Flexible Diaphragm & 3 Shear Walls 4

[Once20036]

I've gotten into some discussions with coworkers recently about whether or not it's appropriate to use only 3 shear walls to stabilize a single story building with a flexible diaphragm.
To create an arbitrary example - say you have a 100' x 100' building with a shear wall or lateral frame on the west, north, and east walls.

When the wind blows north/south, I think we can all agree there aren't any issues.

When the wind blows east/west... for a rigid diaphram nobody in the office sees any issues. The north shear wall would take the load and the north/south would act as a pair to eliminate the eccentricity, but is the same true for a flexible diaphragm?

Typically a flexible diaphragm is analyzed as a simply supported beam, and a simply supported beam isn't stable if there's only one support.

A reasonable counter argument is that flexibility only has to do with the difference in stiffness between the supports and the diaphragm. A diaphragm will still have enough stiffness to utilize the east/west walls as torsional restraint.

The first question is simply how other people treat this condition and whether or not it's typical.
The second question is how to quantify that the deck is stiff enough to utilize the torsional restraint.

Thanks in advance!

 

[JoshPlumSE]

This is, I believe, the type of structure that existed in those apartment buildings that fell down in Northridge.

You can pull the full shear to one side and then design the transverse frames to resist the moment created by the asymmetry. But, you will get very large deflections at the side of the building without a lateral frame. Is this technically unstable? No, but it doesn't have a lick of redundancy either.

If it were me, I would put a series of moment frames on the one end instead of just gravity posts. You're not taking up much more space than the gravity columns, but you are vastly improving the safety / redundancy of the structure.

Just my $0.02.... What do I know about what designers are really doing though? I'm mostly a computer / FEM jockey at this stage of my career.

 

[hokie66]

I avoid that type of structure and provide a load path on all sides. A channel shape is a terrible choice for resisting torsion.

 

[CELinOttawa]

Yup, these are a seismic disaster... And Hokie's comment is dead on; In fact the channel shape created by these three-walled monstrosities would only be torsionnally stable were the load applied out and away from the "middle" wall (check out the location of the Shear Centre for channels).

 

[wannabeSE]

In Guide to the Design of Diaphragms, Chords, and Collectors (

http://shop.iccsafe.org/guide-to-th...ased-on-the-2006-ibc-and-asce-sei-7-05.html),

there is an example problem with a 3 braced frames and a bare metal deck diaphragm. The text strongly recommends against this arrangement.

I don't have the book in front of me and I read it several years ago. I think they treated the diaphragm as a cantilever and calculated the chord forces which is then transmitted into the perpendicular frames.

 

[XR250]

@CELinOttowa

They are stable, but not efficient - just as a channel is stable even though it does not get loaded thru it's shear center.
The APA's diaphragm guide has an design example. I design these quite frequently for garages. Takes some additional detailing, however.
We have little seismic load in our area.

 

[Once20036]

I`m not familiar with the collapse in Northridge, but I'd like to read more about it. When & where was it?

To reiterate - we're only discussing flexible diaphragms here. Does anybody see any issue with this system for rigid diaphragms?

I`ll look into the guides listed above - Thanks.

 

[dcarr82775]

Hard to say without the dimensions. The diaphragm may not be truly flexible or rigid, but somewhere in between. If you want to use flexible diaphragm assumptions then no of course it isn't stable. If you want to utilize rigid behavior than design/analyze it as such. You could design it for both conditions and pick the worst case. I don't really understand the point of the question.

 

[steellion]

This configuration is used often for large warehouse/data centers using tilt-wall panels around the perimeter where there is an expansion joint. This creates very stiff lateral elements on 3 sides and none at the expansion joint. The diaphragm and the lateral elements perpendicular to the load direction must be designed for all of the torsional load cases.

 

[hokie66]

steellion,
That may be true, but not on my watch. I think anyone who designs that type structure is kidding himself.

 

[XR250]

@Hokie

A channel is not efficient for torsion in the traditional sense, but what you have is a very short channel (relatively speaking) with cover plate on top.
Take a piece of channel with similar proportions as a warehouse, weld a cover plate on the top and anchor all corners to a base. It becomes extremely stiff.

 

[hokie66]

EE,
I'm still not buying it with a flexible diaphragm, especially for a large structure in plan with expansion joints. The load path is not reliable enough to suit me.

 

[Once20036]

Of course a real life diaphragm is neither 100% flexible nor 100% rigid, but somewhere in between. For a 4+ lateral frame system I'd agree wholeheartedly with designing for both rigid and flexible and taking the worst case, however, that's not an option here. As truly flexible, it's not stable. As truly rigid, it's fine - but I`m not sure that a rigid assumption is valid here.

