Problem $3.(10$ points$)$ The beam is supported by pins A and rollers $C$ as shown, answer these following questions

$($a$)$ Determine the supporting reaction at points A and $C(2$ points$)$

$($b$)$ Determine the shear and bending moment equations for beam spans $AB$ and $BC(4$ points$)$

$($c$)$ Draw the shear and bending$-$moment diagrams for the beam on the given graphs with proper vertical scales and illustrate the maximum and minimum values in diagrams $(4$ points$).$