Beam Deflection Form
Formula Used
This calculator uses standard elastic beam formulas for small deflection analysis.
| Case | Maximum Deflection Formula | Notes |
|---|---|---|
| Simply supported, center point load | δ = PL³ / 48EI | Maximum deflection occurs at midspan. |
| Simply supported, uniform load | δ = 5wL⁴ / 384EI | Load is spread across the full span. |
| Cantilever, end point load | δ = PL³ / 3EI | Maximum deflection occurs at the free end. |
| Cantilever, uniform load | δ = wL⁴ / 8EI | Uniform load acts along the cantilever. |
| Fixed ends, uniform load | δ = wL⁴ / 384EI | End rotations are restrained. |
| Fixed ends, center point load | δ = PL³ / 192EI | Both beam ends resist rotation. |
Here, δ is maximum deflection, P is point load, w is uniform load, L is span, E is elastic modulus, and I is second moment of area.
How to Use This Calculator
- Select the beam support and load case.
- Enter the beam span in meters.
- Enter elastic modulus in GPa.
- Enter second moment of area in cm⁴.
- Add either point load or uniform load.
- Choose the allowable deflection ratio.
- Press the calculate button.
- Review the result above the form.
- Use CSV or PDF options for records.
Example Data Table
| Beam Case | Span | E | I | Load | Typical Use |
|---|---|---|---|---|---|
| Simply supported, center point load | 6 m | 200 GPa | 8000 cm⁴ | 12 kN | Single equipment load |
| Simply supported, uniform load | 5 m | 200 GPa | 6500 cm⁴ | 4 kN/m | Floor joist check |
| Cantilever, end point load | 2.5 m | 70 GPa | 2400 cm⁴ | 3 kN | Bracket arm |
| Fixed ends, uniform load | 4 m | 200 GPa | 9000 cm⁴ | 6 kN/m | Restrained beam |
Deflection of Beams Calculator Guide
Why Beam Deflection Matters
A beam bends when loads act across its span. The amount of bending is called deflection. It matters in floors, lintels, shelves, shafts, frames, and machine parts. A small deflection may be safe. A large deflection may crack finishes, jam parts, or feel weak. This calculator helps you estimate that movement for common beam cases.
What This Tool Checks
The tool handles simple supports, cantilevers, and fixed end beams. It covers point loads and uniformly distributed loads. You can enter length, modulus of elasticity, second moment of area, load size, and an allowable span ratio. The result shows maximum deflection, support slope, reaction force, bending moment, and a serviceability check.
Why Material Stiffness Matters
Elastic modulus tells how stiff a material is. Steel usually bends less than timber under the same shape and load. Concrete, aluminum, and engineered sections also have different stiffness values. Moment of inertia describes the section shape. Deep sections usually resist bending better than shallow sections. Because deflection depends on length cubed or length to the fourth power, span changes are very important.
Formula Approach
The calculator uses classic small deflection beam equations. These equations assume straight prismatic members, elastic behavior, and loads applied slowly. They also assume that shear deformation is small. That is often acceptable for slender beams. Very deep beams, composite sections, cracked concrete, or dynamic loads need more detailed checks.
Reading The Output
Maximum deflection is shown in millimeters. The allowable deflection is based on L divided by your selected ratio. A ratio of 360 is common for many service checks. The utilization percentage compares estimated deflection against that limit. Values below one hundred percent pass the chosen limit. Values above one hundred percent need review.
Practical Notes
Use consistent values from trusted drawings or section tables. Check units before submitting the form. Compare the result with local codes and project requirements. Do not use this calculator as final structural approval. Real structures may include lateral restraint, holes, joints, load combinations, vibration, creep, and safety factors. Ask a qualified engineer when people, property, or compliance depends on the design.
Record every assumption beside each result. This makes later checking easier, cleaner, and more reliable for teams onsite.
FAQs
1. What is beam deflection?
Beam deflection is the movement of a beam from its original position after loading. It is usually measured at the point where bending is greatest.
2. Which units does this calculator use?
Span is entered in meters. Elastic modulus uses GPa. Moment of inertia uses cm⁴. Point load uses kN. Uniform load uses kN per meter.
3. What is moment of inertia?
Moment of inertia describes how a beam section resists bending. A deeper or better shaped section usually has a larger value and smaller deflection.
4. Why does span affect deflection so much?
Many deflection equations include span cubed or span to the fourth power. Small span increases can therefore create much larger beam movement.
5. What does L over 360 mean?
L over 360 means the allowable deflection equals span divided by 360. It is a common serviceability limit, but project rules may differ.
6. Can this calculator approve a structural beam?
No. It gives an educational estimate only. Final design should include code checks, load combinations, lateral stability, connections, and professional review.
7. Why are fixed beams stiffer?
Fixed ends restrain rotation. This restraint reduces deflection compared with a similar simply supported beam under the same load and span.
8. What if my load is not centered?
This calculator covers common centered or full-span cases. Off-center loads need different formulas or a structural analysis model.