# How to calculate pipe stress due to expansion

Written by dwight chestnut
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Many residential and industrial systems use pipes to transport fluids from one point to another. As fluid flows through pipes, pressure builds and pushes the pipe outward, causing stress, which, if not properly accounted for, can rupture the pipe. For this reason, mechanical engineers perform stress analysis to take these factors into account. This analysis accounts for three types of stress: axial, circumferential and radial.

Skill level:
Moderately Challenging

## Instructions

1. 1

Find the internal pressure, or "pi," and the external pressure, or "po," in units of pounds per square inch, or psi. Refer to piping system schematics and diagrams.

2. 2

Find the inside radius, or "ri," and the external radius, or "ro," in units of inches. Refer to piping system schematics and diagrams.

3. 3

Calculate the axial stress using the formula, sa = (pi ri2 - po ro2 )/(ro2 - ri2), where sa is axial stress. As a calculation example, assume pi is 30 psi, po is 12 psi, ri is 3 inches and ro is 4 inches:

sa = [(30)(3^2) - (12)(4^2)]/[4^2-3^2] = [270 - 192]/(16 - 9) = 78/7 = 11.14 psi

4. 4

Find the radius to a point in the pipe wall, or "r." Refer to piping system schematics and diagrams. As an example, assume r is 3.5 inches.

5. 5

Calculate the circumferential stress using the formula sc = sa - scp, where sc is the circumferential stress, and scp is [ri2 ro2 (po - pi) / r2 (ro2 - ri2)]. Continuing with the example, calculate scp:

scp = [ri2 ro2 (po - pi) / r2 (ro2 - ri2)] = [(3^2)(4^2)(12 - 30)]/[(3.5^2)(4^2 - 3^2)] = [(9)(16)(-18)]/(12.25)(7)] = - 2592/85.75 = - 30.23 psi

Calculating sc:

sc = sa-scp = 11.14 - (- 30.23) = 41.37 psi.

6. 6

Calculate the radial stress using the formula: sr = sa + scp. Continuing with the example:

sr = 11.14 psi + (- 30.23) = -19.09

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