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!

 

[Gumpmaster]

Except you can't idealize it as flexible with moment frames (ASCE 7-10 12.3.1.1). You have to consider the actual diaphragm stiffness.

 

[steellion]

For what it's worth, the ASCE trial problem for this month is a building with masonry shear walls on three sides and a storefront on the fourth wall - no moment frame.

 

[Once20036]

Where do you access these trial problems?
I just checked out the AISC website and didn't see anything.

 

[Hokie93]

The 2014 ASCE Trial Design Problem mentioned by steellion can be accessed from the Structural Engineering Institute (SEI) portion of the ASCE website (

http://www.asce.org).

For convenience, a copy of the 2014 Trial Design Problem is attached. Solutions are due by March 14, 2014 if you wish to submit a solution to ASCE.

 

[CURVEB]

@Hokie93 - it looks like the question is still up on the website. Did they ever publish any findings or common responses that you are aware of?

 

[KootK]

I don't much like the three sided lateral systems either. However, I think that their portrayal in this thread is unduly harsh. To that end, I'll be the devil's advocate for a spell:

1) The ASCE test for rigid versus flexible behaviour is really only germane to an investigation of load distribution to vertical SFRS. It isn't relevant to a load distribution for a three sided building where the load is being applied parallel to the open side and it is obvious where the direct shear goes. That test shouldn't be used as a litmus test for whether or not a three sided building diaphragm can be employed.

2) The argument that the shear centre of a channel is outboard of the channel section only applies to the purely flexural component of shear wall deformation and, then, only if the three shear walls are detailed to act compositely (likely true in CMU, less so in wood frame). In these kind of buildings, often shear deformation dominates. And for pure shear deformation, the shear centre coincides nicely with the shear wall opposite the open side.

3) As Gumpmaster implied, for many real world scenarios involving three sided buildings, the three sides would be so stiff relative to any open side moment frame that there may not be any point to the moment frame. If the three sides were CMU, for example, you'd probably have to utterly destroy the CMU before the moment frame would really kick in. Obviously, much depends on the aspect ratio of the three sided diaphragm.

4) A three sided diaphragm, in any material, is absolutely a rigid diaphragm when considering load directed parallel to the open side. This ties into point #1: questions of diaphragm rigidity are only pertinent when considering load distribution to the vertical shear force resisting system. One of the few nice features of a three sided diaphragm is that load distribution is pretty straight forward.

In answer to the two questions posed by the OP:

1) The first question is simply how other people treat this condition and whether or not it's typical. It is common of a certain class of building, often retail or warehouse. I handle it in a few ways. Firstly, I ensure that I haven't violated any diaphragm aspect ratio limitations that are code mandated for the material being used. Secondly, I'll use discrete diaphragm bracing if I'm not comfortable with the flexibility of the diaphragm. Lastly, for seismic loads, I'll use an old trick of professor Paulay's. I'll make sure that if my direct shear wall yields (rare), the two perpendicular "flange" walls remain elastic.

2) The second question is how to quantify that the deck is stiff enough to utilize the torsional restraint. There is no binary "rule" for this. Calculate drift at the open side considering vertical LFRS flexibility and diaphragm flexibility. I the drift satisfies code limits and is compatible with the deformation capabilities of the cladding, lean-on columns etc, you're done.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[CELinOttawa]

KootK; Say what you like, but I have seen many of these building on the ground following EQs.

Perhaps, and I only say perhaps, this system is fine for non-seismic areas. That said, it would take a great deal of significant detailing, site verification above the norm, and is very unlikely ever to make me (or many other of your peers as shown by this thread) happy with the design.

Codes are a legal minimum, and particularly in the case of high seismic zones, should not be used as a target for buildings outside of the "norm". Without meaning to offend, I will pass on some advice I received from my first mentor upon graduating: Sometimes when everyone is saying "no", it isn't a challenge, but a lesson.

 

[RFreund]

There is some further relevant info here:

http://www.eng-tips.com/viewthread.cfm?qid=356606

Good points by Kootk. Although I'm not sure if I completely understand this:

Lastly, for seismic loads, I'll use an old trick of professor Paulay's. I'll make sure that if my direct shear wall yields (rare), the two perpendicular "flange" walls remain elastic.

Maybe I'm confused by what you mean when you say the wall has 'yielded'.






EIT

http://www.HowToEngineer.com

 

[hokie66]

The comments about the portal frame (or the moment resisting frame if you prefer) across the open end being useless are, in my opinion, incorrect. In ultimate strength design, the most important thing is to have defined load paths. If you had a portal framed building, then introduced stiff walls on one end and two sides, does that make the building less strong? No, it doesn't.

I agree with CEL...there are inherent problems with depending on only three sides, and I won't do it.

