Modal Analysis or Equivalent Lateral Force?

[MacGruber22]

Hey, all.

I have a 3+3 podium-like structure. RC moment frames at the lower 3 levels and wood bearing/shear walls at the upper 3 levels. I have determined that 2 stage ELF analysis is not likely going to work because of the stiffness requirements between the upper and lower, so I have to figure out what I want to do next.

I see two options (unless someone can point me in a different direction)
1. Calculate the period of the structure using FEM software (I use RISA 3D) and then use that value to determine the base and story shear with ASCE 7-10 12.8 ELF procedure. I am not aware of any prescriptive or "simple" analytical procedures to conservatively approximate the period for a structure like this.
2. If I do indeed have to model the structure in FEM in order to calculate the period, I feel like by the time I put all of that effort into imputing the structure into RISA I might as well have RISA complete the modal analysis and provide the base and story shears for me. I have never performed a modal analysis, and I am feeling very cautious to do so. But, if it isn't terrible complicated than I would rather "kill two birds..."

Hopefully one of our RISA experts (I think Josh) notices this post.

 

[asixth]

Personally I would only the model the 3 level rc frame and apply the wood structure as a mass on top of level 3. I am just saying that from my experience with wood frames that I have found them to have a high stiffness and low mass and generally governed by wind provisions. I have never really performed a modal analysis of a mixed material building, particularly one of concrete and wood. I would think during a seismic event the response of the building will be heavily dominated by the concrete frame.

 

[KootK]

Perhaps it would help if you told us more about your building? Just kidding.

My gut instinct matches asixth's comment. Similar to how we'll model a steel braced penthouse on top of a main building as a rigid mass at the top of the main roof. That being said, this is a little different and I don't know of a code provision that sanctions this approach. Maybe the provisions for rigid equipment? A three story "penthouse" on top of a three story base building seems like a bit of a stretch. I like the RISA modelling approach though.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[MacGruber22]

Thanks, asixth. That is an interesting thought. That would certainly make analysis easier.

I knew you would be one of the first to hit this post up, KootK. In Chapter 15 (nonbuilding structures), there is a section on nonbuilding structures supported by another structure. If the nonbuilding structure mass is greater than 25% of the supporting structure AND the fundamental period is less an 0.06, you can do as asixth has mentioned. If the nonbuilding structure is less than 25% of the effective seismic mass of the supporting structure, it is deemed a nonstructural component (chapter 13)

The problem is that last time I checked, a condominium or apartment building is not a nonbuildinng or nonstructural component (nice double negative). Besides, my stick-framed portion will have a period on the order of 7 times higher than 0.06. So, I guess it would make sense that this method is not even included in chapter 12.

Looks like I may be leaning towards RISA to determine the fundamental period and plug into the ELF procedure.

 

[structSU10]

With the modal analysis approach in ASCE, you need to 'scale' it with respect to the results you get from an ELF procedure, ensuring it does not go lower than 85% the ELF value (at least something like that as I recall). So either way, you are stuck doing an ELF procedure. If you model the full building and get the periods, however, you can use that in the ELF calculation and be done with it, or continue with a modal analysis to likely reduce the seismic loads.

You could also try to use Rayleigh's equation for the period Link

If you have a good estimate of the stiffness of each level you can get a reasonable estimate on the period (I found it to be within a few percent generally) without modeling the structure in RISA, and follow an ELF approach.

 

[MacGruber22]

That is a good point, structSU10. Thanks for the link.

I have a feeling that period will be similar to the RC frame alone - somewhere around T = 0.4 sec. or less. I just can't see the upper stories contributing much to raising the period considering how lacking of mass they are. I really one envision the mode shape for the whole building being different from the existing lower 3 stories.

 

[JoshPlumSE]

With a structure like this, one of the things the FEM analysis will tell you is that there probably isn't a single fundamental period. Rather it is likely to have a least two periods with high mass participation. This is why the code puts in those limitations one the ELF procedure (which is based on a single dominant mode) related to mass or stiffness irregularities.

If you end up going with a response spectra / modal analysis procedure, be ready for something of a learning curve. The analysis results will be fine in RISA, but will often cause a lot of confusion to engineers not familiar with the procedure. It all relates to the loss of relative signs when doing an RSA analysis. Some RISANews blog topics on the subject to get you started:

http://risa.com/news/why-does-deflection-plot-response-spectra-solution-look-strange/

http://risa.com/news/why-dont-response-spectra-reactions-satisfy-statics-risa3d/

 

[MacGruber22]

I was thinking that there may not be single fundamental period., as there are more than one degrees of freedom. I kind of figured that the lowest dominating period would be that which would be conservative for ELF. Thank you for the links.

As a side thought, due to the information in my recent post, "Analyzing a 1950's Concrete Frame", I am more than happy to have a super conservative period.

 

[SAIL3]

I agree with asixth in evaluating the lower 3-stories first, however, I would prefer the mass of the upper 3-stories to be placed at it's cg. The question then would be how to connect this mass to the lower 3-stories in the RISA model. Since the OP has an approximate stiffeness of the upper 3-stories, would it be possible to connect this mass by a member or members with the same equivalent stiffeness and have negligible mass themselves.
Now, what to do with the upper 3-stories?. I would model it seperately with spring supports derived from the above analysis and apply the seismic load obtained at the mass from the first analysis. Not sure if this is feasible until I would have tried it and evaluated the results.

 

[MacGruber22]

Sail3, I understand and it "feels" like a reasonable approach, but I am concerned that there is nothing in the code to justify what is proposed.

See this link for very preliminary arch plans and elevations: Link

Of course there is a darn courtyard from level 4 and up, so the mass and stiffness are going to be off-center from the structure below. Because it will be light-framed bearing walls above, I am going to be generous with assigning shear walls throughout. If I can get it to work out, I may be able to balance the mass and stiffness of the upper floors where it will not induce much torsion on the lower RC structure. I want a concentric lateral response in both directions throughout.

 

[KootK]

I kind of figured that the lowest dominating period would be that which would be conservative for ELF.

This will require some judgement to avoid excessive conservatism but I think that it's a valid approach.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[MacGruber22]

Agreed. The good thing is that if my boss doesn't question the story shears and member forces as a result, that may be enough to push him into a more conventional retrofit mindset (I am suggesting concrete wraps at columns, etc. - he liked the idea of that if "required").

Here is his "backdoor escape" verbiage from our proposal:

We will perform non-destructive testing to determine the strengths of existing concrete members using Windsor Probes. Petrographic analyses of the concrete and the use of GPR to determine reinforcement sizes are outside of our scope of work. Rather, for the purpose of analysis, we will assume minimum code-required reinforcing steel is present in concrete members..........Should it be determined that the scope of work is to extend beyond what the existing building is capable of supporting, we will at this time provide you with a proposal to design reinforcement of the existing building or supplemental structure to carry the proposed loads

At least the Windsor Probe is in there??? - we own one. I guess I should just be happy for what I can get.

 

[JoshPlumSE]

It's not the total base shear that I'd be concerned about. It's the vertical distribution of the base shear and the total overturning moment on the structure.

 

[MacGruber22]

I agree, Josh. I may have used "base" to describe the parking deck where the upper three levels of R-2 are bearing.

 

[Ingenuity]

...and the use of GPR to determine reinforcement sizes...

FYI - GPR is not accurately able to determine rebar diameter to the precision of 1/8" increments of rebar sizing.

 

[MacGruber22]

Thanks, Ingenuity.