A rod is clamped between two rigid supports so that it neither bends nor expands. Find the thermal compression force and thermal stress set up in the rod when it is heated through 9°C.

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