 

[KootK]

@RFreund: my strategy is a loose interpretation of the one employed in this paper: Link. In short, if the "web" wall taking the direct shear develops a plastic hinge to cap the seismic demand, I ensure that the two "flange" walls stay comfortably elastic. That way, there's a competent mechanism for resisting torsion throughout the entire load history. This is more likely to be a concern if the web wall is short or if it's a steel brace instead of a wall. The usual configuration that I deal with is masonry or wood walls where the the wall opposite the open side is relatively long compared to the end walls. In that scenario, everything remains elastic.

@CEL: no offense taken. I generally take a lot of heat for being excessively conservative so it's fun for me to be on the other side of the fence for once. If you re-read the first sentence of my last post, however, you will see that I mostly agree with your concern.

@ Everybody: to add some more food for thought:

1) I just got back from a three week tour of Japan and southeast asia. The dominant building form by far in that region consists of permutations of the building shown in the attached photo. 90% of the building stock is multi-story concrete buildings with concrete shear walls on three sides. While there certainly are buildings like this that have collapsed during earthquakes, the overwhelming majority of them seem to have remained standing. And we're talking about tens of millions of them located around the pacific rim from what I saw. In particular, most of the three sided buildings in Kyoto have remained in tact.

2) In my north american experience, most three sided buildings are elongated rectangles where the "web" walls are relatively long compared to the "flange" walls. This "C" shaped system is fundamentally not much different from an "I" shaped system which is quite common in mid rise hotel construction. This is particularly true when one considers the impact of code minimum eccentricity. Do we have the same beef with "I" shaped LFRS configurations? I've done several of these using wood and CMU/precast systems with long "spines" down the corridor.

3) In NZ, there is research interest in looking at buildings braced by a single central core. The question becomes this: when the core develops a plastic flexural hinge due to direct shear, what then is the remaining mechanism for resisting torsion? Great question, particularly if you've considered your elevator banks to be a pseudo-closed sections.

4) Is a cantilever really anything more than half of an equivalent simple span? Just sayin'.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[KootK]

@Hokie:

1) My argument is not that adding a portal frame weakens a three sided building. It doesn't. My argument is that adding a portal frame doesn't strengthen a three sided building if the two systems never get a chance to act concurrently due to stiffness/deformation incompatibility. I agree that there is some improvement in redundancy however. This, particularly, given that the usual scenario will be the "web" wall going plastic rather than losing its load carrying capacity altogether.

2) Under seismic loading, most of our buildings become something akin to three sided buildings at some point in their loading histories. Even in a building with shear walls on all four sides, the two walls taking direct shear will not yield at the same time. After the first wall yields, any subsequent load will be resisted by what is effectively a three sided lateral system. Of course, torsional inertial of the diaphragm comes into play with this as well. Have fun quantifying that. This ties back in with the strategy of Paulay's that I mentioned above.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[CELinOttawa]

Good to know, and I appreciate the clarification.

Re your photo: These are popular in NZ as well, though usually older designs (again similar to the attached) but narrow and long with lots of good connection to multiple floor slabs is not where this becomes a problem.

In discussing a three sided box design, I have been thinking more the car dealership, grocery store, or strip mall type application. Effectively my concerns occur with square or flag-proportion rectangular where the long side is the open wall, not a tube without a cap (though I am still not a fan). In the NZ examples.the front wall is typically detailed as a concrete frame.

Please note that NZ and Japan both tend to use reinforced concrete floors, making the diaphragms here close to ideally rigid. That helps, and along with the proportions, helps a lot.

 

[JAE]

We don't typically allow 3 sided buildings (per hokie66's view) but in some cases we do - these are typically light framed buildings such as one-story garages in apartment complexes where there is a long series of overhead doors. In those cases, the diaphragm aspect ratio is very large such that the diaphragm deflection, and thus the potential for second order effects, is small.

Check out Eng-Tips Forum's Policies here:
faq731-376

 

[KootK]

Here I'll have to disagree CEL. All other things being equal, I think that a rectangular building is better off with one of the long sides being open than it is with one of the short sides being open. Less eccentricity that way. Also, I still contend that diaphragm stiffness is not a particularly relevant parameter for a three sided building. Stiffness only comes into play for the load distribution to the VLFRS and, to a much less important extent, for P-delta effects. In a three sided system there is little redundancy so the load distribution is apparent. Diaphragm strength matters but that's another story and is generally resolvable.

