Concept of Failure and Equivalent Stresses:

While we are testing materials for strength, commonly, we apply one uniaxial component of stress commonly in tension or compression and acquire a value for the limiting state of yield of failure and consider a solid to have failed if in which state is reached.

What is meant through reaching the limiting state? Let us go into the question, a little deeper. While we conduct a tension test on a mild steel rod and find that it yields when the stress reaches a value of 250 MPa, this should be the limiting state as it is obtained by experimental. But one might put a question whether the material has yielded since the general stress reached a limit of 260 MPa or on the contrary because the normal strain has reached a value of 0.0013. The question require not stop here. If you compute the maximum shear stress, you might also ask whether reaching a shear stress of 130 MPa is the limit for yielding of the material. Additionally question may be "whether there are any other criteria for yield?"

Each independent answer to this question had led to a failure theory and we will now learn a few of these theories.