$(20$ 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.