Hello,

We are currently analyzing a piping system on the rack that has been there for almost 20 years. The rack is improperly designed and settlement was not previously considered but now the settlement appeared and this leaves the piping in a complicated state.

Now, due to the different settlement of each beams along the rack, the piping react and now shows that some supports still rest on the beam and some does not, leaving some portions of the piping unsupported. The client asked us to calculate its current stress and give recommendations on how to improve the piping or if needed we can recommend the piping to be replaced.

We have calculated the current elevation of the pipe with respect to each beam and compared it to the original elevation which can be seen on the isometrics. The difference of the current and the original elevation are taken to be its settlement value (meaning the pipe deflected by that much since it was installed).

We want to model its reflecting it current state, but caesar can only put displacements when there is a restraint. Since we wanted to created its profile or deflected shape, the part of the piping that still sits on the beam but has deflected is much easier since we will just input displacement for that particular restraint. For that part of the piping that deflects but is floating(currently unsupported), this leaves us puzzled on how to perform this.

As for now, we created 2 cases.

One case is we modeled the pipe with no imposed displacement and modeled the supports with or without gaps respectively (gaps are measured based on actual conditions on site). This is to check the current stresses of the piping especially on sustained case, considering some part of the piping unsupported.

Second case is that we modeled the piping with all support resting(no gaps) but placed an imposed displacement on each restraint to represent the settlement or deflection of the rack/piping. For this case, we take into account that we want the piping to be fully supported even if some parts are deflected, that is placing additional steel to fill the gaps between the piping and the beam. But by doing this analysis approach, even if we put some displacement on the restraint that has no gaps, the result shows that some support are not taking load during operation; case W+D1+P1+T1, D1 is our settlement.

Please take note that the plant is currently in operation and the measured gaps are taken also during plant operation.


Can anyone help or comments if our approach is correct.

A have an attached for additional info. It shows the original elevation and current pipe's elevation. The delta "y" are the imposed displacement/settlement we calculated with regards to the difference between the original and current elevation.

I was following you until you got into your 2 cases. One "quick" question...

Are you using CNodes to define your settlement?

You can enter a +Y restraint at, say, Node 40 to model a resting support. I suggest you include a CNode (connecting node) for that restraint [we'll use Node 41 here] and then define your settlement at node 41 (not 40).

If you replace a +Y restraint at a node with a displacement, that previous nonlinear (+Y) support turns into a linear (Y) "support".

Your approach matches what I would perform as my first step, as well. Offhandedly, some ideas as to what your problem might be:

• If you look at the classic cantilever beam diagram, you'll note that the length along the horizontal axis remains constant. I.E. curvature of the beam is assumed negligible. CAESAR operates on the same principle, and you might be outside of what CAESAR can simulate due to the butterfly effect.
• Depending on how high the real world stresses are, you may have exceeded the yield stress of the pipe and now have permanently deflected piping, which may react differently. These above-yield stresses could have occurred in any case - sustained, operating, or occasional. And that occasional case might have been wind, earthquake, bypass of a safety device, an operator driving a forklift into it, etc. You won't necessarily know.

I believe the best way to estimate stresses would be to inspect the pipe in two states, sustained and operating, and obtain displacements X/Y/Z, and as best as you are able, rotations X/Y/Z.

Ignore the supports - apply displacements and rotations alone in the sustained and operating cases, but otherwise treat it as a normal analysis in terms of load case setup.

However, I understand this information may not be available, and there may be safety concerns with measuring the pipe in operation.

Hi Dave, yes I am using Cnode and the procedure is the same as what you state. Restraint at node 40 and cnode to node 41.

We are doing this imposed displacement to forcefully bend the piping as to created what we have seen on the site during operation, that the piping is not straight, and then check the stresses after that.

