Prob $6.$ The shaft shown below is fixed at the wall. The

shaft is made of steel $(G=11{10}^3$ksi $)$ and has a length of

$4\mathrm{.}5$ ft $.$ Given that the applied torque is $T=20,000lb*ft.$

$($a$)$ Determine the maximum diameter of the shaft if the

maximum shear stress in the shaft is $8,000$ psi.

$($b$)$ Determine the angle of twist of the free end.