• Earthquakes and Structures
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• 제13권3호
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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.

• Earthquakes and Structures
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• 제11권1호
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• pp.165-178
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• 2016

The goal of energy-based seismic design is to obtain a structural design with a higher energy dissipation capacity than the energy dissipation demands incurred under earthquake motions. Accurate estimation of the story hysteretic energy demand of a multi-story structure is the key to meeting this goal. Based on the assumption of a mode-equivalent single-degree-of-freedom system, the energy equilibrium relationship of a multi-story structure under seismic action is transformed into that of a multi-mode analysis of several single degree-of-freedom systems. A simplified equation for the estimation of the story seismic hysteretic energy demand was then derived according to the story shear force and deformation of multi-story buildings, and the deformation and energy relationships between the mode-equivalent single-degree-of-freedom system and the original structure. Sites were categorized into three types based on soil hardness, namely, hard soil, intermediate hard (soft) soil, and soft soil. For each site type, a 5-story and 10-story reinforced concrete frame structure were designed and employed as calculation examples. Fifty-six earthquake acceleration records were used as horizontal excitations to validate the accuracy of the proposed method. The results verify the following. (1) The distribution of seismic hysteretic energy along the stories demonstrate a degree of regularity. (2) For the low rise buildings, use of only the first mode shape provides reasonably accurate results, whereas, for the medium or high rise buildings, several mode shapes should be included and superposed to achieve high precision. (3) The estimated hysteretic energy distribution of bottom stories tends to be underestimated, which should be modified in actual applications.

• 한국전산구조공학회논문집
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• 제37권3호
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• pp.179-186
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• 2024

본 논문에서는 충격파 형태의 폭발 하중을 받는 부재의 소성 범위를 고려한 SDOF 해석의 수정계수를 개발하였다. SDOF 해석의 수정계수는 MDOF 해석 결과 값을 비교하여 도출하였다. SDOF 해석에 영향을 미치는 매개변수로 부재의 경계조건, 폭발 하중 지속시간과 고유주기 비를 선정하였다. 수정계수는 탄성 하중-질량 변환 계수를 기준으로 산정하였다. 수정계수 곡선은 상한, 하한 매개변수 경계 사이에 있도록 타원 방정식을 이용하여 도출하였다. 서로 다른 단면과 경계조건을 가지는 예제에 수정계수를 적용한 결과 SDOF 해석의 오차율이 15%에서 3%로 감소하였다. 본 연구의 결과는 수정계수를 적용하여 SDOF 해석의 정확도를 높임에 따라 폭발 해석에 널리 활용될 수 있다.

• Structural Engineering and Mechanics
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• 제51권4호
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• pp.531-546
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• 2014

In this paper the extension of a recently established energy-based pushover procedure in order to include the higher mode contributions to the seismic response of structures is presented and preliminary evaluated. The steps of the proposed methodology in its new formulation are quite similar to those of the well-known Modal Pushover Analysis. However, the determination of the properties of the 'modal' equivalent single-degree-of-freedom systems is achieved by a rationally founded energy-based concept. Firstly, the theoretical background and the assumptions of the proposed methodology are presented and briefly discussed. Secondly, the sequence of steps to be followed for its implementation along with the necessary equations is systematically presented. The accuracy of the methodology is evaluated by an extensive parametric study which shows that, in general, it provides better results compared to those produced by other similar procedures. In addition, the main shortcoming of the initial version of the methodology now seems to be mitigated to a large extent.

• Structural Engineering and Mechanics
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• 제13권4호
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• pp.369-385
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• 2002

Ductility capacity is comprehensively studied for steel moment-resisting frames. Local, story and global ductility are being considered. An appropriate measure of global ductility is suggested. A time domain nonlinear seismic response algorithm is used to evaluate several definitions of ductility. It is observed that for one-story structures, resembling a single degree of freedom (SDOF) system, all definitions of global ductility seem to give reasonable values. However, for complex structures it may give unreasonable values. It indicates that using SDOF systems to estimate the ductility capacity may be a very crude approximation. For multi degree of freedom (MDOF) systems some definitions may not be appropriate, even though they are used in the profession. Results also indicate that the structural global ductility of 4, commonly used for moment-resisting steel frames, cannot be justified based on this study. The ductility of MDOF structural systems and the corresponding equivalent SDOF systems is studied. The global ductility values are very different for the two representations. The ductility reduction factor $F_{\mu}$ is also estimated. For a given frame, the values of the $F_{\mu}$ parameter significantly vary from one earthquake to another, even though the maximum deformation in terms of the interstory displacement is roughly the same for all earthquakes. This is because the $F_{\mu}$ values depend on the amount of dissipated energy, which in turn depends on the plastic mechanism, formed in the frames as well as on the loading, unloading and reloading process at plastic hinges. Based on the results of this study, the Newmark and Hall procedure to relate the ductility reduction factor and the ductility parameter cannot be justified. The reason for this is that SDOF systems were used to model real frames in these studies. Higher mode effects were neglected and energy dissipation was not explicitly considered. In addition, it is not possible to observe the formation of a collapse mechanism in the equivalent SDOF systems. Therefore, the ductility parameter and the force reduction factor should be estimated by using the MDOF representation.

