Does anyone have a reference for for an SIF on a taper (i.e. the taper for butt welding 2 different wall thickness pipes together)?

I am aware that the actual girth weld has an SIF of 1, but was wondering how much of an effect the taper has on stress intensification.

Look EN 13480

Wow, I like the question Mike.

Well here is what I think (with some embellishments just 'cause it is me).

Stress Intensification Factor (SIF) - Strictly an ASME B31 Code for Pressure Piping issue. So, review time - we should read Ed Wais' EPRI paper on Stress Intensification Factors (et. al. - Ed also discusses other stress intensifiers) here:

www.epriweb.com/public/000000000001012078.pdf

A B31 SIF can basically be thought of as the ratio of the number of cycles to failure for a tested piping component (other than a straight run of pipe) to the number of cycles to failure for a tested straight run of pipe with a girth butt weld. Therefore the SIF for the straight run of pipe with a girth butt weld is unity. So the SIF is a "band-aid" we put on beam theory to "adjust" for the fact that there will be a difference in the FATIGUE life of some "beams" (i.e., "components" like fittings) when compared to a "normal" round and hollow "beam" (straight pipe). The geometries of the fittings are unlike that of the straight pipe and those "different" geometries complicate beam theory analyses.

The component (bend, elbow, branch connection, reducer (a nasty perturbation of a straight run of pipe), etc) will fail with fewer loading cycles than will a comparable straight run of pipe. Looking at an S-N curve, the lower the beam bending stress, the greater will be the number of cycles to failure and conversely the higher the beam bending stress, there will be fewer cycles to failure. S-N curves for "components" seem to have a similar slope, just a little above that of (parallel to) the straight pipe. When we calculate beam bending "stresses" in "components" using beam theory with SIF's we ARE NOT calculating true elastic stresses in the piping (OMG!!!), rather more like half the true elastic stress. That is the reason that if you use ASME Section III rules for calculating elastic stresses in the piping the calculated stresses will be almost twice those calculated with B31 rules (the girth butt weld really has a stress intensifier of nearly 2.0). And that is the reason that stresses calculated using B31 rules must ONLY be compared to B31 allowable stresses (and allowable stress ranges). So, if you use FEA to analyze a local component it is appropriate to use ASME Section VIII, Division 2, rules to calculate stresses and use ASME Section VIII, Division 2, rules to determine the maximum allowable stresses.

Having said all that, what should be the B31 stress intensification factor for a straight piece of pipe between two girth butt welds? Well, the girth butt welds should be assigned an SIF of 1.0 and the straight pipe between them should be assigned and SIF of 1.0. So when we calculate the beam bending stress according to B31 rules the equation is:

Stress = (SIF) * (bending moment) / (the pipe section modulus) and in this example the SIF applied will be 1.0

Now consider the "tapered" transition piece (aka "pup piece") that is used to connect (by welding) two pieces of pipe that have the same outside diameter but have different wall thicknesses. Assume that the transition piece has been machined to have a constantly decreasing (as a function on length) wall thickness from the thicker wall pipe to the thinner wall pipe. This transition piece is STILL a straight beam (piece of pipe). Will the bending stress vary along its length when loading is applied? Yes, of course it will because its section modulus will continuously vary (and the circumferential (hoop) stress will also continuously vary). So, since there is no gross geometric discontinuity along its length (the reduction in wall thickness was defined as continuous and gradual), the SIF will be 1.0 along the transition piece and 1.0 at the joining girth butt welds. This example describes a very "shallow" taper angle (less than 10 percent). It will be seen in Ed's paper that as the taper angle increases the SIF will be larger and as the taper angle approaches 30 degrees the SIF may go as high as 1.9.

