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.     

Interstory drift ratio of building structures subjected to near-fault ground motions based on generalized drift spectral analysis

This paper focuses on the interstory drift ratio (IDR) demands of building structures subjected to near-fault ground motions having different impulsive characteristics based on generalized interstory drift spectral analysis. The near-fault ground motions considered include the idealized simple pulses and three groups of near-fault ground motions with forward directivity pulses, fling-step pulses and without velocity pulse. Meanwhile, the building systems are equivalently taken as shear-flexural beams with representative lateral stiffness ratios. The IDR distribution of continuous beams subjected to three groups of near-fault ground motions is acquired. It is illustrated that the maximum IDR shifts from the upper half to the lower half of buildings with an increase in lateral stiffness ratio. For long-period systems, the average IDR under impulsive ground motions is significantly greater than that under non-pulse motions. Finally, for moment-resisting frame buildings the forward directivity pulses amplify the drift response of higher modes, while the fling-step pulses excite primarily their contribution in the first mode and generate large deformation in the lower stories. The essential reason for this phenomenon is revealed according to the distinct property of near-fault impulsive ground motions and generalized drift spectral analysis.     

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.     

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.     

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.     

Seismic response analysis using characteristic ground motion records for risk‐based decision‐making (3R method)

The concept of intensity‐based assessment for risk‐based decision‐making is introduced. It is realized by means of the so‐called 3R method (response analysis, record selection and risk‐based decision‐making), which can be used to check the adequacy of design of a new building or of the strengthening of an existing building by performing conventional pushover analysis and dynamic analysis for only a few ground motions, which are termed characteristic ground motions. Because the objective of the method is not a precise assessment of the seismic risk, a simple decision model for risk acceptability can be introduced. The engineer can decide that the reliability of a no‐collapse requirement is sufficient when collapse is observed in the case of less than half of, for example, seven characteristic ground motions. From the theoretical point of view, it is shown that the accuracy of the method is acceptable if the non‐linear response history analyses are performed at a low percentile of limit‐state intensity, which is also proven by means of several examples of multi‐storey reinforced concrete frame buildings. The 3R method represents a compromise between the exclusive use of either pushover analysis or dynamic analysis and can be easily introduced into building codes provided that its applicability is further investigated (e.g. asymmetric structures and other performance objectives) and that the procedure for the selection of characteristic ground motions is automated and readily available to engineers (www.smartengineering.si).     

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。     

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.     

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.     

Approximate incremental dynamic analysis using the modal pushover analysis procedure

Incremental dynamic analysis (IDA)—a procedure developed for accurate estimation of seismic demand and capacity of structures—requires non‐linear response history analysis of the structure for an ensemble of ground motions, each scaled to many intensity levels, selected to cover the entire range of structural response—all the way from elastic behaviour to global dynamic instability. Recognizing that IDA of practical structures is computationally extremely demanding, an approximate procedure based on the modal pushover analysis procedure is developed. Presented are the IDA curves and limit state capacities for the SAC‐Los Angeles 3‐, 9‐, and 20‐storey buildings computed by the exact and approximate procedures for an ensemble of 20 ground motions. These results demonstrate that the MPA‐based approximate procedure reduces the computational effort by a factor of 30 (for the 9‐storey building), at the same time providing results to a useful degree of accuracy over the entire range of responses—all the way from elastic behaviour to global dynamic instability—provided a proper hysteretic model is selected for modal SDF systems. The accuracy of the approximate procedure does not deteriorate for 9‐ and 20‐storey buildings, although their dynamics is more complex, involving several ‘modes’ of vibration. For all three buildings, the accuracy of the MPA‐based approximate procedure is also satisfactory for estimating the structural capacities for the limit states of immediate occupancy, collapse prevention, and global dynamic instability. Copyright © 2006 John Wiley & Sons, Ltd.     

The extended N2 method taking into account higher mode effects in elevation

The N2 method has been extended in order to take into account higher mode effects in elevation. The extension is based on the assumption that the structure remains in the elastic range when vibrating in higher modes. The seismic demand in terms of displacements and storey drifts can be obtained by enveloping the results of basic pushover analysis and the results of standard elastic modal analysis. The approach is consistent with the extended N2 method used for plan‐asymmetric buildings. The proposed procedure was applied to three variants of three steel frame buildings used in the SAC project. The structural response was investigated for two sets of ground motions. Different ground motion intensities were used in order to investigate the influence of the magnitude of plastic deformations. The N2 results were compared with the results of nonlinear response‐history analysis, two other pushover‐based methods (modal pushover analysis (MPA) and modified MPA (MMPA)), and pushover analysis without consideration of higher modes. It was found that a considerable influence of higher modes on storey drifts is present at the upper part of medium‐and high‐rise structures. This effect is the largest in the case of elastic behaviour and decreases with ground motion intensity. The higher mode effects also depend on the spectral shape. The approximate methods (extended N2, MPA and MMPA) are able to provide fair estimates of response in the case of the test examples. Accuracy decreases with the height of the building, and with the intensity of ground motion. The N2 results are generally conservative. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

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.     