• Earthquakes and Structures
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• 제14권5호
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• pp.411-424
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• 2018

This study explores the inelastic behavior of systems with flexible base. The use of a single degree of freedom system (ESDOF) with equivalent ductility to represent the response of flexible base systems is discussed. Two different equations to compute equivalent ductility are proposed, one which includes the contribution of rigid body components, and other based on the overstrength of the structure. In order to asses the accuracy of ESDOF approach with the proposed equations, the behavior of a 10-story regular building with reinforced concrete (RC) moment resisting frames is studied. Local and global ductility capacity and demands are used to study the modifications introduced by base flexibility. Three soil types are considered with shear wave velocities of 70, 100 and 250 m/s. Soil-foundation stiffness is included with a set of springs on the base (impedance functions). Capacity curves of the building are computed with pushover analysis. In addition, non linear time history analysis are used to asses the ductility demands. Results show that ductility capacity of the soil-structure system including rigid body components is reduced. Base flexibility does not modify neither yield and maximum base shear. Equivalent ductility estimated with the proposed equations is fits better the results of the numerical model than the one considering elastoplastic behavior. Modification of beams ductility demand due to base flexibility are not constant within the structure. Some elements experience reduced ductility demands while other elements experience increments when flexible base is considered. Soil structure interaction produces changes in the relation between yield strength reduction factor and structure ductility demand. These changes are dependent on the spectral shape and the period of the system with fixed and flexible base.

• 한국정밀공학회지
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• 제20권12호
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• pp.135-141
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• 2003

For the analysis of machined surface topography and machine-tool chatter, the cutting system is considered to be a single degree of freedom system. This paper presents a modeling method of equivalent vibratory system for precision cutting in end-milling using an impact test, an Autoregressive Moving Average (ARMA) mode] and a bisection method It has been shown that the proposed modeling method provides a good identification of the cutting system. The advantages of the proposed method in comparison to the existing method are that it is very easy and accurate.

• Earthquakes and Structures
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• 제14권2호
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• pp.155-165
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• 2018

Methods based on nonlinear static analysis as simple tools could be used for the seismic analysis and assessment of structures. In the present study, capability of the N2 method as a well-known nonlinear analysis procedure examines for the estimation of the damage index of multi-storey reinforced concrete frames. In the implemented framework, equivalent single-degree-of-freedom (SDOF) models are utilized for the global damage estimation of multi-degree-of-freedom (MDOF) systems. This method does not require high computational analysis and subsequently decreases the required time of seismic design and assessment process. To develop the methodology, RC frames with period range from 0.4 to 2.0 s under 40 records are studied. The effectiveness of proposed technique is evaluated through numerical study under near- and far-field earthquake ground motions. Finally, the results of developed models are compared with two other simplified schemes along with nonlinear time history analysis results of multi-storey frames. To improve the accuracy of damage estimation, a modified relation is presented based on the N2 method results for near- and far-field earthquakes.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2004년도 가을 학술발표회 논문집
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• pp.296-303
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• 2004

In this study, equivalent linear damping and stiffness of a single-degree-of-freedom (SDOF) structure with a rotational friction damper are estimated using the result of experiments and compared with those obtained from non-linear time history analyses. First, the transfer function of the test model is constructed and then the equivalent stiffness and damping are calculated, using the half-power bandwidth (HPB) method. For comparative study, those properties are estimated based on stochastic theory in the time domain. Both equivalent linear systems identified from experiments and numerical analyses correspond well. Further, it is observed that there exists an optimal clamping force on the rotational friction damper from estimated equivalent damping.

• Steel and Composite Structures
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• 제37권4호
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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.