outer tubes. Most of the concrete was still intact with some cracks along the longitudinal direction of the specimens. There were no slipping or detaching between steel tubes and concrete. (i) Before test (ii) After test (a) Circular specimens (i) Before test (ii) After test (b) Square specimens Figure 9.14 Failure modes of CFDST columns under fire New Developments 269 Yang and Han (2008) studied the performance of circular and square CFDST columns subjected to standard fire. For the circular CFDSTs, both the outer and inner skins are circular hollow sections (CHSs). For the square CFDSTs, the inner skin is still a CHS, but the outer steel skin is a square hollow section (SHS). One theoretical model was used to predict the temperature distributions, the fire resistance, and the fire protection material thickness of CFDST columns subjected to fire. The influences of the various parameters on the fire performance of CFDST columns were analysed. Finally, based on the results from the parametric study, formulae for fire resistance and for the thickness of fire protection material of the CFDST columns were presented. If other conditions are kept the same, the fire endurance of CFDST columns was found to be better than tubular columns fully filled with concrete. This is mainly because of the relatively low temperature in the inner steel tube. 9.5 FRP (FIBRE REINFORCED POLYMER) CONFINED CFST FRP (fibre reinforced polymer) has been widely used to strengthen concrete structures (Teng et al. 2002, Oehlers and Seracino 2004). The use of FRP to strengthen metallic structures has become an attractive option (Hollaway and Cadei 2002, Shaat et al. 2004, Cadei et al. 2004, Zhao and Zhang 2007). More recently, some researchers began to explore the possibility of repair/strengthening of CFST columns using CFRP (carbon fibre reinforced polymer). Tests were carried out (Zhao et al. 2005, Tao et al. 2007a) on concrete-filled steel hollow section short columns strengthened by CFRP. The dominating failure mode was found to be a CFRP rupture at outward mechanism locations which was also observed by Shaat and Fam (2006) for CFRP strengthened unfilled long columns. In the tests done by Zhao et al. (2005) the diameter-to-thickness ratio of CHS varied from 23 to 85. The compressive cube strength of the concrete was 55MPa. The increase in load-carrying capacity was found to be 5% to 22% when one CFRP layer was used. The increase in load-carrying capacity became 20% to 44% when two layers of CFRP were applied. It was found that the larger the diameterto-thickness ratio, the more increase in load-carrying capacity. Tao et al. (2007a) found that less increase in load-carrying capacity due to CFRP strengthening was achieved for concrete-filled rectangular hollow sections, although a similar increase in ductility was found for both CHS and RHS. Xiao et al. (2005) developed the CFRP confined concrete-filled tubular (CCFT) columns to avoid hinges from forming at critical locations in buildings. The behaviour of such columns can be controlled by introducing a gap between the FRP and steel tube to achieve enhanced strength as well as sufficient ductility. The static strength increased by 55% and 140% when the number of CFRP layers was two and four respectively. The ductility with the gap is twice that without the gap. Seismic behaviour of CFST columns can be significantly improved by providing additional confinement to the potential hinge region. The local buckling and Concrete-Filled Tubular Members and Connections 270 subsequent rupture of the steel tube were effectively delayed compared with the counterpart CFST specimens. A series of tests were conducted (Tao et al. 2007b, 