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.     

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

The seismic response of the high‐rise reinforced concrete (RC) wall structures is really complicated as several vibration modes other than the fundamental mode normally contribute significantly to the response—commonly recognized as ‘higher mode effects’. Response spectrum analysis (RSA) procedure, which can account for higher mode effects, is usually employed to compute the seismic design demand for the high‐rise structures. Recent studies show that the inelastic seismic force demands obtained from the rigorous nonlinear response history analysis procedure are much larger than the seismic force design demands obtained from the code‐based RSA procedure for the high‐rise RC wall structures. Though, the nonlinear response history analysis procedure is widely accepted for its ability to provide the most accurate estimate of nonlinear seismic responses, the obtained responses are generally so complex that it is quite difficult for engineers to grasp the overall picture of the responses and gain some insight into them and use them to understand the cause of high seismic demands. Another important issue related to the nonlinear seismic response prediction of the high‐rise RC wall structures is the realistic and accurate numerical modeling of RC walls. In this study, a simplified but reasonably accurate procedure called the uncoupled modal response history analysis procedure is used to interpret the complex nonlinear behavior of high‐rise RC wall structures. Moreover, a finite element model based on modified compression field theory is employed for accurate numerical modeling of RC walls by incorporating the axial‐flexure‐shear interaction. This study, by making use of a better computer modeling approach and an in‐depth analysis by modal decomposition, aims to resolve some of the unanswered questions regarding realistic prediction of nonlinear seismic demands of high‐rise structures.     

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.     

A displacement‐based adaptive pushover method considering modal sign reversal for RC frame structures

Nonlinear static procedures are favored tools for practical applications in the structural engineering profession. However, some limitations are associated with them, including their deficiencies to properly reflect higher modal effects and inertial seismic forces fluctuations in their responses. Some different adaptive pushover methods intended to improve these limitations have been proposed in the literature, but each one has come out with a special deficiency. In this study, based on the concepts of the displacement‐based adaptive pushover, a new dual‐run procedure method called Improved DAP (IDAP) has been developed, aiming to improve higher modal and sign reversal consideration of pushover methods. The seismic scope of this study has been focused on near‐fault regions. Four concrete SMRF with different heights have been employed for the evaluations. The results of the proposed method in terms of capacity curves, interstory and shear profiles are compared with those of the IDA method. Results indicate that the ability of the new method in reproducing seismic story forces and capacity curves, as well as interstory drifts, has been improved in comparison with its primitive counterpart. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

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.     

Influence of design procedures on the seismic response of bi‐eccentric plan‐asymmetric systems

This paper investigates, by means of idealized one‐storey models, the seismic behaviour of bi‐eccentric plan‐asymmetric structures and the influence of different design practices on it. All the examined design procedures are based on the use of modal analysis, in order to grant, in any case, a reliable estimate of the elastic response. The first procedure requires the standard application of modal analysis (nominal positions of mass and stiffness centres), while the others employ a double application of the same analysis to reduce the ductility demand in occurrence of strong ground motions. Furthermore, within the aforementioned procedures, the importance and effectiveness of the combination of design internal forces induced by two orthogonal seismic components are discussed. In order to obtain statistically representative information on the structural response to seismic loads the models are subjected to a set of 30 bidirectional accelerograms. A wide parametric analysis allows observations and conclusions, which may be considered reliable for asymmetric models characterized by a wide range of values of the structural parameters. Copyright © 2006 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.     

Design of steel plate shear walls considering inelastic drift demand

The unstiffened steel plate shear wall (SPSW) system has emerged as a promising lateral load resisting system in recent years. However, seismic code provisions for these systems are still based on elastic force-based design methodologies. Considering the ever-increasing demands of efficient and reliable design procedures, a shift towards performance-based seismic design (PBSD) procedure is proposed in this work. The proposed PBSD procedure for SPSW systems is based on a target inelastic drift and pre-selected yield mechanism. This design procedure is simple, yet it aims at an advanced design criterion. The proposed procedure is tested on a four-story test building with different steel panel aspect ratios for different target drifts under selected strong motion scenarios. The designs are checked under the selected ground motion scenarios through nonlinear response-history analyses. The actual inelastic drift demands are found to be close to the selected target drifts. In addition, the displacement profiles at peak responses are also compared with the selected yield mechanism. Future modifications required for this design procedure for different SPSW configurations are identified based on these test cases.     

Assessment of inelastic response of buildings using force‐ and displacement‐based approaches

In recognition of the increasing importance of accurate seismic vulnerability assessment, this paper deals with procedures and the application of inelastic acceleration and displacement spectra in the seismic assessment of buildings. An identification procedure is outlined, whereby an equivalent single degree of freedom (SDOF) system is devised to represent the building. The SDOF system characteristics (stiffness, strength, post‐peak force response and ductility) are readily evaluated from observation of the seismic response of buildings and simple mechanics. The characteristics are then tuned using measurements from instrumented buildings. Based on the earthquake scenario and structural response characteristics, appropriate inelastic acceleration and displacement spectra are selected and used to ‘predict’ the response. Comparison between the measured and predicted responses for the five buildings studied in the paper confirm the feasibility of the procedure and the realism of the results. Copyright © 2000 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.     

