Unfortunate Diaphragm Flexural Detailing

[Once20036]

JAE started a thread about how to handle an unfortunate shear wall location.
I highjacked the thread a bit and started talking about the flexural detailing/stiffness of diaphragms and through it would be best to start a unique thread on the topic.
Some of the conversation is summarized below, the rest is here:

http://www.eng-tips.com/viewthread.cfm?qid=438106

JAE: We have modeled the diaphragm as a series of "horizontal beams" along the edges, so to speak, with a stiffness both in flexure and shear that attempts to mimic the deflection behavior of a metal deck diaphragm under the proposed loads.
Once20036: How do you account for chord forces, given that you're counting on the flexural stiffness?
JAE: There are perimeter steel angles (supporting roof deck on the inside face of the panels that can serve as chords.

Flexural deflection of the diaphragm is proportional to the moment of inertia. SDI defines the I as the area of the chord member * the distance between the chord squared (ax^2, from mechanics of materials).
Using the perimeter angles as a chord makes sense for your geometry, but I suspect that you're actually getting very little flexural stiffness, right?
Do you provide a splice detail for these chord angles? I always call for continuous angles but never actually get them (fortunately I don't use them as chords typically, so its not a big deal).

KootK: In the context of this conversation, the chord could also be the wall panels themselves if the wall panels are interconnected.
Once20036: I agree with you and JAE that a perimeter angle (if continuous) could function as a chord, as could properly detailed and connected walls panels.

Within the context of the above question, how do you calculate the moment of inertia for interconnected wall panels. Is it just ax^2 using the area of steel of the tension reinforcing bars in the wall panels? Seems flimsy, but viable.

Then the show must go on. The concept essentially just takes the deck shear around the bend and utilizes the wall panels as very stiff extensions of the "web" in our beam analogy. Most of us carry truss/beam analogy, WL^2/8 diaphragm model around with us in our heads. I think that an expanded, more nuanced definition of "chord" would be:
Any thing or assemblage of things, located anywhere in space, that sufficiently limits diaphragm strain at the deck edge.
Of course, the more complicated one makes the load path, the more work it takes to demonstrate sufficiently restrained deck strain. For most building morphologies, it's not worth the effort.

We might need to agree to disagree on this one, as I don't see how your sketch limits diaphragm strain at the deck edge.
Take the center of the wall, where "chord tension" is highest. The two chord wall segments closest to the center will move away from one another due to the chord tensions. There is nothing to prevent this movement, or limit the strain between these two walls except the deck. I think that where the deck is perpendicular to the edge, it will flatten out some of the corrugations. Where the deck is parallel with the edge, it seems to me that this could lead to tearing of the deck. With either option (parallel or perpendicular) I`d be concerned about durability of the roof. At this point, I think that all of our flexural equations are suspect because our strain no longer varies linearly across the length of the building. We`ll have these high strain regions (at joist between wall segments) which means that actual deflection will be significantly more than expected deflection.

In your channel analogy, it looks to me like it's three flat plates, with load transfer provided by the vertical plates. This geometry is not stable without a) the flexural capacity of the web member (which we do not have in the building, due to the lack of chords) or b) the continuity/moment connections in the corners (which we do not have in the building).
I think that a more appropriate analogy would be extending the "slots cut by a terrible person" across the entire web, to eliminate any flexural strength of the web.
If I found that channel inside an existing building somewhere I`d absolutely re-reinforce it if I were going to add *any* load to it, and would likely recommend reinforcing it even if it was outside the impact of my work.

Granted, all of this is just focusing on the flexural strength. If you were to ignore all flexural stiffness and do your work based only on the shear stiffness, is your sketch more valid? Honestly, I`m not sure and would need to loop back to that question after billing some hours.

 

[P205]

If I understand correctly, in order for the deck to split/flatten out, the perpendicular (to the force) precast walls need to rotate/deflect for this to happen. I think this might be KootK's premiss here. If the walls are connected and prevented from separating from each other, then the deck can't split/flatten.

I could be misunderstanding though.

 

[msquared48]

Isn't that the purpose of the chord steel- to prevent the wall from separating by taking the chord force of the disphragm?

Some would argue that this steel is not needed too, which I have never agreed with, although I can see the numbers...

Mike McCann, PE, SE (WA)

 

[JAE]

Once20036,
From your statement above (my alterations in red)
[red] The[/red] Flexural [red]portion of the total[/red] deflection of the diaphragm is proportional to the moment of inertia.

