Stress Intensification Factors

A B31 (B31.1, B31.3, B31.4, B31.5, B31.8, B31.9, B31.11) stress intensification factor (SIF) is an empirically derived parameter that allows the designer to estimate the fatigue performance of a piping component or joint. The concept of the parameter was developed in the late 1940s and early 1950s and was incorporated into B31.1 - 1955, which had separate chapters for different piping applications which eventually were published as B31.1, B31.3, B31.4, etc. The original background discussion of SIFs was published in ASME Paper 53-A-51, "Piping-Flexibility Analysis" by A.R.C. Markl. (This paper is highly recommended reading for any serious student of piping design.) In the 1955 B31.1 document, SIFs were tabularized in Chapter 6, but subsequent separate publication of the B31 books (B31.1, B31.3, B31.4, etc.) have in many cases resulted in different SIFs for the same piping components and joints. However, there is absolutely no justification for having different SIFs for different applications. The differences are from a lack of communication between the ASME committees responsible for the development of the B31 books.

The SIF (i) parameter was and still is determined through testing by applying a reversing displacement to, i.e., developing an alternating stress in, an assembly of piping elements containing the piping component or joint under consideration. The reversing displacement is applied to the assembly until a fatigue failure occurs — fatigue failure being defined as crack initiation and propagation through the wall such that a leak occurs in the pressure boundary in or near the piping component or joint under consideration. The process is repeated by applying various reversing displacements to similar assemblies, developing an alternating stress/number of cycles to failure curve for the piping component or joint. The resulting curve is compared to a reference curve to determine the SIF. The reference curve is the failure curve for an as-welded circumferential butt weld, where the SIF for the butt weld is assigned a value of unity (i = 1.0).

But, the actual stress in an as-welded circumferential butt weld in nominal pipe intuitively and logically must be greater than the actual stress in the same size nominal pipe without a weld. However, the B31 "intensified" bending stress at a butt weld is equal to the SIF (i = 1.0) times the nominal stress (M/Z) at the butt weld. Thus, at a butt weld the B31 "intensified" stress is equal to the calculated nominal stress. This has caused and continues to cause considerable confusion in pressure component design, especially amongst serious analytic types who often claim that B31 "intensified" stresses are wrong, i.e., too low, when compared to actual or theoretical stresses. B31 acknowledges that B31 "intensified" stresses (iM/Z) are less than actual or theoretical stresses. However, in this case, what is not understood is that the B31 allowable fatigue (flexibility) stresses are correspondingly low when compared to the allowable fatigue stresses for components when actual or theoretical stresses are evaluated — the factor of safety in a B31 fatigue analysis is comparable to the factor of safety in an actual or theoretical analysis.

When actual or theoretical fatigue stresses are evaluated in nuclear Class 1 piping services, stress indices (not SIFs) are used. Stress indices are theoretically developed parameters that are (like SIFs) a measure of the fatigue performance of a nuclear Class 1 piping component or joint. In this case, however, fatigue failure is defined merely as crack initiation in the piping component or joint (as opposed to through-wall crack propagation). As noted above, the allowable fatigue stresses for nuclear Class 1 services are correspondingly higher than B31 allowable fatigue (flexibility) stresses.

What the B31 designer must remember is that he/she is calculating an "intensified" (or "effective") stress, not an actual or theoretical stress.

But why, in a time approaching an analytic utopia, is the B31 designer still using these "ancient" SIFs? The answer is simple. B31 SIFs are simple to determine and apply (simplified methods are necessary to gain the widest possible application and there's a lot of pipe to design). B31 SIFs are consistent with the technology of the piping industry (we are typically not building watches). Determining actual or theoretical stresses is usually more expensive and complicated (compare a nuclear Class 1 piping analysis with a B31.1 analysis or, if you're not conversant with things nuclear, compare a Section VIII, Division 2 analysis to Section VIII, Division 1 analysis, it's the same difference). And perhaps the best reason for using B31 SIFs is that the piping industry has almost 50 years of validating experience with them (most of the SIFs proposed by Markl are still accurate within the context of good engineering practice and good engineering is more than a worthwhile commodity).

Author: Mr. Ron Haupt, P. E., of Pressure Piping Engineering ( is a member of several piping code committees (B31, B31.1, B31.3, BPTCS, and others). He consults with us in the capacity of Nuclear QA Manager.

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