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Calculate principal stresses, maximum shear stress, and stress transformations using Mohr's circle
đ Mohr's Circle Formulas
Ď_avg = (Ď_x + Ď_y)/2
R = â((Ď_x - Ď_y)²/4 + Ď_xy²)
Ďâ = Ď_avg + R
Ďâ = Ď_avg - R
Ď_max = R
Ď_avg = average stress, R = radius, Ďâ,Ďâ = principal stresses, Ď_max = maximum shear stress
Principal Stress Ďâ:
Principal Stress Ďâ:
Maximum Shear Stress:
Principal Angle:
Average Normal Stress:
Stress State:
đĄ Tips
- Mohr's circle represents stress transformations graphically
- Principal stresses occur at maximum and minimum normal stress
- Maximum shear stress occurs at 45° from principal directions
- Positive shear stress rotates element clockwise
- Circle center is at average normal stress
- Circle radius equals maximum shear stress