# PLANE STRAIN AND TRANSFORMATIONS

Plane strain transformation calculator is used 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.

Plane strain is 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.

The formulas used for plane strain transformation calculations are given in the "List of Equations" section.

### Plain Strain Transformation Calculator: INPUT PARAMETERS Parameter 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 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 example - Sheet metal between rollers

### List of Equations:

 Parameter 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)

### Reference:

• Beer.F.P. , Johnston.E.R. (1992). Mechanics of Materials , 2nd edition. McGraw-Hill