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⚡ Principal Stress Calculator
Calculate principal stresses, maximum shear stress, and stress orientation for plane stress states
📐 Principal Stress Formulas
σ₁,₂ = (σ_x + σ_y)/2 ± √((σ_x - σ_y)²/4 + τ_xy²)
τ_max = √((σ_x - σ_y)²/4 + τ_xy²)
θ_p = ½ arctan(2τ_xy/(σ_x - σ_y))
σ_avg = (σ_x + σ_y)/2
σ₁,₂ = principal stresses, τ_max = maximum shear stress, θ_p = principal angle, σ_avg = average stress
💡 Tips
- Principal stresses are the maximum and minimum normal stresses
- Maximum shear stress occurs at 45° to principal directions
- σ₁ is always greater than or equal to σ₂
- For plane stress, σ₃ = 0 (out-of-plane stress)
- Principal stresses are perpendicular to each other
- Use Mohr's circle for graphical analysis