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.     

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.     

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.     

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.     

Evaluation of seismic behavior improvement in RC MRFs retrofitted by controlled rocking wall systems

Using rocking wall systems is a recent technique to improve seismic behavior in reinforced concrete structures. This paper compares three 10‐story and three 20‐story reinforced concrete frames (moment‐resisting frames) with intermediate ductility, reinforced concrete frames with shear wall, and reinforced concrete frames with controlled rocking wall (RCRW) by the use of pushover analysis. At the end of the research, the wall in a 20‐story RCRW system is post‐tensioned then analyzed, and its results were compared with RCRW results. Simulation and numerical analysis were performed with OpenSees software. The results show that plastic hinge formation and inter‐story drifts are well distributed in the structure with rocking wall system in comparison with the other systems. Meanwhile, energy dissipation and displacement ductility are increased in RCRW frames. With post‐tensioning wall in RCRW, the drift ratios are more uniformed. Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental study on seismic performance of prefabricated rocking wall frame structure

为避免罕遇地震作用下传统混凝土摇摆墙的开裂损伤且充分利用装配式结构的便捷性，设计了采用双层钢板混凝土墙的摇摆墙结构体系，在浇筑混凝土时双层钢板可充当摇摆墙构件的外模板。跨越结构上、下层的摇摆墙之间采用高强螺栓连接，摇摆墙在工厂预制后运到施工现场进行安装。选用金属阻尼器作为耗能连接件连接摇摆墙与主体框架结构，同时传递层剪力并耗散地震能量。为研究该装配式摇摆墙-框架结构的抗震性能，设计并制作了一个纯框架和两个摇摆墙-框架，其中两个摇摆墙-框架的区别在于金属阻尼器的安装位置不同。通过拟静力试验分析了其破坏模式及抗震性能。试验结果表明：预制装配式摇摆墙与主体框架结构协同工作性能良好，金属阻尼器耗能效果得到充分利用，结构承载力、耗能能力大幅增加；在水平位移较大时摇摆墙竖向发生刚体位移，对整体结构的抗震性能产生一定影响，后续将采用附加预应力的形式减轻摇摆墙竖向抬升的影响。     

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.     

装配式摇摆墙-框架结构抗震性能试验研究

为避免罕遇地震作用下传统混凝土摇摆墙的开裂损伤且充分利用装配式结构的便捷性,设计了采用双层钢板混凝土墙的摇摆墙结构体系,在浇筑混凝土时双层钢板可充当摇摆墙构件的外模板。跨越结构上、下层的摇摆墙之间采用高强螺栓连接,摇摆墙在工厂预制后运到施工现场进行安装。选用金属阻尼器作为耗能连接件连接摇摆墙与主体框架结构,同时传递层剪力并耗散地震能量。为研究该装配式摇摆墙-框架结构的抗震性能,设计并制作了一个纯框架和两个摇摆墙-框架,其中两个摇摆墙-框架的区别在于金属阻尼器的安装位置不同。通过拟静力试验分析了其破坏模式及抗震性能。试验结果表明：预制装配式摇摆墙与主体框架结构协同工作性能良好,金属阻尼器耗能效果得到充分利用,结构承载力、耗能能力大幅增加;在水平位移较大时摇摆墙竖向发生刚体位移,对整体结构的抗震性能产生一定影响,后续将采用附加预应力的形式减轻摇摆墙竖向抬升的影响。     

设置碟形弹簧的框架-摇摆墙结构抗震性能试验研究

受控摇摆墙通常采用预应力筋的形式实现，预应力筋基础锚固施工困难，墙体摇摆幅度很小且易与基础发生碰撞。为解决上述问题，研发了一种受控摇摆墙，主要通过基于碟形弹簧的装置实现墙体的受控约束，墙体与主体框架、基础分别采用耗能连接件和V形支撑连接。设计制作了缩尺比为1∶2的对比框架与框架-摇摆墙试件，通过低周往复加载试验研究其抗震性能、破坏模式和自复位特性。结果表明，设置碟形弹簧的框架-摇摆墙较对比框架承载力提高了107.1%，且具有更好的刚度退化性能与耗能性能，框架结构的变形模式得到改善，使得各层的层间位移趋于均匀。连接件是影响框架-摇摆墙结构耗能及协调层间变形的关键，应进一步研究其改进措施及优化设计。     

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.     

