A beam rigidly fixed at one end has a roller support at point D$.$ A point load $\backslash ($ P$=500\backslash$mathrm$\{$~N$\}\backslash )$ is applied in the middle of the beam and a moment is applied at point D which is $7\mathrm{.}5$ meters away from end A $.$

$($a$)$ Using superposition, determine the values of the reactions at the two ends of the beam.

$($b$)$ Draw the shear force and bending moment diagram for the beam.