RC Tapered Beams and Compression Ring? 1

[Trillers]

Attached is a sketch of a rigid (?) concrete frame with tapered beams culminating in a compression ring near the peak. This structure will be built in Seismic Zone D.
In a previous thread I was proposing to design the beam joints at the apex by having them meet at the center which was a fairly straightforward procedure(to which some of you agreed), but the architect has changed his design to allow his accent lights to be recessed in the apex. This now requires me going back to the compression ring as shown in the sketch.
I have reviewed quite a bit of literature to see how I would compute moments and reactions for the beam/ring joints and the column beam joints, but am confused about how the ring would affect the entire beam/column system.
I also need to design the ring and I propose to design it treating each face of the ring as both a column (to support the adjacent ring segments) and a short beam (to support the tapered beam load as shown.
Anyone know of a good reference which addresses designing a similar system?
Or can anyone suggest a procedure to analyze the column/beam/ring interaction?
Also - I intend to treat this as a rigid frame - does this make sense? I only ask this because I have been told by colleagues that the compression ring renders the beam/ring connections as "hinged" connections. I don't agree, but looking for your opinions out there.
Thanks.

http://files.engineering.com/getfil...bfe-8d6b-51ab680af722&file=20131112151524.pdf

 

[BAretired]

If the connections at the base are hinged and the connections at the ring are hinged, the structure is unstable (four hinges).

If the tapered members are hinged at the base and fixed to the ring, the structure can be analyzed as a frame but it is not a straightforward analysis because the ring elements are in compression, bending and torsion.

If the tapered members are fixed at the base and hinged to the ring, the analysis might be simpler but the reaction at the ring would be confined to a horizontal force for each of the four frames. The taper in the column member may be questionable when the magnitude of the base moment is found.

If the tapered members are fixed to both base and ring, the frame will be more rigid, but analysis will still be difficult.

Unsymmetrical loading of the roof members needs to be considered in analyzing this structure.



BA

 

[hokie66]

BA,
For analysis purposes of the frames, I think you could consider the compression ring as one hinge, and analyze the frames as three pin arches. I would make the compression ring circular.

 

[Trillers]

Thanks BA and Hokie - but I have a couple more questions.

Shouldn't the beam ring connections be designed as moment-resisting? Are you saying that the transfer of forces from the beam to the ring will not induce a moment? I see this working if somehow the ring transfers the moment to the opposite beam where the reaction can be analyzed as just horizontal and vertical reactions. Am I understanding this correctly?

I have never designed a pinned connection in RC. Is there any literature or reference discussing pinned connections in RC that I can refer to?

There is a plethora of worked examples for hinged frames and for all types of steel gable/pitched frames, but I can't seem to find any with concrete gable/pitched RC frames. Do either of you know of any good sources?

Also - if the compression ring is constructed circular, how are the horizontal forces from the beams resisted? Would it be the tension bars (outer layer) that would resist these forces? I can see how that would work if I treat the ring as an arch and use the beam forces in different load conditions to analyze the loading under uniform and point loads scenarios. Am I understanding this correctly?

Thanks.

 

[JStephen]

Roark's Formulas for Stress and Strain has a load case for circular rings with N uniformly spaced radial loads.

Gaylord & Gaylord's Structural Engineering Handbook, 2nd Edition, pg 23-5 to 23-6 has a brief discussion of a silo roof of similar construction. It looks like they treat all connections as pinned for analysis, ignore the 4-hinge issue, but then it actually gets built with a moment connection at the compression ring. Lateral support is furnished by the roof plate in that case, and they use the Roark formula for the compression ring. I relay this for information's sake, not suggesting that's how it ought to be approached.

 

[hokie66]

Yes, the horizontal forces would be resisted in compression by the circular arch. As to creating an actual pinned connection, you don't need to do that. At the compression ring, take the frame reinforcement into the ring like you would at the base of a column. Now, my comments are strictly for gravity loading. With your seismic loading, I am not sure how the seismic codes treat the type of structure proposed here, or even if this guidance exists.

 

[Trillers]

Guys, thanks - this discussion has been very informative - I appreciate your input.

Hokie, in terms of the seismic reactions, we will just design the beam/ring connection as we would a beam girder connection.

Again - thanks.

 

[BAretired]

You cannot create a pinned connection at the base and at the connection to the ring. If you do, the structure will be unstable. It will be a mechanism.

You can approximate a two hinged arch as a three hinged arch for the purpose of calculating reactions. The error in so doing will be small, but you must provide for a moment at the connection to the ring and the ring must be capable of transferring that moment to the opposite side. This entails compression, bending and torsion in the ring.

For unbalanced loading on a frame, the vertical shear at the central pin is not zero which means that the maximum moment at the beam/ring junction occurs under unbalanced loading.

I am not keen on the proposed design and would encourage the architect to reconsider.



BA

 

[hanihafiz]

Each segment can be analyzed as hinged-roller frame, and it is a stable system. The ring cannot either resist moment or vertical shear (no vertical support). The tapering shall reduce the connecting moments. In addition, little torsional cracks in the ring beam shall insure the hinge assumption. Only in case of wind or seismic loading, the ring may transfer vertical shear between the two components

 

[Trillers]

Thanks BA and Hanihafiz:

The architect is deadset on this configuration - unfortunately.

So in the case of seismic or wind loading, the ring needs to transfer vertical shear between the two opposite facing beams. Hanihafiz -- are these the two components referred to in your last paragraph, or are you referring to the beam and column?

