• 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.

• 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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• 제32권2호
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• pp.321-335
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• 2009

When a roof frame is subjected to the airblast loading, the conventional way to analyze the damage of the frame or design the frame is to use single degree of freedom (SDOF) model. Although a roof frame consists of beams and girders, a typical SDOF analysis can be conducted only separately for each component. Thus, the rigid body motion of beams by deflections of supporting girders can not be easily considered. Neglecting the beam-girder interaction in the SDOF analysis may cause serious inaccuracies in the response values in both Pressure-Impulse curve (P-I) and Charge Weight-Standoff Diagrams (CWSD). In this paper, an inelastic two degrees of freedom (TDOF) model is developed, based on force equilibrium equations, to consider beam-girder interaction, and to assess if the modified SDOF analysis can be a reasonable design approach.

• 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.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 봄 학술발표회 논문집
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• pp.19-26
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• 2003

In energy-based design, the structures are generally transformed into equivalent SDOF systems to obtain the input and the dissipated energy. In this study the energy demands in multi-story structures were compared with that of equivalent single degree of freedom systems to validate the transformation method. Three-, eight-, and twenty-story steel moment-resisting frames and buckling restrained braced frames are compared with those of equivalent single degree of freedom systems. Sixty earthquake ground motions recorded in different soil conditions were used to compute the input and hysteretic energy demands in model structures. According to the analysis results, in 3 and 8-story structures the hysteretic energy demands computed in the equivalent SDOF structures are compatible with those computed in the original MDOF structures, while in the 20-story structures the transformed equivalent structures underestimated the hysteretic energy demands.

• 한국방재학회:학술대회논문집
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• 한국방재학회 2008년도 정기총회 및 학술발표대회
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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.

• 터널과지하공간
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• 제20권4호
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• pp.292-298
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• 2010

본 연구는 발파진동에 의한 지반진동이 구조물에 미치는 영향을 평가하기 위함이다. 이를 위하여 지반에서 측정한 자료를 토대로 Newmark $\beta$ 방법을 이용하여 단자유도계(SDOF)를 가정한 구조물 동적응답 시간이력과 구조물에서 직접 측정한 진동 시간이력을 비교 하였다. 지반과 구조물의 측정 자료로부터 시간이력을 해석한 결과, 단일공 발파와 20 ms 단차 발파에서 지반진동과 구조물 사이의 진동 크기는 약 3배의 차이로 구조물에서 더 큰 진동을 보이는 것으로 나타났다. 구조물 동적응답 시간이력을 해석한 결과, 그 값은 구조물에서 직접 측정한 자료와 유사한 최대 진동속도를 보였으며, 이것은 구조물 하부 지반에서 측정된 지반진동 측정자료에 근거하여 구조물의 진동특성을 예측할 수 있음을 지시한다.

• Structural Engineering and Mechanics
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• 제42권3호
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• pp.363-381
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• 2012

This study is aimed at providing an efficient analytical model to obtain pressure- impulse diagram of one-way reinforced concrete slabs subjected to different shapes of air blast loading using single degree of freedom method (SDOF). A tri-linear elastic perfectly plastic SDOF model has been used to obtain the pressure-impulse diagram to correlate the blast pressure and the corresponding concrete flexural damage. In order to capture the response history for the slab, a new approximately SDOF method based on the conventional SDOF method is proposed and validated using published test data. The influences of pulse loading shape on the pressure-impulse diagram are studied. Based on the results, a pressure-impulse diagram generation method using SDOF and an analytical equation for the pressure-impulse diagram is proposed to different damage levels and different blast loading shapes.

• Wind and Structures
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• 제6권4호
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• pp.291-306
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• 2003

Many investigations have been conducted to find out the reason behind wind-rain-induced cable vibration in cable-stayed bridges. A single-degree-of-freedom (SDOF) analytical model, which could capture main features of wind-rain-induced cable vibration, was recently presented by the writers. This paper extends the SDOF model to a 2DOF model by including the equation of motion of upper rivulet. The interaction between the upper rivulet and the cable is described in terms of nonlinear damping force, linear restoring force, and inertia force. The computed results using the 2DOF model are first compared with the results from simulated wind-rain tunnel tests, and the comparison is found satisfactory in general. The possible mechanisms of wind-rain-induced cable vibration are discussed and a parametric study is then conducted. Finally, the computed results using the 2DOF model are compared with those predicted by the SDOF model. The 2DOF model is found better than the SDOF model but the SDOF model is still acceptable for its simplicity.

• 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.