Dear Mr. Ay,

I am currently working at a thick wall high pressure piping system – 8” NPS (219 mm OD / 62 mm wall thk), 10” NPS (273 mm OD / 52 mm wall thk), 12” NPS (324 mm OD / 62 mm wall thk); 360 … 600 bar internal gage pressure; 10000#, 15000# pressure rating; low carbon steel (API 5L X60).

The project specification regarding Piping Stress Analysis requires the piping design&analysis to be accomplished based on ASME Code for Process Pressure Piping B 31.3 and the computer stress analysis to be performed using Caesar II software.

Obviously, the piping stress analysis for the system under discussion has to be developed based on ASME Code B 31.3 / Chapter IX – High Pressure Piping.
The piping material consists of thick wall cylindrical structural components. The k = OD/ID ratio (i.e. Outside Pipe Diameter / Inside Pipe Diameter) values are situated around 1.61 … 1.62, and are significantly higher than the limit/reference of 1.1 … 1.2 that separates shell structures of thick walled revolution bodies.

Because it’s first time when I deal with such a piping system, I’ve performed a few preliminary tests consisting in computer analysis of typical simple problems that involved thick walled high pressure pipe behavior, such as double anchored plane “L” and spatial “double L” loop pipes.
The models have been built and analyzed using both the beam theory approach (i.e. piping stress analysis programs – Caesar II, Pipe Plus) and the general finite element method (three-dimensional model – Ansys Software Package).

My big problem is that comparing the results (especially the ANCHOR REACTION FORCES AND MOMENTS), I’ve seen significant discrepancies between the above approaches. Moreover, Caesar II computer analysis appears to be a LESS CONSERVATIVE APPROACH.

Detailing my comments, it should be noted that for the gravitational (weight) and thermal loadings, beam theory results fit the finite element solution in a satisfactory manner. But when we speak about the PRESSURE LOADING CIRCUMSTANCES, the results are highly different. In fact, the anchor reaction force&moment values obtained by the three-dimensional detailed analysis (Ansys – I’ll name them “Reference Values”), are situated BETWEEN the corresponding values assessed by the beam theory approach, so that Caesar II anchor reaction values are lower than the “Reference Values” (20 … 40 % percentage difference), while Pipe Plus anchor reaction values are higher than the “Reference Values” (20 … 50 % percentage difference).

My analyses revealed that the main cause of the discrepancies between Caesar II results and the detailed three-dimensional finite element solution, is THE CURVE PIPE / ELBOW BEHAVIOR MODEL. For a piping system composed by straight pipes only, Caesar II results fit the corresponding finite element solution in a satisfactory manner. But when the elbows are provided, Caesar II beam theory approach doesn’t match any more the finite element method “Reference Values”.

I have to specify that Caesar II analyses (4.40 and 4.50 versions) have been performed using as ACTIVE the “Bourdon Effect – Translation & Rotation” option. The results obtained using the other possible options (i.e. “No Bourdon Effect” and “Bourdon Effect – Translation Only”) conducted to higher differences between the “Reference Values” and Caesar II solution.

Caesar II Forum contains several topics regarding the high pressure piping stress analysis and the pressure elongation effect problem, but all the previous discussions referred to common thin wall piping systems. I’ve performed a test for this alternative and Caesar II results correspond to the finite element method “Reference Values”. But for the special case of thick wall piping systems, Caesar II results are somehow discouraging.

Now, searching within COADE Caesar II article database, I’ve found an article in Mechanical Engineering News – Volume 17 – December 1993, entitled “Estimation of Nozzle Loads Using Caesar II Software”, that contains some considerations regarding the pressured straight and curve pipe element behavior modeling.
All the formulas involving the internal pressure loading effect correspond to the THIN WALLED SHELL STRUCTURE THEORY. In my opinion, this approach COULD BE the main reason of the above discrepancies.

I am aware of the delicacy/difficulty of this problem. Unfortunately, I am not working now home and I cannot use my own books&materials to study this complex problem more carefully. In addition to the above article, I’ve found on Internet Peng’s article entitled “An Interpretation on Pressure Elongation in Piping Systems”, but again, the theory has been developed based on Thin Walled Shell Theory.


