Modal Pushover Analysis Research Articles

A multi-mode adaptive pushover analysis procedure for estimating the seismic demands of RC moment-resisting frames

The main contribution of this paper is to develop a new multi-mode adaptive pushover analysis procedure for estimating the seismic demands of RC moment-resisting frames. The proposed procedure enhances the seismic demands of conventional pushover analysis methods by combining the advantages of ‘multi-modal’ and ‘adaptive’ pushover procedures. The presented method, which has been named the multi-mode adaptive displacement-based pushover (MADP) analysis procedure, estimates the seismic demands of buildings by using several multi-stage modal pushover analyses. Each multi-stage pushover analysis begins with the lateral load pattern proportional to the elastic mode-shape. The pushover analysis is then continued with a new lateral load pattern, constructed based on the story displacements obtained from the previous stage. The lateral force distribution is changed whenever a new plastic hinge is formed in the inelastic structural model. The ‘first-mode’ inelastic mode-shape of the structure is also used by the MADP method to accurately estimate the value of the target-displacement. The final structural responses are determined by combining the seismic demands obtained by the multi-stage modal pushover analyses using an appropriate modal combination rule. The accuracy and efficiency of the MADP procedure is verified using the analysis of four special RC moment-resisting frames with 4-, 8-, 12-, and 20-stories. The structural responses are estimated for two different seismic hazards (intensities). A comparison is then carried out between the estimates from the MADP method with those given by the exact nonlinear response history analysis (RHA). The results from two advanced pushover analysis procedures including the modal pushover analysis (MPA) and consecutive modal pushover (CMP) methods are also presented for the purpose of comparison. The results show that the MADP method is able to satisfactorily estimate the critical seismic demands such as interstory drift ratio and the plastic rotation of the hinges for the example buildings, and to provide an advanced nonlinear static procedure for the seismic performance assessment of RC moment-resisting frames.

Developing a modified IDA-based methodology for investigation of influencing factors on seismic collapse risk of steel intermediate moment resisting frames

Incremental dynamic analysis (IDA) widely uses for the collapse risk assessment procedures of buildings. In this study, an IDA-based collapse risk assessment methodology is proposed, which employs a novel approach for detecting the near-collapse (NC) limit state. The proposed approach uses the modal pushover analysis results to calculate the maximum inter-story drift ratio of the structure. This value, which is used as the upper-bound limit in the IDA process, depends on the structural characteristics and global seismic responses of the structure. In this paper, steel mid-rise intermediate moment resisting frames (IMRFs) have selected as case studies, and their collapse risk parameters are evaluated by the suggested methodology. The composite action of a concrete floor slab and steel beams, and the interaction between the infill walls and the frames could change the collapse mechanism of the structure. In this study, the influences of the metal deck floor and autoclaved aerated concrete (AAC) masonry infill walls with uniform distribution are investigated on the seismic collapse risk of the IMRFs using the proposed methodology. The results demonstrate that the suggested modified IDA method can accurately discover the near-collapse limit state. Also, this method leads to much fewer steps and lower calculation costs rather than the current IDA method. Moreover, the results show that the concrete slab and the AAC infill walls can change the collapse parameters of the structure and should be considered in the analytical modeling and the collapse assessment process of the steel mid-rise intermediate moment resisting frames.

Applying Adaptive Pushover Analysis to Estimate Incremental Dynamic Analysis Curve

