A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of ΔT. The Young’s modulus is E and the coefficient of linear expansion is α. The thermal stress in the rod is

Explanation:

If Rod is free to expand

Free elongation ΔL  = L αΔT

∴ ΔL/L = αΔT

Here Rod is fixed at both ends so strain will be zero but due to restriction given by fixed ends, there will be reaction force at the end.

That reaction force per unit area is known as thermal stress.

It is given by- 

\(\sigma = E\epsilon\)

or, σ = E(ΔL/L) = Eα(ΔT)

Since Rod is fixed at both ends, so thermal strain be zero but there will be thermal stress.

To Revise the concept of Thermal Stress, click here.