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Mohr’s Circle is a 2D graphical depiction of the Cauchy stress tensor to analyze and identify stresses at a specific point. Everyday and shear stresses’ magnitudes are portrayed by the abscissa (σn) and ordinate (τn), respectively. Utilizing our Mohr’s Circle calculator, you can swiftly calculate mean, maximum, principal, and Von Mises stress, enhancing your stress analysis process.
Mohrs Circle formula
![\[C = \sigma_x + \sigma_y / 2\]](https://x-calculator.com/wp-content/ql-cache/quicklatex.com-6c559e6dc9f974d4593daafd1cb73504_l3.png "Rendered by QuickLaTeX.com")
![\[\sigma_1 = \left(\left(\sigma_x + \sigma_y\right) / 2\right) + \sqrt{\left(\left(\sigma_x - \sigma_y\right) / 2\right)^2 + \tau_{xy}^2}\]](https://x-calculator.com/wp-content/ql-cache/quicklatex.com-fbd8519a4d6df30007d3c6186717ccac_l3.png "Rendered by QuickLaTeX.com")
![\[\sigma_2 = \left(\left(\sigma_x + \sigma_y\right) / 2\right) - \sqrt{\left(\left(\sigma_x - \sigma_y\right) / 2\right)^2 + \tau_{xy}^2}\]](https://x-calculator.com/wp-content/ql-cache/quicklatex.com-f69bd2a044c2f14d4d614d97e32f2831_l3.png "Rendered by QuickLaTeX.com")
![\[\tau_{max} = \sqrt{\left(\left(\sigma_x - \sigma_y\right) / 2\right)^2 + \tau_{xy}^2}\]](https://x-calculator.com/wp-content/ql-cache/quicklatex.com-20ea226d627a0e99767836ea33e0dc1b_l3.png "Rendered by QuickLaTeX.com")
![\[\sigma_{VM} = \sqrt{\left(\sigma_x^2 + \sigma_y^2\right) - \left(\sigma_x \sigma_y\right) + \left(3 \tau_{xy}^2\right)}\]](https://x-calculator.com/wp-content/ql-cache/quicklatex.com-0d30bb7efe2d5ace3f5d6043e84bc759_l3.png "Rendered by QuickLaTeX.com")
![\[\tau_{yx} = -\tau_{xy}\]](https://x-calculator.com/wp-content/ql-cache/quicklatex.com-e811f1d282033451f0dffecd544de881_l3.png "Rendered by QuickLaTeX.com")
Where:
- C = Mean Stress
- σ1 = Principal Stress I
- σ2 = Principal Stress II
- τmax = Maximum Shear Stress
- σVM = Von Mises Stress
- τyx = Shear Stress
Mohr’s circle calculator is a tool used in mechanics and materials science to calculate stresses and strains on a material under different loading conditions. It takes in the values of normal and shear stresses on a material in two perpendicular directions and produces a graphical representation of the stress state of the material in the form of a circle. The circle’s center represents the average stress, while its radius represents the difference between the maximum and minimum stresses. Mohr’s circle is a useful tool for visualizing stress state and determining the maximum shear stress on a material.
