Uncoupled Modal Response History Analysis Research Articles

Simplified Procedure for Rapidly Estimating Inelastic Responses of Numerous High-Rise Buildings with Reinforced Concrete Shear Walls

Nonlinear response history analysis (NLRHA) is considered the most accurate procedure for evaluating the seismic performance of high-rise buildings. However, it requires considerable expertise and analysis time, making it inappropriate for some applications involving numerous high-rise buildings (e.g., the seismic loss estimation of a city). To overcome this limitation, a simplified procedure developed based on the uncoupled modal response history analysis (UMRHA) and coupled shear-flexural cantilever beam model (CSFCBM) is proposed. The underlying assumption is that the UMRHA procedure can compute the nonlinear seismic responses mode by mode, where each vibration mode is assumed to behave as a single-degree-of-freedom system. The nonlinear seismic responses are approximately represented by the sum of the modal responses of a few vibration modes. However, UMRHA requires knowledge of the modal properties and modal hysteretic behaviors. Therefore, the CSFCBM was introduced here to estimate the required modal properties and modal hysteretic behaviors. The inelastic seismic demands of the building can be determined using the UMRHA procedure with the computed modal properties obtained by CSFCBM. The accuracy of this proposed procedure was verified considering four high-rise buildings of 19, 30, 34, and 45 stories with reinforced concrete shear walls. The inelastic demands computed by the NLRHA procedure were used as a benchmark and compared with those of the proposed procedure. The results indicate that the proposed procedure provides reasonably accurate demand estimations for all case study buildings. Additionally, the total calculation time for modeling one building, performing dynamic analysis on 24 cases of ground motions, and post-processing the results required by the proposed procedure was about 7 to 45 times lower than that of the NLRHA procedure. Therefore, it can be used for estimating the seismic damage and losses of many high-rise buildings in a city for a specific earthquake scenario or a quick assessment of various seismic design options of a high-rise building in the preliminary design phase.

Three-dimensional non-linear seismic analysis of asymmetric structures on elastic soil

An approximate method for non-linear seismic analysis of three-dimensional two-way asymmetric buildings resting on flexible foundations under bi-directional ground motions is presented. To take into account the soil–structure interface effect, the sub-structuring method with frequency-independent soil springs and dashpots was employed. To consider the non-linear behaviour of the structure, a modal stick with five degrees of freedom was used to simulate the multi-degree-of-freedom modal equations for the soil–structure system. Using the bifurcation characteristic of modal pushover curves, the modal stick was modified, by which the coupled modal non-linear translation and rotation deformations were simulated. The seismic responses of two flexibly supported asymmetric buildings (three and eight storeys) were evaluated by the uncoupled modal response history analysis (UMRHA) method employing the proposed modal stick. The seismic responses of the structures were also obtained by employing the rigorous non-linear response history analysis and the results were compared with the corresponding outcomes from UMRHA method. The comparison showed good agreement between the outcomes of the two analysis methods, thus demonstrating that the proposed three-dimensional non-linear analysis technique developed in this study is an effective and applicable tool for dealing with the non-linear analysis of flexibly supported two-way asymmetric-plan structures.

Simplified seismic analysis of flexibly supported two-way asymmetric-plan buildings

The seismic response of flexibly supported asymmetric-plan structures to severe ground excitations is affected by the interaction of translational and torsional responses of the superstructure and the deformation of the soil underlying the foundation. An innovative simplified method based on uncoupled modal response history analysis (UMRHA) is proposed for soil–two-way asymmetric-plan building systems excited by bi-directional ground motions. A new five degrees of freedom (5DoF) modal stick is introduced to represent the modal equations of the flexibly supported structure. All of the elastic properties in the 5DoF modal sticks are determined by converting the equation of motion of the whole soil–structure system into 8DoF modal equations. The results obtained from the proposed enhanced UMRHA method with the 5DoF modal stick were compared with those obtained from the UMRHA method by solving eight coupled modal equations of motion, conventional modal analysis and rigorous exact analysis. The results demonstrated the high efficiency of the proposed procedure in the evaluation of engineering design parameters.

