$*$include plotted graph for C please$*$ A $5m$ long, simply supported beam shown in figure $1$ is subjected to a point load $1\mathrm{.}5m$ from the left support,

and a uniform load of $5k\frac{N}{m}$ between the centre of the beam and the right support, shown in the Figure

below. The beam has a square cross section, $100mm$ in breadth and depth.

a$)$ Calculate the reaction forces of the beam.

b$)$ Calculate the second moment of area for the beam.

c$)$ Using Macauley's method, evaluate the slope and deflection of the beam, illustrating your answer with

a plotted graph.

Assume the beam is made of stainless$-$steel, Young's Modulus for stainless$-$steel $316$ is $205$ GPa.