고체역학 (Gere) — Torsion: Problem 3.5-10

3.5-10 An aluminum tube has inside diameter \( d_1 = 50 \text{ mm} \), shear modulus of elasticity \( G = 27 \text{ GPa} \), \( \nu = 0.33 \), and torque \( T = 4.0 \text{ kN}\cdot\text{m} \). The allowable shear stress in the aluminum is \( 50 \text{ MPa} \), and the allowable normal strain is \( 900 \times 10^{-6} \). (a) Determine the required outside diameter \( d_2 \). (b) Re-compute the required outside diameter \( d_2 \) if allowable normal stress is \( 62 \text{ MPa} \) and allowable shear strain is \( 1.7 \times 10^{-3} \).