고체역학 (Gere) — Torsion: Problem 3.11-1

3.11-1 A hollow circular tube having an inside diameter of 230 mm and a wall thickness of 30 mm (see figure) is subjected to a torque \( T = 136 \text{ kN}\cdot\text{m} \). Determine the maximum shear stress in the tube using (a) the approximate theory of thin-walled tubes, and (b) the exact torsion theory. Does the approximate theory give conservative or nonconservative results?