Application of earthquake‐induced collapse analysis in design optimization of a supertall building

In recent years, a combination of rapid construction of supertall buildings and frequent occurrence of strong earthquakes worldwide demands a rational seismic design method for structures of this kind. Although earthquake‐induced collapse analysis is one of the most efficient methods to quantify the collapse resistance of buildings, little research has been reported on using the collapse analysis to evaluate the seismic safety of supertall buildings during the design stage. To optimize the design taking into account earthquake‐induced collapses, a real‐world supertall building with a height greater than 500 m is investigated in this work. Throughout its design procedure, earthquake‐induced collapse analyses are performed to optimize the design at three different levels (i.e. the structural system level, design parameter level and component level). At the structural system level, the influence of different lateral force‐resisting systems on the collapse resistance is discussed; at the design parameter level, the influence of minimum base shear force is discussed; and at the component level, the influence of high‐performance shear wall on the collapse resistance is studied. Based on these discussions, the optimal design scheme of the building is established to improve the seismic safety while maintaining the cost of construction. Given more and more supertall buildings will be constructed with new structural system and components, this work will provide important references for the seismic design of supertall buildings and the corresponding collapse resistance research in the future. Copyright © 2016 John Wiley & Sons, Ltd.     

Dynamic characteristics and viscous dampers design for pile‐soil‐structure system

A series of large‐scale shaking table tests are conducted on tall buildings with and without energy dissipation devices on soft soils in pile group foundations, representing pile‐soil‐structure interaction (PSSI) system and the corresponding fixed‐base situations. The superstructure is a 12‐story reinforced concrete (RC) frame. The dynamic characteristics of the test models show that the frequencies decrease and the damping ratio increase in PSSI system by comparison with the fixed‐base structures. The mode shapes of PSSI system are different from that under fixed‐base condition, and the mode shapes of structure without dampers change greater than that with energy dissipation devices under various white noises. An improved method for structural dynamic characteristics, considering the impedance function of piles, is developed to address the issue of modal parameters with PSSI effect. In addition, the structural dynamic parameters of the large‐scale shaking table tests are identified using the modification method and other regulation methods, demonstrating that the improved approach is highly accurate and effective. Subsequently, a design procedure for viscous dampers of structures with PSSI effect is presented based on the dynamic characteristics of the system. Finally, the dynamic responses of the structure with viscous dampers in the practical engineering are decreased effectively, indicating the good performance of designed viscous dampers. The numerical results also show that the damping efficiency of interstory drift is larger than the acceleration and interstory shear force. Therefore, the improved modal parameters method, validated through a series large‐scale shaking table tests, is applicable for identifying dynamic characteristics of pile‐soil‐structure with energy dissipation devices system. The design procedure of viscous dampers, proved by a reinforced concrete frame structure located on a practical Shanghai soft site, can be employed to design the viscous dampers considering seismic PSSI effect.     

An introduction to the structural design of rocking wall‐frames with a view to collapse prevention,self‐alignment and repairability

The purpose of this article is to present a new method of analysis for the structural design of pin‐supported rocking wall‐moment frames with supplementary devices and post‐tensioned stabilizers. The function of the wall is to prevent soft story failure, impose uniform drift and provide support for the supplementary equipment. The proposed methodology lends itself well to several seismic design strategies, ranging from severe damage avoidance, to collapse prevention, to structural self‐alignment and repairability. Repairability means avoiding major damage to columns and foundations. The success of the resulting solutions is due to the single degree of freedom behavior of the combined system and the fact that its overall performance is not significantly affected by minor changes in the stiffness of the wall. The sensitivity of the response to wall rigidity is addressed by comparing the maximum elastic slope of the wall with a fraction of the specified uniform drift. The limitations of rocking wall‐moment frames, as viable lateral resisting systems, have been addressed. Several worked examples have been presented to provide insight and technical information that may not be readily available from electronic output. The proposed solutions are exact within the bounds of the theoretical assumptions and are ideally suited for manual as well as spreadsheet computations. Copyright © 2015 John Wiley & Sons, Ltd.     

