고체역학 (Gere) — Torsion: Problem 3.11-12

3.11-12 A thin tubular shaft with a circular cross section (see figure) and with inside diameter 100 mm is subjected to a torque of 5000 N·m. If the allowable shear stress is 42 MPa, determine the required wall thickness \( t \) by using (a) the approximate theory for a thin-walled tube and (b) the exact torsion theory for a circular bar.