or translation free fy=250mpa & grade of steel 410

Given:-

TSHB 3000 A= 7485 mm$^{2}$ bf=250 tf=10.6 tw=7.6

Izz=Ixx=12545.2$\times10^{4}mm^{4}$

Iyy=2293.6 $\times10^{4}mm^{4}$

$\frac{KL}{ryy}$=compund section

$\frac{KL}{\gamma xx}$= compund section

$\gamma xx=\sqrt{\frac{Ixx}{A}}$

$\gamma yy=\sqrt{\frac{Iyy}{A}}$

A=7458+2(Area of plate)

=7485+2(350$\times$20)

A=24485mm$^{2}$

Ixx of compound section

Ixx=Ixx1+Ixx2

=(1.2545.2$\times 10^{4})+(\frac{350\times20^{3}}{12}+(350\times20)(160)^{2})$

Ixx=484.32$\times10^{6}mm^{4}$

Iyy=Iyy1+Iyy2

=2193.6$\times10^{4}+2(\frac{20\times350^{3}}{12}+(20\times350)\times0)$

Iyy=164.85$\times10^{6}mm^{4}$

$\gamma xx=\sqrt{\frac{484385\times10^{6}}{21485}}$ rxx 150.29mm

$\gamma yy$=87.5ymm

leff=10.000mm

$\gamma=\frac{kL}{\gamma xx}=\frac{2\times50.00}{150.29}=66.53$

$\frac{h}{bf}=\frac{3000}{250}=1.36\gt 1.2$

buckling about z axis class a

thickness of flange 10.6$\lt 40$

buckling about y axis class b

KL/$\gamma $xx $\ \ \ \ \ $fcd

60 $ \ \ \ \ \ \ \ \ \ \ $ 195

66.53 $ \ \ \ \ \ \ $ fcd

70 $ \ \ \ \ \ \ \ \ \ \ \ 18^{2}$

$\frac{70-60}{70-66.53}=\frac{182-195}{182-fcd}$

fcd=186.5N/mm$^{2}$

Pd=Ae$\times$fcd

Pd=21485$\times186.5$

Pd=4005.1 KN

$\frac{KL}{\gamma yy}=\frac{10,000}{87.6}=$114.15

KL/$\gamma yy \ \ \ \ fcd$

110 $ \ \ \ \ \ \ \ $ 104

114.15 $ \ \ \ $ fcd

120 $ \ \ \ \ \ \ \ \ \ $ 91.7

$\frac{120-110}{120-114.15}=\frac{91.7-104}{91.7-fcd}$

fcd=98.8N/mm$^{2}$

Pd=Ae$\times$ fcd

=21485$\times$98.8

PD=2124.5KN

design comp strenght of column=2124.5KN