Modal Pushover Analysis Procedure Research Articles

An improved multidimensional modal pushover analysis procedure for seismic evaluation of latticed arch‐type structures under lateral and vertical earthquakes

SummaryPushover methods for seismic assessment of buildings under multidimensional earthquakes have been studied and retrofitted. However, these current methods are not suitable when applied to widely adopted arch‐type structures characterized by strong geometrical nonlinearity and coupling effects. An improved multidimensional modal pushover procedure with two‐stage analyses is proposed for seismic evaluation of latticed arches. Taking overall multidimensional response into consideration, modal stiffness of the equivalent single‐degree‐of‐freedom system is derived, and its capacity curve is determined during the first‐stage analysis. To provide a deformation profile with algebraic signs of response retained, the second‐stage analysis is conducted using the pushover load pattern derived from modal displacement superposition. The objective of the improved procedure is to overcome the drawback of the conventional modal pushover method, which describes the capacity curve resorting to base shear and roof displacement, and that of quadratic combination rules which eliminate the sign reversals of response. To validate its serviceability, nodal displacements and element stresses, as well as the yielding members, of two typical latticed arches are calculated. Through comparative analysis, the results by the improved procedure exhibit good agreement with those by response history analysis. Additionally, this procedure demonstrates great superiority over the conventional method for its satisfying accuracy.

Prediction of nonlinear seismic demands of high‐rise rocking wall structures using a simplified modal pushover analysis procedure

SummaryThis study presents a simplified analysis procedure for the convenient estimation of nonlinear seismic demands of high‐rise rocking wall structures. For this purpose, the displacement modification approach used in the nonlinear static procedure of ASCE/SEI 41‐13 is adopted. However, in the current study, this approach is extended to every significant vibration mode of the structure whereas the displacement modifying coefficients for different modes are calculated using the typical flag‐shaped hysteresis behavior of rocking walls. The parameters of this hysteresis behavior are selected to represent rocking walls with a practical range of energy dissipation capacity and postgap‐opening stiffness. The computed peak inelastic‐to‐elastic displacement ratios are presented as mean spectra, which can be used for the convenient estimation of pushover target displacement for every significant vibration mode. The accuracy of proposed procedure is examined using the seismic demands obtained from the nonlinear response history analysis of a 20‐story case study rocking wall structure. Furthermore, a modal decomposition technique is used to determine the individual modal seismic demands. The proposed procedure is found to predict both the combined and the individual modal demands with a reasonable accuracy and can serve as a convenient analysis option for the design and performance evaluation of high‐rise rocking wall systems.

Seismic Evaluation of Tall Unstiffened Steel Plate Shear Wall (SPSW) Systems with Emphasis on Reversal Phenomenon in the Higher Mode Pushover Curve

This paper attempts to study the seismic behavior of tall unstiffened steel plate shear wall (SPSW) systems with an emphasis on the higher-mode pushover analysis and to elaborate the relevant pushover curve. Improved pushover analyses (IPAs) including the modal pushover analysis (MPA) and the modified modal pushover analysis (MMPA) are used for the frames in which the higher-mode effects are substantially important. The conventional pushover analysis using the FEMA load distributions is also implemented. To achieve this goal, mid-rise (10 and 15-story) and high-rise (20 and 30-story) SPSW systems are investigated. To consider a detailed behavior of SPSWs in analyses, a three-dimensional (3D) finite element modeling is used. An interesting result is obtained that the higher-mode pushover analysis results in a reversal in the pushover curve for all of the unstiffened SPSW systems studied in this investigation that this phenomenon is rare in performance-based seismic engineering. The results provide evidence that among the above-mentioned pushover analyses, the MPA procedure is accurate enough for the seismic evaluation of tall SPSW systems. Furthermore, the MPA is computationally time efficient in comparison with the nonlinear response history analysis for this kind of structures with 3D finite element modeling in which there exist a large number of frame and shell elements.

An adaptive modal pushover analysis procedure (VMPA-A) for buildings subjected to bi-directional ground motions

A new modal pushover analysis procedure (VMPA-A) is developed and implemented in MATLAB code for three-dimensional buildings subjected to bidirectional ground motions. VMPA-A uses stepwise force patterns to represent changes in the dynamic characteristics because of the accumulated structural damages. The hybrid-spectrum concept is introduced to account for the bidirectional ground motion effects. Due to enactments of the equal displacement rule and the secant stiffness-based linearization process, nonlinear analysis is performed for specific displacement targets without stipulation of full modal capacity curves for each mode. Horizontal components of an earthquake record are considered simultaneously, and the consistency between the force and displacement vectors for each mode is provided. These are the main advantages of the proposed procedure against modal pushover analysis (MPA). An existing 21-story reinforced concrete building is analyzed to exemplify VMPA-A. The response parameters such as displacements, story drifts, internal forces, strains, etc. are discussed by comparing the results of VMPA-A with nonlinear time history analyses, which is accepted as the “exact solution”. Though consistent demand estimations are obtained for story drifts, displacements and deformations, some conservative results are obtained for story shears.