2008; Tao and Han 2007) to investigate the feasibility of using CFRP in repair CFST columns after exposure to fire. It was found that the load-bearing capacity of the fire-exposed CFST columns and beam-columns could also be enhanced by the CFRP jackets to some extent. The strength enhancement from CFRP confinement decreased with increasing of eccentricity or slenderness ratio. At the same time, the influence of CFRP repair on the stiffness was not apparent due to the fact that the confinement from CFRP wraps was moderate when the CFST beam-columns remained in an elastic stage. To some extent, ductility enhancement was observed except those axially loaded shorter specimens with rupture of CFRP jackets at the mid-height occurred near peak loads. 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American code AISC (American Institute of Steel Construction) 14, 58 arch bridges 2-3; elevation of arch rib 8-9 Australian bridge design standard (AS-5100) 14; column curves 91; concrete 24; design member capacity 101; design section capacity (CHS) 73-4, 83-4; design section capacity (RHS) 72; design section capacity (SHS) 79; moment capacity 47; Part-5 24; section slenderness 46 Australian bridge design standard (AS-5100) CHS 52-3; diameter to thickness ratio 52-3; dimensions 52; moment capacity 53; properties 52 Australian bridge design standard (AS-5100) Part-6 19; load factors 27; strength limit state design 26-7 Bergmann, R.: et al 40 blind bolt CFST connections 239 Bradford, M.A. et al 65 British bridge code (BS-5400) 14; column curves 91; combined actions (CFST) 128-31; concrete 24; design section capacity (RHS) 74, 85-6; design section capacity (SHS) 79; nominal section capacity 90 British bridge code (BS-5400) CHS 53-4; dimensions 53; moment capacity 54; properties 53; thickness limit 53 British bridge code (BS-5400) Part-3: compression length 93 British bridge code (BS-5400) Part-5 19-20, 27; design member capacity 102; strength limit state design 27 British bridge code (BS-5400) SHS/RHS 46-9; dimensions 47; moment capacity 48; properties 47; thickness limit 48 British standard (BS-5950) Part-1 43 buckling 58-60 Budynas, R.G.: and Young, W.C. 59 carbon fibre reinforced polymer (CFRP) confined CFST 269-70; jackets 269-70 China: SEG Plaza 2, 5-6 Chinese code (DBJ13-51) 14; CFST steel 20; column curves 93; combined actions (CFST) 131-4; concrete 24; design capacity (SHS) see design section capacity (SHS) DBJ13-51; fire resistance (CFST) design 193, 194, 203-4; strength limit state design 27; ultimate design moment capacity 43 Chinese code (DBJ13-51) CHS 55-7; dimensions 55; moment capacity 55-6; properties 55; thickness limit 55 Chinese code (DBJ13-51) SHS/RHS 49-50; dimensions 49; moment 278 Concrete-Filled Tubular Members and Connections capacity 49; properties 49; thickness limit 49 CIDECT Design Guide No-4: fire resistance (CFST) design 193, 195, 201-2 circular hollow section (CHS) 1-2; (AS-5100) see Australian bridge design standard (AS-5100) CHS; (BS-5400) see British bridge code (BS-5400) CHS; BS-5400 Part-5 20; column stability factor (DBJ13-51) 94-6; combined actions (CFST) BS-5400 147-9; combined actions (CFST) DBJ13-51 149-52; combined actions (CFST) EC4 152-4; compression experimental studies 66-8; concrete strength 72; (DBJ13-51) see Chinese code (DBJ13-51) CHS; design section capacity see design section capacity; Eurocode-4 see Eurocode-4 (EC4) CHS; experimental studies 123; fire resistance (CFST) design 202; limit ratio (width to thickness) 40; moment capacity 39, 41, 52-7; plastic neutral axis 38, 39; ratio of load eccentricity 77, 78; relative slenderness 77; second order effect 133; seismic performance 178-81, 183; slenderness