Theories of failure

Theories of failure under static load :-

1. Maximum principle or normal stress theory ( Rankine theory ) - 

According to this theory the failure or yielding occurs at a point in a member when the maximum principle or normal stress in a Bi-axial system reaches the limiting stress. of  the material in a simple tension test.

2. Maximum shear stress theory -

According to this theory the failure or yielding occurs at a point in a member when the maximum shear stress reaches a value equal to the shear stress at yield point in a simple torsion test.

3. Maximum principal strain theory - 

According to this theory the failure or yielding occurs at a point in a member when the maximum principle strain in a Bi-axial stress system reaches the limiting value of strain under simple tensile test.

4. Maximum strain energy theory -

According to this theory the failure of yielding occurs at a point in a member when the strain energy per unit volume. in a Bi-axial stress system reaches the limiting strain energy per unit volume in a simple tension test.

5. Maximum distortion energy theory -

The failure or yielding occurs at a point in a member when the distortion strain energy ( also called shear strain energy ) per unit volume determine from simple tension test.