Beam Calculator Inputs
The page stays in a single vertical flow. The input area below uses a responsive 3-column, 2-column, and 1-column grid.
Example Data Table
| Beam Case | Span | Load | E | I | Example Maximum Deflection |
|---|---|---|---|---|---|
| Simply Supported - Full Span UDL | 6.0 m | 12.0 kN/m | 200 GPa | 85 cm⁴ | ≈ 69.12 mm |
| Simply Supported - Center Point Load | 4.5 m | 22.0 kN | 200 GPa | 310 cm⁴ | ≈ 20.55 mm |
| Cantilever - End Point Load | 2.8 m | 9.0 kN | 200 GPa | 260 cm⁴ | ≈ 45.11 mm |
| Fixed-Fixed - Full Span UDL | 5.0 m | 8.0 kN/m | 200 GPa | 420 cm⁴ | ≈ 12.40 mm |
These sample rows are for demonstration only. Confirm section properties and design limits from your actual project documents.
Formula Used
The calculator uses linear elastic Euler-Bernoulli beam relationships, where deflection depends on load intensity, span, support condition, elastic modulus, and moment of inertia.
E I d²y/dx² = M(x)
- Simply supported, center point load:
δmax = P L³ / (48 E I) - Simply supported, full span UDL:
δmax = 5 w L⁴ / (384 E I) - Cantilever, end point load:
δmax = P L³ / (3 E I) - Cantilever, full span UDL:
δmax = w L⁴ / (8 E I) - Fixed-fixed, center point load:
δmax = P L³ / (192 E I) - Fixed-fixed, full span UDL:
δmax = w L⁴ / (384 E I)
For eccentric point-load positions, the page uses exact piecewise beam equations along the span. The maximum deflection location is then found numerically from the generated curve.
σ = M / Z is also used when section modulus is supplied to estimate bending stress.
These equations assume small deflection behavior, prismatic members, constant material stiffness, and ideal support conditions.
How to Use This Calculator
- Select the beam case that matches your support and loading condition.
- Enter the beam span and choose the correct span unit.
- Input elastic modulus and moment of inertia from the steel section data.
- Enter the load magnitude and select the correct load unit.
- Provide distance
awhen an offset point load case is chosen. - Set the allowable deflection limit, such as
L/360or another project criterion. - Optionally enter section modulus to estimate bending stress.
- Press Calculate Deflection to show the result above the form.
- Review the summary table, reactions, pass/fail status, and the Plotly graph.
- Use the CSV or PDF buttons to export the calculated result set.
Frequently Asked Questions
1. What does this calculator estimate?
It estimates beam deflection, reaction values, maximum bending moment, maximum slope, serviceability status, and optional bending stress when section modulus is provided.
2. Which beam cases are included?
The page includes simply supported, cantilever, and fixed-fixed beams with center point loads, offset point loads, and full-span uniformly distributed loads.
3. Can I use imperial or metric units?
Yes. The inputs accept metric and imperial options for span, modulus, inertia, section modulus, load, and displayed deflection output.
4. Why is moment of inertia so important?
Deflection is inversely proportional to E I. A larger inertia means a stiffer section, so the beam bends less under the same span and load.
5. What does the pass or fail result mean?
It compares calculated maximum deflection against the allowable deflection based on your chosen limit ratio, such as L/360.
6. Is this enough for final design approval?
No. It is helpful for preliminary checks and quick comparisons. Final design should still follow governing codes, connection design, load combinations, and project review procedures.
7. Why might real beams deflect differently?
Real behavior can differ because of shear deformation, end restraint variation, lateral effects, composite action, residual stresses, construction tolerance, and actual load paths.
8. What should I enter for section modulus?
Use the appropriate elastic section modulus from your steel section table. Leave it blank or zero when you only need deflection and reaction results.