고체역학 (Gere) — Torsion: Problem 3.5-3

3.5-3 A hollow aluminum shaft (see figure) has an outside diameter \(d_2 = 100 \text{ mm}\) and inside diameter \(d_1 = 50 \text{ mm}\). When twisted by torques \(T\), the shaft has an angle of twist per unit distance equal to \(2^\circ/\text{m}\). The shear modulus of elasticity of the aluminum is \(G = 27.5 \text{ GPa}\). (a) Determine the maximum tensile stress \(\sigma_{\text{max}}\) in the shaft. (b) Determine the magnitude of the applied torques \(T\).