Around the failure theories, maximum normal stress failure theory one of the oldest, simplest, and most used failure theories. This failure theory is generally used for brittle materials. Here we explain the maximum normal stress theory on a mathematical basis.

This failure theory is also called Rankine‘s failure theory or maximum principal stress theory.

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## What Is The Maximum Normal Stress Failure Theory?

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If there is a uniaxial tension condition on a stress element or body, this stress theory can be used in the safety calculations. For a uniaxial loading condition, principal stresses** **must be calculated with these loadings. According to the maximum normal stress failure theory, the biggest principal stress is responsible for the failure of the material. Once the biggest principal stress reaches the ultimate failure stress of the material, brittle fracture takes place.

With the formula above, you can calculate the biggest principal stress on a point. But first of all, you need to calculate the loading conditions on that point which can be tensile stresses, compression stresses, torsional stresses, etc.

## Mathematical Expression Of The Maximum Normal Stress Theory

After the calculation of the principal stresses for a system, a comparison can be made between the ultimate fracture stress of the material and the principal stresses. This comparison is generally made by dividing the principal stresses with the ultimate fracture stress. If all the results are between -1 and 1, the region where the fracture analysis is carried out is safe.

## Conclusion

The most basic explanation of the maximum normal stress failure theory can be made like this.

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