As Caesar has no way of inputting displacement without a restraint, we are having a problem doing this. It is easy if all supports are still resting after settlement; we can input directly the imposed displacement(calculated settlement) then check the result if the displacement during operating case is the same as the calculated settlement, then we can check stresses. But since some support location are not acting on the beam, we are having difficulties modeling the existing piping.

Hi Michael,

We are only able to obtain/calculate displacement during operation, displacement are obtained only at every support location. Plotting it on the Caesar model is difficult since some portions are currently not supported, and we cannot input displacement without a restraint.

The piping are low temp about maximum temp of 60°C, ambient temp at 21°C. so the main concern are stresses during sustained, hot-sustained.

On my second case, we only did this because we wanted the end result of our analysis to utilize all the existing beam to redistribute the load.

Our proposal with the current state of the piping (operating), considering all code stresses has been satisfied, the gaps between the beam and the piping will be filled with a steel in order for the pipe to be supported and to prevent any further deflection (all beams are now taking load). So in the operating case (W1+P1+T1+D1), +Y supports should be taking load, but when we model it on our analysis it shows that some of it have zero loads.

Note that the measurements (imposed displacements) are taken during operation.

Another question, if we are analyzing an piping with an operating temp of 60°C and an ambient temp of 21°C, will it be the same if the parameters are reversed? Example the ambient becomes 60°C and the operating temp be 21°C (same temperature difference).


Just a thought of considering to transpose our current operating case to sustained case. This is to consider all the support sitting on the beam during operation after the gaps has been filled with additional steel.

All measurement taken during operating case will be modeled in sustained case including imposed displacement

Ambient temp 60°C
(Sus) W1+P1+D1
(Ope) W1+P1+D1+T1 (with operaing temp of 21°C)

Dear Friends,
Details provided of pipe at support 1: Pipe settlement in Y = - 391 mm in vertically downward direction and further the settlement of the support specified in Y =- 585 mm.

Isn't this a case of large deformation?

In this condition as the pipe is unsupported it would have definitely crossed the elastic limit due to large stresses in sustained case (This represents a case of Geometric non-linearity due to lack of supporting effort due to support settlement).

All beam models in Caesar II as per my understanding are based on small deformation approach where stresses in sustained are limited to within allowable stress limit of the material in sustained case and are evaluated based on original pipe cross-section and section modulus as entered by user in Caesar II input.

In Caesar II as per existing details the user would have modeled support 1 as Rigid +Y support with CNODE having displacement Dy=-391 mm and Gap =175 mm but will Caesar II be able to predict the stresses in pipe due to the support settlement effect as if there is any plastic deformation the actual stresses would change based on the change in original cross-section and section modulus of the pipe and you may not be able to predict the output as desired.

I would request Mr.Dave Diehl to suggest as to what approach could be used to assess the state of stress in such cases..

Best Regards
Benoy Abraham

Yes, these are very large displacements. But if the pipe yields (at more than one point) you would not have the gaps, the pipe would drop along with the supports. Your CAESAR II (elastic) model would not show this yield but you may develop stresses far above the basic allowed stress.

You can define displacement at a point without defining a restraint - those are two separate boundary conditions.

I am unsure of your use of the gap. I would define a +Y restraint with a CNode but no gap and then displace the CNode the full settlement amount. The elastic pipe response will show the pipe disengaged from the settled support or resting on the settled support.

Dear Mr. Dave,

Regarding the use of the gap, I would like to clarify that I have only shared what i presume leo would have modeled in Caesar II based on details shared in the attachment :
The pipe as per the attachment is supported on 5 support beams. I presume that details of settlement of support wrt pipe current position is what has been modeled as the gap i.e. if we refer case of support 1
Support 1:
Pipe current position wrt Original Elevation: 391 mm below i.e. Y=-391 mm and the Support current position wrt Pipe current position: 175 mm below. This 175 mm is what i referred to as the gap that could have been modeled

Hence, modeling this support as Rigid +Y with Dy=-391 mm and Gap = 175 mm seems to be the right boundary conditions and so on the other remaining 4 supports also can be simulated.

