# Tresca’s Maximum Shear Stress Failure Theory

Failure theories are used in different design assessments to see the safety of an engineering system. Maximum shear stress theory is generally used in strength calculations for ductile materials and it gives very good and precise results. Here you can find detailed information about Tresca’s maximum shear stress failure theory.

## What Is The Maximum Shear Stress Failure Theory?

Maximum shear stress theory compares the shear stress that occurs in a uniaxial tension loading condition with the maximum shear stress at the yield point of the material.

Consider a situation that a stress element undergoes stresses like this;

As you see above, the stress element undergoes tensile stresses both in ‘X’ and ‘Y’ directions and shear stress on the positive side.

As you know from the principal stress calculations, principal stresses can be found with these stresses.

Maximum and minimum principal stresses can be found with this equation. Once you calculate the major and minor principal stresses, you can make your comparisons;

According to these equations of the Tresca’s theory, if the safety plane is drawn, it will have a shape like this;

## Conclusion

The most basic explanation of Tresca’s maximum principal stress theory can be made like this.

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