A W$18$x$130$ column $(AB)$ of A$992$ steel, $16$ ft long is to be investigated. The column is part of a braced frame with moment connections $($Fig$.1($a$),$ braces are not shown for clarity$)($sidesway restricted$).$ The axial load and the moments obtained from the $1^{st}$ order analysis of gravity loads $($DL$+$LL$)$ and earthquake loads are shown in Fig. $1($b$).$ The frame is symmetrical and the gravity loads are symmetrically placed. The earthquake load moments are shown in Fig. $1($b$)($ii$).$ All the bending moments are about strong axis. Check the adequacy of the column AB$.$ Load combinations to be used are:

$L.C.=1\mathrm{.}2D+1\mathrm{.}0E+0\mathrm{.}5L$ and $\frac{?}{or}$

$L.C.=1\mathrm{.}2D+1\mathrm{.}6L$

Relevant equations.

$B_1=\frac{c_m}{1-\frac{P_r}{P_{e1}}},C_m=0\mathrm{.}6-0\mathrm{.}4(\frac{M_1}{M_2}),P_{e1}=\frac{{}^{2}E{I}^{**}}{(K_{1}L{)}^2}$

$($i$)$ Gravity

$($ii$)$ Earthquake

Fig. $1($a$)$

Fig. $1($b$)$