A solid shaft with constant diameter is subjected to four torques as shown. The bearing at point A allow the shaft to turn freely$($ i$.$e$.$ no internal torque along $AB)$ Point F is attached to the wall. The shaft shear modulus is G$=45$ GPa. a$.$ Determine and draw the internal torque along BC$,$ CD$,$ DE$,$ and EF$.$

b$.$ Calculate the minimum diameter if the maximum allowable stress in the shaft is $65$ MPa.

c$.$ Calculate the total angle of twist with respect to F$.$