Beam Deflection Calculator

This calculator is based on Euler-Bernoulli beam theory. The Euler-Bernoulli equation describes a relationship between beam deflection and applied external forces. The simplest form of this equation is as follows:

EI × d⁴w / dx⁴ = q(x)

The Shear Force and Moment can be expressed, respectively, as:

Q=-EI × d³w / dx³), M=-EI × d²w / dx²

Beam Moment and Shear Force Calculator

We use these equations along with the boundary conditions and loads for our beams to derive closed-form solutions to the beam configurations shown on this page (simply supported and cantilver beams). The beam calculator uses these equations to generate bending moment, shear force, slope and defelction diagrams.

The beam calculator is a great tool to quickly validate forces in beams. Use it to help you design steel, wood and concrete beams under various loading conditions. Also, remember, you can add results from beams together using the method of superposition.

Steel, Wood and Concrete Beam Calculator

Of course, it is not always possible (or practical) to derive a closed-form solution for some beam configurations. If you have a steel, wood or concrete beam with complex boundary conditions and loads you're better off solving the problem numerically with one of our finite element analysis tools. If you're not worried about design codes and comparing beam demand and beam capacity, try out our easy to use Shear & Moment Calculator. If you need full design checks via AISC 360, NDS, ASD and LRFD for steel or wood beam design and you want to design your next beam in minutes, you might like our Beam Designer tool.