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.

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