Estimating Fundamental Frequencies of Tall Buildings

Dym, Clive L.; Williams, Harry E.

doi:10.1061/(asce)0733-9445(2007)133:10(1479)

Cited by 50 publications

(31 citation statements)

References 14 publications

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“…The results show that the frequency ratio of the Timoshenko beam matches that of a pure bending beam only when it has a large aspect ratio (L∕d ¼ 10), which confirms that a building performs similarly to a pure bending beam only when it is relatively tall and narrow. A point to note is that Miranda and Taghavi (2005) define a similar stiffness ratio r in their coupled shear wall frame structure, but their model behaves like a shear beam for large r and a bending beam for small r. Dym and Williams (2007) explain such a difference as being due to the fact that the Timoshenko beam couples the shear and flexural stiffnesses in series but Miranda's model couples them in parallel.…”

Section: H Cheng and T H Heatonmentioning

confidence: 99%

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

Cheng

Heaton

2015

Earthquake Spectra

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A simple prismatic Timoshenko beam model with soil-structure interaction (SSI) is developed to approximate the dynamic linear elastic behavior of buildings. A closed-form solution with complete vibration modes is derived. It is demonstrated that building properties, including mode shapes, can be derived from knowledge of the natural frequencies of the first two translational modes in a particular direction and from the building dimensions. In many cases, the natural frequencies of a building's first two vibrational modes can be determined from data recorded by a single seismometer. The total building's vibration response can then be simulated by the appropriate modal summation. Preliminary analysis is performed on the Caltech Millikan Library, which has significant bending deformation because it is much stiffer in shear.

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Section: H Cheng and T H Heatonmentioning

confidence: 99%

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

Cheng

Heaton

2015

Earthquake Spectra

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“…The use of continuous systems to model fixed‐base buildings has precedents in the literature, which include the use of Bernoulli–Euler beams, shear beams, coupled beams, and Timoshenko beams . In particular, Taciroglu et al employed a flexible‐base Timoshenko beam model to represent the soil‐structure system in a model‐updating scheme and identified the soil‐foundation dynamic stiffness.…”

Section: Introductionmentioning

confidence: 99%

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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“…Also, in the field of dynamic analyses of tall buildings, plentiful papers can be found. Suitable models have been proposed for estimating fundamental frequencies of tall buildings . Computing the mode shape and natural frequency of tabular systems and combined system of framed tube, shear core, and multioutrigger–belt truss systems is proposed by Malekinejad and Rahgozar through analytic equations.…”

Section: Introductionmentioning

confidence: 99%

Minimum‐weight design of high‐rise structures subjected to flexural vibration at a desired natural frequency

Alavi

Rahgozar

2018

Structural Design Tall Build

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Summary In this paper, a parametric approach for design of high‐rise structures subjected to flexural vibration is proposed. The optimization problem is formed based on a preselected value for the fundamental natural frequency, and it is formulated for minimum structural weight. In a two‐step approach, first, an alternative formulation aimed at maximizing structural stiffness that in turn maximizes structure's fundamental frequency is introduced. Then, optimized results are used in obtaining a closed‐form solution of the actual problem. Because the resulting equations are rather complicated, approximate forms are developed in order to simplify the design process. In all relations, contributions from shear forces to lateral displacement are assumed to be negligible; hence, bending resistance is the only design variable, and its optimal value is computable using simple relations. Two numerical examples are presented in order to illustrate the efficiency of this method in practice.

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Estimating Fundamental Frequencies of Tall Buildings

Cited by 50 publications

References 14 publications

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

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

Bayesian identification of soil-foundation stiffness of building structures

Minimum‐weight design of high‐rise structures subjected to flexural vibration at a desired natural frequency

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