고체역학 (Gere) — Torsion: Problem 3.8-17

3.8-17 A uniformly tapered aluminum-alloy tube AB of circular cross section and length \(L\) is fixed against rotation at A and B, as shown in the figure. The outside diameters at the ends are \(d_A\) and \(d_B = 2d_A\). A hollow section of length \(L/2\) and constant thickness \(t = d_A/10\) is cast into the tube and extends from B halfway toward A. Torque \(T_0\) is applied at \(L/2\). (a) Find the reactive torques at the supports, \(T_A\) and \(T_B\). Use numerical values as follows: \(d_A = 64 \text{ mm}\), \(L = 1.2 \text{ m}\), \(G = 27 \text{ GPa}\), and \(T_0 = 4.5 \text{ kN}\cdot\text{m}\). (b) Repeat part (a) if the hollow section has constant diameter \(d_A\).