What next?
A beam check needs the load, the section and the material.
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 this one is different
Both support reactions are reported, not just the bending moment, along with the maximum shear force and the total load carried — the four figures a section check actually needs. Switching between a point load and a distributed one changes the formula rather than the label, and the working shows which one was applied.
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
Worked example
A simply supported beam spanning 6 m with a 20 kN point load at mid-span:
Mmax = P × L ÷ 4 = 20 × 6 ÷ 4 = 30 kN·m
Vmax = P ÷ 2 = 10 kN
The reactions always sum to the applied load (10 + 10 = 20 kN) — a quick check that the arithmetic is right. For a uniformly distributed load w over the same span, Mmax = wL² ÷ 8 instead.
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.
How does a distributed load differ from a point load?＋
A point load concentrates everything at one spot; a uniformly distributed load spreads it along the span, which halves the peak bending moment for the same total weight. A 20 kN point load at mid-span on a 6 m beam gives 30 kN·m, while the same 20 kN spread evenly gives wL²÷8 = 15 kN·m.
What is a factor of safety and what value should I use?＋
It is the ratio of a material's capacity to the load actually applied. Values depend on the code, the material and the consequences of failure, which is one reason a designer, not a calculator, sets it.
Why is deflection often the governing limit?＋
Because a beam can be nowhere near failing in bending and still bounce or crack finishes. Serviceability limits, commonly expressed as a fraction of the span, frequently size domestic beams before strength does.
Does the support condition change the result?＋
Substantially. A simply supported beam, a cantilever and a fixed-ended beam under the same load have very different maximum moments and deflections, so the assumed condition must match reality.
Related calculators
Assumptions & limitations
Engineering formulas are exact; the situations they model are not. Read your result with these limits in mind:
- Models a statically determinate, simply supported beam — pinned at one end, roller at the other. Fixed or continuous beams behave very differently.
- Assumes a straight, prismatic beam of uniform section and a material behaving elastically.
- Self-weight is not included unless you add it as a load.
- Gives reactions and bending moment only. It does not check bending stress, shear, deflection, lateral-torsional buckling or connections — all of which a real design requires.
- Not a design tool. Structural design is governed by the Eurocodes and equivalents, and must be carried out by a qualified engineer.