Vertical Distribution of Seismic Demand for Multi-Story Buildings w/Flexible Diaphragms & Setbac

If the diaphragm is flexible I'd tend towards your right hand solution. Tributary mass of wall/roof/floor to each wall to work out periods and hence base shear. I assume most of the load is in the walls so the load stays in the wall, though you didn't note the construction of the walls.

I'd consider 60% of the tributary width of the floors/roof portion of loads for working out the loads going to each wall, meant to allow for some stiffness in diaphragm attempting to share some load and to cover some effects like accidental eccentricities, any uncertainties in the simplified approach, etc. I think as a reviewer this sounds logical, and has an apparent element of conservatism. Combined with good diaphragm detailing at perimeter (chords & fixings) and I'd doubt you'd have any issues with a peer review.

I think rigid diaphragm analysis will only show you that it's not a valid approach in this situation and you'd get quite a different distribution to that being proposed and significant transfer of loads at the first level (the kickback effect common in podium/tower configurations). This would be an incorrect assumption if diaphragm is truly flexible.

Agent666 said:

If the diaphragm is flexible I'd tend towards your right hand solution.

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Thanks, it's good to know I'm not the only one who sees it this way. Have you ever known anyone to actually do it this way though?

Agent666 said:

though you didn't note the construction of the walls.

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Wood shear walls. See detail A.

Agent666 said:

Combined with good diaphragm detailing at perimeter (chords & fixings) and I'd doubt you'd have any issues with a peer review.

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I'm not so sure. My limited experience with California residential review thus far has been:

a) It's usually a specialty, external entity doing the code review rather than an AHJ staff member.

b) It's usually not a licensed engineer doing the review.

b) The reviewers are all about ticking off boxes and they like numbers to consistent throughout the plans and calcs.



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kootk said:

Have you ever known anyone to actually do it this way though?

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Happens all the time here, I've done it a few times this year on residential construction. Not everything needs to be done to death via some finite element model.

Understand the review approach, its the same the world over... I just explain the logic in a logic manner in the calculations and never had a problem. Often when I'm doing peer reviews provided what the engineer did sort of slots into the 'it's kinda what I would have done' camp, then if the numbers work out and they aren't invalidating any laws of physics and appropriate detailing is being used then who am I to say it isn't an acceptable approach.

Agent666 said:

Happens all the time here, I've done it a few times this year on residential construction. Not everything needs to be done to death via some finite element model.

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Interesting, I'm surprised to hear that. I was expecting to hear that most designer would consider it pretty onerous to have to recalculate the vertical seismic distribution for each line of shear walls on a project. That said, with the right spreadsheet, I don't think it would be too terrible. I'll be curious to see what others have to say about this proposed practice. If it turns out that I'm the only one who's not been doing this, I'll feel a bit silly.

I feel that someone must surely make the the objection that: doesn't the whole building respond to excitation as a unit? And to an extent, I've no doubt that it does. But then that leans on diaphragm rigidity.

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Caveat: I violated what you said and didn't quite fully digest the sketch, but I'm going to respond anyway!

Assuming flexible diaphragms, I have done separate analyses line by line many times over.

I typically trigger it when I see large discrepancies in mass distribution, or like your case, story discrepancies.

I've also done this in a "single story" steel building with an interior mezzanine along one side of the building. 2 story analysis for the side w/ mezz, 1 story for the other side. I am confident that I have read this as an example in a design guide somewhere, but I can't recall where...

koot said:

But then that leans on diaphragm rigidity.

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Exactly, that's the key differentiator. Even though its 'flexible' it's still probably capable of transferring some load in reality, but generally at some point the diaphragms will yield in some way if you load them hard enough and response gets sloppy as fixings yield and the system reverts to a more simply supported state spanning between walls.

jittles said:

Caveat: I violated what you said and didn't quite fully digest the sketch, but I'm going to respond anyway!

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Meh, sounds like you've got a handle on the issue. Thanks for the input. The mezzanine example is both interesting and salient. I suppose that the effect of a concrete topped mezzanine in that instance would be to shift the SDF location down substantially and thus increase the seismic coefficient that would apply to the load coming into the lateral system from the roof.

I suppose that one saving grace here is that this would usually come up for short buildings where the assumed period probably would not change for the different lines of shear resistance. Having to go all the way back and redo your base shear calculations, in addition to your vertical distribution, would just make the task that much more onerous.

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jittles said:

example in a design guide somewhere, but I can't recall where...

