The strain is unitless quantity. This can be justified by understanding the basic formula of the strain.
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Fig.1: Concrete Strain
Image courtesy:http://koos.hu/2009/05/09/hajlithato-es-ongyogyito-beton-self-healing-concrete/
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The strain is defined as the ratio of change in length to the original length. i.e
Strain = Change in Length / Original length
If the change in length of any body under the action of stress is given by
dl and the original length of the body was
l. Then strain is given by:
Strain = dl/l
As both the numerator and denominator have the same unit, hence the strain is unitless.
In general, the strain is defined as the change in dimension to the original dimension. The dimension can be either length, volume or angle.
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