A copper bar with a rectangular cross section is held without stress between rigid supports $($see figure$).$ Subsequently, the temperature of the bar is raised $50$ degree C$.($a$)$ Determine the stresses on all faces of the elements A and B$,$ and show these stresses on sketches of the elements. $($Assume alpha $=17\mathrm{.}5$ times $10^-6/$degree C and E $=120$ GPa.$)($b$)$ If the shear stress at B is known to be $48$ MPa at some inclination $9,$ find angle theta and show the stresses on a sketch of a properly oriented element.