Hi Ken,
Thank you for expanding your description of the system at issue. It is certainly an "interesting" system. In reading your original post again I can see that I did not fully grasp the situation that you are addressing.
There are (at least) two ways of looking at any piping system. One way is from the point of view of the designer and another way is from the point of view of the structural analyst. Obviously, it is often the case that both tasks are addressed by the same piping engineer. On the other hand, today the “designer” is often the person who is responsible for the “layout” of the system and for developing the AutoCAD drawings or the Inventor model.
B31.1 Paragraph 119.3 would warn the designer that in a system in which there are significant variations in the relative flexibility of the piping components it is possible to unknowingly design “strain concentrators” into the system such that the more flexible components may be subjected to local strains that could result in permanent plastic deformation (and potentially, failure) due to elastic follow up. Paragraph 119.3 provides a few examples of design features that should be avoided by the designer if possible. If “the designer” drafts a system in which there are significant variations in the relative flexibility of components that are in series and immediately adjacent to each other, there could be “a problem” at the point of mutual attachment (weld line) of the two components (it will be the stress analyst’s job to quantify “the problem” in terms of calculated stresses (stress ranges)). The competent designer will understand that it is good practice to avoid abrupt transitions in pipe diameter (section modulus); however, defining “abrupt transitions” is not an easy task. Certainly, using a series of Standard B16.9 welding reducers might ameliorate the problem of abrupt transitions. Using B16.9 reducers (of the appropriate schedule) also assures that pressure design will be adequate. Such design (one or more reducers) might also (slightly) ease the job of the stress analyst as there is at least some guidance in the B31 Codes for determining the stress intensification factors (SIF’s) to be used with reducers in the analysis.
Ah, stress intensification factors! It is essential to use the correct SIF’s. From the point of view of the stress analyst, it is important to recognize at the outset of planning the analysis model that when we use the rules of B31 we are not always calculating true elastic bending stresses. The B31 beam bending equation (generally) defines the calculated stress as the resultant moment times the SIF, divided by the component nominal section modulus. If the SIF (usually as defined by B31.1 Appendix “D”) is greater than 1.0 the equation calculates an “effective bending stress” that can conveniently be compared to Code defined allowable stresses (stress ranges). A recent thread discussed SIF’s et. al. Go here:
http://www.coade.com/cgi-local/ultimatebb.cgi?ubb=get_topic;f=1;t=001304;p=1#000012
You might also want to review John C. Luf’s article in this newsletter:
http://www.coade.com/newsletters/jun00.pdf I think a properly modeled
CAESAR II analysis will always be the first step in the evaluation of designs of this type. The key is to accurately model the flexibility of the individual components that comprise the system and to include the appropriate SIF’s at the points where the strain concentrations will occur. An analysis model with an appropriate level of attention to detail (including correct flexibilities) will accurately determine the distribution of forces and moments over the entire system and for most of the components in the system the (beam model) analysis will provide accurately calculated stresses for comparison to Code maximum allowable stresses (stress ranges). Again, the validity of the stress calculations would depend upon applying the correct SIF’s. An analysis that includes an accurate model of an inexpertly “designed” system will tell the analyst and the “designer” that he/she has “problems”. This of course will require modifications to the design.
The first place to look for SIF’s is in B31.1 Appendix “D”. If you can’t find SIF’s for the components that you are using in Appendix “D”, you would have to use finite element method to determine them (see the cited references for an explanation of what must be considered to obtain SIF’s that can be used in a B31 analysis). Stresses calculated this way would be compared to B31 maximum allowable stresses (stress ranges). Alternately, the calculated forces and moments from the beam model could be applied to a 3D FEA model and the stresses calculated could be compared to allowable stresses from the ASME B&PV Code, Section VIII, Division 2.
When there is a change in wall thickness and a change in diameter it can be effectively addressed in the design by including B16.9 reducers with the appropriate SIF's (see B31.1 Appendix "D"). A rule of thumb that is sometimes used suggests that if the length of the reducer is near to or less than the diameter of the larger adjacent pipe, the reducer can be modeled as a single section of pipe having an average diameter and average wall thickness (the thought here is that this method will result in about the right flexibility). Since this is a false geometry, care must be taken to apply the SIF's at the attachment nodes associated with the true diameters and wall thicknesses of the pipes adjacent to the reducer (this to get the stress calculation correct). To calculate the SIF’s for reducers to be applied in the
CAESAR II model you will have to know the “cone angle” and this varies from manufacturer to manufacturer (it is not standardized by B16.9).
From the standpoint of the designer, due consideration should be given to wall thickness changes at adjacent components. Where there is a change in wall thickness at a point of connection of two pipes of the same diameter, it is prudent to note on the drawing that the matching end of the pipe with the larger wall thickness should be "line bored" with a taper to avoid wall thickness "miss-match" at the weld line (note that the minimum required thickness for pressure design must be maintained). There will be some degree of stress intensification at such welds and this invites a thorough reading of B31.1 paragraph 127.4.2 with attention to subparagraph 127.4.2 (C). Of course, B31.1 Appendix "D", Table D-1 (regarding butt welds with "miss-match") is also to be referenced. I think that if we can get the SIF's right the beam model will provide accurate calculated effective stresses.
In summary, I think that if you can develop an accurate
CAESAR II beam model, including realistic component flexibilities, realistic loadings, realistic boundary conditions and accurate SIF’s (for the stress calculations), the requirement for an "appropriate analytical method" will have been met.
And again, all of this is just my opinion and not necessarily that of ASME or any of the ASME Code Committees.
Regards, John.