SLAB CRACK WIDTH CHECK

What this calculator checks

The calculator verifies the crack width in a reinforced-concrete slab, at Serviceability Limit State, according to EN 1992-1-1 §7.3 (with the EN 1992-3 extension for liquid-retaining elements). It compares the computed crack width \(w_k\) with the allowed limit \(w_{max}\):

\(w_k = s_{r,max} \cdot (\varepsilon_{sm} - \varepsilon_{cm}) \le w_{max}\)

Concrete inevitably cracks in tension — the check does not aim to prevent cracks, but to limit their width to a value that does not impair durability (reinforcement corrosion) or, for tanks, watertightness.

The mechanism: crack spacing × relative strain

The width of a crack is the product of two quantities:

• \(s_{r,max}\) — the maximum crack spacing. It depends on the cover, the bar diameter and the effective reinforcement ratio \(\rho_{p,eff}\): thinner, more closely spaced bars with small cover give more closely spaced, hence finer, cracks.
• \(\varepsilon_{sm} - \varepsilon_{cm}\) — the mean strain of the reinforcement over that of the concrete between cracks. It accounts for the tension stiffening of the concrete between cracks, which partially unloads the reinforcement.

The practical consequence: for the same reinforcement area, many thin bars control cracking better than few thick bars. That is why the codes limit the bar diameter or spacing.

Minimum reinforcement

The calculator also checks the minimum crack reinforcement \(A_{s,min}\) (§7.3.2): the amount needed so that, when the first crack forms, the reinforcement does not yield instantly. Without it, the crack would open suddenly and uncontrolled instead of distributing into fine cracks.

Input data

• Slab geometry — the thickness, the cover; the check is on a 1 m strip.
• Reinforcement — the bar diameter and spacing, in the checked direction.
• The action — the moment at the service combination (quasi-permanent or frequent).
• Concrete class — through \(f_{ct,eff}\) (tensile strength) and the modulus \(E_{cm}\).
• The limit width \(w_{max}\) — by exposure class, or by the watertightness requirement (EN 1992-3).

Assumptions and limitations

• The check is on a 1 m section of slab, with bending in one direction.
• It is an SLS check; resistance (ULS) is checked separately — see the reinforced section.
• The model assumes stabilised cracking (multiple-crack regime), not the isolated first crack.
• Cracking from imposed effects (shrinkage, temperature) is treated only through the minimum-reinforcement term.

Related calculations

• Reinforced section — the ULS check of the same section
• Concrete cover — the cover enters \(s_{r,max}\) directly
• Section analysis — the moment-curvature behaviour in the cracked state
• Punching shear — the other typical slab check