To estimate seismic demand and capacity of structures, it has been suggested by researchers that Incremental Dynamic Analysis (IDA) is one of the most accurate methods. Although this method shows the most accurate response of the structure, some problems, such as difficulty in modeling, time-consuming analysis and selection of the earthquake records, encourage researchers to find some ways to estimate the dynamic response of structures by using static nonlinear analysis. The simplicity of pushover analysis in evaluating structural nonlinear response serves well as an alternative to the time-history analysis method. In this paper, based on the concepts of the displacement-based adaptive pushover (DAP), a new approach is proposed to estimate the IDA curves. The performance of the proposed method has been investigated using 3- and 9-story moment-resisting frames. In addition, the results were compared with exact IDA curves and IDA curves developed by the modal pushover analysis (MPA) based method. For evaluation, IDA curves with 16%, 50% and 84% fractile were estimated. Using the results, [Formula: see text] capacities corresponding to Collapse Prevention (CP) limit state were calculated and assessed. Finite element modeling of the structures has been carried out by using ZEUS-NL software. Based on the achieved results, the proposed approach can estimate the capacity of the structure accurately. The significant advantage of the applied approach is the low computational cost and desirable accuracy. The proposed approach can be used to develop the approximate IDA curves.

Modal pushover analysis on reinforced concrete arch bridge to estimate seismic responses

This paper presents an evaluation study of the performance of reinforced concrete arch bridge structures under earthquake load. The study is aimed to investigate the seismic performance of Wreksodiningrat Bridge, located in the province of Yogyakarta, Indonesia. This bridge is a three spans reinforced concrete arch bridge with a main span length of 75 m and two side spans with a length of 35 m, respectively. This study is a part of a large project carried out by the Ministry of Public Works to study the impact of the new 2016 Indonesia Seismic Design Code for Bridges (SNI 2833:2016). The main objective of this paper is to determine the displacement demands due to earthquake load based on the new seismic code design for bridges, SNI 2833:2016. In addition, demand capacity ratios (D/C) of the main structural components, such as the compression arch and main column (pier) at the fixed support, are also reviewed in this paper. The analysis was carried out using nonlinear modal pushover analysis. The arch bridge modeling is three dimensional, where structural elements such as beams, columns, and compression arches are modeled as frame elements. The plastic hinges are modeled as fiber hinges with unconfined and confined concrete material stress-strain relationship following Mander formula. The analysis result shows that the displacement demands of the bridge are 2.9 cm and 20 cm in the longitudinal and transverse direction, respectively. The D/C ratios of the compression arch due to demand earthquake load are 0.74 and 0.95 in the longitudinal and transverse direction of the bridge, while the D/C ratios of the pier are 0.15 and 0.80 in the longitudinal and transverse direction. Based on the above results, it is concluded that the studied bridge is able to withstand the seismic load requirements in the new Indonesia Seismic Design Code.

Seismic design of a super-tall building: Indonesian experience

This paper summarizes the structural concept and design of the twin 303-meter high “Indonesia-1" supertall building currently under construction in Jakarta. The first tower is a 63-story office building, and the second is 59-story, on top of the seven-level basement structure. The lateral resisting system of the towers is RC core-wall and outrigger, and composite floor system - with concrete slab, metal deck, and steel beams - is used for the gravity resisting system. Since the lateral system is outside the scope of the prescriptive system in the Indonesian Seismic Design Code, Modal Pushover Analysis (MPA) combined with Non-linear Response History Analysis (NLRHA) had demonstrated acceptability to the Jakarta building department and its peer review panel. Some challenges in conducting Performance-based Seismic Design (PBSD) are highlighted. In order to speed up construction, which is a critical factor in supertall building construction, erection columns are installed in the RC columns and CSPCM (Core Structure Preceding Construction Method) is applied. Consistently, the design must account for the associated construction sequence.

Assessment of modal pushover analysis for mid-rise concrete buildings with and without viscous dampers

In light of its tremendous saving in computational effort, the Modal Pushover Analysis (MPA) approximate procedure has been successfully applied to estimate seismic demands of structures with a level of accuracy that makes it a strong competitor to nonlinear response history dynamic analysis (NL-RHA) in steel buildings with short to medium periods. However, the applicability of MPA to reinforced concrete buildings, especially those undergoing large inelastic seismic demands and in the presence of energy dissipation devices, has not been well established. The purpose of this study is to extend the applicability of the MPA method to mid-rise special moment resisting frame (SMRF) concrete buildings with and without energy dissipating devices (linear viscous dampers). Results indicate that that the MPA can predict, with simple modifications, the seismic deformation response of SMRF mid-rise concrete buildings (with or without dampers) with reasonable accuracy compared to NL-RHA.

