1. Shear Force Diagrams ( SFD ) and Equations And Bending Moment Diagrams ( BMD ) and Equations In Beams

2. Beams Beam = a structural member designed to support loads applied perpendicular to the axis of the beam. It is usually long in one direction ( axis of the beam ) compared with the other two directions.

3. External forces Internal forces All shown external and internal forces are positive. Note that the axial (normal) force is usually ignored in beams. However, it does NOT affect V & M if it is considered.

4. Before, we discussed how to determine the internal forces at specific points. Now we need to determine the internal forces at any point x ; that is we need to write V and M as functions of x . V = f ( x ) M = f ( x )

5. Then we plot these functions. (See the examples next.) *Note that there are infinite number of points ! use X.