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Q8) The overall length of a stepped rod is 250 mm with 100 mm of the rod having a diameter of 20 mm and the remainder a diameter of 30 mm. At a temperature of 120^oC the rod is free of stress. It is then cooled to 20^oC and the contraction is restricted to 0.25 mm axially.

Calculate the maximum stress in the rod caused by cooling. (16)

Note: Modulus of Elasticity for the rod material = 200 GN/m².

Coefficient of linear expansion for the rod material = 12 x 10^-4 per ^oC.