Hysteretic Energy Demand Research Articles

UNIFORM HAZARD SPECTRA BASED ON PARK-ANG DAMAGE INDEX

The primary emphases in the performance-based seismic design (PBSD) philosophy are in the accounting for uncertainties in seismic demand/capacity and in the better quantification of seismic damage using suitable inelastic damage parameters. Uniform hazard spectra (UHS) provide probabilistic information regarding a seismic demand on a single degree oscillator for a specific site. UHS are very good tools for probabilistic hazard estimation as intended in PBSD. In the present work, UHS are generated for Park-Ang damage index of an elastic-perfectly plastic oscillator. Park-Ang damage index takes into account the effects of both displacement ductility demand and hysteretic energy demand in low-cycle-fatigue, and therefore is a demand parameter suitable for PBSD. The UHS are generated for a specific site using artificially generated ground motions. Two types of UHS plot are illustrated. A correlation between the probability of exceedance (of certain target damage index) and stated level of structural capacity is also established. Information provided by the UHS are proposed to be used, with the aid of equivalent systems, in the development of a reliability-based seismic design framework considering Park-Ang damage index as the seismic demand parameter.

A methodology to estimate earthquake induced worst failure probability of inelastic systems

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.

Estimation of hysteretic energy demand using concepts of modal pushover analysis

AbstractHysteretic energy dissipation in a structure during an earthquake is the key factor, besides maximum displacement, related to the amount of damage in it. This energy demand can be accurately computed only through a nonlinear time‐history analysis of the structure subjected to a specific earthquake ground acceleration. However, for multi‐story structures, which are usually modeled as multi‐degree of freedom (MDOF) systems, this analysis becomes computation intensive and time consuming and is not suitable for adopting in seismic design guidelines. An alternative method of estimating hysteretic energy demand on MDOF systems is presented here. The proposed method uses multiple ‘generalized’ or ‘equivalent’ single degree of freedom (ESDOF) systems to estimate hysteretic energy demand on an MDOF system within the context of a ‘modal pushover analysis’. This is a modified version of a previous procedure using a single ESDOF system. Efficiency of the proposed procedure is tested by comparing energy demands based on this method with results from nonlinear dynamic analyses of MDOF systems, as well as estimates based on the previous method, for several ground motion scenarios. Three steel moment frame structures, of 3‐, 9‐, and 20‐story configurations, are selected for this comparison. Bias statistics that show the effectiveness of the proposed method are presented. In addition to being less demanding on the computation time and complexity, the proposed method is also suitable for adopting in design guidelines, as it can use response spectra for hysteretic energy demand estimation. Copyright © 2008 John Wiley & Sons, Ltd.

On the estimation of hysteretic energy demands for SDOF systems

AbstractBased on a statistical study of the dynamic response of single degree of freedom (SDOF) systems subjected to earthquake ground motions, a rule to estimate hysteretic energy demands is proposed. Expressions for elastic–perfectly plastic, stiffness degrading and pinching SDOF systems were obtained. The proposed rule does not explicitly depend on the period of the system; instead, it depends on the elastic pseudo‐acceleration and elastic velocity spectra. It is shown that the proposed rule can be applied to compute hysteretic energy demands for systems located at different soil conditions. In addition, information about scatter and bias of the proposed rule is also presented. Copyright © 2007 John Wiley & Sons, Ltd.

Estimation of Hysteretic Energy of MDOF Structures Based on Equivalent SDOF Systems

It is important for obtaining the relationship between seismic energies of single degree-of-freedom (SDOF) systems and multiple degree-of-freedom (MDOF) structures in engineering. In this paper, the formula of hysteretic energy between the MDOF structures and equivalent SDOF systems is developed. Here is also presented the procedure for estimating hysteretic energy of MDOF structures subjected to severe ground motions employing the energy relation equation based on equivalent SDOF systems. Eight examples for two regular and six irregular MDOF structures show that the procedure to obtain the hysteretic energy demands of MDOF structures may be used as a simple and effective energy estimation method.

Hysteretic Energy Demands for SDOF Systems Subjected to Narrow Band Earthquake Ground Motions. Applications to the Lake Bed Zone of Mexico City

This study proposes a way to estimate the hysteretic energy demands for oscillators subjected to narrow-band earthquake ground motions using an equivalent sinusoidal pulse. The parameters required to define the equivalent pulse are: the peak ground acceleration, the maximum of the Fourier amplitude spectrum, and the predominant period of the site. The equivalent pulse is utilized to compute the hysteretic energy demands associated to the design elastic pseudoacceleration spectra prescribed by the Mexico City Building Code and to construct damage index maps for systems designed according to this code and subjected to a seismic event with M = 8 and focal distance of 300 km.

