Shear strain

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Shear strain
Shear strain

Shear strain is a strain that acts parallel to the face of a material that it is acting on. Normal strain acts perpendicular to the face of that it is acting on. There are two ways to interpret shear strain: the average shear strain and the engineering shear strain. The variable used to denote average shear strain is \epsilon \, while \gamma \, denotes engineering shear strain.

Consider an infinitesimal rectangle in the xy plane subject to shear strain. The rectangle becomes a parallelogram where \alpha \, is the displacement from the y axis in the x direction and \delta \, is the displacement from the x axis in the y direction. The average shear strain is

\epsilon_{xy} = 0.5 (\alpha + \delta ) = \epsilon_{yx} \,

[edit] Definition of engineering shear strain

\gamma = \epsilon_{xy} + \epsilon_{yx} = 2 \epsilon_{xy} \,
\gamma = \alpha + \delta = \theta - \beta \,

where

\theta \, is the angle before deformation and
\beta \, is the angle at that same point after deformation.

Therefore \gamma \, describes the total deformation.

[edit] See also

Areal velocity. This classical mechanics-related article is a stub. You can help Wikipedia by expanding it.