Rankine's theory is a theory used in material science to predict the failure of a material under a given set of loading conditions. This theory is also known as the maximum principal stress theory. It assumes that a material will fail when the maximum principal stress in a body exceeds the strength of the material under simple tension or compression.

The following are some important points to note about Rankine's theory:

• Failure criterion: The theory assumes that a material will fail when the maximum principal stress in a body exceeds the strength of the material under simple tension or compression.

• Principal stresses: The theory is based on the concept of principal stresses, which are the normal stresses acting on a plane where the shear stress is zero.

• Maximum principal stress: The theory assumes that failure occurs when the maximum principal stress in a body exceeds the strength of the material under simple tension or compression.

• Shear stress: The theory does not take into account the effect of shear stress on the material failure.

• Limitations: The theory is limited to the prediction of the failure of ductile materials under static loading conditions.

In conclusion, Rankine's theory is a useful tool in predicting the failure of materials under a given set of loading conditions. It assumes that a material will fail when the maximum principal stress in a body exceeds the strength of the material under simple tension or compression. However, the theory has its limitations and cannot be used to predict the failure of brittle materials or under dynamic loading conditions.