고체역학 (Gere) — Torsion: Problem 3.2-5

3.2-5 Solve the preceding problem if the length \(L = 1420 \text{ mm}\), the inner radius \(r_1 = 32 \text{ mm}\), the angle of twist is \(0.5^\circ\), and the allowable shear strain is \(0.0004 \text{ rad}\). [Context from Preceding Problem 3.2-4: A circular steel tube of length \(L\) is loaded in torsion by torques \(T\) (see figure). (a) If the inner radius of the tube is \(r_1\) and the measured angle of twist between the ends is \(\phi\), what is the shear strain \(\gamma_1\) (in radians) at the inner surface? (b) If the maximum allowable shear strain is \(\gamma_{\text{allow}}\) and the angle of twist is to be kept at a specific target by adjusting the torque \(T\), what is the maximum permissible outer radius \((r_2)_{\text{max}}\)?]