A Statistical Method of Determining the Maximum Response of a Building Structure du-ring an Earthquake
01 Jan 1960-pp 781-797
About: The article was published on 1960-01-01 and is currently open access. It has received 298 citations till now. The article focuses on the topics: Ring (chemistry).
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TL;DR: In this paper, a study on the optimal design of a TMD for a single-degree-of-freedom structure under seismic loads was conducted in which the floor decks and isolation system together can be viewed as a giant tuned mass damper to reduce the seismic force of the truss.
Abstract: In seismic retrofit of a long-span truss bridge in Japan, a new retrofit scheme was applied in which the existing bearings of the bridge were replaced by a new floor deck isolation system. The floor decks and isolation system together can be viewed as a giant tuned mass damper (TMD) to reduce the seismic force of the truss. This motivates a study on the optimal design of a TMD for a single-degree-of-freedom structure under seismic loads in this paper. Kanai–Tajimi spectrum is selected to model the earthquake excitation. It is shown that, when ratio of the characteristic ground frequency in the Kanai–Tajimi spectrum to the structural frequency is above three, the ground motion can be assumed to be a white noise to design TMD. For a smaller ground frequency ratio, simple formulas of the optimal TMD parameters are obtained. The dependence of optimal TMD parameters on mass ratio especially for large TMD is highlighted. It is found that the optimal TMD has lower tuning frequency and higher damping ratio as the mass ratio increases. For a large mass ratio, TMD becomes very effective in minimizing the primary structure response and robust against uncertainties in the parameters of the system.
293 citations
TL;DR: In this paper, an optimal design theory for structures implemented with tuned mass dampers (TMDs) is proposed, and the optimal design parameters of TMDs in terms of damping coefficients and spring constants corresponding to each TMD are determined through minimizing a performance index of structural responses defined in the frequency domain.
Abstract: An optimal design theory for structures implemented with tuned mass dampers (TMDs) is proposed in this paper. Full states of the dynamic system of multiple-degree-of-freedom (MDOF) structures, multiple TMDs (MTMDs) installed at different stories of the building, and the power spectral density (PSD) function of environmental disturbances are taken into account. This proposed method allows for a more extensive application and successfully releases the limitations based on simplified models. The optimal design parameters of TMDs in terms of the damping coefficients and spring constants corresponding to each TMD are determined through minimizing a performance index of structural responses defined in the frequency domain. Moreover, a numerical method is also proposed for searching for the optimal design parameters of MTMDs in a systematic fashion such that the numerical solutions converge monotonically and effectively toward the exact solutions as the number of iterations increases. The feasibility of the proposed optimal design theory is verified by using a SDOF structure with a single TMD (STMD), a five-DOF structure with two TMDs, and a ten-DOF structure with a STMD.
247 citations
TL;DR: A versatile, nonstationary stochastic ground-motion model accounting for the time variation of both intensity and frequency content typical of real earthquake ground motions is formulated and validated.
Abstract: A versatile, nonstationary stochastic ground-motion model accounting for the time variation of both intensity and frequency content typical of real earthquake ground motions is formulated and validated. An extension of the Thomson's spectrum estimation method is used to adaptively estimate the evolutionary power spectral density (PSD) function of the target ground acceleration record. The parameters of this continuous-time, analytical, stochastic earthquake model are determined by least-square fitting the analytical evolutionary PSD function of the model to the target evolutionary PSD function estimated. As application examples, the proposed model is applied to two actual earthquake records. In each case, model validation is obtained by comparing the second-order statistics of several traditional ground-motion parameters and the probabilistic linear-elastic response spectra simulated using the earthquake model with their deterministic counterparts characterizing the target record.
226 citations
TL;DR: In this paper, the authors address the topic of the spatial variation of seismic ground motions as evaluated from data recorded at dense instrument arrays, focusing on spatial coherency and its interpretation.
Abstract: This study addresses the topic of the spatial variation of seismic ground motions as evaluated from data recorded at dense instrument arrays. It concentrates on the stochastic description of the spatial variation, and focuses on spatial coherency. The estimation of coherency from recorded data and its interpretation are presented. Some empirical and semi-empirical coherency models are described, and their validity and limitations in terms of physical causes discussed. An alternative approach that views the spatial variation of seismic motions as deviations in amplitudes and phases of the recorded data around a coherent approximation of the seismic motions is described. Simulation techniques for the generation of artificial spatially variable seismic ground motions are also presented and compared. The effect of coherency on the seismic response of extended structures is highlighted. This review article includes 133 references. @DOI: 10.1115/1.1458013#
213 citations
204 citations