Mohr’s Circle for 2D (Planar) Stress Calculator
Mohr’s Circle for 2D Planar Stress
Mohr’s Circle is a graphical representation used in 2D planar stress analysis to determine principal stresses, maximum shear stresses, and stress orientations. For a given state of stress on a 2D plane, Mohr’s Circle provides a visual way to understand how normal and shear stresses transform as the orientation of the plane changes. By plotting the normal stress (σ) on the x-axis and shear stress (τ) on the y-axis, the circle allows engineers to quickly find principal stresses (the maximum and minimum normal stresses with zero shear) and the maximum shear stress, along with their respective orientations.
![\[ \sigma_{1,2} = \frac{\sigma_{xx} + \sigma_{yy}}{2} \pm \sqrt{\frac{1}{4}(\sigma_{xx} - \sigma_{yy})^2 + \sigma_{xy}^2} \quad \text{(Principal Stresses)} \]](http://pttensor.com/wp-content/ql-cache/quicklatex.com-896cd45c18dddc9270fba0e1240d26d2_l3.png "Rendered by QuickLaTeX.com")
![\[ \tan 2\theta_p = \frac{2\sigma_{xy}}{\sigma_{xx} - \sigma_{yy}} \quad \text{(Principal Angle)} \]](http://pttensor.com/wp-content/ql-cache/quicklatex.com-e6442e2596bac7e2164d35cd456e322f_l3.png "Rendered by QuickLaTeX.com")
![\[ \sigma_{xy,\text{max}} = \sqrt{\frac{1}{4}(\sigma_{xx} - \sigma_{yy})^2 + \sigma_{xy}^2} \quad \text{(Radius)} \]](http://pttensor.com/wp-content/ql-cache/quicklatex.com-ce8460efef75648046fb17cb5c849a67_l3.png "Rendered by QuickLaTeX.com")
Related Module(s): Mohr’s circle for 3D Stress, Principal Stresses,
TensorConnect project 2024 by pttensor.com Author: Caesar Wiratama