Subdiaphragm deflection 1

[TehMightyEngineer]

Got an interesting discussion topic from a fellow engineer. In short, it boils down to flexible diaphragms with subdiaphragms and their deflection. For these systems, does the subdiaphragm increase the deflection of the diaphragm (either locally by the subdiaphragm deflecting beyond the diaphragm or by altering the deflection of the diaphragm)?

By my logic it does not in idealized diaphragm design. The way I understand it the subdiaphragms are there primarily to facilitate force transfer and anchorage of the exterior wall into the diaphragm. The tension tie requirements of ASCE 7-10 section 12.11.2.2.1 and similar are there to anchor the diaphragm and ensure that a complete and continuous load path exists in the diaphragm. By exclusion, I feel that subdiaphragms are not there as a structural requirement of the diaphragm and the diaphragm will have strength and stiffness irrespective of the presence of the subdiaphragms. About the only way I can visualize subdiaphragms changing the deflection of the overall diaphragm is that the subdiaphragm essentially "point loads" the diaphragm at the continuous tie points between subdiaphragms. Thus, the diaphragm loading is no longer uniformly distributed (or nearly so) but is evenly spaced point loads.

Thus, I feel that subdiaphragms will not change the deflection of a simple, flexible diaphragm. What do you guys and gals think?

I did a fairly extensive google search and review of literature and wasn't able to find anything specific to the topic one way or another. However, I didn't delve into actual research on diaphragm deflection so perhaps my answer can be found in there.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries

http://www.americanconcrete.com

 

[KootK]

1) The deflected shape of the diaphragm will, of course, reflect the presence of the subdiaphragms to some extent. Little parabolic curve segements following the overall diaphragm curve etc.

2) I would expect a diaphragm with intentionally designed in subdiaphrams to deflect less at all locations than the same diaphragm without the sub diaphragm. The entire sub diaphragm assembly would essentially act as an improved chord, stiffening the diaphragm proper. And any local improvements to sheathing and fastening would have a similar effect.

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.

 

[TehMightyEngineer]

Yay, I'm glad you replied KootK.

1) Would they though? I suppose this falls back into the earlier debate of whether flexible, light diaphragms can take in-plane tension. If they can, then the subdiaphragm can't deflect without "pulling" the rest of the diaphragm with it. However, if you can't put in-plane tension into the diaphragm (which appears to be the proper idealized assumption) then I agree that the subdiaphragm would deflect and create little parabolic curves along the larger parabolic curve of the full diaphragm.

1a) If this is the case, would you say it's reasonable to calculate the deflection of the sub-diaphragms using the SDPWS equations for wood panel diaphragms? Seems like this is the only reasonable option.

2) Would this not (roughly) cancel out the above? Or do you think that a situation could arise where overall diaphragm deflection was only reduced a little by the subdiaphragms but the subdiaphragms were flexible enough to deflect a lot.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries

http://www.americanconcrete.com

 

[KootK]

Old friend + mostly theoretical thread? Like I could stay away...

Your last batch of responses gives me a better sense of where you're going with this. In general, practical design terms, I see sub diaphragms as pertaining to strength and load path primarily. Due to strain compatibility issues, I don't seem them really kicking in any time other than during extreme events that would mostly be limited to seismic stuff. And that, I suppose, reflects code direction as to when sub diaphragms are necessary. I don't see sub diaphragm response contributing meaningfully to diaphragm drift except during extreme, ultimate limit state events.

1) Yeah, that in plane tension business. To the extent that it develops, I see the diaphragm acting as one without the little parabolas for the most part. On the other hand, to the extent that there is some degree of flexibility in the in plane tension connections, perhaps some redistribution is possible. Tough to know with any certainty.

1a) I agree, that strikes me as a reasonable proposal. Technically, you're tension chord will be pulling double duty, being stretched by both the main diaphragm action as well as the sub diaphragm action concurrently. In truth, I don't think that I'd bother with the sub diaphragm deflection except for high seismic drift checks. And even then only in special situations where I felt that it would have a significant impact on stability.

2) My gut feel is that improvement to the overall diaphragm behavior would outweigh the mini-parabolas. Again, it's tough to know without quantifying a particular situation.

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.

 

[TehMightyEngineer]

The overall goal with these questions is to determine whether this will ever be a practical limit that needs to be checked during design or if almost all practical design situations can use diaphragm drift calculated from the overall diaphragm without considering the extra parabolas of the subdiaphragms.

1) Mmmmm, "tough to know" is right. Perhaps the only true answer to this is we really wouldn't know unless we tested this.

1a) Yeah, it would be tricky to make sure the deflection was calculated correctly for the subdiaphragm. For this theoretical discussion lets suppose we're in a high seismic region where reasonably exact diaphragm drift was needed to be calculated and controlled.

2) If I find enough time I'll try to work up a reasonable example and see what I come up with.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries

http://www.americanconcrete.com

 

[Deker]

TME, I agree with your initial assessment. Subdiaphragms are a tool that we use for critical elements to provide an adequate load path into the main body of the diaphragm. They don't necessarily reflect the actual diaphragm behavior. On the other hand, I do believe that their use helps validate the assumption that the entire diaphragm is engaged when resisting loads. Similar to the reasons we provide collectors/distributors across the full depth of the diaphragm.

Where the subdiaphragm is provided with heavier nailing than the rest of the diaphragm, the effect would be to decrease the shear deflection across the entire depth of the main diaphragm by reducing the nail slip. This effect is commonly ignored in practice. Regarding your comment about the subdiaphragm point loading the main diaphragm, consider that the subdiaphragm is only providing a load path for one exterior wall at a time. The other exterior wall and the inertial force from the diaphragm itself can already be considered to be uniformly loading the diaphragm, so I don't think the overall effect is as bad as you think. Especially given the uncertainties with estimating diaphragm deflections.

Below are some excerpts from two great resources for diaphragm and subdiaphragm design. Regarding your comment about diaphragm deflections in high seismic regions, my experience is that deflections are based on the main diaphragm without consideration of the subdiaphragm. The second resource below has a good discussion on diaphragm deflection and its impacts on the rest of the building.

The subdiaphragm used to distribute the anchorage forces into the diaphragm is a part of the total diaphragm and does not act independently. The flange and web shear stresses determined by considering the subdiaphragm as an independent unit are greater in magnitude than those that actually occur. Combining these stresses from local effects with the stresses from overall diaphragm effects seems to be overly conservative and is not current practice.

To prevent subdiaphragms from becoming too flexible compared to the rest of the main diaphragm, ASCE 7-10 Section 12.11.2.2.1 places a limit on the length-to-width ratio of the subdiaphragm at 2.5 to 1. This aspect ratio is assumed to provide sufficient stiffness that the independent deflections between the subdiaphragm and the main diaphragm may be ignored.

 

[TehMightyEngineer]

Great points Deker and star for those two references. I re-skimmed through that WoodWorks article before making this post but missed the key wording of the commentary on the origin of 12.11.2.2.1. Plus, that ATC 7 note is something I missed; for some reason I didn't check ATC 7 and thank you for reminding me to.

I'll put a little more thought into this but so far it seems like we're all correct; subdiaphragms can deflect beyond the overall diaphragm deflection but only if not sufficiently integral with the overall diaphragm which normal practice doesn't appear to typically allow.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries

http://www.americanconcrete.com

 

[TehMightyEngineer]

I suppose one other consideration is subdiaphragms at openings.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries

http://www.americanconcrete.com