accounting for thermal expansion in this shape
accounting for thermal expansion in this shape
(OP)
There's decent formulas and rules of the thumb about for using 90° bends to absorb thermal expansion in pipelines.
How to account for this shape:

The pipeline follows the parapet on the top of a series of vessels.
the pipe is stainless steel, DN 250, to the left it's ~7m to a fixed point (pipe runs through hole in ground) to the right it's ~16m to the next semicircle like the one in the picture. there are four more similar arches long the pipeline
I need to account for 1mm/m of thermal expansion.
I want to avoid expansion joints.
Surely at these obtuse angels these arches are not as good at absorbing expansion as a 90° bend with a long enough leg would be.
My first idea is to fix the middle of the arches and middle of the long segments, using 2D gliding supports in between (stainless steel supports on PTFE). what would be the peak stress in the pipeline due to thermal expansion?
How to account for this shape:

The pipeline follows the parapet on the top of a series of vessels.
the pipe is stainless steel, DN 250, to the left it's ~7m to a fixed point (pipe runs through hole in ground) to the right it's ~16m to the next semicircle like the one in the picture. there are four more similar arches long the pipeline
I need to account for 1mm/m of thermal expansion.
I want to avoid expansion joints.
Surely at these obtuse angels these arches are not as good at absorbing expansion as a 90° bend with a long enough leg would be.
My first idea is to fix the middle of the arches and middle of the long segments, using 2D gliding supports in between (stainless steel supports on PTFE). what would be the peak stress in the pipeline due to thermal expansion?
RE: accounting for thermal expansion in this shape
Try just guiding the straight pipe. Let the center of the bow slide laterally.
RE: accounting for thermal expansion in this shape
the way I see it the distance that's approx. 13.41m in the drawing will be up to 15 mm shorter, while the circular part will be ~15mm longer. Now your comparison to the bow really makes sense!!!
Not sure how much stress this deformation would mean in my pipe and how to calculate.
RE: accounting for thermal expansion in this shape
The only problem I see is fabricating the unusual curved shape of the pipe. Miter joints are usually not allowed on high pressure pipe. Better to hot bend, but expensive. So is making all those miter joints.
RE: accounting for thermal expansion in this shape
What is your code of Record ? ASME B31.1 or B31.3 ? Something else ???
All have rules governing design and use of mitered piping bends. Not every all mitered configuration is acceptable ....
The piping codes will tell you that properly designed mitered bends often require increased wall thickness for pressure reinforcement
What is your wall thickness, design pressure, temperature and specific MOC ? More details equals better answers ...
Hopefully, the piping is at least Schedule 10S .... you are not designing with that Schedule 5S shit are you ?
I believe that your lateral expansion may be much greater than you believe, you may be surprised ...
Of course, your thermal expansion will "bow" outward from the center of the semicircle. Competently engineered pipe supports should be designed for this expansion in that particular direction
You want to use "rules of thumb" offered by strangers but this could be very accurately and completely evaluated using CAESAR-II in an afternoon.
You do not want to use expansion joints and I don't want to visit the dentist .....
Good Luck
MJCronin
Sr. Process Engineer
RE: accounting for thermal expansion in this shape
If these are sch10 there is no reason not to cold bend them.
Even for 250 this isn't that tight of a bend to worry about.
I would be tempted to think about the fixed points as midway along each straight section.
This lets the radius section move inward/outward also.
Shouldn't be too difficult for good software to solve.
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P.E. Metallurgy, consulting work welcomed
RE: accounting for thermal expansion in this shape
to my best knowledge, miter joints at least up to 22.5° are allowed.
Wall thickness 5mm, design pressure 10 bar (testing pressure), temperature 40°C
I calculated axial expansion from -20°C to 40°C at 0.96 mm/m
The comment re. CAESAR-II is noted and probably correct. Just nothing I can do about right now. I'm not wiling to discuss office politics or our relationship to our client and likely contractors here.
ETA: I measured the radius bending of the arch, 7m
RE: accounting for thermal expansion in this shape
MJC don't get excited. He just wants a bit of configuration advice.
Isn't it past time for the little white one?
RE: accounting for thermal expansion in this shape
Rather than think climate change and the corona virus as science, think of it as the wrath of God. Feel any better?
-Dik
RE: accounting for thermal expansion in this shape
Dear Martin,
- Suggest you make available the subject code EN 13480 Part 3: Design and calculation..
- the code allows single miter joints less than 22.5° and more than 22.5° also.. but the allowable internal pressure formula changes..
