Hello RSP,

Yes, I agree. Regrettably, I wrote a confusing (confused) answer. It is important in such discussions to define terms and keep them straight. So, in the interest of brevity I would refer Mucour to the discussion of principal stresses (normal to principal planes), principal planes, shear stresses, unit cubes and combinations of triaxial and shear stresses that is to be found in "Design of Welded Structures" by Blodgett (the Lincoln Arc Welding Foundation). Another excellent reference is Chapter 8 of the book "Steam" by the Babcock and Wilcox Company. These references graphically show applications of the various failure theories in context with how we generally would use them for stress analysis.

The B31 Codes provide protection for various modes of failure. Therefore, various failure theories are used. Primarily, the equations for combining stresses that we are most familiar with use the maximum principal stress failure theory which states that if ANY one of the three principal stresses exceed the yield strength of the material a failure will occur. This theory is the easiest to apply and when used with an appropriate factor of safety it provides a good level of design margin. So, we have an equation (or set of equations) that combine(s) the stresses resulting from bending and torsional moments to determine the greatest principal stress(es).

The exception is found in the B31.3 high pressure chapter where the equation for calculating minimum wall thickness is a Hubert - Von Mises – Hencky derivation. There is a footnote that identifies this methodology in B31.3 but that is the only case that I know of where we have actually identified the evaluation methodology.

Shear is not commonly the limiting or controlling factor in the analysis of stress in piping. The Code provides protection in the cited paragraph such that when shear is the controlling factor the limit is predictable. When the maximum shear stress exceeds one half of the material yield strength at temperature failure is predicted. This sets the limit for shear stress. This is an application of the Tresca theory of failure.

The point that I was trying in haste to make (kids, don't try this at home) was that various theories of failure are used by the B31 Codes to address various modes of failure. While the Tresca and von Mises failure theories are more accurate for predicting failure of ductile material they were judged to be too cumbersome to apply for general application in the B31 Codes. In more rigorous analyses (e.g., in design by analysis applications in nuclear class 1) the Codes do use Tresca maximum shear theory to evaluate combined stresses.

I hope that is somewhat less confusing.

Regards, John.