• Structural Engineering and Mechanics
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• 제29권2호
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• pp.187-201
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• 2008

Earthquake induced hysteretic energy demand for a structure can be used as a limiting value of a certain performance level in seismic design of structures. In cases where it is larger than the hysteretic energy dissipation capacity of the structure, failure will occur. To be able to select the limiting value of hysteretic energy for a particular earthquake hazard level, it is required to define the variation of hysteretic energy in terms of probabilistic terms. This study focuses on the probabilistic evaluation of earthquake induced worst failure probability and approximate confidence intervals for inelastic single-degree-of-freedom (SDOF) systems with a typical steel moment connection based on hysteretic energy. For this purpose, hysteretic energy demand is predicted for a set of SDOF systems subject to an ensemble of moderate and severe EQGMs, while the hysteretic energy dissipation capacity is evaluated through the previously published cyclic test data on full-scale steel beam-to-column connections. The failure probability corresponding to the worst possible case is determined based on the hysteretic energy demand and dissipation capacity. The results show that as the capacity to demand ratio increases, the failure probability decreases dramatically. If this ratio is too small, then the failure is inevitable.

• Steel and Composite Structures
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• 제6권6호
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• pp.479-491
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• 2006

Structures in seismic regions are designed to dissipate seismic energy input through inelastic deformations. Structural or component failure occurs when the hysteretic energy demand for a structure or component subject to an earthquake ground motion (EQGM) exceeds its hysteretic energy dissipation capacity. This paper presents a study on identifying the hysteretic energy demand and distribution throughout the height of regular steel moment resisting frames (SMRFs) subject to severe EQGMs. For this purpose, non-linear dynamic time history (NDTH) analyses were carried out on regular low-, medium-, and high-rise steel SMRFs. An ensemble of ninety EQGMs recorded on different soil types was used in the study. The results show that the hysteretic energy demand decreases from the bottom stories to the upper stories and for high-rise structures, most of the hysteretic energy is dissipated by the bottom stories. The decrease is quite significant, especially, for medium- and high-rise structures.

• Structural Engineering and Mechanics
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• 제23권2호
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• pp.177-193
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• 2006

Determining the hysteretic energy demand and dissipation capacity and level of damage of the structure to a predefined earthquake ground motion is a highly non-linear problem and is one of the questions involved in predicting the structure's response for low-performance levels (life safe, near collapse, collapse) in performance-based earthquake resistant design. Neural Network (NN) analysis offers an alternative approach for investigation of non-linear relationships in engineering problems. The results of NN yield a more realistic and accurate prediction. A NN model can help the engineer to predict the seismic performance of the structure and to design the structural elements, even when there is not adequate information at the early stages of the design process. The principal aim of this study is to develop and test multi-layered feedforward NNs trained with the back-propagation algorithm to model the non-linear relationship between the structural and ground motion parameters and the hysteretic energy demand in steel moment resisting frames. The approach adapted in this study was shown to be capable of providing accurate estimates of hysteretic energy demand by using the six design parameters.

• Structural Engineering and Mechanics
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• 제70권3호
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• pp.289-301
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• 2019

Hysteretic energy is defined as energy dissipated through inelastic deformations during a ground motion by the system. It includes frequency content and duration of ground motion as two remarkable parameters, while these characteristics are not seen in displacement spectrum. Since maximum displacement individually cannot be the appropriate criterion for damage assessment, hysteretic energy has been evaluated in this research as a more comprehensive seismic demand parameter. An innovative methodology has been proposed to establish a new equivalent linear model to estimate hysteretic energy spectrum for bilinear SDOF models under two different sets of earthquake excitations. Error minimization has been defined in the space of equivalent linearization concept, which resulted in equivalent damping and equivalent period as representative parameters of the linear model. Nonlinear regression analysis was carried out for predicting these equivalent parameter as a function of ductility. The results also indicate differences between seismic demand characteristics of far-field and near-field ground motions, which are not identified by most of previous equations presented for predicting seismic energy. The main advantage of the proposed model is its independency on parameters related to earthquake and response characteristics, which has led to more efficiency as well as simplicity. The capability of providing a practical energy based seismic performance evaluation is another outstanding feature of the proposed model.

• Earthquakes and Structures
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• 제12권2호
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• pp.177-189
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• 2017

For energy-based seismic design, a simplified normalized cumulative hysteretic energy spectrum proposed for obtaining hysteretic energy as energy demand is the main objective in this paper. The dimensionless parameter, ${\beta}_{Eh}$, is presented to express hysteretic energy indirectly. The ${\beta}_{Eh}$ spectrum is constructed directly through subtracting the hysteretic energy of single degree-of-freedom (SDOF) system energy equation. The simplified ${\beta}_{Eh}$ spectral formulation as well as pseudo-acceleration spectrum of modern seismic provisions is developed based on the regression analysis of the large number of seismic responses of SDOF system subjected to earthquake excitations, which considers the influence of earthquake event, soil type, damping ratio, and ductility factor. The relationship between PGV and PGA is established according to the statistical analysis relied on a total of 422 ground motion records. The combination of ${\beta}_{Eh}$ spectrum and PGV/PGA equation allows determining the cumulative hysteretic energy as a main aseismic design indicator.

