Dear All,

Greetings!

I'm new to CAESAR II and currently working on piping stress analysis inside steel plant. I have few queries regarding fabric expansion joints. The Pipe size is 1900mm and the client doesn't want any load on the equipment. Can some one suggest me on the stiffness part and pressure thrust force at the expansion joint location?

Suggestions are appreciated.

Regards,
S

For fabric expansion joints, the stiffness and loads are so low as to effectively be 0. Piping movements must be controlled so as not to exceed allowable.

Thank you micheal. Since the stiffness is zero, do we still need to consider the thrust force at the expansion joint connection?

So long as the fabric stiffness is much lower than the pipe stiffness, no.

Thank you for your reply Michael.

The equipment and pipe anchors may still have to withstand the pressure thrust if the pressure is not zero even if the axial stiffness of the joint is small. But since it's a fabric EJ, I'm guessing the pressure is insignificant.

Yes, I agree with Faizal. There is no relationship between expansion joint stiffness and pressure thrust. Pressure thrust is area x internal pressure. The pressure thrust is always there in piping system, it gets nullified in rigid piping but if we introduce flexible (axial flexible) element in piping system, we get effect of pressure thrust on elbows/tees.

Whether or not there exist a pressure thrust from the expansion joint to the piping is strictly a function of the design of the expansion joint.

Most metallic expansion joints will supply some thrust, and some designs will reduce this.

Most flexible expansion joints will not supply a meaningful load onto piping and equipment, so long as you're operating within the expansion joint's operating limits.

I believe you would be incorrect to assert that they will always impart a thrust as it's not out of the realm of reason for a design to have an effectively negative Poisson ratio and actually impart tension onto the piping connections; this is precisely how each of the muscles in your body work.

If by "the design of the expansion joint" you're talking about "pressure balanced" vs. simple untied bellows, then yeah it will make a difference on whether or not the anchors will have to withstand the pressure thrust.

Well, to my knowledge, there's no such thing as a pressure balanced fabric expansion joint, but I can envision a braided hose design whose inner lining is designed to expand due to pressure, and thus provide a tension.

Going back to a simple untied fabric expansion joint, to my understanding if the axial stiffness of the joint is let's say zero, the pressure thrust load on the nozzle is zero. But the pressure thrust load on the anchors upstream and downstream of the joint is not zero, unless the pressure is also zero.

And to add to that, I'm only saying the pressure thrust load on the nozzle being zero because I'm considering the pressure on the convolution of the joint does not get transmitted to the nozzle since the wall is too flexible.

This is a test post

There is no difference if the expansion joint is metal, fabric, rubber or what ever material. Same basic principles apply. There is pressure thrust and there is spring force. The rest is a question of dimensions, pressure, material and expansion joint ancillaries. If the joint is restraint type then the pressure thrust works the same as if there is no expansion joint.

If the unit is unrestrained then the best explanation how the pressure thrust works is in EJMA 9 or 10 Appendix J Example 6. Basically the main anchor sees the full pressure thrust, which is larger than the one calculated pipe/duct inside cross section x pressure. Nozzle sees pressure thrust (bellows effective area - pipe inside area) * pressure.

Spring rate on fabric expansion joint is about 0. Full thrust force can be substantial even if the pressure is low as the cross section area can be large. Not difficult to find a unit that is 10 m x 6 m. Be free to calculate this on 10kPa pressure (32.8' x 19.7', 1.45 psi)

What is the effective area of the joint is not easily available but it will be larger than the inside area of the pipe/duct. Suppliers should be able to give some estimate. Normally these designs are not that critical so I would simply make a good estimate. Google helps here. Search words "fabric expansion joint image" and you get an idea. Note that all of these are without pressure so the belt is not bulged out!

Pressure thrust is poorly understood in general. As I design expansion joints (and supply design programs for them) I see constantly wrong designs because this issue. Mainly by pipe designers and some by manufacturers. Some result in equipment failures and sometimes people die.

