The 'principal stresses' σ1 and σ2 at a point in a 2D stressed body are found from:
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Averaging σx and σy only
σ1,2 = (σx+σy)/2 ± √((σx-σy)²/4 + τxy²) — Mohr''s circle eigenvalues of stress tensor
Only from experimental strain gauges
Multiplying normal by shear stress
Correct Answer
B. σ1,2 = (σx+σy)/2 ± √((σx-σy)²/4 + τxy²) — Mohr''s circle eigenvalues of stress tensor
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Principal stresses from Mohr''s circle: σ1,2 = (σx+σy)/2 ± √(((σx-σy)/2)² + τxy²). Principal planes: no shear stress. Maximum shear: τ_max = √(((σx-σy)/2)² + τxy²) = (σ1-σ2)/2. Principal stress angle: tan(2θp) = 2τxy/(σx-σy). Important: principal stresses are eigenvalues of stress tensor. Used in design: von Mises yield criterion σe = √(σ1²+σ2²-σ1σ2) for biaxial stress.
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