PLANE STRAIN AND PRINCIPAL STRAINS
Principal strains calculation tool was developed to calculate principal strains and
maximum inplane shear strain
at a specific point for plane strain state (ε_{z}=γ_{zx}=γ_{zy}=0)
.
The formulas used for the calculations are given in the "List of Equations"
section.
Note: Use dot "." as decimal separator.
RESULTS 
Parameter 
Symbol 
Value 
Unit 
Maximum normal strain

ε_{max} 


μm/m (μin/in) 
Minimum normal strain 
ε_{min} 


Maximum shear strain (inplane) 
γ_{max (inplane)} 


Angle of principal strain 
θ_{p} 


deg 
Definitions:
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. (ε_{z}= γ_{xz} = γ_{yz} =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

ε_{max} 
(ε_{x}+ε_{y})/2+(((ε_{x}ε_{y})/2)^{2}+(γ_{xy}/2)^{2})^{0.5} 
Minimum normal strain

ε_{min} 
(ε_{x}+ε_{y})/2(((ε_{x}ε_{y})/2)^{2}+(γ_{xy}/2)^{2})^{0.5} 
Maximum shear strain (inplane) 
γ_{max (inplane)} 
((ε_{x}ε_{y})^{2}+(γ_{xy})^{2})^{0.5} 
Principal angle 
θ_{p} 
[atan(γ_{xy}/(ε_{x}ε_{y}))]/2 
Reference: