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.     

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.     

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..     

Multi-hazard performance assessment of a transfer-plate high-rise building

Many urban areas are located in regions of moderate seismicity and are subjected to strong wind. Buildings in these regions are often designed without seismic provisions. As a result, in the event of an earthquake, the potential for damage and loss of lives may not be known. In this paper, the performance of a typical high-rise building with a thick transfer plate (TP), which is one type of building structure commonly found in Hong Kong, is assessed against both earthquake and wind hazards. Seismic- and wind-resistant performance objectives are fi rst reviewed based on relevant codes and design guidelines for high-rise buildings. After a brief introduction of wind-resistant design of the building, various methodologies, including equivalent static load analysis (ESLA), response spectrum analysis (RSA), pushover analysis (POA), linear and nonlinear time-history analysis (LTHA and NTHA), are employed to assess the seismic performance of the building when subjected to frequent earthquakes, design based earthquakes and maximum credible earthquakes. The effects of design wind and seismic action with a common 50-year return period are also compared. The results indicate that most performance objectives can be satisfi ed by the building, but there are some objectives, such as inter-story drift ratio, that cannot be achieved when subjected to the frequent earthquakes. It is concluded that in addition to wind, seismic action may need to be explicitly considered in the design of buildings in regions of moderate seismicity.     

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.     

Three‐dimensional modal pushover analysis of buildings subjected to two components of ground motion,including its evaluation for tall buildings

The modal pushover analysis (MPA) procedure, presently restricted to one horizontal component of ground motion, is extended to three‐dimensional analysis of buildings—symmetric or unsymmetric in plan—subjected to two horizontal components of ground motion, simultaneously. Also presented is a variant of this method, called the practical modal pushover analysis (PMPA) procedure, which estimates seismic demands directly from the earthquake response (or design) spectrum. Its accuracy in estimating seismic demands for very tall buildings is evaluated, demonstrating that for nonlinear systems this procedure is almost as accurate as the response spectrum analysis procedure is for linear systems. Thus, for practical applications, the PMPA procedure offers an attractive alternative whereby seismic demands can be estimated directly from the (elastic) design spectrum, thus avoiding the complications of selecting and scaling ground motions for nonlinear response history analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Pushover analysis of asymmetric-plan buildings based on distribution of the combined modal story shear and torsional moment

A pushover procedure with a load pattern based on the height-wise distribution of the combined modal story shear and torsional moment is proposed to estimate the seismic response of 3D asymmetric-plan building frames. Contribution of the higher modes and torsional response of asymmetric-plan buildings are incorporated into the proposed load pattern. The proposed pushover method is a single-run procedure, which enables tracing the nonlinear response of the structure during the analysis and averts the elusiveness of conducting multiple pushover analyses. The proposed method has been used to estimate the response of two moment-resisting building frames with 9 and 20 stories. The obtained results indicate the appropriate accuracy and efficiency of the proposed procedure in estimating the trend of the drift profiles of the structures resulted from nonlinear time history analyses.     

A three-dimensional drift pushover method for unsymmetrical plan buildings

The drift pushover analysis method for tall and regular buildings is extended in this paper to the third dimension. The focus of study is on the structures with important torsional response. For this purpose, 10, 15, 20 and 30-story steel moment frame buildings having unsymmetrical plans with 5–30% eccentricity ratios are studied. For evaluation of accuracy, nonlinear dynamic response of the buildings is determined under a consistent suit of earthquake ground motions. The maxima of the story drifts and shears and cumulative plastic hinge rotations of stories are calculated under the ground motions and their averages along with those of the modal pushover procedure are compared with the results of the presented method. The comparative analysis establishes the good accuracy of the three dimensional drift pushover method.     

