Hi,

This is with reference to B31.8-2008 para 833.3

For restrained section of pipeline the axial stress calculated by Caesar is not matching with the figure obtained by code equation 833.3a. For example in the attached model at node 25 the axial stress is given as 18337 PSI for load case #1. As per code this value should come out to be E*ALPHA*(T1-T2) + Nu*SH =29500000*0.000006548*(70-185) + 0.3*33033=12304PSI Sx=Sb=0)
As I guess the axial stress reported in the stress report is Rx/Am+nu*SH (Rx: Axial force given in global force report Am: Pipe wall cross sectional area), it seems to me that the axial force reported in global force report is higher that it should be.
Appreciate any clarification.

Thanks,

Tanveer Mukhtar

Be careful of your terms. You are comparing a column in CAESAR II output labeled Axial Stress with the definition of Longitudinal Stress in Paragraph 833.3. That axial stress column is not based on 833.3.
We have a real problem with Codes that define separate rules for Fully-Restrained Lines. To me, a restrained line does not need a comprehensive beam analysis ala CAESAR II - it's all simple slide rule calculations. But you don't really know if it is fully restrained until you analyze it.
Our thermal component of the stress you question is based on "more rigorous analysis" - based on the axial structural load as the thermal strain is resisted by the pipe & soil.

Dear Dave,

Here is the problem I am facing.

A pipeline is designed according to B31.8 rules. The wall thickness is sufficient to meet the requirements of 841.1.1 and combined stress requirement of 833.4. However when the same is modeled in Caesar (with Bourdon Effects activated, to take care of bending due to pressure expansion), it is showing overstressed in the restrained section. I agree that a restrained line don't require beam bending analysis, but since Caesar is showing over stress, I must explain the difference to the authority approving the stress analysis work.

The combined stress calculated as per 833.4 and reported in "Code Stress" column takes two values i.e SH and SL. SH is coming from the “Hoop Stress” column while SL is the axial stress from “Axial Stress” column + bending stress in "Bending Stress" column. In absence of bending the axial stress column therefore represents SL term of B31.8.

What I feel is that difference is because of the way pressure elongation is handled in Caesar. When Bourdon Effects are activated , the axial stress and hence the combined stress (SH-SL) exceed the true value by a factor of approximately 0.2*SH. On the basis of my guess work, it might be explained as below

Element expansion is calculated as

dL=Alpha*L*(T2-T1)+SH/2*L/E-nu*SH*L/E ----(1)
To completely restrain this expansion, the force exerted at the element is
R=-E*Am*Alpha*(T2-T1)-Am*SH/2+Am*nu*SH
This is the force which is shown in element force report
The axial stress is then calculated by
SA=SL=F/Am+nu*SH --- (2) (As per code equation 833.3a where ST is replaced by R/Am as explained in Caesar documentation)

However in restrained section the only axial deflection is because of poisson contraction, hence 2nd term in (1) above should be ignored. Moreover poisson component has already been taken care by 3rd term in (1) and should not be added twice in (2). The net correction required is therefore
-SH/2+nu*SH=-0.2SH

As stated this is all my guess work to explain the difference and is based upon the observed results

Best regards,

Tanveer Mukhtar

Your argument may be sound but I once again must say your rules (or better, the Code's rules for fully-restrained lines) conflict with the structural response of a collection of beam elements under load.

The rule addresses Poisson shrinkage, CAESAR II does not.

The Bourdon effect, in CAESAR II, will either extend straight pipe (option 1) or extend straight pipe and open bends (option 2). I might offer that a fully-restrained line has no response to that Bourdon effect.

I have no easy answer for your approving authority. CAESAR II is a good engineering tool. You and your authority can exercise engineering judgement.

I have noticed this before - results for FAC=0.001 do not correspond to FAC=1 for fully restrained pipe with bourdon effect. This could be considered as conservatism in the code stress implementation. CII overestimates fully restrained stress by about 0.2SHOOP due to its implementation of bourdon effect. Perhaps CII could adjust Fac in its calculation based on the degree of compression, just a thought...

