Problem $2.$ Consider a three$-$bay, two$-$story structure shown below exposed to dead, live and wind loads. The first order moments caused by each load are given in the figure. The bending occurs in strong axis, and the columns are fully braced laterally. The columns are made of W$10$x$39(l_x=209i{n}^4,r_x=4\mathrm{.}27$ inch, $r_y=1\mathrm{.}98$ inch, $($:$A_g=11\mathrm{.}5i{n}^2\}$ and all the beams are made of $)=(1330i{n}^4.$ Check if member $ab$ is sufficient. The member length $L$ is $18$ feet.

$($a$)$ Calculate the compression capacity, $P_n$ of beam$-$column a$-$b;

$($b$)$ Calculate the bending capacity, $M_n$ of beam$-$column a$-$b$.$

$($c$)$ Calculate the amplification factor $B_1$;

$($d$)$ Determine if the section of member $a-b$ is sufficient to carry the given loads.

$\backslash$table$[[$Member $a-b,$Dead,Live,Wind$],[P_b($kips$),45,90,10],[M_{ntb}($kips$-$ft$),14,30,20]]$