• Steel and Composite Structures
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• 제4권6호
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• pp.437-452
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• 2004

A simplified seismic design procedure for steel structures with buckling-restrained braces (BRB) was proposed based on the energy balance concept and the equal energy assumption. The input seismic energy was estimated from a design spectrum, and the elastic and hysteretic energy were computed using energy balance concept. The size of braces was determined so that the hysteretic energy demand was equal to the hysteretic energy dissipated by the BRB. The validity of using equivalent single-degree-of-freedom systems to estimate seismic input and hysteretic energy demand in multi story structures with BRB was investigated through time-history analysis. The story-wise distribution pattern of hysteretic energy demands was also obtained and was applied in the design process. According to analysis results, the maximum displacements of the 3-story structure designed in accordance with the proposed procedure generally coincided with the target displacements on the conservative side. The maximum displacements of the 6- and 8-story structures, however, turned out to be somewhat smaller than the target values due to the participation of higher vibration modes.

• 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.

• Structural Engineering and Mechanics
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• 제31권1호
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• pp.93-112
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• 2009

In this study seismic analyses of steel structures were carried out to examine the effect of ground motion characteristics and structural properties on energy demands using 100 earthquake ground motions recorded in different soil conditions, and the results were compared with those of previous works. Analysis results show that ductility ratios and the site conditions have significant influence on input energy. The ratio of hysteretic to input energy is considerably influenced by the ductility ratio and the strong motion duration. It is also observed that as the predominant periods of the input energy spectra are significantly larger than those of acceleration response spectra used in the strength design, the strength demand on a structure designed based on energy should be checked especially in short period structures. For that reason framed structures with buckling-restrained-braces (BRBs) were designed in such a way that all the input energy was dissipated by the hysteretic energy of the BRBs, and the results were compared with those designed by conventional strength-based design procedure.

• 국제초고층학회논문집
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• 제3권2호
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• pp.107-120
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• 2014

A Reinforced concrete (RC) shear wall system with coupling beams has been known as one of the most promising structural systems for high-rise buildings. However, significantly large flexural and/or shear stress demands induced in the coupling beams require special reinforcement details to avoid their undesirable brittle failure. In order to solve this problem, one of promising candidates is frictional hysteretic energy dissipating devices (HEDDs) as an alternative to the coupling beams. The introduction of frictional HEDDs into a RC shear wall system increases energy dissipation capacity and maintains the frame action after their yielding. This paper investigates the strength demands (specifically yield strength levels) with a maximum allowable ductility of frictional HEDDs based on comparative non-linear time-history analyses of a prototype RC shear wall system with traditional RC coupling beams and frictional HEDDs. Analysis results show that the RC shear wall systems coupled by frictional HEDDs with more than 50% yield strength of the RC coupling beams present better seismic performance compared to the RC shear wall systems with traditional RC coupling beams. This is due to the increased seismic energy dissipation capacity of the frictional HEDD. Also, it is found from the analysis results that the maximum allowable ductility demand of a frictional HEDD should increase as its yield strength decreases.

• 한국지진공학회논문집
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• 제7권2호
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• pp.29-37
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• 2003

본 연구에서는 지진하중에 의하여 철골 모멘트저항골조(MRF)와 좌굴이 방지된 가새골조(BRBF) 그리고 힌지로 접합된 좌굴이 방지된 가새골조(HBRBF)에서 발생하는 층별 이력에너지의 분포에 대하여 고찰하였다. 예제 구조물의 에너지 요구량을 산정하기 위하여 다른 지반조건에서 계측된 60개의 지진기록을 사용하였다. 해석결과에 따르면 MRF와 BRBF에서의 이력에너지는 밑면에서 최대가 되고 상부층으로 갈수록 점진적으로 감소하여, 상부층에서는 부재의 이력거동이 거의 발생하지 않았다. 그러나 HBRBF에서의 층별 이력에너지는 구조물의 높이에 따라 상대적으로 균등하게 분포하였으며, 이러한 경우 손상이 한 층에 집중적으로 발생하지 않아 다른 시스템에 비하여 보다 바람직하다고 할 수 있다. 연암 지반, 연약한 토사, 단층 근처의 지반 조건에 따른 에너지의 분포형태는 거의 동일하게 나타났다.