Modeling Concrete Domes and Ring Beams in RISA3D

[mike20793]

Does anyone have any experience modeling concrete domes with ring beams in RISA3D? I'm having a hard time getting the tension force in the ring beam to match the theoretical force based on shell theory. The meridinal forces are reasonably close (within 0.5%) of the theoretical, but my tension forces are way off. I'm pretty sure it has something with the way I'm restraining the roof. Basically, I modeled the circular roof with a concrete member around the outside. I restrained each node of the concrete beam in the vertical direction. I also restrained one node in the global x and z directions and another node I restrained just the z direction, which is tangential at that node. This allows the ring beam to stretch but not twist; but it is restrained against "stretching" at the pinned node. See the attached plan view of my model for clarity. Note that because it is plan view, the vertical restraints are not shown.

 

[dcarr82775]

Instead of rigid supports, try springs to provide some allowance for spreading?

 

[mike20793]

I tried, it doesn't work. The dome roof goes all over the place in the deflected shape.

 

[mike20793]

Stiffening up the spring seemed to help; I'm closer to the theoretical ring beam tension, but it's still off by quite a bit. I'm getting about 1100 kips in RISA and the theoretical is 1425 kips.

 

[mike20793]

The ring beam tension isn't uniform either, which makes me feel even less certain about it since its a radial pressure on a circle.

 

[JLNJ]

Look at your horizontal reactions. If you have any then there is you trouble.

I would model it with the x and z reactions at the peak of the dome only and just vertical reactions at the ring.

 

[KootK]

Does your theoretical check assume that the ring beam resists all of the circumferential tension rather than sharing it with the adjacent shell?

I might try a single global support restraining all translation and rotation about the vertical axis.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[JoshPlumSE]

Would you prefer to have support conditions that are always tangential to the circle / dome? Rather than defined with respect to the global axes? That's the type of support I recall seeing with a number of tanks and dome type structures. Not that I've ever been the principal on this type of project, I just recall that others have modeled it this way.

If so, then you might check out the Modeling Tips section of the help file / General Reference an look for a sub-topic called "Modeling inclined supports". In that topic you create a short rigid link member in the direction desired (in your case perpendicular to the circle). One side of the link is connected to a rigid support. The other side is connected to the ring beam and you use the end release for the rigid line to restrain the structure in whichever local direction it needs to be restrained. Make sense?

 

[KootK]

I like JLNJ's support modelling suggestion, even better than my own. Symmetry is always a good thing.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[KootK]

I would also add restraint about the vertical axis to the dome apex as well. Of course, Josh is the last word in Risa modelling round these parts so his sugggestion surely has merit as well.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[mike20793]

Thanks for the replies. Before reading everyone's I added tangential restraints at the four corners (easiest to apply) and the ring beam tension force became uniform, as expected. There are no horizontal reactions, which is as expected also. I'm wondering if the results I'm getting are composite between the beam and the shell (I do not have the plane stress box checked). I'm going to play around with the restraints mentioned above and change the plates to plane stress to see how that compares.

Thanks again.

 

[mike20793]

Quick update: The plane stress formulation brought me much closer to the theoretical values. 1353 kips vs 1425 kips theoretical. I'm guessing the difference lies in small errors in modeling. Time to investigate!

 

[dcarr82775]

I like JLNJ's support, wish I'd thunk it

 

[mike20793]

I understand the theory behind shells and the plane elements in FEA, but is that really how a dome roof is going to act? Can I count on out of plane stiffness from these elements?

 

[KootK]

I think that you have to count on some out of plane flexure in order to resist asymmetric loads that would creat a thrust line falling outside the thickness of your shell.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[WARose]

Will the "ring beams" actually be there or is this just a modeling technique? If not, I would assume you could model the whole thing with plates. I've done that with a steel dome myself.

 

[mike20793]

Yes, the ring beam will actually be there. WARose, that is the problem we are running into. For some of our previous domes, that's how we analyzed them, ie plates for the walls and roof. They were fairly small and the forces weren't that large. However, this dome is much bigger in diameter and we first looked at the ring beam to control deflection at the crown. Then the question popped up if we were actually modeling them correctly. Theory says it's okay if you use plane stress plates, but we are having a hard time convincing ourselves there is no out of plane stiffness, at least in the lower part of the roof where it is thickened to meet the walls. All the literature we are finding use plane elements for their modeling, but they are just comparing to theoretical, rather than designing.

 

[mike20793]

Koot, that's a good point and part of our reasoning that they WILL have out of plane stiffness, especially if we are detailing it to take that load. These domes have partial wind loading and the live load is quartered/halved per ASCE 7. Some literature says to use an equivalent uniform load, but that seems like hogwash to me.

 

[WARose]

I really can't see using/designating plane stress elements in this application. Assuming we are talking about reinforced concrete (re-bar in both directions internally) that tie into the rings with re-bar: it won't behave that way and (indeed) would have to have out of plane stiffness to get the wind/lateral load to the rings.

 

[KootK]

Just by visiualizing the deformed shape of the dome, it seams to me that any spread in the ring beam implies in plane flexural strain in the dome shell. The less rigid the ring beam is, the less dome like the behavior, right? I've always assumed that was why it's quite common to post tension large scale ring beams.

I recently read an account of how the Orange Peel hypothesis of cracked domes allows the St. Peter's dome to remain viable post spread (pic below). It's fascinating. To some degree, this redistribution of load will take place even in a reinforced dome as it transitions to the cracked state. I'm not suggesting that you should design your dome this way. This is just fun shop talk. You can take some comfort from knowing that this two way arch behaviour is available as a last resort however.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.