Consider the beam shown in Figure $3.$ The vertical reactions at supports A and $B$ are given. draw free body diagram

a$)$ Considering the reference at the left$-$hand side $($shown in the figure$),$ formulate the shear force and bending moment as functions of $x,$ i$.$e$.,$ determine $V(x)$ and $M(x)$ for all segments of the beam. Provide all the required free body diagrams. $(15)$

b$)$ Draw the shear force and bending moment diagrams. Identify the points with maximum shear force and bending moment.