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Allowable stress range:

1.0 Allowable stress range:

The stress of a piping system lowers within the elasticity range in which plastic flow does notoccur 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 bedue to low cycle fatigue. It is well known that fatigue strength usually depends upon the meanstress 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 stressrange SA is employed as the criterion of the 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 shallitself 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. expansionstress, 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 cyclicconditions as given below:

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 0.922,000 and less 0.8

45,000 and less 0.7

100,000 and less 0.6

250,000 and less 0.5

2.0 Pressure & Bending Stress & Combination Application:

The code confines the stress examination to the most significant stresses created by the diversityof 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,

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fittings, valves and external loading such as wind, earthquake etc.

2.1 Stresses due to the thermal expansion of the line: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 stressrange SA.SE = Sb2 + 4St2

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

Mt = (Mt //2Z) = torsional stressMb = resulting bending movement

Mt / = torsional movement

Z = section modules of pipe

i = stress intensification factor

2.2 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.

2.3 Weight Stress:

The stress induced, self weight of pipe, fluid, fittings etc. as given by SW = M/Z, Where M isbending moment created by the pipe and other fittings, Z is the section modules of the pipe.

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 ofwhich as the latter has been adjusted to allow for them with the following provision.

December 8, 2011