Physics

Principal Stress Calculator

Find the principal stresses from a 2D stress state.

Calculated Output

Major principal stress σ₁ (MPa) 92.426

Minor principal stress σ₂ (MPa) 7.574

Formula: σ = (σx+σy)/2 ± √(((σx−σy)/2)² + τxy²)

Step-by-Step Breakdown

1. Values used:

2. Normal stress σx = 80 MPa

3. Normal stress σy = 20 MPa

4. Shear stress τxy = 30 MPa

6. Major principal stress σ₁ = 92.426MPa

7. Minor principal stress σ₂ = 7.574MPa

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The math behind it

σ₁,₂ = (σx+σy)/2 ± √(((σx−σy)/2)² + τxy²). These define the worst-case tension and compression.

σx 80, σy 20, τ 30 MPa → σ₁ ≈ 92.4, σ₂ ≈ 7.6 MPa.

Why do engineers care?

Failure often begins where the principal stress is largest.