Triaxial Load Envelope

Standard: API TR 5C3 / ISO 10400 — the biaxial (von Mises) pipe-body yield ellipse combines axial stress and hoop (tangential) stress into a single equivalent stress, compared against the material’s minimum yield strength.

Formula basis: σvme² = σa² − σa·σt + σt² = Y² traces the yield boundary. Axial stress relates to axial load through the pipe’s cross-sectional area (σa = Fa ÷ As); hoop stress relates to pressure through the thin-wall relation (σt = P × 2t ÷ (D − t), positive for internal/burst pressure, negative for external/collapse pressure). The chart traces this boundary parametrically and plots your design load point against it. The dashed 95% curve repeats the same trace with Y replaced by 0.95 × Yp, as a rough allowance for mill-yield variation above the stated minimum.

Scope and limitations: This is the pipe body only — no connection rating, no temperature derating, no buckling check, and it does not by itself replace the four-regime API collapse rating for the pure-collapse (Fa = 0) case; see the Collapse Pressure calculator for that. Radial stress is simplified out under the thin-wall assumption, which is standard practice but loses some accuracy on thick-wall pipe (low D/t).

For preliminary screening only. Not a substitute for a certified engineering assessment.

Want the full explanation of why burst and collapse checks alone aren’t enough? Read Why Burst and Collapse Checks Alone Aren’t Enough.