# Fixed Pipes - Stress vs. Change in Temperature

## Temperature changes introduces stress fixed pipes.

With temperature change stress is introduced in fixed pipes. The stress can be calculated as:

σ = α E dt (1)

where

σ = stress (MPa, lb/in^{2})

α = linear expansion coefficient (m/m^{o}K, inch/inch^{o}F)

E = modulus of elasticity of the piping material (MPa, lb/in^{2})

dt = temperature change from installation temperature (^{o}C,^{o}F)

The stress must not exceed maximum allowable stress for the chosen piping material. Be aware that with frequently temperature changes - the stress cycle (with stress well below the maximum allowable limit) may fatigue the pipe.

### Example - Introduced Stress in a Fixed Pipe when Temperature Changes

A carbon steel pipe with linear expansion coefficient *11.7 10 ^{-6} m/m^{o}C* and modulus of elasticity

*29.5 10*is heated from

^{6}psi (203 10^{9}Pa (N/m^{2}), 203000 MPa, 203 GPa)*0*to

^{o}C*50*. The stress introduced in the pipe can be calculated as

^{o}C*σ = ( 11.7 10^{-6} m/m^{o}C) (203 10^{9} N/m^{2}) ((50^{o}C) - (0^{o}C))*

* = 119 10 ^{6} N/m^{2}*

* = 119 MPa*

Depending on the material and the codes used - this may be within maximum allowable stress.

### Stress Calculator

*Linear expansion coefficient* (m/m^{o}C)

* Modulus of elasticity (MPa)*

* Temperature differance ( ^{o}C)*