Effects of soil‐structure interaction and lateral design load pattern on performance‐based plastic design of steel moment resisting frames

The effects soil‐structure interaction (SSI) and lateral design load‐pattern are investigated on the seismic response of steel moment‐resisting frames (SMRFs) designed with a performance‐based plastic design (PBPD) method through a comprehensive analytical study on a series of 4‐, 8‐, 12‐, 14‐, and 16‐story models. The cone model is adopted to simulate SSI effects. A set of 20 strong earthquake records are used to examine the effects of different design parameters including fundamental period, design load‐pattern, target ductility, and base flexibility. It is shown that the lateral design load pattern can considerably affect the inelastic strength demands of SSI systems. The best design load patterns are then identified for the selected frames. Although SSI effects are usually ignored in the design of conventional structures, the results indicate that SSI can considerably influence the seismic performance of SMRFs. By increasing the base flexibility, the ductility demand in lower story levels decreases and the maximum demand shifts to the higher stories. The strength reduction factor of SMRFs also reduces by increasing the SSI effects, which implies the fixed‐base assumption may lead to underestimated designs for SSI systems. To address this issue, new ductility‐dependent strength reduction factors are proposed for multistory SMRFs with flexible base conditions.     

设计性能目标下RC框架结构抗倒塌能力研究

针对小震丙类、小震乙类、中震不屈服和中震弹性4个性能目标,采用增量动力时程分析方法（IDA）对钢筋混凝土框架结构的抗倒塌能力进行了分析。以小震丙类建筑为基准,研究结果表明：抗震措施和地震作用是影响结构抗震性能的重要因素;严格按照抗震规范设计的框架结构,具有较高的安全储备,基本上能够达到“大震不倒”的性能目标;6度设防时,按乙类建筑提高抗震措施或按中震性能目标提高设计地震作用,对结构的抗倒塌能力影响不大;7度设防时,按中震性能目标设计能显著提高结构的抗倒塌能力;8度设防时,提高抗震措施等级和提高设计地震作用都能够大幅提高结构的抗倒塌能力,尤其按中震设计的钢筋混凝土框架结构能够抵御加速度峰值1000gal以上的地震作用。     

Strength reduction factor for MDOF soil–structure systems

In most of the seismic design provision, the concept of strength reduction factor has been developed to account for inelastic behavior of structures under seismic excitations. Most recent studies considered soil–structure interaction (SSI) in inelastic response analysis are mainly based on idealized structural models of single degree‐of‐freedom (SDOF) systems. However, an SDOF system might not be able to well capture the SSI and structural response characteristics of real multiple degrees‐of‐freedom (MDOF) systems. In this paper, through a comprehensive parametric study of 21600 MDOF and its equivalent SDOF (E‐SDOF) systems subjected to an ensemble of 30 earthquake ground motions recorded on alluvium and soft soils, effects of SSI on strength reduction factor of MDOF systems have been intensively investigated. It is concluded that generally, SSI reduces the strength reduction factor of both MDOF and more intensively SDOF systems. However, depending on the number of stories, soil flexibility, aspect ratio and inelastic range of vibration, the strength reduction factor of MDOF systems could be significantly different from that of E‐SDOF systems. A new simplified equation, which is a function of fixed‐base fundamental period, ductility ratio, the number of stories, structure slenderness ratio and dimensionless frequency, is proposed to estimate strength reduction factors for MDOF soil–structure systems. Copyright © 2012 John Wiley & Sons, Ltd.     

Nonlinear seismic response of reinforced‐concrete free‐standing towers with application to TV towers on flexible foundations

Reinforced‐concrete (R/C) free‐standing towers such as TV towers are often analysed using elastic analyses as fixed‐base cantilever beams, ignoring the effect of soil–structure interaction. To take the capacity of structures after yielding into account, most designers usually prefer to decrease the peak values of the elastic response spectrum for the maximum credible earthquake (MCE) anticipated at the site by a factor called the ductility capacity factor, which varies with the design earthquake level and the structural characteristics of the structure neglecting the effect of supporting soil. To investigate the effect of foundation flexibility on the response of R/C free‐standing towers deforming into their inelastic range during intense ground shaking, a linear sway‐rocking model is applied in numerical modelling of the soil–structure system. The effect of concrete cracking and reinforcement yielding on the elements used in the structure modelling is taken into account by introducing a nonlinear model for R/C frame elements using the moment–curvature (M–?) relation. A method called pseudo‐dynamic analysis is presented to quantify the inelastic seismic response spectrum of a soil–R/C free‐standing system using response spectrum analysis method and push‐over analysis technique. The earthquake responses of cracked and uncracked systems for a practical TV tower and a practical range of soil shear wave velocity are calculated and compared with the objective of understanding how soil–structure interaction influences structural responses. Copyright © 2002 John Wiley & Sons, Ltd.     

