Learn: Crack width
A reinforced-concrete crack opens because reinforcement and concrete do not have the same average tensile strain between cracks. Multiplying that strain difference by the characteristic crack spacing estimates the crack width.
What the formula is saying
Subtract εcm from εsm before multiplying. The difference represents relative extension per unit length; applying it over sr turns a dimensionless strain difference into an opening distance.
Read the symbols in plain language
- sr,max
- Maximum crack spacing
Largest modelled distance between adjacent cracks; using millimetres here makes the resulting crack width millimetres.
mmMillimetres measure length; 1000 mm = 1 m.
- εsm
- Mean steel strain
Average longitudinal strain between cracks, expressed as change in length divided by original length; use the same dimensionless scale for both strains.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- εcm
- Mean concrete strain
Average longitudinal strain between cracks, expressed as change in length divided by original length; use the same dimensionless scale for both strains.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- wk
- Result to find
Crack width. Multiply by the crack spacing to obtain a length rather than another strain.
mm
Sort out the units first
sr is in mm and both strains are decimal dimensionless values. For example, 1500 microstrain is 0.0015. The result is in mm, not percent or microstrain.
Assumptions before calculating
The crack spacing and mean strains are already appropriate to the same load combination and tension-stiffening model. This lesson assumes sr > 0 and εsm ≥ εcm ≥ 0 for a nonnegative opening.
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 wk and explain the result in the stated output unit.
- sr,max · Maximum crack spacing
- 200 mm
- εsm · Mean steel strain
- 0.0015
- εcm · Mean concrete strain
- 0.0002
Find the mean strain difference
Only the relative strain between steel and concrete opens the crack in this model.
(0.0015)-(0.0002) = 0.0013Convert relative strain to opening
Multiply by the crack spacing to obtain a length rather than another strain.
(200) × (0.0013) = 0.26 mm
Does this worked answer make sense?
Equal mean strains give zero opening in this simplified final step. Doubling crack spacing at fixed strain difference doubles the estimated width.
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.
- sr,max · Maximum crack spacing
- 150 mm
- εsm · Mean steel strain
- 0.0012
- εcm · Mean concrete strain
- 0.0003
Find the mean strain difference
Only the relative strain between steel and concrete opens the crack in this model.
(0.0012)-(0.0003) = 0.0009Convert relative strain to opening
Multiply by the crack spacing to obtain a length rather than another strain.
(150) × (0.0009) = 0.135 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.
- sr,max · Maximum crack spacing
- 180 mm
- εsm · Mean steel strain
- 0.0014
- εcm · Mean concrete strain
- 0.00025
Find: Learn: Crack width
A hint, not the answer
Subtract εcm from εsm before multiplying. The difference represents relative extension per unit length; applying it over sr turns a dimensionless strain difference into an opening distance.
sr is in mm and both strains are decimal dimensionless values. For example, 1500 microstrain is 0.0015. The result is in mm, not percent or microstrain.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Find the mean strain difference
Only the relative strain between steel and concrete opens the crack in this model.
(0.0014)-(0.00025) = 0.00115Convert relative strain to opening
Multiply by the crack spacing to obtain a length rather than another strain.
(180) × (0.00115) = 0.207 mm
Avoid the common trap
Do not add the two strains. Do not enter microstrain as an unconverted whole number, or interpret a negative difference as a physical negative crack width.
When this method applies — and when it does not
This is the final multiplication in a crack-width model, not a full derivation of spacing or strains. Minimum strain differences, bar spacing rules, loading duration, exposure class and acceptable crack width must be checked separately.
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.
One idea understood. Keep going.
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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: Crack width. 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.