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.     

A pushover procedure for seismic assessment of buildings with bi-axial eccentricity under bi-directional seismic excitation

A new modal pushover procedure is proposed for seismic assessment of asymmetric-plan buildings under bi-directional ground motions. Although the proposed procedure is a multi-mode procedure and the effects of the higher and torsional modes are considered, the simplicity of the pushover procedure is kept and the method requires only a single-run pushover analysis for each direction of excitation. The effects of the frequency content of a specific ground motion and the interaction between modes at each direction are all considered in the single-run pushover analysis. For each direction, the load pattern is derived from the combined modal story shear and torque profiles. The pushover analysis is conducted independently for each direction of motion (x and y), and then the responses due to excitation in each direction are combined using SRSS (Square Roots of Sum of Squares) combination rule. Accuracy of the proposed procedure is evaluated through two low- and medium-rise buildings with 10% two-way eccentricity under different pairs of ground motions. The results show promising accuracy for the proposed method in predicting the peak seismic responses of the sample buildings.     

Assessing the seismic response of existing RC buildings using the extended N2 method

Extensive studies have confirmed the good performance of the N2 method, recommended by Eurocode8, when performing pushover analyses in regular structures. However, this procedure shows lack of accuracy in predicting the torsional motion of plan-asymmetric buildings. In order to overcome this problem, Peter Fajfar and his team have proposed an extension of the method based on a combination of a pushover analysis and of an elastic response spectrum analysis. Since definitive answers about this topic have not yet been reached, this paper intends to proceed the study applying the extended N2 method to real existing RC buildings. Three real plan-asymmetric buildings with three, five and eight storeys were assessed. The results obtained with the extended N2 method were compared with the ones evaluated by means of the original N2 and with the nonlinear dynamic analysis through the use of semi-artificial ground motions. The analyses were performed for different seismic intensities in order to evaluate the torsional response of the building through different stages of structural inelasticity. The results obtained show that the extended N2 method generally reproduces in a very good fashion the real torsional behavior of the analyzed buildings. The conclusions herein outlined, added to the ones already published by the aforementioned authors, seem to confirm that the extended N2 method can be introduced in the next version of Eurocode8 as a nonlinear static procedure capable of accurately predicting the torsional response of plan-asymmetric buildings.     

Predicting torsion‐induced lateral displacements for pushover analysis: Influence of torsional system characteristics

The increasing popularity of simplified nonlinear methods in seismic design has recently led to many proposals for procedures aimed at extending pushover analysis to plan asymmetric structures. In terms of practical applications, one particularly promising approach is based on combining pushover analysis of a 3D structural model with the results of linear (modal) dynamic analysis. The effectiveness of such procedure, however, is contingent on one fundamental requirement: the elastic prediction of the envelope of lateral displacements must be conservative with respect to the actual inelastic one. This paper aims at verifying the above assumption through an extensive parametric analysis conducted with simplified single‐storey models. The main structural parameters influencing torsional response in the elastic and inelastic range of behaviour are varied, while devoting special attention to the system stiffness eccentricity and radius. The analysis clarifies the main features of inelastic torsional response of different types of building structures; in this manner, it is found that the above‐mentioned method is generally suitable for structures characterized by moderate to large torsional stiffness, whereas it cannot be recommended for extremely torsionally stiff structures, as their inelastic torsional response almost always exceeds the elastic one. Copyright © 2010 John Wiley & Sons, Ltd.     

Generalized force vectors for multi‐mode pushover analysis of torsionally coupled systems

A generalized multi‐mode pushover analysis procedure was developed for estimating the maximum inelastic seismic response of symmetrical plan structures under earthquake ground excitations. Pushover analyses are conducted with story‐specific generalized force vectors in this procedure, with contributions from all effective modes. Generalized pushover analysis procedure is extended to three‐dimensional torsionally coupled systems in the presented study. Generalized force distributions are expressed as the combination of modal forces to simulate the instantaneous force distribution acting on the system when the interstory drift at a story reaches its maximum value during seismic response. Modal contributions to the generalized force vectors are calculated by a modal scaling rule, which is based on the complete quadratic combination. Generalized forces are applied to the mass centers of each story incrementally for producing nonlinear static response. Maximum response quantities are obtained when the individual frames attain their own target interstory drift values in each story. The developed procedure is tested on an eight‐story frame under 15 ground motions, and assessed by comparing the results obtained from nonlinear time history analysis. The method is successful in predicting the torsionally coupled inelastic response of frames responding to large interstory drift demands. Copyright © 2014 John Wiley & Sons, Ltd.     