Overstrength and force reduction factors of multistorey reinforced‐concrete buildings

This paper addresses the issue of horizontal overstrength in modern code‐designed reinforced‐concrete (RC) buildings. The relationship between the lateral capacity, the design force reduction factor, the ductility level and the overstrength factor are investigated. The lateral capacity and the overstrength factor are estimated by means of inelastic static pushover as well as time‐history collapse analysis for 12 buildings of various characteristics representing a wide range of contemporary RC buildings. The importance of employing the elongated periods of structures to obtain the design forces is emphasized. Predicting this period from free vibration analysis by employing ‘effective’ flexural stiffnesses is investigated. A direct relationship between the force reduction factor used in design and the lateral capacity of structures is confirmed in this study. Moreover, conservative overstrength of medium and low period RC buildings designed according to Eurocode 8 is proposed. Finally, the implication of the force reduction factor on the commonly utilized overstrength definition is highlighted. Advantages of using an additional measure of response alongside the overstrength factor are emphasized. This is the ratio between the overstrength factor and the force reduction factor and is termed the inherent overstrength (Ω _i). The suggested measure provides more meaningful results of reserve strength and structural response than overstrength and force reduction factors. Copyright © 2002 John Wiley & Sons, Ltd.     

钢筋混凝土框架结构基于性能的抗震设计方法

以变形需求作为设计参数,阐明了RC框架结构基于性能的抗震设计方法的基本原理及步骤：利用弹塑性位移谱法求解结构的位移与变形需求,在层间位移角满足特定要求后,将梁柱塑性铰区的转动量值作为性能设计的参数,结合预期的性能目标由梁柱性能设计方程进行构件变形能力设计。以-10层框架结构为例,给出了RC框架结构基于性能的抗震设计的完整过程,并通过弹塑性时程分析作了比较验证。结果表明：弹塑性位移谱法求解结构位移需求是一种可为工程接受的、简便有效的方法,通过梁柱性能设计方程对变形能力进行定量设计,可将结构的破损程度控制在预先设定的性能目标范围内。     

Analytical investigation of response modification (behaviour) factor,R, for reinforced concrete frames rehabilitated by steel chevron bracing

Steel bracing of reinforced concrete (RC) frames has received noticeable attention in recent years as a retrofitting measure to increase the shear capacity of the existing RC buildings. In order to evaluate the seismic behaviour of steel-braced RC frames, some key response parameters, including the ductility and the overstrength factors, should first be determined. These two parameters are incorporated in structural design through a force reduction or a response modification factor. In this paper, the ductility and the overstrength factors as well as the response modification factor (or seismic behaviour factor) for steel chevron-braced RC frames have been evaluated by performing inelastic pushover analyses of brace-frame systems of different heights and configurations. The effects of some parameters influencing the value of behaviour factor, including the height of the frame and share of bracing system from the applied lateral load have been investigated. It is found that the latter parameter has a more localised effect on the R values and its influence does not warrant generalisation at this stage. However, the height of this type of lateral load-resisting system has a profound effect on the R factor, as it directly affects the ductility capacity of the dual system. Finally, based on the findings presented in the article, tentative R values have been proposed for steel chevron-braced moment-resisting RC frame dual systems for different ductility demands and compared with different type of bracing systems.     

Floor response spectra for light components mounted on regular moment-resisting frame structures

The peak acceleration demands for acceleration-sensitive nonstructural components supported on elastic and inelastic regular moment-resisting frame structures are statistically analyzed. The responses of a variety of stiff and flexible frame structures (with 3, 6, 9, and 18 stories) subjected to a set of 40 ground motions are evaluated. The nonstructural components under consideration are those that can be represented by single-degree-of-freedom systems with masses that are small compared to the total mass of the supporting structure. This study evaluates and quantifies the dependence of peak component accelerations on the location of the nonstructural component in the structure, the damping ratio of the component, and the properties of the supporting structure such as its modal periods, height, stiffness distribution, and strength. The results show that current seismic code provisions will not always provide an adequate characterization of peak component accelerations. Recommendations are provided to estimate peak acceleration demands for the design of nonstructural components mounted on inelastic frame structures.     

钢筋混凝土框架基于位移和延性的等效地震荷载计算

本文提出了在基于位移的抗震设计中利用弹塑性反应谱计算等效地震荷载即基底剪力的方法,并结合相应我国抗震规范的弹塑性反应谱对一个四层钢筋混凝土框架进行了基于不同延性及位移需求的等效地震荷载的计算,最后讨论了基于位移的抗震设计与目前抗震规范设计方法之间的联系与区别,并提出了需要进一步研究的问题.     

