About Concrete Crack Width Calculator (Eurocode 2)
The concrete crack width calculator estimates the characteristic flexural crack width wk of a reinforced-concrete section following Eurocode 2 (EN 1992-1-1 §7.3.4). It combines the maximum crack spacing sr,max with the mean difference between steel and concrete strains to predict the width of cracks at the serviceability limit state.
The tool uses high-bond (ribbed) bar coefficients for bending (k1 = 0.8, k2 = 0.5, k3 = 3.4, k4 = 0.425), the effective reinforcement ratio rho_p,eff = As/Ac,eff, and the modular ratio alpha_e = Es/Ecm. It applies the load-duration factor kt (0.6 short-term, 0.4 long-term) and the lower bound (eps_sm - eps_cm) >= 0.6*sigmaS/Es, then compares wk against the allowable limit, typically 0.3 mm for reinforced concrete.
How It Works
- Choose the load duration: short-term (kt = 0.6) or long-term/sustained (kt = 0.4), which controls the amount of tension stiffening subtracted.
- Enter the bar diameter phi, clear cover c, steel stress sigmaS at the crack, concrete tensile strength fct,eff, the moduli Es and Ecm, the reinforcement area As, and the effective tension area Ac,eff.
- The calculator forms rho_p,eff = As/Ac,eff and alpha_e = Es/Ecm, then computes sr,max = k3*c + k1*k2*k4*phi/rho_p,eff and the strain difference (eps_sm - eps_cm), enforcing the 0.6*sigmaS/Es floor.
- It multiplies sr,max by the strain difference to get wk, then reports the utilisation wk/limit and whether the section satisfies the allowable crack width.
Worked Example
A beam tension zone has phi = 20 mm bars at clear cover c = 35 mm, steel stress sigmaS = 240 MPa under quasi-permanent (long-term, kt = 0.4) loading, concrete fct,eff = 2.9 MPa, Es = 200000 MPa, Ecm = 33000 MPa, As = 1571 mm^2, and effective tension area Ac,eff = 100000 mm^2. Then alpha_e = 200000/33000 = 6.06 and rho_p,eff = 1571/100000 = 0.01571. The maximum crack spacing is sr,max = 3.4*35 + 0.8*0.5*0.425*20/0.01571 = 119 + 216.42 = 335.42 mm. The strain difference is (eps_sm - eps_cm) = [240 - 0.4*(2.9/0.01571)*(1 + 6.06*0.01571)]/200000 = 0.0007957, above the floor 0.6*240/200000 = 0.00072. The crack width is wk = 335.42 * 0.0007957 = 0.267 mm, below the 0.3 mm limit, so the section is adequate.
Formulas
- Crack width (EN 1992-1-1 Eq. 7.8)
wk = sr,max * (eps_sm - eps_cm)- Maximum crack spacing (Eq. 7.11, high-bond bending)
sr,max = k3*c + k1*k2*k4*phi / rho_p,eff [k1=0.8, k2=0.5, k3=3.4, k4=0.425]- Mean strain difference (Eq. 7.9) with lower bound
(eps_sm - eps_cm) = [ sigmaS - kt*(fct,eff/rho_p,eff)*(1 + alpha_e*rho_p,eff) ] / Es >= 0.6*sigmaS/Es- Auxiliary ratios
alpha_e = Es/Ecm ; rho_p,eff = As/Ac,eff ; utilisation = wk / wmax
Standards & References
- EN 1992-1-1 Eurocode 2: Design of concrete structures
- EN 1992-1-1 §7.3.4 (calculation of crack widths)
Frequently Asked Questions
What is the effective tension area Ac,eff?
Ac,eff is the concrete area surrounding the tension reinforcement that participates in tension stiffening. Eurocode 2 takes its depth hc,ef as the least of 2.5*(h-d), (h-x)/3, and h/2, multiplied by the section width. The reinforcement ratio rho_p,eff = As/Ac,eff drives both the crack spacing and the strain difference.
Why is there a lower bound on the strain difference?
Eurocode 2 limits the mean strain difference (eps_sm - eps_cm) to at least 0.6*sigmaS/Es so that tension stiffening cannot reduce the predicted crack width without bound at low stress. When that floor governs, the calculator flags it in the results.
What value of kt should I use?
Use kt = 0.6 for short-term (instantaneous) loading and kt = 0.4 for long-term or repeated (sustained, quasi-permanent) loading. The smaller long-term value reflects reduced tension stiffening over time, which increases the predicted crack width.
What crack-width limit applies?
For most reinforced-concrete members under the quasi-permanent combination, EN 1992-1-1 recommends wmax = 0.3 mm. Tighter limits (for example 0.2 mm) apply to more severe exposure classes or where appearance and durability are critical. The default here is 0.3 mm and can be changed.