고체역학 (Gere) — Torsion: Problem 3.8-13

3.8-13 A solid steel bar of diameter \(d_1 = 50\text{ mm}\) is enclosed by a steel tube of outer diameter \(d_3 = 75\text{ mm}\) and inner diameter \(d_2 = 65\text{ mm}\) (see figure). Both bar and tube are held rigidly by a support at end \(A\) and joined securely to a rigid plate at end \(B\). The composite bar, which has length \(L = 660\text{ mm}\), is twisted by a torque \(T = 2\text{ kN}\cdot\text{m}\) acting on the end plate. (a) Determine the maximum shear stresses \(\tau_1\) and \(\tau_2\) in the bar and tube, respectively. (b) Determine the angle of rotation \(\phi\) (in degrees) of the end plate, assuming that the shear modulus of the steel is \(G = 80\text{ GPa}\). (c) Determine the torsional stiffness \(k_T\) of the composite bar.