$($b$)$ It is required to design a column in the ground floor of a building. The height of the column is $3\mathrm{.}5$ m $.$ The bottorn end of the column may be assumed to be fixed and the top end to be pinned. A square cross$-$section of $\backslash (200\backslash$mathrm$\{$~mm$\}\backslash$times $200\backslash$mathrm$\{$~mm$\}\backslash )$ using grade C$20$ timber has been proposed for this column. $($Properties of C$20$ timber should be obtained from EN$338$: $2009).$

$($i$)$ Determine whether this column should be designed as a short column or a slender column.

$($ii$)$ The actions on the column result from a combination of permanent actions and variable actions due to imposed floor loads. Estimate the value of the largest ultimate compressive axial load that can be safely applied on the column. Assume that the load acts through the centroid of the section without any eccentricity.

$($c$)$ There is a need to allow for a nominal bending moment $\backslash ($ M$\_\{$y$,$ d$\}=7\mathrm{.}0\backslash$mathrm$\{$kNm$\}\backslash )$ in the column considered in $($b$)$ above. Check whether the largest axial load you estimated in $($b$)($ii$)$ above will be satisfactory even with this nominal bending moment.

$($d$)$ Using the calculations in $($c$)$ above, or otherwise, determine the largest ultimate compressive load that the column can safely carry along with the nominal bending moment.