Principal strains calculation tool was developed to calculate principal strains and maximum in-plane shear strain at a specific point for plane strain state (εzzxzy=0) .

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

Principal Strains in Plane Strain State
Parameter Symbol Value Unit
Normal strain
εx μm/m (μin/in)
Normal strain εy
Shear strain γxy


Note: Use dot "." as decimal separator.

Parameter Symbol Value Unit
Maximum normal strain
εmax --- μm/m (μin/in)
Minimum normal strain εmin ---
Maximum shear strain (in-plane) γmax (in-plane) ---
Angle of principal strain θp --- deg


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

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

Principal Angle: The angle of orientation at which principal stresses occur for a specific point.

Principal Strain: Maximum and minimum normal strain possible for a specific point on a structural element. Shear strain is 0 at the orientation where principal strain occurs.

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

List of Equations:

Parameter Symbol Formula
Maximum normal strain
εmax x+εy)/2+(((εxy)/2)2+(γxy/2)2)0.5
Minimum normal strain
εmin x+εy)/2-(((εxy)/2)2+(γxy/2)2)0.5
Maximum shear strain (in-plane)
γmax (in-plane) ((εxy)2+(γxy)2)0.5
Principal angle θp [atan(γxy/(εxy))]/2