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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Comparison between non-linear dynamic and static seismic analysis of structures according to European and US provisions

Several procedures for non-linear static and dynamic analysis of structures have been developed in recent years. This paper discusses those procedures that have been implemented into the latest European and US seismic provisions: non-linear dynamic time-history analysis; N2 non-linear static method (Eurocode 8); non-linear static procedure NSP (FEMA 356) and improved capacity spectrum method CSM (FEMA 440). The presented methods differ in respect to accuracy, simplicity, transparency and clarity of theoretical background. Non-linear static procedures were developed with the aim of overcoming the insufficiency and limitations of linear methods, whilst at the same time maintaining a relatively simple application. All procedures incorporate performance-based concepts paying more attention to damage control. Application of the presented procedures is illustrated by means of an example of an eight-storey reinforced concrete frame building. The results obtained by non-linear dynamic time-history analysis and non-linear static procedures are compared. It is concluded that these non-linear static procedures are sustainable for application. Additionally, this paper discusses a recommendation in the Eurocode 8/1 that the capacity curve should be determined by pushover analysis for values of the control displacement ranging between zero and 150% of the target displacement. Maximum top displacement of the analyzed structure obtained by using dynamic method with real time-history records corresponds to 145% of the target displacement obtained using the non-linear static N2 procedure.     

The extended N2 method considering higher mode effects in both plan and elevation

The extended N2 method has been developed, which takes into account higher mode effects both in plan and 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 drift can be obtained by combining the results of basic pushover analysis and those of standard elastic modal analysis. In the paper, the proposed procedure was summarized and applied to a test example which represents an actual 8-storey reinforced concrete building. The results obtained by the extended N2 method were compared with the results of nonlinear response history analysis and basic N2 analysis without the consideration of higher modes. The extended N2 method was able to provide fair, conservative estimates of response in the case of the test example. In comparison to the basic N2 method, the prediction of seismic demand was greatly improved in the upper part of the building and at the flexible edges.     

Effectiveness of nonlinear static procedures for slender masonry towers

This paper investigates the accuracy of pushover-based methods in predicting the seismic response of slender masonry towers, through comparison with the results from a large number of nonlinear time-history dynamic analyses. In particular, conventional pushover analyses, in both their force- and displacement-based variants, are considered, and seismic assessment through the well-established N2 method is also addressed. The study is conducted by applying a simple non-linear elastic model recently developed and implemented in the computational code MADY to represent slender masonry structures. The model enables both pushover analyses and non-linear dynamic analyses to be performed with a minimum of effort. A multi-record incremental dynamic analysis carried out for a quite large number of structural cases, each of which is subjected to a comprehensive set of dynamic nonlinear analyses, is used to evaluate the accuracy of pushover methods in predicting the global structural response, as represented by the usual capacity curve together with a damage curve, both of which are compared with dynamic envelopes. Local responses, in terms of lateral displacements and the distribution of damage along the tower height are also compared. The results reveal that the key issue in the accuracy of pushover methods is the nature of the lateral load applied, that is, whether it is a force or a displacement. Different ranges of expected deformation are suggested for adopting each type of lateral load to better represent the actual behaviour of masonry towers and their damage under seismic events through pushover methods.     

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.     

Corrective eccentricities for assessment by the nonlinear static method of 3D structures subjected to bidirectional ground motions

Nonlinear static methods are reliable in the evaluation of the seismic response of planar structural schemes, but they are not very effective in the assessment of three-dimensional building structures. The authors of this paper have recently proposed a nonlinear static approach for asymmetric structures, which is an improvement on that stipulated by seismic codes. This method is based on the observation that the distribution of the maximum dynamic displacements of the deck can be enveloped by two pushover analyses performed by applying the lateral force with two eccentricities with respect to the center of mass of the deck. These eccentricities, named “corrective eccentricities”, are defined so that the two corresponding pushover analyses provide displacements that are equal to those evaluated by nonlinear dynamic analysis at the two sides of the deck. In this paper, the corrective eccentricities are determined for a wide set of single-story systems. The equations for their analytical evaluation are determined and their reliability is demonstrated. Finally, the analysis of a multi-story structure is conducted to show how the method can be applied to real buildings. Copyright © 2012 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.     

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.     

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.