Higher modes in simplified inelastic seismic analysis of single column bent viaducts

The influence of the higher modes and their consideration in the pushover analysis of reinforced concrete single column bent viaducts with different degree of irregularity is discussed. Typical multimode pushover‐based methods (modal pushover analysis, modal adaptive non‐linear static procedure and incremental response spectrum analysis) are addressed and compared with a single mode procedure (N2) and inelastic time history analysis. If in the transverse direction the substructure of the viaduct is flexible in comparison with the superstructure, the influence of higher modes is small (the structure is regular) and single mode procedure works well. This typically occurs when the columns are high or considerably damaged. Conversely, for the analysis of irregular structures having short and slightly damaged columns, the multimode methods are needed. In most cases, all the analysed multimode pushover‐based methods have given the results comparable with time history analysis, with the exception of cases where torsional sensitivity is varying during the response. All the methods have limitations (discussed in detail in the paper), which should be fully recognized by the user. Copyright © 2005 John Wiley & Sons, Ltd.     

A comparison of single‐run pushover analysis techniques for seismic assessment of bridges

Traditional pushover analysis is performed subjecting the structure to monotonically increasing lateral forces with invariant distribution until a target displacement is reached; both the force distribution and target displacement are hence based on the assumption that the response is controlled by a fundamental mode, that remains unchanged throughout. However, such invariant force distributions cannot account for the redistribution of inertia forces caused by structural yielding and the associated changes in the vibration properties, including the increase of higher‐mode participation. In order to overcome such drawbacks, but still keep the simplicity of using single‐run pushover analysis, as opposed to multiple‐analyses schemes, adaptive pushover techniques have recently been proposed. In order to investigate the effectiveness of such new pushover schemes in assessing bridges subjected to seismic action, so far object of only limited scrutiny, an analytical parametric study, conducted on a suite of continuous multi‐span bridges, is carried out. The study seems to show that, with respect to conventional pushover methods, these novel single‐run approaches can lead to the attainment of improved predictions. Copyright © 2007 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.     

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.     

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..     

Extension of modal pushover analysis to seismic assessment of bridges

Nonlinear static (pushover) analysis has become a popular tool during the last decade for the seismic assessment of buildings. Nevertheless, its main advantage of lower computational cost compared to nonlinear dynamic time‐history analysis (THA) is counter‐balanced by its inherent restriction to structures wherein the fundamental mode dominates the response. Extension of the pushover approach to consider higher modes effects has attracted attention, but such work has hitherto focused mainly on buildings, while corresponding work on bridges has been very limited. Hence, the aim of this study is to adapt the modal pushover analysis procedure for the assessment of bridges, and investigate its applicability in the case of an existing, long and curved, bridge, designed according to current seismic codes; this bridge is assessed using three nonlinear static analysis methods, as well as THA. Comparative evaluation of the calculated response of the bridge illustrates the applicability and potential of the modal pushover method for bridges, and quantifies its relative accuracy compared to that obtained through other inelastic methods. Copyright © 2006 John Wiley & Sons, Ltd.     

Lateral load pattern in pushover analysis

The seismic capacity curves of three types of buildings including frame, frame-shear wall and shear wall obtained by pushover analysis under different lateral load patterns are compared with those from nonlinear time history analysis. Based on the numerical results obtained a two-phase load pattern; an inverted triangle (first mode) load pattern until the base shear force reachesβ times its maximum value, V_max, followed by a (x/H)^α form, hereβ and α being some coefficients depending on the type of the structures considered, is proposed in the paper, which can provide excellent approximation of the seismic capacity curve for low-to-mid-rise shear type buildings. Furthermore, it is shown both the two-phase load pattern proposed and the invariant uniform pattern can be used for low-to-mid-rise shear-bending type and low-rise bending type of buildings. No suitable load patterns have been found for high-rise buildings.     

