基于MPA方法的结构滞回耗能计算

在能量反应分析中,滞回耗能是最具明确工程意义的而又便于工程应用的能量指标,可用以衡量结构的塑性累积损伤。然而,以往研究中,在计算多自由度体系的滞回耗能时,通常采用时程分析法,计算比较烦杂,不利于工程实际的应用。因此,本文提出了一种采用模态pushover分析（MPA）计算多层结构滞回耗能的简便方法,并通过两个高层结构算例,验证了该方法的精度。结果表明：基于模态pushover分析的结构滞回耗能计算方法精度良好,结果可靠;对于框架结构,可以直接采用第一阶模态（倒三角）加载模式对结构进行pushover分析计算,对于高层框架剪力墙结构,必须组合高阶模态的滞回耗能计算结果。     

Envelope‐based pushover analysis procedure for the approximate seismic response analysis of buildings

An envelope‐based pushover analysis procedure is presented that assumes that the seismic demand for each response parameter is controlled by a predominant system failure mode that may vary according to the ground motion. To be able to simulate the most important system failure modes, several pushover analyses need to be performed, as in a modal pushover analysis procedure, whereas the total seismic demand is determined by enveloping the results associated with each pushover analysis. The demand for the most common system failure mode resulting from the ‘first‐mode’ pushover analysis is obtained by response history analysis for the equivalent ‘modal‐based’ SDOF model, whereas demand for other failure modes is based on the ‘failure‐based’ SDOF models. This makes the envelope‐based pushover analysis procedure equivalent to the N2 method provided that it involves only ‘first‐mode’ pushover analysis and response history analysis of the corresponding ‘modal‐based’ SDOF model. It is shown that the accuracy of the approximate 16th, 50th and 84th percentile response expressed in terms of IDA curves does not decrease with the height of the building or with the intensity of ground motion. This is because the estimates of the roof displacement and the maximum storey drift due to individual ground motions were predicted with a sufficient degree of accuracy for almost all the ground motions from the analysed sets. Copyright © 2013 John Wiley & Sons, Ltd.     

Pushover analysis procedure for systems considering SSI effects based on capacity spectrum method

This paper presents a new procedure to transform an SSI system into an equivalent SDOF system using twice equivalence. A pushover analysis procedure based on the capacity spectrum method for buildings with SSI effects （PASSI） is then established based on the equivalent SDOF system, and the modified response spectrum and equivalent capacity spectrum are obtained. Furthermore, the approximate formulas to obtain the dynamic stiffness of foundations are suggested. Three steel buildings with different story heights （3, 9 and 20） including SSI effects are analyzed under two far-field and two near-field historical records and an artificial seismic time history using the two PASSI procedures and the nonlinear response history analysis （NLhRHA） method. The results are compared and discussed. Finally, combined with seismic design response spectrum, the nonlinear seismic response of a 9-story building with SSI effects is analyzed using the PASSI procedures, and its seismic performance is evaluated according to the Chinese ＇Code for Seismic Design of Buildings. The feasibility of the proposed procedure is verified.     

基于能力谱法的SSI体系抗震pushover分析方法

本文首先经过2次等效将土与结构相互作用的多自由度体系等效为单自由度体系,并给出了修正反应谱和等价能力谱的确定方法,进而提出了基于能力谱法考虑土与结构动力相互作用(SSI)效应的结构体系pushover分析方法(SSIPA);然后对3种不同高度考虑SSI效应的结构体系在5条地震动作用下采用本文提出的方法进行了算例分析,将结果与非线性时程分析的结果进行了比较,研究了本方法的适用性和准确性;最后,与建筑抗震设计规范的设计反应谱相结合,对9层考虑SSI效应的钢结构用本文提出的方法进行了弹塑性地震反应分析,根据我国抗震设计规范的规定进行抗震性能的评估验证了本方法的可行性。     

An improved modal pushover analysis procedure for estimating seismic demands of structures

The pushover analysis （POA） procedure is difficult to apply to high-rise buildings, as it cannot account for the contributions of higher modes. To overcome this limitation, a modal pushover analysis （MPA） procedure was proposed by Chopra et al. （2001）. However, invariable lateral force distributions are still adopted in the MPA. In this paper, an improved MPA procedure is presented to estimate the seismic demands of structures, considering the redistribution of inertia forces after the structure yields. This improved procedure is verified with numerical examples of 5-, 9- and 22-story buildings. It is concluded that the improved MPA procedure is more accurate than either the POA procedure or MPA procedure. In addition, the proposed procedure avoids a large computational effort by adopting a two-phase lateral force distribution..     

