# Thermal Stress

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Thermal stress is the change in the temperature of the material that causes expansion or contraction.  The change in length is porportional to the amount of heat applied.

### Thermal stress formula

$$\large{ \sigma_t = a \; l_i \; \Delta T }$$

$$\large{ \sigma_t = - E \; \alpha \; \Delta T }$$

$$\large{ \sigma_t = E \; \epsilon }$$

Where:

$$\large{ \sigma_t }$$  (Greek symbol sigma) = thremal stress

$$\large{ l_i }$$ = initial length of material

$$\large{ \epsilon }$$  (Greek symbol epsilon) = strain

$$\large{ \Delta T }$$ = temperature differential

$$\large{ \alpha }$$  (Greek symbol alpha) = thermal expansion coefficient

$$\large{ E }$$ = Young's modulus