A column has a hollow square cross$-$section with outside width $150mm$ and inside width carcfully shown in Fig. $1.$ Young's modulus, $E=200$GPa and yield stress, ${}_y=250$MPa.

a$.$ What is the maximum eccentricity of load $P$ in $y$ axis that results in no tensile stress anywhere in the cross section? Assume that column behaves like a short column.

b$.$ Using the result of part $($a$),$ mark the kern$/$core of the cross section.

$[2]$

c$.$ If the axial load $P$ is applied without any eccentricity, find the maximum length of column that $[1]$ in material failure $($yielding$).$ Assume that one end of the column is fixed and the other end is free. $[2]$

d$.$ Determine, with an eccentricity of $65mm,$ the maximum load that can be applied to a column of the same length as determined in part $($c$)$ without any failure. The end conditions of column are same as part $($c$).$

$[3]$