Principal Stresses (Mohr)
Principal stresses and their direction at a point in plane stress. Von Mises predicts yield in ductile materials; Tresca gives a more conservative check.
von Mises stress σ_vM114.9MPa
- Principal stress σ₁
- 94 MPa
- Principal stress σ₂
- -34 MPa
- In-plane maximum shear τ_max
- 64 MPa
- Principal angle θ_p
- 19.3 °
- Tresca equivalent stress
- 128.1 MPa
- Safety factor (von Mises)
- 2.05
- Safety factor (Tresca)
- 1.84
- σ_vM / f_y = 49 %
METHOD
How it is calculated
σ₁,₂ = (σx + σy)/2 ± √(((σx − σy)/2)² + τxy²) tan 2θ_p = 2τxy / (σx − σy) σ_vM = √(σx² − σx·σy + σy² + 3τxy²) σ_Tresca = max(|σ₁ − σ₂|, |σ₁|, |σ₂|) (σ₃ = 0)
ASSUMPTIONS & NOTES
- Tension positive, compression negative.
- For brittle materials (cast iron) use maximum normal stress or Mohr-Coulomb instead.
Results are for preliminary design and checking; base the final design on the governing standard and safety factors.
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