$4\mathrm{.}5-11$ Beam $\backslash ($ A B C D $\backslash )$ is simply supported at $\backslash ($ B $\backslash )$ and $\backslash ($ C $\backslash )$ and has overhangs at each end $($see Fig. a$).$ The span length is $\backslash ($ L $\backslash )$ and each overhang has length $\backslash ($ L $/3\backslash ).$ A uniform load of intensity $\backslash ($ q $\backslash )$ acts along the entire length of the beam.

$($a$)$ Draw the shear$-$force and bending$-$moment diagrams for this beam.

$($b$)$ Repeat part $($a$)$ if the uniform load is replaced with a triangularly distributed load with peak intensity $\backslash ($ q$\_\{0\}=$q $\backslash )$ at mid$-$span $($see Fig. b$).$

$($a$)$

$($b$)$