How to check beam deflection (and what limit to use)

Deflection isn't about strength — a beam can be perfectly safe and still bounce, sag visibly, or crack the finishes below it. That's why deflection is a Serviceability Limit State (SLS) check, with its own load combinations and its own limits.

Step 1 — Use SLS loads, not ULS

Drop the ULS partial factors. The characteristic combination for irreversible deflections is simply Gₖ + Qₖ. The frequent combination uses Gₖ + ψ₁·Qₖ for reversible deflections (ψ₁ ≈ 0.5–0.7 depending on use).

Step 2 — Pick the right deflection formula

δ = 5 · w · L⁴ ÷ (384 · E · I)

δ = P · L³ ÷ (48 · E · I)

For combined load cases, use superposition — calculate δ for each load case separately and add them. Cantilevers, propped cantilevers, fixed-ended beams and continuous beams each have their own coefficients (Roark's Formulas or any structural handbook covers them all).

Step 3 — Compare to the right limit

Eurocode 3 doesn't specify deflection limits — they come from the National Annex, NCCI documents, or client requirements. The most common UK values:

• δtotal ≤ L / 250 — general limit on total deflection
• δimposed ≤ L / 360 — beams supporting brittle finishes (plaster, render)
• δimposed ≤ L / 200 — beams not supporting brittle finishes
• δtip ≤ L / 180 — cantilevers (note: L = cantilever projection, not 2·L)
• δdynamic — separate vibration check for slender floors (e.g. SCI P354)

Step 4 — Add precamber if needed

For long-span steel beams (typically >9 m) where dead-load deflection is visible, you can specify precamber. The fabricator sets a built-in upward bow equal to the dead-load deflection, so the beam ends up flat under permanent load. Specify on the drawings — it doesn't happen automatically.

Quick worked example

305×127×42 UB, span 6.0 m, w = 12 kN/m (unfactored), Iy = 8200 cm⁴, E = 210,000 N/mm². δ = 5 · 12 · 6000⁴ ÷ (384 · 210000 · 8200·10⁴) ≈ 11.7 mm. Limit L/360 = 16.7 mm. OK. If supporting brittle plaster ceiling: imposed deflection only (Qₖ = 5 kN/m, w_imposed = 5 kN/m): δ_imposed ≈ 4.9 mm < L/360 = 16.7 mm. Comfortable.