Maximum Principal strain theory or Saint Venant theory with equation

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

For a 2 – dimensional state of stress system

Where

• 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.

• σ_yt= Maximum Tensile strength in yielding.

• σ_yc =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.