Calculator
Enter the span, loads, and positions. Use partial UDL when the load covers only part of the beam.
Example Data Table
A sample scenario with a partial UDL and two point loads.
| Item | Value | Notes |
|---|---|---|
| Span, L | 8.0 m | Simply supported between two bearings. |
| UDL intensity, w | 4.0 kN/m | Applied from x₁ = 2 m to x₂ = 7 m. |
| Point load P1 | 30 kN at 3 m | Equipment reaction near the left side. |
| Point load P2 | 15 kN at 6 m | Secondary concentrated load on the span. |
| End moments | MA = 0, MB = 0 kN·m | Not applied in this example. |
Formula Used
This tool uses basic static equilibrium for a simply supported beam.
How to Use This Calculator
- Enter the span length, L, between the two supports.
- Add the UDL intensity, then select full-span or partial.
- For partial UDL, set x₁ and x₂ within the span.
- Enter point loads P1–P3 and their positions a1–a3.
- Optionally add end moments MA and MB if applicable.
- Press Calculate to view reactions, then download CSV or PDF.
Technical Article
1) Why bearing reactions matter in construction
Bearing reactions are the first checkpoint in beam design because they control seat loads, baseplate sizing, anchor demands, and local concrete bearing stresses. On site, a reaction can be the governing load for a corbel, ledger, temporary shoring head, or support bracket. Accurate reactions also improve material take-offs and reduce rework when loads shift during installation.
2) Converting distributed loads into a single equivalent load
A uniformly distributed load is represented as an equivalent point load of W = w × ℓ, acting at the centroid of the loaded length. For a partial UDL, the centroid is at (x₁ + x₂) / 2. This simple conversion allows quick moment calculations while preserving the same total force and the same moment effect about a support.
3) Using equilibrium to solve RA and RB
For a simply supported beam, only two vertical reactions exist. The calculator applies ΣV = 0 and a single moment equation. Moment balance about the left support yields RB = [Σ(Pᵢ aᵢ) + W x̄ + M] / L, then RA = (ΣPᵢ + W) − RB. This approach is reliable for routine checks and preliminary sizing.
4) Practical load data you can use
Common preliminary values include floor finishes at 0.5–1.5 kN/m², light partitions around 1.0 kN/m², and equipment loads from 5–50 kN depending on the plant item. For small temporary beams, a partial UDL often represents stacked materials along a portion of the span. Keep units consistent: convert area loads into line loads using tributary width before entering w.
5) Interpreting results and documenting outputs
Compare reactions to bearing capacities, check that reactions are not negative unless uplift is intended, and confirm load positions are within the span. Exporting CSV supports design logs and verification workflows, while the PDF is suitable for attachments to method statements, RFIs, and inspection packs.
FAQs
1) What beam type does this calculator assume?
It assumes a simply supported beam with a left and right support providing vertical reactions only. It is intended for quick checks, preliminary sizing, and documentation of common site loading cases.
2) Can I model a partial uniformly distributed load?
Yes. Select partial UDL and enter x₁ and x₂. The tool converts the partial UDL into an equivalent point load located at the centroid of the loaded length.
3) What if my point load position is outside the span?
If a position is outside 0 to L, the calculator clamps it to the nearest support and shows a note. For design work, correct the input to reflect the actual load location.
4) Why do I sometimes get a negative reaction?
A negative reaction indicates uplift at that support under the entered load set, often caused by a strong eccentric load, an applied end moment, or missing stabilizing dead load.
5) How do I convert area loads to a line load w?
Multiply the area load (kN/m²) by the tributary width (m) carried by the beam to get a line load (kN/m). Enter that value as w in the calculator.
6) Are end moments required for normal cases?
Most routine simply supported beams use zero end moments. Enter end moments only when external couples are applied at the supports and you need the reactions to balance them.
7) Is the output suitable for final structural design?
The results are accurate for the stated assumptions, but final design should follow applicable codes, load combinations, and detailing checks such as bearing stress, shear, and serviceability.