PSA 1.5 — Failure Theories: Rankine, Tresca, von Mises — and What the Codes Use
The tensile test gives yield for one stress acting alone. A pipe wall carries hoop + longitudinal + shear simultaneously . A failure theory converts that 3-D state into one number comparable with Sy. Three classics:
Try it: drag the stress point around all three envelopes and watch each theory's verdict — artifacts/psa-failure-theories.html
Metals yield by slip on crystal planes — a shear mechanism . Hydrostatic tension (all three σ equal) produces zero shear and essentially cannot yield metal — both Tresca and von Mises are blind to hydrostatic stress, which is physically right. Rankine isn't, which is why it's…
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