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.