Question $3[16$ marks$]$

Figure $3$ shows that the steel column is fixed at its base. Its top is constrained to rotate about the $y-y$ axis and free to move along the $y-y$ axis. Also, the column is braced along the $x-x$ axis at its mid$-$height. If $P=25kN,$ determine the maximum normal stress developed in the column. Section properties can be found below.

$A=2860m{m}^2,I_{}=20({10}^6)m{m}^4$

$d=206mm,I_{yy}=1\mathrm{.}42({10}^6)m{m}^4$

$t_w=6\mathrm{.}22mm,r_x=83\mathrm{.}6mm$

$b_f=102mm,r_y=22\mathrm{.}3mm$

$t_f=8mm,$