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While both of these statements are true for the Design By Analysis portions of the old and new Div. 2, neither are correct for the Design By Rules. Part 4, specifically 4.3 uses the maximum normal stress theory - identical to Div. 1. However, for combined loadings, 4.3.10, that uses von Mises (in the 2011 Addenda - however earlier Editions post-2007 used maximum shear stress theory).In 2007 however ASME Div. 2 was changed to use the maximum distortion energy theory (von Mises criteria).
While this used to be true, with the addition of non-unity weld joint efficiency factors into the new Div. 2 it is becoming less true.One must have an understanding of the subtle differences between the two namely in testing criteria, the experimental analysis behind the formulae and more importantly any specified testing requirements e.g NDE.