Nomenclature:

Sign Convention:

- x is positive to the right
- y is positive upward
- M is positive when the top fiber is compressed
- W is positive in the direction of negative Y
- V is positive when the part of the beam to the left of the section tends to move upward under the action of the resultant of the vertical force

Limiting Assumptions:

- The material follows Hooke’s law
- Plane cross sections remain plane
- Shear deflections are negligible
- Deflections are small

The general equations relating load, shear, bending moment and deflection are given in the table below. These equations are given in terms of deflection and bending moments.

The solutions for various single span beams are given in the tables on the following pages. The spreadsheets give worked examples that show the shear force and bending moment diagrams and a plot of beam deflection.