A solid steel bar of diameter 30 mm is enclosed by a steel tube of outer diameter 45 mm and inner diameter 36 mm. Both bar and tube are held rigidly at end A and joined securely to a rigid plate at end B. The composite bar, which is 500 mm long, is twisted by a torque T = 500 N.m acting on the end plate.
(a) Determine the maximum shear stresses and 1τ2τ in the bar and tube, respectively.
(b) Determine the angle of rotation φ (in degrees) of the end plate, assuming that the shear modulus of the steel is G = 80 GPa.
(c) If the maximum allowable shear stress is 69 MPa, determine the allowable value of the torque T.