A $2\mathrm{.}3-$in$-$diameter solid aluminum post is subjected to a horizontal force of $P_x=10\mathrm{.}6$kips, a vertical force of $P_y=23$kips, and a concentrated torque of $T=4\mathrm{.}3$ kip$-$ft$,$ acting in the directions shown. Assume $L=3\mathrm{.}5$ in$.$ The yield strength of the aluminum is ${}_Y=70$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 $K,$ and determine whether the aluminum post satisfies the specifications according to:

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

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

Answers:

$($a$)$ Maximum$-$shear$-$stress theory