Zp=M$\times\frac{8mo}{fy}=3.34\times 10^{6} \times\frac{1.10}{250}$=14696mm$^{3}$

From shear table select ISLC 100 mm having h=100mm, bp=50mm , tf=6.4mm

tw=4mm $\gamma$=6mm, Ixx=164.7$\times 10^{4}$mm Iyy=24.8$\times 10^{4}mm^{4}$, Zxx=32.9$\times 10^{3} mm^{3}$ Zyy=7.3$\times 10^{3}mm^{3}$

Zpz, prov=38.09$\times 10^{3} mm^{3}$

Zpy=Zy$\times$ s

=7.3$\times 10^{3} \times 1.1576$=8.45$\times 10^{3} mm^{3}$

h$_{1}$=74.3mm

sectional classification:

$\frac{b}{tf}=\frac{50}{6.4}=7.8\lt 9.4\epsilon$

$\frac{d}{tw}=\frac{74.3}{4}=18.58\lt 42\epsilon$

section is plastic

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