Mohr's Circle & 2D Principal Stress Calculator
Mathematical mechanics tool for plane stress transformation. Evaluate normal and shear stresses to determine principal planes and maximum shear conditions.
Formula
R = \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2}
sigma_x= Normal Stress in X (MPa)
sigma_y= Normal Stress in Y (MPa)
tau_xy= In-Plane Shear Stress (MPa)
Quick Calculation Result
R = \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2}
Interactive Calculator:
Normal Stress in X (MPa)
Normal Stress in Y (MPa)
In-Plane Shear Stress (MPa)
-- waiting for inputs --
Result
How to Calculate Mohr's Circle & 2D Principal Stress Calculator (Step-by-Step)
- 1
Find Center of the Circle (Average Stress).
- 2
Calculate the Circle's Radius (Max In-Plane Shear).
- 3
Determine Principal Stresses (Sigma 1 and Sigma 2).
- 4
Compute the Principal Plane Angle.
- 5
Evaluate Absolute Maximum Shear Stress for 3D conditions.
Why This Matters
In Mechanical and Structural applications, Mohr's circle is vital for applying failure criteria like Von Mises or Tresca.
Sign Conventions
| Stress Type | Sign |
|---|---|
| Tensile Normal Stress | Positive (+) |
| Compressive Normal Stress | Negative (-) |
| Shear (Clockwise) | Positive (+) |
✓ Design Checklist
- • Include third principal stress (sigma_3 = 0) for absolute max shear calculation.
- • Ensure consistent units across all inputs.
⚠ Common Pitfalls
- • Confusing the 2θ angle on the Mohr's circle with the actual element angle θ.
- • Forgetting to check absolute max shear if both principal stresses have the same sign.