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Principal Strains

Principal Strains Equation


$$ {\epsilon}_{1,2} = \frac{\epsilon_x + \epsilon_y}{2} \pm \sqrt{\left(\frac{\epsilon_x - \epsilon_y}{2}\right)^2 + {\gamma_{xy}}^2 } $$ where:

ε1,2   =   Principal Strains   (Dimensionless)

εx   =   Strain in x direction   (Dimensionless)

εy   =   Strain in y direction   (Dimensionless)

τxy   =   Shear Strain in the xy plane   (Dimensionless)


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Principal Strain 1 (ε1):


Principal Strain 2 (ε2):



Equation Assumptions


  • The material is in a plane stress condition.
  • The material is isotropic.
  • The material is homogeneous.
  • The material exhibits linear elastic behaviour.