An extended modal pushover procedure for estimating the in-plane seismic responses of latticed arches

The vertical displacements induced by the in-plane vibrating modes of an arch formed structure are as important as the lateral ones. Therefore, the vertical response components should be considered in the modal pushover load patterns for the in-plane seismic performance evaluation of latticed arches. Since the equivalent force of the modal equivalent single-degree-of-freedom (ESDF) system is determined by the base shear in conventional modal pushover procedures, which could not reflect the vertical part of the pushover load, an extended modal pushover analysis (MPA) procedure is proposed in this paper. In the extended MPA, the modal ESDF system of the in-plane vibrating mode of a latticed arch is established by the aid of an energy-based structural stiffness parameter, and the equivalent load of theESDF system is obtained according to the static pushover load factor, instead of using the base shear or other kinds of support reactions. The extended MPA approach not only takes the vertical components of the pushover load patterns into consideration, but also maintains the conceptual understandability and simplicity exhibited by conventional MPA procedures. Numerical examples carried out on two latticed arches demonstrate that the proposed extended MPA is more accurate than the conventional MPA, because in the former, the displacement coupling between horizontal and vertical directions are reflected when the arches are excited by in-plane earthquake actions.

Extending the concept of energy-based pushover analysis to assess seismic demands of asymmetric-plan buildings

The energy-based pushover analysis was developed in previous studies to address the issues regarding the distortion of capacity curve in conventional pushover procedures. Despite the conceptual superiority of an energy-based approach, its application is currently restricted to 2D structures. This study aims to extend the concept of this approach to asymmetric-plan buildings and bidirectional seismic excitation. For this purpose, a new energy-based multimode pushover analysis is developed. The overall procedure is quite similar to the well-known Modal Pushover Analysis (MPA). In contrast, however, the work done by lateral loads and torques here is used in preference to displacement of the roof center as an index to establish capacity curves. The efficiency of the proposed procedure is evaluated through seismic assessment of a set of one-way asymmetric (asymmetric around one axis) RC shear wall buildings. The results are compared with those of the MPA, ASCE41-13 pushover procedure, and the nonlinear response history analysis as a benchmark solution. Findings show that the proposed procedure can provide more accurate results than the MPA and ASCE41-13 procedures, in estimating the structural demands such as wall-hinge rotations and drift ratios.

Estimation of floor response spectra using modified modal pushover analysis

A common approach to designing nonstructural components against seismic excitations involves the use of floor response spectra (FRS). FRS can be accurately computed only through a nonlinear time-history analysis of the structure subjected to a specific earthquake ground motion. However, for multi-storey structures, which are usually modeled as multi-degree-of-freedom (MDOF) systems, this analysis becomes computation-intensive and time-consuming and is not suitable for adopting in seismic design guidelines. An alternative method of estimating FRS on MDOF systems is presented here. The proposed method uses multiple ‘generalized’ or ‘equivalent’ single degree of freedom (ESDOF) systems to estimate FRS on a MDOF system within the context of a ‘modal pushover analysis (MPA)’. This is a modified version of the previous MPA procedure as it considers the contribution of the first mode to yielding of higher modes when obtaining multiple ESDOF systems. FRS values for each mode are obtained through nonlinear dynamic analysis of each ESDOF system and then the total FRS values are calculated for the considered modes according to the SRSS combination rule. The efficiency of the modified procedure is tested by comparing FRS based on this method with results from nonlinear dynamic analyses of MDOF systems, as well as estimates based on ESDOF systems built from the traditional MPA method, for several ground motion scenarios. Three steel moment frame structures, of 3-, 9-, and 20-storey configurations, are selected for this comparison. Bias statistics that show the effectiveness of the modified method are presented.

Seismic response estimation of steel plate shear walls using nonlinear static methods

One of the major components for performance based seismic design is accurate estimation of critical seismic demand parameters. While nonlinear seismic analysis is the most appropriate analysis method for estimation of seismic demand parameters, this method is very time consuming and complex. Single mode pushover analysis method, N2 method and multi-mode pushover analysis method, modal pushover analysis (MPA) are two nonlinear static methods that have recently been used for seismic performance evaluation of few lateral load-resisting systems. This paper further investigates the applicability of N2 and MPA methods for estimating the seismic demands of ductile unstiffened steel plate shear walls (SPSWs). Three different unstiffened SPSWs (4-, 8-, and 15-storey) designed according to capacity design approach were analysed under artificial and real ground motions for Vancouver. A comparison of seismic response quantities such as, height-wise distribution of floor displacements, storey drifts estimated using N2 and MPA methods with more accurate nonlinear seismic analysis indicates that both N2 and MPA procedures can reasonably estimates the peak top displacements for low-rise SPSW buildings. In addition, MPA procedure provides better predictions of inter-storey drifts for taller SPSW. The MPA procedure has been extended to provide better estimate of base shear of SPSW.

