$($b$)$ A LONG hollow rectangular column with a hollow$-$section $($the same as the section in Q$.3($a$))$ is subjected to a concentric axial compressive load P$.$ The column with $15m$ long and a section as shown in Figure Q$3$b is fixed at support and pinned at the top. Assess the validity of Euler's formula accordingly and determine the allowable load of the column if the factor of safety is $3.$

Other physical parameters:

$E=200k\frac{N}{m}{m}^2$;${}_y=150\frac{N}{m}{m}^2$

$(10$ marks$)$

Figure Q$3$b