Simply Supported Beam Calculator
Find the maximum bending moment, support reactions and deflection of a simply supported beam in seconds. Enter the span, load and section, and the result is checked live against the FERS finite-element solver — so you can see the closed-form answer and the FE answer agree.
Bending moment and reactions are free. Create a free account to unlock deflections and to save your model.
Formulas used
A simply supported beam has a pin at one end and a roller at the other. For the two most common load cases the maximum bending moment, support reaction and maximum deflection are:
| Load case | Max moment | Reaction | Max deflection |
|---|---|---|---|
| Central point load P | M_max = P·L / 4 | R = P / 2 | δ_max = P·L³ / (48·E·I) |
| Uniformly distributed load w | M_max = w·L² / 8 | R = w·L / 2 | δ_max = 5·w·L⁴ / (384·E·I) |
where L is the span, P a point load, w a distributed load, E Young's modulus and I the second moment of area. The calculator above runs the FERS finite-element solver on your inputs and shows the analytical and finite-element answers agreeing live.
Worked example
Worked example: a 6 m simply supported IPE 240 steel beam (I = 3.89×10⁻⁵ m⁴, E = 210 GPa) with a 10 kN point load at midspan.
- Maximum bending moment, P·L/4
- 15.0 kNm
- Reaction at each support, P/2
- 5.0 kN
- Midspan deflection, P·L³/48EI
- 5.5 mm (≈ L/1090)
Frequently asked questions
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