New Nonlinear Modal Decomposition Method for Seismic Analysis of Tall RC Core Wall Buildings

Significant research has been conducted in the past to develop simplified seismic evaluation procedures for tall buildings. However, most of these procedures are based on the use of fundamental mode response while ignoring the responses from higher modes. Moreover, such seismic evaluation procedures are unable to accurately predict individual-member responses. Evaluation of individual-member responses is an important part of damage and loss prediction estimation due to seismic hazard. In this research work, a new nonlinear modal decomposition approach is proposed for seismic evaluation of tall RC core wall buildings that can take into account the higher mode effects. This procedure is an extension of the classical Uncoupled Modal Response History Analysis procedure. A 44-story reinforced concrete core wall building is selected to verify the accuracy of the proposed procedure. A comparison between the outcomes of the proposed procedure and the nonlinear response history analysis procedure shows that this procedure is reasonably accurate in predicting important global and member responses.

Higher modes contribution for estimating the inelastic deformation ratios and seismic demands of structures

In order to estimate the seismic demand by using the nonlinear static procedure, different approximate methods have been developed. One of the most useful methods is called displacement coefficient method (DCM), which is based on some modification factors. One of these coefficients denoted C1, concerns the inelastic deformation ratio and usually depends on either the yield-strength reduction factor or the ductility factor. In general the evaluation of the inelastic deformation ratio is based on the response of single degree of freedom (SDOF) systems, where the response of the structure is mainly controlled by the fundamental mode, knowing that the inelastic deformation ratio will not capture the contribution of higher modes in the overall structural response. A developed theoretical approach with the aim of estimating the inelastic deformation ratio for structures, considering contribution of higher modes of vibration, is introduced. In this assessment, the normalized yield strength coefficient (η) and the post-to-preyield stiffness ratio (α) are key factors. The results are compared to the uncoupled modal response history analysis (UMRHA) procedure and some existing formulations for a nine story building subjected to the El Centro 1940 ground motion. It appears that the new theoretical approach leads to enough accurate estimation of the inelastic deformation ratio compared to the UMRHA one.

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.

Seismic Evaluation of Tall Buildings Using a Simplified but Accurate Analysis Procedure

A simplified analysis procedure for evaluating the nonlinear seismic responses of tall reinforced concrete (RC) buildings is examined in this study. It is called the Uncoupled Modal Response History Analysis (UMRHA) procedure. It can be viewed as an extended version of the classical modal analysis procedure, where the nonlinear response of each vibration mode is first computed, and they are later on combined into the total response of the structure. The procedure requires the knowledge of the modal hysteretic behavior, which can be obtained from a cyclic modal pushover analysis. The responses of four tall buildings in Bangkok to distant large earthquakes are computed by this procedure and compared with those obtained from the Nonlinear Response History Analysis (NLRHA) procedure. These four buildings have different heights—varying from 20 to 44 stories, different configurations of floor plan, and different arrangement of RC walls. The comparison shows that the UMRHA procedure is able to accurately compute the story shears and story overturning moments, floor accelerations, and inter-story drifts of all these tall buildings. The required computational effort is also extremely low compared to that of the NLRHA procedure. Moreover, since the UMRHA procedure computes the response of each individual vibration mode, it provides more understanding and insight into the complex nonlinear seismic responses of these tall buildings.

