$(40$ points$)$ Determine the LRFD design strength $cPn$ and the ASD allowable strength $P\frac{n}{}c$ for a W $1265$

$($ASTM A$992)$ column with $L=35ft.$ with a fixed support at top and pinned support at 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$).$

$($e$)$ If supports are added to brace the column in the weak axis only at $10$ ft $.$ and $20$ ft $.$ from the bottom support,

determine the new LRFD$/$ASD strengths using the critical stress values in Table $4-22.$ Repeat the problem using

Table $4-1$ of the AISC Manual. Discuss how the added braces affected the column strength.