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two-stage analysis 3

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Daniel-PRE

Daniel-PRE

Specifier/Regulator
Sep 5, 2023
13
I'm reviewing a design where the engineer is wanting to use two stage analysis to get out of loading the roof with seismic weight from the concrete topped mezzanine deck. The problem is the base for the upper structure is not all at one level. This doesn't seem like the right use of the two stage analysis, but they're adamant they can use it. Am I missing something? See image below showing how they propose the analysis will work for the "upper" and "lower" structures...


two-stage_example_ehn4vj.png
 
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I think I understand what they are trying to do, but dual stage analysis is not the technique to get there.

The mezzanine is not a transfer structure. If they were going to truly use dual stage analysis, then mezzanine level should support the entire upper level structure. Not the case.

What they should do is design the mezzanine lateral system independently from the rest of the structure if they want to justify their assumed vertical distribution of forces. Typically the mezzanine is locked into the rest of the structure so its a bit of a leap to say they aren't acting together.

I feel that you could shut down this line of reasoning easily by asking for demonstration that each of the requirements in 12.2.3.2 be demonstrated. It doesn't make any sense to try to apply those requirements to this configuration so I imagine one would have a hard time justifying it out.
 
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This article provides a good discussion of this type of building, and has a link to a study based on shake table testing:
Basically, the approach they outline is to design each individual frame line or brace line with its own tributary seismic load per conventional ELF method frame analysis. This approach assumes a flexible roof diaphragm, so frame lines without tributary seismic load from the mezzanine are considered to be uninfluenced by the presence of the mezzanine.
 
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Daniel-PRE said:
I'm reviewing a design where the engineer is wanting to use two stage analysis...
Click to expand...

I question whether or not the engineer really means "two stage analysis" in the ASCE7 sense of that term. To me, this just looks like "two separate structure analysis". The captions in the EOR's sketch would support this.

Daniel-PRE said:
...to get out of loading the roof with seismic weight from the concrete topped mezzanine deck.
Click to expand...

I certainly agree with that part of what the EOR is proposing based on what they've set up. Since the upper and lower structures do not, ostensibly, share any common VLFRS elements, the weight of the mezzanine should not affect the seismic acceleration of the roof diaphragm. It's still unconventional, but I think that I get what they're trying to do.

Daniel-PRE said:
The problem is the base for the upper structure is not all at one level.
Click to expand...

I disagree. The seismic base is where the the seismic VLFRS touches down. Since the parts of the upper structure that touch down at the higher level are not part of the VLFRS, those parts of the structure will not affect the seismic base location.

The key to this, I think, is to view the portion of the roof that is above the mezzanine as "ride along" diaphragm that rides along with the main building VLFRS.
 
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An interesting wrinkle in what I think the EOR is trying to do is that the roof over the mezzanine will add a P-Delta demand to any environmental lateral loads imposed on the mezzanine.
 
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It looks like these two structures are essentially independent of each other. At least at first glance. Can you explain how they structurally connect to each other?

It looks like there are a couple of columns that continue from the mezzanine all the way to the roof. If so, I would propose that the rigid boundary conditions for those columns (in the upper structure model) be replaces with two way springs based on the lateral stiffness of the lower model at those locations.

How do you figure out those spring values. Apply a unit load to that point (on the lower structure) and see how much it moves. It's that simple. If P-Delta is a major concern then you apply the vertical load to the lower structure when applying your unit point load in the lateral direction.

It can be a little bit of a pain because you have to do it a number of times (for each spring you want to calculate). But, it really shouldn't be that difficult.
 
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My interpretation of the OP was that the structures are NOT independent, and share members in the VLFRS. I think the second screenshot is showing how that combined structure was discretized into pseudo independent structures for a two stage analysis. I really don't agree with that approach at all.
 
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This passage from the research justifies the notion that the mezzanine and building frames cannot be decoupled, because the mezzanine directly influences the sway behavior of the columns.

Research paper - pg. 52 said:
The performance difference for Specimen B3 is that at higher magnitudes (IV 300) the mezzanine restricted one column from swaying laterally, which caused lateral deformation to concentrate at the frame knee causing panel zone buckling, cracking, and failure with high stiffness degradation compared to Specimens B1 and B2 [the frames tested without mezzanines]
Click to expand...

Screenshot_2023-09-06_133527_dehst4.png
 
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bones206 said:
My interpretation of the OP was that the structures are NOT independent, and share members in the VLFRS.
Click to expand...

What members of the VLFRS is it that you think they share?

I only see the main building sharing some gravity columns with the mezzanine which, conveniently, appear to be modelled as pinned where they hit the mezzanine deck. This is probably where differential movement issues may require some attention.

I envision the main building lateral system being the independent system shown below, 3-sided affront to robust schematic layout that it is....

c01_owh327.png
 
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bones206 said:
This passage from the research justifies the notion that the mezzanine and building frames cannot be decoupled, because the mezzanine directly influences the sway behavior of the columns.
Click to expand...

