• Structural Engineering and Mechanics
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• v.46 no.6
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• pp.755-773
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• 2013

One of the main requirements of the seismic design codes must be its easy application by structural engineers. The use of practically-applicable models or simplified models as single-degree-of-freedom (SDOF) systems is a good alternative to achieve this condition. In this study, deterministic and probabilistic response transformation factors are obtained to evaluate the response in terms of maximum ductility and maximum interstory drifts of multi-degree-of-freedom (MDOF) systems based on the response of equivalent SDOF systems. For this aim, five steel frames designed with the Mexican City Building Code (MCBC) as well as their corresponding equivalent SDOF systems (which represent the characteristics of the frames) are analyzed. Both structural systems are subjected to ground motions records. For the MDOF and the simplified systems, incremental dynamic analyses IDAs are developed in first place, then, structural demand hazard curves are obtained. The ratio between the IDAs curves corresponding to the MDOF systems and the curves corresponding to the simplified models are used to obtain deterministic response transformation factors. On the other hand, demand hazard curves are used to calculate probabilistic response transformation factors. It was found that both approaches give place to similar results.

• Earthquakes and Structures
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• v.19 no.4
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• pp.243-259
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• 2020

This study aims to optimize, design, and predict the MTMDs performance in SDOF systems using spectral analysis, and then apply their results to MDOF structures. Given the importance of spectral analysis in the design of new engineering structures, achieving a method for designing TMDs based on this theory can be of great importance for structural designers. In this study, several convenient combinations of MTMDs in an SDOF system are first considered to minimize the maximum displacement. For calculating the frequency ratios of dampers, an innovative technique is adopted in which the values of different modal responses obtained from the spectral analysis are approached together. This procedure is done using a harmony search (HS) algorithm. Also, using the random vibration theory, the damping ratio of the dampers is obtained. Then, an equation is presented for predicting the performance of MTMDs. For evaluating this equation, three structures with different stories are designed. Some of the presented combinations of dampers are added to them. The time history analyses are employed to analyze the structures under 30 different accelerograms. The findings indicated that the proposed equation could efficiently predict the performance of the MTMDs. Furthermore, four different patterns of damper distribution along the height of the structures are defined. The effect of them on the maximum deformation of the structures in time history analyses is discussed, and an equation is presented to estimate this effect. The results indicated that the average and maximum error percentages of the proposed equations are about three and seven percent, respectively, compared to the time history analyses results, which are negligible values.

• Earthquakes and Structures
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• v.1 no.4
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• pp.327-344
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• 2010

This paper summarizes results of a comprehensive analytical study aimed at evaluating the influence of strong ground motion duration on residual displacement demands of single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems. For that purpose, two sets of 20 earthquake ground motions representative of short-duration and long-duration records were considered in this investigation. While the influence of strong ground motion duration was evaluated through constant-strength residual displacement ratios, $C_r$, computed from the nonlinear response of elastoplastic SDOF systems, its effect on the amplitude and height-wise distribution of residual drift demands in MDOF systems was studied from the response of three one-bay two-dimensional generic frame models. In this investigation, an inelastic ground motion intensity measure was employed to scale each record, which allowed reducing the record-to-record variability in the estimation of residual drift demands. From the results obtained in this study, it was found that long strong-motion duration records might trigger larger median $C_r$ ratios for SDOF systems having short-to-medium period of vibration than short strong-motion duration records. However, taking into account the large record-to-record variability of $C_r$, it was found that strong motion duration might not be statistically significant for most of the combinations of period of vibration and levels of lateral strength considered in this study. In addition, strong motion duration does not have a significant influence on the amplitude of peak residual drift demands in MDOF systems, but records having long strong-motion duration tend to increase residual drift demands in the upper stories of long-period generic frames.

• Journal of the Earthquake Engineering Society of Korea
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• v.15 no.1
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• pp.39-48
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• 2011

In this present study, a response modification factor for a lightweight steel panel-modular system which is not clarified in a current building code was proposed. As a component of the response modification factor, an over-strength factor and a ductility factor were drawn from the nonlinear static analysis curves of the systems modeled on the basis of the performance tests. The final response modification factor was then computed by modifying the previous response modification factor with a MDOF (Multi-Degree-Of-Freedom) base shear modification factor considering the MDOF dynamic behaviors. As a result of computation for the structures designed as a dual frame system, ranging from 2-story to 5-story, the value of 4 was estimated as a final response modification factor for a seismic design, considering the value of 5 as an upper limit of the number of stories.

• Steel and Composite Structures
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• v.12 no.4
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• pp.353-379
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• 2012

The accuracy of the 30% and SRSS rules, commonly used to estimate the combined response of structures, and some related issues, are studied. For complex systems and earthquake loading, the principal components give the maximum seismic response. Both rules underestimate the axial load by about 10% and the COV of the underestimation is about 20%. Both rules overestimate the base shear by about 10%. The uncertainty in the estimation is much larger for axial load than for base shear, and, for axial load, it is much larger for inelastic than for elastic behavior. The effect of individual components may be highly correlated, not only for normal components, but also for totally uncorrelated components. The rules are not always inaccurate for large values of correlation coefficients of the individual effects, and small values of such coefficients are not always related to an accurate estimation of the response. Only for perfectly uncorrelated harmonic excitations and elastic analysis of SDOF systems, the individual effects of the components are uncorrelated and the rules accurately estimate the combined response. In the general case, the level of underestimation or overestimation depends on the degree of correlation of the components, the type of structural system, the response parameter, the location of the structural member and the level of structural deformation. The codes should be more specific regarding the application of these rules. If the percentage rule is used for MDOF systems and earthquake loading, at least a value of 45% should be used for the combination factor.

