Q$.1$ A steel column in simple construction between floors of a multi$-$storey building is subjected to the following eccentric loadings due to beam support reactions as shown in Figure Q$1.$ Assume the stiffnesses of the upper and the lower columns are the same.

Check the structural adequacy of class $1$ steel column section $356368177k\frac{g}{m}$ UC $($Grade S$355)$ if the actual column height is $6$ m and the effective length of the column is $5\mathrm{.}1$ m for both axes. All the loadings shown below are factored loads. All moment factors are assumed to be $1\mathrm{.}0$ unless stated otherwise.

Given:

$P=2000kN($compression$)$ including self$-$weight acting at the centre of the column.

$P_{xt}=800kN($compression$)$ with an eccentricity $e_y$ of $190$ mm measured from the $y-$axis, due to beam reactions.

$P_{yt}=600kN($compression$)$ with an eccentricity $e_x$ of $300$ mm measured from the x $-$axis, due to beam reactions.

$P_{y2}=750kN($compression$)$ with an eccentricity $e_x$ of $270$ mm measured from the x $-$axis, due to beam reactions.

Moment amplification factor due to $P-$ effect for all moments $=1\mathrm{.}1.$

$($a$)$ Determine the total axial load and moment about $x-x$ axis and moment about $y-y$ axis acting on the steel column.

$($b$)$ Check the cross section capacity of the steel column.

$($c$)$ Check the member buckling resistances of the steel column.