$[$Question ID $807108]$: A horizontal beam with a length of $5$ m is subjected to the shown loading. The forces are vertical and the couple moment is applied at point $D.$

The figure is not to scale.

$($a$)$

Motivate with substantiating explanations and clear and applicable calculations why the beam is in equilibrium.

$[3$ marks$]$

$($b$)$

Draw the shear force and bending moment diagrams for the beam. Calculate all local maxima and minima, zeros and points where the diagrams change shape, and show these values and points on the diagrams.

$[12$ marks$]$