A modified response spectrum analysis procedure to determine nonlinear seismic demands of high‐rise buildings with shear walls

The standard response spectrum analysis (RSA) procedure prescribed in various design codes is commonly used by practicing engineers to determine the seismic demands for structural design purpose. In this procedure, the elastic force demands of all significant vibration modes are first combined and then reduced by a response modification factor (R) to get the inelastic design demands. Recent studies, however, have shown that the response of higher vibration modes may experience much lower level of nonlinearity, and therefore, it may not be appropriate to reduce their demand contributions by the same factor. In this study, a modified RSA procedure based on equivalent linearization concept is presented. The underlying assumptions are that the nonlinear seismic demands can be approximately obtained by summing up the individual modal responses and that the responses of each vibration mode can be approximately represented by those of an equivalent linear SDF system. Using 3 high‐rise buildings with reinforced concrete shear walls (20‐, 33‐, and 44‐story high), the accuracy of this procedure is examined. The inelastic demands computed by the nonlinear response history analysis procedure are used as benchmark. The modified RSA procedure is found to provide reasonably accurate demand estimations for all case study buildings.     

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

This 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.     

Reduction of inelastic seismic demands in a mid‐rise rocking wall structure designed using the displacement‐based design procedure

Precast post‐tensioned rocking wall structural system has been developed in the recent past as a damage‐avoidance structural system for seismic regions. For a widespread use of this structural system, suitable design procedures are required to ensure a reliable and well‐predicted performance under different levels of seismic hazard. In the current study, a mid‐rise 20‐story rocking wall structure is selected and designed using the displacement‐based design procedure. Furthermore, two different capacity design procedures are used to predict the increased force demands due to higher mode effects. The time history results against moderate and severe level of seismic hazards show the effectiveness of displacement‐based design procedure in predicting and controlling the displacement and drift demands, while the simplified procedure and the modified modal superposition procedure for the capacity design are found to be unconservative and conservative, respectively. To further investigate the seismic demands, modal decomposition of inelastic seismic responses is carried out, and the contribution of different modes in the total responses is calculated. Based on this improved understanding, a mitigation technique of dual gap opening is employed. A detailed discussion about the location and design strength of the extra gap‐opening is carried out by considering different performance parameters. Copyright © 2016 John Wiley & Sons, Ltd.     

An improved consecutive modal pushover procedure for estimating seismic demands of multi‐storey framed buildings

An improved consecutive modal pushover (ICMP) procedure is proposed to enhance the accuracy of conventional CMP procedure for estimating seismic demands of tall buildings. It accounts for inelastic structural properties and interaction between vibration modes. The displacement increment at the roof of buildings used in each stage of pushover analyses is modified based on the displacement contribution of each mode. The performance of the proposed ICMP procedure is verified against three high‐rise frames subjected to various ground motions. The results obtained from the ICMP procedure are compared with those from the nonlinear time history analysis, conventional pushover analysis, and CMP analysis. The comparison shows the advantages of the ICMP over the other pushover procedures. It is concluded that the ICMP procedure is more accurate than the CMP procedure.     

On the applicability of pushover analysis for seismic evaluation of medium‐ and high‐rise buildings

The assumption that the dynamic performance of structures is mainly determined from the corresponding single‐degree‐of‐freedom system in pushover analysis is generally valid for low‐rise structures, where the structural behaviour is dominated by the first vibration mode. However, higher modes of medium‐ and high‐rise structures will have significant effect on the dynamic characteristics. In this paper, the applicability of pushover analysis for seismic evaluation of medium‐to‐high‐rise shear‐wall structures is investigated. The displacements and internal forces of shear wall structures with different heights are determined by nonlinear response history analysis, where the shear walls are considered as multi‐degree‐of‐freedom systems and modelled by fibre elements. The results of the analysis are compared with those from the pushover procedure. It is shown that pushover analysis generally underestimates inter‐storey drifts and rotations, in particular those at upper storeys of buildings, and overestimates the peak roof displacement at inelastic deformation stage. It is shown that neglecting higher mode effects in the analysis will significantly underestimate the shear force and overturning moment. It is suggested that pushover analysis may not be suitable for analysing high‐rise shear‐wall or wall‐frame structures. New procedures of seismic evaluation for shear‐wall and wall‐frame structures based on nonlinear response history analysis should be developed. Copyright © 2009 John Wiley & Sons, Ltd.     

