Mohr's Circle Calculator | 2D Stress Transformation Tool for Engineers
Free online Mohr's Circle calculator for 2D stress analysis. Calculate principal stresses, maximum shear stress, and visualize stress transformations instantly. Essential tool for mechanical and civil engineers
Stress Components (MPa)
Material Properties
Stress Transformation
Mohr's Circle Analysis Results
Input Stresses: σx = 15 MPa, σy = 5 MPa, τxy = 4 MPa
Safety Factor: Safe
| Parameter | Value | Unit | Notes |
|---|---|---|---|
| Maximum Principal Stress (σ1) | MPa | Maximum normal stress | |
| Minimum Principal Stress (σ2) | MPa | Minimum normal stress | |
| Angle for σ1 Direction (θσ1) | degrees | Orientation of maximum principal stress | |
| Angle for σ2 Direction (θσ2) | degrees | Orientation of minimum principal stress | |
| Maximum Shear Stress (τmax) | MPa | Maximum shear stress | |
| Center of Mohr's Circle (σavg) | MPa | Average normal stress | |
| Radius of Mohr's Circle (R) | MPa | Radius of Mohr's circle | |
| Von Mises Equivalent Stress | MPa | Based on distortion energy theory | |
| Factor of Safety | - | Based on selected failure criterion |
Mohr's Circle Visualization
Stress State Summary
Design Guidelines
- Principal stresses represent the maximum and minimum normal stresses
- Maximum shear stress occurs at 45° to principal planes
- For ductile materials, use Von Mises criterion for yield prediction
- For brittle materials, use Maximum Principal Stress criterion
Stress Element Visualization
Stress Distribution
Failure Criteria Comparison
Understanding Mohr's Circle: A Powerful Tool for Stress Analysis
Visual representation of Mohr's Circle for stress transformation
Mohr's Circle is an essential graphical technique that every mechanical and civil engineer should master. Developed by Christian Otto Mohr in 1882, this powerful method simplifies complex stress transformation calculations and provides intuitive visual insights into stress states at different orientations.
What Exactly is Mohr's Circle?
Mohr's Circle is a two-dimensional graphical representation of the transformation equations for plane stress. It allows engineers to:
- Determine principal stresses (σ₁ and σ₂) quickly
- Calculate maximum shear stresses (τmax)
- Find stress components at any orientation angle
- Visualize the relationship between normal and shear stresses
- Understand stress states without complex calculations
Practical Applications in Engineering
Mohr's Circle isn't just academic - it's used daily in these real-world scenarios:
1. Structural Engineering
When analyzing beams, columns, and connections, engineers use Mohr's Circle to:
- Determine critical stress combinations
- Identify potential failure planes
- Calculate safety factors against yielding
2. Mechanical Design
Machine component designers rely on Mohr's Circle for:
- Shaft and pressure vessel analysis
- Gear tooth stress evaluation
- Bearing and connection design
Pro Tip
While our calculator handles the math, we recommend all engineering students learn to draw Mohr's Circle manually. This builds fundamental understanding that helps when interpreting computer analysis results.
Frequently Asked Questions
Principal stresses (σ₁ and σ₂) are the maximum and minimum normal stresses that occur on planes with zero shear stress. The maximum shear stress (τmax) occurs on planes rotated 45° from the principal planes and equals half the difference between the principal stresses.
While Mohr's Circle is primarily for 2D stress states, three circles can represent principal stresses in 3D (Mohr's Circles for three dimensions). However, our calculator focuses on the more common 2D plane stress case.