Enhanced nonlinear static analysis with the drift pushover procedure for tall buildings

In this study a new method for nonlinear static analysis based on the relative displacements of stories is proposed that is able to be implemented in a single stage analysis and considers the effects of an arbitrary number of higher modes. The method is called the extended drift pushover analysis procedure (EDPA). To define the lateral load pattern, values of the relative displacements of stories are calculated using the elastic modal analysis and the modal combination factors introduced. For determining the combination factors, six different approaches are examined. Buildings evaluated in this study consist of four special steel moment-resisting frames with 10–30 stories. Responses including relative displacements of stories, story shear forces and rotation of plastic hinges in each story are calculated using the proposed approaches in addition to modal pushover analysis and nonlinear dynamic time history analyses. The nonlinear dynamic analysis is implemented using ten consistent earthquake records that have been scaled with regard to ASCE7-10. Distribution of response errors of story shears and plastic hinge rotations show that a major part of error corresponds to the second half of the buildings studied. Thus, the mentioned responses are corrected systematically. The final results of this study show that implementing the EDPA procedure using the third approach of this research is able to effectively overcome the limitations of both the traditional and the modal pushover analyses methods and predict the seismic demands of tall buildings with good accuracy.     

An improved upper-bound pushover procedure for seismic assessment of high-rise moment resisting steel frames

In recent years, nonlinear static procedures (NSPs) have gained considerable popularity as an efficient tool in the performance based seismic design practice. This was backed by extensive corroboration studies that have demonstrated its good accuracy in estimating the seismic response of regular structures. Despite the numerous improvements of the original versions of NSPs, their use to assess the seismic response of irregular structures and high-rise buildings is still challenging; they are not able to predict with sufficient accuracy all the complexities associated to the seismic response of this type of structures. Thus, an improved upper-bound (IUB) pushover procedure for seismic assessment of plane frames is presented in this paper, aiming to enhance the accuracy of existing methods in predicting the seismic behaviour of high-rise buildings. The novelty of this proposal is based on the adjustment of the pattern of the lateral load of the upper-bound pushover method applied to tall structures. The accuracy of the procedure is tested using nine, twelve, fifteen and twenty storeys steel buildings. The results of the (IUB) are compared to those of the capacity spectrum method, the modal pushover analysis, the upper bound pushover analysis, the modified upper bound pushover analysis and the non-linear time history analysis (NTHA). In most cases, the proposed procedure shows better results and closer to those obtained by NTHA.     

循环往复加载的地下结构Pushover分析方法及其在地震损伤分析中的应用

考虑到地震作用下地下结构往往受到双向往复荷载作用,本文提出了循环往复加载的地下结构Pushover分析方法.介绍了该方法的实施步骤、基本功能与特点.该方法考虑了地震作用下地下结构双向受力的特点,利用多点位移控制的推覆分析算法进行地震作用下正向加载-卸载-反向再加载的全过程分析.该方法将一次循环加载过程近似看作一次地震作用过程,提出了基于循环往复加载Pushover分析的损伤模型,避免了对土-结构整体模型进行复杂的动力相互作用分析;通过一次循环往复加载的Pushover分析,根据结构构件刚度的改变对结构损伤进行有效评估.结合实际工程进行算例分析初步验证了循环往复加载Pushover分析及地震损伤模型的有效性.     

The applicability of the N2 method to the estimation of torsional effects in asymmetric base‐isolated buildings

