For this situation principal stresses and principal stress directions are calculated.

The principal stresses σ

σ_{x} | τ_{xy} | τ_{xz} |

τ_{yx} | σ_{y} | τ_{yz} |

τ_{zx} | τ_{zy} | σ_{z} |

In the shaded areas between the circles possible pairs of stress values (σ, τ) may be found.

The 3 red points represent stress values according to the given values with repespect to a xyz-coordinate system:

(σ

The yellow points mark the principal stresses. Under the associated directions there will be no shear stresses.

A special case is the 2-dimensional stress state given by σ

In this case we can determine 2 points on Mohr's circle:

(σ

The center of the circle is ((σ

For a normalized direction vector

σ

|τ

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