Calculator inputs
Example data table
These sample entries help you test the page quickly and compare common beam cases.
| Example | Load case | L (m) | E (GPa) | I (m⁴) | Load | Query x (m) |
|---|---|---|---|---|---|---|
| 1 | Simply supported + center point load | 6.0 | 200 | 8.5e-6 | 15 kN | 3.0 |
| 2 | Simply supported + full-span UDL | 5.0 | 210 | 6.0e-6 | 7.5 kN/m | 2.5 |
| 3 | Cantilever + end point load | 3.5 | 70 | 4.2e-6 | 8 kN | 3.5 |
| 4 | Cantilever + full-length UDL | 4.0 | 200 | 9.0e-6 | 4.5 kN/m | 4.0 |
Formula used
This calculator applies Euler–Bernoulli beam theory for small deflections, linear elastic material behavior, and prismatic members.
1) Simply supported beam with center point load, P
Reactions: RA = RB = P / 2
Maximum moment: Mmax = P L / 4
Maximum deflection: δmax = P L³ / (48 E I)
Support slope magnitude: θ = P L² / (16 E I)
2) Simply supported beam with full-span uniform load, w
Reactions: RA = RB = w L / 2
Maximum moment: Mmax = w L² / 8
Maximum deflection: δmax = 5 w L⁴ / (384 E I)
Support slope magnitude: θ = w L³ / (24 E I)
3) Cantilever beam with end point load, P
Fixed shear: V = P
Fixed moment: M = P L
Maximum deflection: δmax = P L³ / (3 E I)
Free-end slope: θ = P L² / (2 E I)
4) Cantilever beam with full-length uniform load, w
Fixed shear: V = w L
Fixed moment: M = w L² / 2
Maximum deflection: δmax = w L⁴ / (8 E I)
Free-end slope: θ = w L³ / (6 E I)
Stress estimate
Bending stress: σ = M / Z
When rectangular dimensions are entered, the page computes I = b h³ / 12 and Z = b h² / 6 automatically.
How to use this calculator
- Select the beam and loading case that matches your problem.
- Enter the beam length and elastic modulus in SI units.
- Choose whether to enter section properties directly or use a rectangular section.
- Provide the point load in kN or the distributed load in kN/m.
- Enter a query position to inspect local shear, moment, deflection, and slope.
- Add an allowable bending stress if you want a quick utilization check.
- Submit the form to display the result block above the input area.
- Review the charts, then export the summary with the CSV or PDF buttons.
Frequently asked questions
1) What theory does this calculator use?
It uses Euler–Bernoulli beam theory. That means plane sections remain plane, shear deformation is neglected, and the beam is treated as linearly elastic under small deflection assumptions.
2) Which beam cases are supported?
The page supports a simply supported beam with a center point load, a simply supported beam with a full-span uniform load, a cantilever with an end point load, and a cantilever with a full-length uniform load.
3) What units should I enter?
Use meters for geometry, gigapascals for elastic modulus, kN for point loads, and kN/m for distributed loads. The output table reports reactions, moments, slopes, and deflections in consistent engineering units.
4) Can I estimate bending stress too?
Yes. Enter a section modulus directly, or let the rectangular option calculate it from width and height. The page then estimates maximum bending stress and compares it with the allowable value if provided.
5) Why do the charts show positive and negative values?
Shear and moment signs follow the chosen internal convention. The summary table shows maximum magnitudes for quick design checks, while the charts preserve sign so you can interpret shape and balance correctly.
6) Does this cover all real beam conditions?
No. It does not include tapered members, variable stiffness, partial-span loads, point loads away from midspan, shear deformation, plastic behavior, or dynamic effects. Use detailed analysis for those cases.
7) Why is the deflection result in millimeters?
Deflection is often easier to interpret in millimeters, especially for serviceability checks. Internally the calculation uses meters, then converts to millimeters for the displayed table and charts.
8) When should I use the rectangular section option?
Use it when you know the section width and depth but do not want to calculate I and Z manually. It is convenient for quick steel, timber, or aluminum member screening during early design checks.