Crack Width Calculator — Gergely-Lutz Method, ACI 318-19M
Cracking is unavoidable in reinforced concrete, but its width can — and should — be controlled. The Gergely-Lutz formula remains the most-cited method for estimating the maximum surface crack width at the tension face. This calculator gives you w_max in millimetres and compares it to common limits.
Formulas
| Quantity | Formula |
|---|---|
| Gergely-Lutz crack width | w = 11 · 10⁻⁶ · β · f_s · ³√(d_c · A) (in inches/psi units) |
| Beta (geometry) | β = (h − c) / (d − c), typically ≈ 1.20 |
| Effective tension-area concept | A = (2·d_c · b) / N (effective tension area per bar) |
| Common limits | Interior exposure: 0.41 mm (0.016 in); exterior: 0.33 mm (0.013 in); marine: 0.18 mm (0.007 in) |
How to use it
- Enter cover c_c, total depth h, effective depth d, and beam width b.
- Enter the number of tension bars N and the bar diameter.
- Enter the steel stress f_s under service load (typically 0.6·f_y for unfactored loads).
- Read w_max in mm.
- Compare against the exposure-class limit.
Frequently Asked Questions
Why is Gergely-Lutz still relevant if ACI 318 dropped explicit crack-width checks?
ACI now uses the bar-spacing rule s ≤ 380(280/f_s) − 2.5c_c (§24.3.2), which implicitly limits crack width. Gergely-Lutz remains the standard when an actual crack-width number is needed (e.g., water-tight tanks, exterior exposure, owner-specified limits).
What's the maximum allowable crack width?
ACI 224R-01 gives 0.41 mm for dry air, 0.33 mm for humid/exterior, and 0.18 mm for sea-water exposure. Eurocode 2 limits 0.3 mm for normal exposure.
Should I use service or factored loads?
Service loads. Crack-width is a serviceability check, not strength.
Is the steel stress 0.6·f_y a safe assumption?
It's a common shorthand for unfactored service stress when you don't have load combinations handy. For more accuracy, calculate the service-load moment and find f_s from the cracked-section transformed stiffness.