$(25$ points$)$ Select the lightest available W$12$ section $($ASTM A$992)$ through the LRFD and ASD methods for the

column loads $P_D=500k,P_{Lr}=650k$ and $P_W=600k$ for a $40$ ft $.$ long column with fixed supports at top and

bottom, and an additional support at mid$-$span to brace the column in the weak axis only. Assume the section is

nonslender. 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 $50$ 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 $4-1$ of the AISC Manual and compare with part $($a$).$