고체역학 (Beer) — Torsion: Problem 3.106

3.106 The hollow shaft shown is made of steel which is assumed to be elastoplastic with \(\tau_Y = 145 \text{ MPa}\) and \(G = 77.2 \text{ GPa}\). Determine the magnitude \(T\) of the torque and the corresponding angle of twist (a) at the onset of yield, (b) when the plastic zone is \(10 \text{ mm}\) deep.