Stress Tensor (3D) Principal Stress Calculator
Principal Stress Calculator
Principal Direction Calculator
Input Stress Tensor Components
Input Principal Stress (σ_p)
l: -
m: -
n: -
What is Stress Tensor and It’s Principal Values?
A stress tensor is a mathematical representation of the internal forces within a material. It captures the intensity and direction of stress acting on different planes within a solid object. For a 3D object, the stress tensor is typically represented as a 3×3 matrix with normal stresses (σxx, σyy, σzz) along the diagonal and shear stresses (τxy, τxz, τyz) on the off-diagonals.
Due to the equilibrium, the stress tensor matrix is symmetry. If you put non-symmetry matrix in the calculator, the result will be unphysical!
Principal stresses are special values that represent the maximum and minimum normal stresses experienced by the material in certain directions. They are derived from the stress tensor and correspond to orientations where shear stresses vanish, meaning that the stress acts purely in the direction of the principal stresses. These stresses are crucial in engineering because they help identify critical points where materials are most likely to fail.
Stress Tensor
![\[ \bar{\sigma} = \begin{bmatrix} \sigma_{xx} & \sigma_{xy} & \sigma_{xz} \\ \sigma_{xy} & \sigma_{yy} & \sigma_{yz} \\ \sigma_{xz} & \sigma_{yz} & \sigma_{zz} \end{bmatrix} \]](http://pttensor.com/wp-content/ql-cache/quicklatex.com-df2e2bde9d2cdcd1964e13d78dba5659_l3.png "Rendered by QuickLaTeX.com")
Plane Stress (2D)
If you want to calcualte plane stress, just input zero values for Z components (σzz = τxz = τyz = 0)
Related module(s): Stress Invariants, Cauchy’s Equation, Hydrostatic, deviatoric, octahedral, Mohr’s circle 2D, Mohr’s circle 3D.
TensorConnect project 2024 by pttensor.com Author: Caesar Wiratama