$20$ points$)$ The shaft below has a fixed support at A and is subjected to the torques shown. The

shaft is made from A$36$ steel $($E$=29,000$ ksi and G$=11,000$ ksi$).$ The shaft is solid from A to B

$($diameter $0\mathrm{.}4$ in$)$ and hollow from B to D $($outside diameter$=0\mathrm{.}4$ in with inside diameter $=0\mathrm{.}25$

in$).$

$($a$)$ Provide the internal torque diagram along the shaft$$s length $($with Torque, T on the y$-$axis

and length on the x axis$).$

$($b$)$ Determine the maximum shear stress in the entire shaft in units of psi.

$($c$)$ Determine the displacement $($angle of twist$)$ of A with respect to D$,$ in radians or degrees.