Alternative approach to compute shear amplification in high-rise reinforced concrete core wall buildings using uncoupled modal response history analysis procedure

Alternative approach to compute shear amplification in high-rise reinforced concrete core wall buildings using uncoupled modal response history analysis procedure

An Improved Seismic Intensity Measure of Inelastic Spectral Acceleration Based on MPA to Reduce the Dispersion in IDA

We present a new seismic intensity measure (IM) to reduce the dispersion in incremental dynamic analysis (IDA), which commonly use the elastic spectral acceleration as the IM. We propose using the inelastic spectral acceleration based on the principles of modal pushover analysis (MPA) as the seismic IM of ground motion. Unlike other methods of computing inelastic spectral acceleration, this new metric is calculated from the result of equivalent single degree-of-freedom (SDF) systems under the lateral force mode using the uncoupled modal response history analysis procedure. These equivalent SDF systems consider the constantly changing elastic–plastic hysteretic behaviour of the structure itself with different seismic intensities. The results indicate that the improved IDA method can more accurately estimate nonlinear structural responses in many intensity levels covering the entire range of structural responses—all the way from elastic behaviour to global dynamic instability. When the structure enters into the inelastic range, the seismic performance of the IDA’s dispersion using the inelastic spectral acceleration as the seismic IM is better than that using peak ground acceleration or elastic spectral acceleration.

Simplified procedure for seismic demands assessment of structures

Methods for the seismic demands evaluation of structures require iterative procedures. Many studies dealt with the development of different inelastic spectra with the aim to simplify the evaluation of inelastic deformations and performance of structures. Recently, the concept of inelastic spectra has been adopted in the global scheme of the Performance-Based Seismic Design (PBSD) through Capacity-Spectrum Method (CSM). For instance, the Modal Pushover Analysis (MPA) has been proved to provide accurate results for inelastic buildings to a similar degree of accuracy than the Response Spectrum Analysis (RSA) in estimating peak response for elastic buildings. In this paper, a simplified nonlinear procedure for evaluation of the seismic demand of structures is proposed with its applicability to multi-degree-of-freedom (MDOF) systems. The basic concept is to write the equation of motion of (MDOF) system into series of normal modes based on an inelastic modal decomposition in terms of ductility factor. The accuracy of the proposed procedure is verified against the Nonlinear Time History Analysis (NL-THA) results and Uncoupled Modal Response History Analysis (UMRHA) of a 9-story steel building subjected to El-Centro 1940 (N/S) as a first application. The comparison shows that the new theoretical approach is capable to provide accurate peak response with those obtained when using the NL-THA analysis. After that, a simplified nonlinear spectral analysis is proposed and illustrated by examples in order to describe inelastic response spectra and to relate it to the capacity curve (Pushover curve) by a new parameter of control, called normalized yield strength coefficient (). In the second application, the proposed procedure is verified against the NL-THA analysis results of two buildings for 80 selected real ground motions.

Estimation of Floor Response Spectra Using the Uncoupled Modal Response History Analysis

In performance-based earthquake engineering, probabilistic seismic demand models are usually developed by using methods which need a large number of nonlinear dynamic analyses to be run. In order to reduce the numerical effort, simplified methodologies of analysis have been proposed. Objective of the present study is to use the uncoupled modal response history analysis for the estimation of acceleration floor spectra, engineering demand parameters commonly used for measuring seismic demand in acceleration-sensitive non-structural elements. The procedure is evaluated for a 6-story reinforced concrete frame case study, designed to be representative of an existing structure lacking in specific capacity design rules.

Seismic response and damage development analyses of an RC structural wall building using macro-element

Numerical simulation of the non-linear behavior of (RC) structural walls subjected to severe earthquake ground motions requires a reliable modeling approach that includes important material characteristics and behavioral response features. The objective of this paper is to optimize a simplified method for the assessment of the seismic response and damage development analyses of an RC structural wall building using macro-element model. The first stage of this study investigates effectiveness and ability of the macro-element model in predicting the flexural nonlinear response of the specimen based on previous experimental test results conducted in UCLA. The sensitivity of the predicted wall responses to changes in model parameters is also assessed. The macro-element model is next used to examine the dynamic behavior of the structural wall building-all the way from elastic behavior to global instability, by applying an approximate Incremental Dynamic Analysis (IDA), based on Uncoupled Modal Response History Analysis (UMRHA), setting up nonlinear single degree of freedom systems. Finally, the identification of the global stiffness decrease as a function of a damage variable is carried out by means of this simplified methodology. Responses are compared at various locations on the structural wall by conducting static and dynamic pushover analyses for accurate estimation of seismic performance of the structure using macro-element model. Results obtained with the numerical model for rectangular wall cross sections compare favorably with experimental responses for flexural capacity, stiffness, and deformability. Overall, the model is qualified for safety assessment and design of earthquake resistant structures with structural walls.

