Problem C$2.$ The column ab as shown in Fig. P$2$ is under $500$ kips factored load, and has pinned support at joint a$.$

The column is connected to two beams at joint $b$ in strong axis bending. The column has fully supported in weak

axis. The column is made of $W14x48(A_g=14\mathrm{.}1i{n}^2,I_x=484i{n}^4,r_x=5\mathrm{.}85in,r_y=1\mathrm{.}91in)$ and the beams are made of

W$18$x$65(I_x=1070i{n}^4).$ All the members are made of $50$ksi steel $(\{$:$F_y=50$ksi,$F_u=65$ksi,$E=29000$ksi$).$

$($a$)$ Find the effective lengths in $x$ and $y$ directions;

$($b$)$ Find the slenderness in $x$ and $y$ directions;

$($c$)$ Calculate the column capacity, $P_n.$