How to Check Crack Width in Reinforced Concrete: Gergely-Lutz Method with a Worked Example

A reinforced concrete beam or slab can be sized correctly for flexure and shear and still disappoint its owner in service if the tension face cracks too widely. Concrete is expected to crack under tension — that alone is not structural distress. What matters is keeping crack widths small enough that the reinforcing steel stays protected from corrosion, water-retaining elements stay watertight, and finished surfaces remain acceptable to occupants. This article covers the classic Gergely-Lutz crack width equation, the maximum bar-spacing rule that ACI 318-19 now uses instead, and a fully worked numeric example in SI units.

Why Crack Width Control Matters

Three concerns drive crack-width limits. First, corrosion protection: once a crack reaches the reinforcement, moisture, chlorides, and carbon dioxide reach the steel far faster than through sound cover concrete — especially relevant in coastal, humid ASEAN environments. Second, water-tightness: tanks, reservoirs, and basements need cracks narrow enough to self-seal, or leakage becomes a serviceability failure even if the member remains structurally safe. Third, appearance — a visibly cracked soffit undermines occupant confidence even when it is structurally sound. NSCP 2015, which adopts ACI 318 serviceability provisions, addresses all three through the checks covered here.

The Gergely-Lutz Crack Width Equation

Before 1999, ACI 318 commentary gave an explicit way to estimate the maximum flexural crack width at the tension face, developed by Gergely and Lutz from statistical regression on measured crack widths. In SI units, with steel stress in MPa and distances in millimeters:

where w is the estimated maximum crack width, mm, and:

• f_s — service-load stress in the tension reinforcement, MPa. Absent a rigorous cracked-section analysis, f_s is commonly approximated as roughly 0.6f_y.
• β — β = (h − c)/(d − c), where h is overall depth, d is effective depth, and c is the neutral-axis depth of the cracked section. For ordinary beams this is typically 1.15–1.25 and is commonly taken as β ≈ 1.2; for thin one-way slabs, roughly 1.35 is more representative.
• d_c — concrete cover measured from the extreme tension fiber to the center of the nearest bar, mm.
• A — effective tension area of concrete around the reinforcement (same centroid as the steel), divided by number of bars, mm². For a rectangular section with n bars spread across width b, A ≈ (2d_c × b)/n.

The equivalent US customary form, with f_s in ksi and d_c, A in inches, is w (×10^-3 in) = 0.076 × β × f_s × (d_c × A)^1/3 — numerically consistent with the SI form once units are converted.

How Wide Is Too Wide? Typical Crack Width Limits

The pre-1999 ACI 318 commentary distinguished interior from exterior exposure, and the crack-control guidance still published in ACI 224R expands this into a table of tolerable crack widths by exposure condition rather than one universal number:

Note that the drier, more sheltered condition allows the wider crack — humidity, chemicals, and direct water contact drive the limit down. Water-retaining and marine structures should generally follow stricter environmental-engineering provisions (such as ACI 350) rather than this generic table.

ACI 318-19's Shift: Maximum Bar Spacing Instead of a Crack-Width Number

Because Gergely-Lutz is a statistical fit to scattered data, individual crack widths on a real member can vary well above or below the predicted value even with correct inputs. ACI 318 therefore dropped the explicit crack-width and z-factor checks in favor of a simpler, more robust criterion: a maximum center-to-center spacing of the tension reinforcement nearest the tension face. This is carried forward in ACI 318-19's provisions on distribution of flexural reinforcement (Section 24.3), and governs current NSCP-based design. In SI units:

Here s is the maximum allowable bar spacing, mm; c_c is the least clear cover to the flexural reinforcement, mm (measured from the tension face to the surface of the main bars, so it includes the stirrup diameter); and f_s is again the service-load steel stress, MPa — ACI 318-19 permits taking f_s as 2/3f_y if not computed directly. The upper-bound term 300(280/f_s) keeps the rule from allowing unrealistic spacing on thin-cover members. Unlike Gergely-Lutz, this rule does not predict an actual crack width — it simply keeps bars close enough, given stress and cover, that cracks stay fine and well-distributed. Satisfying it is deemed sufficient for crack control without a separate Gergely-Lutz calculation.

