Modal Response Spectrum Analysis Forces for Foundation Design

[fracture_point]

Response spectrum forces are often outputted from design software (e.g. ETABS) as MAX and MIN envelope values, as in the worst case loading but these load cases do not occur at the same time (it may show two columns going into compression or tension instead of tension & compression couple).

How do you guys go about designing your foundations for the overturning moment caused by the response spectrum analysis? I thought about creating an equivalent static load cause to give the same base moment that the response spectrum gives but capture and compression and tension action, but this would lose the distribution of forces to each core wall system in the building and would lose the impact of significant torsion if this mode was sensitive.

 

[Guest262653]

I don't use ETABS as I have access to SAP2000 only. Either way, if it's an isolated footing I use the results directly. When it's a combined footing, if its height is enough to be considered rigid, I create a section cut with the two (or more) frames and respective base nodes and design to the forces thus obtained. If the foundation is flexible, I model it explicitly. However, if it's only a couple of combined foundations, I tipically choose by inspection the loads that matter to the design.

 

[JoshPlumSE]

There is no easy answer to this question. But, my thoughts are the following:
1) If you have a "dominant mode", meaning that your structure has one mode that has 70% mass participation or more and can be said to dominate the dynamic response.... then you should be able to assign positive and negative values to the uplift forces based on that mode shape. And, get a good representation of the overturning moments for each shear wall or moment frame. Some program may be capable of doing this if you tell them which mode to use.

2) If you do NOT have a dominant mode, then you hope you can define a particular output result that you want to get an RSA result for have the software do a CQC or SRRS or such result for that value. That will be more accurate than item #1. But, I don't know for sure if any programs do this. I know this is one of the arguments that I had over at RISA where wall panel axial and moment results were just not correct for response spectra analysis.

3) Use engineering judgment.... This would be sort of like item #1. But, where you might use different modes depending on which area of the model you are looking at.

4) For safety sake, you want to take a look at the Equivalent Lateral Force procedure and make sure that the results are of the same order of magnitude that you got from the other methods. If not, then you may not have done the other methods correctly.

 

[WARose]

I typically don't trust the computer to do this internally. I let it spit a base shear out at me....but the vertical distribution I do manually in a separate model. This distribution is based on the SRSS or CQC method (the CQC being the more favored for closely shaped modes, in fact it is the most favored at this point period). This is discussed in Section 12.9 of ASCE 7-10 and most structural dynamics text books. Another good source on this is '246 Solved Structural Engineering Problems' (by Buckner). I thought he had a good practical example. Albeit one dimensional......speaking of that......

..........one issue that typically comes up in these things is figuring a "composite" mode shape vector value (normally normalized to one) per floor. I've typically wound up using a weighted average. E.g. [(m₁Ø₁)+(m₂Ø₁)+(m₃Ø₁)]/[m₁+m₂+m₃].....where a clear dominant mode (per floor) is not observed.

In many cases, your outcome is comparable to the ELF. (In fact, 12.9, IIRC, requires you to scale by it under some circumstances.)

Hope this helps.

 

[fracture_point]

Joshplum - I do have dominant modes in each direction. So you recommend looking at this mode in particular and taking the force direction for that? Do I have to split up the response spectrum modes into individual modes and add them up myself?

 

[JoshPlumSE]

Well, the idea is that if you really have a dominant mode, then it's good enough to look at the results at the base and then just given them a sign based on that one mode. This is a shortcut that only works when you have a dominant mode.

I've done what WARose suggested and I feel really smart when I get it right. But, it is an awful lot of work.

 

[fracture_point]

Josh - I do have a dominant mode. The problem I'm having is that my building is torsionally sensitive, and I'm struggling to create a static load case that gives me the equivalent M22 and M33 for my stairwall core walls as well as captures the torsion do to the shape of the building. Can you recommend any literature for me to read?

 

[JoshPlumSE]

How many floor? Diaphragms at each level?

 

[fracture_point]

Josh:
- 3 story RC building
- Modelled with semi-rigid diaphragms
- High seismic zone
- H shaped building
- Torsional irregularity
- Large re-entrant corners

Unfortunately a lot of preliminary design decisions were made in the initial stages which I was not involved in, and now I'm trying to accurately analyse a crazy arrangement for a seismic zone which is a challenge.

See attached image for approximate building footprint and core layout.

I have used a response spectrum analysis to capture the torsional sensitivity, which has about a 5% mass participation in both the dominant X and Y modes. I have no problem in designing the wall forces for response spectrum max and mins, but as I said the difficulty is coming in analysing the raft foundation for each core which will be supported on piles. The piles are governed by a very poor tensile capacity (poor soil conditions).

I am trying to design the upper left and lower left foundation as one large raft, and it would be convenient to be able to export loads from ETABS to SAFE to analyse the pile forces. I tried creating an equivalent static load case to give me the same forces in the walls as given by the response spectrum, but as expected, it is difficult to capture the torsional effect in a static load case. I guess my best bet is to look at the response spectrum and assign them + and - forces to create the push pull couple in the rectangular walls.

 

[Guest262653]

I really think that you need to get those forces in each core using either a section cut or defining a single pier for the core (is this possible in ETABS?).

Regarding the Max and Min outputs, I forgot to add that what I do is to conservatively "unfold" each seismic combination result in Excel, combining all axial and moment responses for each core. Then, if the cap is stiif enough to be considered a rigid body, I determine pile forces using a simple spreadsheet.

The other alternative is to include explicitly the cap and the piles in the global analysis model. That will give you the correct (vertical) forces in each pile.