• Earthquakes and Structures
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• v.10 no.1
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• pp.211-238
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• 2016

The Maximum seismic responses of steel buildings with perimeter moment resisting frames (MRF), modeled as complex MDOF systems, are estimated for several incidence angles of the horizontal components and the critical one is identified. The accuracy of the existing rules to combine the effects of the individual components is also studied. Two and three components are considered. The critical response does not occur for principal components and the corresponding incidence angle varies from one earthquake to another. The critical response can be estimated as 1.40 and 1.10 times that of the principal components, for axial load and interstory shears, respectively. The rules underestimate the axial load but reasonably overestimate the shears. The rules are not always inaccurate in the estimation of the combined response for correlated components. On the other hand, totally uncorrelated (principal) components are not always related to an accurate estimation. The correlation of the individual effects (${\rho}$) may be significant, even for principal components. The rules are not always associated to an inaccurate estimation for large values of ${\rho}$, and small values of ${\rho}$ are not always related to an accurate estimation. Only for perfectly uncorrelated harmonic excitations and elastic analysis of SDOF systems, the individual effects of the components are uncorrelated and the rules accurately estimate the combined response. The degree of correlation of the components, the type of structural system, the response parameter under consideration, the location of the structural member and the level of structural deformation must be considered while estimating the level of underestimation or overestimation.

• Journal of the Korean Geotechnical Society
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• v.38 no.6
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• pp.17-28
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• 2022

The effect of the soil-structure interaction (SSI) on has been recently evaluated in shaking table tests. However, most of these tests were conducted on single-degree-of-freedom (SDOF) superstructures and a single-pile. This study investigates the inertial interaction effect of a multi-degree-of-freedom (MDOF) superstructure system with a group piles on a large-scale shaking table test. Whereas the SDOF superstructure system shows a single-frequency amplification tendency, the MDOF superstructure system exhibited amplification tendencies of the acceleration phase and frequency responses for multiple frequencies. In addition, the amplification phenomenon between the footing and the column-type superstructure exceeded that between the footing and the wall-type superstructure, indicating a greater inertial interaction effect of the column-type superstructure. The relationship between shear force and inertial force, the relative vertical and horizontal displacements on the footing was figured out. Also, the ananlysis of dynamic p-y curve at each depth was conducted. In summary, the MDOF and SDOP superstructure systems exhibited different behaviors and the column-type superstructure exerted a higher interaction effect than the wall-type superstructure.

• Smart Structures and Systems
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• v.14 no.6
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• pp.1131-1150
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• 2014

One of the issues in extending the range of applicable problems of real-time hybrid simulation is the computation speed of the simulator when large-scale computational models with a large number of DOF are used. In this study, functionality of real-time dynamic simulation of MDOF systems is achieved by creating a logic circuit that performs the step-by-step numerical time integration of the equations of motion of the system. The designed logic circuit can be implemented to an FPGA-based system; FPGA (Field Programmable Gate Array) allows large-scale parallel computing by implementing a number of arithmetic operators within the device. The operator splitting method is used as the numerical time integration scheme. The logic circuit consists of blocks of circuits that perform numerical arithmetic operations that appear in the integration scheme, including addition and multiplication of floating-point numbers, registers to store the intermediate data, and data busses connecting these elements to transmit various information including the floating-point numerical data among them. Case study on several types of linear and nonlinear MDOF system models shows that use of resource sharing in logic synthesis is crucial for effective application of FPGA to real-time dynamic simulation of structural response with time step interval of 1 ms.

• Journal of Korean Association for Spatial Structures
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• v.13 no.1
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• pp.69-77
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• 2013

This study is the research appling the representative Displacement-Based Design which is the basic concept of Direct Displacement Based Design proposed by Chopra and Goel to original Reinforced Concrete moment frame and determining the thickness of retrofit Steel Jacket about the Maximum design ground acceleration, and developing the more improved Algorithm as well as program by the Retrofit Design method and Nonlinear analysis by the Performance design method before and after reinforcement appling the determined retrofit thickness. It also shows the result of the seismic performance improvement which is the ratio of seismic performance appreciation result yield displacement 19%, yield strength ratio 24%, displace ductility ratio the maximum 27% comparing Multi degree of freedom, column member of Reinforced Concrete with the performance improvement column member considering the thickness of the determined Steel Jacket. The developed Algorithm and program are easy to apply seismic design and application to the original Reinforced Concrete building, at the same time, it applicate to display well the design result of Target displacement performance level about nonlinear behavior.

• Structural Engineering and Mechanics
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• v.20 no.5
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• pp.527-542
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• 2005

The main objective of this study is to examine the accuracy of the complete quadratic combination (CQC) rule with the modal responses defined by the ordinates of the uniform hazard spectra (UHS) to evaluate the peak responses of the multi-degree-of-freedom (MDOF) systems subjected to nonstationary seismic excitations. For the probabilistic analysis of the peak responses, it is considered that the seismic excitations can be modeled using evolutionary power spectra density functions with uncertain model parameters. More specifically, a seismological model and the Kanai-Tajimi model with the boxcar or the exponential modulating functions were used to define the evolutionary power spectral density functions in this study. A set of UHS was obtained based on the probabilistic analysis of transient responses of single-degree-of-freedom systems subjected to the seismic excitations. The results of probabilistic analysis of the peak responses of MDOF systems were obtained, and compared with the peak responses calculated by using the CQC rule with the modal responses given by the UHS. The comparison seemed to indicate that the use of the CQC rule with the commonly employed correlation coefficient and the peak modal responses from the UHS could lead to significant under- or over-estimation when contributions from each of the modes are similarly significant.