An energy balance method for seismic analysis of cable-stayed bridges

A seismic evaluation procedure for a cable-stayed bridge based on the energy balance concept is presented. In this method, the capacity curve obtained from the modal pushover analysis of the cable-stayed bridge is converted to a modal energy capacity diagram. Then, by intersecting this diagram and the energy demand diagram for a selected ground motion, the dynamic target point is obtained. The method was employed on a cable-stayed bridge under Imperial Valley earthquakes with different peak ground motions and the seismic demands were compared with the results from modal pushover and non-linear response history analyses. It was found that this energy balance method can estimate the seismic responses under the selected ground motions with good accuracy. OpenSees software was employed for modelling and analysis of the cable-stayed bridge.

Performance Based Seismic Rehabilitation of Steel Structures with Different Types of Shear Walls

Seismic rehabilitation provides existing buildings with more resistance to seismic activity, ground motion, or geotechnical failure as a result of earthquakes. Performance-based rehabilitation is a general concept through which the retrofitting criteria are defined regarding to performance objectives when the structural and nonstructural members are subject to different levels of earthquake hazards. In this study, several moment resistant steel frames with different numbers of stories were initially designed as vulnerable models. These models were retrofitted in consonance with the current seismic rehabilitation standards and codes criteria. Three models of shear walls were applied to retrofitting the vulnerable structures. In the first model, the wall surrounds column perimeter as boundary elements. In the second model, wall is connected to the column and in the 3rd model, wall is placed with a small gap from the column, and there is no contact between them. The nonlinear behavior of buildings is evaluated applying adaptive modal pushover and incremental dynamic analysis before and after rehabilitation.

Adaptive upper-bound pushover analysis for high-rise moment steel frames

In this paper, a new nonlinear static analysis procedure is proposed to assess the seismic performance of tall buildings, which considers both the higher modes effects as well as the progressive changes in the dynamic characteristics of structures during the inelastic response. In this method, the applied load pattern computed using the upper-bound (UB) method is updated at each analysis step considering only the first two modes of vibration and corrected by combining this applied load pattern with a uniform load distribution. The accuracy of the proposed adaptive upper-bound (AUB) procedure is tested using four steel moment resisting frame buildings. The results from the (AUB) are compared to those of the (UB) pushover analysis, improved upper-bound (IUB) method, modal pushover analysis (MPA), displacement-based adaptive pushover (DAP) procedure, and the nonlinear time history analysis (NTHA). In most cases, the proposed procedure leads to more adequate results and closer to those obtained by NTHA.

Performance Evaluation of a New NSP for Estimation of Seismic Demands of Nonlinear Irregular BRB Frames

Nonlinear static procedures are commonly used to compute seismic demands of structural systems. This paper combines the modified capacity spectrum method (MCSM) and modal pushover analysis (MPA) and proposes a new nonlinear static method called MPA–MCSM. To evaluate the accuracy of the proposed method, 30 different buckling-restrained braced (BRB) structures which consist of 3-, 9- and 20-story BRB frames with irregularities in plan and in elevation are selected. Each structure was analyzed subjected to seven pairs of ground motions. As a measure for the performance assessment of the proposed method, four structural seismic demands: (1) peak roof displacement, (2) story drift, (3) story shear and (4) base shear, are computed for each considered structure. The accuracy of MPA–MCSM responses is checked against the results obtained from nonlinear time-history analysis (NL-THA). The results reveal that MPA–MCSM provides conservative seismic demands for BRB frames.