Assessment of modal pushover analysis and conventional nonlinear static procedure with load distributions of federal emergency management agency for high‐rise buildings

The nonlinear static pushover analysis technique is mostly used in the performance‐based design of structures. However, the pushover analysis with load distributions of Federal Emergency Management Agency (FEMA) loses its accuracy in estimating the seismic responses of long‐period structures where higher mode effects are important. Recently, modal pushover analysis (MPA) has been proposed to consider these effects. Hence, FEMA load patterns and MPA are evaluated in the current study and compared with inelastic response history analysis. These approximate procedures are applied to medium‐rise (10 and 15 stories) and high‐rise (20 and 30 stories) buildings; advantages and limitations of them are elaborated. It is shown that MPA procedure presents significant advantage over FEMA load distributions in predicting story drifts. MPA is able to compute hinge plastic rotations better than FEMA load distributions at upper floor levels of high‐rise buildings due to considering higher mode effects by this procedure, but both are unsuccessful in predicting hinge plastic rotations with acceptable accuracy. Copyright © 2008 John Wiley & Sons, Ltd.     

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

Recently, 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.     

A new pushover procedure for two‐way asymmetric‐plan tall buildings under bidirectional earthquakes

Conventional pushover analyses despite of extensive applications are unable to estimate the general responses of asymmetric‐plan tall buildings because of ignoring the effects of higher modes and torsion. A consecutive modal pushover procedure is one of the recent nonlinear static pushover procedures that used to analyse the seismic response of one‐way asymmetric‐plan tall buildings under one‐directional seismic ground motions. In this paper, a modified consecutive modal pushover procedure (MCMP) has been proposed to estimate the seismic demands of two‐way asymmetric‐plan tall buildings under two horizontal components of earthquakes simultaneously. The accuracy of the MCMP procedure is evaluated using different buildings and comparing with the results of FEMA (Federal Emergency Management Agency) procedures, the practical modal pushover procedure and nonlinear time history analyses as an exact solution. The results show the proposed MCMP procedure is able to estimate the displacements and storey drifts accurately and introduces a great improvement in predicting the plastic hinge rotations. Copyright © 2013 John Wiley & Sons, Ltd.     

Nonlinear seismic assessment of irregular coupled wall systems using high‐performance fiber‐reinforced cement composites

Reinforced concrete coupled wall systems that consist of multiple shear walls linked by coupling beams are known to be very effective for resisting lateral loads in high‐rise buildings. As to improving the seismic capacity of coupled wall systems, high‐performance fiber‐reinforced cement composites (HPFRCCs) have been recently considered. These materials are characterized by tension strain‐hardening behavior that can improve the ductility and toughness of structures subjected to reversed cyclic loading. In this study, nonlinear finite element analyses were conducted to investigate the effects of HPFRCCs on the seismic behavior of irregular tall buildings with coupled wall systems. The coupling beams were modeled using moment hinge elements, and the structural walls were modeled using fiber elements. Comparisons between analysis and test results of coupled wall specimens with and without HPFRCCs indicate that the modeling methods used well predict both the overall and local behaviors. The responses of a 56‐story irregular tall building with coupled walls are discussed with focus on the effects of HPFRCCs. It is noted that the use of HPFRCCs in coupling beams and structural walls of one‐fourth height from the base greatly affects the failure mode. For irregular tall buildings, nonlinear response history analysis indicates higher mode effects are critical.     

