You have a steel rectangular hollow section $($RHS$)$ with dimensions d $\backslash$times b $\backslash$times t$.($depth $\backslash$times breadth $\backslash$times thickness$).$ You should assume the corners are perfect right angles. The beam cross section is oriented so that self weight causes the beam to bend about the stiffer axis.

Information on your beam and its loading is:

$$ It is a horizontal cantilever beam. Its length is a function of the total depth of the section, and the L$/$d

ratio given below.

$$ You are given the breadth, b$,$ and the aspect ratio, d$/$b$.$ The thickness is initially unknown.

$$ If required, you should use g $=10$ m$/$s$2.$

$$ The beam experiences the following loading

o Its own self weight, wself.

o An additional UDL along the entire length, w$,$ given by w $=15$wself.

$$ You are given maximum $($absolute$)$ values of bending moment, and shear force, that the fixed

connection can withstand.

Your task is to calculate the maximum thickness, t$,$ for the RHS without exceeding the maximum bending moment and shear force values. Round your answer down to the nearest $0\mathrm{.}1$ mm $($eg $4\mathrm{.}234$ mm should be given as $4\mathrm{.}2$ mm$.$ If your answer was exactly $4\mathrm{.}2$ mm$,$ then leave it as $4\mathrm{.}2$ mm$).$

d$/$b $=1\mathrm{.}5$

L$/$d $=7\mathrm{.}5$

b $=300$ mm

Mmax $=30$ kNm

Vmax $=50$ kN