• Steel and Composite Structures
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• v.37 no.4
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• pp.447-462
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• 2020

In this paper, a simplified seismic design method for low-rise dual frame-steel plate shear wall (SPSW) structures is proposed in the framework of performance-based seismic design. The dynamic response of a low-rise structure is mainly dominated by the first-mode and the structural system can be simplified to an equivalent single degree-of-freedom (SDOF) oscillator. The dual frame-SPSW structure was decomposed into a frame system and a SPSW system and they were simplified to an equivalent F-SDOF (SDOF for frame) oscillator and an equivalent S-SDOF (SDOF for SPSW) oscillator, respectively. The analytical models of F-SDOF and S-SDOF oscillators were constructed based on the OpenSees platform. The equivalent SDOF oscillator (D-SDOF, dual SDOF) for the frame-SPSW system was developed by combining the F-SDOF and S-SDOF oscillators in parallel. By employing the lateral force resistance coefficients and seismic demands of D-SDOF oscillator, the design approach of SPSW systems was developed. A 7-story frame-SPSW system was adopted to verify the feasibility and demonstrate the design process of the simplified method. The results also show the seismic demands derived by the equivalent dual SDOF oscillator have a good consistence with that by the frame-SPSW structure.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2003.09a
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• pp.205-212
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• 2003

To evaluate the seismic performance of multistory building structures use an equivalent SDOF model. This paper presents a method of converting a MDOF system into an equivalent SDOF model. The principal objective of this investigation is to evaluate appropriateness of converting method through perform nonlinear time history analysis of a multistory building structures and an equivalent SDOF model. The hysteresis rules to be used an equivalent SDOF model is obtained from the pushover analysis. The conclusion of this study is following; A method of converting a MDOF system into an equivalent SDOF model through the nonlinear time history response analysis is valid. The representative lateral displacement of a moment resisting reinforced concrete frames is close to the height of the first modal participation vector $_1$$\beta$｛$_1$u｝=1. It can be found that the hysteresis rule of an equivalent SDOF model have influence on the time history response. Therefore, it is necessary for selecting hysteresis rules to consider hysteresis characteristics of a moment resisting reinforced concrete frames.

• Journal of the Earthquake Engineering Society of Korea
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• v.8 no.5 s.39
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• pp.25-33
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• 2004

To evaluate the seismic capacity of a multistorey building structures in performance based seismic design, it is needed to convert MDOF model into equivalent SDOF model. This paper presents predictions for interstory drift of multistorey structures using method of converting a MDOF system into an equivalent SDOF model. The principal objective of this investigation is to evaluate appropriateness of converting method through performing nonlinear time history analysis of a multistory building structures and an equivalent SDOF model. Comparing the interstory drift of multistorey structures calculated by time history analysis and those evaluated by an equivalent SDOF model, the adequacy and the validity of converting method is verified. The conclusion of this study is following; A method of converting a MDOF system into an equivalent SDOF model through the nonlinear time history response analysis is valid. Inelastic first mode shapes are expected to be more accurate than elastic first mode shapes in obtaining interstory drift of multistorey structures from equivalent SDOF model.

• Earthquakes and Structures
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• v.13 no.3
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• pp.231-239
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• 2017

Fundamental period is one of the most critical parameters affecting the seismic design of buildings. In this paper, a very simple approach is presented for estimating the fundamental period of multiple-degree-of-freedom (MDOF) structures. The basic idea behind this approach is to replace the complicated MDOF system with an equivalent single-degree-of-freedom (SDOF) system. To realize this equivalence, a procedure for replacing a two-degree-of-freedom (2-DOF) system with an SDOF system, known as a two-to-single (TTS) procedure, is developed first; then, using the TTS procedure successively, an MDOF system is replaced with an equivalent SDOF system. The proposed approach is expressed in terms of mass, stiffness, and number of stories, without mode shape or any other parameters; thus, it is a very simple method. The accuracy of the proposed method is investigated by estimating the fundamental periods of many MDOF models; it is found that the results obtained by the proposed method agree very well with those obtained by eigenvalue analysis.

