Stress Categorization & Linearization Alpha · 2026-06-22

Through-wall stress linearization (membrane + bending) + polynomial coefficients — BS 7910 §6.4 & API 579

Stress Categorization & Linearization (BS 7910 §6.4 / API 579)

This tool turns a through-wall stress profile into the stress representations a fracture assessment needs: the membrane component \sigma_m, the bending component \sigma_b, and the through-wall polynomial coefficients. It is category-neutral — run it on your primary stress profile and import the result into P_m / P_b (or the polynomial \sigma_0..\sigma_5); run it again on a secondary (thermal) profile and import into Q_m / Q_b. The primary/secondary split matters because primary stress is not self-limiting and drives plastic collapse (it affects both L_r and K_r), while secondary stress is self-limiting and affects only K_r.

You enter the through-wall stress profile as data points, the wall thickness B, and the flaw depth a. Two linearization regions follow BS 7910 Figure 6.1:

• Full wall thickness (Fig 6.1(b)) integrates the profile from 0 to B.
• Flaw-height-only (Fig 6.1(a)) fits an envelope over 0 to a and extrapolates through the thickness.

The same profile is also least-squares fit to the through-wall polynomial coefficients:

• \sigma_0..\sigma_5 for BS 7910 Annex M (Eq M.14).
• \sigma_0..\sigma_4 for API 579 Annex 9B (Eq 9B.3).

Inputs and results are shown in SI (mm, MPa) or US (in, ksi) units.

This tool does the linearization only. Weld residual stress (transverse and longitudinal directions, through-wall) is handled by the dedicated residual-stress calculators — BS 7910 Annex Q and API 579 Annex 9D — whose results feed Q_m / Q_b. It does not compute the stress profile itself or run the full FAD assessment.

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