고체역학 (Gere) — Torsion: Problem 3.4-2

3.4-2 A circular tube of outer diameter \(d_3 = 70 \text{ mm}\) and inner diameter \(d_2 = 60 \text{ mm}\) is welded at the right-hand end to a fixed plate and at the left-hand end to a rigid end plate (see figure). A solid, circular bar with a diameter of \(d_1 = 40 \text{ mm}\) is inside of, and concentric with, the tube. The bar passes through a hole in the fixed plate and is welded to the rigid end plate. The bar is \(1.0 \text{ m}\) long and the tube is half as long as the bar. A torque \(T = 1000 \text{ N}\cdot\text{m}\) acts at end \(A\) of the bar. Also, both the bar and tube are made of an aluminum alloy with a shear modulus of elasticity \(G = 27 \text{ GPa}\). (a) Determine the maximum shear stresses in both the bar and tube. (b) Determine the angle of twist (in degrees) at end \(A\) of the bar.