고체역학 (Gere) — Torsion: Problem 3.4-1

3.4-1 A stepped shaft $ABC$ consisting of two solid circular segments is subjected to torques $T_1$ and $T_2$ acting in opposite directions, as shown in the figure. The larger segment of the shaft has a diameter of $d_1 = 58 \text{ mm}$ and length $L_1 = 760 \text{ mm}$; the smaller segment has a diameter of $d_2 = 45 \text{ mm}$ and length of $L_2 = 510 \text{ mm}$. The material is steel with shear modulus $G = 76 \text{ GPa}$, and the torques are $T_1 = 2300 \text{ N}\cdot\text{m}$ and $T_2 = 900 \text{ N}\cdot\text{m}$. (a) Calculate the maximum shear stress $\tau_{\max}$ in the shaft and the angle of twist $\phi_C$ (in degrees) at end $C$. (b) If the maximum shear stress in $BC$ must be the same as that in $AB$, what is the required diameter of segment $BC$? What is the resulting twist at end $C$?