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A cuboid$-$shaped block having dimensions of $(bcd)$ is made up of an elastic material having

a Young's modulus of $E,$ Poisson's ratio $v$ and coefficient of thermal expansion $.$ The block is

placed within a tight$-$fitting container with smooth, rigid walls. The front and rear faces $($the $z-$

faces$)$ are left unconstrained. A rigid plate is pressed downward on the block by a force P acting

on the mechanism shown. Simultaneously, the temperature of the block is uniformly raised by an

amount of $T.$ Consider the weight of the mechanism, plate and block to be small.

a$)$ Determine the three normal components of stress and the three normal components of strain

in the block.

b$)$ Determine the reaction forces on the block by the rigid side walls of the container.

Leave your answers in terms of$,$ at most, $P,E,v,,T,b,c$ and $d.$