"Using the perimeter angles as a chord makes sense for your geometry, but I suspect that you're actually getting very little flexural stiffness, right?"
Using an L4x4x3/8, with A = 2.86in^2, and a 60 ft. building width I get an Ix of about 741,000 in^4.
For a 120 ft. long building (diaphragm span) and a 20 ft. height - with 25 psf wind load I get a flexural deflection of 0.055 inches due to flexural deflection only.
Granted - that doesn't include any slip in connections or splices. So not very large - i.e. most deflection is shear deflection.

Do you provide a splice detail for these chord angles?
Yes



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[KootK]

Within the context of the above question, how do you calculate the moment of inertia for interconnected wall panels. Is it just ax^2 using the area of steel of the tension reinforcing bars in the wall panels? Seems flimsy, but viable.

Yeah, that's certainly one way. As with all thing in our world, you're telling a story and, as the author, it's a bit of a choose your own adventure kind of tale. A few of things to consider:

- Often, chord forces are of such a magnitude that you're unlikely to crack the wall panels.

- Even when the deck angles are not made continuous, they generally still exist in the non-continuous manifestation. So, as far as strain and strength go across the length of an individual panel, you've still got the angle. The angle and the wall really. In this sense, meaningful chord strain really just boils down to what ever slip may occur at the in-plane connection between panels. A bit like hold down slip in shear walls.

- I'm probably not the best person to answer this question because, as you've no doubt surmised, I don't take chord action too seriously for this particular building morphology. I see the deck angle business as more of a code check compliance convenience rather that a likely load path. For these kinds of buildings, my diaphragm concerns are mostly about the P-delta effects that JP mentioned in the other thread and the wall panels separating from the deck in the out of plane direction under seismic. If there are examples of massive "chord failure" disasters having occurred in big box industrial buildings, even under severe seismic load, I've not been made aware of them. That kind of thing is always fun to say here because somebody is almost always able to produce an example.

If I understand correctly, in order for the deck to split/flatten out, the perpendicular parallel (to the chord force) precast walls need to rotate/deflect for this to happen. I think this might be KootK's premiss here. If the walls are connected and prevented from separating from each other, then the deck can't split/flatten.

Any chance you actually meant that? If so, that's just what I'm saying.




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]

[blue](Once20036)[/blue]

Using the perimeter angles as a chord makes sense for your geometry, but I suspect that you're actually getting very little flexural stiffness, right?

It's worth noting that with most structures you are getting a lot of help (whether most realize it or not) from the collective behavior of the numerous chords (i.e. flexural members attached to the diaphragm) at locations other than the perimeter. I've always suspected that most diaphragms (especially in wood buildings) are much stiffer (as a result) than we give credit for. It can also hurt in some situations.

A good paper on this:

http://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1070&context=aen_fac

 

[P205]

@KootK I originally meant perpendicular to the wind/seismic force direction, which also works.
Basically the walls along the chords.

 

[Once20036]

If I understand correctly, in order for the deck to split/flatten out, the perpendicular (to the force) precast walls need to rotate/deflect for this to happen. I think this might be KootK's premiss here. If the walls are connected and prevented from separating from each other, then the deck can't split/flatten.

KootK's sketch in the previous thread showed some walls connected and some walls unconnected. I think that we're all on the same page that if all of the walls are connected, we have a continuous chord, and no problems. To me, the interesting conversation is whether or not its ok to have gaps in the walls and no continuous axial chord member at the roof level.
I don't want to speak for KootK, but I think he's saying that's ok, provided sufficient detailing at the foundation level.

Isn't that the purpose of the chord steel- to prevent the wall from separating by taking the chord force of the disphragm?

What if there's no chord at the roof level?

most deflection is shear deflection

The effectiveness of an L4x4 is much bigger than I thought! That x^2 goes a long way. Thanks.

 

[Once20036]

If the walls are connected and prevented from separating from each other

Did I miss this along the line somewhere? I agree that if we're connected, we're fine. This connection could take many forms (continuous spliced edge angle, wall to wall tension ties, masonry bond beams, a wacky load path that jogs in an out of the walls and a discontinuous edge angle, etc)

It's when there is no connection at the roof level that I worry.
While unconnected walls will mitigate the movement, I worry about what happens to the deck at these joints and all of the second order impacts that are a result of that movement.
What would happen to your deflection diagram if you had spikes in your strain at 1/10th points along the length of the beam? Isn't that analagous to these gaps in the perimeter walls?

