Beam ABC is loaded as shown $($note that the loading in segment $BC$ is acting upward$).$ The beam is supported by a fixed end at A and a roller at C $.$ A hinge is located at B $.$

a$)$ Determine the magnitude and direction of all reactions at A and $C.$

b$)$ Draw the shear and moment diagrams for the beam. Clearly indicate the points at which shear and moment are zero and their positions along the beam.

Step $1$: Separate structure to beam $AB$ and beam $BC$ and draw for each FBD and find all reactions at $A,B$ and $C.$

Step$2$: For the beam, AB make a cut $"1"$ between A and B $(Bx1=x-12xV(x)M(x)0$