A $2\mathrm{.}7-$in$.-$diameter solid aluminum post is subjected to a horizontal force of $P_x=9$kips, a vertical force of $P_y=22\mathrm{.}8$kips and a concentrated torque of $T=4\mathrm{.}3$kip$-ft,$ acting in the directions shown. Assume $L=4\mathrm{.}5in.$ The yield strength of the aluminum is $Y=47$ksi, and a minimum factor of safety of $F{S}_{\text{m}\text{i}\text{n}}=1\mathrm{.}67$ is required by specification. Consider points $H,$ and determine whether the aluminum post satisfies the specifications according to:

$($a$)$ the maximum$-$shear$-$stress theory.

$($b$)$ the maximum$-$distortion$-$energy theory.