The cause of unproportionately large higher mode contributions in the inelastic seismic responses of high‐rise core‐wall buildings

SUMMARYIn the conventional seismic design of high‐rise reinforced concrete core‐wall buildings, the design demands such as design shear and bending moment in the core wall are typically determined by the response spectrum analysis procedure, and a plastic hinge is allowed to form at the wall base to limit the seismic demands. In this study, it is demonstrated by using a 40‐story core‐wall building that this conventional approach could lead to an unsafe design where the true demands—the maximum inelastic seismic demands induced by the maximum considered earthquake—could be several times greater than the design demands and be unproportionately dominated by higher vibration modes. To identify the cause of this problem, the true demands are decomposed into individual modal contributions by using the uncoupled modal response history analysis procedure. The results show that the true demands contributed by the first mode are reasonably close to the first‐mode design demands, while those contributed by other higher modes are much higher than the corresponding modal design demands. The flexural yielding in the plastic hinge at the wall base can effectively suppress the seismic demands of the first mode. For other higher modes, however, a similar yielding mechanism is either not fully mobilized or not mobilized at all, resulting in unexpectedly large contributions from higher modes. This finding suggests several possible approaches to improve the seismic design and to suppress the seismic demands of high‐rise core‐wall buildings. Copyright © 2012 John Wiley & Sons, Ltd.

Modal pushover procedures for seismic evaluation of reinforced concrete structures: using new nonlinear single degree of freedom systems

This study performs a pushover procedure called Modified-UMRHA for seismic analysis of a reinforced concrete structure, based on the UMRHA (uncoupled modal response history analysis) procedure proposed by Chopra and Goel. The objective is to investigate three approaches for setting up nonlinear single degree of freedom systems drawn from modal pushover curves. These curves are obtained using a non-adaptive load pattern equal to the consistent mass matrix times the modal shape. These approaches are applied on the 14-storey Grenoble City Hall studied in the framework of the ARVISE French research program. The results obtained from the Modified-UMRHA using different proposed nonlinear single degree of freedom systems are compared with those from a rigorous nonlinear response history analysis. Cette étude présente une procédure de pushover nommée Modified-UMRHA pour l’analyse sismique des structures en béton armé, basée sur la procédure UMRHA proposée par Chopra et Goel. L’objectif est d’examiner trois approches se distinguant par la définition de systèmes non linéaires à un degré de liberté à partir des courbes de modal pushover. Ces courbes sont obtenues en utilisant un chargement non adaptatif égal à la matrice de masse consistante multipliée par la déformée modale. Ces approches sont appliquées sur un bâtiment de 14 étages, l’Hôtel de Ville de Grenoble étudié dans le cadre du programme de recherche ARVISE. Les résultats obtenus de la procédure Modified-UMRHA en utilisant différents systèmes non linéaires à un degré de liberté, sont comparés avec ceux issus de l’analyse non linéaire dynamique rigoureuse.

