Bending Moment Calculator

About the Bending Moment Calculator

Calculates the maximum bending moment in a simply-supported beam for either a central point load or a uniformly distributed load.

How to use this calculator

1. Choose whether your beam has a point load or a uniform distributed load.
2. Enter the load size, using \(P\) for a point load or \(w\) for a uniform load.
3. Enter the beam span \(L\).
4. Read the maximum bending moment result, then compare it with your design limit or allowable moment.

The formula explained

For a simply supported beam with a center point load, the maximum bending moment is \(M_{point}=\frac{PL}{4}\). For a uniformly distributed load over the full span, the maximum bending moment is \(M_{UDL}=\frac{wL^2}{8}\).

• \(M_{point}\) = maximum bending moment for a center point load
• \(M_{UDL}\) = maximum bending moment for a uniform distributed load
• \(P\) = point load
• \(w\) = uniform load per unit length
• \(L\) = beam span or length between supports

Step by step method

1. Identify the load type, point load or uniform distributed load.
2. Write down the load value and the beam length.
3. Substitute the values into the matching formula and calculate \(M\).

Worked example

Problem. A simply supported beam has a center point load of \(P=12\) kN and a span of \(L=6\) m. Find the maximum bending moment.

1. Use the point load formula, \(M_{point}=\frac{PL}{4}\).
2. Substitute the values, \(M_{point}=\frac{12\times 6}{4}\).
3. Compute the result, \(M_{point}=18\) kN m.

Tips and common mistakes

• Make sure you use the correct formula for the load type, because point loads and uniform loads give different results.
• Keep units consistent, for example \(P\) in kN and \(L\) in m, so the moment comes out in kN m.

Frequently asked questions