The paper deals with the applicability of the extended N2 method to base‐isolated plan‐asymmetric building structures. The results obtained by the usual pushover analysis of a 3D structural model are further combined with the aid of linear dynamic (spectral) analysis to account for the dynamic effects caused by structural asymmetry. In the paper, the method has been applied to the seismic analysis of a mass‐eccentric four‐storeyed RC frame building isolated with lead rubber bearings. Three different positions of the center of isolation system (CI) with respect to the center of mass (CM) and the center of stiffness of the superstructure (CS) were considered. The response was analyzed for three different eccentricities, three different torsional to lateral frequency ratios of the superstructure, and two ground motion intensities. The stiffness of the isolators was selected for three different protection levels, which resulted in elastic as well as moderately to excessively damaged superstructure performance levels. The results are presented in terms of the top, base and relative displacements, as well as the stiff/flexible side amplification factors. A more detailed insight into the nonlinear behavior of the superstructure is given in a form of ductility factors for the flexible and stiff side frames. The results of the extended N2 method for selected lateral load distributions are compared with the average results of nonlinear dynamic analyses. It was concluded that the extended N2 method could, with certain limitations, provide a reasonable prediction of the torsional influences in minor to moderately asymmetric base‐isolated structures. Copyright © 2010 John Wiley & Sons, Ltd.     

Extended consecutive modal pushover procedure for estimating seismic responses of one-way asymmetric plan tall buildings considering soil-structure interaction

Performance based design becomes an effective method for estimating seismic demands of buildings. In asymmetric plan tall building the effects of higher modes and torsion are crucial. The consecutive modal pushover (CMP) procedure is one of the procedures that consider these effects. Also in previous studies the influence of soil-structure interaction (SSI) in pushover analysis is ignored. In this paper the CMP procedure is modified for one-way asymmetric plan mid and high-rise buildings considering SSI. The extended CMP (ECMP) procedure is proposed in order to overcome some limitations of the CMP procedure. In this regard, 10, 15 and 20 story buildings with asymmetric plan are studied considering SSI assuming three different soil conditions. Using nonlinear response history analysis under a set of bidirectional ground motion; the exact responses of these buildings are calculated. Then the ECMP procedure is evaluated by comparing the results of this procedure with nonlinear time history results as an exact solution as well as the modal pushover analysis procedure and FEMA 356 load patterns. The results demonstrate the accuracy of the ECMP procedure.     

Prediction of the largest peak nonlinear seismic response of asymmetric buildings under bi-directional excitation using pushover analyses

A simplified procedure is proposed to predict the largest peak seismic response of an asymmetric building to horizontal bi-directional ground motion, acting at an arbitrary angle of incidence. The main characteristics of the proposed procedure is as follows. (1) The properties of two independent equivalent single-degree-of-freedom models are determined according to the principal direction of the first modal response in each nonlinear stage, rather than according to the fixed axis based on the mode shape in the elastic stage; the principal direction of the first modal response in each nonlinear stage is determined based on pushover analysis results. (2) The bi-directional horizontal seismic input is simulated as identical spectra of the two horizontal components, and the contribution of each modal response is directly estimated based on the unidirectional response in the principal direction of each. (3) The drift demand at each frame is determined based on four pushover analyses considering the combination of bi-directional excitations. In the numerical example, nonlinear time-history analyses of six four-story torsionally stiff (TS) asymmetric buildings are carried out considering various directions of seismic inputs, and these results are compared with the predicted results. The results show that the proposed procedure satisfactorily predicts the largest peak response displacement at the flexible-side frame of a TS asymmetric building.     

Effects of torsion on the behavior of peripheral steel‐braced frame systems

In this study, the torsional response of buildings with peripheral steel‐braced frame lateral systems is evaluated. A three‐dimensional model of a three story braced frame with various levels of eccentricity is created and the effects of torsion on the seismic response is assessed for four hazard levels. The response history analysis results indicate that, unlike frame structures, the torsional amplifications in the inelastic systems exceed those of corresponding elastic systems and tend to increase with an increase in the level of inelasticity. The ability of two simplified procedures, elastic response spectrum analysis and pushover analysis, to capture the torsional amplifications in steel‐braced frames is evaluated. Copyright © 2010 John Wiley & Sons, Ltd.     

