고체역학 (Gere) — Torsion: Problem 3.5-5

3.5-5 A tubular bar with outside diameter \(d_2 = 100 \text{ mm}\) is twisted by torques \(T = 8.0 \text{ kN}\cdot\text{m}\) (see figure). Under the action of these torques, the maximum tensile stress in the bar is found to be \(46.8 \text{ MPa}\). (a) Determine the inside diameter \(d_1\) of the bar. (b) If the bar has length \(L = 1.2 \text{ m}\) and is made of aluminum with shear modulus \(G = 28 \text{ GPa}\), what is the angle of twist \(\phi\) (in degrees) between the ends of the bar? (c) Determine the maximum shear strain \(\gamma_{max}\) (in radians)?