An Analytical Model for Dynamic Response of an Elastic Sdof System Fixed on Top of a Rocking Single-Story Frame Structure: Experimental Validation

Bachmann, Jonas A.; Jost, Christoph; Studemann, Quentin; Vassiliou, Michalis F.; Stojadinović, Božidar

doi:10.7712/100016.2164.10112

Cited by 12 publications

(20 citation statements)

References 13 publications

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“…

A rocking podium structure is a class of structures consisting of a superstructure placed on top of a rigid slab supported by free-standing columns. This was experimentally confirmed for other elastic uplifting systems [32,34,57].

Uplift works as a mechanical fuse that limits the forces transmitted to the superstructure, while rocking enables large lateral displacements.…”

mentioning

confidence: 56%

Dynamics of rocking podium structures

Bachmann

Vassiliou

Stojadinović

2017

Earthq Engng Struct Dyn

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Summary A rocking podium structure is a class of structures consisting of a superstructure placed on top of a rigid slab supported by free‐standing columns. The free‐standing columns respond to sufficiently strong ground motion excitation by uplifting and rocking. Uplift works as a mechanical fuse that limits the forces transmitted to the superstructure, while rocking enables large lateral displacements. Such ‘soft‐story’ system runs counter to the modern seismic design philosophy but has been used to construct several hundred buildings in countries of the former USSR following Polyakov's rule‐of‐thumb guidelines: (i) that the superstructure behave as a rigid body and (ii) that the maximum lateral displacement of the rocking podium frame be estimated using elastic earthquake displacement response spectra. The objectives of this paper are to present a dynamic model for analysis of the in‐plane seismic response of rocking podium structures and to investigate if Polyakov's rule‐of‐thumb guidelines are adequate for the design of such structures. Examination of the rocking podium structure response to analytical pulse and recorded ground motion excitations shows that the rocking podium structures are stable and that Polyakov's rule‐of‐thumb guidelines produce generally conservative designs. Copyright © 2017 John Wiley & Sons, Ltd.

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“…

Uplift works as a mechanical fuse that limits the forces transmitted to the superstructure, while rocking enables large lateral displacements.…”

mentioning

confidence: 56%

Dynamics of rocking podium structures

Bachmann

Vassiliou

Stojadinović

2017

Earthq Engng Struct Dyn

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“…1), 2 linking plates (Nr. 26 Further investigation of contact surface stiffness and imperfection effects on rocking motion are available in ElGawady et al 44 and Wittich and Hutchinson. 3).…”

Section: Shaking Table Testsmentioning

confidence: 99%

“…16,17 As the response of the rocking oscillator is highly nonlinear because of its negative stiffness, 18 many have suggested treating the rocking oscillator as a "chaotic system," in the sense that small perturbations of its governing parameters (be it the oscillator properties or the excitation) result to widely diverging outcomes. 26 This has generated a discussion on Housner's approach to determine the energy losses during impact and has resulted in various different energy dissipation models. Even if the coefficient of restitution is estimated accurately, or determined experimentally, the rocking oscillator is so sensitive that predicting the entire seismic response time history is practically impossible.…”

Section: Introductionmentioning

confidence: 99%

Is rocking motion predictable?

Bachmann

Strand

Vassiliou

et al. 2017

Earthq Engng Struct Dyn

105

115

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Summary An argument of engineers and researchers against the use of rocking as a seismic response modification technique is that the rocking motion of a structure is chaotic and the existing models are incapable of predicting it well. This argument is supported by the documented inability of rocking models to predict the motion of a specimen excited by a single ground motion. A statistical comparison of the experimental and the numerical responses of a rigid rocking oscillator not to a specific ground motion, but to ensembles of ground motions that have the same statistical properties, is presented. It is shown that the simple analytical model proposed by Housner in 1963 is capable of predicting the statistics of seismic response of a rigid rocking oscillator.

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“…It represents structures that are designed to rock and their contact surfaces are designed such that the impact forces are concentrated as close to the corner as possible, in an e↵ort both to increase damping and to decrease the uncertainty concerning the position of the impact forces. It has been shown [27] that, even if the impact forces are forced by design to act as close to the corner as possible, and even if this results to an excellent prediction of the coe cient of restitution, the rocking problem is so sensitive that it is impossible to predict the entire time history response. Thus, the need for probabilistic treatment arises.…”

Section: Rocking Specimenmentioning

confidence: 99%

“…Researchers that have tried to experimentally validate Housner's model [20][21][22][23][24][25][26] have shown that, given the modelling uncertainty (especially of the one related to impact), it is di cult to confidently predict the time history response of a rocking block to a specific ground motion. Even if the coe cient of restitution is relatively well predicted, or determined via experiments, the response of the system to a ground motion is so sensitive that predicting the whole time history is practically impossible [27]. This has generated a lot of discussion about Housner's approach to determine the energy losses during impact and has resulted in various di↵erent energy dissipation models [28][29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Validation of the Housner Rocking Model

Bachmann¹,

Strand²,

Vassiliou³

et al. 2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract.The rocking oscillator has drawn the attention of many researchers since the publication of Housner's [1] seminal paper. As the response of the rocking oscillator is highly non-linear and exhibits negative sti↵ness [2] many researchers have suggested treating the rocking oscillator as a chaotic system, in the sense that small perturbations of its governing parameters result to widely diverging outcomes. Researchers that have tried to experimentally validate Housner's model have shown that, given the modelling uncertainty, it is hard to confidently predict the time history response of a rocking block to a specific ground motion. This makes practicing engineers hesitant to adopt rocking as an earthquake response modification strategy.However, accurately predicting the response to a single ground motion would be ideal but it is not a necessary condition to trust a model: there is so much uncertainty in the expected ground motion that could overshadow the modelling uncertainty. To take the former uncertainty into account, in common practice, engineers use an ensemble of ground motions when they perform a time history analysis. Therefore, it is reasonable to try to compare numerical experimental testing results in terms of their statistics. If the numerical model is capable of capturing the statistics of the experimental testing, then, in terms of civil engineering design, the model is trustworthy. The first ones to adopt a probabilistic approach were Yim, Chopra and Penzien [3] who as early as in 1980 observed some order in rocking motion when they studied it from a probabilistic point of view. They observed specific trends in their numerical results when, instead of using only one, they used 10 synthetic ground motions. This paper compares the numerical and experimental response of a rigid rocking block when excited by an ensemble of 100 ground motions that share the statistical properties of original ground motion.

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An Analytical Model for Dynamic Response of an Elastic Sdof System Fixed on Top of a Rocking Single-Story Frame Structure: Experimental Validation

Abstract: Abstract. It has been shown that assemblies of large rocking bodies

Cited by 12 publications

References 13 publications

Dynamics of rocking podium structures

Dynamics of rocking podium structures

Is rocking motion predictable?

Probabilistic Validation of the Housner Rocking Model

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