Beam Deflection Calculator
Calculate beam deflection for different loading conditions and support types
Introduction
Beam deflection is the degree to which a structural element bends under a load. Understanding deflection is crucial for structural design to ensure safety, functionality, and serviceability of buildings, bridges, and mechanical components.
This calculator helps engineers and designers predict beam deflection under various loading conditions, enabling proper material selection and dimensioning for structural applications.
How to Use
- Enter the load value (N or N/m for distributed)
- Input the beam length (m)
- Specify the elastic modulus (Pa) - Steel: 200×10⁹ Pa
- Enter the moment of inertia (m⁴)
- Click "Calculate" to get deflection results
- Review the deflection and stiffness values
Calculator
Steel: 200×10⁹ Pa
I-Beam: 8×10⁻⁸ m⁴
Formula
δ = PL³/48EI
δ = Deflection (m)
P = Load (N) or w = distributed load (N/m)
L = Beam length (m)
E = Elastic modulus (Pa)
I = Moment of inertia (m⁴)
k = P/δ
Beam stiffness (N/m)
Beam Deflection Formulas
Simply Supported Beam
δ = (F × L³) ÷ (48 × E × I)
Where δ = deflection, F = force, L = length, E = modulus of elasticity, I = moment of inertia
Cantilever Beam
δ = (F × L³) ÷ (3 × E × I)
For point load at free end of cantilever beam
Key Parameters
E (Modulus of Elasticity): Material stiffness property
I (Moment of Inertia): Cross-sectional resistance to bending
L (Length): Beam span between supports
Use Cases
Structural Engineering
- Building floor design
- Bridge beam analysis
- Roof structure design
- Support beam sizing
Mechanical Design
- Machine frame design
- Shaft deflection analysis
- Bracket design
- Load-bearing components
Understanding Your Results
Deflection (δ)
The amount the beam bends under load, measured in millimeters or inches. Lower values indicate stiffer beams.
Stiffness (k)
Force required to cause unit deflection, measured in N/m or lb/in. Higher values mean more rigid beams.
Safety Factors
Always consider safety factors in design. Typical safety factors range from 1.5 to 3.0 depending on application.
Frequently Asked Questions
What is acceptable deflection?
Acceptable deflection depends on the application. For floors, typically L/240 to L/360 of the span length. For precision equipment, much smaller deflections are required.
How does moment of inertia affect deflection?
Higher moment of inertia significantly reduces deflection. I-beams have high I values for their weight, making them efficient for structural applications.
What is the difference between simply supported and cantilever?
Simply supported beams have supports at both ends, while cantilever beams are fixed at one end and free at the other. Cantilever beams typically deflect more under the same load.
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Conclusion
Beam deflection calculations are fundamental to structural engineering and mechanical design. This calculator provides essential tools for predicting structural behavior under various loading conditions, ensuring safe and efficient designs.
Understanding beam deflection helps engineers select appropriate materials, dimensions, and support configurations to meet performance requirements while maintaining structural integrity and serviceability.