ASCE 7 Response Spectrum with less modal mass less than 90%

[alexbzeta]

I am having problems getting more than 90% modal mass participation in my response spectrum analysis.

The structure consists of 2 framed levels below grade, a large 3 story podium above grade, and then three towers extending up from the podium for a total of 21 stories (including basement). The shared podium and basement make the structure very bottom heavy.

When I set the base shear to come out at grade (Level 1), I can get >90% using the first 24 modes. However, we are using concrete shear walls that are continuous down to the basement (B3). The software utilized laterally restrains the base shear level and all levels below it (in this case L1, B1, and B2). This causes an unrealistically high portion of the overturning moment to be resolved as a horizontal couple at L1 and B1 instead of a vertical couple at the foundation. In order to consider some deformation at and below grade, I need to set the base shear to come out at the basement instead of at grade as well as consider the stiffness of the diaphragm (non-rigid). When I do this, I need to run many, many more modes. In fact, running 100 modes only gets me to 88% modal mass participation. Has anyone else had these issues? Any suggestions other than going to the equivalent lateral force procedure?

One workaround is to disconnect the shear wall nodes from the diaphragms at grade and below, and then reconnecting the walls to the diaphragm using beams calibrated to the stiffness of the diaphragm. Getting the beam properties "right" will be very tricky, especially with respect to torsional stiffness (we have cores, not blade walls). I'm not enthusiastic about this option.

Is there any way to justify using less than 90%? I suspect the bulk of the missing mass is below grade, which should not have any meaningful impact to the structural behavior.

 

[KootK]

You could discontinue your model at grade.

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.

 

[alexbzeta]

KootK, do you mean delete it? I still need to design the walls, etc. below grade.

 

[KootK]

I do mean to delete it. As fun as ETABS is, I feel that the below grade modeling is of questionable value in a situation like this. There's just too much redundancy and too many unknowns. That spring that you're looking for to represent the diaphragm flexibility? It's impossible to determine with any accuracy. You just have to feel good that any flexibility will substantially reduce the back stay effect.

Two additional things to consider:

1) Regardless of how you model your structure for design purposes, I would have no problem with using a separate, above grade only model to justify that you satisfy the 90% business.

2) If you've got a big podium with three towers and no expansion joints, you probably satisfy the requirements for ASCE's two stage podium analysis procedure. And that's essentially saying that you can consider the superstructure separately.


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.

 

[alexbzeta]

KootK,

I agree regarding your point about diaphragm flexibility. As to the others:

1. Separate models would work, but I would rather not maintain 2 models. Transferring the reactions from walls above to walls below will also be cumbersome. Still, it's a valid approach.

2. My structure doesn't qualify for ASCE's two stage procedure, and even if it did, I don't have any need for it. The towers on the podium are working just fine - same building materials and same lateral system type. There might be some advantage to reducing the seismic shear in the towers, but those are primarily governed by wind anyway. Seismic is only playing a role where I have to use amplified load combinations.

 

[WARose]

Are you considering soil-structure interaction for the portion below grade (if there is any)? Usually when I have low mass participation....overestimating the support stiffness is typically the culprit.

 

[alexbzeta]

WARose,

No consideration of soil-structure interaction. The perimeter foundation wall is idealized (perhaps poorly) as a shear wall.

 

[WARose]

You just have to look at how it will behave under a lateral event. (Is the lower level cast against soil....will they interact?)

Some years back I had a building where I was using the response spectrum history analysis too. I just modeled the bases is "fixed" (for all 6 dof). And I just wasn't getting there. But I made some reasonable guesses at the base stiffness and got the mass well over 90% participating.

 

[KootK]

When you guys model the below grade structure like this, the seismic mass associated with it is "turned off" somehow, right?

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.

 

[alexbzeta]

I didn't turn off the mass. For the software I'm using, it would be pretty easy to do. That might be the easiest solution. Anyone see any issues with that?

 

[KootK]

I would argue that it would be incorrect to not turn off the mass for the below grade structure unless you're getting very detailed with your soil/structure interaction modelling. The usual assumption is that the seismic base is near grade and that the below grade structure moves in unison with the soil rather than vibrating independently. This depends, to some degree, on the number of stories above and below of course.

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.

 

[alexbzeta]

That's my sense as well, and I'm a little embarrassed that I hadn't that done already. I've used that solution for other problems in the past. It appears I may have uncovered a bug with the software, because using the over-write for story mass is not affecting my modal participation at all. I've sent it into tech support to confirm.

 

[slickdeals]

I have been involved in a project with a lot of back and forth, which basically led to the conclusion that due to the number of unknowns, it is best to assume the base at the foundation level. Assuming the base at ground level would mean a large majority of the force being transferred into the soil in passive resistance perpendicular to the force and skin friction parallel to the force.

 

[alexbzeta]

Update:

I blanked the mass at grade and below (well, actually set it to 1 k-s^2/ft) and assigned those three diaphragms (Level 1, B1, and B2) as rigid. Then I disconnected the core nodes from the diaphragm and reconnected them using custom beams that provide restraint similar to considering below grade flexibility.

With these two changes (dropping below grade mass and core attachment) I get achieve >90% modal mass participation with 15 modes.

Thanks for the help!

 

[KootK]

Then I disconnected the core nodes from the diaphragm and reconnected them using custom beams that provide restraint similar to considering below grade flexibility.

It's great that things are working out. I'd love to hear more about how the custom beams are set up to simulate below grade flexibility. Can you elaborate?

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.

 

[alexbzeta]

Sure. I took the subgrade floor plate as a standalone FEM. I restrained the perimeter and then imposed lateral displacements in two orthogonal directions at the core-floor interface parallel to the walls. The reactions gave me a target spring value.

Back in the full model, I could add beams at the corners of the core and calibrate the area and modulus to match the stiffness. In the spring_beams image, ignore spring144. I was just too lazy to give those beams a different property. Their only purpose is to support the meaningful springs. spring247,576,511,and 562 are my "spring beams". spring247 is a beam that is 247 in^2 with E = 10,000 ksi. I proportioned the springs so EA/L matched on both faces of the core, hence the larger area on the longer beam.

 

[RFreund]

Alex-
First thanks for following up, so rarely people do.

Couple quick questions as I've been following along...

[ol 1]
[li]So the spring beams are representing the flexibility of the diaphragm at grade?[/li]
[li]What program do you use? Looks like RAM elements/ Ram SS?[/li]
[/ol]

Thanks

EIT

http://www.HowToEngineer.com

 

[alexbzeta]

Yes and yes. Although we don't use RAM exclusively. We typically use ETABS for systems using 2-way slabs and RAM for everything else, unless there's something requiring nonlinear behavior or a sequence analysis.

 

[JoshPlumSE]

I'm confident that the bulk of your missing is below grade as well. But, doesn't ETABs have an option to include residual mass vectors? I think may refer to them as Static Correction Vectors. That would basically say that the "missing mass" acts at the zero period acceleration of your spectra. I would think that would be better than just ignoring the below grade mass.

I don't know much about ETABs modeling, so I can't give you any suggestions on how to deal with the rigid boundary conditions at L1, B1, et cetera.

 

[alexbzeta]

I'm not familiar with that feature in ETABS, but this is a RAM project so it doesn't apply in this case.