고체역학 (Gere) — Torsion: Problem 3.3-2

3.3-2 A solid copper bar of circular cross section has length \( L = 1.25 \text{ m} \) and shear modulus of elasticity \( G = 45 \text{ GPa} \). The bar is designed to carry a \( 250 \text{ N}\cdot\text{m} \) torque acting at the ends. If the allowable shear stress is \( 30 \text{ MPa} \) and the allowable angle of twist between the ends is \( 2.5^\circ \), what is the minimum required diameter?