assume rolled I section

assume $\lambda$=100 $fcd=\frac{kL}{xyy}=118$

zz axis class a yy axis class b

service load =700kN

factored load=$1.5\times$700=1050kN

length=7m-----z axis

length=5m--- z axis

Ae=2

P=Ae$\ast fcd$

1050$\ast 10^{3}=Ae\ast118$

Ae=8898.30mm$^{2}$

select ISHB 350 haviing area 9221 mm$^{2}$

ISHB 350 A=9221mm$^{2}$ bf=250 ff=11.6 fw=10.6

rxx=146.5mm

ryy=52.2mm

$\lambda x=\frac{kL}{rzz}=\frac{7000}{146.5}=47.78\lt 180$ $\ \ \ \ Is \ pg \ 20$

$\lambda \ y=\frac{kL}{\gamma yy}=\frac{5000}{52.2}=95.78\lt180 \ \ Ix \ \ pg \ \ \ 20$

$\frac{hf}{bf}=\frac{350}{250}=1.4\lt1.2 buckling \ z \ axis \ class \ Is \ \ pg 44$

tf=11.6$\lt$40 buckling axis calss b

$\frac{KL}{\gamma yy}$=95.78

Kl/$\gamma yy$ $\ \ \ \ $ fcd

90 $\ \ \ \ \ \ \ \ $134

95.78 $\ \ \ \ $fcd

100 $\ \ \ \ \ \ $118

$\frac{100-90}{100-95.78}=\frac{118-134}{118-fcd}$

fcd=124.75

Pd=9221$\times$124.75

Pd=1150KN

$\frac{ky}{\gamma yy}=$47.78

$\frac{ky}{\gamma yy}$ $\ \ \ \ \ \ $ fcd

40 $\ \ \ \ \ \ \ \ \ \ $213

50 $\ \ \ \ \ \ \ \ \ \ $205

47.78 $\ \ \ \ \ \ $fcd

$\frac{50-40}{50-47.78}=\frac{205-213}{205-fcd}$

fcd=206.76 nmm$^{2}$

Pd=9221$\times$206.76

Pd =1906kN