框架剪力墙结构模态静力非线性抗震分析方法研究

本文在模态pushover分析方法基础上推导建立了模态静力非线性分析方法,对一栋10层框架剪力墙结构进行了静力非线性分析,提出了目标位移求解的等效单自由度体系弹塑性时程分析迭代法,计算结果与相应时程分析结果进行了比较,表明两者吻合较好,验证了本文计算方法的有效性。另外,对同一结构,计算分析了在不同水平荷载模式下的静力非线性分析结果,比较不同荷载模式对计算结果的影响,为静力非线性分析方法的推广使用提供参考。     

芦山7.0级地震单层砖柱排架厂房震害特征及抗震分析

单层砖柱排架厂房是我国中小企业生产用房的主要形式,目前此类结构仍广泛存在于经济欠发达的地区。历次地震震害资料表明,单层砖柱排架厂房在地震中比较容易损坏。本文通过对芦山地震中单层砖柱排架厂房的震害现场调查,总结了单层砖柱排架厂房的震害特征并分析其破坏原因;统计了几次地震中单层砖柱排架厂房的震害资料,给出了修正的未设防单层砖柱排架厂房地震易损性矩阵;最后,采用了逐步回归法,柱顶位移角法及模糊震害指数法分别对单层砖柱排架厂房进行震害预测,并将各种方法的震害预测结果与实际震害情况进行了对比分析。本文研究对认识该类结构的易损性、震害机理和抗震薄弱部位,指导抗震加固有着重要意义。     

Generalized force vectors for multi‐mode pushover analysis

A generalized pushover analysis (GPA) procedure is developed for estimating the inelastic seismic response of structures under earthquake ground excitations. The procedure comprises applying different generalized force vectors separately to the structure in an incremental form with increasing amplitude until a prescribed seismic demand is attained for each generalized force vector. A generalized force vector is expressed as a combination of modal forces, and simulates the instantaneous force distribution acting on the system when a given response parameter reaches its maximum value during dynamic response to a seismic excitation. While any response parameter can be selected arbitrarily, generalized force vectors in the presented study are derived for maximum interstory drift parameters. The maximum value of any other response parameter is then obtained from the envelope of GPAs results. Each nonlinear static analysis under a generalized force vector activates the entire multi‐degree of freedom effects simultaneously. Accordingly, inelastic actions develop in members with the contribution of all ‘instantaneous modes’ in the nonlinear response range. Target seismic demands for interstory drifts at the selected stories are calculated from the associated drift expressions. The implementation of the proposed GPA is simpler compared with nonlinear response history analysis, whereas it is less demanding in computational effort when compared with several multi‐mode adaptive nonlinear static procedures. Moreover, it does not suffer from the statistical combination of inelastic modal responses obtained separately. The results obtained from building frames have demonstrated that GPA is successful in estimating maximum member deformations and member forces with reference to the response history analysis. When the response is linear elastic, GPA and response spectrum analysis produce identical results. Copyright © 2010 John Wiley & Sons, Ltd.     

Modified consecutive modal pushover procedure for seismic investigation of one-way asymmetric-plan tall buildings

The effects of higher modes and torsion have a significant impact on the seismic responses of asymmetric-plan tall buildings.A consecutive modal pushover(CMP) procedure is one of the pushover methods that have been developed to consider these effects.The aim of this paper is to modify the(CMP) analysis procedure to estimate the seismic demands of one-way asymmetric-plan tall buildings with dual systems.An analysis of 10-,15-and 20-story asymmetric-plan buildings is carried out,and the results from the modified consecutive modal pushover(MCMP) procedure are compared with those obtained from the modal pushover analysis(MPA) procedure and the nonlinear time history analysis(NLTHA).The MCMP estimates of the seismic demands of one-way asymmetric-plan buildings demonstrate a reasonable accuracy,compared to the results obtained from the NLTHA.Furthermore,the accuracy of the MCMP procedure in the prediction of plastic hinge rotations is better than the MPA procedure.The new pushover procedure is also more accurate than the FEMA load distribution and the MPA procedure.     