My best hope for the SE asia building type is that the concrete floors and walls will form kind of a shitty moment frame. I think that was your point in your second sentence. Unfortunately, I got to see a few of these under construction while I was there. The slab / to wall rebar detailing leaves much to be desired. While in Hanoi, I spent a few days at a local structural engineering office. They tell me that these buildings are usually "designed" by the contractor rather than by an engineer. The examples that I saw seemed to have way to much bottom steel and not nearly enough top steel / corner bars at the slab to wall connection.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[msquared48]

If the shear system is shaped like an I beam, I have no problem with it. Not so if it is in the basic shape pf a U. Never would do it either.
.

Mike McCann, PE, SE (WA)

 

[hokie66]

I agree, Mike. The I shaped resisting system is fundamentally different than the C shaped system, and I don't understand why KootK thinks otherwise.

 

[KootK]

Maybe KookK is crayyyyyyyyyyyyyz. It's entirely possible. KootK hasn't slept in days, since returning from Asia, due to the worst case of jet lag imaginable. I wish I had a scanner at home. Let's see what I can do with just prose.

Firstly, imagine a channel and a wide flange beam, both with flanges of equal dimensions that will be held constant. Next, extend the overall depth of both sections towards infinity and note the effect on the shear center of the channel. It moves towards the center of the web. So, taken to the limit of this mental experiment, the torsional behavior of the the two sections is the same. That's why I feel that, for the normal north american case of the open wall length >> than the side wall length, the torsional behavior of a "C" shaped shear wall configuration is not so bad compared to that of an "I" configuration. And we generally seem to be quite comfortable with the "I" shaped layout for some reason.

The previous paragraph assumes that flexural deformation predominates and that the wall segments act compositely. For the usual case of a three sided low rise building, that's unlikely -- shear deformation will predominate. Moreover, if the construction is wood, the walls will not normally be assumed to act compositely. And, of course, if the wall segments simply don't touch, they again won't act compositely. All of this means that, for a low rise building, the assumption of independently acting shear walls is more reasonable than the assumption of composite action. And the shear center eccentricity for a group of walls in a non-composite "C" layout is less than it is for the same group of walls viewed as flexurally composite. So, again, this adds more credibility to the notion that "C" configurations aren't that much worse than "I" configurations.

For sport, imagine a hotel that is 60' x 300' in plan with non-composite shear walls. Give it 60' shear walls at the short ends and a single 250' shear wall on one side of the corridor, say 5' off center. Assume that accidental torsional eccentricity amounts to 5'. Call this the "I" configuration. The "C" configuration would have the 300' wall moved all the way to one side of the plan. The direct shear on the 300' wall will be the same in for each case (V). For the "I" configuration, the end wall shear would be [V x 10' / 300' = V/30]. For the "C" configuration, the end wall shear would be [V x 35' / 300' = V/8.6]. Yeah, it's three times as much as the "I" configuration. However, it's still a relatively small and manageable number.

I misspoke somewhat in my previous post. For a three sided building, diaphragm stiffness does matter. It matters very much for drift prediction and overall P-delta stability. It does not matter, however, for determining the load distribution to the VLFRS. Nor does the ratio of diaphragm to VLFRS deflection matter in the ASCE "rigid diaphragm" classification sense.

In several threads, I've seen this analogy whereby it's proposed that a cap plate welded to the end of the cantilevered channel would significantly improve that channel's torsional properties. Is that really the case? I would think that a cap plate would do next to nothing to improve warping torsion response just like web stiffeners in a torsionally loaded wide flange do next do nothing to improve warping torsion response. In both cases, you just create discrete points where the individual plate elements cannot move relative to one another.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[CELinOttawa]

I still don't think you are technically wrong, KootK, but that it is simply unwise and poor engineering.

Judgement still counts for something in this profession. I judge a three sided system to be a poor, crappy, trouble prone system.

Also, about the long buildings in Asia, I forgot to mention that the often have many interior load bearing walls accross the short dimensions. They aren't really the three sided boxes we are all wringing our hands about.

 

[DaveAtkins]

I don't think KootK is crazy. I designed a three sided industrial facility in SDC B several years ago. I wasn't thrilled about it (and still am not), but I followed all of the load paths, allowed for accidental torsion, provided for diaphragm deflection at the open side, etc.

So...I guess I agree with both sides of the argument here. It is best to avoid the configuration (mainly because a four sided diaphragm has more redundancy), but it can be done.

DaveAtkins

 

[msquared48]

Thinking about the moment frame idea to close the open side of the "C", I have a serious problem... as does Hokie...

The wood diaphragm deflection is not only dependent on the diaphragm stiffness, but also the variable transverse rotational deflection of the end walls, adding to that deflection. This total deflection is not directly calculable and is inherently the problem. Without the actual deflection, you cannot model, or equate, the stiffesses of the diaphragm and frame to equate the deflections.

I just do not trust the "C" scenario, and never will. It just feels unstable, inherently unstable.

Mike McCann, PE, SE (WA)