 

[JAE]

In our particular building case (from the first post) we have individual precast walls which do have only limited inter-connectivity.

However, the precasters typically don't design these connections to serve as part of a diaphragm chord system unless they are specifically directed to do so....which is rare.

Most precast wall-to-wall connections are typically kept away from any connecting diaphragms - perhaps at the 1/3 points of the wall height. This allows the panels to have some
level of flexibility from thermal, or other building movements.

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[JoshPlumSE]

If we take a Terry Malone type of approach (which I try to do) for the case of the chord tension ties varying between walls and (where walls are discontinuous) angle ledgers or such:

You've got a slight plan discontinuity in your diaphragm. So, you need to make sure that chord force can adequately transfer from the angle into the wall and vice versa. Provided that works, then I don't see any problems with this type of approach.

If those force transfers are not checked, what do you have? In reality (which is what I think KootK is saying) if this doesn't quite calc out it is unlikely to be a brittle failure. You'll get some localized diaphragm failures, maybe some extra deformation. But, unless you get some brittle unzipping of your shear anchors, then I imagine the failure is going to be pretty ductile.

While I may not personally feel comfortable relying on this, I understand what he's getting at. It's too aggressive of a strategy for me, but that doesn't mean it's truly wrong or dangerous.

Now, if someone started teaching a class with this concept or wrote a book saying that the chord forces are just going to take care of themselves, then I'd have a real issue. Because it wouldn't be doing an effective job of teaching design concepts / theory to the next generation of engineers. But, once you fully understand those design concepts, I believe each engineer deserves a bit of leeway based on their own engineering judgment.

 

[KootK]

We might need to agree to disagree on this one

Seems premature to me. Given the effort already expended, I'd much prefer to continue and hopefully have one or both of us learn something.

@KootK I originally meant perpendicular

Check.

Isn't that the purpose of the chord steel- to prevent the wall from separating by taking the chord force of the disphragm?

It's definitely one of the purposes in many systems. However, in the case of precast wall panels, I'd argue that wall separations isn't actually a problem for the walls themselves (kind of pre-cracked) and it's more about the roof deck.

The two chord wall segments closest to the center will move away from one another due to the chord tensions. There is nothing to prevent this movement, or limit the strain between these two walls except the deck.

Sure there is. Movement at the tops of the walls is limited by the walls acting, rather excellently, as shear walls. It's good enough for limiting drift in 30 story buildings, right? What's a little deck shear by comparison?

At this point, I think that all of our flexural equations are suspect because our strain no longer varies linearly across the length of the building. We`ll have these high strain regions (at joist between wall segments) which means that actual deflection will be significantly more than expected deflection.

Were our diaphragm flexural equations ever not suspect? The whole beam treatment on diaphragms is really a pretty serious stretch in the first place. You get this same phenomenon, with walls messing with the strain locally, whether you want it or not, every time that a chord is attached to a wall. And chords are attached to walls pretty much always because they're collectors in the other direction. Plus you've got the whole connection slip thing muddying the waters as JAE pointed out. AND most of the deflection is shear related.

We`ll have these high strain regions (at joist between wall segments) which means that actual deflection will be significantly more than expected deflection.

I think it will be exactly the reverse. Deformation is the integration of strain along the length. Over most of the length, there will be almost no strain.

In your channel analogy, it looks to me like it's three flat plates, with load transfer provided by the vertical plates. This geometry is not stable without..

You're reading far too much into this I'm afraid. I had assumed that, like most of us, your training in diaphragm theory started with the ubiquitous analogy of a wide flange beam. Roof deck = web, deck angle = chord/flange... the kindergarten stuff. Therefore, I'd hoped that the channel treatment, by way of parallel argument, might smooth things along on our journey through deeper waters.

This geometry is not stable without a) the flexural capacity of the web member (which we do not have in the building, due to the lack of chords) or b) the continuity/moment connections in the corners (which we do not have in the building)

It is stable, with no flexural capacity in the web, so long as you have:

1) A transverse lateral system at the ends and;
2) A mechanism for resisting OT in the the little "shear wall" bits between slots.

Both of those things are present in real buildings.

I think that a more appropriate analogy would be extending the "slots cut by a terrible person" across the entire web, to eliminate any flexural strength of the web.