Simplified seismic demand estimation for existing tall buildings in Thailand

A study of the performance evaluation of non-seismically designed buildings in Thailand is summarised and a simple methodology for quicker estimation of their seismic demands is presented. Using six case study high-rise buildings (20 to 44 storeys) and different types of input ground motions, it was found that the peak inelastic displacements of taller structures (with natural periods >1 s) can be significantly higher than their elastic counterparts, especially for ground motions with peak spectral acceleration occurring at longer periods. In such cases, use of the equal-displacement assumption may result in significantly non-conservative estimates of seismic demands. A simplified modal pushover analysis was then applied to the case study buildings. The combined seismic demands were determined by combining the peak modal demands obtained from a series of pushover analyses. The target displacement of the first vibration mode was determined by directly applying a modifying factor to the corresponding elastic displacement, while higher vibration modes were assumed to remain elastic. The seismic demands obtained from the detailed non-linear response history analysis procedure were used as benchmarks. The simplified analysis procedure was able to predict overall seismic demands and individual modal contributions of the case study buildings with reasonable accuracy. The method provides a relatively quick analysis option for performance evaluation of a large number of non-seismically designed existing high-rise buildings in Thailand.

Improved factored modal combination method for evaluating in-plane seismic demands of latticed arches

An improved factored modal combination method is developed for evaluating the in-plane seismic demands of latticed arches. In the method, an improved equivalent static earthquake load profile (ESELP) is proposed and expressed as a combination of several modal ESELPs. Two factors, an extended modal combination factor and a modal load modification factor, are proposed and used to establish the modal ESELPs, in which higher mode and geometrical nonlinear effects are taken into account. A set of improved ESELPs are established by combining the modal ESELPs of the selected modes that contribute significantly to the structural response. The structural demands are obtained from the envelope result of nonlinear pushover analyses using all the improved ESELPs. Three circular latticed arch models and two non-circular latticed arch models are built, and 30 seismic excitations are selected to investigate the applicability of the proposed method. The results show that, for latticed arches whose number of significant modes is less than or equal to three, the proposed method provides relatively high accuracy in the estimation of seismic demands. The mean errors of the seismic demands given by the proposed method are relatively low compared with those obtained from the factored modal combination method and the extended modal pushover analysis.

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.

Estimating seismic demands of singly symmetric buildings by spectrum-based pushover analysis

Buildings with the singly symmetric plan are more vulnerable to earthquake actions than the buildings with a symmetric-plan arrangement since the torsional effect caused by the asymmetricity will induce higher seismic demand and may cause unexpected damage to the buildings. Thus, it is a crucial challenge for researchers and engineers to predict seismic demands of asymmetric-plan buildings for the possible strengthening and retrofitting. Although some pushover-based analysis methods have been proposed for the fast prediction of asymmetric-plan buildings, most of them do not reasonably consider the dynamic coupling of vibration modes. This paper expands the spectrum-based pushover analysis (SPA) procedure, which is proved to be effective in predicting seismic demands of buildings with symmetric building plans, to three-dimensional structure systems, to estimate the seismic demands of singly symmetric structures. A comprehensive case study, which includes six frame buildings with different structural heights and mass eccentricity ratios under various levels of the input motions, was conducted to investigate the feasibility of the SPA method in estimating the seismic demands of one-way asymmetric-plan buildings. It is found from the comparison of seismic demands computed from the SPA method, the nonlinear response time history analysis, the consecutive modal pushover analysis and the modal pushover analysis that the SPA method is capable of predicting the seismic demands very well, in particular, the demands on the heavy side of the structure, where the seismic demand and damage are more significant.