limit 41, 43; stress distribution 33, 34 column curves 91-100 column curves (AS-5100) 91; modified slenderness 91; RHS and CHS 92 column curves (BS-5400) Part-3 102 column curves (BS-5400) Part-5 91; length 91; non-dimensional slenderness 91; RHS and CHS 92 column curves (DBJ13-51) 93; slenderness reduction factor 93; steel ratio 93 column curves (Eurocode-4) 100, 100; idealised end restraints 100; non-dimensional slenderness 100 column stability factor (DBJ13-51): CHS 94-6, 103; RHS 97-99103 combined actions (CFST) 123-60; bending and torsion 157; biaxial bending 131; CHS 125, 155; compression, bending and shear 159; compression, bending and torsion 157, 158; compression, bending, torsion and shear 159; compression and torsion 156-60; contraflexure point 157; (DBJ13-51) 131-4; interaction diagrams (various codes) 127, 135-6; RHS 125; SHS comparison of standards 145; strength 124; stress distribution 124-5, 126; torsion capacity 156 combined actions (CFST) BS-5400 128-31; allowed axial force 145; bending about the major axis 129-30; bending about the minor axis 128-9; slenderness reduction factor (CHS) 128-9; slenderness reduction factor (RHS) 128-9 combined actions (CFST) BS-5400 (CHS) 147-9; bending moment 149; capacities under separate loading 147; conditions 147; design moment capacity 147; design section capacity 147; factors 147 combined actions (CFST) BS-5400 (SHS) 137-9; applied axial load 139; capacities under separate loading 138; conditions 138; factors 138 combined actions (CFST) CHS: torsion capacity 156 combined actions (CFST) DBJ13-51: allowed axial force 145; biaxial bending 134; CHS 132; combined axial force 131, 132; moments 132, 136; RHS 132; uniaxial bending 131, 132, 134 combined actions (CFST) DBJ13-51 (CHS) 149-52; capacities under separate loading 150; factors 150; member capacity check 150-1; section capacity check 150 combined actions (CFST) DBJ13-51 (SHS) 139-42; capacities under separate loading 140; design moment Index capacity 140; design section capacity 140; member capacity check 141; second order effect 141 combined actions (CFST) Eurocode-4 134-5; allowed axial force 146; applied moment 135; biaxial bending 135; combined compression 134, 135; interaction formulae 134-5; uniaxial bending 134 combined actions (CFST) Eurocode-4 (CHS) 152-4; allowed bending moment 154; applied moment 153; capacities under separate loading 152-3; design section capacity 153; interaction formula 153; second order effect 153 combined actions (CFST) Eurocode-4 (SHS) 143-5; applied moment 144; capacities under separate loading 143; design moment capacity 143, 144; design section capacity 143; interaction formula 144; second order effect 143 combined actions (CFST) RHS: torsion capacity 156 compression: design yield stress 76; local buckling 69; nominal section capacity 76 compression CFST 65-116; experimental studies 66-8; research from (1960s) 65-6; stress-strain relationship 70, 71 compression and torsion 156-60 compressive member capacities: CHS 116; RHS 110 concrete 24-6; confinement 70, 71; properties 25; strength 25-6; stress vs. strain 26; vs. steel tube 70 concrete filled hollow steel 19-20 concrete strength: CHS 72 concrete-filled double skin tubes (CFDST) 69, 69, 257-69; bending capacity 261; Bisteel 257; collapse behaviour 260; combined compression and bending 264-6; cross-sectional area 261; cyclic 279 loading 266; dimensions 258; dynamic loading 266-7; energy absorption 259; failure modes comparison 258, 262; fire 267-9, 268; impact loading 267; interaction formulae 264; mechanics models 264; neutral axis positions 262, 263; section capacity 259; stability reduction factor 265; static loading 257; steel-concrete-steel