Consider a rod of length L, area of cross-section A, clamped between the two rigid supports so that it neither expands nor bends.
Heat the rod so that its temperature increases by θ°C.
As the rod is neither allowed to expand nor bend, therefore a compressive force or stress is set up in the rod. This force or stress is called thermal force or thermal stress.
Let be the coefficient of linear expansion and Y be the Young’s modulus of material.
If the ends of rod were free, then its length would increase by,
The rod being clamped, does not expand but a strain is produced in the rod.
The strain in the rod is given by,
The stress in the wire is,
Thermal stress = Y x strain
Thermal force developed in the rod is,
Thermal force = Thermal Stress x Area