How to use this calculator
- Choose the load type (point or distributed).
- Enter the beam span and the load.
- Read the maximum bending moment and support reactions.
What your result means
The maximum bending moment is the peak internal force the beam must resist — the value a section is sized against. It assumes a simply-supported beam under ideal conditions; real designs add safety factors and also check deflection and shear. Use it for guidance, not final structural design.
Why bridges are thickest in the middle
A loaded beam bends most at its centre, where the bending moment peaks — which is exactly why bridges, floor joists and shelves are reinforced there. Get the moment wrong and the structure sags, cracks or collapses.
These simply-supported figures are the first calculation in any structural check: they tell you how hard the beam is working before you ever pick its size.
How it works
A simply supported beam rests on a support at each end. The supports share the load as vertical reactions, and the beam bends most where the bending moment peaks — at mid-span for both a central point load and a uniform load. These figures are the starting point for choosing a beam size against its allowable stress.
Formulas
UDL: M = w·L² ÷ 8 · R = w·L ÷ 2
Frequently asked questions
Is this a substitute for structural design?＋
No. It gives textbook values for a simply supported beam for learning and quick checks. Real structural design must be done by a qualified engineer to the relevant code.
What's the difference between the two load types?＋
A point load acts at a single spot (here, mid-span); a uniformly distributed load spreads evenly along the beam, like a floor's self-weight.