Beam Deflection Calculator
Structural analysis tool to calculate max deflection for beams. Supports various load types (Point, Distributed) and boundary conditions. Auto-calculates Moment of Inertia.
1. Dimensions & Load
2. Material (Stiffness E)
3. Cross Section (I)
About
Beam deflection is a governing criterion in structural design, often overriding strength requirements. Even if a beam is strong enough to carry a load without breaking, excessive sagging can cause plaster to crack, doors to stick, or puddling on flat roofs. Calculating the maximum vertical displacement (δ) ensures the structural member meets serviceability limits (e.g., L/360 or L/480).
This calculator solves the differential equations of the elastic curve for common setups. It integrates a database of Young's Modulus (E) for standard construction materials, eliminating the need for external lookups. Additionally, it computes the Moment of Inertia (I) based on cross-section geometry, feeding these critical stiffness parameters directly into the deflection formulas.
Formulas
Standard formulas for maximum deflection (δmax):
1. Simply Supported Beam, Uniform Distributed Load (w):
2. Simply Supported Beam, Center Point Load (P):
3. Cantilever Beam, End Point Load (P):
Reference Data
| Material | Young's Modulus (E) - GPa | Young's Modulus (E) - ksi |
|---|---|---|
| Structural Steel | 200 | 29,000 |
| Aluminum 6061 | 69 | 10,000 |
| Wood (Douglas Fir) | 11 - 13 | 1,600 - 1,900 |
| Wood (Oak) | 12 - 15 | 1,700 - 2,200 |
| Concrete (High Strength) | 30 - 35 | 4,350 - 5,000 |
| Titanium | 110 | 16,000 |
| Brass | 100 - 125 | 15,000 - 18,000 |
| Glass | 70 | 10,150 |