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 …