Equivalent linear model for fully self‐centering earthquake‐resisting systems

Modern rocking and stepping cores have been known as the efficient self‐centering earthquake‐resisting systems (SC‐ERSs). The current article proposes an approximate equivalent linear (EL) model for rapid estimation of the SC‐ERS displacement. An equivalent damping ratio and effective stiffness are formulated for flag‐shaped hysteresis of a fully SC‐ERS. The approximate EL model is first established using secant stiffness and Jacobsen's damping model. Nonlinear response history analyses are carried out to compare exact and approximated peak displacements. Findings reveal that EL analysis of the SC‐ERS based on Jacobsen's damping leads to underestimation of the maximum inelastic displacement. Accordingly, a new optimal damping formula is proposed using a genetic algorithm and nonlinear regression analyses. The improved EL model is validated by practical examples, and the results show acceptable accuracy in design‐level displacement estimation.     

Forward directivity near‐fault and far‐fault ground motion effects on the behavior of reinforced concrete wall tall buildings with one and more plastic hinges

Near‐fault (NF) ground motion having forward directivity and far‐fault (FF) earthquakes can generate different responses on tall reinforced concrete cantilever walls. In this paper, the behavior of the core wall buildings were examined by performing nonlinear time history analyses on 20‐story, 30‐story and 40‐story fiber element models. The concept of one, two, three and extended plastic hinge in the core walls subjected to the NF motions having forward directivity (pulse‐like) and FF motion was studied by carrying out inelastic dynamic analysis. At the upper levels of the walls, NF pulse‐like ground motions can produce considerably larger curvature ductility, inter‐story drift and displacement demands as compared with the FF motions. A new approach was proposed to obtain the moment demand and reinforcement required to balance the curvature ductility demand along the height of a core wall. Copyright © 2015 John Wiley & Sons, Ltd.     

山地掉层框架-摇摆墙结构抗震性能研究

竖向刚度不均匀是山地掉层框架结构的突出特点,其在地震作用下的动力反应特性与普通框架结构存在较大的差异,山地掉层框架结构在地震中易在上接地层出现层屈服破坏机制。为改善该类结构的抗震性能,在山地掉层框架结构外部附加底部铰接、具有一定转动能力的摇摆墙,形成山地掉层框架-摇摆墙结构体系。对3个总层数为七层的掉不同层不同跨的山地掉层框架摇摆墙结构进行动力弹塑性分析结果表明,附加摇摆墙的山地掉层框架结构的基本周期较原结构的相差不大。摇摆墙设置在不同位置的山地掉层框架摇摆墙结构动力反应特性不同。摇摆墙的加入能够均匀结构各层层间变形,有效改善山地掉层框架结构的抗震性能,可避免原薄弱层上接地层的破坏集中现象,实现了整体耗能机制。     

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.     

Performance evaluation of infilled rocking wall frame structure

Conventional reinforced concrete (RC) frame structures are prone to soft‐story mechanism. This deficiency can be eliminated by introducing rocking wall system. Previously studied rocking wall systems usually have the rocking wall situated outside the frame, which results in some challenges and inconvenience. In the study, a novel infilled rocking wall frame (IRWF) system is proposed, which uses infilled RC wall to create a rocking wall within the RC frame. To evaluate seismic performance of the proposed system, both an IRWF model and an RC frame (RCF) model were designed according to Chinese seismic design code. Time history analysis and incremental dynamic analysis were conducted to compare both systems. The results show that IRWF system has more uniform drift and higher collapse margin ratio compared to the RCF system. Economic evaluation of IRWF system was investigated using the state‐of‐the‐art ATC‐58 performance‐based assessment methodology. The result shows superior performance of the IRWF system. The annualized loss of the IRWF model is about 28% less than the RCF model. This shows IRWF system is a viable and efficient alternative resilient seismic force resisting system.     

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.     

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.     

Experimental study on the seismic behavior of a shear wall with concrete‐filled steel tubular frames and a corrugated steel plate

Shear walls and core tubes in shear walls constitute the core anti‐earthquake vertical systems of high‐rise buildings. This paper proposes a new type of composite shear wall with concrete‐filled steel tubular frames and corrugated steel plates. The seismic behavior of the new shear wall is studied using a cyclic loading test and damage analysis. The failure mode, load‐carrying capacity, ductility, stiffness degradation, hysteresis behavior, and energy dissipating capacity exhibited in the test are studied. The test results show that when the proposed wall is broken, the tension side of concrete‐filled steel tubes is torn. The concrete at the bottom of the wall is detached and peels off along the through cracks. The energy dissipation capacity of concrete walls is more fully utilized. The proposed wall exhibits excellent deformability, energy dissipation capacity, and the stiffness degradation was slower than that of other walls. The use of corrugated steel plate significantly improved the seismic performance while simultaneously increasing the ductility and reducing the damage. In addition, this paper modified the energy dissipation factor in the Park & Ang model based on the situation of the specimen and experiment. It can be used to evaluate the damage degree of this new type of shear wall.     

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.