고체역학 (Gere) — Torsion: Problem 3.5-9

3.5-9 The normal strain in the \(45^\circ\) direction on the surface of a circular tube (see figure) is \(880 \times 10^{-6}\) when the torque \(T = 85 \text{ N}\cdot\text{m}\). The tube is made of copper alloy with \(G = 42 \text{ GPa}\) and \(\nu = 0.35\). (a) If the outside diameter \(d_2\) of the tube is \(20 \text{ mm}\), what is the inside diameter \(d_1\)? (b) If the allowable normal stress in the tube is \(96 \text{ MPa}\), what is the maximum permissible inside diameter \(d_1\)?