고체역학 (Gere) — Torsion: Problem 3.3-20

3.3-20 A hollow aluminum tube used in a roof structure has an outside diameter \(d_2 = 104 \text{ mm}\) and an inside diameter \(d_1 = 82 \text{ mm}\) (see figure). The tube is \(2.75 \text{ m}\) long, and the aluminum has shear modulus \(G = 28 \text{ GPa}\). (a) If the tube is twisted in pure torsion by torques acting at the ends, what is the angle of twist (in degrees) when the maximum shear stress is \(48 \text{ MPa}\)? (b) What diameter \(d\) is required for a solid shaft (see figure) to resist the same torque with the same maximum stress? (c) What is the ratio of the weight of the hollow tube to the weight of the solid shaft?