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

service column loads $P_D=500k$ and $P_L=800k$ for a $30$ ft $.$ long column with a pinned support at top, fixed

support at bottom and an additional pin support in the weak axis direction only at mid$-$span. 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$).$