A thin plate is placed inside a rigid in-plane constraint with initial gaps as shown. No constraint is placed on the plate along the z-axis. The plate is made of steel with an elastic modulus E = 29000 ksi, a Poisson's ratio of = 0.32, and a coefficient of thermal expansion = 6.60 x 10-6 /F. The temperature of the plate is now increased by T = 100 F. (a) Determine the all the normal stress components. (b) Determine the change in thickness of the plate. (c) What is the largest temperature change allowed to avoid developing stresses in the plate