The composite shaft consists of two steel pipes that are connected at flange b and securely attached to rigid walls at a and c. steel pipe (1) has an outside diameter of 7.75 in., a wall thickness of 2.74 in., and a length of l1 = 16 ft. steel pipe (2) has an outside diameter of 5.75 in., a wall thickness of 1.78 in., and a length of l2 = 22 ft. both pipes have a shear modulus of 13500 ksi. if a concentrated torque of 45 kip-ft is applied to flange b, determine: (a) the maximum shear stress magnitudes τ1, τ2 in pipes (1) and (2). (b) the rotation angle φb/a of flange b relative to support a.