If the single mitre bend with an angle θ not greater than 22,5 ° , the maximum allowable internal pressure, pa, is calculated in accordance with 6.3.4.
If the single mitre bend with an angle θ is greater than 22,5 ° , the maximum allowable internal pressure, pa, shall
be calculated from equation (6.3.5-1),( which is more stringent )..
I am not sure for that i got the full picture but i would prefer fixed supports at middle of the arches, sliding supports at the mid of the straight portions , and sliding supports at both directions at 75 degr. bends..
You may post the full piping sketch together with more data , to get better responds..
Good luck..
RE: accounting for thermal expansion in this shape
RE: accounting for thermal expansion in this shape
It is 13.4m across, but that isn't a semi-circle. I estimated the size of the actual radius.
And thanks for saying that about anchors clearer than I did.
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P.E. Metallurgy, consulting work welcomed
RE: accounting for thermal expansion in this shape
RE: accounting for thermal expansion in this shape
The offset between the outermost part of the arch and the straight run is 4,86 m
If I put fixed supports in the middle of the straight run, 9 mm elongation => 3.2m
At some places situations I'm forced to put the fixed support at the end of straight run (because of branching pipes) => 18 mm elongation => 4.6 m
The formula I use above doesn't really apply, because of the different angles. But it seems to indicate that at least the long elongation cannot be absorbed by the arches => compensators are required.
Is my thinking logical?
RE: accounting for thermal expansion in this shape
What do you mean by 9 mm elongation => 3.2m
18 mm elongation => 4.6 m
I do not understand.
RE: accounting for thermal expansion in this shape
This one is a bit tricky as you have the 45 degree followed by the multiple 10-15 degree mitres or elbows?.
i generally agree with mr 44 - guide the straight bits and bend the bendy bit a bit more.
But working out stresses without ceasar or something similar??
Far from easy.
The bending on those flanges either side of the bow will also be problematic.
what's your neutral temp of installation? You only need to think about min and max temp from that neutral point. you seem to be taking 60 degrees of expansion - though I might be mistaken.
Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
RE: accounting for thermal expansion in this shape
@littleInch
10-15° elbows
Good point re. temperature - I'm thinking -20 (coldest winter plus failure of trace heating) to +40°C (operating temp.), installation will happen at 10-20°C or so.
RE: accounting for thermal expansion in this shape
A "--> U <--" bend or "expansion loop" absorbs elongation by flexing as the loose ends, as the elbows, are pushed together. Elbows are relatively rigid when compared to pipe. It is the pipe that bends, not the elbows, hence stress at elbows are increased. Basically you assume that the elbows do not bend at all and all displacement is being accommodated by a pipe's ends moving relative to each other, bending the pipe, to meet the new elbow positions. A 90°Elbow remains at 90°.
That's why LittleInch says a small angle elbow makes things worse. All you do is misaligned the pipe, create eccentric axial load that get concentrated at the most rigid component. It's the entire loop with all its offsets and pipe lengths that adds flexibility and accepts movement by trading axial stress for bending stress. Axial stiffness of pipe is large, hence large axial stresses.
Bending stiffness of pipe is small = large displacements and little stress.
RE: accounting for thermal expansion in this shape
Should have used this sketch:
As for the rest I understand and agree.
RE: accounting for thermal expansion in this shape
If you are operating and the trace heating fails, will it cause a shut down? If you remain operating, your pipe temperature will probably not drop to -20. If your pipe drops to -20, you will probably not be operating for long, so I think that operating pressure at -20 is not a valid design concern. Check operating pressure with thermal from +20 to 40 and again for non-operating 0 pressure from +20 to -20.
RE: accounting for thermal expansion in this shape
If you have four of these in a row as you state then they might end up finding the weakest link and concentrating all the expansion into one location.
But for sure I would only be looking at 30 degrees of expansion or contraction, not 60.
Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
RE: accounting for thermal expansion in this shape
RE: accounting for thermal expansion in this shape
The pipe is redundant, 90+% of the time it will just sit and be filled with water. In addition to the control of the trace heating, each segment of pipe gets it's own temperature guard TA L.
My thinking right now is to
- only consider +20 to +40° in elongation,
- +20 to 0 as contraction
- make clear to the client that there is a risk of damage to the pipe if the trace heating fails in severe winter while the pipe is not in operation
As for the pipe supports, 1 fixed between to tanks arches (in the middle if possible, near where I'm constrained if not), other supports as gliders.
Thanks for the many helpful pointers!