StressEqns 313


Stress Due to Sustained Loads
The equation for the stress due to sustained loads,such as pressure and weight, SL, is provided in eq.
(23a).
The equation for the stress due to sustained bending moments, Sb, is provided in eq. (23b).
where
Ii = sustained in-plane moment index. In the absence of more applicable data, Ii is taken as the greater of 0.75ii or
1.00.
Io = sustained out-plane moment index. In the absence of more applicable data, Io is taken as the greater of
0.75io or 1.00.
Mi = in-plane moment due to sustained loads, e.g., pressure and weight
Mo = out-plane moment due to sustained loads, e.g., pressure and weight
Z = sustained section modulus. Z in eqs. (23b) and (23c) is described in para. 319.4.4 but is computed
in this paragraph using nominal pipe dimensions less allowances; see para. 320.1
The equation for the stress due to sustained torsional moment, St, is
where
It = sustained torsional moment index. In the absence of more applicable data, It is taken as 1.00.
Mt = torsional moment due to sustained loads, e.g., pressure and weight
The equation for the stress due to sustained longitudinal force, Sa, is
where
Ap = cross-sectional area of the pipe, considering nominal pipe dimensions less allowances; see para.
320.1
Fa = longitudinal force due to sustained loads, e.g.,pressure and weight
Ia = sustained longitudinal force index. In the absence of more applicable data, Ia is taken as 1.00.
The sustained longitudinal force, Fa, includes the sustained force due to pressure, which is PjAf unless the
piping system includes an expansion joint that is not designed to carry this force itself, where Pj is the
internal operating pressure for the condition being considered,Afp_d2/4, and d is the pipe inside diameter
considering pipe wall thickness less applicable allowances; see para. 320.1. For piping systems that
contain expansion joints, it is the responsibility of the designer to determine the sustained longitudinal force
due to pressure in the piping system.
42
The computed displacement stress range, SE, in a piping system (see para. 319.4.4) shall not exceed the
allowable displacement stress range, SA (see paras. 319.2.3 and 319.3.4), calculated by eq. (1a)
When Sh is greater than SL, the difference between them may be added to the term 0.25Sh in eq. (1a). In
that case, the allowable stress range is calculated by eq. (1b)
For eqs. (1a) and (1b) f is the stress range factor, calculated by eq. (1c)
fm = maximum value of stress range factor; 1.2 for ferrous materials with specified minimum tensile
strengths not more than517 MPa (75 ksi) and at metal temperatures not more than 371°C (700°F);
otherwise fm = 1.0
N = equivalent number of full displacement cycles during the expected service life of the piping
system5
Sc = basic allowable stress6 at minimum metal temperature expected during the displacement
cycle under analysis = 138 MPa (20 ksi) maximum
Sh = basic allowable stress6 at maximum metal temperature expected during the displacement cycle under
analysis = 138 MPa (20 ksi) maximum
SL = stress due to sustained loads; in systems where supports may be active in some conditions and
inactive in others, the maximum value of sustained stress, considering all support conditions, shall be used
When the computed stress range varies, whether from thermal expansion or other conditions, SE is defined
as the greatest computed displacement stress range. The value of N in such cases can be calculated by
eq. (1d)
where
NE =number of cycles of maximum computed displacement stress range, SE
Ni = number of cycles associated with displacement stress range, Si
ri = Si/SE
Si = any computed displacement stress range smaller than SE
The sum of the longitudinal stresses, SL, due to sustained loads, such as pressure and weight, and of the
stresses produced by occasional loads, such as wind or earthquake, may be as much as 1.33 times the
basic allowable stress . Wind and earthquake forces need not be considered as acting concurrently.
When detailed analysis is performed, the stresses shall be computed and combined using eqs. (23a)
through (23d) with the applicable loads for the condition being evaluated
For t D/6, the internal pressure design thickness for straight pipe shall be not less than that calculated
in accordance with either eq. (3a) or eq. (3b)
c = sum of the mechanical allowances (thread or groove depth) plus corrosion and erosion allowances. For
threaded components, the nominal thread depth (dimension h of ASME B1.20.1, or equivalent) shall apply.
For machined surfaces or grooves where the tolerance is not specified, the tolerance shall be assumed to
be 0.5 mm (0.02 in.) in addition to the specified depth of the cut.
D = outside diameter of pipe as listed in tables of standards or specifications or as measured
d = inside diameter of pipe. For pressure design calculation, the inside diameter of the pipe is the max.
value allowable under the purchase specification.
E = quality factor from Table A-1A or A-1B
P = internal design gage pressure
S = stress value for material from Table A-1
T = pipe wall thickness (measured or minimum in accordance with the purchase specification)
t = pressure design thickness, as calculated in accordance with para. 304.1.2 for internal pressure
or as determined in accordance with para. 304.1.3 for external pressure
tm = minimum required thickness, including mechanical, corrosion, and erosion allowances
W = weld joint strength reduction factor in accordance with para. 302.3.5(e)
Y = coefficient from Table 304.1.1, valid for t D/6 and for materials shown. The value of Y may
be interpolated for intermediate temperatures.
For t D/6, the internal pressure design thickness for straight pipe shall be not less than that calculated
in accordance with either eq. (3a) or eq. (3b)