# Saint Venant’s Maximum Normal Strain Theory

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This is the corresponding failure theory to maximum normal stress theory in which the principal strain values of a point are used. This theory is also applicable to brittle materials such as cast iron. Among the other failure theories, the maximum normal strain theory is not generally used because of the accuracies of the results. Here you can find a mathematical explanation of the maximum normal strain theory.

## What Is The Maximum Normal Strain Theory?

Maximum normal strain theory deals with the maximum principal strain value of the complex loading conditions on a stress element or point. Consider a situation triaxial stresses are acting on a stress element. With these stresses, the maximum principal strain value can be calculated.

Consider that the maximum principal strain has occurred in the direction of ‘x’.

This principal strain is calculated with the formula below;

In this formula, ‘E’ is the elasticity modulus of the material. ‘v’ is the Poisson’s ratio of the material. ‘σ1’, ‘σ2’, and ‘σ3’ are the elements of the triaxial loading on a stress element. If this principal stress value exceeds the maximum corresponding strain value to failure, the design is not safe.

## Conclusion

This is the general explanation of Saint Venant’s maximum normal strain theory.

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