Given a simply supported beam with distributed loads on segments $AB$ as shown in the figure below. A concentrated moment of $150kN$ and concentrated load of $50kN$ are applied at $B$ and $C,$ respectively. The beam has constant bending cross$-$section property $EI.$

a$)$ Draw shear and moment diagrams for the beam.

b$)$ Write the equations of moment diagrams for each segment $AB,BC,$ and $CD$ versus coordinate $x$ start from support at $A.$

c$)$ Use double integration method, calculate deflections $($versus $EI)$ at $B$ and $C$ of the beam. Which location has the larger displacement?

d$)$ Use Moment$-$area theorem and calculate deflections $($versus $EI)$ at $B$ and $C$ of the beam $AC$ and check the results with question c$).$

Hints: Use the table of area properties uploaded on Blackboard to find location of the centroid and shape areas.

Please give detailed answers.