Beam Deflection Calculator
Calculate maximum deflection and bending moment for a simply supported beam.
A simply supported beam with a center point load is one of the most common structural scenarios. The maximum deflection occurs at the center and is proportional to PL³/(48EI). Acceptable deflection limits are typically L/240 for floor beams and L/360 for beams supporting brittle finishes. This calculator helps structural engineers check serviceability requirements.
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Frequently asked questions
With E = 200 GPa and I = 1000 cm⁴, δ = 1000 × 27 / (48 × 200e9 × 1e-5) = 0.281 mm. The span/deflection ratio is about 1/10,667 - well within limits.
Typically L/240 for live load. For a 3 m beam, that is 12.5 mm maximum. Beams supporting tile or glass have stricter limits of L/360 (8.33 mm) or L/480 (6.25 mm).
Deflection scales with L³. Doubling the span increases deflection 8 times. A 6 m beam deflects 8× more than a 3 m beam under the same load and cross-section.
Rearrange: I = PL³/(48Eδ). For 1 kN on 3 m with 2 mm max deflection in steel: I = 1000 × 27 / (48 × 200e9 × 0.002) = 1.406 × 10⁻⁶ m⁴ = 140.6 cm⁴.
M = PL/4. For 1 kN on a 3 m span, M = 1000 × 3/4 = 750 N·m. The bending stress is σ = Mc/I where c is the distance from the neutral axis to the outer fiber.