Shear strain: Definition from Answers.com

Shear strain
Measured in (SI unit):	1, or radian
Commonly used symbols:	γ or ϵ
Expressed in other quantities:	γ = τ / G

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shear strain

Shear strain is a strain that acts parallel to the surface of a material that it is acting on. Normal strain, in contrast, acts perpendicular to the surface. There are two ways to interpret shear strain: the average shear strain ( $\epsilon\,$ ) and the engineering shear strain ( $\gamma\,$ ).

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

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

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.
Shear Strain: Just as an axial stress results in an axial strain, which is the change in the length divided by the original length of the member, so does shear stress produce a shear strain. Both Axial Strain and Shear Strain are shown in Diagram 2. The shear stress produces a displacement of the rod as indicated in the right drawing in Diagram 2. The edge of the rod is displaced a horizontal distance, from its initial position. This displacement (or horizontal deformation) divided by the length of the rod L is equal to the Shear Strain. Examining the small triangle made by , L and the side of the rod, we see that the Shear Strain, /L , is also equal to the tangent of the angle gamma, and since the amount of displacement is quite small the tangent of the angle is approximately equal to the angle itself. Or we may write: Shear Strain = \delta/L

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Shear strain

Definition of engineering shear strain

See also