The beam shown below carries point and linearly distributed loads and is supported by a pin on

the left and a roller on the right. Note that rollers can be assumed to react to either tensile or

compressive loads.

a$)$ For each beam, draw all necessary free$-$body diagrams using the method of sections and

find functions for the internal shear force $(V(x))$ and bending moment $(M(x))$ due to the

external forces where $x$ is a horizontal coordinate along the length of each beam, measured

from the left end of each beam, as shown in the figure. Your expression$($s$)$ must allow to

obtain internal reactions for $0xL,$ where $L$ is the length of each beam. Make sure you

use the numerical values of the reactions at the supports to get your expressions. Note that

$"$k$"$ stands for "kip" $(1000$ lbs$)$ in the labels for the point loads and distributed loads.

b$)$ Plot $V(x)$ and $M(x)$ using the expressions you obtained above using a computer program.

You will lose points if hand$-$drawn plots are submitted.