Optimal reduction of inelastic seismic demands in high‐rise reinforced concrete core wall buildings using energy‐dissipating devices

SUMMARYRecently, the issue of large inelastic seismic force demands at severe ground shakings such as maximum considered earthquake level has been highlighted in the conventionally designed high‐rise reinforced concrete core wall buildings. Uncoupled modal response history analysis was used in this study to identify the modes responsible for the large inelastic seismic force demands. The identification of dominant modes and mean elastic design spectra of seven representative ground motions for different damping ratios has led to the identification of three control measures: plastic hinges (PHs), buckling‐restrained braces (BRBs) and fluid viscous dampers (FVDs). The identified control measures were designed to suppress the dominant modes responsible for the large inelastic seismic force demands. A case‐study building was examined in detail. Comparison of the modal as well as the total responses of the case‐study building with and without the control measures shows that all the control measures were effective and able to reduce the inelastic seismic demands. A reduction of 33%, 22% and 27% in the inelastic shear demand at the base and a reduction of 60%, 22% and 26% in the inelastic moment demand at mid‐height were achieved using the PHs, BRBs and FVDs, respectively. Furthermore, a reduction of about 30–40% in the inelastic seismic deformation demands was achieved for the case of the BRBs and FVDs. The study enables us to gain insight to the complex inelastic behavior of high‐rise wall buildings with and without the control measures. Copyright © 2011 John Wiley & Sons, Ltd.

Identification of Reasons for High Inelastic Seismic Demands in High Rise RC Core Wall Buildings

Recently, the issue of high inelastic seismic demands at severe ground shakings such as MCE level has been highlighted in the conventionally designed high rise reinforced concrete (RC) core wall buildings. Furthermore, it is also found that the MCE level demands obtained from more rigorous non-linear response history analysis (NLRHA) are much greater than the DBE level demands obtained from the response spectrum (RS) procedure. In this study, different factors responsible for the high inelastic seismic demands and large difference between the demands obtained from the RS method and NLRHA are identified. A case study building is analyzed by the RS and NLRHA procedures using DBE response spectrum and the seven MCE spectrum compatible ground motions respectively. The factors which could be apparently responsible for large difference between the demands by the RS and NLRHA method are identified as: overstrength factor, excitation intensities, and different damping ratios. The effect of these factors on seismic demands is quantitatively estimated by performing the NLRHAs at different combination of damping ratios and excitation levels. Apart from three obvious factors, some other factors, which cannot be explained by the NLRHA, are also found to be responsible for the high inelastic seismic demands and large difference between the DBE demands by the RS procedure and MCE demands by the NLRHA procedure. To identify those factors, modal decomposition of the inelastic responses of the case study building using uncoupled modal response history analysis (UMRHA) is in progress.

내진성능의 증분동적해석을 위한 비선형 약산법의 비교 검토

구조물의 내진 성능 평가는 구조물에 가해진 지진력에 대한 변위요구와 같은 구조물의 성능 평가를 필요로 한다. 증분동적해석(IDA)은 지진하중에 대한구조물의 성능 평가를 위해 최근에 알려진 해석 방법이다. 이 방법은 구조물의 탄성 단계에서부터 항복, 파단에 이르기까지 지반가속도의 증가 수준에 따른 구조물의 전체 거동을 파악할 수 있는 방법이다. 대부분의 구조물들은 강한 지진을 받을 경우, 비선형 거동의 변형이 예상된다. 여러 가지 비선형해석법 가운데 구조물의 내진역량을 계산하기 위한 가장 정확한 방법은 비선형 시간이력해석(NRHA)이긴 하나 많은 시간과 노력이 요구되고 있다. 따라서 구조물의 비선형 거동을 보다 간편하게 예측하기 위한 정확하고 실용적인 비선형 약산해석법에 관한 연구들이 활발히 진행되고 있다. 비선형 모드중첩법(UMRHA)은 pushover곡선으로부터 구한 등가단자유도계를 비선형 시간이력해석 또는 응답스펙트럼을 이용하여 구조물의 비선형 응답을 구할 수 있는 방법이다. 직접스펙트럼해석법(DSA)은 pushover 해석으로부터 구조물의 선형 진동주기와 항복강도를 구한 다음, 반복계산 없이 비선형 응답을 직접 산정하는 약산법이다. 본 연구에서는 내진성능의 증분동적해석을 위한 비선형 약산법의 정확성과 신뢰성을 비교 검토한다. Seismic performance evaluation of structure requires an estimation of the structural performance in terms of displacement demand imposed by earthquakes on the structure. Incremental Dynamic Analysis(IDA) is a analysis method that has recently emerged to estimate structural performance under earthquakes. This method can obtained the entire range of structural performance from the linear elastic stage to yielding and finally collapse by subjecting the structure to increasing levels of ground acceleration. Most structures are expected to deform beyond the limit of linearly elastic behavior when subjected to strong ground motion. The nonlinear response history analysis(NRHA) among various nonlinear analysis methods is the most accurate to compute seismic performance of structures, but it is time-consuming and necessitate more efforts. The nonlinear approximate methods, which is more practical and reliable tools for predicting seismic behavior of structures, are extensively studied. The uncoupled modal response history analysis(UMRHA) is a method which can find the nonlinear reponse of the structures for ESDF from the pushover curve using NRHA or response spectrum. The direct spectrum analysis(DSA) is approximate nonlinear method to evaluate nonlinear response of structures, without iterative computations, given by the structural linear vibration period and yield strength from the pushover analysis. In this study, the practicality and the reliability of seismic performance of approximate nonlinear methods for incremental dynamic analysis of mixed building structures are to be compared.