But that is because, in the typical PEMB case, the mezzanine ties in to a beefy, flexural continuous column spanning from foundation to roof. My sense with the structure at hand is that the EOR seeks to avoid precisely that flexural column continuity between "storeys".
 
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I was assuming these highlighted yellow were moment frames in the short direction, but I could be wrong.

Screenshot_2023-09-06_134326_uiliwn.png
 
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Thanks Bones!

If those are indeed moment frames for the main structure, then I don't see how you can separate them.... given that research you pointed out.

I had assumed that the shared columns were merely gravity only columns shared between the two structure. That wouldn't be a problem in my book. Provided you analyzed them properly considering P-Delta.
 
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bones206 said:
I was assuming these highlighted yellow were moment frames in the short direction, but I could be wrong.
Click to expand...

I certainly understand your perspective if those are indeed moment frames. That said, I see nothing at all in the EOR's sketches to suggest that is the case other than, perhaps, the general undesirability of creating a three sided main building. And I feel that we ought to kind of take the EOR at their word here in order to ensure that they get a fair shake in this conversation in absentia.
 
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@Daniel-PRE: you can help us clear this up and, in the process, help us advise you better:

1) What kind of columns are the columns highlighted in yellow below? HSS? WF? Tapered Pre-Engineered Building?

2) What do the connections look like at the circled locations? Does anything thing about them suggest their deliberate design for moment transfer?

c01_ejctio.png
 
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JoshPlumSE said:
If those are indeed moment frames for the main structure, then I don't see how you can separate them.... given that research you pointed out.
Click to expand...

Agreed, particularly if they are tapered PEMB columns. But, then, I would hope that a designer's intuition would lead them to this conclusion even without the testing. One could analogously replace the stocky column shown below with a shear wall in which case the dynamics of the situation become much less ambiguous and it's obvious that the mass of the mezzanine would amplify seismic acceleration at the roof level. And that's really what we're getting at with this "loading the roof with seismic weight from the concrete topped mezzanine deck" business.

c02_dfh1th.png
 
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Sorry for the long silence! I thought I'd get a notification of responses, but I'm new to using the forum.

@Bones206 has it pretty close to correct. They're trying to say the frames above (including the end frame) are ordinary moment frames pinned at the mezzanine level. They then transfer forces (this is the two-stage analysis bit) to the braced frames of the mezzanine to get down to the foundation.

They're trying to do this because otherwise they'd have to switch to intermediate moment frames since the SDC D doesn't allow ordinary unless they're one story (12.2.5.6). We have a local amendment allowing small mezzanines, but they greatly exceed the seismic mass limit we require.

Thanks everyone for your responses so far!
 
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Daniel-PRE said:
They then transfer forces (this is the two-stage analysis bit) to the braced frames of the mezzanine to get down to the foundation.
Click to expand...

This bit sounds more like a vertical combination of lateral systems.

If treated properly as a vertical combination then it can probably work out just fine.

Here they are looking to use lower detailing requirements, on a typical 2-stage analysis building you're looking to reduce upper story diaphragm demands by not including the podium weight in the vertical distribution of base shear on the wood building.

The 'penalty' the code requires is listed in ASCE7 12.2.3.1. Your R factor on the bottom level cannot be higher than the R factor of the top level.

So in this case assuming ordinary frames.
R upper = 3.5, Cd = 3, Om = 3
R lower = 3.25, Cd = 2, Om = 3.25

Forces reacting from the upper structure get scaled by 3.5/3.25.
Seems perfectly reasonable to me to just use R=3.25 for the entire structure and do only 1 check for drift using Cd = 3.

The key distinction is the vertical distribution of base shear must include all of the weight from levels above the foundation. The upper level will see a higher proportion of base shear than the lower level. A 2-stage analysis doesn't account for this, a vertical combination of systems does.
 
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@driftlimiter, the problem is the limitation on an OMF in SDC D, it can only be used in a one-story structure.
 
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Daniel-PRE said:
@Bones206 has it pretty close to correct.
Click to expand...

Bones206 contemplated a mezzanine that would load the moment frames. This is the reverse: moment frames that would load the mezzanine.

dL said:
The key distinction is the vertical distribution of base shear must include all of the weight from levels above the foundation. The upper level will see a higher proportion of base shear than the lower level. A 2-stage analysis doesn't account for this, a vertical combination of systems does.
Click to expand...

Based on what the EOR is proposing, I don't feel that it makes sense for the mezzanine weight to be part of the vertical distribution of base shear. This, because dynamically the mezzanine will not increase the acceleration of the roof under seismic motion if the mezzanine lateral is stiff enough relative to the frames.

Daniel-PRE said:
@driftlimiter, the problem is the limitation on an OMF in SDC D, it can only be used in a one-story structure.
Click to expand...

Weird as the situation is, I feel that a two stage approach may well be justified here. It's not inconceivable that a single story moment frame might be 10X as flexible as a single story braced frame. In fact, a designer might tune the system to bring about that very outcome.
 
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