고체역학 (Gere) — Torsion: Problem 3.3-11

3.3-11 A circular tube of aluminum is subjected to torsion by torques $T$ applied at the ends (see figure). The bar is $0.75\text{ m}$ long, and the inside and outside diameters are $28\text{ mm}$ and $45\text{ mm}$, respectively. It is determined by measurement that the angle of twist is $4^\circ$ when the torque is $700\text{ N}\cdot\text{m}$. (a) Calculate the maximum shear stress $\tau_{\max}$ in the tube, the shear modulus of elasticity $G$, and the maximum shear strain $\gamma_{\max}$ (in radians). (b) If the maximum shear strain in the tube is limited to $2.2 \times 10^{-3}$ and the inside diameter is increased to $35\text{ mm}$, what is the maximum permissible torque?