The real question is how many discrete sections should this transition piece be broken down into for developing the analysis model. What we are after is getting the flexibility of the transition piece to some degree of accuracy (as this also affects the calculated stresses). So it should probably be a function of the pipe size. So if the transition piece is 12 inches long and it is NPS 4 pipe, the engineer might decide that its flexibility could be adequately represented by modeling it as 4 sections (no welds) each one of which has a 25 percent reduction in wall thickness from the heavier wall pipe to the lighter wall pipe. So, for purposes of practicality we have accepted some simplifying assumptions as the thickness is modeled as a step function rather than a gradual thinning (mea culpa). The standard beam theory bending stress equation will be applied and approximate "B31 stresses" (as opposed to true elastic stresses) will be calculated along the length of the transition piece and approximate local flexibility will be applied.

What do you think?

Regards, John.

John, thanks for the very useful and informative post and referenced paper. You've raised a couple more questions;

1. Is the SIF value of 1 that you quoted for a shallow taper of less than 10 percent, from general experience, FEA or somewhere else?

2. The B31 codes only appear to apply the SIF to bending stresses (Sb). If a straight pipe (e.g. a buried pipeline) was subjected to cyclic pressure changes, should an SIF be applied to the longitudinal pressure stress term at stress raising locations such as 30° tapers? These stress raising locations could fatigue faster than straight pipe when subjected to cyclic pressures. I understand that the SIFs were developed from bending tests, so their application to axial loading may be tenuous.

SIFs are applied to bending stresses seen commonly in ABOVE ground piping systems the B31 codes assume that thermal displacement strains are commonly accommodated by said bending stresses.


Having said this no they do not apply to pressure stress cycling... however some factors very well may and do apply...

FEA may be your best help see PRG research FEPIPE....


Hmm maybe Sect III ("CAESAR II" look at section II NC I want to indicate the CAESAR II indices but instead the bulletin board takes over and renames it CAESAR II, k2) indices????

Hi Mike,

The ideally perfect (no flaws) straight piece of pipe with a gradually tapering wall thickness has no gross geometric discontinuities. At any specific point along the transition piece the classic beam bending stress equation cited can be applied (and of course the calculated stresses will vary with the difference in the section modulus). Applying an SIF to the moment in the equation would only be needed to describe a stress intensifier (an abrupt variation in the geometry from the adjacent sections).

1. Is the SIF value of 1 that you quoted for a shallow taper of less than 10 percent, from general experience, FEA or somewhere else?

From Markl's work. Markl briefly discusses a few (3) bending moment fatigue tests on 4 x 2 Standard B16.9 reducers. He found the stress intensification factor to be 1.0 and the failures occurred at the circumferential butt welds where the reducer joined the smaller pipe (reference Rodabaugh in TID-25553). This is interesting because we have the conical section and anywhere on that cone the SIF would (from limited testing) be 1.0 or less, remember that the GBW is 1.0. Note that B31.3 does not require an SIF for the cone so it defaults to 1.0. The failures occurred at the GBW and the Code SIF there is (ordinarily) 1.0. The abrupt geometric discontinuity in the reducer is at the cone-to-circular section interface and the failures did not occur there (implicitly then, the SIF there cannot be greater than 1.0). The thickness transition at the attaching weld of a pipe-to-valve (or other heavy walled component) is discussed in B31.1, paragraph 127.4.2(B) and in B31.1 Appendix D (see Table D-1). This applies only to the geometry of the tapered GBW and the SIF at the weld can vary between 1.3 (limited by mismatch et. al.) and 1.9 (at the extreme 30 degrees taper) and note that tapers greater than 30 degrees are not allowed). Obviously, the untreated weld harbors such horrors as residual stress and heat affected material so it is an obvious "fuse" in the system (and again the SIF for that "good" GBW is 1.0).

