$(35$ points$)$ For a $44$ ft $.$ column in a parking garage structure, with a fixed support at the top, pinned support at the bottom and additional supports at $18$ ft $.$ from the top and $13$ ft $.$ from the bottom to brace the column in the weak axis only. Select the lightest available rectangular HSS $1210,$ HSS $128$ or HSS $126$ section $($ASTM A$500$ Grade B$)$ through the LRFD and ASD methods for the column loads $P_D=60k,P_L=55k$ and $P_E=65k.$ Make sure you include units in all your final answers.

$($a$)$ Select the section by trial$-$and$-$error method by making an initial assumption of $75$ for the slenderness ratio and then using the critical stress values in Table $4-22$ of the AISC Manual.

$($b$)$ Repeat the problem using Table $4-3$ of the AISC Manual and compare with part $($a$).$

Giqhest HSS$1$E$\backslash$times $10$

$P_0=60K$

$13$ ft