b$.$ The beam shown in FIGURE Q$2$b is simply supported with a pin and roller at both ends, and is subjected to a distributed loading of $w.$ The cross$-$sectional area of the beam is shown as in the figure.

FIGURE Q$2$b

i$.$ Construct the shear and moment diagrams for the beam.

$[4$ marks$]$

ii$.$ If the beam is designed to sustain maximum bending stress and shear stress of $2\mathrm{.}5$ MPa and $0\mathrm{.}5$ MPa $,$ respectively, determine the maximum value of the distributed load, $w$ that can be imposed to the beam.

$[8$ marks$]$