📏 Beam Deflection Calculator
Calculate beam deflection for structural engineering
How to Use This Calculator
Enter Span
Input the beam span in feet. This is the distance between supports.
Enter Load
Input the load in pounds per foot for uniform loads, or total load for point loads.
Enter Beam Dimensions
Input beam width and depth in inches. Standard beams are 4×8, 6×10, etc.
Select Load Type and Material
Choose load type (uniform, point at center, point at end) and material modulus of elasticity. Click "Calculate Deflection" to see results.
Formula
Uniform Load: δ = (5 × w × L⁴) / (384 × E × I)
Point Load at Center: δ = (P × L³) / (48 × E × I)
Moment of Inertia: I = b × d³ / 12
Where: δ = deflection, w = load per unit length, L = span, E = modulus, I = moment of inertia
Example: 12 ft span, 40 lbs/ft uniform load, 4×8 beam (E = 1,600,000 psi)
Step 1: I = 4 × 8³ / 12 = 170.67 in⁴
Step 2: L = 12 × 12 = 144 inches
Step 3: δ = (5 × 40/12 × 144⁴) / (384 × 1,600,000 × 170.67) = 0.393 inches
Step 4: L/360 limit = 144/360 = 0.400 inches (OK)
About Beam Deflection Calculator
The Beam Deflection Calculator is an essential tool for structural engineers, architects, contractors, and builders who need to calculate beam deflection. This calculator eliminates guesswork by providing precise deflection calculations based on span, load, beam dimensions, and material properties, helping you ensure beams meet structural requirements and building codes.
When to Use This Calculator
- Structural Design: Calculate beam deflection for structural engineering projects
- Code Compliance: Verify beams meet deflection limits (L/360 for live loads, L/240 for total loads)
- Beam Sizing: Determine appropriate beam sizes to limit deflection
- Load Analysis: Analyze deflection under different loading conditions
- Material Selection: Compare deflection for different materials and grades
Why Use Our Calculator?
- ✅ Accurate Calculations: Precise deflection calculations using standard structural formulas
- ✅ Multiple Load Types: Supports uniform loads, point loads at center, and point loads at end
- ✅ Material Properties: Pre-configured modulus of elasticity for common materials
- ✅ Code Limits: Automatically checks against L/360 and L/240 deflection limits
- ✅ Time Savings: Instant calculations eliminate manual math and lookups
Understanding Beam Deflection
Deflection Limits: Building codes typically limit beam deflection to L/360 for live loads (visible deflection) and L/240 for total loads (structural safety). L/360 means the beam should not deflect more than span divided by 360. For example, a 12-foot span has a L/360 limit of 0.4 inches.
Modulus of Elasticity: Different materials have different stiffness properties. Standard lumber has E = 1,600,000 psi, while steel has E = 29,000,000 psi. Higher E values mean stiffer beams with less deflection.
Tips for Best Results
- Use Accurate Values: Enter exact span, load, and beam dimensions for precise calculations
- Consider All Loads: Include live loads, dead loads, and any additional loads
- Check Code Limits: Ensure deflection is within L/360 (live) and L/240 (total) limits
- Consult Engineers: For critical structures, consult a structural engineer
- Verify Material Properties: Use actual material specifications for accurate results
Frequently Asked Questions
What is beam deflection?
Beam deflection is the vertical displacement of a beam under load. Excessive deflection can cause visible sagging, cracking, and structural problems. Building codes limit deflection to L/360 for live loads and L/240 for total loads.
How do I calculate beam deflection?
For uniform loads: δ = (5 × w × L⁴) / (384 × E × I), where w is load per unit length, L is span, E is modulus of elasticity, and I is moment of inertia. The calculator performs these calculations automatically.
What is the L/360 limit?
L/360 is a deflection limit where beam deflection should not exceed span divided by 360. For example, a 12-foot (144-inch) span has a L/360 limit of 0.4 inches. This limit prevents visible sagging and cracking.
What is modulus of elasticity?
Modulus of elasticity (E) is a material property that measures stiffness. Higher E values mean stiffer beams. Standard lumber has E = 1,600,000 psi, while steel has E = 29,000,000 psi. The calculator includes common values for different materials.
What if my beam exceeds deflection limits?
If deflection exceeds limits, increase beam depth (most effective), increase beam width, use a stiffer material, reduce span, or reduce load. Always consult a structural engineer for critical applications.