钢筋混凝土杆系结构的耗能机理和延性设计

在分析了地震荷载作用下结构刚度对结构破坏的影响的基础上，研究了在地震荷载作用下杆系结构的耗能机理和影响结构构件特性的各种因素，提出了框架结构延性设计的理论方法和计算公式，结合工程实例探讨了影响框架结构延性的因素（材料强度、钢筋数量、箍筋、截面轴向力、截面形状等）。最后得出结论：只有同时满足强度和延性要求并使之很好匹配的结构抗震设计才能在地震荷载下发挥其抗震作用。     

配置HRB500钢筋的框架结构非弹性地震反应分析

为实现建筑行业的可持续发展,中国土木建筑工程界正在推广应用HRB500级高强钢筋,但是,以HRB500钢筋作为主要受力钢筋的混凝土结构的抗震性能研究还相对缺乏.该文按<混凝土结构设计规范>最新修订稿设计了3个配置不同强度钢筋的8度0.3 g区一级抗震等级的混凝土框架结构,并完成了该3个结构在多波输入下的非弹性地震响应分...     

Experimental and modeling study on the progressive collapse resistance of a reinforced concrete frame structure under a middle column removal scenario

A reinforced concrete (RC) frame structure is one of the widely used structural system. A localized damage caused by extreme events may lead to progressive collapse of entire structures. In this paper, progressive collapse test of three 1/3‐scaled reinforced concrete frame, including a single‐story without a slab, single‐story with a slab, and double‐story with slabs, are reported. Experimental results show that the progressive collapse process of RC frame consisted of five stages: an elastic stage, yield stage, beam mechanism stage, transient stage and catenary stage. The reinforced concrete slabs contribute to large progressive collapse resistance force compared with the specimen without slab. Furthermore, validation of the test results by using a refined solid finite element model was established. The effect of extensive parameters, including slab thickness, beam section height, seismic design intensity, and so forth, on the progressive collapse performance of RC frame structures was simulated as well. The simulation results indicated that the collapse resistance of RC structures was substantially improved with the increased of the slab thickness and seismic design intensity. Finally, a simplified model is proposed in accordance with experimental and numerical results to calculate the collapse resistance of RC frame structures.     

Seismic response of a submerged spherical structure supported on a flexible foundation

The seismic response of a submerged spherical structure supported on a flexible foundation is investigated. An optimum yield displacement is found to exist for which the maximum displacement of the system is a minimum. Response spectra for optimum yield displacement and the corresponding ductility factor, and the associated lateral force coefficient in the optimum system, are generated for the N-S component of the May 1940 El Centro earthquake for different shear wave velocities and strain hardening ratios. The results indicate that for stiffer structures, the soil condition has a significant influence on the optimum yield displacement and corresponding ductility factor. For the system with optimum yield displacement, the maximum displacement is always less than that of the elastic system. Thus, the response spectra may be used as a guide in selecting members for a displacement constrained design.     

Flexural ductility design of high‐strength concrete columns

In the seismic design of a structure, it is necessary to provide not only sufficient strength, but also a minimum level of flexural ductility for reinforced concrete (RC) columns. Eurocode EN1998‐1 directly specifies such minimum flexural ductility, while Chinese code GB50011 limits the normalized design axial force to achieve a nominal minimum flexural ductility. American code ACI 318‐08 uses the tension steel strain at peak resisting moment to control the failure mode. To provide the required flexural ductility, a much lower axial strength reduction factor is assigned to compression‐controlled failure than to tension‐controlled failure. To develop an effective strategy for flexural ductility design of RC columns, it is necessary to identify the essential parameters and control them properly. This is particularly important to those cast of high‐strength concrete that is inherently more brittle. The essential parameters identified include the maximum normalized axial force and maximum normalized neutral axis depth at peak resisting moment, as they help to guarantee various flexural ductility requirements. Their relationship with the flexural ductility is studied using a rigorous full‐range moment‐curvature analysis procedure. Empirical formulae and tables are also developed to facilitate flexural ductility design of RC columns. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of elaborate plastic hinge definition on the pushover analysis of reinforced concrete buildings

Due to its simplicity, lumped plasticity approach is usually used for nonlinear characterization of reinforced concrete (RC) members in pushover analysis. In this approach, the inelastic force deformation of hinges could be defined as either the nonlinear properties suggested in FEMA‐356 and ATC‐40 or defined hinges quantified on the basis of the properties of RC members. However, the nonlinear response of RC structures relies heavily on the inelastic properties of the structural members concentrated in the plastic hinges. To provide a comparative study, this paper attempts to show the results of pushover analyses of RC structures modeled on the basis of the FEMA nonlinear hinges and defined hinges. Following the validation of the adopted models, the force–deformation curves of the defined hinges are determined in a rigorous approach considering the material inelastic behavior, reinforcement details and dimensions of the members. For the case studies, two four‐story and one eight‐story frames are considered in order to represent low‐rise and mid‐rise buildings with different ductility. Nonlinear responses of both models are elaborated in terms of the inter‐story drift, hinging pattern, failure mechanism and the pushover curve. It is confirmed that FEMA hinges underestimate the strength and more importantly the displacement capacity, especially for the frame possessing low ductility. Copyright © 2012 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.     