At the end of this topic, two more problems I’d like to submit related to Thick Walled High Pressure Piping stress analysis.
First subject is related to the material allowable stresses as per ASME B 31.3, Chapter IX (“High Pressure Piping”) and appendix/table K-1. Maybe I do not know enough Caesar II software, but I haven’t found any option that allows the user to “tell” to the program to compute the allowable stresses following the rules under discussion (par. K303.3.2). Certainly, user can define his own allowable stresses, but I think it would be useful to provide this tool in the future.
The second subject is related to the Pressure Stress Assessment and Checking. Paragraph K302.3.5.a (Limits of Calculated Stresses Due to Sustained Loads and Displacement Strains – Internal Pressure Stresses) stipulates a different approach than the classical method “slp = p*Di^2 / (Do^2 – Di^2)” and “shp = p*Di / (2*T)”, consisting in the pipe wall thickness checking (par. K304). Obviously, for the thick walled high pressure pipe components, Caesar II calculates accurately only the longitudinal pressure stress (slp); the hoop pressure stress classical calculation [“shp = p*Di / (2*T)”] is not valid any more and, in my opinion, depending on OD/ID ratio value, it should be amended, because, as it is well known, the maximum hoop pressure stress is developed at the inside pipe wall surface.


I would like to know your pertinent opinion regarding these subjects. Certainly, any Forum member remark or comment will be highly appreciated.


Thank you for your time,

Dorin Popescu

Senior Pipe Stress Engineer
Washington Engineers&Constructors Romania

Just to start things off, here are a few preliminary answers. I have personally never worked with high pressure piping or Chapter IX, but ...

As you noted, the results vary based on your Bourdon setting. Unfortunately you won't find any information on Bourdon pressure effects in the codes or other literature. We can't attest to how anybody else calculates Bourdon loads, but CAESAR II uses the formula first implemented in MEC-21, the original computer pipe stress program. (As an aside, Bourdon loads, which are applied as a uniform axial strain along the pipe, does not really coincide with real-life pressure loadings. See for yourself: a pressurized straight pipe running between two nozzles will put no pressure thrust load on the nozzles in real life, but Bourdon loading will put outward thrust loads on the nozzles. Bourdon is available in CAESAR II only due to their traditional inclusion in pipe stress programs.)

Typically, pressure is assumed to cause no displacements or loads on a piping system (unless you have an expansion joint). The only effect of pressure is the longitudinal pressure stress component (since this is how the piping codes direct that pressure be treated). Ansys on the other hand (I believe), assumes each pipe element is “closed ended”, and thus picks up a P*A pressure load, so there would be pressure thrust loads on the anchors (but pressure stress would be calculated incorrectly according to the piping codes).

This could be caused by the “pressure stiffening” assumption in the code - it is unlikely that Ansys honors the pressure stiffening requirements of the B31.3 code. Have you tried turning this off via the configuration file? You could also try un-checking the “bend axial shape function” in the configuration and see if that has any effect. Also, the impact of modeling pressure as a thrust load would be much more likely to show up where there are intermediate bends, than in straight pipes (since in straight pipes the thrust load at the ends of each segment would tend to cancel each other out immediately).

This article discusses many modeling nuances, several of which are activated only at the discretion of the user (rather than as default behavior). I am not aware of to what extent they are applicable to thin wall vs. thick wall pipe.

You haven’t missed anything, this is not an option in CAESAR II.

You can alter how the program computes the hoop stress via the configuration file. Options are: inside diameter, outside diameter, mean diameter, and Lame’s equation. I think the Lamé's option will give you the results that you seek.

Thank you for your prompt reply.

A few answers to your suggestions:

1. Yes, the “Base Hoop Stress On” option (set to “Lamé”) from Configuration file solved the problem regarding the maximum hoop stress computation accuracy.
However, the problem related to pressure stress checking in accordance with ASME B 31.3 par. K 302.3.5,a / K 304 still remains. The maximum equivalent stress value (or stress intensity, at the pipe wall inside surface) is assessed correctly, but the Code checking criteria refers to the pipe wall thickness checking (par. K304, formulas 34 a, b and 35 a, b).
In my opinion, in order to obey ASME B 31.3 Chapter IX philosophy, it is necessary to modify the existing longitudinal pressure stress checking approach. I think it would be more appropriate to calculate the “Maximum Allowable Code Pressure Stress” S from 35 a or b formulas (par. K304.1.2) in order to compare it with the material allowable stress from table K-1.

2. During my tests, I’ve taken also into account the “pressure stiffening” option. Enabling or disabling of this option had minor effects on the anchor reaction values (less than 2% for my models).

3. I’ve followed your suggestion and I’ve checked the “Bend Axial Shape” option impact on the results. Disabling this option caused an insignificant changing of the anchor reaction force&moment values (less than 2% for my models).

4. The detailed finite element analyses (Ansys software) have been accomplished using three-dimensional models that had been built using solid (or the so-called “brick”) elements. In other words, I’ve modeled the whole geometry of the tubular components (straight pipes + bends) enough accurately as I think (three elements distributed along the wall thickness, comparable dimensions of the brick elements along the main local directions).
Therefore I haven’t used pipe&elbow elements (or beam type elements, generally speaking) because I am aware of the involved inherent drawbacks. Under such circumstances, I suppose that the finite element models reflect suitably the actual behavior of the systems under discussion.