Further development of a multimodal pushover analysis procedure for seismic assessment of bridges

An improvement is first suggested to the modal pushover analysis (MPA) procedure for bridges initially proposed by the writers (Earthquake Engng Struct. Dyn. 2006; 35 (11):1269–1293), the key idea being that the deformed shape of the structure responding inelastically to the considered earthquake level is used in lieu of the elastic mode shape. The proposed MPA procedure is then verified by applying it to two actual bridges. The first structure is the Krystallopigi bridge, a 638 m‐long multi‐span bridge, with significant curvature in plan, unequal pier heights, and different types of pier‐to‐deck connections. The second structure is a 100 m‐long three‐span overpass bridge, typical in modern motorway construction in Europe, which, although ostensibly a regular structure, is found to exhibit a rather unsymmetric response in the transverse direction, mainly due to torsional irregularity. The bridges are assessed using response spectrum, ‘standard’ pushover (SPA), and MPA, and finally using non‐linear response history analysis (NL‐RHA) for a number of spectrum‐compatible motions. The MPA provided a good estimate of the maximum inelastic deck displacement for several earthquake intensities. The SPA on the other hand could not predict well the inelastic deck displacements of bridges wherever the contribution of the first mode to the response of the bridge was relatively low. Copyright © 2009 John Wiley & Sons, Ltd.     

基于推覆分析的RC框架地震倒塌易损性预测

基于倒塌率的结构倒塌易损性分析是目前评价结构抗倒塌能力最合理的方法.但是,目前基于增量动力分析(IDA)的倒塌率分析方法,工作量和实施难度大,很难直接用于工程设计,因此有必要研究便于工程应用的新方法.本文基于18个典型多层RC框架结构的IDA倒塌率分析和静力推覆分析,发现RC框架在大震下的倒塌率及抗倒塌安全储备(CMR)与静力推覆得到的结构位移安全储备之间存在较好的相关关系.依据此关系,建议了保证大震倒塌率的推覆位移安全储备,并通过9个RC框架结构算例进行了验证.本文方法简单易行,可供规则多层RC框架结构抗倒塌设计参考.     

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.     

Pushover分析方法的发展及其在桥梁结构中的应用

非线性静力分析方法（Pushover分析方法）可以较好地检验结构的变形能力,找到结构的薄弱环节,控制强烈地震作用下结构破坏程度,对工程设计有很强的指导意义。但目前Pushover分析方法的种类很多,各自有着不同的优缺点和适用范围,针对桥梁结构,阐述静力非线性分析方法（Pushover）的原理及其研究发展概况,评述了各种Pushover方法的优缺点,并分析了Pushover方法用于桥梁结构的基本原理和评价方法,指出Pushover方法用于桥梁结构存在的问题。     

Nonlinear analysis of out‐of‐plane masonry façades: full dynamic versus pushover methods by rigid body and spring model

The paper proposes a systematic comparison between two methods of analysis that are well established in the field of earthquake engineering: nonlinear dynamic analysis and nonlinear static procedure (NSP), applied to the out‐of‐plane seismic response of two masonry façades representative of many ancient Italian churches. The comparison is based on extensive numerical analyses, which focus on the flexural and torsional mechanisms, while the in‐plane damage mechanisms and the possible detachment between the façade and the lateral walls because of a poor connection have been presently disregarded. The computations, both in the static and in the dynamic field, are based on a rigid body and spring model specifically implemented for this issue, computationally efficient and equipped with a realistic model of damage and hysteresis at the mesoscale. An innovative aspect of this study is the heuristic modelling of three‐wythe masonry, to include some typical texture effects on the macroscale nonlinear response. For each façade, two different masonry textures were considered, performing extensive dynamic analyses that offered a detailed overview about the performance under earthquakes of different intensities. In parallel, NSP and the classical N2‐based seismic assessment were applied. A critical discussion and comparison of the results of the two methods is presented to rationally appraise limits and opportunities. In particular, flexural and twisting out‐of‐plane mechanisms were clearly appraised in the dynamic field, whereas NSPs were not always able to describe the collapse, because they missed the partial failures determined by higher vibration modes, as could be expected. Copyright © 2012 John Wiley & Sons, Ltd.     