sandwich (SCSS) 257; structure 257; stub columns 257; ultimate moment capacity 261; unified theory 264; vs. outer steel tube 259, 260 concrete-filled steel tubes (CFST) 1-15; advantages 10-13, 11-13; beam-columns 10, 123, 125; combined actions see combined actions (CFST); connections see connections (CFST); fire resistance see fire resistance (CFST); international standards 14; limit states design (LSD) see limit states design (LSD); material properties 19-26; research projects 13; sections 1-2, 1; seismic performance see seismic performance (CFST); spacious construction 4; subject to compression 65-116; subjected to bending 31-61; used in a workshop 3; vs. unfilled tubes 10 concrete-filled steel tubes (CFST) beams: experimental studies 31; slenderness limits 46 concrete-filled steel tubes (CFST) columns 2; compression experimental studies68; curves see column curves; member capacity 90-1; short stub 90; subway station 3 concrete-filled steel tubes (CFST) legs: transmitting pole 4 concrete-filled steel tubes (CFST) sections: square hollow sections (SHC) see square hollow sections (SHS) concrete-filling: flexural-torsional 280 Concrete-Filled Tubular Members and Connections buckling 59 connections (CFST) 219-40; fatigue application 240; used in buildings 219; vs. unfilled tubular 219 connections (CFST) classification 219-20; blind bolt 239; braced frames 220; reduced beam section (RBS) 239-40, 240; rigid see rigid connections; semi-rigid see semi-rigid connections; simple see simple connections; unbraced frames 220 Corbett, G.: et al 267 concrete-filled CHS (AS-5100) 73-4, 83-4; concrete-filled CHS (BS-5400) 74-6, 75, 75, 85-6; concrete-filled CHS (DBJ13-51) 76, 87-9; concrete-filled CHS (EC4) 78, 88; concrete-filled RHS (AS-5100) 72; concrete-filled RHS (BS-5400) 74, 86; concrete-filled RHS (DBJ13-51) 76; concrete-filled RHS (EC4) 77, 82; international standards 90, 90 design section capacity (SHS) 78-82, 103-10; AS-5100 79 design section capacity (SHS) AS-5100: dimensions 103; elastic flexural stiffness 104; member capacity 105; member slenderness reduction factor 105; modified member slenderness 104; properties 103-4; relative slenderness 104 design section capacity (SHS) BS-5400 79-80; concrete contribution factor 80; dimensions 105; member capacity 106-7; properties 105; select column curve 106; slenderness reduction factor 106; thickness limit 80 design section capacity (SHS) DBJ13-51 80-1; column stability factor 107; design compression strength 81; design constraining factor 81; dimensions 107; member slenderness 107; nominal member capacity 108; properties of composite section 81 design section capacity (SHS) Eurocode-4 81-2; member capacity 109; non-dimensional slenderness 108-9; slenderness reduction factor 109; steel contribution factor 82 developments 247-70 Domone, P.L. 255 design member capacity 101-16 design member capacity (AS-5100) 101; cold-formed tubes 101; slenderness reduction factor 101 design member capacity (BS-5400) 102; slenderness reduction factor 102 design member capacity (CHS) AS-5100 110-11; dimensions 110; effective elastic flexural stiffness 111; modified member slenderness 111; properties 110; relative slenderness 111; section capacity 111; slenderness reduction factor 111 design member capacity (CHS) BS-5400: dimensions 112; properties 112; section capacity 112; select column curve 112; slenderness reduction factor 113 design member capacity (CHS) DBJ13-51 113-14; column stability factor 114; dimensions 113; member slenderness 114; properties 113; section capacity 114 design member capacity (CHS) Eurocode-4 115-16; dimensions 114; non-dimensional slenderness 115-16; properties 114; section capacity 