Solid Mechanics
Mohr's Circle Simulator
Analyze 2D stress elements and calculate principal stresses, maximum shear stress, and orientation angles. Rotate planes dynamically using the playback controls or manual slider to trace Mohr's Circle.
Stress State
2D Plane Stress
Isotropic material
Mesh Resolution
19 nodes
Sweep data
Output Format
CSV
Export ready
Input Parameters
Element angle sweep
Stress Governing Model
Average Stress
σ_avg = (σ_x + σ_y) / 2
Circle Radius
R = √[((σ_x - σ_y)/2)² + τ_xy²]
Principal Stresses
σ_1,2 = σ_avg ± R
Stress Transformation
σ_x' = σ_avg + ((σ_x - σ_y)/2)cos(2θ) + τ_xy sin(2θ)
Principal stresses σ1 = 62.4 MPa and σ2 = -22.4 MPa occur when the element is oriented at θp = 22.5°.
Maximum shear stress τmax = 42.4 MPa occurs on planes oriented at θs = -22.5°.
Rotated Stress Element
Normal σ_x'
50.0 MPa
Normal σ_y'
-10.0 MPa
Shear τ_x'y'
30.0 MPa
Max Principal (σ1)
62.4MPa
Min Principal (σ2)
-22.4MPa
Max Shear (τmax)
42.4MPa
Principal Angle (θp)
22.5°
Mohr's Circle Plot
Inclined Plane Sweep
| Plane θ (°) | σ_x' (MPa) | σ_y' (MPa) | τ_x'y' (MPa) |
|---|---|---|---|
| 0° | 50.0 | -10.0 | 30.0 |
| 10° | 58.5 | -18.4 | 17.9 |
| 20° | 62.3 | -22.3 | 3.7 |
| 30° | 61.0 | -21.0 | -11.0 |
| 40° | 54.8 | -14.8 | -24.3 |
| 50° | 44.3 | -4.3 | -34.8 |
| 60° | 31.0 | 9.0 | -41.0 |
| 70° | 16.3 | 23.7 | -42.3 |
| 80° | 2.1 | 37.9 | -38.5 |
| 90° | -10.0 | 50.0 | -30.0 |
| 100° | -18.4 | 58.5 | -17.9 |
| 110° | -22.3 | 62.3 | -3.7 |
| 120° | -21.0 | 61.0 | 11.0 |
| 130° | -14.8 | 54.8 | 24.3 |
| 140° | -4.3 | 44.3 | 34.8 |
| 150° | 9.0 | 31.0 | 41.0 |
| 160° | 23.7 | 16.3 | 42.3 |
| 170° | 37.9 | 2.1 | 38.5 |
| 180° | 50.0 | -10.0 | 30.0 |