$($d$)$ The solid steel rectangular column is fixed at its ends having dimension as illustrate in Figure $6.$ The column is braced at its midpoint along $x-x$ axis using struts that are pin connected. Given that the modulus of elasticity is $200$GPa, factor of safety is $2\mathrm{.}5$ and yield strength is $250$MPa.

iv$)$ Sketch the buckling shapes of the column.

v$)$ Determine the largest allowable length of the column.

vi$)$ Calculate the slenderness ratio of the column.

vii$)$ Determine the ratio of axial stress corresponding to the buckling load and elastic strength of the materials.