There are back of fag packet methods and spreadsheet calcs to do this, many incorrect and often with no audit trail. The safe way is to use recognised software to do a proper stress and load analysis, such as Caesar II or Autopipe.
There are simple chart form solutions for most common loop shapes in Kellogg Design of Piping Systems, or the venerable Spielvogel book amongst many others. These are reliable sources. It is not practical to write equations here.
Good Reference book "The Process Plant Layout and Piping Design"
The Process Plant Layout and Piping Design Course has a 66 hour duration and provides education in the following areas
(see details by clicking on the link in the left hand border that points to 'Layout Unit 1 Introduction to Plant Layout Design (4 Hours)
Unit 2 Plant Layout Specifications (2 Hours)
Unit 3 Plot Plans (4 Hours)
Unit 4 Compressors (8 Hours)
Unit 5 Drums (4 Hours)
Unit 6 Exchangers (4 Hours)
Unit 7 Furnaces (6 Hours)
Unit 8 Pumps (4 Hours)
Unit 9 Reactors (4 Hours)
Unit 10 Towers (6 Hours)
Unit 11 Pipe Racks (2 Hours)
Unit 12 Structures (2 Hours)
Unit 13 Underground Piping (4 Hours)
Unit 14 Instrumentation (2 Hours)
Unit 15 Storage Tanks (4 Hours)
Unit 16 Stress Aanalysis(4 Hours)
Unit 17 Computer-Aided Design (2 Hours
steel pipe expands or contracts at 0.000006 x length /ºF
Thus, when the axial growth is fully restrained, the axial stress is 0.000006 x E. If it is not restrained it is zero.
E = Young's modulus
The basic bending forces in an expansion loop are exactly the same as in a plane inverted "U" frame when you pinch the bottom legs together. That (maximum) pinch distance would be the axial growth of any pipe attached to the bottom of the "U", provided that the other ends of those pipes were fully anchored.
Since axial growth "rigidity" is so much more than the rigidity provided by the loop as it flexes in bending, effectively all axial growth of the horizontal pipe at the bottom is permitted by the loop, as the bottom of the loop moves together. Axial stresses in the horizontal pipe are reduced from say 100 kips to almost zero (but NOT zero), say 1 or 1.5 kips or so, and that resultant load causes bending stresses to be developed, increasing upwards in the vertical pipes and becoming a maximum at the loop elbows. That bending moment stays at that maximum bending moment level for the entire length of the top horizontal pipe until it gets to the next elbow and starts reducing until it reaches the bottom pipe on the other side of the loop.
As the loop gets higher, both axial resultant stress in the horizontal pipes and the bending moments in the loop are reduced.
ASHRAE published several equations to calculate the width and depth of an expansion loop in their 2004 HVAC Systems and equipment Handbook Chpt 41.12. The equation I've seen used for temps up to 400[°]F was this
L=6.225[√]([Δ]G x D)
L/5=W
2W=H
Where: L=growth factor
6.225= constant for steel(A53) and B88 hard drawn copper
[Δ]G=linear expansion in inches
D=outside diameter of pipe
W=Width of loop
H=Heigth of loop
This produces a loop configuration like BigInche referenced.
Guides should be placed no closer than twice the heigth of the loop and anchored at both ends. The stress range was listed at 15,000 psi. I would recommend reading through the section. There are several different loop types to consider with varying equations. Just my two cents. Hope that helps.
I'm not a real engineer, but I play one on T.V.
A.J. Gest, York Int./JCI
I found your response a bit harsh, I don't think it is productive to belittle people for posting questions in this forum (you may know where to look for solutions but others may not). I know this is off topic but if it bugs you so much simply direct them to a relevant post or simply don't comment. Just my two cents.
Everyone wants to help someone who stumbles, and that includes me too..
However, I suspect that the original poster preferes to have strangers "spoonfeed" him an answer without any real effort on his part.
If you carefully read the first post, you will notice that there is no real question asked....there only seems to be the reassignment of work that the poster was asked to perform.
I have no problem with helping to answer real questions posted by those that are truly making an effort. I do have a big problem with being tricked into performing the work that was assigned to those too lazy to perform it.
Piping expansion loops are easy.... we all know it. let's not waste everyones time and energy with these knid of questions
I consider myself a master googler and have seen hundreds of pages on expansion loops but nothing that goes through a rigorous derivation of where the tables come from. . .I'm sure much of the data out there is correct but until it can be proved on paper, it has to be assumed to be incorrect since responsibility ultimately falls on the engineer designing the system.
Sort of off topic yet equally on topic but has anyone seen anything like this out there?
"If experience was always the only factor, how would we get to the moon?"
Expansion loop problems are solved by formulation and graphs in "Piping Handbook" reprinted by Hydrocarbon Processing, 1968 under the Section called "Piping Design Method Beats Computer" by M.S. Haque. This section is very good for the estimation of expansion loops, considers several type of loops and I believe you still need to verify the result by a pipe analysis program for final.
There is another section called "A simplified Computer Program for Pipe Expansion Loop Design" by W.W. Shull and G. N. Bogel that gives a print of Fortran IV program.
This book gives a lot of practical information for the design issues of piping and plant and 144 pages in total.
I do not know if there is still copyright of this book. Thus I can not leave the scanned copy of the related section here now. In case someone clarify the copyright issue with Gulf Publishing Company and if they allow me to leave the scanned pages of these two sections here, so I will.
I guess that you may be able to find this book in university or state libraries.
I just read this thread and based on my experience there is an omission in the discussion of the function of expansion loops that is almost equally important as thermal expansion. This function is to take care of events that can cause violent movements of the steam line. I have witnessed two such events where the Powerhouse made some error in our 650@750F steam distribution system, for lack of a better term, that caused a surge. These events caused every relief valve at the PRVs' on this system to lift and reseat several times. This event caused the inside elbows of the expansion loops to come together along with breaking a few hangers including the one on the outside of this loop. I don't know what would have happened if the loops hadn't been in place to take some of the line movement. None of the mechanical engineers believed this could happen without completely wrecking the loops.
I witnessed the first such event as I was leaving a control room where the sidewalk went under one of affected loops during my first month on the job. The elbows hit on about the third time I heard the local relief valves lift. The coming together was enough to leave witness marks in the insulation on the outside of the elbows.
I never heard what caused the problem as the investigation was kinda hush, hush with a lot CMA. There was no freedom of information in those days. Fortunately this line was fabricated with 100% RT and the welds held.
The hydrocarbon handbook series is awesome and I have been looking for all of the books. They are very hard to locate. I only have the piping and foundation design books. If anyone has any leads where to find the other books, I'd sure appreciate it...
