고체역학 (Gere) — Torsion: Problem 3.3-15

3.3-15 A hollow steel shaft used in a construction auger has an outer diameter \(d_2 = 175 \text{ mm}\) and inner diameter \(d_1 = 125 \text{ mm}\) (see figure). The steel has a shear modulus of elasticity \(G = 80 \text{ GPa}\). For an applied torque of \(20 \text{ kN}\cdot\text{m}\), determine the following quantities: (a) shear stress \(\tau_2\) at the outer surface of the shaft, (b) shear stress \(\tau_1\) at the inner surface, and (c) rate of twist \(\theta\) (degrees per unit of length). Also, draw a diagram showing how the shear stresses vary in magnitude along a radial line in the cross section.