Some clarifications:

CAESAR operation:
1. CAESAR calculates pressure thrust as Effective ID squared * PI/4 * pressure.
2. CAESAR applies this load in both directions, axially.
3. (And while not touched upon it above) CAESAR does not calculate thermal expansion for expansion joints.
4. The stiffness values dictate how the two nodes are permitted to move and rotate with respect to each other.

Physics theory vs. physics application:
We have inconsistent terminology and competing ideas that do not make sense when mixed together, and I think we're pouring gasoline onto the fire.

Take your example. 32.8' x 19.7' @ 1.45 psi. Let's put it in orbit around the earth. Let's put a weightless blind on either end of it and pressure it up.

You're telling us that the expansion joint is exerting 135,000 lbs of force out of either end of it, just as a function of pressure, meaning 130 kips of tension in the fabric.

Without pressure, I could otherwise hang a 135,000 lb weight from one end of it (back on Earth) while in the vertical and it'll be the same exact thing.

And if we assume the material is 1/8" thick, for a total area of about 1.1 square inches, the stresses in the axial is some 120 ksi.

The ultimate tensile strength of titanium is 63 ksi.

This line of reasoning simply does not make sense.

All unrestrained expansion joints have to have full anchors on both sides of the joint (plus guides). Anchors can be concrete blocks, steel structures or equipment like pumps or vessels. Irrespective what they are those anchors must be designed for the full pressure thrust, which is calculated effective area x pressure. Force can be high/very high... Pipe/duct can be square, rectangular, round or any other shape and the force calculation remains the same. Because of the high forces unrestrained expansion joints should be avoided where possible. Often it is simply not possible to have sufficiently strong anchors.

Element that can be metal, fabric, rubber or what ever other material is not there to take the pressure thrust force. It will fail. Unfortunately I cannot remember anymore how to include images on this forum to show what happens when the anchors fail.

CAESAR II may not calculate expansion of the element but there is no reason to do so as the expansion is simply compressing the element a bit (in hot case). When doing the modelling correctly program does calculate expansion/contraction on rods and center pipe.

Element stiffness values have impact but especially in axial direction element will compress or extend easily as the spring rates are low compared to pipe/duct material. Rotation is an other low force case. Lateral force can be low or high depending on the design.

Here is a short explanation of the pressure thrust:
https://www.youtube.com/watch?v=deSF1MFLCMM

Pipe designers tend to worry more about the bellows spring rates that the pressure thrust. Most of the time the spring force is small compares to the pressure thrust where unrestraint units are used. In very many cases the bellows element stresses are well over the yield point. As a result in a case like in the video when the pipe heats up there is a spring force on the tank nozzles pushing the nozzles but when the pipe cools down the force changes direction because the element is past the elastic range. This is not considered in calculations.

Better to spend time to figure out the pressure thrust than the spring force.

There is a lot of videos and material on the internet on expansion joints. Very little actual training. One EJMA member has on line courses and Becht corporation has done quite a bit of training. I have 2 to 3 day onsite training course but more than that I do not know. Good reading material is EJMA standard available from www.ejma.org. This is absolute minimum reading before any expansion joint is used by any pipe designer.

Jouku's reasoning is sound. The Pressure Thrust (P*A) exists on either side of the fabric joint. The inside "diameter" area force goes to the equipment or pipe/ducting on each side and must be restrained by those items. For example on a HRU (large Heat Recovery Unit) the vendor has physical stops (round not slotted holes) at one of the foundation column lines on either side of the fabric joint location.

If you put a fabric joint on the inlet to the HRU, then the pipe/duct must consider this thrust force in the pipe/duct system. The Flange will see the net bellows area thrust ("convolution" area) distributed around the flange face.

If the stress engineer misses or does not understand this, the system may have survived without much blow apart deflections if the items on either side of the fabric joint were heavy and the frictional forces limited the perceived "perpetual motion machine" deflections.

Thanks to Michael for the explanation on adding files. Hopefully the images show.

Just to show some cases what can happen. Worst case I know is Fixborough incident. There are couple reasons given why it happened but most probably line failed because pressure thrust was not understood. I have investigated one case where people died. Rest of the cases I have been asked to look at have been equipment and line failures.

