A hollow steel shaft with an outside diameter of 81 mm and a wall thickness of 6 mm is subjected to a pure torque of T = 6700 N-m. The shear modulus of the steel is G = 66 GPa.

a. Determine the maximum shear stress in the hollow shaft.
b. Determine the minimum shear stress in the hollow shaft and the corresponding location.
c. Determine the angle of twist at the free end of the hollow shaft and at a location 3 m from the fixed end
d. Determine the minimum diameter of a solid steel shaft for which the maximum shear stress is the same as in part (a) for the same torque T