• 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.

• Structural Engineering and Mechanics
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• v.84 no.5
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• pp.675-684
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• 2022

The conventional single-degree-of-freedom (SDOF) system is appropriate for dynamic response analysis of paneltype structures without an opening. However, the typical building structures usually have four-sided fixed walls having an opening. Therefore, it may induce a considerable error when dynamic responses are estimated based on the conventional SDOF system, since the SDOF system cannot consider the effect of an opening during the SDOF analysis. For this reason, this study proposes a new SDOF system to consider the effect of an opening by adjusting its load-mass factor. The load-mass factor can be modified based on the assumption that the behaviors of the four-sided fixed wall with an opening is very similar to the behaviors of the same size wall without an opening, when the uniformly distributed blast loaded area is identical. In order to confirm a feasibility of the proposed SDOF system, a series of numerical simulations were carried out for the four-sided fixed reinforced concrete (RC) wall under a blast load. The dynamic responses estimated from the proposed SDOF system and the conventional SDOF system were compared with the dynamic responses evaluated from the finite element (FE) analysis. Especially, for the maximum dynamic responses except for 50% opening case, the proposed SDOF system had about 1.1% to 25.7% normalized errors while the conventional SDOF system had about 4.1% to 49.1% normalized errors.

• 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 Computational Structural Engineering Institute of Korea
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• v.37 no.3
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• pp.179-186
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• 2024

In this paper, a modification coefficient for equivalent single degree of freedom (SDOF), considering the plasticity range of the member subjected to shock wave type of blast load, was developed. The modification coefficient for the equivalent SDOF was determined through comparison with the analysis of a multi-degree of freedom (MDOF) system. The parameters influencing the equivalent SDOF system analysis were chosen as the boundary conditions of the member and the ratio of the duration of blast load to the natural period of the member. The modification coefficient was calculated based on the elastic load-mass transformation factor. The modification coefficient curve was derived using an elliptical equation to ensure it exists between the upper and lower parameter bounds. Using the modification coefficient on examples with varying cross sections and boundary conditions reduced the SDOF analysis error rate from 15% to 3%. This study shows that using the modification coefficient significantly improves the accuracy of SDOF analysis. The modification coefficient proposed in this study can be used for blast analysis.

• 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 Korean Society of Steel Construction
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• v.22 no.6
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• pp.553-561
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• 2010

The purpose of this paper is to analytically find the approximate supplement damping ratio of the viscous damper installed in self-centering (SC) single-degree-of-freedom (SDOF) systems with maximum displacements that are similar to those of elasto-plastic (EP) SDOF systems. The behavior of an SC SDOF system under harmonic cyclic loading was first described. Then an analytical model that can capture the behavior of the viscously damped SC SDOF system was introduced. Analysis parameters that characterize the hysteresis of the EP and SC SDOF systems were chosen, and nonlinear time-history analyses were performed using 20 historical accelerograms. Most of the SC SDOF systems with viscous dampers with approximately 10-15% damping ratios presented mean maximum displacement values that were similar to those of the EP SDOF systems. To investigate in detail the seismic performance of both systems, three EP SDOF systems and six corresponding SC SDOF systems were selected. The analyses showed that all the SC SDOF systems eliminated the residual displacements after the end of their shaking, and that the SC SDOF systems with 15% damping ratios performed better than the EP SDOF systems in terms of maximum displacement and acceleration response.

• Structural Monitoring and Maintenance
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• v.11 no.3
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• pp.219-234
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• 2024

The strength reduction factor spectrum is traditionally obtained from a single-degree-of-freedom (SDOF) system with a constant damping coefficient. However, according to the principle of Rayleigh damping, the damping coefficient matrix of a system changes with the stiffness matrix, and the damping coefficient of an equivalent SDOF system changes with the tangent stiffness coefficient. In view of that, this study proposes an equivalent SDOF system with an adaptive damping coefficient and derives a standardized reaction balance equation. By iteratively adjusting the strength reduction factor, the corresponding spectrum with an equivalent ductility factor is obtained. In addition, the ratio between the strength reduction factor that considers adaptive damping and the traditional strength reduction factor, denoted by η, is determined, and the η-μ-T relationship is obtained. Seismic records of Classes C, D, and E sites are selected as excitations. Moreover, a nonlinear response time-history analysis is performed to establish the relationship between the η and T values for the equivalent ductility factor μ. Further, by exploring the effects of the site class, ductility factor, second-order stiffness coefficient, and period T on the mean value of η, a simplified calculation equation of mean η is derived, and η is used as a modified value for the traditional strength reduction factor R spectrum.

• 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.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.