Allowable Stress for Wind and Seismic Loads on Pipe
Rev. 0
Page 1 of 9
Allowable Stress for Wind and Seismic Loads on Pipe
Rev. 0
Page 2 of 9
Table of Contents
Section
Page number
Purpose and Scope -------------------------------------------3
Design Input ------------------------------------------------------3
Assumptions -----------------------------------------------------3
Approach: Methodology and Acceptance Criteria -3
Calculations ------------------------------------------------------7
Results -------------------------------------------------------------7
References -------------------------------------------------------9
8. Attachments ------------------------------------------------------9
1.
2.
3.
4.
5.
6.
7.
Allowable Stress for Wind and Seismic Loads on Pipe
Rev. 0
Page 3 of 9
1. PURPOSE AND SCOPE
In the Introduction to ASME B31.1 Power Piping (Code) (Ref. 1), the Code states:
“The specific design requirements of the Code usually revolve around a simplified
engineering approach to a subject. It is intended that a designer capable of applying a
more complete and rigorous analysis to special or unusual problems shall have latitude in
the development of such design and the evaluation of complex or combined stresses. In
such cases the designer is responsible for demonstrating the validity of his approach.”
This paper is intended to demonstrate the validity of an approach for the evaluation of stresses in
small bore piping systems, caused by the application of wind loads.
2. DESIGN INPUT
See References.
3. ASSUMPTIONS
We have assumed that 2 1/4 Cr 1 Mo (Grade 22) and 9Cr 1Mo-V (Grade 91) alloy materials
exhibit ductile stress-strain behavior at elevated temperatures (see Ref. 3).
4. APPROACH
Design Acceptance Criteria
The analysis of piping under the action of wind or seismic loads treats the loading as a uniformly
distributed load acting laterally on the pipe. This loading is transferred from the pipe to the
supporting structure through the pipe guides which are located along the length of the pipe. For a
sustained wind load or seismic load, the load on the pipe is limited by the ability of the pipe to
resist this load under the action of beam bending of the pipe. “Failure” under this loading
condition may be said to be characterized by the formation of a plastic hinge at the point of
maximum moment in the pipe, resulting in gross distortion or deformation of the piping. Thus,
stresses must be kept below a limit to prevent the creation of such a plastic hinge.
The stress level allowed by the Code for occasional loads is 1.2*Sh. The Code defines Sh (see
Ref. 2) as the lesser of the several material property criteria which include:
1. 2/3 of the yield strength (2/3*Sy) of the material at room temperature or at the elevated
operating temperature.
2. ¼ of the Ultimate strength ( ¼*Su )of the material at room temperature or at the elevated
operating temperature.
3. 0.8* the Minimum or 0.67* the Average stress to cause creep rupture in 100,000 hours.
4. 100% of the Average stress to produce a creep strain rate of 0.01% per 1,000 hours.
Allowable Stress for Wind and Seismic Loads on Pipe
Rev. 0
Page 4 of 9
The last two criteria are functions of creep properties which are time and temperature related
phenomena, in other words, creep effects require a load to be sustained over a long period of
time before the effects of creep are seen in the pipe. The development of the stress values for Sh
are thus based on the assumption that the load will be imposed continuously for the life of the
system (as is the case for the design of pipe wall thickness to resist internal pressure).
However, for the case of wind or seismic loads, the loads will not be applied for long enough
periods of time (in a given single direction) for creep strains of any engineering significance to
develop. Thus it will be appropriate for this occasional loading condition to use the short term
yield and ultimate strength properties to develop equivalent stress criteria for wind loads.
For occasional loads, the Code (ASME B31.1-2022) uses the following equation to evaluate
stresses due to wind loads
(B31.1 eqn 16)
The Fb force and Mxb moment terms in the above equation represent the sum of the sustained
loads, which are kept within the allowable stress range governed by creep effects by virtue of
their being able to satisfy the Code Equation (15) stress allowable (Sh), and the wind or seismic
loads. However, the occasional load forces and moments components in the equation do not act
for long periods of time and are thus not governed by long term creep effects due to the short
time these loads are applied, but rather should be limited by short term yield and tensile
properties. A similar approach to the allowable stress for such occasional seismic loads is given
in ASME B31E (Ref. 6) where the allowable stresses for such occasional loads are based on
short term yield, it allows 2.4S or 1.5 Sy or 60 ksi for bending stresses and Sy for axial tensile
loads.
For design not in the creep range, the value of 1.2*Sh can be related to the yield strength of the
material by:
2

