A compound beam AD is built-in at A and supported by a
roller at C. Two loads are supported by the beam: a
rectangular load of magnitude 2W that spans the middle of
the beam, and a hanging weight of W at point D.
 

Draw FBDs for the full beam and the two segments
AB and BD. 

Set up and solve the 2D system of equations for beam segment BD to show the reaction at B to have a magnitude of
3W/2. For your moment equation, please take the moment around B.

Draw the shear and moment diagrams for the compound beam, labelling important values at points A-E. 

Your respected engineer colleague tells you that point C is a roller support, and that moments are usually
zero at supports. Explain why you agree or disagree in this particular case. 

y 22 A 2W B D W L 2L 3L 4L K