• Journal of the Earthquake Engineering Society of Korea
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• v.7 no.1
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• pp.9-16
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• 2003

To evaluate the seismic performance of multistory building structures use an equivalent SDOF model to represent the resistance of the structure to deformation as it respond in its predominant mode. This paper presents a method of converting a MDOF system into an equivalent SDOF model. The principal objective of this investigation is to evaluate appropriateness of converting method through perform nonlinear time history analysis of a multistory building structures and an equivalent SDOF model. The hysteresis rules to be used an equivalent SDOF model is obtained from the pushover analysis. Comparing the peak inelastic response of a moment resisting reinforced concrete frames and an equivalent SDOF model, the adequacy and the validity of the converting method is verified. The conclusion of this study is following; A method of converting a MDOF system into an equivalent SDOF model through the nonlinear time history response analysis is valid. The representative lateral displacement of a moment resisting reinforced concrete frames is close to the height of the first modal participation vector \ulcorner$_1{\beta}$${_1{\mu}}=1$. It can be found that the hysteresis rule of an equivalent SDOF model have influence on the time history response. Therefore, it necessary for selecting hysteresis rules to consider hysteresis characteristics of a moment resisting reinforced concrete frames.

• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.655-664
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• 2023

Reinforced concrete (RC) shear wall structures are one of the most widely used structural systems to resist seismic loading all around the world. Although there have been several efforts to provide conceptually simple procedures to reasonably assess the seismic demands of structures over recent decades, it seems that lesser effort has been put on a number of structural forms such as RC shear wall structures. Therefore, this study aims to represent a simple linear response spectrum-based method which can acceptably predict the nonlinear displacements of a non-ductile RC shear wall structure subjected to an individual ground motion record. An effective period and an equivalent damping ratio are introduced as the dynamic characteristics of an equivalent linear SDOF system relevant to the main structure. By applying the fundamental mode participation factor of the original MDOF structure to the linear spectral response of the equivalent SDOF system, an acceptable estimation of the nonlinear displacement response is obtained. Subsequently, the accuracy of the proposed method is evaluated by comparison with another approximate method which is based on linear response spectrum. Results show that the proposed method has better estimations for maximum nonlinear responses and is more utilizable and applicable than the other one.

• Structural Engineering and Mechanics
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• v.46 no.5
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• pp.595-613
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• 2013

A new effective model for calculation of the equivalent uniform blast load for non-uniform blast load such as close-in explosion of a one-way square and rectangle reinforced concrete slab is proposed in this paper. The model is then validated using single degree of freedom (SDOF) system with the experiments and blast tests for square slabs and rectangle slabs. Test results showed that the model is accurate in predicting the damage level on the tested RC slabs under the given explosive charge weight and stand-off distance especially for close-in blast load. The results are also compared with those obtained by conventional SDOF analysis and finite element (FE) analysis using solid elements. It is shown that the new model is more accurate than the conventional SDOF analysis and is running faster than the FE analysis.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.370-377
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• 2002

Hwang et al (2001) proposed a new method for an evaluation of equivalent damping ratios of a linear structure with linear or nonlinear damping devices. This procedure has a disadvantage that it requires time history analysis for the whole system including damping devices, which may be troublesome for practical application. To tackle this problem closed form formulas for equivalent damping ratios are proposed in this study. It is assumed that the responses of MDOF system can be reproduced by an equivalent SDOF system which vibrates in a fundamental mode. The numerical analyses of a ten-story building equipped with linear viscous damper or active mass damper or friction damper show the effectiveness of equivalent SDOF model and closed form formulas.

• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.459-466
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• 2002

The purpose of this study is to propose a new method for evaluating equivalent damping ratios of a structure with supplemental damping devices to assess their control effect quantitatively. A MDOF system is transformed to an equivalent SDOF system based on the assumption that the first mode dominates structural response. Approximate closed-form formulas for the evaluation of the first damping ratio are presented for various damping devices. Through numerical analysis of a ten-story building equipped with damping devices, the effectiveness of equivalent SDOF model and closed form formulas are verified.