고체역학 (Gere) — Torsion: Problem 3.2-4

3.2-4 A circular steel tube of length \( L = 1.0 \text{ m} \) is loaded in torsion by torques \( T \) (see figure). (a) If the inner radius of the tube is \( r_1 = 45 \text{ mm} \) and the measured angle of twist between the ends is \( 0.5^\circ \), what is the shear strain \( \gamma_1 \) (in radians) at the inner surface? (b) If the maximum allowable shear strain is \( 0.0004 \text{ rad} \) and the angle of twist is to be kept at \( 0.45^\circ \) by adjusting the torque \( T \), what is the maximum permissible outer radius \( (r_2)_{\text{max}} \)?