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You may be refer to FEM 451 Design Examples. There is one for a pre-engineered building with a mezzanine.

Typical practice in CA would be to have SW1 designed for Cs. Vertical distribution is accounting for the likelihood that the building will not see all floors see peak accelerations at the same time. The peak accelerations will still be dampened regardless of the behavior of the diaphragm. The "drag" from the two story portion will still impact the lower roof and reduce loads on the wall. You are still designing the diaphragm and connections for a force level above the wall force and yielding of the wall means extra energy absorption and a reduced peak acceleration.

sandman21 said:

Typical practice in CA would be to have SW1 designed for Cs.

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Thanks for the input. It is indeed starting to sound as though I'm the only nut-ball not doing this.

sandman21 said:

Vertical distribution is accounting for the likelihood that the building will not see all floors see peak accelerations at the same time.

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Can you expand upon this a bit sandman? My understanding is this:

1) It is the case that accelerations suggested by the vertical distribution of base shear will not be large enough to capture the maximum acceleration that any individual, MDOF diaphragm may experience in a seismic event. Hence the ASCE7 section prescribing higher loads for diaphragms.

2) It is not the case that the vertical distribution of base shear is a result of individual, MDOF diaphragms not seeing peak accelerations concurrently. The code prescribed distribution is what it is as a result of the SDOF shear building assumption alone.

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I’ve also had times where I struggled to reconcile the code vertical force distribution with rigid wall/flexible diaphragm buildings. That said, for the example you’ve shown, I would stick with normal practice. Structural engineering is complicated enough without overthinking these things (which I am guilty of doing often). As long the shearwall design force is reasonable—i.e. not so excessively low that its ductility capacity will be exceeded—and your building is detailed properly in the spirit of capacity design, I wouldn’t be losing sleep over this.

I’ll disagree with sandman21 that it is common practice in CA to design SW1 for Cs. If this were more of an appendage like a small mezzanine in a warehouse, then I agree. But for your case where the low roof and floor share a common diaphragm, my experience is that the walls are typically designed for their tributary share of the story force at each level.

KootK said:

Thoughts? I very much want to do as I've shown below but I fear that it might catch unwanted AHJ review attention (California).

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Feel free to design as you wish, but definitely only include your detail C analysis in the submittal calcs. Especially if you expect that the plan checker will be non-licensed or, worse, a PE (they often know just enough to be dangerous). Even if you knew the reviewer would be an SE, sure they could follow along, but I doubt they'd push back on your normal analysis. I just don't see the benefit for you to document any above and beyond code design in your submittal calcs.

The higher loads on the diaphragm is to account for the chance that any one level may see its peak acceleration but the building as a whole will not have all floors at peak acceleration. The vertical distribution formula is a simplified first mode analysis with k being used to account for higher modes. If you review higher modes for a general building you will see that different floors will peak at different times.

Most DSA reviewers and a number of firms will design the wall for Cs.

Thanks for taking the time to clarify sandman.

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sandman21 said:

Most DSA reviewers and a number of firms will design the wall for Cs.

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sandman21: I believe we both practice in the Greater LA area. I don't doubt your experience, but again, my experience as a designer (DSA projects included) and as a peer reviewer leads me to believe that it is far from common to design the condition shown in KootK's sketch for Cs. If there were an offset in the floor elevations or some other type of irregularity, then yes, but even then it's still a judgement call. Perhaps you can direct me to a DSA amendment / bulletin / IR that can convince me otherwise.

It's worth noting that ASCE does address this, but it's in the simplified section of the seismic chapter. And for the purpose of this discussion, I think that's helpful since it's more binary. While Section 12.8.4 requires that the design story shear be distributed based on the relative stiffness of the diaphragm and vertical elements, Section 12.14.8.3.1 (written specifically for flexible diaphragms) requires that the story shear be distributed based on tributary area (as opposed to the tributary mass being used to determine the vertical force distribution).

For those who would tend to design based on KootK's detail D, does that hold true for any configuration with flexible diaphragms? Or is it more of a judgement call based on the proportions presented in the original sketch? What about for the configurations shown below? Again, assuming flexible diaphragms.

