Structural Beam Load Calculator
Estimate the load-bearing stiffness of a simply supported structural beam based on its span, cross-section, and material. Use this when sizing floor joists, headers, or steel beams for construction projects.
Last updated: September 2026
Formula below · 2 sources (asce.org, Wikipedia) · Updated Sep 2026
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About this calculator
This calculator finds the uniform load that makes the beam deflect by span/360, the IBC live-load deflection limit for floors. For a simply supported beam under a uniform load w, midspan deflection is δ = 5wL⁴ / (384EI). Setting δ = L/360 and solving gives w = 384·E·I / (5 × 360 × L³), with L in inches (feet × 12), E in psi and I in in⁴, giving w in lb per inch; multiplying by 12 gives lb/ft. Fixed-fixed beams deflect one fifth as much (δ = wL⁴ / 384EI), so they carry 5 times the load for the same deflection; a fixed-pinned (propped) beam (δmax = wL⁴ / 185EI) carries about 2.41 times. This is a serviceability limit only. The beam must also be checked for bending strength (moment = wL²/8 against the allowable moment from its section modulus and yield strength) and shear; on short spans strength, not deflection, usually governs, and the real capacity can be lower than this value.
How to use
Consider a 16-ft simply supported steel beam with E = 29,000,000 psi and I = 50 in⁴. Convert span to inches: 16 × 12 = 192 in, and 192³ = 7,077,888. Numerator: 384 × 29,000,000 × 50 = 556,800,000,000. Denominator: 5 × 360 × 7,077,888 = 12,740,198,400. w = 43.7 lb/in, or 43.7 × 12 ≈ 524 lb/ft for L/360 (deflection 0.53 in). A fixed-fixed beam (×5) reaches L/360 at about 2,622 lb/ft and a fixed-pinned beam (×2.41) at about 1,264 lb/ft. The defaults (12 ft, I = 100 in⁴) give about 2,486 lb/ft. Check bending and shear strength separately.
Frequently asked questions
What is the moment of inertia and how does it affect beam stiffness?
The moment of inertia (I) is a geometric property of a beam's cross-section that measures how effectively the material is distributed away from the neutral axis. A larger I means more material is located far from the centroid, which dramatically increases bending stiffness and reduces deflection. For example, a wide-flange steel I-beam concentrates material in its top and bottom flanges, giving it a high I value relative to its weight. Doubling the moment of inertia exactly doubles the stiffness and halves the midspan deflection for the same applied load. Standard values of I for structural steel sections are tabulated in AISC Steel Construction Manual references.
How does beam span length affect deflection and load capacity?
Beam span has an extremely powerful effect on deflection because span appears raised to the fourth power in the deflection formula. Doubling the span of a simply supported beam increases midspan deflection 16 times for the same load, and because the L/360 limit itself grows with span, the load that reaches L/360 falls with the cube of the span (doubling the span cuts it to one eighth). Building codes typically limit live-load deflection to span/360 for floor beams. Adding an intermediate support is often the most effective way to control deflection.
What is the difference between a beam stiffness check and a beam strength check?
A stiffness check — also called a serviceability check — determines whether a beam deflects too much under load, which can cause discomfort, damage to finishes, or ponding on roofs. It is governed by the elastic modulus and moment of inertia, and is compared against code-specified deflection limits like L/360 or L/240. A strength check, by contrast, determines whether the beam can carry the applied loads without rupturing, yielding, or failing structurally. Strength is governed by bending moment capacity (plastic section modulus and yield strength) and shear capacity. Both checks must be satisfied independently — a beam can be strong enough to carry a load but still deflect too much, or vice versa.