Estimating seismic demands for performance-based engineering of steel buildings

Author(s): Reyes, Juan Carlos | Advisor(s): Chopra, Anil K | Abstract: Earthquake engineering practice is increasingly using performance-based procedures for evaluating existing buildings and proposed designs of new buildings. Both nonlinear static and nonlinear response history analyses (RHA) are used for estimating engineering demand parameters (EDPs)--floor displacements, story drifts, internal forces, hinge rotation, etc--in performance-based engineering of buildings. Topics related to both analysis procedures are investigated in this dissertation.In the first part, the original modal pushover analysis (MPA) to estimate seismic demands due to one component of ground motion is extended to consider two horizontal components simultaneously in three-dimensional analysis of buildings, and to estimate internal forces and plastic hinge rotations directly from pushover analyses. Subsequently, the accuracy of MPA in estimating EDPs for tall buildings and unsymmetric-plan buildings is evaluated. Seismic demands for recently designed and built 48- and 62-story buildings with ductile concrete core walls--designed according to the alternative provisions of the 2001 San Francisco Building Code (SFBC)--due to an ensemble of 30 ground motions are computed by MPA and nonlinear RHA, and compared. We demonstrate that MPA procedure shows degree of accuracy that is sufficient for practical application in estimating median values of EDPs for tall buildings subjected to two horizontal components of ground motion. The accuracy of the extended MPA procedure is also evaluated for low- and medium-rise unsymmetric-plan buildings with ductile frames designed in accordance with the 1985 Uniform Building Code (UBC85) and the 2006 International Building Code (IBC06). Seismic demands are computed for six unsymmetric-plan buildings due to 39 ground motions acting simultaneously in two orthogonal horizontal directions. Comparing these results with those from nonlinear RHA, we demonstrate that MPA provides good estimates of EDPs whereas the procedures specified in the ASCE/SEI 41-06 standard and the Eurocode 8 are not satisfactory for estimating seismic demands for unsymmetric-plan buildings.The second part of the dissertation concerns nonlinear response history analysis of buildings. With the goal of developing effective procedures for selection and scaling of multi-component ground motions to be used in nonlinear RHA, a modal-pushover-based-scaling (MPS) procedure is developed in this investigation. The developed MPS procedure is an extension of the original MPS procedure for one component of ground motion to two horizontal components. In this investigation, each horizontal component of ground motion is scaled by a factor selected to match the deformation of its inelastic SDF system to a target inelastic deformation that may be estimated using a design (or response) spectrum. The properties of the inelastic SDF system are determined by pushover analysis of the building using the first-mode distribution. Based on the results for medium-rise symmetric-plan and unsymmetric-plan buildings with ductile frames, we demonstrate that the MPS procedure provides much superior results than the scaling procedure specified in the ASCE/SEI 7-05 standard.

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.

A macro-level global seismic damage model considering higher modes

For modal pushover analysis procedures, the model proposed by Ghobarah et al. (called the G model hereafter, 1999) has been extended to account for the contributions of transient higher modes to global seismic damage of structures excited by strong ground motions. The proposed model has physically and perfectly bridged the G model and the final softening model proposed by DiPasquale and Cakmak (1988). Modal damage indexes corresponding to all considered vibration modes are combined by the CQC rule or the SRSS rule. Incremental dynamic analysis (IDA) is performed on three example RC frames to validate the proposed model, and a comprehensive comparison is carried out. The demonstration indicates that the proposed model is easy to implement and reflects the influence of the transition in transient vibration periods and modes on structural damage evolution. Some limitations associated with the proposed model are also addressed. Further experimental validations are needed to improve the model in the future.

An improved multidimensional MPA procedure for bidirectional earthquake excitations.

Presently, the modal pushover analysis procedure is extended to multidimensional analysis of structures subjected to multidimensional earthquake excitations. an improved multidimensional modal pushover analysis (IMMPA) method is presented in the paper in order to estimate the response demands of structures subjected to bidirectional earthquake excitations, in which the unidirectional earthquake excitation applied on equivalent SDOF system is replaced by the direct superposition of two components earthquake excitations, and independent analysis in each direction is not required and the application of simplified superposition formulas is avoided. The strength reduction factor spectra based on superposition of earthquake excitations are discussed and compared with the traditional strength reduction factor spectra. The step-by-step procedure is proposed to estimate seismic demands of structures. Two examples are implemented to verify the accuracy of the method, and the results of the examples show that (1) the IMMPA method can be used to estimate the responses of structure subjected to bidirectional earthquake excitations. (2) Along with increase of peak of earthquake acceleration, structural response deviation estimated with the IMMPA method may also increase. (3) Along with increase of the number of total floors of structures, structural response deviation estimated with the IMMPA method may also increase.

