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Tips April - June 2007

Displacement Stress vs. Expansion Stress

Question: I always considered a displacement stress to be different from an expansion stress. To me, a displacement stress would be "thermal anchor motion" separate from the "thermal expansion stress." Comments?

Reply: Not according to B31.3. The B31.1 rules were adapted from B31.3 rules. "Displacement stress" is merely the term applied to thermal expansion-type stresses, i.e., both thermal expansion and anchor movement stresses from any source. "Displacement stress" is used to define the category of stresses which typically lead to fatigue failure as opposed to collapse in the same way as secondary stress is the "design by analysis" term used to define thermal expansion and anchor movement stresses. I don't know the origin of the B31.3 term but I assume it is derived from shortening either the term "displacement limited stress" or "stress caused by restraint of free-end displacement." The reason for having two terms that apply to the same stress phenomena, of course, is that the value of "displacement stress" in an elbow is different from the value of the "secondary stress" in a comparable elbow, i.e., the difference between the stress intensification factor (i-factor) and the product of the secondary bending stress index and the peak stress index C2K2 (see ASME Boiler Code, Section III, Subsection NC/ND-3673.2(h)). With the terms "sustained stress" and "displacement stress" now defined in the B31.1 code, users may understand the difference between "design by rule" stresses (B31 stresses) and "design by analysis" stresses (Nuclear Class 1 or SC VIII, Div. 2 stresses) and that it is inappropriate to add "secondary" and "displacement" (or "primary" and "sustained") stresses together. Note peak stress is mentioned in the B31.1 definitions now, noting that the term is not used but the effect is included in the evaluation of "displacement stresses" (using stress intensification factors developed by testing).

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.

SIFs, SCFs and Stress Indices


Stress intensification factors (SIF's) are empirically developed factors that, in the context of B31 piping design, are a measure of the fatigue performance of a pressure piping component. In this case, fatigue failure is defined as crack initiation and propagation through the wall such that a leak occurs in the pressure boundary.


Stress indices are theoretically developed factors that, in the context of nuclear piping design, are a measure of the collapse performance or the fatigue performance of a nuclear Class 1 piping product. In this case, collapse failure is defined as buckling of the pipe cross-section such that fluid flow is seriously impeded and fatigue failure is defined as crack initiation in the pipe wall.


Nominal stresses are computed or measured for regions of components with constant or gradually changing thicknesses and smooth surface contours. The presence of corners, grooves, holes, threads, welds, and so on, results in an alteration of the nominal stress distributions so that locally higher stresses occur. This localized stress condition is referred to as a stress concentration. It is characterized by a stress concentration factor, which is defined as the ratio of the localized high stress to the nominal stress.

Excerpted from SST301: Piping Design and Analysis Seminar Notes, Sec 3H