Hysteretic Energy Demand in SDOF Structures Subjected to an Earthquake Excitation: Analytical and Empirical Results

To address the irrationality of making a structure subjected to bidirectional ground motions equivalent to an SDOF system, a new approach method is presented in this paper. The ratio between modal participation factors of the two components of the structure is expressed as γ, and the superposition of bidirectional ground motions is regarded as one-directional earthquake excitation for the equivalent SDOF system. Based on this, an energy balance equation is established, and a method used to estimate normalized hysteretic energy (NHE) is proposed. Analysis of the ratio between NHE (γ ≠ 0) and NHE (γ = 0) is suggested in order to analyze the influence of bidirectional ground motions on hysteretic energy demand, and then, “α1 = NHE (γ ≠ 0)/NHE (γ = 0)” is defined, and bidirectional ground motion records for different soil sites are selected for establishing superimposed excitations. In addition, the period range of 0–5 s for the energy spectrum is divided into 6 ranges. In each period range, the means of α1 are defined as α. The curves of α of constant ductility factors for different soil sites are established, in which α is the vertical coordinate and γ is the horizontal coordinate. Through nonlinear response history analysis, the influence of soil types at different sites, the ductility factor, the ratio of modal participation factors, and the period on the values of α are analyzed. According to the analytical results, correction coefficient αs (the simplified value of α) is obtained so that the hysteretic energy demand under bidirectional ground motions can be determined.

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Identifying the hysteretic energy demand and distribution in regular steel frames

Steel and Composite Structures ◽

10.12989/scs.2006.6.6.479 ◽

2006 ◽

Vol 6 (6) ◽

pp. 479-491 ◽

Cited By ~ 2

Author(s):

Bulent Akbas ◽

Jay Shen ◽

Hakan Temiz

Keyword(s):

Energy Demand ◽

Steel Frames ◽

Hysteretic Energy

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The Use of ARMA Models in Earthquake Response Spectra

Volume 3: Structural Integrity; Nuclear Engineering Advances; Next Generation Systems; Near Term Deployment and Promotion of Nuclear Energy ◽

10.1115/icone14-89023 ◽

2006 ◽

Author(s):

Malek Brahimi ◽

Sidi Berri

Keyword(s):

Linear Response ◽

Energy Demand ◽

Arma Model ◽

Response Spectra ◽

Response Analysis ◽

Arma Models ◽

Maximum Displacement ◽

Ductility Demand ◽

Displacement Ductility ◽

Hysteretic Energy

Structural design spectra are based on smoothed linear response spectra obtained from different events scaled by their peak values. Such an approach does not incorporate other characteristics of the excitation represented by measured data. This study investigate the use of non-stationary models which can be considered characteristic and representative of specific historical earthquakes. An earthquake record is regarded as a sample realization from a population of such samples, which could have been generated by the stochastic process characterized by an Autoregressive Moving Average (ARMA) model. ARMA models are developed for four major earthquakes after processing by a variance stabilizing transformation. Samples of acceleration records are generated for each event. In this earthquake modeling procedure, parameters describing the modulating function of the record and the stabilized series are estimated. Maximum displacement ductility demand and normalized hysteretic energy demand for linear and stiffness softening single degree of freedom system systems are computed for the samples generated for each event. The sensitivity and dependence of demand spectra on earthquake model characteristics are examined to develop a response prediction model. Non linear response analysis of the four events indicates that ARMA (2,1) process using samples of twenty simulated earthquakes provide a reliable description of the information contained within acceleration records. Empirical relationships for displacement ductility and Normalized hysteretic energy demand spectra are developed.

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Hysteretic Energy Demands in Multi-Degree-of-Freedom Systems Subjected to Earthquakes

Buildings ◽

10.3390/buildings10120220 ◽

2020 ◽

Vol 10 (12) ◽

pp. 220

Author(s):

Emrah Erduran

Keyword(s):