Simplified multi‐degree‐of‐freedom model for estimation of seismic response of regular wall‐frame structures

A simplified multi‐degree‐of‐freedom (MDOF) model is developed for estimation of seismic response of tall wall‐frame structures. By using the continuum technique for the structure and adopting the bilinear hysteretic model for material properties, procedure for the development of the simplified MDOF model is derived. The numerical study for a 20‐storey reinforced concrete (RC) wall‐frame structure is conducted to investigate the accuracy of seismic response predicted by the proposed model. Results from the nonlinear response history analyses based on the proposed MDOF model and the detailed structural model with member‐by‐member representation are compared and show very good agreement. The proposed simplified MDOF model is shown to provide a simple, efficient and accurate method for estimation of seismic performance of tall wall‐frame structures. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Assessment of modified consecutive modal pushover analysis for estimating the seismic demands of tall buildings with dual system considering steel concentrically braced frames

According to the previous researches, conventional nonlinear static procedure (NSP), which is limited to single mode response, cannot predict the seismic demands of tall buildings with reliable accuracy. To estimate the seismic demands in upper stories for tall buildings the effects of higher modes should be included. In the recent years, developing traditional pushover analysis to consider the effects of higher modes conducted researchers to propose several methods, such as N2, MPA and MMPA procedures, that have a specific approach to estimate seismic demands of structures but the accuracy of them is doubtable for estimating of hinge plastic rotations. Recently consecutive modal pushover (CMP) procedure was proposed to consider the effects of higher modes with acceptable accuracy especially in prediction of hinge plastic rotations. The CMP procedure was limited to include two or three modes, and use of higher modes might cause some inaccuracy at results of upper stories. In CMP procedure, estimation of modal participating factors is important and choosing inadequate modes may cause large errors. In this paper some changes have been applied to the CMP procedure to improve accuracy of the results and the modified method is proposed and named modified consecutive modal pushover (MCMP) procedure. In this modified method the contribution of mode is used of effective modal participating mass ratio. The comparison of MCMP procedure to exact values derived by nonlinear response history analysis (NL-RHA) demonstrated the reliable predictions and it can overcome the limitations of traditional pushover analysis.     

Displacement estimation of nonlinear structures using the force analogy method

Significant effort has gone toward developing accurate and efficient displacement estimation procedures for the nonlinear multi‐degree‐of‐freedom (MDOF) system. Although the dynamic nonlinear analysis is capable of providing the high computational precision through the step‐by‐step time integration method, the simplified method is still expected and imperative for seismic design practices. The work presented in this paper focuses on the implementation of using the modal superposition method to estimate displacement responses of the nonlinear MDOF system based on the force analogy method (FAM). The current research demonstrated that the equation of motion for the nonlinear MDOF system can be decoupled, but other two governing equations in the FAM about the internal force, such as the moment and force of structural members, are not decomposable. Thus, the FAM is incorporated with the modal pushover analysis (MPA) method to determine the basic parameters of each mode such that the modal superposition method can be suitable for the solution of the nonlinear MDOF system. The procedure presented here is an approximately estimation method due to the application of MPA method. However, the value and potential for the maximum displacement estimation of the nonlinear MDOF system were demonstrated through the application in a framed structure. Copyright © 2014 John Wiley & Sons, Ltd.     

A consecutive modal pushover procedure for estimating the seismic demands of tall buildings

The nonlinear static procedure (NSP), based on pushover analysis, has become a favourite tool for use in practical applications for building evaluation and design verification. The NSP is, however, restricted to single-mode response. It is therefore valid for low-rise buildings where the behaviour is dominated by the fundamental vibration mode. It is well recognized that the seismic demands derived from the conventional NSP are greatly underestimated in the upper storeys of tall buildings, in which higher-mode contributions to the response are important. This paper presents a new pushover procedure which can take into account higher-mode effects. The procedure, which has been named the consecutive modal pushover (CMP) procedure, utilizes multi-stage and single-stage pushover analyses. The final structural responses are determined by enveloping the results of multi-stage and single-stage pushover analyses. The procedure is applied to four special steel moment-resisting frames with different heights. A comparison between estimates from the CMP procedure and the exact values obtained by nonlinear response history analysis (NL-RHA), as well as predictions from modal pushover analysis (MPA), has been carried out. It is demonstrated that the CMP procedure is able to effectively overcome the limitations of traditional pushover analysis, and to accurately predict the seismic demands of tall buildings.     

