For the structure shown in Figure $2,$ with a uniformly distributed

factored load w$\_($u$)=4$kip$($s$)/($f$)$t applied to beam BC $,$ answer the following questions:

$($a$)$ Draw the bending moment, shear force, and normal force diagrams.

$($b$)$ Find the minimum area of steel required to serve as a cross section for member AB $.$

Assume welded connections and shear lag factor U$=0\mathrm{.}75$

$($c$)$ Find the minimum plastic modulus a standard rolled W section must have to adequately

resist the bending moments in beam BC $.$ Assume that the top flange is continuously

laterally braced. Neglect the effect of axial load

$($d$)$ Select the lightest W section for beam BC assuming no lateral bracing for the top flange.

Neglect the effect of axial load. Check the adequacy of the cross section in shear.

$($e$)$ Using the section from part $($d$)$ and considering the effect of the axial load along BC$,$

determine the amplification factor $\backslash$beta $\_(1)$ and explain why $\backslash$beta $\_(2)$F$\_($y$)=36$ksi and F$\_($u$)=58$ksi for member AB and F$\_($y$)=50$ksi for member BC