Beam Load Calculator

Calculate the maximum bending moment, shear, and deflection for a simply-supported beam under a uniformly distributed load.

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Enter your beam's span, load, and section properties to find its maximum bending moment, shear, and deflection — for preliminary estimates only.

Beam span (m) *

Uniformly distributed load (kN/m) *

Elastic modulus (GPa) *

200 GPa for structural steel, ~30 GPa for concrete, ~11 GPa for typical structural timber.

Moment of inertia (cm⁴) *

Get this from your beam section's properties table (depends on its shape and size).

Your result

2.083

Max deflection

Max bending moment20

Max shear force20

AI explanation

Formula

M = wL²/8; V = wL/2; δ = 5wL⁴/(384EI) — standard simply-supported beam formulas for a uniformly distributed load

Worked example

4m span, 10 kN/m load, steel beam (E=200GPa, I=8000cm⁴)

Worked example: 4m span, 10 kN/m load, steel beam (E=200GPa, I=8000cm⁴)
Field	Value
Beam span (m)	4
Uniformly distributed load (kN/m)	10
Elastic modulus (GPa)	200
Moment of inertia (cm⁴)	8000
Max bending moment	20
Max shear force	20
Max deflection	2.0833

Assumptions

Assumes a simply-supported beam (free to rotate at both ends) under a single uniformly distributed load, with linear-elastic material behavior — real beams may have different support conditions, point loads, or combined loading.

Frequently asked questions

What is a uniformly distributed load (UDL)?

A load spread evenly along the full length of the beam (like the beam's own weight, or a uniform floor load), as opposed to a point load concentrated at one location.

Where do I find my beam's moment of inertia?

From a structural steel/timber section properties table for your specific beam size and shape (e.g. an I-beam's published section properties), or calculate it directly from the cross-section geometry.

Is this deflection acceptable for my project?

Deflection limits (often expressed as span ÷ 250 or span ÷ 360, depending on use) are set by the applicable building code and depend on the beam's application — a structural engineer should verify against the correct limit for your project.

Related calculators

This calculator provides a preliminary, educational estimate using standard simply-supported beam formulas. It does not account for load combinations, safety factors, lateral-torsional buckling, or material-specific design code requirements. Any beam design used for actual construction must be verified by a licensed structural engineer.

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