Given

w=40kN (Service load)

leff=40(of beam)

Required - Design laterally supported beam

factored load=40$\times$1.5=60kN

w=$\frac{60}{4(leff)}$=15kN/m

Step I determine max factor shear face (v) and Bm(m) for given loading and support condition

v=$\frac{wl}{2}=\frac{15\times4}{2}$=30kN

m=$\frac{wl^{2}}{8}=\frac{15\times4^{2}}{8}$=30kN.m

Step II Trial section

zpreq=$\frac{m.req}{fy}$

=$\frac{(30\times10^{6})\times1.1}{250}$

Zpreq=132$\times10^{3}mm^{3}$

ISMB175 zp=166.08$\times10^{3}mm^{3}$

h=175 bf=90mm tf=8.6

tw=5.5 r=10

IZ=12.75$\times10^{4}mm^{4}$

Ze=Zxx=145.4$\times 10^{3}mm^{3}$ …