The W$12$x$40$ column below with $Fy=50$ksi, is pinned at each end and appears in a braced frame. The two transverse loads $T_u$ are applied to the weak axis. Determine the maximum axial load $P_u$ that can be applied on the column. Note: you may leave your answer as a single expression that has $P_u$ as the only unknown $($such that $P_u$ could be algebraically solved for$).$ Given: midspan deflection of a simple span beam with two point loads $P$ placed at the span $\frac{1}{3}$ points is: $\frac{23P{L}^3}{648EI}.$ DO NOT USE CONSERVATIVE APP PXIMATIONS.