고체역학 (Gere) — Torsion: Problem 3.3-4

3.3-4 A copper tube with circular cross section has length \(L = 1.25\text{ m}\), thickness \(t = 2\text{ mm}\), and shear modulus of elasticity \(G = 45\text{ GPa}\). The bar is designed to carry a \(300\text{ N}\cdot\text{m}\) torque acting at the ends. If the allowable shear stress is \(25\text{ MPa}\) and the allowable angle of twist between the ends is \(2.5^\circ\), what is the minimum required outer diameter \(d\)?