Well, I hope the above comments have cleared the main aspects of the problem under discussion.

Thank you for your time,

Dorin Popescu

Senior Pipe Stress Engineer
Washington Engineers&Constructors Romania

Dorin Popescu: Regards (Ansys Analysis) have you bench mark your using "FE-PIPE"?

http://www.paulin.com/

Leonard@thill.biz

Dorin,

This may be a bit off-topic, but...

Did the owner/client actually direct you to use Chapter IX? Per paragraph K300 (a),

"Applicability. This Chapter pertains to piping designated by the owner as being in High Pressure Fluid Service. Its requirements are to be applied in full to piping so designated. High pressure is considered herein to be pressure in excess of that allowed by the ASME B16.5 PN 450 (Class 2500) rating for the specified design termperature and material group. However, there are no specified pressure limitations for the application of these rules."

While reading your post, I didn't see the client requirement for using this chapter. I agree your application may fall into this category, but not unless the client requires it. You state the specifications require analysis and design based on ASME B31.3, but not specifically to Chap. IX. It is my understanding that Chap. IX is not mandatory, as it is not part of the base Code. I have fallen into this trap before and wasted many hours trying to apply this to 10,000# psig service and the client didn't require it.

This doesn't answer any of your questions, but is something else to consider.

Richard,

Your remark is justifiable.

Yes, the piping classes (agreed previously by the client) have been developed under B 31.3 Chapter IX authority.

Regards,

Dorin

So lets see...

A simplified beam analysis using simplified analysis rules (per code) yields different results then a 3 dimensional analysis... Wow, a true unsuprise.

Maybe thats why Chpt IX has different rules. Conversely CAESAR II or any other beam element program will not provide results the same as a three dimensional (FEA) model.

The main starting subject of this topic regards THE ANCHOR REACTION (FORCES and MOMENTS) VALUES quantified for the thick wall high pressure piping systems.
I believe that everybody agrees that the accuracy of these stress analysis results are very important in order to ensure a proper design of the piping layout and a corresponding safe exploitation of connected equipment (especially the sensitive rotating equipment, such as centrifugal compressors in this case).

Nobody expects to obtain identical results using the "beam theory" approach and general 3D FEA analysis method for piping systems.
I think that inherent differences REGARDING THE ANCHOR REACTION VALUES of 10...20 % can be considered acceptable for the common engineering practice.

But for the thick wall HP piping systems, the percentage differences reach 40% (for a few simple cases at least) and, moreover, Caesar results are situated BELOW the reference FEA values.
That's why it appears the Caesar II yields to less accurate and less conservative results REGARDING THE ANCHOR REACTION VALUES (the equipment nozzle load values actually).
Generally, for spatial complex piping systems, it is practically impossible to estimate the error under discussion without a detailed FEA analysis, but, unfortunately, such investigation (if can be accomplished actually) is extremely complex and expensive, and requires huge resources.

Chapter IX of B 31.3 refers mainly to the piping component design and does not contain requirements or recommendations regarding the equipment nozzle load assessment.

Regards,

Dorin Popescu

The B31 Code evaluates the sustained and expansion cases separately, giving each different allowable stresses while not addressing the combined sustained plus expansion case. Your loads are for the combined case and are a valid concern, but the methodology is less defined without a specific Code basis to follow. There are a number of switches for configuring the analysis in CAESARII. Along with the Bourdon setting, have you considered the "Use PD/4t" and "Add F/A in stresses" parameters in the configuration tab for the 'SIFs and Stresses' ?
There is a commentary by Ron Haupt with the perspective of viewing pressure deflections as expansion displacements that may be interesting,
http:\\www.sstusa.com/02aprjun.htm#apr02

"Use PD/4t" and "Add F/A in stresses" options doesn't have any impact on the anchor reactions magnitude.
Enabling or desabling these option modify only the stresses values. First option is suitable only for THIN WALL piping and regards the longitudinal pressure stress value. The second option includes the axial tensile/compression stress in the longitudinal code stress.
In conclusion, both options are used AFTER the pipe element forces&moments are computed.

Generally, the pipe element forces&moment assessment and the anchor reaction computation are not influenced by the piping design code.
As a general practice for the most projects I worked for, the loads acting on the anchors (i.e. equipment nozzles) are assessed/considered/checked for the basic loading cases (operating and sustained cases). Certainly, when specific checking methods are involved (such as WRC 107&297), then the thermal/expansion restraints are used for the corresponding stress evaluation.

Thank you for the reference article. I'll study it carefully.

Best regards,

Dorin