Piping stress bending

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3.0 Allowable stress:

From stress strain diagram of a material like carbon steel we know about yield strength as also

ultimate tensile strength. For our design purpose and allowable stress value is fixed which is

based on a certain factor of safety over the yield strength or ultimate tensile strength. For

higher temperature applications creep strength also comes in picture. Various codes detail theallowable stress basis. The basis adopted in ANSI B31.3 and IBR are described herein. These

two codes have the maximum usage among the Indian pipe stress Engineers for

Petrochemical/ Refinery.

3.1 Allowable stress as per ACSI:

As per Petroleum refinery piping code ANSI B31.3 the basic allowable stress values are the

min. of the following values.

a) 1/3 of the minimum tensile strength at room temp.

b) 1/3 of tensile strength of design temp.

c) 2/3 of Min. yield strength of room temp.

d) 2/3 of Min. yield strength at design temp.

e) 100% of average stress for creep rate of O/D 1% per 1000 hrs.

3.2 Allowable Stress as per IBR:

As pe the Indian Boiler Regulations the allowable working stress is calculated as shown

below:

i) For temperatures at or below 454 Deg.C, the allowable stress is the lower of the

following values:

Et = 1.5 or R = 2.7

ii) For temperatures above 454 Deg.C the allowable stress is lower of the

Values:

Et = 1.5 or Sr = 1.5

Where

R = Min. tensile strength of the steel at room temp.

Et = Yield point (02% proof stress) at the temp.

Sr = Average stress to produce rupture in 100,000 hrs. at a temp. and in


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No case more than 1.33 times the lowest stress to produce rupture at temp.

Sc = Average stress to produce an elongation of 1% creep in 100,000 hrs. All these

values have been made available after carrying on repeated laboratory tests on the

specimen.

4.0 Allowable stress range:

The stress of a piping system lowers within the elasticity range in which plastic

flow does not occur by self-spring during several initial cycles even if the

calculation value exceeds the yield point, and thereafter-steady respective stress is

applied. Hence repture in a piping system may be due to low cycle fatigue. It is

well known that fatigue strength usually depends upon the mean stress and the

stress amplitude. The mean stress does not always become zero if self spring takes

place in piping system but in the ANSI code, the value of the mean stress is

disregarded while the algebraic difference between the maximum and the

minimum stress namely only the stress range SA is employed as the criterion ofthe strength against fatigue rupture.

The maximum stress range a system could be subjected to without producing flow

neither in the cold nor in the hot condition was first proposed by ARC Mark as

follows:

a) In cold condition the stress in the pipe material will automatically limit itself to

the yield strength or 8/5 of Sc because Sc is limited to 5/8th

of Y.S. therefore,

Ye = 1.6 Sc.

b) At elevated temperatures at which creep is more likely the stress in the pipe

material shall itself to the rupture strength i.e. 8/5th

Sh = 1.6 Sh.

Therefore stress range = 1.6f(Sc = Sh)

However, the code limits the stress range conservatively as 1.25f(Sc + Sh)

which includes all stresses i.e. expansion stress, pressure stress, hot stresses

and any other stresses inducted by external loads such as wind and earthquake,f is the stress range reduction factor for cyclic conditions as given below:


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To determine the stress range available for expansion stress alone we subtract

the stresses inducted by pressure stress and weight stress which itself cannot

exceed sh.

Therefore the range for expansion stress only is

SA = f(1.25 Sc + 0.25 Sh)

VALUES OF FACTOR f

Total number of full f factor

Temp. Cycles over expected life

7,000 and less 1

14,000 and less 0.9

22,000 and less 0.8

45,000 and less 0.7

100,000 and less 0.6

250,000 and less 0.5

5.0 Pressure & Bending Stress & Combination Application:

The code confines the stress examination to the most significant stresses

created by the diversity of loading to which a piping system is subjected. They

are:

i) Stress due to the thermal expansion of the line.

ii) The longitudinal stresses due to internal or external pressure.

iii) The bending stress created by the weight of the pipe and its insulation, the

internal fluid, fittings, valves and external loading such as wind,

earthquake etc.

5.1 Stresses due to the thermal expansion of the line:


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Temperature change in restrained piping cause bending stresses in single plane

systems, and bending and torsional stresses in three-dimensional system. The

maximum stress due to thermal, changes solely is called expansion stress SE.

This stress must be within the allowable stress range SA.

SE = Sb2

+ 4St2

Sb = I (Mb / Z) = resulting bending stress

Mt = (Mt//2Z) = torsional stress

Mb = resulting bending movement

Z = section modules of pipe

i = stress intensification factor

5.2 Longitudinal stress due to internal or external pressure:

The longitudinal stress due to internal/external pressure shall be expressed as P

(Ai / Am)

Where Ai is inside cross sectional area of pipe, Am is the metal area, P is the

pressure.

5.3 Weight Stress:

The stress induced, self weight of pipe, fluid, fittings etc. as given by SW =

M/Z, Where M is bending moment created by the pipe and other fittings, Z is

the section modules of the pipe.


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The stresses due to internal pressure and weight of the piping are permanently

sustained. They do not participate in stress reductions due to relaxation and are

excluded from the comparison of which as the latter has been adjusted to allow

for them with the following provision.

6.0 Flexibility and stress intensification factor:

Some of the piping items (say pipe elbow) show different flexibility than

predicted by ordinary beam theory. Flexibility factor of a fitting is actually the

ratio of rotation per unit length of the fitting in question under certain value of

moment to the rotation of a straight pipe of same nominal diameter and

schedule and under identical value of moment. The pipefitting item, which

shows substantial flexibility, is a pipe elbow/bend.

One end is anchored and the other end is attached to a rigid arm to which a

force is applied. The outer fibers of the bend/elbow will be under tension and

the inner fibers will be under compression. Due to shape of bend both tension

and compression will have component in the same direction creating

distortion/slottening of bend. This leads to higher flexibility of the end as there

is some decrease in moment of inertia due to distortion from circular to

elliptical shape and also due to fact that the outer layer fibers, which are under

tension has to elongate less and the inner layer fibers which are under

compression has to contract less to accommodate the same angular rotation

leading to higher flexibility. Piping component used in piping system has

notches/discontinuities in the piping system, which acts as stress raisers. For

example a fabricated tee branch. The concept of stress intensification comes

from this and is defined as the ratio of the bending moment producing fatigue

failure in a given number of cycles in straight pipe of nominal dimensions to

that producing failure in the same number of cycles for the part under

consideration. Both flexibility factor and stress intensification factors have

been described in PROCESS PIPING CODE(ASME B31.3) and is also

included in the various pipe stress analysis computer programmes.

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Piping stress bending