$J=\frac{(d_o^4-d_i^4)}{32},=\frac{T_i{L}_i}{J_i{G}_i},=\frac{T_{}}{J},{}_{\text{m}\text{a}\text{x}}=\frac{Tc}{J}{}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=\frac{{}_{\text{f}\text{a}\text{i}\text{l}}}{F.S},$ where $c=\frac{d_0}{2}$

Question $1$

$10$ pts

The shaft shown in the figure, which is clamped at A and C$,$ has a circular hollow cross$-$section in section BC with wall thickness $t=0\mathrm{.}5$ inches, and a solid circular cross section in section $AB.$ The diameter of segment $AB$ is equal to $1\mathrm{.}5$ inches and the outer diameter of segment $BC$ is equal to $d=3$ inches. The total length of the shaft is $L=30in.$ If section BC is known to be critical, the failure shear stress in the shaft is $24000$ psi, and the application requires a safety factor of $3,$ what is the maximum torque $(T_0{)}_{\text{m}\text{a}\text{x}}$ that may be applied at point $B?$