John, thanks for the very useful and informative post and referenced paper. You've raised a couple more questions;

1. Is the SIF value of 1 that you quoted for a shallow taper of less than 10 percent, from general experience, FEA or somewhere else?

2. The B31 codes only appear to apply the SIF to bending stresses (Sb). If a straight pipe (e.g. a buried pipeline) was subjected to cyclic pressure changes, should an SIF be applied to the longitudinal pressure stress term at stress raising locations such as 30° tapers? These stress raising locations could fatigue faster than straight pipe when subjected to cyclic pressures. I understand that the SIFs were developed from bending tests, so their application to axial loading may be tenuous.