One image shows NB150/NB200 water line where anchor failed. Bellows element is extended and basically destroyed. Pressure is low enough that the element did not fail. Second image is NB600 air line with under 6 bar pressure. That concrete block is partially buried into the ground. It was pushed out of position by the pressure thrust. It was stopped only when the externally pressurized expansion unit reached its maximum movement/end stop.

On nearby installation far worse situation. Anchors were totally destroyed. I recommend to the owner to barricade substantial area for safety reasons until the complete line is repaired. Line was couple kilometers long.

One image shows a diesel line where the line guiding was insufficient. Originally line failed in a similar manner during an installation pressure test. Guiding was improved but it failed again when there was a "water" hammer on rapid valve closure.

Heavily reinforced unit id NB 500 feed water hinge unit with 100 bar pressure. High pressure thrust at about 2290 kN or 514590 lb.

These are not fabric compensators but same rules and problems apply.

Please regard the diagrams I've posted.

Think about the ramifications of what happens when convolutions become larger in diameter relative to inlet and outlet. Keep the inlet and outlet finite while the convolutions diverge to infinity. Force also diverges to infinity.

Think about the ramifications of shrinking the inlet and outlet into non-existence, but you maintain an object that's physically connected to the pipe and is allowed to pressurize (via some side port or what have you). The force is still finite, despite the fact that the cross sectional area of the inlet/outlet converge to 0.

While we can tie thrust to pressure times area (or modified area), it is only a tool we use to emulate reality. Yes, manufacturers tend to use this as the standard to design to, particularly for metal expansion joints.

My contention is this logic breaks down for fabric expansion joints. More to follow soon...

Attached you'll find some more images. Imagine a situation your "fabric expansion joint" is more akin to a flexible rubber hose. And suppose it inflates like a rubber balloon. We could likely all agree that when it inflates, the ends could expand outwards, and thus would exert a force on whatever is on the ends of it.

Let's not concern ourselves just yet to commiserate what the forces might be on the ends.

Let's instead take that same flexible hose/expansion joint and attach a sleeve to it. Our sleeve consists of braided fibers, which surround the piece in a helical fashion. My image shows 2 such fibers that are parallel, but let's say we have many more fibers, and half run perpendicular to this helix, i.e. in the opposite direction. Unlike our flexible rubber material, let's assume the fibers are inextensible. As the "balloon" inflates, it causes the fibers to go into tension, and they in turn cause the entire unit to shorten - not elongate.

Are you going to say that the net resultant force on your piping elements is outwards from the center of the expansion joint, or inwards?

I have absolutely no idea what above means. Pressure doesn't know if the element is steel or fabric so the pressure thrust is there in both cases.

Here is some additional info:
http://www.hyspan.com/pdfs/PressureThrustNotes.pdf
Fabric expansion joint has basically one convolution and it has very low axial spring rate. "Convolution" height can be high where the belt has to be protected against the heat or relatively low where such is not needed.

Pressure thrust is not number of convolutions x effective area x pressure like some claim it to be. It doesn't matter if there is one or 5 convolutions. Pressure thrust is still the same. Fabric joint has one "convolution" and metal most of the time multiple, rubber has one...

CAESAR II doesn't ask expansion joint element material. If the material would be required to calculate the pressure thrust it would be one input variable.

There are few things here.

Yes.Fabric expansion joint bulges outwards limited by how much there is free fabric. More it bulges larger the effective area and therefore higher pressure thrust. Metal expansion joint works similar. It is just more rigid and doesn't bulge so much especially round. If you have rectangular or square the bulging can be a lot if the design is not correct.

Flex hose with braiding is restraint design. Braiding holds the axial force and therefore works like solid pipe. Rubber expansion joints have internal fibers. Steel, or some other material. They increase the pressure capacity and axial stiffness a bit. Pressure thrust issue remains exactly the same as on metal element.

