Problem $5$

The composite compression member whose cross section is shown in the figure has a column length $Lx=26$ for bending$/$buckling about the $x-x$ axis. For the bending about $y-y$ axis, the column has lateral support at mid$-$height in the weak direction, i$.$e$.,Ly=13ft.$ The column has pin supports at top and bottom and at lateral support locations $($i$.$e$.Kx=Ky=1\mathrm{.}0).$ The steel yield strength is Fy $=50$ksi for W $12$ x $96$ and fy $=60$ksi for the rebars. The concrete has a compressive strength is $f^{\text{'}}c=8$ksi.

Compute the LRFD design compressive strength of the composite column, $Pn$

Plot the Pn$-$Mn interaction diagram of the column about the strong axis $($use equations given at the end of thils HW$.$

Cover $=2\mathrm{.}5in$ to centerline of the longitudinal bar