Building height for dynamic analysis period (shear calibration) 1

[BHHH]

Hey,

When doing a dynamic analysis of a building, do you include the basement levels of the structure when comparing the equivalent static period to the dynamic model's period?

To clarify, in the attached image, hn would be used for the equivalent static fundamental period. When running the modal analysis (in etabs for example) would you block (i.e. pin) the structure at the grade level in order to compare the building's above grade dynamic period? or would you leave the structure unrestrained down to the foundations (hn + hb)?

I am used to blocking the structure at the ground floor in order to compare the same net height of the building (a more conservative approach).

I am using the latest NBCC and CSA A23.3.

Thanks!

 

[HTURKAK]

The sketch shows 9 storey upper floor and 4 storey basement and the basement levels seems to be surrounded with stiff walls.
The building codes (in general ) allow two-stage static analysis for this type of structures .

(ASCE 7-16 12.2.3.2 )the two-stage analysis is allowed for the systems in which the lower portion is at least 10 times as stiff as the upper portion and for which the period of the entire structure is not greater than 1.1 times the period of the upper portion of the structure,
If the two conditions satisfied ,You may perform a two-stage ELF procedure .

You may perform RSA analysis for the whole structure with R = 1 and assign the actual R values on a member-by-member basis and for drifts In this case, would be multiplied by (C d / R) , using the actual R values.

 

[BHHH]

HTURKAK, when doing a two-stage analysis, the period used for the upper structure is based on a model of the above-grade structure only? Or is the below grade portion included in the period computation, but then analyzed in a separate model?

 

[JoshPlumSE]

This is honestly a great question. Though I can't say I know of any definitive answers about this. There's a lot of places I'd look (starting with FEMA / NEHRP). Maybe ASCE-41. Not because this is a pushover or performance based design, but because there are lots of case studies / design examples that might spell this out better.

A couple of comments / questions:
1) How is this modeled? Are you modeling it so that the supports are only at the base of the building and the 4 levels underground don't dissipate any seismic energy to the surrounding ground? Or, are you modeling some passive pressure springs at the underground floor levels?

2) What I'm getting at is reality vs modeling. If the structure were entirely below ground (meaning the above grade stories don't exist) it would have very little seismic force at all. It simply moves with the surrounding soil. Right? Sure, you'd want to do some mononabe-okabe (or similar) type seismic loading on the retained soil. But, that would be it.

3) In that respect, I think the height for period calculation is based on the above ground height only. Assuming that the below grade floors don't really contribute to seismic force much. In fact, they decrease the seismic response from above. That's closer to the reality of the dynamic behavior.... So, that's my assumed starting point. Like an embedded pile that extends down to bedrock. Do you model the bed rock as the only source of lateral resistance for the pile, or does the soil above resist the piles lateral movement?

 

[HTURKAK]

[quote........ when doing a two-stage analysis, the period used for the upper structure is based on a model of the above-grade structure only? Or is the below grade portion included in the period computation, but then analyzed in a separate model?][/quote]

The answer is YES.... But in order to perform two stage analysis,

i ) Perform the analysis for total system and catch the period of the total system and perform another analysis for the flexible upper portion supported on the base (upper level of rigid basement) and compare the two periods and be sure the period of the entire structure is not greater than 1.1 times the period of the upper portion of the structure,
ii) Compare the stiffness of the upper portion with rigid basement. Although the code is not clear for the stiffness requirements how to calculate , i think IMHO, apply a nominal tip load say 100 to both systems and compare the displacements.

If both conditions satisfied, you can perform ELF or RSA for upper portion and ELF only for lower portion.

 

[HTURKAK]

This is the second time i pressed to submit instead of preview. I just want to add, when you perform RSA for total system , you will observe that the basement floor masses will participate the higher modes ( with having short periods ) rather than initial periods.

 

[JoshPlumSE]

Hturkak -

FYI: If you posted something, then you should be able to an "edit" button at the bottom of the post. I make liberal use of this because I always find some typos in my posts. But, only AFTER I've submitted them.

 

[BHHH]

JoshPlumSE,
1) No soil modeled when modeling the entire structure. I planned to include this effect in the below-grade analysis model.
2) Yes I completely agree. However if I assume the base of the structure is below grade (to increase the period) is it fair to say the below-grade elements don't contribute to the seismic mass?
3) I agree that it is more conservative to use the above grade structure only to calculate the period (i.e. lower period and higher forces)

HTURKAK,
Sounds about right.

Thank you both for your responses!

 

[HTURKAK]

Dear JoshPlumSE thank you..

The picture depicts soil deformation vs depth from (NCHRP ,Seismic Analysis and Design of Retaining Walls, Buried
Structures )

This document is useful to see the soil -str. interaction, backstay effects

https://www.nehrp.gov/pdf/nistgcr12-917-22.pdf

 

[JoshPlumSE]

However if I assume the base of the structure is below grade (to increase the period) is it fair to say the below-grade elements don't contribute to the seismic mass?

I'm probably not the best one to ask as my most practical design experience (industrial structures) did not involve any basements. However, my general approach is that anything below grade does not contribute to seismic mass.

The challenge here is that (without going into detailed soil-structure interaction), my tendency is to design it two ways where the assumptions aren't compatible.

1) Once model that only models the above ground structure with the structure supported at ground level. Run that design / analysis in ETABS (or whatever program you're using).

2) When designing the below ground levels, apply the seismic reactions from the above ground structure at the top of the below ground levels... then pretend the below ground level are supported at the base mat (or pile cap) at the lowest level. Conservative for overturning moment.

That being said, I'm eager to go through HTurkak's document to see if it challenges my approach. I've gone through the document before, but only related to the basics of base slabs. And, I never looked at it with an eye towards structure / foundation interaction.

 

[HTURKAK]

My personnel interpretation and respond to these questions ;


For the upper flexible portion this approach is O.K. provided that ( 12.2.3.2 ) both conditions satisfied.

The rigid basement storeys ( having concrete peripheral walls ) will also attract seismic loads. In general , ELF procedure is allowed. The seismic force for the rigid basement block could be calculated using PGA. ( F= PGA *Wb * Ib/1.5 ). The RC peripheral walls shall also be designed for EQ soil loading ( Similar to Mononabe Okabe ).


In past , ( around 20 yrs ago ) we had a similar project ( flexible upper structure with several podium basement storeys with rigid peripheral walls ) we performed the analysis with the following steps,
- perform the RSA for total structure using R=1 , with response spectrum curve upgraded for foundation level soil cond's. The surrounding soil modelled with half value of passive soil springs ,
- Use the actual R values on a member-by-member basis and check the drifts ,
- compare the results with ELF procedure findings.

I attached the previous document to draw attention for soil-structure interaction , backstay effects and top podium slab which is transferring the seismic load to peripheral walls.

I think , it is worth to dig more this subject ( soil structure interaction ) and would like to see responds of other fellow engineers.

The following document is useful to see the case

https://www.nehrp-consultants.org/publications/download/nistgcr12-917-21REV1.pdf