Problem $2\mathrm{.}6-8$

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 $50C$

$($a$)$ Determine the stresses on all faces of the element A and $B.$

$($Assume $=\frac{{17\mathrm{.}510}^{-6}}{}C$ and $E=120$GPa.$)$

$($b$)$ Show the stresses from in part $($a$)$ on sketches of the elements.

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$($c$)$ If the shear stress at $B$ is known to be $48$ MPa at some inclination $,$ find angle $.$

$($d$)$ Show the stresses from in part $($c$)$ on a sketch of a properly oriented element.