Identifying the hysteretic energy demand and distribution in regular steel frames

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.

The effect of soil-structure interaction on hysteretic energy demand of buildings

The effect of soil-structure interaction on hysteretic energy demand of buildings

A neural network model to assess the hysteretic energy demand in steel moment resisting frames

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.

Merging energy-based design criteria and reliability-based methods: exploring a new concept

This paper examines the potential development of a probabilistic design methodology, considering hysteretic energy demand, within the framework of performance-based seismic design of buildings. This article does not propose specific energy-based criteria for design guidelines, but explores how such criteria can be treated from a probabilistic design perspective. Uniform hazard spectra for normalized hysteretic energy are constructed to characterize seismic demand at a specific site. These spectra, in combination with an equivalent systems methodology, are used to estimate hysteretic energy demand on real building structures. A design checking equation for a (hypothetical) probabilistic energy-based performance criterion is developed by accounting for the randomness of the earthquake phenomenon, the uncertainties associated with the equivalent system analysis technique, and with the site soil factor. The developed design checking equation itself is deterministic, and requires no probabilistic analysis for use. The application of the proposed equation is demonstrated by applying it to a trial design of a three-storey steel moment frame. The design checking equation represents a first step toward the development of a performance-based seismic design procedure based on energy criterion, and additional works needed to fully implement this are discussed in brief at the end of the paper. Copyright © 2006 John Wiley & Sons, Ltd.

DEMANDAS DE ENERGÍA HISTERÉTICA EN OSCILADORES ELASTOPLÁSTICOS SUJETOS A RUIDO BLANCO GAUSSIANO

Se presenta una solución teórica para estimar la energía histerética por unidad de masa disipada por un oscilador elastoplástico sujeto a una familia de ruidos blancos gaussianos. La solución fue obtenida con base en el modelo propuesto originalmente por Karnopp y Scharton. Con el métodoque se propone, los resultados sólo dependen del periodo y de la resistencia del oscilador, del nivel de amortiguamiento y de la densidad espectral de potencia de la familia de ruidos blancos. Las expresiones propuestas son de carácter más general que las expresiones de Karnopp y Scharton y, a diferencia de estas últimas, son aplicables a sistemas con propiedades comúnmente utilizadas en ingeniería sísmica.

Energy-based seismic design of buckling-restrained braced frames using hysteretic energy spectrum

An energy-based seismic design procedure for framed structures with buckling-restrained braces is proposed using hysteretic energy spectra and accumulated ductility spectra. The procedure is based on the premise that the gravity load-resisting elements, such as beams and columns, are designed to remain elastic during earthquake, and all the seismic input energy is dissipated by the buckling-restrained braces. The proposed design procedure requires hysteretic energy spectra and accumulated ductility spectra corresponding to various target ductility ratios. The cross-sectional area of braces required to meet a given target displacement is obtained by equating the hysteretic energy demand to the accumulated plastic energy dissipated by braces. The design procedure was applied to three- and eight-story framed structures with buckling-restrained braces. Twenty earthquake records were utilized to construct the spectra and to verify the validity of the design procedure. According to analysis results, the mean values for the top story displacement correspond well with the given performance target displacements. Also, the inter-story drifts turned out to be relatively uniform over the structure height, which is desirable because uniform inter-story drifts indicate uniform damage distribution.

ESTIMATION OF NEAR-SOURCE GROUND MOTION AND SEISMIC BEHAVIOUR OF RC FRAMED STRUCTURES DAMAGED BY THE 1999 ATHENS EARTHQUAKE

