A simply$-$supported beam is loaded as shown in the Figure. The weight of the beam itself can be ignored and it has a constant cross$-$section. The flexural rigidity EI of the beam is $1$ MNm$2.$

Use Macaulay step functions to write an expression for the bending moment as a function of x $($the distance along the beam from the left$-$hand end$).$ Illustrate your answer with a free body diagram for the entire beam. Sketch the bending moment distribution along the beam $($i$.$e$.$ you DO NOT need to use graph paper or plot in Excel$).$ Mark important values on the graph, including labels for the axes, the values of bending moment at the supports and at the discontinuities in the beam loading.