Beam Bending Calculator

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. 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 beam with complex boundary conditions?

Try the New Shear & Moment Calculator »



Unit System
Constants


Load & Dimensions

Calculate

Extremes
Max Displacement @
Max Shear @
Max Moment @
Displacement ()
Slope (degrees)
Moment ()
Shear ()
Data

About the Beam Bending 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 base 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 and loads it is often better to solve the problem numerically with something like the finite element method like this: Shear & Moment Calculator.