Diaphragm Chord Design - Rigid Diaphragm Analysis 1

[engjg]

IBC/ASCE 7 permit rigid diaphragm assumptions under certain situations for both untopped metal decks and concrete filled metal decks diaphragm. Does the code require diaphragm chord forces be evaluated (designed for) if you are permitted to use a rigid analysis assumption?

 

[MrHershey]

To my knowledge, the code doesn't really comment on it. In theory, if your diaphragm is perfectly rigid and can't deform then you don't have a chord force. No strain = no stress. Would think in practice if you qualify as a rigid diaphragm under ASCE 7's definition then your chord force would be pretty small anyways.

 

[KootK]

Since no diaphragms are truly rigid, yes, you would still have to evaluate diaphragm chord forces. In my experience, once diaphragm moments are established, most engineers will design the chords just as they would for a flexible diaphragm. Namely, with discrete boundary members taking all of the flexural tension. In many cases, one could argue that tension chord action may be distributed throughout a large width of the slab. In that case, it's important to note that:

1) this assumption will increase unit shear stress within your diaphragm.

2) this assumption, combined with yield stress in the interior of the slab, may result in excessive strains at the exterior of the slab.

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.

 

[sandman21]

The requirements of 12.10 apply to diaphragms, flexible or rigid. Our assumption that a diaphragm is rigid is just a means of approximating the behavior to determine load distribution.

 

[engjg]

Thanks all for the responses

KootK: What about if you have modeled using a semi rigid model and found minimal axial stresses in diaphragm due to bending?

Also would you agree standard for our industry is:

Untopped metal deck: chord element typically designed as perimeter angle
Concrete filled metal deck: added reinforcement designed as chord element (edge angle does not seem viable due to splicing at columns)

sandman21: What about if your project's governing code exempts seismic requirements but you have high wind; are you aware of anything codified in IBC/ASCE 7 when lateral design is governed by wind?

 

[Once20036]

Personally, I always think about a beam and a diaphragm as being roughly analogous.
In a beam, whether its a relatively flexible W8 or a relatively rigid W33, your moment is your moment and needs to be resisted by your flanges. Using a rigid beam doesn't change this.
For a building with a rigid frame on each exterior wall, your bending moment and chord forces will be identical regardless of whether you call it a rigid diaphragm or a flexible diaphragm. If you add an intermediate frame, your moment diagrams will change (2 simple spans for flexible, vs 1 continuous span for rigid), but these moments still need to be resisted by chords.

Perimeter angles in an untopped metal deck are not sufficient for the chord forces (both tension and compression) that I typically see in a building, plus, the erectors are not accustomed to slicing these angles to create the continuity that you need. I specify an axial force in the connections of my perimeter beams and use these as my chords.

None of this changes for wind loads vs seismic loads. When you have a bending force on a beam, you need flanges to resist that bending, regardless of whether the load comes from dead load or live load. Equivalently, you need to chords regardless of wind vs seismic.

 

[KootK]

KootK: What about if you have modeled using a semi rigid model and found minimal axial stresses in diaphragm due to bending?

As I mentioned in my first post, one can assume that the chord is distributed throughout the diaphragm rather than localized at the edges. When doing that, however, one needs to ensure that their assumptions are sensible. For example, you may not want to rely on the flexural tension capacity of your diaphragm concrete if you're unable to guarantee that same concrete won't develop through thickness cracks due to restrained shrinkage etc.

Also would you agree standard for our industry is...

Those are indeed the normal practices in my market.

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.

 

[Once20036]

KootK, I`m curious about the assumed behavior you describe and wonder if it's because we're talking about different diaphgrams.
I typically deal with metal deck diaphragms and it's how I read the original questions.

Are you statements above based on a reinforced concrete diapgragm, such you that don't need a steel collector and instead provide some distributed reinforcing over some perimeter zone to resist the "chord forces" in the concrete?

If not, and we're both talking about an untopped metal deck/roof diaphragm, how to you evaluate the tensile/compressive strength of the deck? How do you determine the "effective width" that can be used to resist the tension/compression?

 

[BAretired]

Deep beam theory?

BA

 

[KootK]

Are you statements above based on a reinforced concrete diapgragm, such you that don't need a steel collector and instead provide some distributed reinforcing over some perimeter zone to resist the "chord forces" in the concrete?

That's exactly the case that I had in mind. Either CIP slab or composite deck. Which isn't to say that the same concept might not apply to more exotic materials like CLT or the congealed "slime" that my daughter continues to make despite her nearly being able to drive a car.

If not, and we're both talking about an untopped metal deck/roof diaphragm, how to you evaluate the tensile/compressive strength of the deck? How do you determine the "effective width"

I don't. Although:

- I'd be game for it if the flexural tension and compression forces ran parallel to the flutes and I had some guidance for how to evaluate capacity.

- On occasion, I've used framing lines inboard of the perimeter as my chords. I do this where there's lot of articulation in the perimeter and all the drag struts start to look nutty. It warrants a strain check at the true perimeter.

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.

 

[DaveAtkins]

I have toyed with the idea of treating an untopped steel deck as a rectangular beam with no flanges--thereby eliminating the need for actual chord members around the perimeter. Of course, this is strictly prohibited by code, I believe. I even read a paper where someone played with the same idea. He said if you were to carry this to its logical extreme, the shear at each end support would not be uniform--it would be maximum at mid-depth of the diaphragm (think fv = (3/2)(V/A) in a rectangular wood beam).

If you look at the diaphragm this way, the maximum tension or compression would be at the two edges of the diaphragm, varying to zero at mid-depth. Or, when the shear force is parallel to the flutes, the supporting members (such as open web joists) would all carry some tension or compression, again varying from a maximum at each edge of the diaphragm to zero at mid-depth. This type of analysis is actually done with wood post frame buildings, where wood purlins are topped with steel roof deck. The wood purlins nearest the edges of the diaphragm carry the most tension or compression, where the purlins at mid-depth have zero force.

DaveAtkins

 

[BAretired]

Using deep beam theory, plain sections do not remain plain and normal beam theory does not apply. Nevertheless, it is probably simpler to assume chord forces at the edge of the diaphragm.



BA

 

[KootK]

I mostly just do this when it's a CIP slab. With seven billion pieces of rebar flying around, it's always seemed a bit ridiculous to me to be saying "these two #4 bars, those are the chord". Waste of everybody's time. I don't even bother to investigate unless its something weird with openings or a high aspect ratio.

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.