On September 7, 1999 an earthquake with magnitude M W =5.9 occurred close to the city of Athens in Greece. More than 80 buildings collapsed, about 150 deaths and hundreds of injuries were reported. Soon after the event a damage investigation was carried out by two of the authors in the most heavily struck areas. The most serious damages were observed in the northern suburbs of Athens, where reinforced concrete frames and masonry buildings represent the prevalent construction systems. The hysteretic energy demands imposed on RC buildings should have been rather severe considering the structural systems characteristics and the inadequate construction details. However, over-strengths, redundancy and especially the presence of infill walls, provided a significant increase of the seismic capacity and contributed to the survival of many buildings. The objective of the present work is to reproduce and analyse the response of typical RC frames subjected to the 1999 Athens earthquake in areas where the observed damage was particularly severe but no recordings of the ground motion were available. After a general overview of the seismotectonic environment, seismological data, observed macro-seismic intensities, structural typologies and observed building behaviour, an attempt is made to identify representative excitations in the meizoseismal area. Specifically, the required accelerograms are obtained by modifying available records so as to reproduce a given global energy content and to be consistent with the observed damage. To study the seismic response of RC models, the obtained accelerograms are used to perform nonlinear dynamic analyses.

Energy-based seismic design of structures with buckling-restrained braces

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.

이력에너지 스펙트럼을 이용한 비좌굴 가새골조의 내진설계

본 연구에서는 단자유도계 시스템에서 작성한 이력에너지 스펙트럼과 누적된 변위 연성비 스펙트럼을 이용하여 비좌굴 가새골조의 내진설계법을 제안하였다. 먼저 목표 연성비에 해당하는 이력에너지 스펙트럼과 누적된 연성비 스펙트럼을 작성하였다. 주어진 목표 변위를 만족하기 위하여 필요한 가새의 단면적은 이력에너지 요구량과 가새에 의하여 소산된 누적 소성에너지를 같다고 하여 산정하였다. 스펙트럼을 작성하고 설계절차의 유효성을 검증하기 위하여 20개의 지진기록을 이용하였다. 제안된 방법에 따라 설계된 3층과 8층 비좌굴 가새골조의 해석결과에 따르면 최상층 변위의 평균값이 성능 목표 변위에 잘 부합됨을 알 수 있다. 또한 층간변위는 구조물 높이에 따라 비교적 일정하였는데 이것은 손상 분포가 일정하기 때문에 바람직하다. 그러므로 제안된 에너지 설계법은 기존 강도설계법의 대안으로 비좌굴 가새골조의 신뢰할만한 설계법이라고 할 수 있다. In this study seismic design procedure for buckling-restrained braced frame systems was proposed using hysteretic energy spectrum and accumulated ductility spectrum constructed from single degree of freedom systems. The hysteretic energy spectra and accumulated ductility spectra corresponding to target ductility ratio were constructed first. The cross-sectional area of braces required to meet a given target displacement was obtained by equating the hysteretic energy demand to the accumulated plastic energy dissipated by braces. Twenty earthquake records were utilized to construct the spectra and to verify the validity of the design procedure. According to analysis results of three- and eight-story buckling-restrained braced frame structures designed using the proposed method, the mean values for the top story displacement correspond well with the given performance target displacements. Also, the inter-story drifts turned out to be relatively uniform over the structure height, which is desirable because uniform inter-story drifts indicate uniform damage distribution. Therefore if was concluded that the proposed energy-based method could be a reliable alternative to conventional strength-based design procedure for structures with buckling-restrained braces.

An energy-based methodology for the assessment of seismic demand

A methodology for the assessment of the seismic energy demands imposed on structures is proposed. The research was carried out through two consecutive phases. Inelastic design input energy spectra for systems with a prescribed displacement ductility ratio were first developed. The study of the inelastic behavior of energy factors and the evaluation of the response modification in comparison with the elastic case were performed by introducing two new parameters, namely: (1) the Response Modification Factor of the earthquake input energy ( R E), representing the ratio of the elastic to inelastic input energy spectral values and (2) the ratio α of the area enclosed by the inelastic input energy spectrum in the range of periods between 0.05 and 4.0 s to the corresponding elastic value. The proposed design inelastic energy spectra, resulting from the study of a large set of strong motion records, were obtained as a function of ductility, soil type, source-to-site distance and magnitude. Subsequently, with reference to single degree of freedom systems, the spectra of the hysteretic to input energy ratio were evaluated, for different soil types and target ductility ratios. These spectra, defined to evaluate the hysteretic energy demand of structures, were described by a piecewise linear idealization that allows to distinguish three distinct regions as a function of the vibration period. In this manner, once the inelastic design input energy spectra were determined, the definition of the energy dissipated by means of inelastic deformations followed directly from the knowledge of hysteretic to input energy ratio. The design spectra of both input energy and hysteretic to input energy ratio were defined considering an elasto-plastic behavior. Nevertheless, other constitutive models were taken into account for comparison purposes.