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1. Dimensions & Load

2. Material (Stiffness E)

3. Cross Section (I)

Max Deflection (δ):0.00Units match input (e.g. mm)
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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.

structural engineering beam deflection mechanics statics construction

Formulas

Standard formulas for maximum deflection (δmax):

1. Simply Supported Beam, Uniform Distributed Load (w):

δmax = 5wL4384EI

2. Simply Supported Beam, Center Point Load (P):

δmax = PL348EI

3. Cantilever Beam, End Point Load (P):

δmax = PL33EI

Reference Data

MaterialYoung's Modulus (E) - GPaYoung's Modulus (E) - ksi
Structural Steel20029,000
Aluminum 60616910,000
Wood (Douglas Fir)11 - 131,600 - 1,900
Wood (Oak)12 - 151,700 - 2,200
Concrete (High Strength)30 - 354,350 - 5,000
Titanium11016,000
Brass100 - 12515,000 - 18,000
Glass7010,150

Frequently Asked Questions

Young's Modulus is a measure of a material's stiffness. A higher E value means the material is more rigid and will deflect less under the same load. Steel (200 GPa) is much stiffer than wood (11 GPa).
The Moment of Inertia reflects how the cross-sectional shape resists bending. A deeper beam (higher 'd') has a exponentially higher "I" than a shallow one. For a rectangle, I = bd³/12, meaning doubling the depth increases stiffness by 8 times.
No. This tool calculates Deflection (displacement). A beam can be safe regarding stress (it won't break) but fail regarding deflection (it bends too much). Both checks are required for a complete design.