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# Mohrs Circle Calculator

A 2D graphical representation for Cauchy stress tensor is said to be as Mohrs circle. It is used to analyse and find the stress components acting on a coordinate point. Abscissa, σn and ordinateτn are the magnitudes of normal and shear stress. Find the mean, maximum, principal and Von Mises stress with this this mohrs circle calculator.

## Mohrs Circle for 2d Stress Analysis

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A 2D graphical representation for Cauchy stress tensor is said to be as Mohrs circle. It is used to analyse and find the stress components acting on a coordinate point. Abscissa, σn and ordinateτn are the magnitudes of normal and shear stress. Find the mean, maximum, principal and Von Mises stress with this this mohrs circle calculator.

#### Formula:

C = σx + σy / 2 σ1 = ((σx + σy) / 2) + √(((σx - σy) / 2)2 + τxy2) σ2 = ((σx + σy) / 2) - √(((σx - σy) / 2)2 + τxy2) τmax = √(((σx - σy) / 2)2 + τxy2) σVM = √((σx2 + σy2) - (σx * σy) + (3 * τxy2)) τyx = - τxy Where, C = Mean Stress σ1 = Principal Stress I σ2 = Principal Stress II τmax = Maximum Shear Stress σVM = Von Mises Stress τyx = Shear Stress

### Example

#### Mohr's 2D Circle Calculation

If the Normal Stress σXX is 100 and σYY is -65, shear stress, τxy is 60 and Rotation about Principal Axes is 2, then
C = 100 - 65 / 2
C = 35 / 2 = 17.5

σ1 = ((100 - 65) / 2) + √(((100 + 65) / 2)^2 + 602)
σ1 = 119.511

σ2 = ((100 - 65) / 2) - √(((100 + 65) / 2)^2 + 602)
σ2 = -84.511

τmax = √(((100 + 65) / 2)^2 + 652)
τmax = 102.011

σVM = √((1002 + (-65)2) - (100* 65) + (3 * 602))
σVM = 177.5528

τyx = - 60