• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.2
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• pp.173-182
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• 2003

In equivalent static nonlinear analysis and in energy-based design, the structures are generally transformed into an equivalent SDOF system. In this study the seismic energy demands in multi story structures, such as three-, eight-, and twenty-story steel moment-resisting frames(MRF), buckling restrained braced frames(BRBF) and a damage tolerant braced frame(DTBF), are compared with those of equivalent single degree of freedom(ESDOF) systems. Sixty earthquake ground motions recorded In different soil conditions, which are soft rock, soft soil, and neat fault, were used to compute the input and hysteretic energy demands in model structures. In case the modal mass coefficient is less than 0.8, the effects of higher modes are considered in the process of converting into ESDOF According to the analysis results, the hysteretic and input energies obtained from 3 story and 8 story MRF and DTBF agreed well with the results from analysis of equivalent SDOF systems. However in the 20 story BRBF the results from ESDOF underestimated those obtained from the original structures.

• 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.

• 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.

• Journal of Korean Society of Steel Construction
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• v.16 no.6 s.73
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• pp.793-805
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• 2004

The main objective of this paper is to evaluate the ductility and strength factors that are key components of the response modification factor for special steel moment-resistant frames. The ductility factors for special steel moment-resistant frames were calculated by multiplying the ductility factor for SDOF systems and the MDOF modification factors. Ductility factors were computed for elastic and perfectly plastic SDOF systems undergoing different levels of inelastic deformation and periods when subjected to a large number of recorded earthquake ground motions. Based on the results of the regression analysis, simplified expressions were proposed to compute the ductility factors. Based on previous studies, the MDOF modification factors were also proposed to account for the MDOF systems. Strength factors for special steel moment resisting frames were estimated from the results of the nonlinear static analysis. A total of 36 sample steel frames were designed to investigate the ductility and strength factors considering design parameters such as number of stories (4, 8, and 16 stories), seismic zone factors (Z = 0.075, 0.2, and 0.4), framing system (Perimeter Frames, PF and Distributed Frames, DF), and failure mechanism (Strong-Column Weak Beam, SCWB, and Weak-Column Strong-Beam, WCSB). The effects of these design parameters on the ductility and strength factors for special steel moment-resisting frames were investigated.

• Earthquakes and Structures
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• v.18 no.2
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• pp.263-273
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• 2020

The use of energy concepts in seismic analysis and design of structures requires the understanding of the input energy response of multi-degree-of-freedom (MDOF) systems subjected to strong ground motions. For design purposes and non-time consuming analysis, however, it would be beneficial to associate the input energy response of MDOF systems with those of single-degree-of-freedom (SDOF) systems. In this paper, the theoretical formulation of energy input to MDOF systems is developed on the basis that only a particular portion of the total mass distributed among floor levels is effective in the nth-mode response. The input energy response histories of several reinforced concrete frames subjected to a set of eleven horizontal acceleration histories selected from actual recorded events and scaled in time domain are obtained. The contribution of the fundamental mode to the total input energy response of MDOF frames is demonstrated both graphically and numerically. The input energy of the fundamental mode is found to be a good indicator of the total energy input to two-dimensional regular MDOF structures. The numerical results computed by the proposed formulation are verified with relative input energy time histories directly computed from linear time history analysis. Finally, the elastic input energies are compared with those computed from time history analysis of nonlinear MDOF systems.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.446-453
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• 2001

System-level ductility is an essential parameter for seismic performance evaluation of multistory building structures. The ductility demands for single degree of freedom structures or individual structural members can be determined easily. However, there is no clearly established method to determine the ductility demands for structural systems. The system ductility demands are estimated in this study by the equivalent SDOF system methods and proposed method which used the representative responses obtained from the MDOF systems directly. And seismic performance of building structures is evaluated by the modified Capacity Spectrum Method using the representative responses, and the result was compared with those of the inelastic time history analysis.

• 한국방재학회:학술대회논문집
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• 2008.02a
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• pp.257-259
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• 2008

Acceleration time history (ATH) used in the seismic analysis should envelop a target power spectral density (PSD) function in addition to the design response spectrum in order to have sufficient energy at each frequency for the purpose of ensuring adequate load. Even though design regulations require the ATH used in seismic analysis to meet a target PSD function, the reason that ATHs meet to a target PSD function is not described. Thus, artificial ATHs for high PSD function and artificial ATHs for low PSD function are generated. And then elastic and inelastic single-degree-of-freedom (SDOF) systems are loaded with these artificial time histories as the earthquake load. As a result, linear response and inelastic response of SDOF systems are affected by PSD function.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2006.03a
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• pp.519-526
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• 2006

This paper compares the seismic response control performance of linear and non-linear models fer tuned liquid damper (TLD). The existing linear and nonlinear TLD models were used for the numerical analysis of single degree of freedom (SDOF) and multi degree of freedom (MDOF) systems with TLD. The nonlinear model considers the variation of the frequency and damping of the TLD with varying excitation amplitude while the linear one has the invariant parameters. Numerical analysis results from SDOF systems indicate that the nonlinear model shows about 5% better control performance than linear one when the mass ratio is 2% and the optimal parameters for reducing peak responses are dependent on the characteristics of the excitation earthquake loads.

• Structural Engineering and Mechanics
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• v.66 no.1
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• pp.139-149
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• 2018

Many practical engineering problems are associated with nonlinear systems subjected to nonstationary random excitations. Equivalent linearization methods are commonly used to seek for approximate solutions to this kind of problems. Compared to various approaches developed in the frequency and mixed time-frequency domains, though directly solving the system equation of motion in the time domain would improve computation efficiency, only limited studies are available. Considering the fact that the orthogonal functions have been widely used to effectively improve the accuracy of the approximated responses and reduce the computational cost in various engineering applications, an orthogonal-function-based equivalent linearization method in the time domain has been proposed in the current paper for nonlinear systems subjected to nonstationary random excitations. In the numerical examples, the proposed approach is applied to a SDOF system with a set-up spring and a SDOF Duffing oscillator subjected to stationary and nonstationary excitations. In addition, its applicability to nonlinear MDOF systems is examined by a 3DOF Duffing system subjected to nonstationary excitation. Results show that the proposed method can accurately predict the nonlinear system response and the formulation of the proposed approach allows it to be capable of handling any general type of nonstationary random excitations, such as the seismic load.

• Smart Structures and Systems
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• v.17 no.2
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• pp.231-256
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• 2016

This study concerns the derivation of optimum tuning formulas for a passive Tuned Mass Damper (TMD) device, for the case of benchmark ideal excitations acting on a single-degree-of-freedom (SDOF) damped primary structure. The free TMD parameters are tuned first through a non-linear gradient-based optimisation algorithm, for the case of harmonic or white noise excitations, acting either as force on the SDOF primary structure or as base acceleration. The achieved optimum TMD parameters are successively interpolated according to appropriate analytical fitting proposals, by non-linear least squares, in order to produce simple and effective TMD tuning formulas. In particular, two fitting models are presented. The main proposal is composed of a simple polynomial relationship, refined within the fitting process, and constitutes the optimum choice. A second model refers to proper modifications of literature formulas for the case of an undamped primary structure. The results in terms of final (interpolated) optimum TMD parameters and of device effectiveness in reducing the structural dynamic response are finally displayed and discussed in detail, showing the wide and ready-to-use validity of the proposed optimisation procedure and achieved tuning formulas. Several post-tuning trials have been carried out as well on SDOF and MDOF shear-type frame buildings, by confirming the effective benefit provided by the proposed optimum TMD.