115; slenderness reduction factor 116 design member capacity (DBJ13-51): RHS and CHS 103 design member capacity (Eurocode-4) 103 design section capacity 72-82; earthquake: RBS connections 239; Sichuan 163-4 effective elastic flexural stiffness 73, 78 effective length factors for members with idealised end restraints 73 Index El-Badawy, A.: et al 257 elastic buckling load: second order effect 133 Elchalakani, M.: et al; failure mode 32; and Zhao, X.L. 167 ENICOM Computer Centre (Tokyo) 207 Eurocode-3: Part-1.1 20; unfilled RHS 45 Eurocode-4 (EC4) 14; column curves 100, 100; concrete 24-5; concrete-filled CHS 45; local buckling 45; second order effect 137; strength limit state design 28 Eurocode-4 (EC4) Annex H: fire resistance (CFST) design 197 Eurocode-4 (EC4) CHS 56-7; diameter to thickness ratio 56; dimensions 56; moment capacity 57; properties 56 Eurocode-4 (EC4) Part-1.2: fire resistance (CFST) design 197, 202 Eurocode-4 (EC4) RHS: limiting value 70; steel contribution ratio 77 Eurocode-4 (EC4) SHS/RHS 50-1; dimensions 50; moment capacity 51; overall depth-to-thickness ratio 50; properties 50 experimental studies: CHS 123; RHS 124 Fam, A.Z. and Rizkalla, S.H. 31 fibre reinforced polymer (FPR) confined CFST 269-70 Finland: Tecnocent (Oulu) 207 fire exposure (CFST): stage-1 189; stage-2 189; stage-3 189; typical behaviour 189 fire protection thickness (CFST) 208 fire resistance (CFST) 189-213; circular columns 190, 196, 198; concrete core 190; concrete-filled tubes 200; experimental studies 191, 192; factors 191; North America 199-201, 204-6; post-fire performance 191, 208-9; protection material 193; research 191; square columns 190, 196, 198; 281 temperature (steel tube) 189, see also fire exposure fire resistance (CFST) design 193-207; bending moment and eccentricity 201; CHS 202, 204-6; CIDECT Design Guide No-4 193, 195, 201-2; column design 201; column size 201; DBJ13-51 193, 194, 203-4; degree of utilization 200; EC4 Annex H 197; EC4 Part-1.2 197, 202; effective buckling length 201, 202; energy absorption 213; ENICOM Computer Centre (Tokyo) 207; external protection 201; fire load ratio 200; fire protection thickness 208; material strength 201; Nakanoshima Intes (Japan) 207; reinforcement of concrete 201; repairing after fire 212, 213; residual strength index (RSI) 209, 210, 211, 211; Rochdale bus station (UK) 207; Ruifeng International Trading Centre (China) 207; SEG Plaza (China) 207, 208; SHS 204-6; Tecnocent building (Finland) 207; Wuhan International Stock Centre (China) 207 flexural-torsional buckling 58-60; concrete-filling 59; elastic buckling moment 59; lateral buckling capacity 58; torsion constant 59 Gardner, A.P.: and Goldsworthy, H.M. 239 Grzebieta, R.H.: and Zhao, X.L. 10, 37, 166, 261 Han, L.H.: elevation of arch rib (bridge) 8-9; et al 168-9, 175, 208-9, 212, 225, 247-8, 249, 264, 267; and Huo, J. 209; and Lin, X.K. 210; SEG Plaza fire protection 208; and Tao, Z. 270; transmitting pole 4; workshop 3; and Yang, Y.F. 168-9, 208, 224, 228, 248, 268; and Yao, J.T. 254; and Zhao, X.L. 257 Han, L.H. et al: compression, bending 282 Concrete-Filled Tubular Members and Connections and shear 159; compression and torsion 156-8, 158; moment vs. curvature diagrams 43 hollow steel tubes 3 Huo, J.: et al 209; and Han, L.H. 209 curve 249-51, 250; sectional capacities 251 Loh, H.Y.: et al 239 long-term load effect 247-9; self-consolidating concrete (SCC)-filled steel tubes 247; shrinkage value of concrete core 247, 248; strength index 248, 249 Lu, H. 267 International Committee for the Development and Study of Tubular Structures (CIDECT) 13 International Institute of Welding (IIW) 13 international standards/codes 14, 66; design section capacity 