고체역학 (Beer) — Torsion: Problem 3.63

3.63 An annular plate of thickness $t$ and modulus $G$ is used to connect shaft $AB$ of radius $r_1$ to tube $CD$ of radius $r_2$. Knowing that a torque $T$ is applied to end $A$ of shaft $AB$ and that end $D$ of tube $CD$ is fixed, (a) determine the magnitude and location of the maximum shearing stress in the annular plate, (b) show that the angle through which end $B$ of the shaft rotates with respect to end $C$ of the tube is \[ \phi_{BC} = \frac{T}{4\pi Gt} \left( \frac{1}{r_1^2} - \frac{1}{r_2^2} \right) \]