基于位移的抗震设计方法中的等效阻尼模型的研究

对基于位移的抗震设计方法单自由度体系弹塑性位移计算的等效线性化方法中的等效阻尼模型进行研究.在统计分析的基础上,提出了考虑场地类别和设计地震分组的等效阻尼比公式,并与不同阻尼比公式进行了比较.对不同等效线性化方法的计算误差进行了统计分析,结果表明,本文建议的公式在预测单自由度体系位移反应方面与动力弹塑性分析结果在统计意义上吻合得最好.     

基于能量被动耗能结构抗震设计方法的研究

将结构前两阶振型各自等效为单自由度,采用模态pushover分析确定各等效单自由度的屈服强度系数和延性系数,然后由反应谱计算各阶振型耗散能量需求,利用各振型能量分布曲线,求得各层耗散能量需求,叠加得到各层地震总能量需求,据此确定耗能装置的类型及设计参数.运用该方法对9层钢框架进行了设计,并通过非线性动力分析进行了验证,结果表明该方法精确度符合实际工程需求.     

Self-centering seismic retrofit scheme for reinforced concrete frame structures: SDOF system study

This paper presents the results of a parametric study of self-centering seismic retrofit schemes for reinforced concrete (RC) frame buildings. The self-centering retrofit system features flag-shaped hysteresis and minimal residual deformation. For comparison purpose,an alternate seismic retrofit scheme that uses a bilinear-hysteresis retrofit system such as buckling-restrained braces (BRB) is also considered in this paper. The parametric study was carried out in a single-degree-of-freedom (SDOF) system framework since a multi-story building structure may be idealized as an equivalent SDOF system and investigation of the performance of this equivalent SDOF system can provide insight into the seismic response of the multi-story building. A peak-oriented hysteresis model which can consider the strength and stiffness degradation is used to describe the hysteretic behavior of RC structures. The parametric study involves two key parameters -the strength ratio and elastic stiffness ratio between the seismic retrofit system and the original RC frame. An ensemble of 172 earthquake ground motion records scaled to the design basis earthquake in California with a probability of exceedance of 10% in 50 years was constructed for the simulation-based parametric study. The effectiveness of the two seismic retrofit schemes considered in this study is evaluated in terms of peak displacement ratio,peak acceleration ratio,energy dissipation demand ratio and residual displacement ratio between the SDOF systems with and without retrofit. It is found from this parametric study that RC structures retrofitted with the self-centering retrofit scheme (SCRS) can achieve a seismic performance level comparable to the bilinear-hysteresis retrofit scheme (BHRS) in terms of peak displacement and energy dissipation demand ratio while having negligible residual displacement after earthquake.     

Effects of vertical irregularity and thickness of unreinforced masonry infill on the robustness of RC framed buildings

Presence of irregularities in reinforced concrete (RC) buildings increases seismic vulnerability. During severe seismic shaking, such buildings may suffer disproportionate damage or even collapse that can be minimized by increasing robustness. Robustness is a desirable property of structural systems that can mitigate susceptible buildings to disproportionate collapse. In this paper, the effects of vertical irregularity and thickness of unreinforced masonry infill on the robustness of a six‐story three‐bay RC frame are quantified. Nonlinear static analysis of the frame is performed, and parametric study is undertaken by considering two parameters: absence of masonry infill at different floors (i.e., vertical irregularities) and infill thickness. Robustness has been quantified in terms of stiffness, base shear, ductility, and energy dissipation capacity of the frame. It was observed that the infill thickness and vertical irregularity have significant influence on the response of RC frame. The response surface method is used to develop a predictive equation for robustness as a function of the two parameters. The predictive equation is validated further using 12 randomly selected computer simulations. Copyright © 2013 John Wiley & Sons, Ltd.     

Performance spectra based method for the seismic design of structures equipped with passive supplemental damping systems

A new direct performance‐based design method utilizing design tools called performance‐spectra (P‐Spectra) for low‐rise to medium‐rise frame structures incorporating supplemental damping devices is presented. P‐Spectra are graphic tools that relate the responses of nonlinear SDOF systems with supplemental dampers to various damping parameters and dynamic system properties that structural designers can control. These tools integrate multiple response quantities that are important to the performance of a structure into a single compact graphical format to facilitate direct comparison of different potential solutions that satisfy a set of predetermined performance objectives under various levels of seismic hazard. An SDOF to MDOF transformation procedure that defines the required supplemental damping properties for the MDOF structure to achieve the response defined by the target SDOF system is also presented for hysteretic, linear viscous and viscoelastic damping devices. Using nonlinear time‐history analyses of idealized shear structures, the accuracy of the transformation procedure is verified. A seismic performance upgrade design example is presented to demonstrate the usefulness of the proposed method for achieving design performance goals using supplemental damping devices. Copyright © 2012 John Wiley & Sons, Ltd.     

