Simply Supported Beam Calculator

Calculate reactions and maximum bending moments instantly.

meters
kN
meters
kN/m
Reaction at Left Support (RA)
0.00 kN
Reaction at Right Support (RB)
0.00 kN
Max Bending Moment (Mmax)
0.00 kNm

What is a Simply Supported Beam?

A simply supported beam is one of the most basic structures in civil and mechanical engineering. It consists of a rigid horizontal member that is supported at both ends. Usually, one end is a pinned support, which prevents horizontal and vertical movement but allows rotation, while the other end is a roller support, which only prevents vertical movement. This configuration ensures that the beam is statically determinate, meaning the internal forces and reactions can be calculated using basic equilibrium equations.

How to Use This Calculator

This tool is designed to help students, engineers, and DIY builders quickly determine the support reactions and maximum bending moments for a beam subjected to both a concentrated point load and a uniformly distributed load (UDL). To get accurate results, follow these steps:

  • Enter the total Span (L) of the beam in meters.
  • Provide the magnitude of the Point Load (P) and its Position (a) measured from the left support.
  • Input the magnitude of any Uniformly Distributed Load (w) acting across the entire length.
  • The calculator will automatically sum the effects of both load types using the principle of superposition.

Understanding the Formulas

The reactions are calculated based on the sum of moments and vertical forces. For a point load P at distance 'a' from the left support, the reactions are RA = P(L-a)/L and RB = Pa/L. For a UDL 'w', the reactions are simply wL/2 at each end. The maximum bending moment for a point load occurs directly under the load, whereas for a UDL, it occurs at the center of the span (wL²/8). This calculator identifies the peak stress point to help in material selection and safety factor analysis.

Frequently Asked Questions

What is the maximum moment? The maximum moment is the point along the beam experiencing the highest internal bending stress. It is crucial for determining if a beam will fail under a specific load.

Can I use different units? Yes, as long as you remain consistent. If you use feet and pounds, your results will be in pounds (force) and foot-pounds (moment).