Seismic Performance and Evaluation of Controlled Spine Frames Applied in High-rise Buildings

A controlled spine frame system consists of moment frames and spine frames with concentrated energy-dissipating members. This system guarantees the continuous usability of buildings against Japanese Level-2 earthquake events (similar to DBE events in California), and the authors have confirmed its excellent performance in preventing damage concentration in low-rise buildings. This study further investigates the effect of diverse structural properties on the seismic performance of controlled spine frames applied in high-rise buildings. The effect of building height, yield drift of dampers, spine-to-moment frame stiffness ratio, and damper-to-moment frame stiffness ratio are illustrated in detail, and optimal values are discussed. Also, a segmented spine frame system is proposed for high-rise buildings. The simple evaluation procedure proposed by the authors for low-rise buildings, based on equivalent linearization techniques and response spectrum analyses, was modified to include higher-mode effects for high-rise buildings based on modal analysis. The modified evaluation method was verified by modal pushover and time-history analyses.

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

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

Prediction of the force demands of tall buildings through the enhanced pushover procedures

SummaryThis paper attempts to comprehensively evaluate the accuracy of the enhanced pushover procedures in estimating the force demands of tall building structures. In this process, the efficiency of different pushover methods in taking the higher modes effect into account for the computation of the force demands is assessed. The enhanced pushover methods including the modal pushover analysis, force‐based adaptive pushover, displacement‐based adaptive pushover, consecutive modal pushover (CMP), single‐run multimode pushover (SMP), nonadaptive displacement‐based pushover, and adaptive force‐based multimode pushover procedures, as well as the conventional pushover analysis, are applied to the three special steel moment‐resisting frames to compute the internal force demands of structural members. The seismic force demands resulting from the enhanced pushover procedures are compared with those from the nonlinear response history analysis (NL‐RHA) as a benchmark solution. Furthermore, in order to evaluate approximately the degree to which the higher modes may affect deformation and force demands of tall buildings, the ratio of structural demands computed by the NL‐RHA to those obtained by the conventional pushover analysis is determined. The results demonstrate that the CMP and SMP procedures can accurately estimate the force demands of tall buildings. It is shown that the effects of higher modes on the story drifts and column shear forces and bending moments are larger than those on the other force demands.

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.

Extended spectrum-based pushover analysis for predicting earthquake-induced forces in tall buildings

Achievements have been made in the development of effective and accurate simplified methods for predicting the seismic demand of tall buildings. However, most of these methods are primarily focused on the estimation of seismic deformation of buildings, while no analysis and calculation of earthquake-induced forces in the structures have been presented. Based on the spectrum-based pushover analysis (SPA) for estimating the seismic demand of tall buildings, where the complicated vibration mode coupling in the nonlinear vibration of structures is simplified, an extended spectrum-based pushover analysis (ESPA) is developed for the fast prediction of earthquake-induced forces of tall buildings. In ESPA, a linear response spectrum analysis procedure is incorporated into SPA to consider the modal combination in the linear stage of vibration. A case study of two high-rise, special steel moment-resisting frame buildings subjected to different levels of ground-motion intensity is conducted to investigate the applicability and accuracy of the ESPA method. Comparisons of the results of earthquake-induced forces are made among ESPA, nonlinear response time history analysis (NLRHA), N2 method, modal pushover analysis (MPA) and consecutive modal pushover analysis (CMP). It is seen that the earthquake-induced forces, including bending moments and shear forces, predicted by the proposed ESPA method agree very well with those of NLRHA.

Ground motion scaling for seismic response analysis by considering inelastic response and contribution of the higher modes

This paper proposes a new scaling procedure to consider the inelastic response of structure along with the effect of higher modes in scaling the selected ground motions for seismic response analysis. This is done by obtaining the corresponding inelastic Single-Degree-of-Freedom (SDOF) system of the structure through performing a single-run modal pushover analysis with a load pattern consistent with the combined-modal-story-shear profile obtained from response spectrum analysis. Therefore, the effect of the higher modes and interaction between them in the nonlinear phase are reflected in the inelastic SDOF. The scaling process is performed such that the peak displacement of the inelastic SDOF system under the scaled record matches the inelastic spectral displacement (target displacement). The proposed procedure is evaluated through three regular and one irregular tall building. The results demonstrate the superiority of the proposed procedure in estimating the engineering demand parameters of structures with/without important higher modes effects.