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

AbstractAn 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.

Performance evaluation and damage assessment of steel frame buildings under main shock–aftershock earthquake sequences

AbstractStructures subjected to earthquake ground motions may be subjected to one or more aftershocks within a short period following the occurrence of the principal earthquake shock. Strong aftershocks have the potential to cause extensive structural damage, property losses and injuries to building occupants. This paper investigates the potential for aftershocks to cause additional damage to steel moment frame buildings, and provides a probabilistic description of structural damage states prior to and following those aftershocks. Statistics of structural response and damage states for steel frame buildings subjected to main shock–aftershock sequences are calculated using the enhanced uncoupled modal response history analysis (EUMRHA) method, a modification of an efficient and accurate method for predicting nonlinear response of frames. The frame connections are modelled by a moment–rotation relationship that takes brittle fracture of the connection welds into account. Damage accumulation is analysed in terms of a normalized ‘damage ratio’ and maximum inter‐storey drift. Simple probabilistic tools are proposed for purposes of rapid structural evaluation and condition assessment of damaged buildings. Copyright © 2007 John Wiley & Sons, Ltd.

Simplified seismic analysis of asymmetric building systems

AbstractThe paper reviews the uncoupled modal response history analysis (UMRHA) and modal pushover analysis (MPA) procedure in the analysis of asymmetric structures. From the pushover curves in ADRS format, showing the relationships of base shear versus roof translation and base torque versus roof rotation, a bifurcating characteristic of the pushover curves of an asymmetric structure is observed. A two‐degree‐of‐freedom (2DOF) modal stick is constructed using lump mass eccentrically placed at the end of beam which is connected with the column by a rotational spring. By converting the equation of motion of a whole structure into 2DOF modal equations, all of the elastic properties in the 2DOF modal sticks can be determined accurately. A mathematical proof is carried out to demonstrate that the 2DOF modal stick is consistent with the single‐degree‐of‐freedom (SDOF) modal stick at elastic state. The bifurcating characteristic of modal pushover curves and the interaction of modal translation and rotation can be considered rationally by this 2DOF modal stick. In order to verify the effectiveness of this proposed 2DOF modal stick, a two‐storey asymmetric building structure was analysed by the UMRHA procedure incorporating this novel 2DOF modal sticks (2DMPA) and conventional SDOF modal sticks (SDMPA), respectively. The analytical results are compared with those obtained by nonlinear response history analysis (RHA). It is illustrated that the accuracy of the rotational response histories obtained by 2DMPA is much better than those obtained by SDMPA. Consequently, the estimations of translational response histories on flexible side (FS) and stiff side (SS) of the building structure are also improved. Copyright © 2006 John Wiley & Sons, Ltd.