Beam and Load Inputs
Use downward forces and clockwise moments for common loading. Upward and counterclockwise options are included for mixed cases.
Example Data Table
| Beam Length | Load Type | Magnitude | Location | Equivalent Vertical Load | Moment About Support |
|---|---|---|---|---|---|
| 6 m | Point load | 8 kN downward | 2 m | -8 kN | -16 kN·m |
| 6 m | Distributed load | 3 kN/m downward | 3 m to 6 m | -9 kN | -40.5 kN·m |
| 6 m | Applied moment | 5 kN·m clockwise | 6 m | 0 kN | -5 kN·m |
| Example Totals | -17 kN | -61.5 kN·m | |||
| Support Reactions | 17 kN upward | 61.5 kN·m counterclockwise | |||
Formula Used
∑Fy = 0 → Ry + ∑Fexternal = 0
∑MA = 0 → MA + ∑Mexternal about A = 0
M = F × x
W = w × (b - a)
M = W × [(a + b) / 2]
An external couple adds directly to the support moment sum.
This page uses the standard statics sign convention. Upward force is positive. Counterclockwise moment is positive. The fixed-end reactions are the negatives of the summed external effects.
How to Use This Calculator
- Enter the beam length and choose matching units.
- Activate one or more load cases.
- Select point load, distributed load, or applied moment.
- Enter magnitude and position values for each active case.
- Use end position only for distributed loads.
- Choose the load direction carefully before calculating.
- Press the calculate button to show support reactions.
- Review the table, graph, and export files if needed.
FAQs
1. What reactions does a cantilever support provide?
A cantilever support resists vertical force, horizontal force, and moment. This calculator focuses on vertical loading and applied moments, so it reports the fixed-end vertical reaction and resisting moment.
2. Why does the fixed end carry a moment?
Loads placed away from the support create rotation tendencies. The built-in end must generate an equal and opposite moment to keep the beam in static equilibrium.
3. How is a distributed load handled?
The calculator converts the distributed load into an equivalent single force. That force acts at the centroid of the loaded segment and creates the same support reaction effect.
4. Can I mix several load types together?
Yes. You can combine point loads, partial distributed loads, and applied moments. The calculator adds all external force and moment contributions before finding the support reactions.
5. What sign convention is used here?
Upward force is positive. Counterclockwise moment is positive. Downward loads and clockwise moments therefore appear as negative external contributions in the detailed results table.
6. Does the location of an applied moment matter?
For reaction calculation, a pure couple contributes the same moment regardless of where it is applied along the beam. The position is still useful for documentation and plotting.
7. Is beam deflection included in this calculator?
No. This page is for static support reactions only. Deflection requires material properties, section stiffness, and a separate beam deformation analysis.
8. When should I verify results manually?
Always verify important design work manually or with engineering software. Independent checks are especially important when loads are unusual, units change, or safety-critical decisions depend on the results.