We don't do this for the wide flange beam analogy so I didn't feel it necessary for the channel analogy. Moreover, showing a bunch of slots in the web seems as though it would cause more confusion than it would resolve. After all, how is a shear panel web with a bunch of slots across it supposed to resist shear, it's primary job?

If I found that channel inside an existing building somewhere I`d absolutely re-reinforce it if I were going to add *any* load to it, and would likely recommend reinforcing it even if it was outside the impact of my work.

Again, reading far too much into the analogy. I'd never meant to suggest the channel business as some literal, messed up element that one might actually have to deal with in the wild.

If you were to ignore all flexural stiffness and do your work based only on the shear stiffness, is your sketch more valid?

Absolutely not. As I mentioned in the other thread, equilibrium requires both a shear load bath and a flexural load path. One or the other might dominate flexibility but neither can be omitted outright.

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]

Given the many references to my sketch in the other thread, it seems prudent to include it here.

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]

To me, the interesting conversation is whether or not its ok to have gaps in the walls and no continuous axial chord member at the roof level.
I don't want to speak for KootK, but I think he's saying that's ok, provided sufficient detailing at the foundation level.

That is a correct interpretation.

Did I miss this along the line somewhere?

Not sure. Regardless, I contend that there is a viable load path and strain resistance mechanism both with and without an in-plan tension connection between wall panels.

What would happen to your deflection diagram if you had spikes in your strain at 1/10th points along the length of the beam? Isn't that analagous to these gaps in the perimeter walls?

Not much. Local discontinuities won't mess with the overall behavior all that much. And, similar to JAE's calc, if you run the numbers you'll find that the tops of these little shear walls aren't moving too far. Without question, it's of no concern when the corrugations run perpendicular to the wall.

Now, if someone started teaching a class with this concept or wrote a book saying that the chord forces are just going to take care of themselves, then I'd have a real issue. Because it wouldn't be doing an effective job of teaching design concepts / theory to the next generation of engineers. But, once you fully understand those design concepts, I believe each engineer deserves a bit of leeway based on their own engineering judgment.

I'm afraid that I object to this. I'm not saying that chord forces "just take care of themselves". I'm saying that there are alternate, valid load paths that can be exploited with purpose. I'm also saying that when walls are very stiff, this isn't just an alternate load path, it's the most likely load path (see my CMU wall example from the other thread).

JLNJ nailed it the other thread. I'd much prefer that students truly understand load path rather than just blindly sticking to the one presentation that shows up in print simply because it shows up in print.

When you understand load path, a whole world opens up to you.

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]

For those not already familiar with it, reviewing this thread might be of benefit: Link. It covers much of the same theory but from a somewhat different angle.

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]

I'm not saying that chord forces "just take care of themselves". I'm saying that there are alternate, valid load paths that can be exploited with purpose.

Well, you started out saying something pretty similar to that, though I shouldn't have put words in your mouth. I'm just thinking that's how a young engineer would/could have interpreted it when reading it in a book or taking a class. To your credit, you then started justifying your actual thought process and the probable (but relatively complex) load path involved.

My biggest objection to this is merely, that I prefer a "cleaner" chord force concept for my structures. Not that your concept is wrong.

I do, however, feel strongly that we should teach the classic concept to young engineers. Once they grasp that theory fully, then they can "graduate" to something more complex like you describe if they so choose. But, to teach that early on, feels like it would undermine the classic concept at a time when those concepts need to be be reiterated and reinforced again and again.

 

[KootK]

Well, you started out saying something pretty similar to that

It is true that I feel that way so it's unsurprising if the sentiment leaked into my comments.

My biggest objection to this is merely, that I prefer a "cleaner" chord force concept for my structures.

Agreed. I'm pretty sure that I said something similar my self in the other thread. The alternate coneption just seems to be what folks are interested in discussing.

But, to teach that early on, feels like it would undermine the classic concept at a time when those concepts need to be be reiterated and reinforced again and again.

I go the reverse. I think that a fundamental understanding of shear transfer behavior should precede the use of analogy short cuts. Or, at best, the analogies should be used simply as a means of aiding the understanding of the fundamental concepts. It's not like shear transfer theory is particle physics. You just need to "see it" once or twice. Instead, we've got everybody gummed up trying to satisfy the analogy rather than the true fundamentals. Anybody that truly understand diaphragm theory should be able to look at my sketch and "see it" without much fuss. Whether or not the path is stiff or strong enough are separate questions and pretty much just boil down to the "engineering".

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.