Temperature Stresses

1. When the temperature of a material change, then there will be a corresponding change in the dimension of the material.

2. When a member is free to expand or contract due to the increase or decrease of temperature, then there will be no stresses induced in the member.

3. But if the natural change in length due to rise or fall of temperature be prevented, then there will be stresses induced.

Free expansion of member δ=αTl

When the expansion is fully prevented then,

Temperature Stress= αTE

(Where α is the coefficient of linear expansion, T is the change in temperature and E is the Young's Modulus)

Suppose a rod of length l, when subjected to a rise of temperature is permitted to expand only by δ, then the temperature strain is

e=(Expansion prevented)/(Original Length)

e=(αTl-δ)/l

Since, Modulus of Elasticity (E) =Stress (p)/strain (e).

Therefore, temperature stress (p) = temperature strrain(e)xE

p=(E(αTl-δ))/l