$3\mathrm{.}8-1$ A solid circular bar ABCD with fixed supports is acted upon by torques $T_0$ and $2T_0$ at the locations shown in the figure.

$($a$)$ Obtain a formula for the maximum angle of twist ${}_{\text{m}\text{a}\text{x}}$ of the bar. $[$Hint: Use Eqs. $(3-50$a and b$)$ of Example $3-9$ to obtain the reactive torques.$]$

$($b$)$ What is ${}_{\text{m}\text{a}\text{x}}$ if the applied torque $T_0$ at $B$ is reversed in direction?

PROB. $3\mathrm{.}8-1$