MulticalcBeam Deflection Calculator
Calculate beam deflection for structural analysisEnter beam parameters to calculate deflection.
Beam Deflection Guide
Understanding Beam Deflection
Beam deflection is the displacement of a beam under load. Excessive deflection can cause structural damage, cracking, and serviceability issues.
Deflection Formulas:
- Simply Supported, Point Load: δ = PL³/(48EI)
- Simply Supported, Distributed: δ = 5wL⁴/(384EI)
- Cantilever, Point Load: δ = PL³/(3EI)
- Cantilever, Distributed: δ = wL⁴/(8EI)
- Fixed-Fixed, Point Load: δ = PL³/(192EI)
- Fixed-Fixed, Distributed: δ = wL⁴/(384EI)
Key Parameters:
- P: Point load (kN or kips)
- w: Distributed load per unit length (kN/m or kips/ft)
- L: Beam span length
- E: Modulus of elasticity (material stiffness)
- I: Moment of inertia (cross-section property)
Deflection Limits:
- Floor beams: L/360 (residential), L/480 (commercial)
- Roof beams: L/240 (typical), L/180 (minimum)
- Cantilevers: L/180 to L/240
- L/δ ratio: Higher is stiffer (less deflection)
Common Materials
- Steel: E ≈ 200 GPa (29,000 ksi)
- Aluminum: E ≈ 70 GPa (10,000 ksi)
- Concrete: E ≈ 25-35 GPa (3,600-5,000 ksi)
- Wood: E ≈ 10-15 GPa (1,500-2,200 ksi)
Pro Tips
-
Stiffness
Deflection is inversely proportional to EI. Doubling I halves deflection. -
Length Effect
Deflection increases with L³ or L⁴. Small length changes have big effects! -
Check Ratio
L/δ ratio is a quick serviceability check. Higher = better.
Example
Simply supported steel beam:
- L = 6 m, P = 50 kN (center)
- E = 200 GPa, I = 5000 cm⁴
- δ = 50×6³/(48×200×50000)
- δ ≈ 2.25 mm
- L/δ = 6000/2.25 ≈ 2667 ✓
Frequently Asked Questions
A: Beam deflection is the vertical displacement of a beam under load. Excessive deflection can cause: cracking in finishes, ponding on roofs, misalignment of equipment, and perception of unsafe conditions. Building codes limit deflection to prevent these issues.
A: L/δ (span-to-deflection ratio) is a common deflection check. Higher values mean less deflection. Typical limits: L/360 for floor beams (residential), L/480 (commercial floors), L/240 for roof beams, L/180 for cantilevers. For example, a 20-foot beam with L/360 limit can deflect max 20×12/360 = 0.67 inches.
A: For standard shapes (I-beams, channels, tubes), look up I in steel/aluminum handbooks or manufacturer catalogs. For rectangular sections: I = bh³/12 (b=width, h=height). For circular sections: I = πd⁴/64. Our calculator assumes you know I from section properties.
A: Simply supported beams rest on supports that allow rotation (like a pin). Fixed beams are rigidly attached at supports (no rotation). Cantilevers are fixed at one end, free at the other. Fixed beams deflect less than simply supported beams under the same load (stiffer support = less deflection).
A: No, this calculator uses classical beam theory (Euler-Bernoulli) which assumes deflection from bending only. For deep beams (span/depth < 10) or very short beams, shear deflection can be significant. For typical slender beams, bending deflection dominates and this calculator is accurate.
A: This calculator is for single-span beams with one load type (point or distributed). For continuous beams, multiple point loads, or complex loading, use structural analysis software or superposition principles. For preliminary design of simple cases, this calculator is sufficient.
Disclaimer
Important Notice:
- This calculator provides theoretical deflections based on classical beam theory (Euler-Bernoulli) for simple loading cases.
- Calculations assume: elastic behavior, small deflections, homogeneous material, prismatic cross-section, and loads applied at specific locations (center for point loads).
- Actual deflections may differ due to: material nonlinearity, large deflections, shear deformation, support conditions, load distribution, temperature effects, and construction tolerances.
- This tool is for preliminary design and education only. For final structural design, use professional structural analysis software and consult licensed engineers.
- Building code compliance requires consideration of: dead loads, live loads, load combinations, deflection limits, vibration, and other factors not included in this calculator.
- Point loads are assumed at mid-span. Distributed loads are assumed uniform over entire span. For other load positions or patterns, use structural analysis software.
- Safety factors are not included. Professional design requires appropriate safety factors per applicable codes (IBC, AISC, ACI, etc.).
- Moment of inertia (I) must be calculated correctly for the beam's cross-section and orientation. Incorrect I values will give incorrect deflections.
- This calculator does not check: strength, buckling, shear, bearing, fatigue, or other failure modes. Deflection is only one aspect of beam design.
- We are not responsible for any errors, structural failures, code violations, or other consequences resulting from the use of this calculator.
Always consult with licensed structural engineers for building design and follow applicable building codes and standards.
Beam Deflection
Calculate beam deflection for structural analysis. Supports 3 beam types and 2 load types with accurate engineering formulas!
Supported Configurations
- ✓ Simply Supported
- ✓ Cantilever
- ✓ Fixed-Fixed
- ✓ Point Load (Center)
- ✓ Distributed Load
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Did You Know?
The Eiffel Tower can sway up to 7 cm (2.75 inches) in strong winds! Engineers must account for deflection in all structures, from beams to skyscrapers.