The maximum shear stress criterion, also known as Tresca yield criterion, is based on the Maximum Shear stress theory.

This theory predicts failure of a material to occur when the absolute maximum shear stress (τ_{max} ) reaches the stress that causes the material to yield in a simple tension test. The Maximum shear stress criterion is used for ductile materials.

τ_{max} >= σ _{limit} / 2

τ_{max} is the greatest of abs (σ_{12}, σ_{23}, σ_{13}) where:

σ_{1}, σ_{2}, σ_{3 } are the principal stresses in descending order.

The Factor of safety (FOS) is given by:

FOS = σ _{limit} / (2 * τ_{max} )

Comparing the von Mises and Tresca Stress Criteria

The maximum shear stress criterion is more conservative than the von Mises stress criterion since the hexagon representing the shear stress criterion is enclosed within the ellipse representing the von Mises stress criterion.

For a condition of pure shear, von Mises stress criterion predicts failure at (0.577*yield strength), whereas the shear stress criterion predicts failure at 0.5 yield strength.

Actual torsion tests used to develop pure shear have shown that the von Mises stress criterion gives more accurate results than the maximum shear stress theory.

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