Beam Deflection

Calculate the maximum displacement of a simply supported beam under uniform loads.

Material & Beam Data

Span Length (in)

Uniform Load (lb/in)

Material

Elastic Modulus (PSI)

Moment of Inertia (in⁴)

Deflection Results

Analyzing structural load?

Provide the beam span, material properties, and the applied load to calculate the maximum vertical displacement.

Overview

Beam deflection is the degree to which a structural element is displaced under a load. It depends on the beam's material (Elastic Modulus), its shape (Moment of Inertia), and the distance between supports. Managing deflection is critical for preventing drywall cracks (L/360 rule) and ensuring user comfort—no one likes a 'bouncy' floor.

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Pro Tips

If deflection is too high, adding depth to the beam is much more effective than adding width, because depth contributes to the cube of the Inertia.
For standard lumber, the Moment of Inertia for a rectangular section is (b × h³) / 12.
Check that your units are consistent (e.g., all inches or all meters) to avoid exponential errors.

Fun Facts

"The 'L/360' rule is a common code requirement, meaning the beam shouldn't deflect more than 1/360th of its total length under live loads."
"Doubling the span of a beam doesn't just double the deflection—it increases it by a factor of 16 (2 to the 4th power!)."
"Steel has an Elastic Modulus roughly 20-30 times higher than most construction timbers."

Formula: δ = (5 × w × L⁴) / (384 × E × I)

Used with this

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