BS 7910:2019 Annex D — stress magnification factor k_m from joint misalignment
A building block for the fracture and SIF calculators. When the two sides of a welded joint are not perfectly aligned — an axial offset of the centre-lines, or an angular distortion — applying membrane tension also bends the joint. This secondary bending adds stress at the weld, so the effective stress is higher than the nominal membrane stress alone. BS 7910 Annex D quantifies this with the misalignment stress magnification factor k_m=1+\sigma_s/P_m (Eq. D.1), where \sigma_s is the secondary bending stress.
You pick the joint family:
The calculator then routes to the matching closed-form \sigma_s/P_m from Annex D Tables D.1 (a–g, including ovality) and D.2 (a–b). Inputs are the joint geometry: misalignment e or angular distortion \alpha, thickness(es), plate lengths, restraint factor \kappa and, for angular families, the end condition (fixed or pinned).
For angular families an optional tanh straightening correction (\le 1) reduces k_m as the joint straightens under load (switching it off is conservative). Axial and angular contributions can be superposed per Eq. D.3 (v1 uses a same-sign conservative sum). The result is k_m and its components, ready to feed into the Annex M SIF and Clause 7 fracture calculators.
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