90, 90 Japan: Nakanoshima Intes (Osaka City) 207 Japanese code (AIJ) 14; bond strength equation 231; load transfer mechanism 232; rigid CFST connections 229-30 Kodur, V.K.R. 199; and MacKinnon, D.H. 200 Kurobane, Y.: et al 164, 221, 223, 226, 229, 231 Lam, D. and Gardner, L. 65 Lan, S.: et al 257 lateral buckling see flexural-torsional buckling Liew, J.Y.R.: and Wang, T.Y. 257 limit ratio (width to thickness): concrete-filled CHS 40; concrete-filled RHS 40 limit states design (LSD) 26-9; AS-5100 Part-6 26-7; BS-5400 Part-5 27; DBJ13-51 27; EC4 28; factors 28; serviceability limit states 26, 28-9; ultimate strength 26-7 Lin, M.L.: and Tsai, K.C. 266 Lin, X.K.: and Han, L.H. 210 local buckling 70; compression 69-70; EC4 45; RHS 43; unfilled tubular sections 32 local compression effects 249-52, 250; area ratio 250, 252; load-deformation MacKinnon, D.H.: and Kodur, V.K.R. 200 Mashiri, F.R.: and Zhao, X.L. 241 Matsui, C.: et al 70 moment capacity 35-9; AS-5100 47; AS-5100 (CHS) 53; BS-5400 (CHS) 54; BS-5400 (SHS/RHS) 48; comparison 38, 52, 58; DBJ13-51 43; DBJ13-51 (CHS) 55-6; DBJ13-51 (SHS/RHS) 49-50; design 40; EC4 (CHS) 57; EC4 (SHS/RHS) 51; nominal 42, 44; ultimate 37; ultimate design 43 Nakanishi, K.: et al 267 Nakanoshima Intes (Osaka City: Japan) 207 Nethercot, D.A. 14 North America: fire resistance (CFST) 199-201, 204-6 Orten, A.H.: and Wang, Y.C. 197 Park, S.: et al 240 plastic moment capacity 33-9 Poisson’s ratio 251, 252 pre-load effect 253-5; CFST column during construction 253, 253; pre-load ratio 254; slenderness ratio 254; strength index 254 rectangular hollow section (RHS) 1-2, 67; (BS-5400) see British bridge code (BS-5400) SHS/RHS; BS5400 Part-5 20; buckling ratio 61; column stability factor (DBJ 13-51) 97-9; Index concrete-filled 10, 12; (DBJ13-51) see Chinese code (DBJ13-51) SHS/RHS; design section capacity see design section capacity; elastic buckling moment 59; Eurocode-4 see Eurocode-4 (EC4) SHS/RHS; experimental studies 124; fire resistance (CFST) design 202; limit ratio (width to thickness) 40, 44; local buckling 43; moment capacity 32, 35-6, 41; moment capacity (comparison) 52; neutral axis 36, 37; ratio of average compressive stress 41; rigid connections 230-1; with rounded corners 36-7; second order effect 133; seismic performance 181, 183-4; stress distribution 33, 33, 34; torsion capacity 156; unfilled beams 10, 12; without rounded corners 33-4 reduced beam section (RBS) CFST connections 239-40, 240; earthquakes 239 reinforced concrete (RC) 1 rigid connections 220, 223-4, 224, 225; anchor stiffeners 224; external diaphragm 224, 229; RC ring 224; RHS 230-1; variable width RC beam 224 rigid connections design 227-31; bond strength 231-2; critical location 227-8; failure mode 228; load action 227-8; load transfer mechanism 232; yield capacity 228-9 rigid connections steel I-beam 236-8; bond strength 238; diaphragm thickness 236; Type-I diaphragm connection 237; Type-II diaphragm connection 237; Type-III diaphragm connection 238; yield capacity 237 rigid-plastic theory 45 Rochdale bus station (Lancashire, UK) 207 Ruifeng International Trading Centre (China) 207 second order effect 133, 136; CHS 133; 283 combined actions (CFST) DBJ13-51 (SHS) 141; combined actions (CFST) EC4 (SHS) 143; EC4 137, 153; elastic buckling load 133; RHS 133 SEG Plaza (Shenzhen, China) 2; fire protection 207, 208; under construction 5-6 seismic behaviour (CFST) 210 seismic performance (CFST) 165-85; bending moment 180, 181; braces 168; curvature (yielding moment) 180; cyclic bending 164-5, 165; cyclic lateral load vs. lateral deflection 169, 184, 212; cyclic loading on bending strength 167; direct cyclic loading 168; ductility 163-73; ductility