Effect of small axial force on flexural ductility design of high‐strength concrete beams

Small axial forces may appear in beams in a reinforced concrete (RC) structure. The presence of compressive axial force, even at a low level, has an adverse effect on the flexural ductility of RC beams, which is a key attribute for seismic design. For example, Eurocode EN1998‐1 explicitly specifies such minimum flexural ductility, whereas Chinese code GB50011 limits the depth of equivalent rectangular stress block at peak resisting moment to achieve indirectly a certain nominal flexural ductility. Therefore, ignoring the presence of compressive axial force may be risky. In this study, the effect of small compressive axial force on the flexural ductility performance of both normal‐strength and high‐strength concrete beams is evaluated on the basis of a rigorous full‐range moment–curvature analysis. An effective strategy for flexural ductility design of RC beams with small compressive axial force is identified so that various flexural ductility requirements can be satisfied. The essential control parameter proposed is the maximum difference of tension and compression reinforcement ratios. Empirical formulae and tables are developed for convenient implementation. Copyright © 2015 John Wiley & Sons, Ltd.     

防屈曲支撑-钢筋混凝土框架结构基于能量平衡的抗震塑性设计

为确定防屈曲支撑在结构中的布置方式以使结构抗震性能充分发挥,提出了基于能量平衡的防屈曲支撑 钢筋混凝土框架结构抗震塑性设计方法。构建了结构的“强柱弱梁”整体屈服机制,采用侧力比将总结构体系离散为防屈曲支撑体系和纯框架体系,并建立了结构的双线性能力曲线。基于能量平衡方法计算结构的设计基底剪力并分别得到支撑体系和框架体系的设计侧向力,进而完成支撑的截面设计。按照塑性内力分配机制和考虑支撑屈服后性能,计算梁柱构件内力需求。以一幢5层结构为例,分别设计了不同侧力比的14个结构模型,对比了基底剪力、防屈曲支撑面积和梁柱钢筋用量等。通过22条地震波下的弹塑性时程分析,研究了不同侧力比结构的最大层间位移角、屈服机制、楼层剪力比、支撑最大位移延性、累积位移延性和结构残余层间位移角。分析结果表明：所提出的方法能实现结构的预期失效模式,并满足结构的抗震性能要求,并建议设计侧力比选取在0.3~0.5之间。     

不同连接方式预制复合墙板填充墙对框架抗震性能的影响

为研究不同连接方式的预制复合墙板填充墙对钢筋混凝土(RC)框架抗震性能的影响,进行了1榀RC纯框架、1榀普通砌块填充墙RC框架及3榀连接方式不同的复合墙板填充墙RC框架的低周反复加载试验,复合墙板填充墙与框架之间的连接方式分为刚性连接、半柔性连接和柔性连接3种。通过试验分析不同连接方式的墙板填充墙对框架承载力、刚度、延性、耗能能力等的影响。试验结果表明：刚性连接复合墙板填充墙能使RC框架的抗侧刚度、水平承载力大幅提高,同时延性变差;柔性连接和半柔性连接的复合墙板填充墙RC框架的抗侧刚度、水平承载力高于砌块填充墙RC框架的,延性好于砌块填充墙RC框架;加载过程中,半柔性连接的复合墙板填充墙RC框架墙板和框架依次破坏,表现出良好的耗能能力。建议工程应用中复合墙板填充墙与框架之间采用柔性连接或半柔性连接构造方式。     

ISCS method for the performance‐based seismic design of vertically irregular reinforced concrete frame structures

The procedure to obtain the inelastic demand curves for the multi‐degree‐of‐freedom system, composed of inter‐story shear versus inter‐story displacement curve is introduced. The demand curves are established by using mode spectrum method, and the dynamical characteristic of structure under different earthquake hazard levels is taken into account. The relation of structure performance object and displacement ductility is adopted to deduce the relation of structure performance object and inter‐story demand curve. Therefore, the inter‐story demand curves take into account the inelastic behavior of structure under earthquake action adequately. Then, considering the seismic responding characteristic and the capacity curve of the frame structure, a new method named Inter‐Story Capacity Spectrum (ISCS) is put forward for the performance‐based seismic design of vertically irregular frame structures. Examples are presented to demonstrate the applicability and the utility of the proposed method. It is concluded that the new method can control the inter‐story drift, the order and position of hinges of vertically irregular structures under different earthquake hazard levels. Comparing with time‐history analysis method, it leans to safe and is superior to direct displacement‐based design method. Copyright © 2011 John Wiley & Sons, Ltd.