Flexural Deflection Calculator with Graphs
Professional engineering tool for calculating beam deflection with step-by-step solutions, interactive graphs, and comprehensive analysis
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Go to Calculator tab, enter values, and click Calculate to see results here.
Understanding Flexural Deflection
Flexural deflection is the bending displacement of a structural member under load. It's a critical consideration in structural engineering that affects both serviceability and safety.
Key Formulas
Simply Supported Beam - Center Load:
δ = (P × L³) / (48 × E × I)
δ = (P × L³) / (48 × E × I)
Cantilever Beam - End Load:
δ = (P × L³) / (3 × E × I)
δ = (P × L³) / (3 × E × I)
Simply Supported Beam - Uniform Load:
δ = (5 × w × L⁴) / (384 × E × I)
δ = (5 × w × L⁴) / (384 × E × I)
Cantilever Beam - Uniform Load:
δ = (w × L⁴) / (8 × E × I)
δ = (w × L⁴) / (8 × E × I)
Engineering Parameters
- P = Concentrated load (Newtons)
- w = Distributed load (N/m)
- L = Span length (meters)
- E = Young's Modulus (GPa)
- I = Moment of Inertia (mm⁴)
- δ = Maximum deflection (mm)
Deflection Limits
Building codes specify maximum allowable deflections:
- Floor beams: L/360 to L/240
- Roof beams: L/240 to L/180
- Cantilevers: L/180 to L/120
- Industrial structures: L/250 to L/400
Practical Applications
This calculator helps engineers and students analyze beam behavior for:
- Structural design verification
- Serviceability checks
- Educational purposes
- Preliminary design calculations
Note: This tool provides theoretical calculations. Actual engineering design should consider safety factors, building codes, and professional judgment.
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