框架——剪力墙结构的静力弹塑性分析研究

静力弹塑性方法作为一种评价结构抗震性能和计算结构弹塑性变形的简化方法,近年来得到了广泛应用。但由于传统的定侧力模式的静力弹塑性方法只考虑第一振型,无法反映高层建筑结构的高阶振型影响。为考虑高阶振型的影响,Chopra在振型分解反应谱组合法的基础上,提出了MPA方法。本文首先讨论了应用MPA方法需注意的问题,然后用一个18层钢筋混凝土框架—剪力墙结构为算例,以逐步增量弹塑性时程分析结果为基准,对传统定侧力模式静力弹塑性方法和MPA方法的分析结果进行了对比研究。结果表明,相比于定侧力模式静力弹塑性分析结果,MPA方法的分析结果更接近弹塑性时程分析结果。     

Fragility assessment of high‐rise reinforced concrete buildings considering the effects of shear wall contributions

The effect of shear wall configurations on seismic responses of high‐rise RC buildings is investigated in this paper using fragility analysis method. Four lower high‐rise RC buildings that have the same plan dimensions and height but are different in configurations in lateral force resisting systems, were firstly designed following the standard code procedure. To consider uncertainties in earthquake motions, 16 real ground motion pairs were selected and scaled, then applied orthogonally to the four RC building models during the Incremental Dynamic Analysis (IDA). Fragility relationships were therefore derived based on the IDA results for the three limit states including slight damage, moderate damage and collapse to show the probabilistic comparison of seismic responses among the four buildings in both x and y‐directions. It was observed that generally adding shear walls will improve buildings' seismic performance at all limit states. However, shear wall configuration also plays a significant role in seismic behavior of the lower high‐rise regular RC buildings' and internal shear walls are generally more effective than external shear walls in improving building's seismic resistance. Copyright © 2016 John Wiley & Sons, Ltd.     

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

Pushover 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.     

Pushover方法的准确性和适用性研究

Pushover方法作为一种建筑结构弹塑性地震响应的简化近似计算方法和抗震性能评价方法已得到广泛应用。但由于其理论基础不严密,其准确性需要给予必要确认,同时其适用性也应受到一定的限制。本文以逐步增量弹塑性时程方法的结果为基准,分别以一个普通6层RC框架结构和一个18层RC框架-剪力墙结构为例,对Pushover方法的准确性和适用性进行了分析研究。结果表明,Pushover方法仅适用于以第一振型为主的高度不大的结构,且应采用两种以上的侧力模式;对于高阶振型影响较大的结构,该方法的准确性较差,承载力预测显著偏低。     

考虑高阶振型影响的非自适应Pushover分析方法的研究进展

近年来,Pushover分析方法作为一种评估建筑结构抗震性能的方法得到了广泛的应用,而且已经被列入许多国家的建筑抗震设计规范之中。由于传统的Pushover分析方法存在许多不足之处,为此很多学者进行了深入的研究并提出了一系列的改进方法。本文结合模态非耦联弹塑性时程分析方法的基本理论,简述了多种考虑高阶振型影响的非自适应Pushover分析方法,并将其中一些方法的分析结果与采用非线性时程分析方法所得的结果进行比较,评价了它们的准确性,最后指出这些Pushover分析方法存在的问题和未来发展方向。     

Incremental dynamic collapse analysis of RC core‐wall tall buildings considering spatial seismic response distributions

Despite wide‐ranging studies on fragility analysis and collapse safety assessment of short to medium‐rise reinforced concrete (RC) structures, a new interest in the topic is still valuable and even necessary for tall RC buildings. This study aims at establishing fragility relationships as well as collapse probability of high‐rise RC core‐wall buildings under maximum considered earthquake ground motions. This study is carried out in a probabilistic framework on a case study of a fully 3‐dimensional numerical model developed to simulate seismic behavior of a 42‐story building having a RC core‐wall system. Proposing planar and vertical distributions of ductility and damage indices, the incremental dynamic analysis, and the multi‐direction nonlinear static (pushover) analyses were employed to reach the research goal. Median collapse‐level capacities were defined in terms of seismic responses (e.g., ductility/damage indices) as well as several intensity measures by employing statistical analyses and cumulative density functions. Available and acceptable collapse margin ratios were next estimated to quantify collapse safety at maximum considered earthquake shaking level. On an average basis, the statistics indicated 9%–10% and 5%–6% collapse probability of the building subjected to near‐ and far‐field ground motions, respectively.