$11-20$ Design problem in an unbraced frame$-$using loads and moments obtained using the requirements of the Direct Analysis Method. Using the LRFD method, select the lightest W$12,10ft$ long beam$-$column in an unbraced frame. Based on a first$-$order analysis, the member supports the following factored loads: $P_{nt}$ load of $140k$ and $P_{tt}$ load of $105k.$ The member also supports factored moments: $M_{ntx}$ moment of $60ft-k,M_l$ moment of$90ft-k,M_{nty}$ moment of $40ft-k$ and $M_{lty}$ moment of $75ft-k.P_{\text{s}\text{t}\text{o}\text{r}\text{y}}=5,000k,P_{\text{e}\text{s}\text{t}\text{o}\text{r}\text{y}x}=40,000k,$

$P_{e\text{s}\text{t}\text{o}\text{r}\text{y}y}=30,000k,C_{mx}=C_{my}=1\mathrm{.}0,C_b=1\mathrm{.}0$ and $F_y=50$ksi steel