The above would simulate the condition that the pipe is pulled down at this support location 1 by 391 mm and any further pipe movement in -ve Y will not be supported till 175 mm gap is closed.

Pipe is subjected to pulling force in -ve Y equivalent to that produced by 391 mm and further as the support 1 is not active till pipe further moves by 175 mm in -ve Y from current position shown in attachment, we can approximate support 2 as a fixed end of a cantilever end and bending stresses can be evaluated to determine effect of forced displacement in Y.

Reason: Support 2 and 4 are resting in pipe current position and supporting the pipe and hence, will offer resistance to pipe bending.

Based on, Deflection of cantilever beam subjected to UDL, Dy = wL^4/8EI

Force developed in Y due to forced displacement of 391 mm in -ve Y is P = 391 *(8EI/L^3)

and corresponding bending stress, Mb =PL/Z

Where L is the unsupported span of pipe due to settlement of support 1 till support 2

This bending stress then could be compared with allowable stress of material to determine the extent of damage.

However, my point was related to change in geometric (cross-sectional area, I, Z etc) and material properties of the pipe (E, G etc.) when subjected to such large deflections. In such cases direct interpretation of results may not be correct based on linear elastic models.

Best Regards

Benoy Abraham

Hello sirs,

Yes, we modeled the piping before same as to what Benoy have stated(having displacement -391mm and 175 gap on support). We did this on every beam, placing zero gaps on the ones that are still resting. However, we are not convinced with the result. We expect to see -391mm on the operating displacement result (w1+P1+T1+D1), but it shows a different dispalcement.

We also tried to model the piping with all support on beam resting and having imposed displacement on each restraint (zero gaps). Upon doing this model the pipe reacts and some support lifted, while some support produced a load of 96kN too great for a 16" pipe.



What we really want is to create the model the same as current operating condition of the piping (same with the sketch I made), with the piping slightly bent (due to the effect of the settlement and the pipe's reaction to it), with the pipe deflected and support resting as seen on site. We want to start the analysis from there.

Because it is difficult to model and reflect the measured/calculated displacement same as with the operating case result, I asked in my previous post if anyone have done modeling the operating piping in sustained case while switching the ambient with the operating temp of the pipe (considering ope temp only). Maybe someone can give some thought if the result would be similar since the temperature difference is same only the reaction would be reversed. In line with this, since all measurements are taken/calculated in the operating conditon, I am also considering modeling the operating piping in the sustained case (W1+P1+D1, Ambient temp 60°C), read/correct the displacement to make it same as what we have measured/calculated, check stresses in Sustained and restraint loads. After that consider the shutdown case with piping ope temp at 21°C. Any thoughts on this appproach?

No answers here just a few points...
I guess I introduced a second way to model a resting support that settles over time.
The original approach here simply put a gap on the +Y restraint while I suggested defining the restraint settlement as a -Y displacement for a CNode on the +Y restraint. Both approaches should give the same results.
But I question the gap you provide. The gap should be referencing the neutral, unloaded position of the pipe. (Here, I assume you are looking at a pipe in operation that sags 391 mm below this neutral position while the resting support is 175 mm below the pipe.) If you run an operating case, you should see that pipe drop the 391 mm and not close the gap. You should not be defining 391 mm as an imposed Y displacement on the pipe - that 391 mm is an observed result,not input.
A second point - CAESAR II has no means for automatically addressing pipe yield. I guess you could go through the academic exercise of building "plastic hinges" in your model or perhaps entering a few, well-placed cut shorts/cut longs but I don't think that will give you numbers you can use.

Yes Dave, I got your point thank you very much.

As for the imposed displacement in Caesar ii, please correct me if I am wrong, every imposed displacement that we put in the model will be equivalent for an additional force? Similar to the equation of deflection=FL/AE?

Almost.
No load will be generated if I specify an imposed displacement that matches the equilibrium position of the other components of a load case.

Thank you Dave.