Q$.3($b$)$ A LONG column with a rectangular cross$-$section is subjected to a concentric axial compressive load $P.$ The column has a pinned support at its top and a pinned support at its bottom as shown in Figure Q$3$b$.$ Assess the validity of Euler's formula accordingly and determine the allowable load of the column if the factor of safety is $2.$

Other physical parameters:

$E=205k\frac{N}{m}{m}^2$;${}_y=500\frac{N}{m}{m}^2$

$(11$ marks$)$