MecMovies 4.0 : M13.1: Strain Transformation Example

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 equation can also be expressed in terms of double angle functions as:

ε_{n} = \frac{ε_{x} + ε_{y}}{2} + \frac{ε_{x} - ε_{y}}{2} \cos 2 θ + \frac{γ_{xy}}{2} \sin 2 θ

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.