A new simplified approach for assessing nonlinear seismic response of plan-asymmetric structures considering soil-structure interaction

An innovative approximate method is presented to consider the plan asymmetry, nonlinear structural behaviour and soil-structure interaction (SSI) effects simultaneously. The proposed method so-called Flexible base 2DMPA (F2MPA) is an extension of 2 degrees of freedom modal pushover analysis (2DMPA) approach to consider foundation flexibility in seismic response analysis of plan asymmetric structures which itself were developed based on Uncoupled Modal Response History Analysis method for inelastic fixed-base asymmetric structures. In F2MPA for each mode shape using 2DMPA procedure, the elastic and inelastic properties of 2DOF modal systems corresponding to the fixed-base structure are initially derived. Then in each time step, displacements and inelastic restoring forces of the superstructure are computed from modal equations of the flexibly-supported structure. In each time step, the nonlinear secant stiffness matrix corresponding to the n-th MDOF modal equations of soil-structure system is updated using the corresponding modal 2DOF system of fixed-base structure. To update the transformed modal stiffness matrix of the SSI system, this matrix is partitioned and it is assumed that the non-linear variation of the superstructure can be estimated from the variation of modal stiffness matrix of the fixed-base structure. Accuracy of the proposed method was verified on an 8-story asymmetric-plan building under different seismic excitations. The results obtained from F2MPA method were compared with those obtained by nonlinear response history analysis of the asymmetric soil-structure system as a reference response. It was shown that the proposed approach could predict the results of the nonlinear time history analysis with a good accuracy. The main advantage of F2MPA is that this method is much less time-consuming and useful for the practical aims such as massive analysis of a nonlinear structure under different records with multiple intensity levels.     

基于中美抗震设计规范的双向水平地震效应组合方法的有效性评估

在地震来临时,一般假设建筑结构同时受到两个正交水平方向分量与一个竖向分量的地震动作用。双向水平地震效应组合方法用于估计两个正交水平分量地震动同时作用时结构的内力效应。本文主要对我国与美国抗震设计规范中规定使用的平方和开平方根（SRSS）方法与百分比组合方法的有效性进行了评估。首先,对比了我国与美国规范在考虑双向水平地震效应时的适用情况及相关规定上的异同。以一4层中心支撑-框架结构为工程案例,考虑两国规范在适用情况上的规定,设置了三个结构布置方案。对三个结构布置方案建立有限元模型,选取22组地震动,开展了动力时程分析。提出了针对SRSS方法与百分比组合方法的评估指标,基于时程分析结果,发展了双向水平地震效应组合的概率性评估方法。评估结果表明:SRSS方法与百分比组合方法用于平面扭转不规则结构的设计较为保守。在简化组合规则的适用条件上,美国规范对平面扭转不规则结构不进行考虑有一定的合理性。建议我国规范对中心支撑-框架结构中含双向受压柱的设计要求考虑双向水平地震效应组合。     

Simplified seismic analysis of asymmetric building systems

The paper reviews the uncoupled modal response history analysis (UMRHA) and modal pushover analysis (MPA) procedure in the analysis of asymmetric structures. From the pushover curves in ADRS format, showing the relationships of base shear versus roof translation and base torque versus roof rotation, a bifurcating characteristic of the pushover curves of an asymmetric structure is observed. A two‐degree‐of‐freedom (2DOF) modal stick is constructed using lump mass eccentrically placed at the end of beam which is connected with the column by a rotational spring. By converting the equation of motion of a whole structure into 2DOF modal equations, all of the elastic properties in the 2DOF modal sticks can be determined accurately. A mathematical proof is carried out to demonstrate that the 2DOF modal stick is consistent with the single‐degree‐of‐freedom (SDOF) modal stick at elastic state. The bifurcating characteristic of modal pushover curves and the interaction of modal translation and rotation can be considered rationally by this 2DOF modal stick. In order to verify the effectiveness of this proposed 2DOF modal stick, a two‐storey asymmetric building structure was analysed by the UMRHA procedure incorporating this novel 2DOF modal sticks (2DMPA) and conventional SDOF modal sticks (SDMPA), respectively. The analytical results are compared with those obtained by nonlinear response history analysis (RHA). It is illustrated that the accuracy of the rotational response histories obtained by 2DMPA is much better than those obtained by SDMPA. Consequently, the estimations of translational response histories on flexible side (FS) and stiff side (SS) of the building structure are also improved. Copyright © 2006 John Wiley & Sons, Ltd.     

