Beam Reactions Calculator
The reactions at the two supports of a simply supported beam under a uniform load and a point load — plus the maximum bending moment and shear, and where the moment peaks — the first calculation in sizing any beam.
A simply supported beam rests on two supports and the loads on it must be balanced by them: the sum of the reactions equals the total load, and moments about one support fix how it splits.
How the beam reactions calculator works
A simply supported beam rests on two supports and the loads on it must be balanced by them: the sum of the reactions equals the total load, and moments about one support fix how it splits. A uniform load's moment peaks at midspan at wL²/8; a point load's at the load, at Pab/L. Together they give the maximum moment the beam section must resist, and the shear that the connections must carry.
Formula: R_A = wL/2 + Pb/L; R_B = wL/2 + Pa/L; M_max ≈ max over the span of R_A x − w x²/2 − P(x − a)
Worked examples
| Inputs | Maximum bending moment (kN·m) | Note |
|---|---|---|
| 6 m span, 8 kN/m and 20 kN at 2 m | 58.778 | about 62 kN·m |
| Uniform load only | 36 | wL²/8 at midspan |
| Point load at midspan | 30 | PL/4 |
FAQFrequently asked questions
What is a simply supported beam?
One resting on a support at each end that stops it moving down but lets it rotate — a joist on two walls, a lintel over an opening. Most beams in ordinary construction are designed this way.
How do I find the reactions?
Total load is shared so that moments about either support balance: a point load splits in inverse proportion to its distance from each support, and a uniform load splits equally.
Where is the maximum moment?
Where the shear force crosses zero. For a uniform load that is midspan; for a point load it is at the load; for both together it is one of those, and the page checks each.
What is the section modulus row?
The moment divided by an allowable bending stress — 165 MPa here, typical for steel in simple working-stress design — gives the section property a beam needs. It is a sizing guide, not a design; codes, deflection and lateral stability decide the final section.
What about several point loads?
Superpose: reactions add, and the moment at any point is the sum of each load's contribution. For more than one point load, run the page per load and add the diagrams.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.