### Mohr's Circle and Principal Stresses

In case of the general 3-dimensional state stress in structures is represented through 6 stress values.

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

The principal stresses σ_{1}, σ_{2}, σ_{3} are the eigenvalues of the stress tensor:

σ_{x} | τ_{xy} | τ_{xz} |

τ_{yx} | σ_{y} | τ_{yz} |

τ_{zx} | τ_{zy} | σ_{z} |

The principal stresses and the Mohr circles are visualized graphically.

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

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

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

For a given direction the normal stress and shear stress can be calculated.

more JavaScript programs