Figure P.15.19 shows a frame pinned to supports at A and B. The frame centreline is a circular arc and its section is uniform, of bending stiffness EI and depth d. Find the maximum stress in the frame produced by a uniform temperature gradient through the depth, the temperature on the outer and inner surfaces being raised and lowered by an amount T. The coefficient of linear expansion of the material of the frame is α. (Hint. Treat half the frame as a curved cantilever builtin on its axis of symmetry and determine the horizontal reaction at a support by equating the horizontal deflection produced by the temperature gradient to the horizontal deflection produced by the reaction).
Ans. 1.29 ETα.