Pressure Thrust due to Expansion Bellow

This is in relation to Latest topic discussed on same subject.
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In EJMA std manual calculation for Nozzle loads are given. e.g.C-1.3.2
This is for axial expansion joint without tie rods.
For calculating Forces and moments at Flange it has considered the actual effective area.
i.e. Nozzle inside area is deducted from Bellow effective area.
This results in reduced axial forces at flange as area gets reduced. Caesar calculates the forces
with full effective area of expansion joint which results in higher axial forces.
I am not sure which one is better and realistic approach? Pls. advice.

I believe the issue here is the location of the thrust loads in the CAESAR II model. The program applies a load to either end of the bellows element equal to the the effective area of the bellows times the bellows pressure. The effective area is computed from the input value given for the effective inside diameter of the bellows. This effective area is greater than the inside area of the pipe but less than the maximum area of the bellows convolution.

But locating this total pressure load at either end of the bellows may not be appropriate given your piping layout. To determine where these loads truly act, I imagine I'm inside the bellows looking upstream and downstream the pipe. Whatever surface I see is the surface on which the pressure load is acting. Now part of that load is acting on the last bellows convolution and is equal to the pressure times the differential area between the bellows effective area and the pipe inside area. The remaining pressure thrust load (pressure times inside area of pipe) is acting on the surface of the next elbow or beyond a nozzle. Our model is pretty good if the load is on an elbow since in most cases it doesn't matter whether you push or pull a straight run of pipe as the structural response will be the same. But there would be issues if you are looking though a nozzle for then this pressure thrust component may not load the pipe. It would be loading the back of the pump or the back of the vessel or some other "anchored" piece of equipment where the load path does not have this thrust load come back to the piping.

So, when a "supported" nozzle is in line with an untied bellows, I would place smaller tension loads on either side of the bellows and a larger, unbalanced, pressure thrust load on the elbow on the other side. I trust there will be some anchor between the bellows and that elbow but this is a design issue rather than a modelling issue.

Let me know if I missed your point.

I agree with the prior discussions as far at the actual locations of these pressure thrust loads, but suggest that the engineer must also keep in mind the intent of what he/she is attempting to simulate. Is it actual pipe stresses or resulting loads on equipment?

In the case of pump nozzle loads, the limit on nozzle loads in API 610 is indented to maintain the machines alignment, and is not based on pump casing stress. This limits any misalignment between the pump casing and the driver or gearbox.

If you then consider the pump casing as a totally rigid body it does not matter where the pressure thrust force is applied, either at the unrestrained expansion joint or split between the expansion joint and rear of the pump housing. Both will result in the same effect on machine misalignment.

When considering nozzle loads on rotating I would always recommend:
1) With an unrestrained bellows in the system, simply applying the pressure thrust force (based on the effective area the expansion joint x pressure) at the expansion joint connections.
2) Without an unrestrained bellows in the system, the pressure thrust forces are contained within the pressure containing metal (pipe and pump casing) and will not be seen externally, therefore no external loads need be included in the model.

I hope this as helped on the understanding of this issue