The Guided Cantilever Method for Quickly Checking Piping Flexibility - Part 1
When I started out in engineering, as a twenty-one year old back in the 1970's, I was a pipe stress analyst. My mentor was a very senior, very experienced engineer named Norman Blair. Computerized analyses of piping systems were common in those days but it was time consuming to prepare the input (yes, generating punched cards) and computers were expensive to use. (We only had those big mainframes in those days!) So we still did a lot of manual piping stress analyses.
There were two types of pipe stress that we had to analyze. Primary stresses due to sustained loadings such as weight and secondary stresses due to the pipe undergoing temperature changes that caused it to cyclically expand and contract. (Usually because of the the hot/cold fluids running through them.) Keeping secondary stresses within code allowables required insuring the piping had adequate flexibility to absorb the expansions/contractions without over-stressing.
Supporting a pipe's weight was easy. For thermal analyses, Norm gave me a copy of Spielvogel's Piping Stress Calculations Simplified to read and to help me develop a good understanding of what piping flexibility analysis was all about. It turns out I didn't actually employ very many of the manual techniques in the book. That would have been more time consuming than preparing computer analyses of them. But Norman did introduce me to a quick, conservative way to manually eliminate piping systems from having to undergo computer analysis at all.
Most piping designers were pretty good at guessing at how much flexibility may be needed. I became adept at quickly verifying the acceptable flexibility of perhaps over 80% of the systems I encountered in typical oil refineries or chemical process plants without resorting to using a computer at all. This translated into significant savings of time and material.
The method I used for most of these manual verifications is called the Guided Cantilever Method. The best basic description of the method that I could google is Quick Check on Piping Flexibility by L. C. Peng. However, Peng doesn't mention the crucial trick that makes the method extremely practical -- fictitious anchors. In fact, I could not google a relevant reference to "fictitious anchors" at all. So allow me to document the trick here.
The main reason I want to to document the Guided Cantilever Method is because, IMHO, there is a tendency among pipe stress engineers nowadays to go ahead and run a computerized analysis on almost every piping system they encounter. However, I think that even in this age of desktop computers with great GUI interfaces, manual analyses still have their place. Perhaps I can encourage some pipe stress engineers to do more manual analyses where cost effective.
I will go through the method in some detail, in upcoming Part 2 of this post, because if engineers actually want to use the method, they will have to understand what makes the method conservative so they will be able to identify when the assumptions being made might not be applicable in some unusual case. And it is the unusual cases that cause the biggest failures in analyses.