Evaluation of three‐dimensional modal pushover analysis for unsymmetric‐plan buildings subjected to two components of ground motion

The accuracy of the three‐dimensional modal pushover analysis (MPA) procedure in estimating seismic demands for unsymmetric‐plan buildings due to two horizontal components of ground motion, simultaneously, is evaluated. Eight low‐and medium‐rise structures were considered. Four intended to represent older buildings were designed according to the 1985 Uniform Building Code, whereas four other designs intended to represent newer buildings were based on the 2006 International Building Code. The median seismic demands for these buildings to 39 two‐component ground motions, scaled to two intensity levels, were computed by MPA and nonlinear response history analysis (RHA), and then compared. Even for these ground motions that deform the buildings significantly into the inelastic range, MPA offers sufficient degree of accuracy. It is demonstrated that PMPA, a variant of the MPA procedure, for nonlinear systems is almost as accurate as the well‐known standard response spectrum analysis procedure is for linear systems. Thus, for practical applications, the PMPA procedure offers an attractive alternative to nonlinear RHA, whereby seismic demands can be estimated directly from the (elastic) design spectrum. In contrast, the nonlinear static procedure specified in the ASCE/SEI 41‐06 Standard is demonstrated to grossly underestimate seismic demands for some of the unsymmetric‐plan buildings considered. Copyright © 2011 John Wiley & Sons, Ltd.     

模态pushover分析方法的研究和改进

鉴于传统pushover方法不能考虑结构高阶振型的贡献,从而难以应用到高层结构中,有学者提出采用考虑多阶振型组合作用的模态pushover分析方法。本文通过考虑结构屈服后地震作用发生变化这一特性,对此方法进行了改进并通过算例进行了验证。结果表明本文改进的方法有很好的精度。     

Seismic evaluation of geometrically irregular steel moment resisting frames with setbacks considering their dynamic characteristics

A setback building has a sudden discontinuity in the frame geometry along the height. This kind of irregularity causes an abrupt discontinuity in stiffness, strength and mass of the building frame. In this study, a total of nineteen mid-rise 9-story steel moment resisting frames with setbacks including the broad range of different geometrical configurations were studied. An eigenvalue analysis was performed to evaluate and scrutinize the dynamic characteristics of setback structures. The effect of geometrical configurations on the seismic responses of setback frames was studied by means of nonlinear response history analysis using a set of far-field ground motion records. Moreover, due to the rapidly increasing use of pushover analysis for the seismic evaluation of structures in recent years, enhanced pushover analyses (EPAs) including the modal pushover analysis, the upper bound pushover analysis, the consecutive modal pushover and the extended N2 methods were implemented as a main part of this study. The findings show that two factors including the location of setback and the degree of setback are of key importance and influence the dynamic characteristics and seismic responses of setback structures. The degree of accuracy of the enhanced pushover analysis methods generally depends on the dynamic characteristics (geometrical configuration) of the setback frames. The largest error in the EPAs in predicting the story drifts generally occurs in a setback frame with a larger amount of the ratio between the effective modal participating mass ratio of the higher modes and that of the first mode.     

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.     

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。     

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.     

Seismic safety of low ductility structures used in Spain

The most important aspects of the design, seismic damage evaluation and safety assessment of structures with low ductility like waffle slabs buildings or flat beams framed buildings are examined in this work. These reinforced concrete structural typologies are the most used in Spain for new buildings but many seismic codes do not recommend them in seismic areas. Their expected seismic performance and safety are evaluated herein by means of incremental non linear structural analysis (pushover analysis) and incremental dynamic analysis which provides capacity curves allowing evaluating their seismic behavior. The seismic hazard is described by means of the reduced 5% damped elastic response spectrum of the Spanish seismic design code. The most important results of the study are the fragility curves calculated for the mentioned building types, which allow obtaining the probability of different damage states of the structures as well as damage probability matrices. The results, which show high vulnerability of the studied low ductility building classes, are compared with those corresponding to ductile framed structures.     

