Problem $3$

The beam shown below is fixed at the left end and a distributed load with constant magnitude $w($force per unit length$)$ is applied. Your answers for the following will be in terms of $w,a,$ and $b.$

$($a$)$ Using free body diagram, determine the reaction forces and moments at the fixed end.

$($b$)$ Sketch the shear$-$force $(V)$ distribution diagram.

$($c$)$ Sketch the moment $(M)$ distribution diagram. Evaluate and capture the slope $d\frac{M}{d}x$ of the curve at locations $O,$A and $B.$

$($d$)$ Determine the location and value of the maximum bending moment.