Beams are one of the main design elements a structural engineer will work with. This is a loaded simply supported beam:
For the PE exam, a loaded beam has two main options for failure, shear and bending.
Moment diagrams are similar to shear diagrams, use them to find the location and value of the maximum positive and negative moment, or the moment at any specific location.
The easiest and fastest way to construct a moment-diagram is by using the areas of the regions in the shear-diagram. Before doing this you must solve for all the reactions, and solve the shear diagram.
Here is a member that is solved to the desired state to begin working on the moment diagram. The start of a moment diagram (M) is below the existing shear diagram (V).