Learn: Total shrinkage strain
A simplified concrete shrinkage model separates drying shrinkage from autogenous shrinkage. Their compatible strain contributions add to give the total shrinkage strain at the specified age.
What the formula is saying
Add the drying component εcd and autogenous component εca. This lesson treats both as positive contraction magnitudes; a structural strain convention may assign contraction a negative sign later.
Read the symbols in plain language
- εcd
- Drying shrinkage strain
Drying shrinkage strain. Use the drying component for the same material age and exposure as the autogenous component.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- εca
- Autogenous shrinkage strain
Autogenous shrinkage strain. Compatible contraction strain magnitudes add without changing their dimensionless unit.
ratio / no unitA dimensionless ratio has no physical unit; 0.01 as a ratio is 1% when the percent option is selected.
- εcs
- Result to find
Total shrinkage strain. Compatible contraction strain magnitudes add without changing their dimensionless unit.
ratio / no unit
Sort out the units first
Both inputs and the result are dimensionless strain ratios. Convert microstrain to strain by dividing by one million before entering the base unit. Do not add a percentage to a decimal strain without conversion.
Assumptions before calculating
Assume the two components come from a compatible material model and refer to the same concrete, age and environmental history. Use positive contraction magnitudes for both inputs.
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 εcs and explain the result in the stated output unit.
- εcd · Drying shrinkage strain
- 0.0003
- εca · Autogenous shrinkage strain
- 0.00005
Identify the drying shrinkage component
Use the drying component for the same material age and exposure as the autogenous component.
(0.0003) = 0.0003Add the autogenous shrinkage component
Compatible contraction strain magnitudes add without changing their dimensionless unit.
(0.0003) + (0.00005) = 0.00035
Does this worked answer make sense?
The total contraction magnitude must be at least as large as either nonnegative component. Multiplying the strain by an unrestrained reference length gives the modeled shortening magnitude.
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.
- εcd · Drying shrinkage strain
- 0.00025
- εca · Autogenous shrinkage strain
- 0.00008
Identify the drying shrinkage component
Use the drying component for the same material age and exposure as the autogenous component.
(0.00025) = 0.00025Add the autogenous shrinkage component
Compatible contraction strain magnitudes add without changing their dimensionless unit.
(0.00025) + (0.00008) = 0.00033
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.
- εcd · Drying shrinkage strain
- 0.0004
- εca · Autogenous shrinkage strain
- 0.00006
Find: Learn: Total shrinkage strain
A hint, not the answer
Add the drying component εcd and autogenous component εca. This lesson treats both as positive contraction magnitudes; a structural strain convention may assign contraction a negative sign later.
Both inputs and the result are dimensionless strain ratios. Convert microstrain to strain by dividing by one million before entering the base unit. Do not add a percentage to a decimal strain without conversion.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Identify the drying shrinkage component
Use the drying component for the same material age and exposure as the autogenous component.
(0.0004) = 0.0004Add the autogenous shrinkage component
Compatible contraction strain magnitudes add without changing their dimensionless unit.
(0.0004) + (0.00006) = 0.00046
Avoid the common trap
Do not combine components at different ages or opposite sign conventions. Do not add creep merely because it is also time-dependent, and do not call the sum a displacement without multiplying by a reference length.
When this method applies — and when it does not
This addition does not predict either component from humidity, drying start, cement type or member size. It is free shrinkage strain, not restrained stress or crack width. Creep, thermal strain and elastic load strain are not part of this two-term total.
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: Total shrinkage strain. 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.