A steel shaft $A$ and an aluminum sleeve $B$ are connected at the right end (see Fig, P.14.23) by a rigid support and at the left end by a rigid plate C. A torque $T_1=500$ $\mathrm{ft}-\mathrm{lb}$ is applied to the plate and a second torque $T_2=800 \mathrm{ft}-\mathrm{lb}$ is applied to the sleeve as shown. What is the maximum torsional shear stress in each member'? What is the angle of twist at the rigid plate? Take $G_A=15 \times 10^6$ psi and $G_B=10$ $\times 10^{\circ}$ psi. (Hint: Consider free-body diagrams of sleeve $B$, shaft $A$, and end plate $C$.)
Figure P. 14.23.