MecMovies 4.0 : M13.2: Strain Transformation Example

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To use these equations, the following sign conventions are required:

1) Tensile strains are positive.

2) Shearing strains that decrease the angle between the two lines at the origin are positive.

3) Angles measured counterclockwise from the reference $x$ -axis are positive.

The normal strain $ε_{n}$ acting at an arbitrary orientation $θ$ is given by the strain transformation equation:

$ε_{n} = ε_{x} \cos^{2} θ + ε_{y} \sin^{2} θ + γ_{x y} \sin θ \cos θ$

The shear strain $γ_{n t}$ is given by:

$γ_{n t} = - 2 (ε_{x} - ε_{y}) \sin θ \cos θ + γ_{x y} (\cos^{2} θ - \sin^{2} θ)$