Consider the prismatic beam with a circular cross$-$section of $15$ cm diameter shown in Figure $2.$ Assume the beam is linearly elastic, homogeneous, isotropic and has negligible weight compared to the given loads.

$($a$)$ Calculate the reaction forces and$/$or moments at the supports. Show your free body diagram and equations as part of your work.

$($b$)$ Draw the shear and moment diagrams. Show how you derive the diagrams. Label axis along with units and show the shear and moment values at zero points and peaks in your diagrams.

$($c$)$ Calculate the maximum compressive normal stress in the x$-$direction. Report your answer in kilopascals. Indicate the point in the beam where this maximum stress occurs.