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Presentation Overview • Pipe stress analysis programs are in wide use to
evaluate the structural integrity of piping systems.
• If a system is modeled side-by-side using one of those tools and with a general purpose finite element tool like ANSYS, different results are obtained.
• This presentation will seek to explain why those differences occur.
• Illustrative examples will be used to demonstrate the differences.
ANSYS Model Results: Max stress at pipe end equals 37,800 psi This is in close agreement to that calculated “by hand”, which was 37,646 psi…less than 1% discrepancy.
Max stress in elbow is found to be 138,940 psi. This would equate to a stress multiplier of 3.7, which is reasonable.
• In solid mechanics, a stress concentration factor (often denoted as k) is used to estimate the maximum theoretical stress in a given geometry. • Stress Intensification Factors (SIF’s) are established to predict a stress value that accounts for both static and fatigue loading in accordance with compliance to a particular piping code. (In the example, ASME B31.3 was used.) • Analogously, ANSYS calculated the maximum theoretical stress in the elbow, the pipe stress analysis program calculated the code stress for that loading.
“One of the less well known aspects of piping flexibility analysis per the ASME B31 Codes is that in piping stress analysis, the calculated stress range due to bending loads is about one-half of the peak stress range. This is because the stress concentration factor for typical as-welded pipe butt welds is two. Since the stresses are compared to a butt-welded pipe fatigue curve, one-half of the actual peak stresses is calculated. Thus, the theoretical stress, for example, in an elbow due to bending loads is two times what is calculated in a piping flexibility analysis following Code procedures. This is not significant when performing standard design calculations, because the Code procedures are self-consistent. However, it can be very significant when trying to do a more detailed analysis, for example, in a fitness-for-service assessment.” 1
A critical point that is subtly incorporated into the ASME piping code is the following:
1 “Process Piping - The Complete Guide to ASME B31.3”, Third Edition, by Charles Becht IV, Copyright 2009, ASME Press, Page 81
One can compare stresses from a pipe design program directly to code allowable values.
OR
In most cases, one can calculate the maximum stresses with a general purpose finite element tool (like ANSYS), divide those results by two, and compare those to code allowable values.
A footnote indicates that this SIF relationship may become non-conservative if the branch line diameter (d) to main line diameter (D) connected by the weld-o-let exceeds a ratio of 0.5. Thus, the SIF relationship is not applicable if the d/D ratio is within the range:
If ANSYS results are assumed to be accurate, then when the d/D ratio requirement is met, the piping analysis program overestimates the stress…a conservative approach.
(Recall that the maximum theoretical stress divided by 2 should equal the code stress, so here the true code stress might be approximately 42,697 psi.)
When the d/D rule is violated, then the pipe stress analysis program reports a stress lower than what may actually be present. True code stress ≈ 5,042 psi / 2 = 2,521 psi. The pipe stress analysis tool reported a value that may be 25% too low.
• Those interpreting the output of any simulations need to understand the distinction between pipe code stresses and theoretical maximum stresses.
• The SIF relationships provided in Appendix D of the ASME code must be strictly applied only to those geometries for which they were developed. Ignoring any of the limits of their applicability can result in unsafe and misleading system evaluations.
• Appendix D SIF’s should not be extrapolated to geometries that only resemble the specified configurations in the code. In cases where a component is not explicitly accounted for in the code, SIF’s must be developed for the specific case using either experimental methods, or finite element modeling.