Accounting for flexibility of adjacent elbows when R/t below 70 1

[nickelkid]

In piping designs with elbows that do not have at least 4D of straight pipe on each end, is it an acceptable approach to address elbow flexibility by considering it to have a single flanged end without FEA justification? Is FEA always necessary for addressing elbow interaction effect on flexibility with small bore piping?

I realize that a lot of work has been done and is on-going on this topic. But has there been enough information published to allow a designer to make responsible assumptions without additional FEA or testing in small bore piping below 16 inch and 750F? My query is resulting from API 610 nozzle loading verification with B31.3 piping.

 

[JohnBreen]

RCHandy

Assuming a single flanged end is quite conservative. That will take away about 30 percent of the flexibility of a 90 degree bend. Of course pressure stiffening can also be an important factor once the pipe is larger that NPS 14 and the schedule is less than 40. If you have access to TID-25553, Survey Report on Structural Design of Piping Systems and Components, December 1970, Rodabaugh and Pickett you will want to look at chapter 7, Curved Pipe and Miters. This survey reports on work going back to Karmann and Hovgaard. Also reported are the works of Vigness(1943) and Beskin(1945).

WRC Bulletin 179, Stress Indices and Flexibility Factors for Moment Loadings on Elbows and Curved Pipe, by W.G. Dodge and S.E. Moore. December 1972 can be found in technical libraries and it is worth reading.

There is a 1993 paper that is available that is useful for predicting stiffnesses on bends that is much better than the B31 method:

http://www.osti.gov/energycitations/product.biblio.jsp?osti_id=5903228

This paper reports the results of a program of FEA modeling of curved pipe and suggests an approach for calculating flexibility factors and stress intensifiers that are more accurate that the Vigness methods that were the basic of the Markl (et. al.) work.

Mourad's 1999 MS thesis

http://www-personal.umich.edu/~hmourad/PDF/MS_Thesis.pdf

presents another good literature survey but stops short of practical estimates of flexibilities. This because of the uncertainties of non-linear responses that are present in most hot piping and especially pipe bends. The trouble with FEA is that it assumes that all pipe is round and hollow (unless otherwise noted) and in fact there simply is no such thing as perfectly round pipe. And of course, the process of bending pipe introduces additional "as manufactured" ovality. As we all know, the added flexibility in pipe bends results directly from the increasing ovality induced by moment loadings (the locations of the "extreme fibers" of the "beam" are altered as the oval section will have a major axis and a minor axis).

I suppose that from a practical point of view taking the more conservative approach (single flange) will envelope the range of possible flexibilities (stiffnesses) in the bend but it will not give much relief from high nozzle loads. You might try additional rational assumptions in concert with the conservative (single flange) bend flexibilities - e.g., use the hot modulus of elasticity in the analysis (using the hot modulus will also result in more accurate spring hanger design). Depending upon the operating temperature, start-up may present the highest loadings as there may be some relaxation and "self-springing" over a period of time but again this is unpredictable. Another uncertainty is the "delivered wall thickness" of the bends. Many pipe suppliers will deliver bends and elbows that are one schedule thicker "to be sure" of complying to the requirements of pressure design.

I suppose it will all come down to what can be documented and conservative approaches regarding the flexibility in the bends are preferred (by owners) in the absence of absolute certainty. However, The effect of using the hot modulus of elasticity can be demonstrated. But of course that analysis is only good for calculating equipment loadings as the B31 Codes require the cold modulus to be used for the calculation of stresses.

Good luck.

Regards, John.

 

[nickelkid]

Thanks John, great tip on using the hot modulus of elasticity.