交错桁架多层钢结构推倒分析方法研究

随着基于性能的抗震设计思想的发展,推倒分析开始成为罕遇地震下多、高层结构抗震设计的有力工具。本文以交错桁架多层钢结构为例,采用推倒分析对其在E l Centro波作用下的地震反应进行研究,分别采用位移系数法和能力谱法确定结构目标位移,同时进行结构在相同地震动下的弹塑性时程分析。研究表明,推倒分析能准确地评价交错桁架多层钢结构的抗震性能,采用位移系数法和能力谱法确定的结构顶点侧移均与弹塑性时程分析吻合较好,对层间位移及塑性铰分布的预测,能力谱法比位移系数法更为准确。     

Modal-based ground motion selection procedure for nonlinear response time history analysis of high-rise buildings

The selection of representative input ground motions (IGMs) is important for a proper nonlinear response time history analysis (NLRHA) of modern structures. The prevailing IGM selection procedure requires that the response spectra of selected ground motions are matched with the code-specified design spectra, while the effect of the frequency contents combination in the time domain on the multimode interactions is not considered. Ignoring the effect of the frequency contents combination in the time domain of IGMs may cause significant variations in the analysis results for selected IGMs, although they are matched to the same design spectrum. In this paper, a modal-based ground motion selection (MGMS) procedure is proposed as a supplement to spectrum matching-based IGM selection procedures for selecting proper IGMs that can sufficiently induce the multimode interactions. In the proposed procedure, three equivalent single-degree-of-freedom (ESDOF) systems are developed by pushover analysis. NLRHA is then conducted for these ESDOF systems with a set of 20 seed IGMs chosen by the spectrum-matching–based selection procedure. Finally, seven IGMs are selected from the seed IGMs for NLRHA in the full structural model. To verify MGMS, seismic demands of high-rise buildings were computed by NLRHA with seven MGMS-selected IGMs, seven IGMs with closest spectrum matching, and groups of seven randomly selected IGMs derived from three different sets of 20 seed IGMs. The computed seismic demands with MGMS-IGMs show very good agreement with the mean demands determined using the whole set of seed IGMs, while the deviation is much lesser compared with those groups of randomly selected IGMs.     

约束混凝土砌块结构抗震性态研究

性态抗震设计已成为结构抗震设计的发展趋势,本文以约束混凝土砌块结构为对象,在提出约束混凝土砌块墙承载力计算公式的基础上,建立了砌块墙片的恢复力模型。对3座不同层数的典型约束混凝土砌块结构,在代表不同场地类别、不同地震动强度的输入下分别进行了动力非线性时程分析和静力非线性分析。通过计算结果的对比,讨论了2种分析方法中场地类别、地震动强度、静力非线性分析中侧力分布模式等影响,所得结论可以为用静力非线性分析估计砌块结构的抗震性能提供有益的参考依据。     

Evaluation of FEMA-440 for including soil-structure interaction

Replacing the entire soil-structure system with a fixed base oscillator to consider the effect of soil-structure interaction (SSI) is a common analysis method in seismic design. This technique has been included in design procedures such as NEHRP, ASCE, etc. by defining an equivalent fundamental period and damping ratio that can modify the response of the structure. However, recent studies indicate that the effects of SSI should be reconsidered when a structure undergoes a nonlinear displacement demand. In recent documents on Nonlinear Static Procedures (NSPs), FEMA-440 (2005), a modified damping ratio of the replacement oscillator was proposed by introducing the ductility of the soil-structure system obtained from pushover analysis. In this paper, the damping defined in FEMA-440 to include the soil-structure interaction effect is evaluated, and the accuracy of the Coefficient Method given in FEMA-440 and the Equivalent Linearization Method is studied. Although the improvements for Nonlinear Static Procedures (NSPs) in FEMA-440 are achieved for a fixed base SDOF structure, the soil effects are not perfectly obtained. Furthermore, the damping definition of a soil-structure system is extended to structures to consider bilinear behavior.