Comparative assessment of nonlinear static and dynamic methods for analysing building response under sequential earthquake and tsunami

This paper presents a comprehensive comparison of different dynamic and static approaches for assessing building performance under sequential earthquakes and tsunami. A 10-storey reinforced concrete seismically designed Japanese vertical evacuation structure is adopted as a case study for the investigation. The case study building is first assessed under sequential earthquake and tsunami nonlinear response history analyses: the first time this is done in the literature. The resulting engineering demand parameters are then compared with those obtained when the analysis procedure is systematically simplified by substituting different static approaches for the nonlinear response history analyses in both the earthquake and tsunami loading phases. Different unloading approaches are also tested for the cases when an earthquake pushover is adopted. The results show that an earthquake nonlinear response history analysis, followed by a transient free vibration and a tsunami variable depth pushover, provides the best alternative to full dynamic analyses in terms of accuracy and computational efficiency. This structural analysis combination is recommended and has the advantage that it does not require the tsunami inundation time history to be known in advance. The proposed double pushover approach is instead deemed only suitable for the collapse assessment of regular low to mid-rise buildings and for the development of collapse fragility functions. An important observation made is that sustained earthquake damage seems not to affect the tsunami resistance of the case study building when the fully dynamic analysis is carried out for the sequential loading. This observation will be the subject of future work.     

The extended consecutive modal pushover procedure for estimating the seismic demands of two-way unsymmetric-plan tall buildings under influence of two horizontal components of ground motions

This paper aims to extend the consecutive modal pushover (CMP) procedure for estimating the seismic demands of two-way unsymmetric-plan tall buildings subjected to bi-directional seismic ground motions taking the effects of higher modes and torsion into account. Multi-stage and single-stage pushover analyses are carried out in both X and Y directions. Inelastic seismic responses obtained by multi-stage and single-stage pushover analyses for X and Y directions are combined using the SRSS combination scheme. The final seismic responses are determined by enveloping the combined results of multi-stage and single-stage pushover analyses. To evaluate the accuracy of the proposed procedure, it is applied to two-way unsymmetric-plan tall buildings which include torsionally stiff and torsionally flexible systems. The results derived from the CMP procedure are compared with those from nonlinear response history analysis (NL-RHA), as a benchmark solution. Moreover, the advantages of the proposed procedure are demonstrated by comparing the results derived from the CMP to those from pushover analysis with uniform and fundamental effective mode distributions. The proposed procedure is able to accurately predict amplification or de-amplification of the seismic displacements at the flexible and stiff edges of the two-way unsymmetric-plan tall buildings by considering the effects of higher modes and torsion. The extended CMP procedure can accurately estimate the peak inelastic responses, such as displacements and storey drifts. The CMP procedure features a higher potential in estimating plastic hinge rotations at both flexible and stiff sides of unsymmetric-plan tall buildings under bi-directional seismic excitation when compared to the uniform and fundamental effective mode force distributions.     

An improved displacement-based adaptive pushover procedure based on factor modal combination rule

An accurate estimation of the applied load pattern is an essential component in each pushover procedure. Recently, a number of adaptive pushover methods have been proposed in which the effects of the higher modes as well as the progressive changes in the dynamic characteristics of structures are taken into account to compute the applied load pattern. The basic shortcoming of these advanced pushover methods is related to employing the quadratic modal combination rule, whereby the sign reversals of the modal load vectors are suppressed. In this study, an improved displacement-based adaptive pushover method is developed in which the applied load pattern is computed using the factor modal combination rule(FMC). In the proposed procedure, multiple load patterns, depending on the number of the modes considered, are determined in order to take into account the sign reversals of different modal load vectors. The accuracy of the proposed method is verifi ed for seven moment resisting frame buildings of 3, 9 and 20 stories with regularity or vertically geometric and mass irregularities subjected to 60 earthquake ground motion records. The results showed that the proposed methodology is capable of reproducing the peak dynamic responses with very good accuracy.     

Simplified seismic sidesway collapse analysis of frame buildings

This paper presents the development and assessment of a simplified procedure for estimating the seismic sidesway collapse margin ratio of building structures. The proposed procedure is based on the development of a robust database of seismic peak displacement responses of nonlinear single‐degree‐of‐freedom systems for various seismic intensities and uses nonlinear static (pushover) analysis without the need for nonlinear time history dynamic analysis. The proposed simplified procedure is assessed by comparing its collapse capacity predictions on 72 different building structures with those obtained by nonlinear incremental dynamic analyses. The proposed simplified procedure offers a simple, yet efficient, computational/analytical tool that is capable of predicting collapse capacities with acceptable accuracy for a wide variety of frame building structures. Copyright © 2013 John Wiley & Sons, Ltd.