What are the different theories of failure under static load, explain briefly?

The major theories of failure of a member subjected to bi-axial stress are as below:

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

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

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

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

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