3-sided braced diaphragm: chord?

[jtse]

Straightforward question: if you have a diaphragm braced on 3 sides, is there a chord force generated when the load is parallel to the single brace? It seems to me that, no, there is not, but rather 2 perpendicular shears that restore the torsional moment (possibly generating collector forces through the diaphragm). But no true chord force. I've seen people analyze the situation as a cantilevered beam, but the analogy breaks down at the 1-sided brace: where the chord force is highest, the chord terminates and nothing is there to resist the force. I've never seen this addressed in a reference.

If there is not a chord force in a 3-sided diaphragm, I have a follow-up question for a typical (4-sided braced) diaphragm.

 

[atrizzy]

Yes, there may well be a chord force in a 3 sided diaphragm. If the lateral force resisting system components on the two parallel walls don't constitute the entire length of the wall, for instance. The 'moment' on the diaphragm due to the torsion will exist until it meets the lateral resisting components on each of the parallel walls. By the time the parallel lateral resisting components are done resisting the moment, the chord forces return to 0, just in time to meet with the perpendicular shear wall.

 

[jtse]

If I'm following you, I think we're saying the same thing. The perpendicular shear walls push a shear force through the diaphragm (perpendicular to the lateral load), which I referred to as a collector force. But this would in theory not need to extend the full diaphragm width, as the diaphragm isn't really 'spanning' to anything. It would just need to distribute the perpendicular shear wall reaction to the point it is within the allowable shear capacity of the diaphragm.

My follow up question is this: if this concept works for a 3-sided diaphragm, what about when you add back in the 4th wall? It seems like a chord may be redundant; the 2 parallel walls take the shear forces and the 2 perpendicular stabilize the diaphragm with shears as well, but no true moment is required.

I'd personally still put one in, it's just got me thinking about it.

 

[sticksandtriangles]

JTSE,

I have thought about this exact same thing. Not sure why we can't do the same thing in a 4 sided set up like we do in a 3 sided box.
I agree, it feels redundant to have a chord and shearwalls in a 4 sided setup when in the 3 sided box, we rely on the perpendicular walls to take out our chord/collector forces.

S&T.

 

[KootK]

To the extent that there is any confusion here, I think that's just a matter of semantics. It seems to me that you've got a pretty good handle on the mechanics of the situation. Here's a way of defining things that I find expedient:

I consider the "diaphragm" to truly be just the diaphragm. No chords, no collectors. If a diaphragm has only one source of external shear resistance in which to dump the direct shear component of the applied load, then it is a cantilevered diaphragm. If there is more than on source, then it is a simple spanning diaphragm (or perhaps continuous multi-span).

Every differential element within a diaphragm has complementary shears on all four sides. At the boundaries of the diaphragm, as I've previously defined it, those shears need to dump into something. At the location(s) of direct shear resistance, the shears dump into the collectors. At the boundaries running perpendicular to the load, the shears must dump into something as well. And that something is what I deem to be the "chord".

The chord itself needs to be prevented from translating along it's own axis of course. However, where that resistance is supplied doesn't, in my mind, change the chord's primary function. In a cantilevered diaphragm, the resistance could be supplied at the tip of the cantilever, the base of the cantilever, anywhere within the span of the cantilever, or even somewhere beyond the span of the cantilever. None of this affects the diaphragm proper. Nor does it affect whether or not there will be a "chord". Defined this way, there's always a chord.

In analyzing the chords themselves, the locations of resistance to chord translation (braced frames etc) do matter. They'll affect:

- the peak force in the chord.
- the distribution of force in the chord.
- the manner in which the chord's axial deformation will add a flexural component of deformation to the diaphragm's shear deformation.

As for the four sided diaphragm case: sure, we could treat that as a pair of cantilevered diaphragms. Similarly, we could treat a simple span wide flange beam as a pair of cantilevers that are fixed to one another at mid-span and "cantilevering" from that mid span connection. And whether we go with a simple span diaphragm or a pair of faux cantilevered diaphragms, there will be "chords". Just differently loaded chords. I think that we typically go with with the simple span assumption on four sided diaphragms because:

- It's simple.
- For the most part, we expect it to be a better representation of true behavior.
- For the shear component of diaphragm deformation, it actually makes no difference.
- It does not require the presence of lateral resisting element along the chords which is expedient.

In my experience, it is true that the presence of lateral load resisting elements along chords alters their behavior and loading in ways typically not accounted for by designers. That's often conservative but not always. I, myself, do it no differently and no better than anyone else. I just think about it pretty hard.







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.