The column shown is fabricated from two C$250330$ standard steel shapes $($see Appendix B for its cross$-$sectional properties$)$ that are oriented back$-$to$-$back with a gap of $25$ mm between the two channels. The column is fixed at its base and free to translate in the $y$ direction at its upper end. Translation in the $z$ direction, however, is restrained at its upper end. A load $P$ is applied at an offset distance of $490$ mm from the channel

flanges. Use the AISC equations given in Section $16\mathrm{.}5,$ and assume that $L=4\mathrm{.}7m,s=25mm,E=200$GPa,${}_Y=245$MPa, and $({}_{\text{a}\text{l}\text{l}\text{o}\text{w}}{)}_b=135$MPa. Using the interaction equation method, determine

$($a$)$ whether the column is safe for a load of $P=80kN$; report the value of the interaction equation.

$($b$)$ the magnitude of the largest load $P$ that may be applied to the column.

Cross section.

Determine the effective slenderness ratio for the column for bending about the z centroidal axis. Note whether or not this column is categorized as a long column for bending about the z centroidal axis.

Answer: $(K_z\frac{L}{r_z})=$