WRC 107 calculation on ellipsoidal head 1

[RNDguy]

To carry out external load calculations on ellipsoidal head, WRC 107 recommends to use a mean radius Rm to approximate local area as a sphere, and then use relevant graphs for spherical shell to calculate local stresses. My question is: what mean radius Rm to use?

You see, on an ellipsoidal head, there are always two local radii, one in the meridional direction, and the other in the hoop direction. The values of these two radii anywhere on the ellipsoidal surface are quite different.

 

[codeeng]

Typically you would use the crown radius which is 0.9 d on a 2:1 head.

 

[RNDguy]

This could be true in the crown portion of the head. But away from the crown, this would be completely wrong. If the vessel supports are away from the crown and not exactly on but near the knuckle region, then local radii are very different indeed. Now here's what article 3.5.3 of WRC 107 says:
"The method applied in the text may be applied to ellipsoidal pressure vessel heads with reasonable accuracy if the mean shell radius Rm at the juncture with the attachment is used in the applicable formulas".

Please note the words "juncture with attachment". But then what is the mean radius at this point? Rt (hoop direction) or RL (meridional direction) radius, or some "mean" of these, or does "mean" here stands for mean membrane radius across its thickness, either in the L or t direction?

Any help would be appreciated. It is always in the interpretations where all these Codes seem to thrive in.

 

[codeeng]

If your attachment were near the knuckle then any WRC analysis based on the larger crown radius would be conservative. This had always been my logic prior to moving onto FEA, which will takes into account the additional stiffness of the knuckle region.

 

[RNDguy]

codeeng,
I wonder how softwares like COMPRESS or PVELITE tackle this?
Do they use FEA? If not, they must be doing WRC 107 calculations for external local loads even on knuckle region of ellipsoidal head. So what mean radius Rm would they assume at a point like that?
I propose the following: use the local radius in 'L' (longitudinal or meridional) direction for finding parameter U, & subsequently finding parameters Nx, Mx, Ny & My from relevant graphs in WRC 107 for points A & B (please refer to the figure in Table 2 & 3); and use the local radius in 't' direction (hoop) for finding U, and then Nx, Mx, Ny & My from graphs for points C & D. Is this logical and correct?

If we use crown radius in regions away from crown, it could give quite an uneconomical design. I will like to remain safe but still remain reasonably economical.

Fellow engineers, I need some experienced tips here.

 

[codeeng]

For WRC, Compress takes the crown radius regardless of attachment location. If you want to be more economical then use FEA as WRC does not cover double curvature geometry. Compress has a separate FEA module or you can use NozzlePro. They're both based on FEPipe.

 

[RNDguy]

codeeng,
Thank you for your valuable comments.
Since I do not have an FEA software available to me, therefore, the best recourse for me is to do what I proposed above and accordingly solve thru WRC 107 method. (Any more comments there?)

However, I am going to use a maximum limit for membrane plus bending stresses of 2 times Code allowable stress Sa, and for membrane stress intensity only upto Sa. Bednar suggests the same, although in many of the previous threads in this forum, people have argued that the limit for bending plus membrane stresses can be 3 times Sa.
B.T.W., in the book "Pressure Vessel design", ed. by J. Spence & A.S. Tooth, there is an interesting discussion where they discuss that membrane stresses (primary due to pressure and local primary due to external load) can be upto 1.2 times Sa (i.e. 0.8 yield stress for most materials), and 2 times Sa for membrane plus bending stresses. They clearly state that it is a misinterpretation of taking the latter limit to be 3 times Sa.

 

[jte]

RNDguy-

I'm not familiar with the Spence and Tooth book, so I'm not sure where they are coming from. It appears from your description above that they are missing something. I'd suggest reading VIII Div. 2 Appendix 4-130 etc. with a particular emphasis on Fig 4-130.1.

Be careful with using the term "Sa". I believe by "Sa" you mean the allowable stress per Div. 1 more commonly abbreviated as "S". When I see "Sa" I interpret that as an alternating stress per VIII-2 Appendix 5.

Now pull out your copy of VIII-1 (presuming that you are dealing with a Division 1, not Div. 2, vessel) and flip to UG-23. Read parts (c) thru (e). Part of part (e) reads The primary plus secondary stresses at these discontinuities shall be limited to Sps, where Sps=3S, and S is the maximum allowable stress of the material at temperature... This seems pretty clear, and I'm not sure why Spence and Tooth feel that going to 3S is a misinterpretation. In essence, Div. 1 adopted the stress limits which were already commonly used but were not explicit in the Code: Using a Div. 2 stress categorization approach with the Div. 1 S as a basis instead of the Div. 2 Sm.

What you need to be very careful with is in determining whether your stresses (not loadings) are primary or secondary. A strong argument has been made (and, in my opinion, sucessfully defended) at the last two ASME Pressure Vessels and Piping conferences that a thermal piping load (commonly considered to cause secondary stresses) can cause stresses which behave as though they are primary at the vessel shell.

The only place I see the Spence and Tooth factor of 1.2S coming up is for wind or seismic loadings (UG-23(d)).

Having argued that going to 3S is acceptable in some cases, I'll agree with you that limiting your design allowable stress to 2S is reasonable. Read the forward to WRC-107 and you'll see that the accuracy of the results can be somewhat in doubt. Couple that with your difficult geometry and other unknowns and I'd say that it is prudent to limit yourself to 2S. The 3S limit is best left for more detailed/accurate analysis such as FEA.

jt

 

[StressGuy]

"A strong argument has been made (and, in my opinion, sucessfully defended) at the last two ASME Pressure Vessels and Piping conferences that a thermal piping load (commonly considered to cause secondary stresses) can cause stresses which behave as though they are primary at the vessel shell."

JTE - Are there any papers from those conferences that I could take a look at regarding that point?

Edward L. Klein
Pipe Stress Engineer
Houston, Texas

"All the world is a Spring"

All opinions expressed here are my own and not my company's.

 

[jte]

StressGuy-

This year's paper by Seipp, George, and Morrison was titled Classification of Shell Stresses from Piping Nozzle Loads, PVP2005-71535. If your company sent someone to the PVP then they should have the CD which has the paper on it.

Last year's paper was by the same trio; don't have the title handy.

jt

 

[codeeng]

Interesting though, both Div 1 and 2 has recently increased allowable combined stress intensities from 3S (3Sm) to 2Sy in cases where Sy < 0.7UTS. I wonder when we'll all get on the same page!