Force balance in the element is shown in the PDF file in the previous post. Stresses and therefore forces in the element material are key design issue for expansion joint designer. Attached is an explanation how the formulas work. Paper is for EJMA 6. Latest is EJMA 10. Basics are still the same. Details of the formula have changed. Author is in a way "father" of EJMA standard. Element stresses are limited to allowable stress of the material with some correction factors - pls see EJMA or ASME VIII Div 1 App 26.

Where the expansion joint is standard design and the pressure inside is higher than outside the pressure thrust is trying to push the unit longer. If the pressure is higher outside the force direction changes and unit wants to become shorter. If the expansion joint is special externally pressurized design the element gets shorter but the assembly extends if the pressure inside the pipe is higher than outside.

Be free to do some experiments using CAESAR II. It is not expansion joint design program (like the software I have developed and supply) but by putting anchors and looking loads on them or without anchors look into the end movements. COADE consulted long time ago Robert (Bob) K. Broyles and as a result if the program is used correctly the results are good.

Thanks for the responses. I suppose the only way we can correct our errors in thinking is by presenting our thoughts for critique...

To summarize my misgivings from above, for bellows, F=P*A' where A' is approximately based on the average of the convolutions' largest inner diameter and the pipes' inner diameter, which may be approximately that of pipe's inner diameter.

We also must be mindful whether our fabric expansion joint is actually under pressure, or if we have some arbitrary design point for selection of wall thickness. I.E. A process or project engineer doesn't know the ramifications of what they're asking for.

One final concern (that probably isn't one), regarding the modeling of fabric expansion joints.

The only way it can have 0 stiffness is if it is installed in compression, and the supports prevent it from extending beyond neutral.

This is also the only way F=PA can apply to your supports. Once your fabric expansion joint becomes taut, whether it's due to pressure or temperature, it is absorbing part of the load that would otherwise be transmitting to the supports in the 0 stiffness scenario.

Understandably, your position as provider for the fabric expansion joint is that you would design for it to never be in tension, and therefore, it should be modeled as 0 stiffness.

However, such an expansion joint installed in neither compression nor tension will have no choice to see tension as a result of pressure, and the balance is stored between the supports and the joint at ratio equivalent to that of the ratio of their stiffnesses. But, you could also argue that even in tension, the stiffness of an expansion joint is so low that the lion's share ends up in the supports anyways...

All expansion joints are difficult. I have been in this business well over 20 years, worked for a manufacturer (metal/fabric), head of design, software developer, international consultant, training... and there is always new items to learn. Today designed 5 units with drawings for a big tender.

Effective diameter definition as used in specifications is given in EJMA, ASME VIII Div 1 App 26 and EN14917. You can find it there.

Expansion joint design and their use in stress analysis is not for those who think that the result is accurate to 8 decimals. For metal expansion joints spring rates given have easily tolerance of +-30%. What spring rate to use for fabric type is estimation/thump suck. Spring rate in this case has so minor impact that it doesn't matter. Fabric must not be stretched/loaded by pipe movement - maybe a bit. If too much it will tear.

I recently visited a plant where they had expansion joint related problems. One was fabric expansion joint. It keeps failing. It was not difficult to find the reasons. Too tight when cold. Even small duct movement would tear the belt. Bigger problem was that during the shutdown water gets to the insulation material of the expansion joint. On start up they let over 400 C air into the duct. Water changes to steam and local pressure increase destroys the belt.

EJMA has extensive explanations and sample calculations how to calculate anchor loads. Basically the load is a sum of the spring load and pressure thrust. Forces are vectors so directions need to be considered. For anchor design spring loads are small compared to pressure thrust.

There is one special type metal expansion joint that works slightly different. This is thick wall expansion joints, see ASME VIII Div 1 App 5. Those joints are very stiff so in low pressure cases spring force can be meaningful. But those thick elements compress/extend minimal so although spring rate is high the force can still be small. These thick units are used in heat exchangers. There is old manual calculation method for which I have software. Same is included also into PV Elite. However recommended method is given in latest TEMA. It is based on FEA.