Mohr's Circle Calculator – Stress Analysis
Calculate principal stresses and maximum shear stress using Mohr's circle
How to Use
- Enter the normal stress in X direction (σx)
- Enter the normal stress in Y direction (σy)
- Enter the shear stress (τxy)
- Select the stress unit
- Click calculate to see principal stresses and maximum shear stress
What is Mohr's Circle?
Mohr's circle is a graphical representation of the transformation equations for plane stress. It's a powerful tool used to determine principal stresses, maximum shear stress, and the orientation of principal planes.
Developed by German civil engineer Christian Otto Mohr in the 19th century, Mohr's circle simplifies complex stress transformation calculations and provides visual insight into stress states.
How Mohr's Circle Works
Mohr's circle represents stress states on a coordinate system where:
- The horizontal axis represents normal stress (σ)
- The vertical axis represents shear stress (τ)
- The center of the circle is at the average normal stress
- The radius equals the maximum shear stress
Principal stresses occur at the points where the circle intersects the horizontal axis, representing planes with zero shear stress.
Calculations
The calculator uses the following formulas:
- Average normal stress: σ_avg = (σx + σy) / 2
- Circle radius: R = √[((σx - σy) / 2)² + τxy²]
- Principal stress 1: σ₁ = σ_avg + R
- Principal stress 2: σ₂ = σ_avg - R
- Maximum shear stress: τ_max = R
- Principal angle: θ = (1/2) × arctan(2τxy / (σx - σy))
Applications
Mohr's circle analysis is essential in:
- Structural engineering and building design
- Mechanical engineering and machine design
- Aerospace engineering
- Materials science and failure analysis
- Geotechnical engineering
- Civil engineering infrastructure
Frequently Asked Questions
- What are principal stresses?
- Principal stresses are the maximum and minimum normal stresses that occur on planes where shear stress is zero. These are the most important stress values for determining material failure.
- What is the difference between normal stress and shear stress?
- Normal stress acts perpendicular to a plane, while shear stress acts parallel to the plane. Normal stress causes stretching or compression, while shear stress causes sliding deformation.
- Why is Mohr's circle useful?
- Mohr's circle provides a visual and computational method to determine principal stresses, maximum shear stress, and stress orientations without complex matrix calculations. It's particularly useful for understanding stress transformations.
- What units should I use for stress?
- Common stress units include Pascals (Pa), kilopascals (kPa), megapascals (MPa), pounds per square inch (psi), and kilopounds per square inch (ksi). Use consistent units throughout your calculation.