12
. * S h  12
. *  * S y   0.8 * S y
3

(2)
This value still has a substantial factor of safety with respect to the formation of a plastic hinge,
since for all shapes, the ratio of the fully plastic moment to the moment required to initiate the
onset of yielding in the most extreme fibers is always greater than 1. For example for
rectangular shapes the ratio of the moment to cause a plastic hinge to the moment required to
initiate yielding at the outermost fibers of the section is 1.5: 1, for solid circular sections, the
Allowable Stress for Wind and Seismic Loads on Pipe
Rev. 0
Page 5 of 9
ratio is 1.7:1. To obtain equivalent ratios for hollow circular pipe sections the following
derivation is provided:
From Marks (Ref. 4) we find, “The shape factor may also be determined by dividing the first
moment of area about the neutral axis by the section modulus (Z).”
From Roark (Ref. 5, Appendix B) we find “(first moment of an area) With respect to an axis the
sum of the products obtained by multiplying each element of the area dA by its distance from the
axis y; it is therefore the quantity
 dA  y  first _ moment _ of _ an _ area
(3)
thus the shape factor F is given by:
F
 dA  y
Z
(4)
For a solid semi-circle, the area is given by
A1 
  R2
2
(5)
The centroid of this area with respect to the bottom of the semicircle (center of a full circle) is
given by:
y1 
4 R
3
(6)
The first moment of inertia is then just the sum of the product of the two areas (above and below
the neutral axis of the circle) and the centroid dimensions.
The hole is represented by a negative product using equations similar to the above, but replacing
the outside radius R with the inside radius r , or:
A2 
and
  r2
2
(7)
Allowable Stress for Wind and Seismic Loads on Pipe
Rev. 0
Page 6 of 9
y2 
4r
3
(8)
combining the above equations to calculate the first moment of a hollow circle (pipe section)
yields:
 dA  y  2  A  y  2  A  y
1
1
2
2
(9)
or
   R 2 4  R     r 2 4  r  

dA

y

2



 


3   2 3  
 2
(10)
or
4
 dA  y  3   R  r 
3
3
(11)
The section modulus of a hollow circular section is given by Ref 5, Table A.1.16:
Z
   R4  r 4 
4 R
(12)
The shape factor F for a pipe cross section is thus given by:
4
3
3 
 3  R  r 
F
   R4  r 4 


4 R






(13)
Using the above equation, if we let the inside radius become zero, the shape factor becomes 1.7
which is the published shape factor for a solid circular area.
Computer Programs Used
Allowable Stress for Wind and Seismic Loads on Pipe
Rev. 0
Page 7 of 9
EXCEL in MS OFFICE 365 X32, S&L program No.03.2..435-16.0.16626.2017, status
“Support”, on PC # PL15802 was used to generate data regarding shape factors for typical piping
sizes.
5. CALCULATIONS
Using equation (13) above, the shape factor for small bore piping (NPS < 2) has a minimum
shape factor of 1.36 (see spreadsheet in Attachment 1). In other words, a plastic hinge will not
form until the applied load (moment) is greater than or equal to 1.36 times the load required to
cause yielding to initiate at the extreme outer fibers in the pipe cross section. For pipe up to NPS
24 for all schedules the minimum shape factor is 1.29. This means that for larger pipes, a
moment 1.29 times greater than the moment to produce yield stress at the outer fibers is required
to produce a plastic hinge.
The file for shape factor data analysis is contained on :
plas-mom.xlsx, 01/24/2025 3:07 PM
The printout of this file is in Attachment 1.
6. RESULTS
Applicable Stress Allowable for P22 and P91 Materials
By limiting the calculated stresses for the sum of the wind and sustained loads to the yield
strength criteria of the Code, and by applying the occasional load allowance, as shown above in
equation (2), we can find an equivalent allowable stress to be:
0.8*Sy
Where Sy is taken as the minimum stress at the given temperature from the various sources
shown in the graphs shown below which were taken from the calculation in Attachment 2.
Allowable Stress for Wind and Seismic Loads on Pipe
Rev. 0
Page 8 of 9
Allowable Stress for Wind and Seismic Loads on Pipe
Rev. 0
Page 9 of 9
This stress level still provides a safety factor of 1.7:1 against the formation of a plastic hinge in
small bore pipe and 1.6:1 for large bore pipe, and thus still provides an adequate margin (see Ref.
4) against failure for this material under this temporary loading condition.
7. REFERENCES
1. ASME B31.1- Power Piping , 1995 Edition, including Addenda B31.1b.
2. ASME BPVC, Section II, Part D, Appendix 1, 1995 Edition.
3. API 579-1/ASME FFS-1-2016, “Fitness-For-Service”, API, Washington, D.C. and
ASME NY, NY, 2016
4. Baumeister, T and L. S. Marks, Standard Handbook for Mechanical Engineers, Seventh
Edition, McGraw-Hill Book Company, 1967, “Plastic Design” pg. 5-19 to 5-20.
5. Roark, R. J., Formulas for Stress and Strain, Seventh Edition, McGraw-Hill Book
Company, New York, 2002, 1989.
6. ASME B31Ea-2010, “Standard for the Seismic Design and Retrofit of Above‐Ground
Piping Systems”, ASME, 2010
8. ATTACHMENTS
1. Printout of EXCEL spreadsheet of pipe shape factors for small bore pipe (6 pages)
2. Calculation of yield stresses from API 579-1/ASME FFS-1-2016 (11 Pages)