고체역학 (Gere) — Torsion: Problem 3.2-6

3.2-6 A circular aluminum tube subjected to pure torsion by torques $T$ (see figure) has an outer radius $r_2$ equal to 1.5 times the inner radius $r_1$. (a) If the maximum shear strain in the tube is measured as $400 \times 10^{-6}$ rad, what is the shear strain $\gamma_1$ at the inner surface? (b) If the maximum allowable rate of twist is $0.125^\circ/\text{m}$ and the maximum shear strain is to be kept at $400 \times 10^{-6}$ rad by adjusting the torque $T$, what is the minimum required outer radius $(r_2)_{\text{min}}$?