Question $2$: $[10$ marks$]$

A timber beam has a rectangular cross$-$section, $150mm$ wide by $300mm$ deep, and is simply supported over a span of $4m.$ The beam carries a point load of $95kN$ at a distance of $1m$ from the left hand support and a point load of $85kN$ at a distance of $1m$ from the right hand support.

$3\mathrm{.}1$ Calculate the shear stress at a distance of $75mm$ from the top fibre of the beam.

$3\mathrm{.}2$ Calculate the maximum shear stress.

$3\mathrm{.}3$ Draw the shear stress distribution over the height of the cross section.