Local Stress in Radial Nozzles on Spherical Shells due to Internal Pressure

[FreddieH]

Hi,

After searching around for awhile with no luck I have decided to write a post.

I am sizing and assessing a cylindrical nozzle positioned in the centre of a torispherical head. I have completed evaluations of intersecting cylinders, however I cannot find a WRC Bulletin or any other material that provides formulae to calculate membrane stress and surface stress intensity on nozzles or vessels in spherical shells with a cylindrical nozzle. I can only find area reinforcement rules for radial nozzles on spherical shells, however I am required to assess the nozzle against stress criteria.

I need to calculate stress due to internal pressure, I have used WRC Bulletin 537 to find the stress due to external loading. Although, when using WRC 537, the attachment parameters Gamma and rho lay outside of the data range so I had to make up a much weaker thinner nozzle with no reinforcement to get the parameters to lie within the usable range. (Is that normal, because using area reinforcement rules I had to INCREASE the size of the tapered reinforcement), but then to analyse the stresses I had to REDUCE the taper to return to a straight thin cylinder attached to the torispherical head. This caused an issue as now with a reduced vessel and nozzle wall section when calculating the stress from the dimensionless membrane force, it becomes very very large unless I then revert back to using the actual vessel wall thickness. Which may be a problem as it is a different vessel wall thickness to that which was used to calculate the dimensionless membrane force.

The stresses in radial nozzles on spherical shells due to internal pressure seems to be lacking, In the mean time I have calculated the force the internal pressure exerts inside the nozzle (circular area inside nozzle * pressure) and then summed that with the external loading and calculated the stress assuming all loading is in the form of external loads. I read here [URL unfurl="true"]http://www.carmagen.com/news/engineering_articles/news30.htm[/url] that this is a conservative method.

Does anyone have any understanding of this type of problem?

Thank you in advance.

 

[FreddieH]

Noone up for the challenge? I'm surprised. Someone must have looked at the problem of local stresses in radial nozzles on spherical shells.

 

[fegenbush]

Are you determining the allowable external piping stress? WRC 537 is intended to determine the stress due to external sources, not necessarily vacuum pressure. To what code is the vessel designed?

 

[FreddieH]

Yes, 537 is for external nozzle loadings. The problem is the attachment parameters that the data set accomodates is very small and the 50 mm NB nozzle does not lay inside the range.

I am designing the nozzle for known internal pressure & shock pressure & external nozzle loading due to attached pipework. I need to show that the design at least initial design withstands the assessed loading against ASME NB criteria.

The missing part is the ability to find local stresses in the vessel and nozzle walls due to internal pressure.

Thanks again.

 

[TomBarsh]

In my experience, the problem is similar to the one we all studied in basic strength of materials: you have an "infinite" flat plate under uniform tension, and there is a hole in the middle. What is the stress in the plate at the hole? The maximum local stress is 3 times the general stress. Texts on theory of elasticity derive this as well as general equations for the distribution of stresses all around the opening. Given that a cylinder under internal pressure experiences both circumferential and longitudinal stress the principle of superposition for elastic stresses could be used to determine the combined stress around the opening. Of course, this solution is for a flat plate, not a cylindrical shell, but for a "relatively thin" range of r/t I would be comfortable using the method. But the actual nozzle opening is strengthened by the presence of the nozzle neck itself. So the stresses calculated by the "simple" method would likely be pretty conservative (but easy to calculate).

Possibly the best work done on determining a useful method for practical design is the new analysis method given for nozzles in ASME Boiler and Pressure Vessel Code, Section VIII, Division 2, in part 4.5. This is a stress-based analysis and can be manipulated to calculate the stress at the opening due to internal pressure. This is an averaged local membrane plus bending stress, and not a peak stress. WRC bulletin 529 describes this method in detail; originally it was published in the ASME PVP volume 399. Division 1 Appendix 1-10 is essentially the same method, although it's a slightly earlier version of the final method given in Division 2.

 

[TGS4]

Do a literature search yourself. Look for papers published at ASME PVP Conferences, the ASME Journal of Pressure Vessel Technology, etc.

 

[FreddieH]

@ Tom Barsh - thank you for your reply, I agree it is very similar and an approach of solely looking at stress around an opening and applying a stress concentration factor with no reinforcement would be conservative. I've seen the ASME Boiler and Pressure Vessel Code, Section VIII, Division 2, part 4.5 before was told my lead engineers that it is not to the required standard, Section VIII is

I was hoping there existed similar formulae to WRC Bulletin 368 but for spherical vessels,

i.e. Maximum membrane stress intensity on vessel (intersecting cylinders):

sigma=[0.5315-(0.06342((D/d)^1.25)*((D/T)^-0.25)*((t/T)^-0.75))+(0.4372(D/d)((D/T)^-0.25)*(t/T)^-0.25]*[(d/sqrt(Dt))*(PD/2T)]

There are 3 more equations like this for intersecting cylinders e.g. max surface stress (vessel), max membrane stress (nozzle) etc...

However, I have not come across any such for spherical shells.

@TGS4 - your comment is as useful as a hole in the head, I suppose your other 1118 replies are filled with equally helpful gems of wisdom.

 

[TGS4]

FreddieH - if you want spoon feeding, you've come to the wrong place. Where exactly did you do your "searching around"? I pointed you to some useful locations to look. I'm not doing the looking for you.

BTW - I see that you're new here, with this being your first post. You've probably noticed the little pink stars (LPSs) where someone can "like" a post. The folks here are rather stingy with the LPSs. Since you've seen that I have over 1000 replies, perhaps you've noticed that I have almost 90 LPSs, which puts me in the top 5 for this forum. So, ya, my replies have been deemed to be pretty helpful. I had actually thought about looking at some of my PVP Conference CDs to find appropriate authors to search for, but now I've decided that I have better things to do.