The effect is not limited to the restrained part of the line, but is carried to the results of partially restrained part as well. Typically a partial retrained condition occurs in buried piping between a change in pipeline direction (bend or a tee) and fully restrained point. The max of this 0.2SH is at fully restrained point and 0 at the point of minimum restraint (bend or tee)
Moreover when defined as fully restrained CAESAR will not include longitudinal pressure stress in axial stress calculation. Again given axial stress (assuming compressive) will be overestimated by 0.2SH at the point of minimum restraint and 0 for fully restrained point.

Therefore in my opinion when bourdon effects are active, 0.2SH (tensile) should be added globally to portion of the pipeline defined as filly restrained.

Very often thermal beam bending stresses are added to axial stress to calculate SL and thereby equivalent stress by B31.8 equation 833.4.a/b and B31.4 equation 402.7, an approach that is questionable, but when followed should consider this correction in axial stresses.

Best Regards,

Tanveer Mukhtar

The CAESAR II buried modeler will compute the appropriate axial stress in the fully restrained buried pipeline segments as well as the partially restrained buried pipeline segments that are consistent with the design code equations. However, in order to accomplish this, the appropriate input specifications / settings / commands need to be activated /invoked, and vary somewhat with the different code check options.

The primary items to check are as follows:

1) Make sure that the appropriate specification is activated such that the buried modeler knows which segment(s)are buried (are to be restrained by soil springs) and which segments are not. If this is not properly accomplished, the axial stresses reported by CEASAR II will be erroneous.

2) Most code equations use the outside diameter for computing stresses in pipelines. Check to see if this option is properly specified. By default CAESAR II will use the inside diameter, and the stresses computed by CEASAR II will diverge from the code equations that use the outside diameter.

3) Based on experience, it is always "safe" to invoke the "Bordon Effects" option for buried pipeline analysis, especially when evaluating transition areas into above ground scraper trap locations.

When visually interrogating the axial stress report, look for where the axial stress becomes effectively "constant" from one node to the next. This is a good indication that this reach of pipe is "fully restrained". This relatively "constant" axial stress is the stress to check against the code equations. You will also find that this reach of buried pipe is remote from buried bend locations and above ground/below ground pipeline transitions. In this manner, if your manual check against the code equations for restrained pipe axial stress does not closely match the CEASAR II report results, either the pipe is indeed not fully restrained (since it is too close to buried bends or transitions) or something else is causing CAESAR II not to recognize that the pipe is buried and is restrained by soil springs (i.e. refer to items 1 thru 3 above).

If you cannot figure out the problem, it is always prudent to model a simple buried pipe problem consisting of a long straight section of buried pipe (at least 3 to 4 km) at a constant cover depth that protrudes straight out from the ground (with no bends) at each end for 6 inches or less, and is flanged or capped at both ends. Both ends are specified free to move. You can then experiment with different internal pressure and delta T load combinations. You will find that there is a distance from each end where the pipe is only partially restrained and exhibits nodal displacements, and then reaches a point called the "virtual anchor" where the pipe becomes fully restrained by the soil axial friction springs and there is no nodal displacements at these fully restrained nodes. The axial stress at these fully restrained nodes is the stress to check the code restrained pipe equations against.

If you are unable reach a reasonable comparison of the code equation check against the CAESAR II results for the restrained axial stress, then there is something still amiss with your CAESAR II input information / specification / settings in the buried modeler. However, if you reach a reasonable comparison of axial stress results, then your input specification / settings in the CEASAR II buried modeler are correct, and you can repeat the same settings in your more complex pipeline configuration model.

The simple problem described above has a closed form solution approximation, as described by P. J. Schnackenberg, "Pipeline Rules of Thumb Handbook". In order to closely match this closed form solution analysis against the CEASAR II simple model described above, you will need to specify a very large stiffness for the CAESAR II buried modeler axial restraint soil spring such that the full ultimate axial soil restraint is mobilized at the slightest pipe movement.

Ken Nyman