Simplification of strong ground motion considering inelastic responses of structures

Simplification of strong ground motions to 1 cycle sine waves was investigated from the elastic and inelastic earthquake response analyses and response analyses under sine wave input using single‐degree‐of‐freedom systems. Strong ground motions could be simplified to 1 cycle sine waves if large plastic deformations, with ductility factor more than 2, were assumed. This is because the approximate maximum responses from input sine waves are determined by the initial response cycle, due to period elongation and plastic energy dissipation of the systems. A sine wave whose acceleration amplitude is the peak ground acceleration (PGA) and whose period is that of an equivalent 1 cycle sine wave is proposed. The period of an equivalent sine wave is easily obtained from the elastic response acceleration spectrum of a seismic record. This means that the inelastic responses are approximately determined by the PGA and an equivalent 1 cycle sine wave period. Therefore, an equivalent 1 cycle sine wave period provides a single index to express the frequency characteristics of a strong ground motion. Copyright © 2000 John Wiley & Sons, Ltd.     

A modal pushover analysis procedure to estimate seismic demands for unsymmetric‐plan buildings

An Erratum has been published for this article in Earthquake Engng. Struct. Dyn. 2004; 33:1429. Based on structural dynamics theory, the modal pushover analysis (MPA) procedure retains the conceptual simplicity of current procedures with invariant force distribution, now common in structural engineering practice. The MPA procedure for estimating seismic demands is extended to unsymmetric‐plan buildings. In the MPA procedure, the seismic demand due to individual terms in the modal expansion of the effective earthquake forces is determined by non‐linear static analysis using the inertia force distribution for each mode, which for unsymmetric buildings includes two lateral forces and torque at each floor level. These ‘modal’ demands due to the first few terms of the modal expansion are then combined by the CQC rule to obtain an estimate of the total seismic demand for inelastic systems. When applied to elastic systems, the MPA procedure is equivalent to standard response spectrum analysis (RSA). The MPA estimates of seismic demand for torsionally‐stiff and torsionally‐flexible unsymmetric systems are shown to be similarly accurate as they are for the symmetric building; however, the results deteriorate for a torsionally‐similarly‐stiff unsymmetric‐plan system and the ground motion considered because (a) elastic modes are strongly coupled, and (b) roof displacement is underestimated by the CQC modal combination rule (which would also limit accuracy of RSA for linearly elastic systems). Copyright © 2004 John Wiley & Sons, Ltd.     

Estimation of hysteretic energy demand using concepts of modal pushover analysis

Hysteretic 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.     

A static predictor of seismic demand on frames based on a post‐elastic deflected shape

Predictors of seismic structural demands (such as inter‐storey drift angles) that are less time‐consuming than nonlinear dynamic analysis have proven useful for structural performance assessment and for design. Luco and Cornell previously proposed a simple predictor that extends the idea of modal superposition (of the first two modes) with the square‐root‐of‐sum‐of‐squares (SRSS) rule by taking a first‐mode inelastic spectral displacement into account. This predictor achieved a significant improvement over simply using the response of an elastic oscillator; however, it cannot capture well large displacements caused by local yielding. A possible improvement of Luco's predictor is discussed in this paper, where it is proposed to consider three enhancements: (i) a post‐elastic first‐mode shape approximated by the deflected shape from a nonlinear static pushover analysis (NSPA) at the step corresponding to the maximum drift of an equivalent inelastic single‐degree‐of‐freedom (SDOF) system, (ii) a trilinear backbone curve for the SDOF system, and (iii) the elastic third‐mode response for long‐period buildings. Numerical examples demonstrate that the proposed predictor is less biased and results in less dispersion than Luco's original predictor. Copyright © 2006 John Wiley & Sons, Ltd.     