Direct displacement‐based seismic assessment procedure for multi‐span reinforced concrete bridges with single‐column piers

In Italy, as in other high seismic risk countries, many bridges, nowadays deemed ‘strategic’ for civil protection interventions after an earthquake, were built without antiseismic criteria, and therefore their seismic assessment is mandatory. Accordingly, the development of a seismic assessment procedure that gives reliable results and, at the same time, is sufficiently simple to be applied on a large population of bridges in a short time is very useful. In this paper, a displacement‐based procedure for the assessment of multi‐span RC bridges, satisfying these requirements and called direct displacement‐based assessment (DDBA), is proposed. Based on the direct displacement‐based design previously developed by Priestley et al., DDBA idealizes the multi DOF bridge structure as an equivalent SDOF system and hence defines a safety factor in terms of displacement. DDBA was applied to hypothetical bridge configurations. The same structures were analyzed also using standard force‐based approach. The reliability of the two methods was checked performing IDA with response spectrum compatible accelerograms. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic response predictions of multi‐span steel bridges through pushover analysis

In the new trend of seismic design methodology, the static pushover analysis is recommended for simple or regular structures whilst the time‐history analysis is recommended for complex structures. To this end, the applicable range of the pushover analysis has to be clarified. This study aims at investigating the applicability of pushover analysis to multi‐span continuous bridge systems with thin‐walled steel piers. The focus is concentrated on the response demand predictions in longitudinal or transverse directions. The pushover analysis procedure for such structures is firstly summarized and then parametric studies are carried out on bridges with different types of superstructure‐pier bearing connections. The considered parameters, such as piers' stiffness distribution and pier–0.5ptdeck stiffness ratio, are varied to cover both regular and irregular structures. Finally, the relation of the applicability of pushover analysis to different structural formats is demonstrated and a criterion based on the higher modal contribution is proposed to quantitatively specify the applicable range. Copyright © 2003 John Wiley & Sons, Ltd.     

Evaluation of the structural response under seismic actions using non‐linear static methods

The paper investigates the degree of accuracy achievable when some non‐linear static procedures based on a pushover analysis are used to evaluate the seismic performance. In order to assess the significance of different sources of errors, three types of structural systems are analysed: (i) single‐degree‐of‐freedom (SDOF) systems with different hysteretic behaviour; (ii) shear‐type multi‐degree‐of‐freedom (MDOF) systems with elastic–perfect plastic (EPP) shear force–interstorey drift relationships; (iii) a steel moment‐resisting frame with rigid joints and EPP moment–curvature relationship. In SDOF systems, the source of approximation comes only from the calibration of the demand spectrum, while in MDOF systems some further errors are introduced by the schematization with an equivalent SDOF system. The non‐linear static procedures are compared with rigorous time‐history analyses carried out by considering ten generated earthquake ground motions compatible with the Eurocode 8 elastic spectra. It was found that SDOF systems with longer periods satisfy the equal displacement approximation regardless of the hysteretic model, while hysteresis loops with smaller energy dissipated indicate lower response for shorter periods. This is the opposite of what predicted by the ATC‐40 capacity spectrum method, which underestimates and overestimates, respectively, the actual response of low‐ and high‐ductility systems. Conversely, the inelastic spectrum method proposed by Vidic, Fajfar and Fischinger leads to the most accurate results for all types of structural systems. The analyses carried out on EPP shear‐type frames point out a large concentration of the ductility demand on some storeys. However, such a concentration markedly reduces when some hardening is accounted for. Copyright © 2006 John Wiley & Sons, Ltd.     

结构Pushover分析的侧向力分布及高阶振型影响

Pushover分析方法是逐渐得到广泛应用的一种评估结构抗震性能的简化方法,已被引入我国新的建筑结构抗震设计规范。侧向力分布的选取是结构Pushover分析中的一个关键问题,尤其高阶振型影响显著时其选取直接影响Pushover分析的结果。本文通过拟合规范反应谱,挑选了适用Ⅱ类场地的4条地震动记录和4条人工波,对比了典型地震动下非线性时程分析和采用5种不同侧向力分布的Pushover分析的5层、10层和15层钢筋混凝土结构在不同地震动强度时的反应。通过结构振型参与系数量化了各个结构的高阶振型的影响。研究发现,随着结构层数的增加和地震动强度的增加高阶振型的影响变大,侧向力的选取变得十分重要。本文对在高阶振型影响下钢筋混凝土框架结构的Pushover分析中侧向力的选取提出了建议。