$(40-$points$)$ A $14-$ft long W$10$x$54$ section is part of an unbraced frame $($i$.$e$.$ sidesway allowed$).$ A

first$-$order analysis has produced the following loads:

$P_{nt}=70-k,P_{lt}=28-k$

$M_{ntx}=46ft-k,M_{ltx}=18ft-k$

$M_{nty}=18-ft-k,M_{lty}=6ft-k$

The following additional information is also available about the frame:

$C_{mx}=C_{my}=0\mathrm{.}85$;$P_{\text{s}\text{t}\text{o}\text{r}\text{y}}=1604-k$; the ratio of $\frac{P_{mf}}{P_{\text{s}\text{t}\text{o}\text{r}\text{y}}}=0\mathrm{.}333$; the story shear, $H=33\mathrm{.}4-k$;

and the drift indices are $(\frac{{}_H}{L}{)}_x=0\mathrm{.}002$ and $(\frac{{}_H}{L}{)}_y=0\mathrm{.}0034.$ Assume $K_x=1\mathrm{.}31$ and $K_y=$

$1\mathrm{.}25.$

Using LRFD$,$ determine whether the W$10$x$54$ section is adequate for the given loads using the

Approximate Analysis method of Appendix $8.$ Be sure to calculate the moment and axial

amplification factors to consider both P$-$ AND P$-$ effects.