Worked Example

Consider a simply supported rectangular beam exposed to humid outdoor conditions (an open corridor beam), with the following properties:

Step 1 — Geometry. Distance from the tension face to the center of the main bars: d_c = 40 + 10 + 25/2 = 62.5 mm. Effective depth: d = h − d_c = 500 − 62.5 = 437.5 mm.

Step 2 — Effective tension area per bar. A = (2 × d_c × b) / n = (2 × 62.5 × 300) / 4 = 37,500 / 4 = 9,375 mm² per bar.

Step 3 — Service stress (Gergely-Lutz estimate). f_s ≈ 0.6f_y = 0.6 × 415 = 249 MPa.

Step 4 — β factor. Using the common beam approximation, β ≈ 1.2.

Step 5 — Crack width. d_c × A = 62.5 × 9,375 = 585,937.5 mm³. The cube root of 585,937.5 is approximately 83.68 mm. Then:

Checking against the humid/exterior-exposure limit of 0.30 mm from the table above, 0.275 mm < 0.30 mm — the beam satisfies crack-width control with roughly an 8% margin. It would also easily satisfy the more lenient dry/interior limit of 0.41 mm.

Our free ACI 318-19M crack width calculator automates both checks above, so you can run these numbers instantly for your own beam or slab geometry.

Assumptions & Limitations

• f_s = 0.6f_y is a quick approximation, not a substitute for computing actual stress from the service moment and a cracked transformed-section analysis when a result is close to a limit.
• β = 1.2 is typical for ordinary rectangular beams; compute it from the actual neutral-axis depth for slabs, deep beams, T-sections, or unusually shallow members.
• Gergely-Lutz is a statistical best-fit with substantial scatter — treat its output as a representative estimate, not a guarantee no individual crack exceeds it.
• Both methods apply to normal-weight, non-prestressed concrete with deformed bars. Prestressed members follow separate ACI 318 provisions, outside this article's scope.
• Water-retaining, marine, and chemically aggressive exposures typically warrant project-specific limits (e.g., ACI 350) rather than the generic ACI 224R table above.
• Neither check substitutes for adequate cover, concrete quality, and control of shrinkage/thermal cracking, which are governed by separate detailing and construction provisions.

Related reading: Crack Width Calculation per ACI 318-19M (Gergely-Lutz) — the calculator walkthrough.

Frequently Asked Questions

Do I need to run both the Gergely-Lutz check and the ACI 318-19 spacing check?

Not for routine design. For members designed under ACI 318-19 or NSCP 2015, satisfying the maximum bar-spacing rule is sufficient for flexural crack control on its own. Gergely-Lutz remains useful when you need an estimated crack width in millimeters — for example, against a client's explicit limit, or to evaluate a structure designed under an older code edition.

What value of f_s should I use if I have not calculated the actual service stress?

For Gergely-Lutz, 0.6f_y is a widely used approximation. For the ACI 318-19 spacing rule, the code permits taking f_s as 2/3f_y when not computed directly. The two are close but not identical — for a more accurate check, derive f_s from the actual service moment using a cracked-section elastic analysis.

If my beam satisfies the spacing rule, does that mean it will never show visible cracks?

No. Both checks address only load-induced flexural cracking under service loads. Shrinkage, thermal, settlement, and restraint-related cracking are controlled by separate measures — curing, control joints, minimum shrinkage-temperature reinforcement, and sound mix design — not by the Gergely-Lutz equation or the ACI 318-19 spacing rule.

Browse all of our free web tools for reinforced concrete design and serviceability checks, or visit the Download page for offline NSCP-based spreadsheets. Readers wanting a wider set of calculators can also try the dedicated crack width calculator on our sister site, RHCES, which offers more than 150 free structural and civil engineering calculators.