Beam geometry and loading
Use downward forces as positive values. Use positive moments for counterclockwise rotation.
Static equilibrium relations
For a simply supported beam, the vertical reactions come from force and moment equilibrium.
1. Sum of vertical forces: RA + RB = ΣF
2. Sum of moments about support A: RB(xB - xA) + ΣM - Σ(Fx) = 0
3. Reaction at B: RB = [Σ(Fx) - ΣM] / (xB - xA)
4. Reaction at A: RA = ΣF - RB
5. For each UDL, the equivalent point load is wL acting at the segment midpoint.
Positive force inputs are treated as downward loads. Positive moments are treated as counterclockwise actions.
Calculation workflow
- Enter the beam length and both support locations.
- Set your preferred force and length units.
- Add any point loads with magnitudes and positions.
- Add distributed loads by entering intensity, start, and end positions.
- Add applied moments using positive values for counterclockwise rotation.
- Click Calculate reactions to show the support forces above the form.
- Review the equilibrium checks, breakdown tables, and resultant location.
- Use the export buttons to save the calculation summary as CSV or PDF.
Sample beam reaction case
| Parameter | Value | Notes |
|---|---|---|
| Beam length | 8 m | Support A at 0 m and Support B at 8 m |
| Point loads | 12 kN at 2 m, 18 kN at 6 m | Both are downward loads |
| UDL | 4 kN/m from 3 m to 7 m | Equivalent to 16 kN at 5 m |
| Applied moment | 10 kN·m at 5 m | Counterclockwise positive |
| Reaction at A | 20.75 kN upward | From force equilibrium |
| Reaction at B | 25.25 kN upward | From moment equilibrium |
Common questions
1. What beam type does this calculator solve?
It solves statically determinate, simply supported beams with two vertical supports. Point loads, distributed loads, self weight, and applied moments can be combined in one model.
2. How are point loads treated?
Each point load acts directly at its entered position. Positive values are taken as downward forces. Negative values can represent uplift or upward actions.
3. How does the calculator handle distributed loads?
Each uniform distributed load becomes an equivalent point load equal to intensity multiplied by loaded length. That equivalent acts at the loaded segment midpoint.
4. Why can a reaction be negative?
A negative reaction means the support force acts downward under the chosen sign convention. This can happen when moments or uplift loads shift equilibrium strongly.
5. Does the moment position change the reactions?
For a pure applied couple on a statically determinate beam, the reaction effect depends on the moment magnitude and sign, not its listed position.
6. What is the resultant load location?
It is the single equivalent position of all vertical loads only. Applied moments are excluded because they create rotation without adding net vertical force.
7. What do the equilibrium checks confirm?
They verify that the final reactions satisfy vertical force balance and moment balance. Values near zero indicate the calculation is internally consistent.
8. Can I use different units?
Yes. Enter any consistent force and length units, such as N and mm or kN and m. Moment units update automatically from those choices.