Shear & Moment Diagrams

Shear and moment diagrams are drawn by areas, not by writing equations for every segment. Each diagram is the running area under the one above it.

• The change in shear between two points equals the load between them (downward load reduces V).
• The change in moment between two points equals the area of the shear diagram between them.
• Maximum moment occurs where the shear crosses zero, or at a concentrated load.
• A concentrated force makes the shear jump; a concentrated moment makes the moment jump.

Worked: a floor beam

A 24 ft simply supported beam carries 2 kip/ft. Each reaction is 24 kips, the shear falls linearly to zero at midspan, and the moment there is the triangle’s area: ½ × 12 ft × 24 kips = 144 ft-kips, the same as wL²/8.