消能摇摆高位隔震结构体系的地震反应特性

双段消能摇摆结构体系是通过两段串联的摇摆结构,控制主体结构各楼层在地震作用下均匀变形,抑制薄弱层的产生,也降低了主体结构对于摇摆结构的刚度需求。在变形集中的摇摆结构底部布设位移型阻尼器,可进一步提高结构的抗震性能。但是该体系存在承载力较低、上段结构地震反应相对较大的不足。基于此,提出了消能摇摆高位隔震结构体系,即在双段消能摇摆结构体系的分段楼层位置增设劲性支撑,以抑制上段结构的摇摆运动,提高结构的刚度与承载力;同时,下段结构允许发生摇摆,发挥高位隔震层的作用。以消能摇摆高位隔震结构体系为研究对象,分析对比了其他三种结构体系：传统支撑框架结构体系、双段消能摇摆结构体系、不含位移型阻尼器的摇摆高位隔震结构体系。采用OpenSees软件建立了弹塑性有限元分析模型,对四种结构体系进行弹塑性抗震分析和增量动力时程分析。研究表明,消能摇摆高位隔震结构体系的刚度与承载力较高,地震反应较小,抗震性能与抗倒塌性能良好。在摇摆结构分段位置加设劲性支撑层,可以抑制上段结构在地震作用下的变形,并发挥下段摇摆结构的隔震作用。布设于分段位置与摇摆结构底部的阻尼器,可以充分消耗地震能量,提高结构体系的抗震性能。     

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.     

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.     

Capacity design for composite partially restrained steel frame‐reinforced concrete infill walls with concealed vertical slits

This paper presents an innovative capacity‐based design procedure that aims to achieve the ideal seismic performance for the composite partially restrained (PR) steel frame‐reinforced concrete (RC) infill wall with concealed vertical slits (PSRCW‐CVS). The proposed method adopts the direct capacity design principles and preselected preferred plastic mechanism such that the RC infill wall undergoes ductile failure prior to the other steel components in the event of a rare‐level earthquake (i.e., earthquake with a 2% probability of exceedance in 50 years). Based on the ultimate resisting capacity of RC infill walls, the free‐body diagrams and simplified design formulae for the surrounding steel components, including the vertical boundary element (VBE), horizontal boundary element (HBE), PR connection, and shear connectors, were proposed. To demonstrate the reasonability of the capacity‐based design procedure, a five‐story PSRCW‐CVS structure was designed according to the proposed design method, followed by a series of nonlinear time history analyses. The overall seismic response of this example was evaluated in terms of story displacement, interstory drift ratio, residual story displacement, and residual interstory drift ratio. The proposed method yielded a more uniform interstory drift ratio distribution along the height of the five‐story PSRCW‐CVS structure. Structural damage was controlled by achieving the preselected preferred plastic mechanism.     

Experimental study of L‐shaped precast RC shear walls with middle cast‐in‐situ joint

Precast shear walls, as an environmentally friendly building system, have been vigorously developed in China. There are many vertical and horizontal joints on precast reinforced concrete shear wall system, which certainly have a significant effect on seismic performance of structures. In this paper, 3 L‐shaped precast reinforced concrete shear walls that were assembled by 2 precast parts through a middle cast‐in‐situ joint and a compared 1 completely cast‐in‐situ were tested under low frequency cyclic loading to investigate their seismic behaviors. The vertical distributed reinforcements in the three precast specimens were equivalently spliced by grouting sleeves arranged along the center line of the wall, and the horizontal reinforcements were directly anchored in cast‐in‐situ joints. The experimental results, including failure mode, yielding load and displacement, skeleton curve, energy dissipation, stiffness degradation, ductility, and so forth were presented in the paper. The results show that the precast specimens have similar bearing capacity whereas much better deformation capacity and ductility compared to the cast‐in‐situ specimen. Additionally, the experimental results of ultimate shear capacity of specimens were also compared with that of the calculation results. These results indicate that the tested precast shear walls have good and reliable seismic performance and can be used as a structural member in engineering projects.     

Integrated multi‐type sensor placement and response reconstruction method for high‐rise buildings under unknown seismic loading

Structural health monitoring system has been implemented on high‐rise buildings to provide real‐time measurement of structural responses for evaluating their serviceability, safety, and sustainability. However, because of the complex structural configuration of a high‐rise building and the limited number of sensors installed in the building, the complete evaluation of structural performance of the building in terms of the information directly recorded by a structural health monitoring system is almost impossible. This is particularly true when seismic‐induced ground motion is unknown. This paper thus proposes an integrated method that enables the optimal placement of multi‐type sensors on a high‐rise building on one hand and the reconstruction of structural responses and excitations using the information from the optimally located sensors on the other hand. The structural responses measured from multi‐type sensors are fused to estimate the full state of the building in the modal coordinates using Kalman filters, from which the structural responses at unmeasured locations and the seismic‐induced ground motion can be reconstructed. The optimal multi‐type sensor placement is simultaneously achieved by minimizing the overall estimation errors of structural responses at the locations of interest to a desired target level. A numerical study using a simplified finite element model of a high‐rise building is performed to illustrate the effectiveness and accuracy of the proposed method. The numerical results show that by using 3 types of sensors (inclinometers, Global Positioning System, and accelerometers), the proposed method offers an effective way to design a multi‐type sensor system, and the multi‐type sensors at their optimal locations can produce sufficient information on the response and excitation reconstruction.