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.     

Estimation of seismic drift and ductility demands in planar regular X‐braced steel frames

This paper summarizes the results of an extensive study on the inelastic seismic response of X‐braced steel buildings. More than 100 regular multi‐storey tension‐compression X‐braced steel frames are subjected to an ensemble of 30 ordinary (i.e. without near fault effects) ground motions. The records are scaled to different intensities in order to drive the structures to different levels of inelastic deformation. The statistical analysis of the created response databank indicates that the number of stories, period of vibration, brace slenderness ratio and column stiffness strongly influence the amplitude and heightwise distribution of inelastic deformation. Nonlinear regression analysis is employed in order to derive simple formulae which reflect the aforementioned influences and offer a direct estimation of drift and ductility demands. The uncertainty of this estimation due to the record‐to‐record variability is discussed in detail. More specifically, given the strength (or behaviour) reduction factor, the proposed formulae provide reliable estimates of the maximum roof displacement, the maximum interstorey drift ratio and the maximum cyclic ductility of the diagonals along the height of the structure. The strength reduction factor refers to the point of the first buckling of the diagonals in the building and thus, pushover analysis and estimation of the overstrength factor are not required. This design‐oriented feature enables both the rapid seismic assessment of existing structures and the direct deformation‐controlled seismic design of new ones. A comparison of the proposed method with the procedures adopted in current seismic design codes reveals the accuracy and efficiency of the former. Copyright © 2007 John Wiley & Sons, Ltd.     

Evaluation of approximate methods to estimate residual drift demands in steel framed buildings

This paper presents the evaluation of two approximate methods recently proposed in the literature to estimate residual (permanent) drift demands at the end of earthquake excitation for seismic assessment of buildings. Both methods require an estimate of the peak (maximum) interstory drift demand and the corresponding drift demand at significant yielding of the building. Additionally, an approximate method is proposed as part of this study. The introduced method follows a coefficient‐based approach similar to the Coefficient Method included in several US documents. For evaluating the approximate methods, five moment‐resisting steel framed buildings having different number of stories were analyzed under four sets of earthquake ground motions. Quantification of the accuracy of the approximate methods to estimate residual drift demands with respect to results from nonlinear time‐history analyses was performed through error measures computed for each building and each set of earthquake ground motions. Results show that the mean standard error tends to increase as the seismic hazard level increases. Between the two methods, the method introduced by Erochko et al. seems more effective in predicting residual drift demands than that proposed in the FEMA P‐58 recommendations in the USA. It is demonstrated that including additional sources of stiffness and strength in the modeling approach constrains the amplitude of residual drift demands. As a beneficial consequence, the accuracy of both approximate methods in predicting residual drift demands is significantly improved (i.e., mean standard error decreases). The introduced method also provides similar accuracy than the approximate methods available in the literature. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

A method for computing interstory drift spectra with consideration of gravity effects

Vertical loads such as gravity may have an important influence on the seismic response of buildings. In this paper, the continuous shear-beam model is extended to study the seismic demand of shear buildings with consideration of the gravity load effect under near-field ground motions. An analytical solution of the free motion equation of as gravity shear beam model is provided in terms of a Bessel series. A method for computing interstory drift spectra is proposed. The interstory drift spectra for two near-field records with distinct pulses are presented to illustrate the effects of gravity and the damping ratio. The interstory drift spectra are also used to analyze the spectral characteristics of near fault ground motion during the 2008 Wenchuan earthquake. The effects of the gravity load ratio, damping ratio and higher modes are investigated and discussed.     

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.     

Seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions

An approximation approach of seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions is proposed. The procedures of uncoupled modal response history analysis (UMRHA) are extended to two‐way asymmetric buildings simultaneously excited by two horizontal components of ground motion. Constructing the relationships of two‐way base shears versus two‐way roof translations and base torque versus roof rotation in ADRS format for a two‐way asymmetric building, each modal pushover curve bifurcates into three curves in an inelastic state. A three‐degree‐of‐freedom (3DOF) modal stick is developed to simulate the modal pushover curve with the stated bifurcating characteristic. It requires the calculation of the synthetic earthquake and angle β. It is confirmed that the 3DOF modal stick is consistent with single‐degree‐of‐freedom modal stick in an elastic state. A two‐way asymmetric three‐story building was analyzed by UMRHA procedure incorporating the proposed 3DOF modal sticks. The analytical results are compared with those obtained from nonlinear response history analysis. It is shown that the 3DOF modal sticks are more rational and effective in dealing with the assessment of two‐way asymmetric building systems under two‐directional seismic ground motions. Copyright © 2007 John Wiley & Sons, Ltd.