Envelope‐based pushover analysis procedure for the approximate seismic response analysis of buildings

SUMMARYAn 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.

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.

Assessment of FEMA356 nonlinear static procedure and modal pushover analysis for seismic evaluation of buildings

Nonlinear static analysis as an essential part of performance based design is now widely used especially at design offices because of its simplicity and ability to predict seismic demands on inelastic response of buildings. Since the accuracy of nonlinear static procedures (NSP) to predict seismic demands of buildings affects directly on the entire performance based design procedure, therefore lots of research has been performed on the area of evaluation of these procedures. In this paper, one of the popular NSP, FEMA356, is evaluated and compared with modal pushover analysis. The ability of these procedures to simulate seismic demands in a set of reinforced concrete (RC) buildings is explored with two level of base acceleration through a comparison with benchmark results determined from a set of nonlinear time history analyses. According to the results of this study, the modal pushover analysis procedure estimates seismic demands of buildings like inter story drifts and hinges plastic rotations more accurate than FEMA356 procedure.

A consecutive modal pushover procedure for nonlinear static analysis of one-way unsymmetric-plan tall building structures

Seismic responses of unsymmetric-plan tall buildings are substantially influenced by the effects of higher modes and torsion. Considering these effects, in this article, the consecutive modal pushover (CMP) procedure is extended to estimate the seismic demands of one-way unsymmetric-plan tall buildings. The procedure uses multi-stage and classical single-stage pushover analyses and benefits from the elastic modal properties of the structure. Both lateral forces and torsional moments obtained from modal analysis are used in the multi-stage pushover analysis. The seismic demands are obtained by enveloping the peak inelastic responses resulting from the multi-stage and single-stage pushover analyses. To verify and appraise the procedure, it is applied to the 10, 15, and 20-storey one-way unsymmetric-plan buildings including systems with different degrees of coupling between the lateral displacements and torsional rotations, i.e. torsionally-stiff (TS), torsionally-similarly-stiff (TSS) and torsionally-flexible (TF) systems. The modal pushover analysis (MPA) procedure is implemented for the purpose of comparison as well. The results from the approximate pushover procedures are compared with the results obtained by the nonlinear response history analysis (NL-RHA). It is demonstrated that the CMP procedure is able to take into account the higher mode influences as well as amplification or de-amplification of seismic displacements at the flexible and stiff edges of unsymmetric-plan tall buildings. The extended procedure can predict to a reasonable accuracy the peak inelastic responses, such as displacements and storey drifts. The CMP procedure represents an important improvement in estimating the plastic rotations of hinges at both flexible and stiff sides of unsymmetric-plan tall buildings in comparison with the MPA procedure.

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

AbstractThe 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.

Studies and Improvements on Modal Pushover Analysis and Application on Bridge

Because the traditional pushover analysis can not take the contributions of higher modes into account, To overcome this limitation, a modal pushover analysis procedure (MPA) is proposed by some researchers, which can involve the combination of multi-mode contributions to response. In this paper, much improvement on MPA procedure is made with consideration of the changes of seismic response after structural yielding and anew distribution of inertia forces. The method is verified by one example of bridge structure. It is concluded that the improvement part-sectionalized MPA presented in this paper has high accuracy.

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

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

Assessment of modal pushover analysis procedure for seismic evaluation of buckling–restrained braced frames

Buckling-restrained braced frame (BRBF) has become a viable choice of lateral-force resisting system for earthquake resistant buildings as its hysteretic behaviour is non-degrading and much hysteretic energy can be dissipated. Meanwhile, an improved pushover analysis procedure, called Modal Pushover Analysis (MPA), has been proposed by Chopra and Goel [(2002), Earthquake spectra, 20(1), 255–271] to include contributions of higher ‘modes’ in estimating seismic demands of buildings. The MPA procedure was demonstrated to provide reasonably accurate seismic demands compared with non-linear response history analysis (NL-RHA) when analysing moment-resisting frames. This research further examined the bias and accuracy of MPA procedure when it is applied to analyse 3-, 6-, 10- and 14-storey BRBF buildings due to two sets of strong ground motions having 2% and 10% probability of being exceeded in 50 years. The MPA estimates are compared with ‘exact’ results from NL-RHA. It was found that the peak roof displacement...