Problem $1(30$ points$)$

Consider the beam with an overhang shown in the figure.

a$)$ Draw the free body diagram of the structure

b$)$ Determine the reaction force at A

c$)$ Determine the shear force $V$ and bending moment $M$ at a cross section located $18$ ft from the left$-$hand end $A.$

d$)$ Find the required magnitude of load intensity $q,$ acting on the right half of member $BC$ that will result in a zero shear force on the cross section $18$ ft from $A.$