index 170; ductility ratio 168-72, 171, 184-5; high strength concrete 165; high strength steel tubes 165; hinge mechanism (frame structures) 164; hysterectic behaviour 163, 173; incremental cyclic loading 168; large deformation cyclic loading 169; lateral cyclic loading 164-7, 166; lateral load (ultimate) 178; lateral load vs. lateral deflection 175, 176-7, 178, 182, 213; load vs. deformation relations 163, 182; maximum bending moment 167; moment vs. curvature 173, 174-5, 178, 179; plastic design 172; stiffness in elastic stage 178, 180-1, 182; strength 163, 182; typical beam-columns 164, 165; unfilled steel tubular beam 168; weak columns/soft-storey-mechanism 163; yielding moment 178, 181 self-consolidating concrete (SCC)-filled steel tubes 247, 255-6; mixture proportion 255; slump flow test 256; studies 256; test in L-box 256; workability 255, 255, 256 semi-rigid connections 220-3, 223; I-section beam 221, 223 Sichuan earthquake 163-4 simple connections 219-21, 222, 225; fin plate 221, 222; hollow section to 284 Concrete-Filled Tubular Members and Connections hollow section 222; shear plate 222; stiffened seat 222; T-connection 221, 222; through plate 221, 222 simple connections design 225-6; bearing failure of shear plate/beam web 226; bolt shear failure 226; fracture fear of shear plate 226; geometric dimensions 227; local buckling 226; punch shear failure 226; shear capacity calculation 227; shear failure of steel tube adjacent to beam web 226; shear yield of steel tube 226; weld shear failure 226; yielding of shear plate 226 simple connections (steel I-beam) 233-6; bolts 233; bond strength 235-6; fracture failure of shear plate 234; shear failure check 234; shear plate failure paths 235; shear plate length 234; shear plate thickness 234; slenderness requirement 233; steel tube adjacent to beam web 235; weld shear failure check 234; yielding of shear plate 235 slenderness limits: CFST beams 46 spacious construction: CFST 4 square hollow section (SHS) 1-2; (BS-5400) see British bridge code (BS-5400) SHS/RHS; combined actions (CFST) BS-5400 137-9; combined actions (CFST) DBJ13-51 139-42; combined actions (CFST) EC4 143-5; comparison of standards (combined actions) 145; (DBJ 13-51) see Chinese code (DBJ13-51) SHS/RHS; design section capacity 78-82; design section capacity see design section capacity (SHS); Eurocode-4 see Eurocode-4 (EC4) SHS/RHS; filled with normal concrete 46; fire resistance (CFST) design 204-6 steel plates: tensile strength 20, 21-2; yield stress 20, 21-2 steel sections (classification) 32; AISC 32; AS-4100 32; BS-5950 Part-1 32; Eurocode-3 32 steel tubes 19-20; vs. concrete 70 stress distribution 33 subway station: CFST columns 3 swing methods 3 Tao, Z.: et al 14, 264, 269-70; and Han, L.H. 270 Tecnocent building (Oulu, Finland) 207 Tong, L.W.: et al 241 torsion constant 59 transmitting pole: CFST legs 4 Tsai, K.C.: and Lin, M.L. 266 Twilt, L.: et al 195, 206, 207 unfilled tubes: vs. CFST 10 United Kingdom (UK): Rochdale bus station 207 Uy, B. 70 Wang, T.Y.: and Liew, J.Y.R. 257 Wang, W.D.: et al 240 Wang, Y.C. 197; and Orten, A.H. 197 Wardenier, J. 10 de Winkel, G.D. 223 Wright, H.D. 70 Wuhan International Stock Centre (China) 7, 207 www.corusconstruction.com 257 Xiao, Y.: et al 269 Yang, Y.F.: and Han, L.H. 168-9, 208, 224, 228, 248, 269 Yao, H.: et al 239 Yao, J.T.: and Han, L.H. 254 Young, B. and Ellobody, E. 65 Young, W.C.: and Budynas, R.G. 59 Zhao, X.L.: and Elchalankani, M. 167; et al 58, 168, 170, 172, 258, 260; and Grzebieta, R.H. 10, 37, 166, 261; and Han, L.H. 257; and Mashiri, F.R. 241 Zhao, Y. et al 269 Zhong, S.T.: et al 172 Zhou, P.: and Zhu, Z.Q. 3

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