For the beam shown below;

a$)$ Calculate the support reactions.

b$)$ Calculate the value of the shear and moment in the beam $4\mathrm{.}5$ m to the right of support A using equilibrium considerations and a free body diagram including support A$,$ i$.$e$.$ a FBD to the left of the cut.

$($For additional practice, in your own time, consider an FBD to the right of the cut including support B$.)$

c$)$ Derive the general mathematical expressions for the shear force and bending moment in the beam in the region $0$ x $<mtext></mtext><mn>8</mn>$m$,$ where x $=0$ corresponds to the location of support A$.$ Check your answer in part b$)$ by substituting x$=4\mathrm{.}5$m into your general moment equation.

$($For additional practice, in your own time, derive equations where the origin lies at the cantilever tip C$.$ You can check the equivalency of your equations by substituting in numerical values.$)$

d$)$ Draw the Shear force and Bending moment diagrams and sketch the corresponding deflected shape. It is recommended you draw your SFD and BMD aligned with the beam based on the lines shown below.