Mohr’s Circle is a simple way to analyze 2D stress at a point. It helps you:

• Find principal stresses (σ1σ1​ and σ2σ2​).
• Determine the maximum shear stress (τmaxτmax​).
• Calculate the angle of the principal planes.

This tool automates these steps and shows an interactive graph.

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Input Fields

1. Normal Stress (σxσx​):
   Enter the normal stress along the xx-axis. Use positive for tensile stress and negative for compressive stress.
2. Normal Stress (σyσy​):
   Enter the normal stress along the yy-axis. Like before, positive is for tensile, and negative is for compressive.
3. Shear Stress (τxyτxy​):
   Enter the shear stress on the x−yx−y plane. Positive typically means counterclockwise.

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Outputs

1. Principal Stresses (σ1,σ2σ1​,σ2​):
   These are the highest and lowest normal stresses the material experiences.
   On the principal planes, the shear stress is always zero. The calculator displays these automatically.
2. Maximum Shear Stress (τmaxτmax​):
   This is the largest shear stress on the material. It occurs at ±45∘±45∘ from the principal planes.
3. Principal Plane Angle (θpθp​):
   This angle tells you how the principal planes are oriented relative to the xx-axis.

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Graphical Features

Mohr’s Circle Plot

• The horizontal axis represents normal stress (σσ).
• The vertical axis represents shear stress (ττ).

Interactive Mouse Tracker

• Hover over the graph to see exact coordinates (σ,τσ,τ).
• Crosshairs move with your mouse to make the graph easier to read.

Principal Points

• The edges of the circle on the horizontal axis give the principal stresses (σ1,σ2σ1​,σ2​).
• The circle’s diameter equals 2 τmaxτmax​.

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Steps to Calculate

1. Input Your Stress Values
   Enter σxσx​, σyσy​, and τxyτxy​ in the fields.
2. Find the Center and Radius of the Circle
   • The centre is the average of the normal stresses:
     C=σx+σy2C=2σx​+σy​​
   • The radius is based on the stresses:
     R=(σx−σy2)2+τxy2R=(2σx​−σy​​)2+τxy2​​
3. Calculate Principal Stresses
   • The maximum stress is:
     σ1=C+Rσ1​=C+R
   • The minimum stress is:
     σ2=C−Rσ2​=C−R
4. Find Maximum Shear Stress
   • The maximum shear stress is simply the circle’s radius:
     τmax=Rτmax​=R
5. Determine the Principal Plane Angle
   • The angle of the principal planes is:
     θp=12arctan⁡(2τxyσx−σy)θp​=21​arctan(σx​−σy​2τxy​​)
6. See the Visualization
   The graph shows the stress as a circle, displaying output values for quick reference.

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Why Use This Calculator?

• Saves Time: No manual calculations.
• Accurate Results: Reduces errors in stress analysis.
• Interactive Graph: Move your mouse to explore stress points.
• Engineer’s Tool: Great for analyzing failure risks and material performance.