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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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

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