Two shafts, one of aluminum alloy and the other of steel, are coupled end to end. The steel shaft is 2 m long and is hollow with an external diameter of 100 mm and an internal diameter of 50 mm. The aluminum shaft is solid with a 100 mm diameter throughout its length of 1 m. The compound shaft is fixed at ends and a torque of 15 kN-m is applied to the coupling. Neglecting the effect of coupling, find:
(a) Maximum shear stresses in the two portions of the shaft.
(b) Angle of twist at the coupling.
Take CSteel = 80 GN/m^2, and CAluminum = 25 GN/m^2.