I'm trying to understand why any moments at the end of tapered beams from the lateral loads cannot be handled by the ring beam - wouldn't the torsion be caused by the moments at the beam/ring connection? I agree with BA that the ring needs to be able to transfer moment to the opposite side, thus the torsion effect.

H-hafiz - am I misunderstanding your point about the ring not being able to resist moments?

 

[prex]

What you call torsion in the ring is actually bending. It is the same as for a vessel flange: it is subject to distributed 'torsional' moments but it works in bending. You'll find this situation treated in many textbooks.
With the proportions in your sketch it seems to be difficult to transfer any significant moment at the top between members. I concur with others here, you should treat the ring as a hinge for all the frames (and if you want to make it octagonal, you should connect the frames at the apices, not in the middle of the sides, but a circular ring would be simpler and equally suitable).
The lateral stability could be granted by braces in the roof or in the vertical walls, or by the roof itself, as suggested by JStephen, if structurally suitable.

prex
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[hanihafiz]

In the previous post attachment, I assume this frame as a component. The opposite frame which has another wind loading,for example, is the other component.
As per ACI318 -clause 11.5.2.2, you may limit fixation at ring beam to the compatibility torsion value of its section. You may choose the tapered section at ring location and the ring section itself to limit this moment. Or,another way you may solve the frame as hinged-roller, and check the ring beam for this compatibility torsion.

 

[hanihafiz]

Add a fixation degree of freedom to the pinned joint, and solve. If the resulting moment below cracking torsion, check ring beam torsional capacity for this moment. If it is higher, check for cracking torsion value.

 

[BAretired]

If the architect is dead set on this configuration, it can be done, but it is actually four 2 hinged arches meeting in the middle. The notion that it can be analyzed as eight hinged-roller frames and will be stable is simply wrong...it can't.

If the ring is octagonal and as shown on the sketch, there will be torsion in each ring element because that is the only way the tapered beam moment can be resisted by the ring.

BA

 

[hanihafiz]

BA, hinged-roller frame is unstable, I agree if the roller is free to move horizontally, but in attachment to my first post, the roller is free to move vertically only, same concept as 3-hinged frame, but the advantage you got clear the reaction on ring beam . In a final analysis, the whole structure, by software can be easily analyzed handled as 3-D model.

 

[BAretired]

hanihafiz,

You are mistaken. If the roller is free to move vertically, it means (a) shear is zero at the roller location and (b) there is no horizontal movement at the roller, neither of which is correct for all possible load combinations.

Trillers,

Without shear walls or diagonal bracing on the exterior walls, this structure is incapable of resisting a significant moment about a vertical axis, i.e. it has low torsional resistance. You must ensure that proper bracing is provided to prevent a torsional collapse.

BA

 

[JoshPlumSE]

What about the stability effects on the tapered frame?

The stability effects of tapered frames are not all that straight forward to do via hand-calc. Then if you add in the Direct Analysis method considerations I think you are in a good bit of trouble. I just can't see a way around doing a 3D FEM analysis of this system. Do you simple hand-calc for sure as a ball-part check on your FEM results. But, this is the type of analysis where hand-calcs are just not going to be able to capture the level of accuracy that you'd get from a good computer program.

Some thoughts about the program:
1) Make sure the program is accurately modeling tapered members. Some programs merely use the average of the start-end properties (which is NOT accurate).

2) Know what you have to do to capture the stability effects. This may involve sub-dividing the member into smaller pieces (or in RISA's case just adding joints along the length of the member).

3) If you program provides code checks on tapered members, then what is the criteria / code upon which these code checks are based. I tend to recommend AISC Design Guide 25. But, there are likely other codes / criteria out there as well.

Caveat: I work for an analysis company (RISA) that does a pretty good job on tapered frames per AISC design guide 25. So, you can dismiss this message as a sales pitch if you like. Though I'mm really just using the knowledge I gained during RISA's DG 25 implementation to flag this structure as one which sounds particularly susceptible to the types of stability and analysis issues that prompted the industry to really demand this type of design guide.

 

[BAretired]

Josh,

I would never accuse you of making a sales pitch because I have noted in the past that you always declare your involvement with RISA. Notwithstanding, if you make the simplifying assumption that the analysis can be that of a three hinged arch, the structure is statically determinate and hand calculations are straightforward. Admittedly, it is not a perfectly elastic solution but it is, in my opinion good enough for the problem at hand.

The fundamental point to recognize is that the connections between the tapered members and the ring cannot be hinges. And the ring must be capable of handling the moments arising from four frames crossing at a central point with various possible load conditions.

BA

 

[JoshPlumSE]

BA -

My comments are really based on the overall impression I got from design guide 25. It's not like my post was based on a well documented study or code reference.

The analysis of that type of frame can be pretty simple when your member properties are constant. But, these are tapered beams and columns. So, that will have impact on the analysis results. In addition, it makes the 2nd order effects much more difficult to account for by hand (B1-B2 method?).

That being said, I haven't done any examples / studies which demonstrate that the RISA (or other FEM analysis for Tapered members) results are greatly superior to hand calc examples. Perhaps if I get a significant amount of free time on my hands I'll put something together to see what sort of differences we're talking about.

That same design guide does allow for a first order method (FOM) to be used. So, it boils down to an educated guess on my part that this frame is going to be particularly susceptible to analysis inaccuracies.

 

[JLNJ]

BA - I like your style. Sometimes stability or lack thereof is not so obvious.

Is this RC frame cast-in-place or precast? Tilt-up? Do you have a tension ring at the eave?

So many details to consider. What an interesting problem.