The map: any plane-stress state is a point (σ₁, σ₂). Inside an envelope = that theory predicts no yield. Von Mises (ellipse) matches ductile-metal tests best; Tresca (hexagon) is slightly conservative — it lives inside the ellipse; Rankine (square) is only meaningful for brittle materials. Note the 4th quadrant (σ₁ tension, σ₂ compression): Tresca and von Mises predict yield well before Rankine — exactly the shear-dominated region where torsion lives. B31 codes' expansion-stress check SE=√(S_b²+4S_t²) is a maximum-shear (Tresca-family) form.