Calculator Inputs
Example Data Table
| Case | Support | Span | Point Load | UDL | Section | Material |
|---|---|---|---|---|---|---|
| Floor beam | Simply supported | 6 m | 20 kN | 5 kN/m | 300 × 150 × 12 × 8 mm | Steel |
| Balcony cantilever | Cantilever | 2.5 m | 8 kN | 3 kN/m | 250 × 125 × 10 × 7 mm | Steel |
| Fixed machinery beam | Fixed ended | 4 m | 12 kN | 4 kN/m | 220 × 110 × 9 × 6 mm | Steel |
Formula Used
I beam inertia from dimensions:
I = [bf × h³ - (bf - tw) × (h - 2tf)³] / 12
Simply supported center point load:
δ = P L³ / 48 E I, M = P L / 4
Simply supported uniform load:
δ = 5 w L⁴ / 384 E I, M = w L² / 8
Cantilever end point load:
δ = P L³ / 3 E I, M = P L
Cantilever uniform load:
δ = w L⁴ / 8 E I, M = w L² / 2
Bending stress:
σ = M c / I, where c = h / 2.
How to Use This Calculator
- Select the unit system first.
- Choose the beam support condition.
- Select the load mode.
- Enter span, load, material, and section data.
- Choose whether inertia is calculated or entered directly.
- Enable self weight when the beam weight matters.
- Enter the deflection limit ratio, such as L/360.
- Press Calculate Deflection to view results above the form.
- Use the CSV or PDF buttons for export.
I Beam Deflection Guide
Why Deflection Matters
I beam deflection is the vertical movement caused by load. A beam can be strong and still feel flexible. Excessive movement can crack finishes. It can also affect machinery, doors, partitions, and floors. This calculator checks deflection and bending stress together. That gives a better view of service behavior and strength.
Main Inputs
Span length has a large effect on movement. Deflection rises quickly as span increases. Load type is also important. A uniform load spreads weight along the full beam. A point load concentrates force at one position. The calculator supports simple, cantilever, and fixed-ended cases. It also combines point load and uniform load when needed.
Section Stiffness
The moment of inertia controls stiffness. A deeper I beam usually deflects less. Wider and thicker flanges also improve bending resistance. The web carries shear and connects the flanges. You can calculate inertia from dimensions. You can also enter a catalog inertia value directly. This helps when using standard rolled sections.
Material Behavior
Elastic modulus measures material stiffness. Steel has a higher modulus than aluminum or timber. Higher modulus means lower elastic deflection. Yield strength helps estimate bending safety. The calculator compares stress with the entered strength. It also checks your required safety factor.
Using Results
Maximum deflection is compared with the selected limit. Common limits include L/240, L/360, and L/480. The best limit depends on the project. The graph shows the expected deflected shape. Use the exported report for early design review. Final structural work should be checked by a qualified engineer.
FAQs
1. What does this calculator measure?
It estimates maximum I beam deflection, slope, reaction, bending moment, bending stress, and safety factor for common support and load cases.
2. Can I use catalog inertia values?
Yes. Select the direct inertia option. Enter the published moment of inertia in cm⁴ for metric or in⁴ for imperial units.
3. What is a good deflection limit?
Common service limits include L/240, L/360, and L/480. The correct value depends on use, finishes, vibration, and local design rules.
4. Does the calculator include self weight?
Yes. Tick the self weight box. The tool uses section area, density, and gravity to add beam weight as a uniform load.
5. Which point load location is assumed?
For simply supported and fixed beams, the point load is centered. For cantilever beams, the point load is placed at the free end.
6. Why does beam depth matter so much?
Depth strongly increases moment of inertia. A deeper beam usually becomes much stiffer, reducing deflection under the same load.
7. Can this replace structural design?
No. It is a calculation aid for estimates and study. Real projects need code checks, connection design, load combinations, and professional review.
8. Why do fixed beams deflect less?
Fixed ends restrain rotation. This creates end moments and reduces midspan movement compared with a similar simply supported beam.