$(30$ points$)$ Determine the LRFD design strength $cPn$ and the ASD allowable strength $P\frac{n}{}c$ for a W$12$x$87$

$($ASTM A$992)$ column with $L=20ft.$ and fixed supports at top and bottom. Make sure you include units in all

your final answers.

$($a$)$ First determine whether the section is "slender" or "nonslender" by calculations.

$($b$)$ Calculate the LRFD$/$ASD strengths using the equations of AISC Section E$3.$

$($c$)$ Using the critical stress values in Table $4-22$ of the AISC Manual, determine the LRFD$/$ASD strengths and

compare with part $($b$).$

$($d$)$ Repeat the problem using Table $4-1$ of the AISC Manual and compare with parts $($b$)$ and $($c$).$