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KootK...one other thing to consider...will you be providing special detailing to break your diaphragm chords at the interior shearwall? If not, how will you distribute the seismic mass of the 2nd floor / low roof to your shearwalls? Will you follow standard practice and use tributary areas (25/50/25)? Or will you consider diaphragm continuity (19/62/19)? Or will you bracket the two (25/62/25)? I'd argue that any of these options are reasonable despite the significant difference, and larger is not always better, particularly without a commensurate increase in the upstream load path. I know you understand this, and I only bring it up to reemphasize that the force level we use for seismic design is far, far less important than the detailing. As long you are designing to current codes and not using 3.7% base shear from 1948, I would try not to sweat it.

You would never get a DSA amendment, bulletin or IR for this condition at most you could try and get a form 60. I doubt you would get a response. It is a common enough condition that both the LA and San Diego office will routinely request an overlap design. Clearly not every reviewer has made the comment but enough have commented that we do it as standard practice. We are not the only practice that does it, I feel confident say that it is more typical than using just vertical dis.. The use of Cs would still use trib. area to determine the only difference is that the lateral load will be higher than just vertical dis. Case 1, 2 and 3 would be overlapped with Cs being used for the outer walls. You do not need to do this but the time and cost for some reserve capacity in the building is so minor to not justify arguing with a reviewer.

For us non Canadians, can someone briefly outline what 'Cs' is in terms of this discussion?

CA = California
Cs is seismic response coefficient. Seismic load = CS*weight

Deker said:

For those who would tend to design based on KootK's detail D, does that hold true for any configuration with flexible diaphragms?

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Yes.

Deker said:

Or is it more of a judgement call based on the proportions presented in the original sketch?

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Certainly, more extreme situations nag at my gut feel for the situation more than others. A 50'x50' L2 over a 50'x65' L1 gives me no grief. For the actual building that I'm working on, which is close in proportion to your case 1, my visceral response to the thing is that little of the Cs response should be getting "siphoned" away to the multi-story part of the building. That, particularly, given that my low roof has gravel & pavers making that area a more mass intensive than the rest.

It's a weird thing though. I'm highly analytical by nature. Once I put myself in the zone with respect to "flexible diaphragm" it's hard for me to turn it off and remain objective.

Deker said:

What about for the configurations shown below?

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All four for me. Case four is particularly bothersome. With the two stories, I'm confident that all of the walls will have very short periods and that the risk of inducing meaningfully different vibratory responses among the walls is small. As it gets taller, I start to worry more about individual walls doing their own seismic dance as it were. The higher up in the air a diaphragm is, the more I like it to be rigid.

Deker said:

KootK...one other thing to consider...will you be providing special detailing to break your diaphragm chords at the interior shearwall?

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Are you being facetious? I can't tell. I've never even heard of such detailing. And I wouldn't be providing it either way. I'm very much in the old school camp where tying every damn thing together as much as possible is a virtue to be discarded with care.

Deker said:

If not, how will you distribute the seismic mass of the 2nd floor / low roof to your shearwalls? Will you follow standard practice and use tributary areas (25/50/25)? Or will you consider diaphragm continuity (19/62/19)? Or will you bracket the two (25/62/25)?

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25/50/25. It's worth noting that the true shear deformation of the diaphragm actually does tend to respond this way so 19/62/19 is a non-possible. I take your point though.

Rest assured that I've not allowed myself to get bogged down with this. It's more a matter of curiosity. As I was executing my design, I simply had an a-ha moment where I suddenly felt it ridiculous to be designing the far wall for less that Cs. And it's been beneficial for me to find out that, at the least, others have been thinking the same thoughts.

What I actually did for the project du jour is this:

1) Assumed the SDOF to be at the low roof level for working out the upper level contribution to the shear walls. F2/W = 0.31 ~ 2 x Cs. No meaningful penalty.

2) Assumed the SDOF to be at the low roof level for working out the lower level contribution to the shear walls F1/W = 0.15 = Cs

3) Dialed back the upper floor contribution to the lower level walls such that the base shear at each wall is correct at (F2_+ F1)/W = Cs

It sounds like a mouthful but was actually super easy to execute. It's also reliably conservative, but not excessively so, in my opinion.

Deker said:

I know you understand this, and I only bring it up to reemphasize that the force level we use for seismic design is far, far less important than the detailing.

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Yes and no. In my particular example, the effect would be to shave off about 25% of the shear to some of the low walls. And while I believe that wood buildings are ductile in aggregate, I've not found the ductility of individual walls and their connections to be that convincing. Of course, if I had my druthers, nothing in the realm of single family timber residences would be getting engineered to begin with. Rough stuff indeed.


HELP! I'd like your help with a thread that I was forced to move to the business issues section where it will surely be seen by next to nobody that matters to me: