The main theories of failure of a member subjected to bi-axial stress are as follows:

☛ > Maximum principal stress theory ( Rankine’s theory): This theory states that failure occurs at a point in member where the maximum principal or normal stress in a bi-axial system reaches the maximum strength in a simple tension test.

☛ > Maximum shear stress theory ( Guest’s or Tresca’s theory): This theory states that failure occurs when the biaxial stress reaches a value equal to the shear stress at yield point in a simple tension test.

☛ > Maximum principal strain theory ( Saint Venant theory): This theory states that failure occurs when bi-axial stress reaches the limiting value of strain.

☛ > Maximum strain energy theory ( Haigh’s theory): This theory states that failure occurs when strain energy per unit volume of the stress system reaches the limiting strain energy point.

☛ > Maximum distortion energy theory ( Hencky and Von Mises theory): This theory states that failure occurs when strain energy per unit volume reaches the limiting distortion energy.