Learn: Maximum crack spacing — coefficient form
Crack spacing is influenced by cover, bar size, bond and effective reinforcement ratio. This teaching expression adds a cover-related term to a reinforcement-related term to estimate the maximum crack spacing for its stated model.
What the formula is saying
The cover term is k3 c. The other term grows with bar diameter and decreases as effective reinforcement ratio grows. Adding the two shows why cover and reinforcement density affect spacing in different ways.
Read the symbols in plain language
- k3
- Coefficient k3
Coefficient multiplying concrete cover in the crack-spacing relationship; it is not a bar spacing.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- c
- Cover
Cover. The cover coefficient multiplies the distance from the concrete surface to the reinforcement.
mmMillimetres measure length; 1000 mm = 1 m.
- k1
- Bond coefficient
Bond-quality coefficient for the reinforcement type in the selected crack-spacing model.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- k2
- Strain distribution coefficient
Coefficient representing the strain distribution across the tension zone.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- k4
- Coefficient k4
Coefficient multiplying the bond/strain/bar-diameter contribution before division by effective reinforcement ratio.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- φ
- Bar diameter
Bar diameter. Bar diameter and the supplied bond and strain factors are divided by effective reinforcement ratio.
mmMillimetres measure length; 1000 mm = 1 m.
- ρp,eff
- Effective reinforcement ratio
Effective reinforcement ratio As/Ac,eff for the tension area involved in cracking, not automatically the gross-section ratio.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- sr,max
- Result to find
Maximum crack spacing — coefficient form. Both terms are lengths in millimetres and together give this model’s crack-spacing estimate.
mm
Sort out the units first
Cover c, diameter φ and spacing are in mm. k1–k4 and ρ are dimensionless; ρ is a decimal effective reinforcement ratio, not a whole-number percentage and not automatically As divided by the entire gross section.
Assumptions before calculating
Use the first-generation EC2 teaching model and the supplied design coefficients. Material strengths, geometry, load situation and coefficients must be mutually compatible; selecting them from the adopted code and National Annex is outside this calculation.
This is a first-generation Eurocode teaching relationship or an explicitly simplified coefficient calculation. The numbers supplied here are exercise data, not a recommendation for any country. Check the adopted edition, relevant clause, National Annex, applicability conditions and all other limit states before any real design.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
Read the supplied values as one complete study case. Find sr,max and explain the result in the stated output unit.
- k3 · Coefficient k3
- 3.4
- c · Cover
- 30 mm
- k1 · Bond coefficient
- 0.8
- k2 · Strain distribution coefficient
- 0.5
- k4 · Coefficient k4
- 0.425
- φ · Bar diameter
- 16 mm
- ρp,eff · Effective reinforcement ratio
- 0.01
Calculate the cover contribution
The cover coefficient multiplies the distance from the concrete surface to the reinforcement.
(3.4) × (30) = 102 mmCalculate the reinforcement contribution
Bar diameter and the supplied bond and strain factors are divided by effective reinforcement ratio.
(0.8) × (0.5) × (0.425) × (16) ÷ (0.01) = 272 mmAdd the two spacing contributions
Both terms are lengths in millimetres and together give this model’s crack-spacing estimate.
(102) + (272) = 374 mm
Does this worked answer make sense?
Increasing ρ reduces only the reinforcement term, not the cover term. As ρ becomes small, spacing becomes large; zero reinforcement ratio is invalid for this expression.
A second worked example — different values
A second case uses different data. Predict which way the answer will change, then calculate it without reusing the first answer.
- k3 · Coefficient k3
- 3.4
- c · Cover
- 25 mm
- k1 · Bond coefficient
- 0.8
- k2 · Strain distribution coefficient
- 0.5
- k4 · Coefficient k4
- 0.425
- φ · Bar diameter
- 12 mm
- ρp,eff · Effective reinforcement ratio
- 0.015
Calculate the cover contribution
The cover coefficient multiplies the distance from the concrete surface to the reinforcement.
(3.4) × (25) = 85 mmCalculate the reinforcement contribution
Bar diameter and the supplied bond and strain factors are divided by effective reinforcement ratio.
(0.8) × (0.5) × (0.425) × (12) ÷ (0.015) = 136 mmAdd the two spacing contributions
Both terms are lengths in millimetres and together give this model’s crack-spacing estimate.
(85) + (136) = 221 mm
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Solve this separate case yourself. Use only the values below; the two worked examples use different data. Give the requested result in the selected unit.
- k3 · Coefficient k3
- 3.4
- c · Cover
- 35 mm
- k1 · Bond coefficient
- 0.8
- k2 · Strain distribution coefficient
- 0.5
- k4 · Coefficient k4
- 0.425
- φ · Bar diameter
- 20 mm
- ρp,eff · Effective reinforcement ratio
- 0.012
Find: Learn: Maximum crack spacing — coefficient form
A hint, not the answer
The cover term is k3 c. The other term grows with bar diameter and decreases as effective reinforcement ratio grows. Adding the two shows why cover and reinforcement density affect spacing in different ways.
Cover c, diameter φ and spacing are in mm. k1–k4 and ρ are dimensionless; ρ is a decimal effective reinforcement ratio, not a whole-number percentage and not automatically As divided by the entire gross section.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Calculate the cover contribution
The cover coefficient multiplies the distance from the concrete surface to the reinforcement.
(3.4) × (35) = 119 mmCalculate the reinforcement contribution
Bar diameter and the supplied bond and strain factors are divided by effective reinforcement ratio.
(0.8) × (0.5) × (0.425) × (20) ÷ (0.012) ≈ 283.3333333 mmAdd the two spacing contributions
Both terms are lengths in millimetres and together give this model’s crack-spacing estimate.
(119) + (283.3333333) ≈ 402.3333333 mm
Avoid the common trap
Do not divide the whole sum by ρ; only the reinforcement term uses that divisor. Do not use gross reinforcement ratio without checking the effective tension area or confuse clear cover with effective depth.
When this method applies — and when it does not
The effective tension area, bond conditions, strain distribution and bar-spacing applicability must already have been established. Alternative spacing expressions, large bar spacing, pure tension, different reinforcement layers and crack-width acceptance are not resolved here.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Reading focus: Maximum crack spacing — coefficient form. First-generation EN 1992 teaching: material properties and the relevant bending, shear, serviceability, detailing or prestress relationship. Read the applicability conditions as well as the expression.
Lesson updated: · Both examples and the separate practice case are checked against an independent high-precision numerical implementation. This verifies arithmetic for the stated model, not engineering certification.