Free Web Tool

Crack Width & Serviceability

Estimate crack width in reinforced concrete beams using the Gergely & Lutz expression (ACI 224R). Compare against exposure-class allowable limits.

Inputs

Bar Size db (mm)

# of Bars

Beam Width b (mm)

Beam Depth h (mm)

Effective Depth d (mm)

Cover dc (mm)

Steel Stress fs (MPa)

Service Moment Ms (kN·m)optional — sets fs

Exposure

Method — Gergely & Lutz (ACI 224)

w = 0.011·β·fs·∛(dc·A) ·10⁻³ (mm), with β = (h-c)/(d-c) ≈ 1.20 typical.
A = 2·dc·b / nbars (effective area of concrete around one bar).
Compare with allowable per exposure (ACI 224R typical limits).

Results

Effective Tension Area A—

β factor—

Crack Width w—

Allowable wmax—

Status—

About this calculator

This tool estimates the maximum flexural crack width at the tension face of a reinforced concrete beam using the Gergely–Lutz expression (as summarized in ACI 224R), and compares it against a selectable exposure-class allowable limit. It's a quick serviceability check for beams and slabs where crack control governs the design.

Method & formulas

The Gergely–Lutz crack-width expression, in the SI form used here:

w = 0.011 · β · f_s · ∛(d_c·A) × 10⁻³ (w in mm, f_s in MPa, d_c & A in mm/mm²)

β accounts for strain amplification from the steel centroid out to the extreme tension fiber, and A is the effective tension area of concrete tributary to one bar:

β = (h − c)/(d − c) ≈ (h − d_c)/(d − d_c) A = 2·d_c·b / n (n = number of bars)

The computed w is compared to an allowable w_max that depends on exposure — this tool offers interior (0.30 mm), exterior/weather (0.40 mm), and aggressive (0.18 mm) presets, consistent with the range of limits historically associated with ACI 224R guidance.

Worked example

Tool defaults: d_b=20 mm, n=4 bars, b=300 mm, h=500 mm, d=450 mm, d_c=50 mm, f_s=240 MPa, interior exposure (w_max=0.30 mm).

A = 2×50×300/4 = 7500 mm² β = (500−50)/(450−50) = 1.125 w = 0.011 × 1.125 × 240 × ∛(50×7500) × 10⁻³ = 0.011 × 1.125 × 240 × ∛375,000 × 10⁻³ , ∛375,000 ≈ 72.1 w ≈ 0.214 mm 0.214 mm < 0.30 mm allowable → OK

Assumptions & limitations

Gergely–Lutz is a statistical fit calibrated on beam test data — treat the result as an estimate, not an exact prediction of any single crack.
Assumes flexural cracking only, with reinforcement distributed roughly uniformly across the tension zone — not valid for direct tension, shear, or torsion cracking.
f_s must be the actual service-load (unfactored) steel stress; the Service Moment field is informational only in this version — the tool does not compute f_s from it automatically, so enter f_s directly.
Exposure limits shown are typical/simplified presets — the governing code or owner specification may set different values, or may instead control cracking indirectly through a maximum bar-spacing rule.
Verify results against the governing code and a licensed engineer's judgment before relying on them for serviceability sign-off.

FAQ

Q: What does the β factor represent?

A: It scales the crack width computed at the level of the steel up to the larger crack width expected at the extreme tension face, based on the geometric ratio of distances from the neutral axis to the two locations.

Q: Why does the effective area A use d_c twice?

A: The Gergely–Lutz "effective tension area" is conventionally a rectangle of concrete centered on the bar, extending a cover thickness d_c to each side of the tension face over a tributary width b/n — so its depth term is 2·d_c.

Q: Is a smaller crack width always better?

A: Only up to a point — tighter limits generally mean more or smaller-diameter bars at closer spacing, which helps control corrosion risk in aggressive exposure, but the intent is durability, not zero cracking, so match the limit to the actual exposure condition rather than over-designing.

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