$11-15.$ Analysis problem in an unbraced frame $-$ using loads and moments obtained using

the requirements of the Effective Length Method.

A W$848$ section consisting of $50$ksi is used for a $14ft$ long beam$-$column in a one

story building frame. It is unbraced in the plane of the frame $(x-x$ axis$)$ but is braced

out of the plane of the frame $(y-y$ axis$)$ so that $K_y=1\mathrm{.}0.K_x$ has been determined to

equal $1\mathrm{.}67.$ A first$-$order analysis has been completed and the results yielded a $P_{nt}$ load

of $52k$ and a $P_{lt}$ load of $16k.$ The factored $M_{ntx}$ moment was found to be $96ft-k$ and

a factored $M_{ltx}$ moment of $50ft-k.$ The member is pinned at the base and is laterally

braced only at the top and the bottom. There are no transverse loads between the

ends and $C_b=1\mathrm{.}0.$ The $P_{\text{s}\text{t}\text{o}\text{r}\text{y}}=104k$ and the ratio of $\frac{P_{mf}}{P_{\text{s}\text{t}\text{o}\text{r}\text{y}}}=1\mathrm{.}0.$ The story

shear, $H,$ is equal to $4\mathrm{.}4k$ and the drift index $(\frac{{}_H}{L})$ is $0\mathrm{.}0025.$ Using the LRFD

method, is the member adequate? $($Ans$.$ OK $0\mathrm{.}985$ LRFD$)$