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.