The lightest W$12$ section $($A$992$ steel$)$ for the beam$-$column shown below.

The member is laterally braced at $R,S,T$ and $U.$ All forces are factored.

Disregard shear strength and deflection requirements.

$P=$ factored concentrated axial load

$F=$ factored concentrated transverse load

$=165$kips

$=35$kips

$=0\mathrm{.}50\frac{k}{f}t$

$W=$ factored uniform distributed load $=35$kips

$If$ you used a table $or$ graph for answering a ques $=0\mathrm{.}50\frac{k}{f}t$

$($It includes the self$-$weight of the beam$)$ number of a table or graph for answering a question, indicate the corresponding reference and write the number of the equation used to calculate that value. Justify the use of that equation.

vistivuted ioad inciuaes the selt$-$weight of the member

Laterally supported at R$,$S$.$T$.$ and U