Ground Motion ◽

Energy Demand ◽

Relative Strength ◽

Degree Of Freedom ◽

Special Focus ◽

Hysteretic Energy ◽

Demand Distribution ◽

Single Degree ◽

Energy Demands ◽

Energy Based Design

Reliable estimation of energy demands imposed on a structure by a design ground motion is a key component of energy-based design. Although several studies have been conducted to quantify the energy demands in single-degree-of-freedoms systems, few have focused on multi-degree-of-freedom systems. This study aims to build on the knowledge from previous studies on multi-degree-of-freedom systems with special focus on the distribution of hysteretic energy demands among the components of the structure. Nonlinear response history analyses conducted under ground motion sets representing three different hazard levels show that the total input and hysteretic energy demands of multi-degree-of-freedom systems can be accurately estimated from equivalent single-degree-of-freedom systems for low- and medium-rise buildings. The distribution of hysteretic energy demands over the height of the multistory structures has been shown to vary significantly from ground motion to ground motion. Analyses results also show that the relative strength of adjoining beams and columns has a significant influence on the hysteretic energy demand distribution. On the other hand, the energy distribution is relatively insensitive to the damping model used in the analysis of the multi-degree-of-freedom system.

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

STRUCTURAL ENGINEERING AND MECHANICS ◽

10.12989/sem.2006.24.5.641 ◽

2006 ◽

Vol 24 (5) ◽

pp. 641-645 ◽

Cited By ~ 3

Author(s):

M. Nakhaei ◽

M.A. Ghannad

Keyword(s):

Energy Demand ◽

Soil Structure ◽

Soil Structure Interaction ◽

Hysteretic Energy ◽

Structure Interaction

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An Estimate on Distribution of Hysteretic Energy Demand in Seismic Precast Concrete Frame Structures

Journal of Earthquake Engineering ◽

10.1080/13632469.2019.1605950 ◽

2019 ◽

pp. 1-27 ◽

Cited By ~ 3

Author(s):

Bin Du ◽

Zheng He ◽

Guohui Huang

Keyword(s):

Energy Demand ◽

Precast Concrete ◽

Frame Structures ◽

Hysteretic Energy ◽

Concrete Frame

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A Nonstationary Mathematical Model for Acceleration Time Series

Mathematical Modelling and Engineering Problems ◽

10.18280/mmep.080211 ◽

2021 ◽

Vol 8 (2) ◽

pp. 246-252

Author(s):

Tahar Brahimi ◽

Tahar Smain

Keyword(s):

Time Series ◽

Energy Demand ◽

Spectral Response ◽

Qualitative Description ◽

Response Analysis ◽

Model Parameters ◽

Ductility Demand ◽

Displacement Ductility ◽

Acceleration Time ◽

Hysteretic Energy

The choice of nonstationary stochastic models for the study is fully justified by the limitation of acceleration time series number. The three acceleration time series under consideration are used to generate a new, artificial series of ten per historical one using autoregressive moving average model. Subsequently, the average of nonlinear is utilized for the ten acceleration time series in order to obtain the spectral response of a system with single degree of freedom. Modeling of acceleration time series involves critical estimation of metrics that characterize nonstationary acceleration time series. Thus, for the stiffness degrading systems and bilinear systems, the metrics of hysteretic energy demand and displacement ductility demand during displacement are used. The applicability of artificially generated acceleration time series for the qualitative description of information was shown. More specifically, ARMA (2,2) showed the best results in the study for three accelerated time series through nonlinear response analysis. In addition, as a result, normalized hysteretic energy demand, empirically valid displacement ductility relationships, and model parameters were proposed.

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Attenuation of Hysteretic Energy Spectra of Strong Ground Motion

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.166-169.2453 ◽

2012 ◽

Vol 166-169 ◽

pp. 2453-2456

Author(s):

Mao Sheng Gong ◽

Jing Sun ◽

Li Li Xie

Keyword(s):

Energy Demand ◽

Ground Motions ◽

Energy Spectra ◽

Energy Structure ◽

Site Class ◽

Hysteretic Energy ◽

Ductility Factor ◽

Scenario Earthquakes ◽

Nonlinear Regression Method ◽

Strong Ground

Based on 266 strong ground motions from 15 significant earthquakes in California of America, the attenuation law of hysteretic spectra is established by using nonlinear regression method, and the effects of site class and ductility level on the hysteretic spectra constructed from the attenuation relationship are discussed in the paper. The results show that the site has significant effects on hysteretic energy spectra, and the more soft the site is, the more hysteretic energy structure will suffer from earthquake. Moreover, for ductility level scaled by ductility factor, the results show that structure with greater ductility factor can dissipate more input energy from the earthquake by means of the plastic deformation. The up limit design value of ductility factor for a structure is proposed as 4 because there is little difference between the hysteretic energy demand for ductility factor 4 and larger values. The hysteretic energy demand for structures at a given site in scenario earthquakes can be evaluated according to the results of the paper.

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