Simulating Building Motions Using Ratios of the Building's Natural Frequencies and a Timoshenko Beam Model

Cheng, Ming; Heaton, Thomas H.

doi:10.1193/011613eqs003m

Cited by 33 publications

(28 citation statements)

References 23 publications

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“…Note that in accordance with that in other literature, a Timoshenko beam that acts as a surrogate for an actual building can assume the dimensions of that building, including the height and plan dimensions of the building. Therefore, the dimensionless parameter R and the length of the beam L will take on the values of the building under consideration and will not be treated as unknowns.…”

Section: Methodsmentioning

confidence: 60%

Bayesian identification of soil-foundation stiffness of building structures

Shirzad-Ghaleroudkhani

Mahsuli

Ghahari

et al. 2017

Struct Control Health Monit

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Summary A probabilistic method is presented for identifying the dynamic soil‐foundation stiffnesses of building structures. It is based on model updating of a Timoshenko beam resting on sway and rocking springs, which respectively represent the superstructure and the soil‐foundation system. Unlike those previously employed for this particular problem, the proposed method is a Bayesian one, which accounts for the prevailing uncertainties due to modeling and measurement errors. As such, it yields the probability distribution of the system parameters as opposed to average/deterministic values. In this approach, the joint probability density function of the parameters that control the flexible‐base Timoshenko beam model, together with the fundamental natural frequency and mode shape of the system, forms the prior distribution. Using Bayes' theorem, a posterior distribution is obtained by updating the prior distribution with a sparsely measured mode shape and frequency. The most probable realizations of the system parameters are then determined by maximizing the posterior distribution. For this purpose, first‐ and second‐order derivatives of the objective function are analytically computed via direct differentiation. The proposed method is verified using a synthetic example. Additionally, sensitivity analyses are carried out on both the system parameters and standard deviations of the sources of error. Subsequently, the proposed method is applied to real‐life data recorded at the Millikan Library building, which is located at the California Institute of Technology campus in Pasadena, California, and the results are compared with a previous deterministic study.

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Section: Methodsmentioning

confidence: 60%

Bayesian identification of soil-foundation stiffness of building structures

Shirzad-Ghaleroudkhani

Mahsuli

Ghahari

et al. 2017

Struct Control Health Monit

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“…We believe the reason that may have prevented the third EW mode from being accurately identified from the force vibration test data was the termination of the frequency sweep at 9.7 Hz, which, in turn, fell short in exciting the actual third EW mode. In a recent study, Cheng and Heaton [17] observed the same inconsistency between their findings and Bradford et al [9] and cited the same reason as the source of this inconsistency. • The third NS and torsional modes and the fourth EW mode have not been identified by any study other than the present one.…”

Section: Identification Resultsmentioning

confidence: 81%

Blind identification of the Millikan Library from earthquake data considering soil-structure interaction

Ghahari

Abazarsa

Avcı

et al. 2015

Struct. Control Health Monit.

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SUMMARYThe Robert A. Millikan Library is a reinforced concrete building with a basement level and nine stories above the ground. Located on the campus of California Institute of Technology (Caltech) in Pasadena California, it is among the most densely instrumented buildings in the U.S. From the early dates of its construction, it has been the subject of many investigations, especially regarding soil-structure interaction effects. It is well accepted that the structure is significantly interacting with the surrounding soil, which implies that the true foundation input motions cannot be directly recorded during earthquakes because of inertial effects. Based on this limitation, input-output modal identification methods are not applicable to this soil-structure system. On the other hand, conventional outputonly methods are typically based on the unknown input signals to be stationary whitenoise, which is not the case for earthquake excitations. Through the use of recently developed blind identification (i.e. output-only) methods, it has become possible to extract such information from only the response signals because of earthquake excitations. In the present study, we employ such a blind identification method to extract the modal properties of the Millikan Library. We present some modes that have not been identified from force vibration tests in several studies to date. Then, to quantify the contribution of soil-structure interaction effects, we first create a detailed Finite Element (FE) model using available information about the superstructure; and subsequently update the soil-foundation system's dynamic stiffnesses at each mode such that the modal properties of the entire soil-structure system agree well with those obtained via output-only modal identification.

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“…If the natural frequency ratios of the target building are different from those of a shear beam, then mode shapes from a Timoshenko beam can be adopted when significant flexural response is observed. Cheng and Heaton (2013) developed a Timoshenko beam model with lateral and rotational springs at the base, which simulate the soilstructure interaction effect, to approximate the dynamic linear elastic behavior of the buildings. Mode shapes can be closely approximated by the knowledge of the natural frequencies of the first two translational modes in a particular direction of the building and the building dimensions.…”

Section: Discussionmentioning

confidence: 99%

Prediction of Wave Propagation in Buildings Using Data from a Single Seismometer

Cheng¹,

Kohler²,

Heaton³

2014

Bulletin of the Seismological Society of America

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Crowd-sourced seismic networks in buildings collect important scientific data, in addition to allowing a diverse audience to visualize the vibrations of buildings. Visualization of a building's deformation requires spatiotemporal interpolation of motions from seismometers that are located wherever the crowd places them. In many cases, a crowd-sourced building network may actually be just a single seismometer. A method to rapidly estimate the total displacement response of a building based on limited observational data, in some cases from only a single seismometer, is presented. In general, the earliest part of the response is simulated by assuming a vertically propagating shear wave. Later motions are simulated using mode shapes derived from a beam model (a shear beam, or more generally a Timoshenko beam), the parameters of which are determined from the ratios of the modal frequencies and the building's exterior dimensions. The method is verified by (1) comparing predicted and actual records from a 54-story building in downtown Los Angeles, California, and (2) comparing finite-element simulations of the 17-story University of California, Los Angeles (UCLA) Factor building. The response of each of these buildings can be simulated with a simple shear beam. The importance of including the traveling wave part of the solution depends on the characteristics of the base ground shaking; the traveling wave becomes more apparent as the excitation becomes more impulsive. The method can be straightforwardly applied to multiple instrumented buildings, resulting in a tool to visualize linear elastic motions of those buildings.

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Simulating Building Motions Using Ratios of the Building's Natural Frequencies and a Timoshenko Beam Model

Cited by 33 publications

References 23 publications

Bayesian identification of soil-foundation stiffness of building structures

Bayesian identification of soil-foundation stiffness of building structures

Blind identification of the Millikan Library from earthquake data considering soil-structure interaction

Prediction of Wave Propagation in Buildings Using Data from a Single Seismometer

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