고체역학 (Gere) — Torsion: Problem 3.8-16

3.8-16 A steel shaft (\(G_s = 80\text{ GPa}\)) of total length \(L = 3.0\text{ m}\) is encased for one-third of its length by a brass sleeve (\(G_b = 40\text{ GPa}\)) that is securely bonded to the steel (see figure). The outer diameters of the shaft and sleeve are \(d_1 = 70\text{ mm}\) and \(d_2 = 90\text{ mm}\), respectively. (a) Determine the allowable torque \(T_1\) that may be applied to the ends of the shaft if the angle of twist between the ends is limited to \(8.0^\circ\). (b) Determine the allowable torque \(T_2\) if the shear stress in the brass is limited to \(\tau_b = 70\text{ MPa}\). (c) Determine the allowable torque \(T_3\) if the shear stress in the steel is limited to \(\tau_s = 110\text{ MPa}\). (d) What is the maximum allowable torque \(T_{\text{max}}\) if all three of the preceding conditions must be satisfied?