The composite shaft shown in the figure is manufactured by shrink-fitting a steel sleeve over a brass core so that the two parts act as a single solid bar in torsion. The outer diameters of the two parts are d1 = 40 mm for the brass core and d2 = 50 mm for the steel sleeve. The shear moduli of elasticity are Gb = 36 GPa for the brass and Gs = 80 GPa for the steel.
Assuming that the allowable shear stresses in the brass and steel are Tb = 48 MPa and Ts = 80 MPa, respectively, determine the maximum permissible torque Tmax that may be applied to the shaft. (Use Eqs. 3-44 a and b to find the torques.)

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Steel sleeve Brass core 0 di di Probs. 3.8-12 and 3.8-13