Problem $3$:$(30$ points$)$

Considering the beam in the figure below, where the support $A$ is a hinge and $B$ is a roller. Assume $w=12k\frac{N}{m},$ and $a=b=2m.$

a$)$ What are the reaction forces at A and B $?$

$(5$ points$)$

b$)$ Draw the SFD and BMD$.$ Specify numerical values at relevant points and mention the order of the curves in your SFD and BMD $($such as linear, quadratic or cubic$).$

$(20$ points$)$

c$)$ What are the values of the shear and moment at point $C?$

$(5$ points$)$