Problem $1$

For the cantilever beam and loading shown,

$($a$)$ Derive equations for the shear force $V$ and the bending moment $M$ for any location in the beam. $($Place the origin at point $A.)$

$($b$)$ Plot the shear$-$force and bending$-$moment diagrams for the beam using the derived functions.

Problem $2$

Use the graphical method to construct the shear$-$force and bending$-$moment diagrams for the beam shown. Label all significant points on each diagram and identify the maximum moments $($both positive and negative$)$ along with their respective locations. Clearly differentiate straight$-$line and curved portions of the diagrams.