基于能量原理的钢筋混凝土筒体结构抗震性能研究

本文通过能量法研究了钢筋混凝土筒体结构的抗震性能。文中采用振型分解法按等效单自由度体系求解筒体结构的滞回输入能;用pushover法分析了滞回耗能在结构层间的分布规律及结构自身的耗能能力;根据楼层滞回耗能与弹塑性层间位移的关系求出了薄弱层的弹塑性位移。对一高层钢筋混凝土框架-筒体结构在7度罕遇地震下的抗震性能进行了评估,通过与非线性动力时程分析的对比,证明了方法的可行性。     

Residual displacement ratios for assessment of existing structures

Results of an analytical study aimed at evaluating residual displacement ratios, C_r, which allow the estimation of residual displacement demands from maximum elastic displacement demands is presented. Residual displacement ratios were computed using response time‐history analyses of single‐degree‐of‐freedom systems having 6 levels of relative lateral strength when subjected to an ensemble of 240 earthquake ground motions recorded in stations placed on firm sites. The results were statistically organized to evaluate the influence of the following parameters: period of vibration, level of relative lateral strength, site conditions, earthquake magnitude, and distance to the source. In addition, the influence of post‐yield stiffness ratio in bilinear systems and of the unloading stiffness in stiffness‐degrading systems was also investigated. A special emphasis is given to the uncertainty of these ratios. From this study, it is concluded that mean residual displacement ratios are more sensitive to changes in local site conditions, earthquake magnitude, distance to the source range and hysteretic behaviour than mean inelastic displacement ratios. In particular, residual displacement ratios exhibit large levels of record‐to‐record variability and, therefore, this dispersion should be taken into account when estimating residual displacements. A simplified expression is presented to estimate mean residual displacements ratios for elastoplastic systems during the evaluation of existing structures built on firm soil sites. Copyright © 2005 John Wiley & Sons, Ltd.     

A fuzzy–random analysis model for seismic performance of framed structures incorporating structural and non‐structural damage

Past earthquake experiences indicate that most buildings designed in accordance with modern seismic design codes could survive moderate‐to‐strong earthquakes; however, the financial loss due to repairing cost and the subsequent business interruption can be unacceptable. Designing building structures to meet desired performance targets has become a clear direction in future seismic design practice. As a matter of fact, the performance of buildings is affected by structural as well as non‐structural components, and involves numerous uncertainties. Therefore, appropriate probabilistic approach taking into account structural and non‐structural damages is required. This paper presents a fuzzy–random model for the performance reliability analysis of RC framed structures considering both structural and non‐structural damages. The limit state for each performance level is defined as an interval of inter‐storey drift ratios concerning, respectively, the non‐structural and structural damage with a membership function, while the relative importance of the two aspects is reflected through the use of an appropriate cost function. To illustrate the methodology, herein the non‐structural damage is represented by infill masonry walls. The probabilistic drift limits for RC components and masonry walls from the associated studies are employed to facilitate the demonstration of the proposed model in an example case study. The results are compared with those obtained using classical reliability model based on single‐threshold performance definition. The proposed model provides a good basis for incorporating different aspects into the performance assessment of a building system. Copyright © 2005 John Wiley & Sons, Ltd.     

Applicability of pushover methods for the seismic analysis of single‐column bent viaducts

An overview of the applicability of a typical single‐mode pushover method (the N2 method) and two typical multi‐mode pushover methods (the modal pushover analysis (MPA) and incremental response spectrum analysis (IRSA) methods) for the analysis of single column bent viaducts in the transverse direction is presented. Previous research, which was limited to relatively short viaducts supported by few columns, has been extended to longer viaducts with more bents. The single‐mode N2 method is accurate enough for bridges where the effective modal mass of the fundamental mode is at least 80% of the total mass. The applicability of this method depends on (a) the ratio of the stiffness of the superstructure to that of the bents and (b) the strength of the bents. In short bridges with few columns, the accuracy of the N2 method increases as the seismic intensity increases, whereas in long viaducts (e.g. viaducts with lengths greater than 500 m) the method is in general less effective. In the case of the analyzed moderately irregular long viaducts, which are common in construction design practice, the MPA method performed well. For the analysis of bridges where the modes change significantly, depending on the seismic intensity, the IRSA method is in principle more appropriate, unless a viaduct is torsionally sensitive. In such cases, all simplified methods should be used with care. Copyright © 2008 John Wiley & Sons, Ltd.     

Rigid‐plastic models for the seismic design and assessment of steel framed structures

This paper demonstrates the applicability of response history analysis based on rigid‐plastic models for the seismic assessment and design of steel buildings. The rigid‐plastic force–deformation relationship as applied in steel moment‐resisting frames (MRF) is re‐examined and new rigid‐plastic models are developed for concentrically‐braced frames and dual structural systems consisting of MRF coupled with braced systems. This paper demonstrates that such rigid‐plastic models are able to predict global seismic demands with reasonable accuracy. It is also shown that, the direct relationship that exists between peak displacement and the plastic capacity of rigid‐plastic oscillators can be used to define the level of seismic demand for a given performance target. Copyright© 2009 John Wiley & Sons, Ltd.