Beam Input Form
Use this form for a simply supported beam carrying one point load.
Example Data Table
| Case | Point Load | Span | Load Position | E | I | Left Reaction | Right Reaction | Max Moment | Deflection at Load |
|---|---|---|---|---|---|---|---|---|---|
| Example 1 | 12 kN | 6 m | 2.5 m | 200 GPa | 8.5×10-6 m4 | 7.0000 kN | 5.0000 kN | 17.5000 kN·m | 30.0245 mm |
| Example 2 | 18 kN | 8 m | 4 m | 210 GPa | 1.20×10-5 m4 | 9.0000 kN | 9.0000 kN | 36.0000 kN·m | 47.6190 mm |
Formula Used
This calculator assumes a simply supported beam with one concentrated load. Let P be the point load, L the span, a the distance from the left support, and b = L - a.
- Left reaction: RA = P × b / L
- Right reaction: RB = P × a / L
- Maximum moment: Mmax = P × a × b / L
- Load-point deflection: δ = P × a² × b² / (3 × E × I × L)
- Bending stress: σ = M × c / I, where c = section depth / 2
The graph is built from piecewise shear, moment, and elastic-curve equations. Maximum deflection is estimated from sampled points across the span.
How to Use This Calculator
- Enter the point load magnitude and choose its force unit.
- Enter the beam span and the distance from the left support.
- Provide elastic modulus and second moment of area for the section.
- Optionally enter beam depth to estimate extreme fiber bending stress.
- Choose sample points for smoother chart curves if needed.
- Click Calculate Beam Response to place results above the form.
- Use the CSV or PDF buttons to save the current result set.
Frequently Asked Questions
1. What beam type does this calculator analyze?
This version analyzes a simply supported beam carrying one concentrated point load. It does not model fixed supports, cantilevers, distributed loads, or multiple loads in one run.
2. What is the load position reference point?
The load position is measured from the left support. Enter zero at the left support and the full span at the right support. Most practical checks use a value somewhere between both supports.
3. Why are reactions different when the load is off-center?
An eccentric load creates unequal support forces. The support closer to the load carries the larger reaction, while the farther support carries less. Static equilibrium controls the split.
4. What is the second moment of area?
It is a geometric property describing how strongly a section resists bending. Larger values usually reduce deflection and bending stress for the same material and load.
5. Why does the calculator ask for elastic modulus?
Elastic modulus defines material stiffness. A higher modulus reduces beam deflection for the same load and section shape. Steel usually deflects less than wood when geometry matches.
6. Is the maximum moment always under the point load?
For a simply supported beam with one point load, yes. The bending moment peaks directly under the load because the shear sign changes there.
7. Why is there an optional section depth field?
Depth helps estimate extreme fiber bending stress using σ = M × c / I. Leave it blank if you only need reactions, moment, shear, and deflection.
8. Can I use the graph for design sign-off?
The chart is useful for fast checking and reporting, but final design should still be reviewed against code requirements, load combinations, serviceability limits, and project-specific assumptions.