Maximum Principal strain theory or Saint Venant theory with equation

Wednesday, February 8, 2012 16:09
Posted in category Mechanics of Solids 2
Views: 6,856 views

Maximum principal strain theory :

This theory states that “ Yielding in a member subjected to complex/compound stress system commences when maximum principal strain of the system becomes equal to the strain corresponding to the yield point under simple tension test of the same material.”


For a 3 – dimensional state of stress system

maximum principal strain theory 3-d stress system


For a 2 – dimensional state of stress system



  • є1 = maximum principal strain.
  • υ = Poisson’s ratio.
  • σ1= Major principal stress in x direction.
  • σ2 = Minor principal stress in y direction.
  • σ3 = Minor principal stress in z direction.
  • σyt= Maximum Tensile strength in yielding.
  • σyc =Maximum Compressive strength in yielding.

 Merits :

  • It computes the failure load based on all 3 values of principal stresses.

De merits :

  • This theory gives unsatisfactory results for various materials.
  • This theory is not much used for design purposes.
  • This is not a very popular theory.
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