고체역학 (Gere) — Torsion: Problem 3.3-3

3.3-3 Repeat Problem 3.3-1, but now use a circular tube with outer diameter $d_o = 63 \text{ mm}$ and inner diameter $d_i = 38 \text{ mm}$. [From Problem 3.3-1]: A solid steel bar of circular cross section has diameter $d = 63 \text{ mm}$, length $L = 1.5 \text{ m}$, and shear modulus of elasticity $G = 80 \text{ GPa}$. The bar is subjected to torques $T = 400 \text{ N}\cdot\text{m}$ at the ends. Calculate: (a) the angle of twist between the ends. (b) the maximum shear stress. (c) the shear stress at a distance $r_A = 25 \text{ mm}$ measured from the center of the bar.