It is also interesting to look at how Markl (et. al., Mr. Rodabaugh was in attendance) set up the cyclic fatigue tests in that he arranged at the "anchored end" of the pipe assembly to have a machined "upset end" to damp out the effect of concentrating the moment at the anchor (see "Fatigue Tests of Piping Components", figure 18). Much like a very long reducer, at the anchor end of the specimen a larger diameter and thickness (larger than the NPS 4 schedule 40 size of the specimens) tapered to the "normal" diameter and thickness of the pipe component at issue. There were NO failures in this transition which implies that (relative to the GBW) the interface of the transition to "normal" section modulus (this would be at the most egregious geometric discontinuity of the "normal" straight pipe section) the SIF was no more than 1.0 (likely "less" (if that is possible) as a radiused transition was used).

Getting back to the transition piece with the uniformly tapered wall thickness, the greatest likelihood for a region of SIF greater than 1.0 would have to be at the intersection of the (slightly) conical inside diameter to the circular ID's at both ends of the transition (likely emphasized at the larger ID end). However, even if this transition were very abrupt it still would not be as discontinuous as the geometry presented at an "as welded" GBW.

2-a. The B31 codes only appear to apply the SIF to bending stresses (Sb).

Yes, the SIF's were developed from cyclic bending tests.

2-b. If a straight pipe (e.g. a buried pipeline) was subjected to cyclic pressure changes, should an SIF be applied to the longitudinal pressure stress term at stress raising locations such as 30° tapers? These stress raising locations could fatigue faster than straight pipe when subjected to cyclic pressures.

The SIF's developed for cyclic bending stresses would absolutely be inappropriate as SIF's can only be applied to beam bending equations. At this time the B31 Codes for Pressure Piping do not provide specific guidance for cyclic pressure loadings. For further reading on this issue I would refer you to TID-25553 (E.C. Rodabaugh and A.G. Pickett, 1970), Chapter 10, "Girth Transition Joints". The cited reference presents a theory developed by Rodabaugh and Atterbury for "internal pressure loading at the tapered transition joint" (other theories are also included). The cited publication also reports much theory and experimental test results from many years of cyclic pressure testing. Testing seem to point to the longitudinal weld in seam welded pipes as being the point of highest stress in pressure cycling as the pipe cross section at that point is (if I will be allowed to exaggerate) "heart shaped" (with the circumference depressed by the weld)and every pressure "pulsation" tends to strain the pipe section at that point to momentarily bring the pipe section closer to a "round" shape (after the pulse, it momentarily goes back its "as welded" shape). The vast majority of the cyclic pressure test failures occurred at the seam welds and those that did not seemed to "find" other flaws in the pipe section. Some shell theory pressure loading analyses (applying Peterson's "Stress Factors") are reported in the cited reference but this posting has already gotten to be too verbose and I will stop here (I promise).

Regards, John.

Breen take work break!

from an unnamed source but something that may help your quest on the design of components for pressure cycling...

304.8 Fatigue Analysis
304.8.1 – Pressure Cycling Fatigue due to pressure cycles of components and other piping elements shall be substantiated by one or more of the following means (calculations and documentation showing compliance shall be available for the owners approval):
(a) Extensive successful service experience under comparable conditions with similarly proportioned components of the same or like material.
(b) Experimental stress analysis such as described in BPV Code, Section VIII, Division 2, Part 5.
(c) Pressure fatigue test utilizing methodology contained in BPV Code, Section VIII, Annex 5.F or equivalent. Leak testing in accordance with para. 345 shall be required at intervals to be determined by the designer to verify the integrity of the pressure boundary and certify the component’s expired number of test cycles.
(d) For any of the above, the designer may interpolate between sizes, wall thicknesses, and pressure classes and may determine analogies among related materials.

Yessir Mr. Luf :-) After all, I promised that I would stop there!


Regards, John

CAESAR II has an SIF for "tapered transition". I believe that's what you have here. I believe that while this is not defined in B31.3 Appendix D, it is defined in B31.1 and/or in Section III.
I'm away from my office now so I cannot check. Can you?

Mike,

Can you give us a description of what it is you have? A little more description would help us.

Regards John.