Mohr’s Circle For 3D Stress Calculator
What is Mohr’s Circle for Stress?
Mohr’s Circle is a graphical representation used in engineering to visualize and analyze stress states at a point in a material. It provides insights into the normal and shear stresses on various planes passing through that point. Mohr’s Circle helps identify principal stresses (maximum and minimum normal stresses) and maximum shear stress, which are critical in assessing material strength and failure.
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")
Some notes on Stress Tensor
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!
Related Module(s): Mohr’s circle for strain,
TensorConnect project 2024 by pttensor.com Author: Caesar Wiratama