고체역학 (Beer) — Torsion: Problem 3.117

3.117 After the solid shaft of Prob. 3.116 has been loaded and unloaded as described in that problem, a torque $T_1$ of sense opposite to the original torque $T$ is applied to the shaft. Assuming no change in the value of $\phi_Y$, determine the angle of twist $\phi_1$ for which yield is initiated in this second loading and compare it with the angle $\phi_Y$ for which the shaft started to yield in the original loading. Reference from Prob. 3.116: The solid shaft shown is made of a steel that is assumed to be elastoplastic with $\tau_Y = 145 \text{ MPa}$ and $G = 77.2 \text{ GPa}$. The torque is increased in magnitude until the shaft has been twisted through $6^\circ$; the torque is then removed. Data from Fig. P3.116: Length $L = 0.6 \text{ m}$, Radius $c = 16 \text{ mm} = 0.016 \text{ m}$.