I agree that a small steel channel with a cap plate would be suitable in torsion, however, this approximates a rigid diaphragm. What about a channel without the cover plate? Someone mentioned large deflections for the opposite walls under the torsional load case - I assume this would be out-of-plane deformations?

As discussed above, I've seen this scenario come up for large warehouses with an expansion joint, sometimes with tilt up walls sometimes without, and it also comes up with new construction adjacent to an existing building.

The point of the question? To learn a little something and better understand how buildings behave.

 

[Gumpmaster]

Well, a couple of the above posts mentioned it, but this can't be idealized as either flexible or rigid per ASCE 7-10 section 12.3. You have to take into account the actual diaphragm stiffness. This would then be classified as an extreme torsional irregularity per Table 12.3-1 and you then have to run a modal response spectrum analysis on a 3D model. You also have to increase forces and apply several other provisions.

It's not prohibited, and it happens (think an aircraft hangar with an open front), but it's not ideal.

 

[a2mfk]

To add to what Gumpmaster and maybe some others said, it depends on the relationship between the diaphragm stiffness and the shear wall (or frames) stiffness. This is what determines if it is rigid, semi-rigid, or flexible. This is true for all structural systems. For a lot of common systems, say a one story retail building with CMU/concrete walls, three walled building with an open storefront with no shear wall at the front, and steel deck diaphragm, the problem is the deflection of the diaphragm will almost always exceed that of the shear wall story drift (for common one story configurations), making it a flexible diaphragm. Of course, it depends a lot on the geometry of the overall building, lengths of the shear walls, openings in the shear walls, stiffness of shear walls, etc.

I have never been comfortable modeling steel deck as anything other than flexible and then using braced or moment frames along the front of the building, or adding enough CMU wall along the front to make it work.

It has been a while, but I think the Steel Deck Institute Design Guide has three-sided diaphragm examples.

This link is Canadian and deals specifically with wood-frame, the concepts are well explained and illustrated.

http://www.fpinnovations.ca/ResearchProgram/AdvancedBuildingSystem/Diaphragm_flexibility.pdf

 

[JoshPlumSE]

I really meant all columns. From an analysis standpoint, I think it is possible that these secondary shears / moments will get almost entirely sucked into the lateral columns.

But, I think that's a case where I'd be concerned enough about the gravity only columns, that I'd take a really close look at the analysis results for them. If the analysis did not show them getting any decent moment then I would design them to resist the a moment equal to their axial force times the diaphragm displacement at that location. I would also want to look at the diaphragm to column connection and make sure that it could adequately handle the displacement and shear that would be produced by this. Beefing up the column does little good if the middle of the diaphragm doesn't have sufficient connectors to ensure that these leaner columns stay connected.

Not sure that these "leaner" columns will ever really see this moment. But, this system has so little redundancy that I wouldn't feel comfortable about it if I didn't do that.

Even so, this is a totally theoretical discussion for me. I'm not putting my stamp on any drawings these days. Even if I were, I would not use this system in a high or even moderate seismic zone.

 

[hokie66]

Gumpmaster,
All the hangars I have seen have a portal frame across the front.

 

[CELinOttawa]

Portal frames on hangars seems to be the norm for warm climats, while massive flat moment resisting frames or end-wall openings are most common in cold climats. Either way, these are not examples of three walls with a diaphragm.

 

[Gumpmaster]

True, but the portal frames at the front of the hangars are significantly less stiff than the other three sides. I've seen several helicopter hangars that were 12" CMU on three sides with steel portal frams in the front. When you look at the relative rigidities the portal frames might as well not be there and you still have an extreme torsional irregularity. Different in the specifics, but the same effect.

 

[a2mfk]

Gumpmaster- In your example, assuming the roof system is steel deck, I think you would most likely have to analyze it as a flexible diaphragm, because the diaphragm deflection will greatly exceed the CMU shear wall story drift. Then with a simple flexible diaphragm the front portal frames will resist half the lateral load when the lateral load is parallel to the front. But you would have to make sure the portal frame story drift is less than half (I think) of your diaphragm deflection.

Take that same hangar example, add some concrete to the deck to make the diaphragm rigid, then I agree that the CMU walls will attract all the shear and the portal frames will become useless.

Found this article about diaphragms which cites the IBC:

http://www.gostructural.com/magazin...on_1617.5.3_horizontal_distribution-4764.html