Given

w=56kN/m

factored load =56$\times1.5=8^{4}$kN/m

length of span=2m

Required =design laterally unsupported beam

1) V=$\frac{wd}{2}=\frac{84\times 2}{2}$=84kN

m$=\frac{wl^{2}}{8}=\frac{8^{4}\times 2^{2}}{8}$=42kN.m

2) Trial section

Zpreq=$\frac{M}{fbd}$

Assume $\lambda$=100 $\frac{h}{tf}$=25mm

fcrb=291.4 Md

250 $ \ \ \ \ $ 152.3

291.4 $ \ \ $ fbd

300 $ \ \ \ \ \ $163.6

fbd=161.65 …