Mohr’s Circle Calculator

PHYIC CALCULATOR Mohrs Circle Calculator A precise tool.
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What is the Mohrs Circle Calculator & How does it work?

In two‑dimensional stress analysis the state at a point is described by the normal stresses (sigma_x) and (sigma_y) acting on orthogonal faces, and the shear stress (tau_{xy}) acting on those faces. Mohr’s circle provides a geometric method to transform these stresses to any rotated coordinate system, revealing the principal stresses where shear vanishes and the maximum shear stress.

The principal stresses (sigma_{1}) and (sigma_{2}) are obtained from the quadratic equation derived from equilibrium conditions. They are given by the well‑known formula:

sigma_{1,2}=frac{sigma_x+sigma_y}{2}pmsqrt{left(frac{sigma_x-sigma_y}{2}right)^2+tau_{xy}^2}
sigma_{1,2} = principal stresses (maximum and minimum normal stress); tau_{max} = radius of Mohr’s circle = maximum shear stress.

By locating the centre of the circle at ((sigma_x+sigma_y)/2) and its radius as (sqrt{((sigma_x-sigma_y)/2)^2+tau_{xy}^2}), engineers can quickly assess failure criteria, design safe structures, and understand material behavior under complex loading.

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Frequently Asked Questions
What is Mohr’s Circle?
Mohr’s Circle is a graphical representation used in mechanics to visualize the transformation of stress components at a point in a material.
How do I use this calculator?
Enter the normal stresses σx and σy, and the shear stress τxy. The calculator will display the principal stresses and maximum shear stress.
What are principal stresses?
Principal stresses are the maximum and minimum normal stresses acting on a plane at a point in a material where there is no shear stress.
How do I interpret the results from Mohr’s Circle?
The center of the circle represents the average normal stress, and the radius represents the maximum shear stress. The principal stresses are found at the points where the circle intersects the σ-axis.
Can this calculator handle three-dimensional stress analysis?
No, this calculator is specifically for two-dimensional stress analysis. For three-dimensional analysis, a different method or tool would be required.

Results are for informational purposes only and do not constitute professional advice.