Mohr's Circle Calculator
Analyze plane stress and visualize Mohr's Circle
Calculator
Enter normal and shear stresses to compute principal stresses, maximum shear stress, and draw Mohr's Circle.
Mohr's Circle
About the Mohr's Circle Calculator
The Mohr's Circle Calculator helps you quickly analyze and visualize the stress state of a material. It calculates principal stresses, maximum shear stresses, and the orientation of stress planes based on the input normal stresses (σx, σy) and shear stress (τxy). This tool is ideal for engineers, students, and researchers working in mechanics of materials and structural analysis.
What You Can Calculate
- Principal Stresses (σ1, σ2): The maximum and minimum normal stresses acting on specific planes.
- Maximum Shear Stress (τmax): The largest shear stress that occurs on a plane within the material.
- Stress Orientation: The angles of the planes where principal and maximum shear stresses occur.
Formulas Used in the Calculator
The calculator uses standard equations from mechanics of materials to determine stress values:
- Average Normal Stress: σavg = (σx + σy) / 2
- Radius of Mohr's Circle: R = √[((σx − σy)/2)² + τxy²]
- Principal Stresses: σ1,2 = σavg ± R
- Maximum Shear Stress: τmax = R
- Stress Plane Angles: θp = 0.5 × atan(2τxy / (σx − σy))
How to Use the Calculator
- Enter the normal stresses σx and σy, and the shear stress τxy.
- The calculator computes principal stresses, maximum shear stress, and displays Mohr's Circle.
- Interpret the results to understand the stress distribution and critical planes in the material.
Applications of Mohr's Circle
Mohr's Circle is essential for stress analysis, structural design, and failure prediction. Engineers use it to determine safe load limits, optimize material usage, and ensure mechanical components operate reliably under complex stress states.