Closed-form solutions to simple beam bending problems.

Welcome to the Beam Bending Calculator. Calculate reactions, deflection, moments and shear forces in simply supported and cantilever beams.
This free beam bending calculator generates shear force diagrams, bending moment diagrams, deflection curves and slope curves.
Select a beam and enter dimensions to get started. Then scroll down to see shear force diagrams, moment diagrams, and tabular results.

Looking for shear and moment diagrams for beams with complex boundary conditions?

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((d^4w)/dx^4)=q(x)`

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

`Q=-EI((d^3w)/dx^3), M=-EI((d^2w)/dx^2)`

The nice thing about this theory is that we can 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. The bending
moment, shear force, slope and defelction diagrams are all calculated using the above equations.

Of course, it is not always possible (or practical) to derive a closed-form solution for some beam configurations.
If you have a beam with complex boundary conditions and loads you're better off solving the problem numerically with
the finite element method like this:
Shear & Moment Calculator.