Shell Stresses of Single Anchor Ring w/ Long. Force/Moment

[croy2]

I am unable to find a (non-FEA) method for determining the shell and ring stresses of a single ring subjected to a longitudinal force and moment (usually at four points, 90 deg. apart), that is welded to a shell (usually 12-48" OD). I can find formulae for double rings and rings that have radial forces, but not for this.


Any tips or guidance would be most appreciated. Thanks.

Chris

 

[prex]

I would follow this method:
1)First would exclude collaboration from shell plate to the strength of the support ring: the only stress left in shell is the longitudinal one, that will unlikely have an impact on shell thickness (though this cannot be excluded)
2)Then the strength of the support ring is the only one involved (including the pad plate, if there is one).
3)This ring, if continously supported on a circumference, will behave as the well known ring under false torsion under the action of the distributed couple arising from the lever arm between the shell (where weight acts) and the support circumference. This case is treated by many textbooks and leads in fact to a bending load for the ring.
4)For the case of point supports Roark has the necessary formulae in chapter for curved beams loaded normal to the plane of curvature (chapter 8 in my fifth ed.). There you should superpose a uniformly distributed lateral load to a uniformly distributed torque, and choose the end conditions as suggested in a note by Roark.

prex

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[croy2]

Prex, thanks for the quick input on this. Unless you have an enormous (expensive) and correspondly highly rigid ring (in comparison to the shell) there is a significant amount of bending transmitted to the shell rather than just a longitudinal force. For the sizes I usually deal with, the ring stress is generally much lower than the shell stress; the ring is just thickened in order to reduce the shell stress, and you will start to approach the situation you described (only longitudinal or membrane stress in shell) as the ring becomes thicker and more rigid.

Sometimes we use floating rings for high temp designs with shear rings, where the type of analysis you described would probably be right on.

Chris

 

[prex]

I understand your position, but my position is that you don't need to account for those bending stresses.
Think of a flange calculation per code. You have exactly the same situation: a ring resisting to out of center forces generating a moment and a shell or pipe that, due to flange rotation, is subject to bending stresses. Did you ever check those bending stresses in a shell with a girth flange?
The explanation for this is that those bending stresses are secondary in nature (if the ring resists alone the bending) and, under ASME VIII Div.1, you are not required to evaluate them.

prex

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[croy2]

I guess what you're saying is that even though we are talking about a sustained load on the ring, that the stresses in the shell are self-limited due to the ring's resistance to the bending moment/torsion? That does sound reasonable. Couldn't this computation in certain cases be conservative if you are not including the shell's contribution to the rigidity of the structure? I suppose that this may be a tradeoff for increased simplicity of analysis.

On the other hand, the other potential problem is that the longitudinal force on the shell will not be acting uniformly around the circumference of the ring id/shell OD interface. Most of it will be right under where the load is applied. This would lead to a non-conservative estimation of a primary membrane stress component in the shell, wouldn't it? How could one determine this portion of the shell under the applied ring load that is subject to the long. force? Besides the geometry of the situation (e.g., how close the ring load is to the shell), I would think the ring rigidity would have a major bearing as well. (if the ring were perfectly rigid, then the load would be transfered uniformly to the shell, but then there wouldn't be any shell bending either). Maybe I should just stick to the FEA on this one, since it's a rather rapid analysis anyway.

Thank you for your valuable input.

 

[prex]

In my opinion the method I outlined is always conservative: as I pointed out it is normally used for flanged joints.
Of course you are right when you point the finger on a possible effect of non uniformity around the circumference: after all on large girth flanges there are dozens of bolts, whilst for a support ring to have 4 support points only is a common situation.
However I think that this effect may be accounted for quite easily.
First one has to note that the increased membrane stress near the support would be classified as a local stress under Div.2 coverage, and thus limited to 1.5S. Also this is a longitudinal stress, so its value is unlikely to impact on shell thickness, that, I assume, is normally determined by circumferential stress under pressure.
As a consequence you might conservatively estimate the width of shell subject to the longitudinal support stress as follows: take the effective supported width of ring (e.g. width of the supporting beam), add the height of the ring, this will give a conservative width of shell onto which to distribute the support load. If you can pass this check with 1.5S as the allowable (also considering buckling effects under compression, if you have this), then you should be on the conservative side.

prex

http://www.xcalcs.com

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[prex]

In my last post above please read '...add two times the height of the ring...' in place of '...add the height of the ring...'

prex

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[arto]

Look in Blodgett "Design of Weldments" & Bednar's "Pressure Vessel Design Handbook" under column supports.

Also Harvey's "Pressure Component Construction" for Discontinuity stresses; & 3rd ed Roark Table XIII case 9 for Ring on a shell.

 

[JoeTank]

croy2,
Are you describing an anchored vessel with four anchor chairs? Also, is there a ring around the shell such that it serves as the top plate of the anchor chairs. Is my mental image of your situation is correct?

Steve Braune
Tank Industry Consultants

http://www.tankindustry.com

 

[croy2]

Steve,

I think you could picture it as ring in the horizontal double welded with fillet welds to a vertical cylinder or vessel. There are four vertical point loads applied normal to the ring. They are usually 90 deg from each other and several inches away from the shell. It could be a vertical vessel supported by a single ring at four places. Prex's method would probably work for a conservative estimate, but I'd like to know if there's something out there more "exact" that's non-FEA. Thanks.

Chris