# PLANE STRAIN AND TRANSFORMATIONS

Plane strain transformations tool was developed to calculate normal strains and shear strain  at a specific point for plane strain state (εzzxzy=0) after the element is rotated by θ around the Z-axis.  If the plane strains are known for a specific point on a member, then plane strains for different orientation (in the same plane) can be calculated with this calculator.

The formulas used for the calculations are given in the List of Equations section.

 INPUT PARAMETERS Parameter Symbol Value Unit Normal strain εx μm/m (μin/in) Normal strain εy Shear strain γxy Transformation angle θ deg

###### Note: Use dot "." as decimal separator.

 RESULTS Parameter Symbol Value Unit Normal strain after transformation εx' --- μm/m (μin/in) Normal strain after transformation εy' --- Shear strain after transformation γxy' ---

##### Definitions:

Normal Strain: The ratio of length change to original length of the material. ε=σ/E

Shear Strain: The angular distortion on element caused by shear stress. γ=τ/G.

Plane Strain: A state where normal and shear strains occur within a plane and no strains occur perpendicular to this plane. (εz= γxz = γyz =0). This situation occurs in a plate subjected along its edges to uniformly distributed loads and restrained from expanding or contracting laterally by smooth, rigid and fixed supports. An example to this can be rolling of the sheet metal between rollers. In this situation, expansion of the metal is constrained by rollers in perpendicular direction.

 Plane strain example - Sheet metal between rollers
##### List of Equations:

 Parameter Symbol Formula Normal strain after transformation εx' (εx+εy)/2+Cos(2θ)(εx-εy)/2+γxySin(2θ)/2 Normal strain after transformation εy' (εx+εy)/2-Cos(2θ)(εx-εy)/2-γxySin(2θ)/2 Shear strain after transformation γxy' -Sin(2θ)(εx-εy)+γxyCos(2θ)