延性需求谱在基于性能的抗震设计中的应用

基于性能的抗震设计理论涉及如何简便而合理地确定结构在指定强度地震下的弹塑性位移需求。本文给出了利用延性需求谱求解结构位移需求的一般步骤:借助模态Pushover分析将多自由度体系分解为几个非线性单自由度体系,以考虑各阶振型的影响;利用延性需求谱计算对应模态的等效单自由度体系的延性及位移需求,并以一定方式组合转化为多自由度体系位移需求。最后,通过算例分析表明:利用延性需求谱求解结构位移需求是一种具有一定精度可为工程接受的简便方法,在基于性能的抗震设计中具有较好的应用前景。     

Scaling of constant-ductility residual displacement spectrum

Structures undergoing inelastic displacements during earthquake ground motions are known to sustain some amount of residual displacements, which may make those unusable or unsafe. In this study an attempt is made to estimate residual displacements for elastic-perfectly-plastic single-degree-of-freedom oscillators with a given ductility ratio. Such oscillators belong to the class of bilinear hysteresis models applicable to steel structures, with post-yield-stiffness ratio taken as zero, and may be used for the conservative estimates of residual displacements when the post-yield-stiffness ratio is unlikely to become negative. Statistical estimation of residual displacement spectrum via normalization with respect to inelastic or elastic spectral displacements is considered and expressions are proposed for both types of normalizations. The statistical dependence of residual displacement on the seismological and site parameters and strong motion duration is also studied and a simple scaling model is proposed in terms of earthquake magnitude, epicentral distance, and geologic site condition parameter for the seismic region of western U.S.A. According to this model, the variation of residual displacement with period primarily depends on the site conditions, and the residual displacements are more sensitive to ductility ratio at low ductility ratios.     

Characterization of displacement demand for elastic and inelastic SDOF systems

The results of a research concerning the characterization of elastic and inelastic displacement spectral demand as a function of magnitude, source-to-site distance, and soil type are presented. The displacement spectra were computed for single degree of freedom systems subjected to a large set of strong ground motion records.In the elastic case, design displacement spectra, modeled in a simplified way with a bilinear shape in the period range 0–4 s, are then proposed for the estimation of the displacement demand to structures located on different local soil condition, at different distance from the causative fault, and for different levels of magnitude. In order to evaluate the reliability of the proposed design displacement spectra, probabilistic displacement spectra corresponding to different levels of probability of non-exceedance were also carried out.The inelastic displacement demand to elasto-plastic systems was analyzed through the ratio between inelastic and elastic spectral displacements. Simplified relationships of the inelastic displacement ratio are then proposed as a function of displacement ductility, soil condition and period of vibration. Finally, as a comparison, the inelastic displacement ratios were also estimated considering other constitutive models.     

弹塑性地震反应谱的长周期特性研究

在基于性能抗震设计中弹塑性反应谱在计算结构地震位移反应方面越来越受到重视。利用统计分析方法研究了等强度的延性需求谱和等延性的强度折减系数谱的长周期(至5 s)区段的特性,关注的重点是等位移准则和场地条件影响。给出了若干具有工程价值的结论:一是周期介于1.5Tg(地震动特征周期)和2.5 s之间的结构可近似认为等位移准则成立且与场地条件关系不大,这样确定的强度折减系数当位移延性系数小于等于4时结果将是偏于安全的;二是结构周期大于2.5 s后以硬土场地等延性强度折减系数谱或等强度延性需求谱代替软土场地谱求解系统强度需求或延性需求,将会得到偏于安全的结果。     

Constant-ductility strength demand spectra for seismic design of structures

In displacement-based seismic design, constant-ductility strength demand spectra （CDSDS） are very useful for preliminary design of new structures where the global displacement ductility capacity is known. The CDSDS can provide the required inelastic lateral strength of new structures from the required elastic lateral strength. Based on a statistical study of nonlinear time-history for an SDOF system, the mean CDSDS corresponding to four site conditions are presented and approximate expressions of the inelastic spectra are proposed, which are functions of the structural period and ductility level. The effects of site conditions, structural period, level of ductility, damping and post-yield stiffness of structures on CDSDS are also investigated. It is concluded that site conditions, ductility level and structural period have important effects on the CDSDS and damping, post-yield stiffness effects are rather complex and of minor importance. The damping, post-yield stiffness effects depend on both the level of ductility and the natural period of structures.     

On the inelastic torsional response of single‐storey structures under bi‐axial excitation

An attempt has been made to explore the general trends in the seismic response of plan‐asymmetric structures without any restrictions imposed by a particular code. Systems with structural elements in both orthogonal directions under bi‐directional excitation were studied. Idealized single‐storey models with bi‐axial eccentricity were employed. The systems were torsionally stiff and, in the majority of cases, mass‐eccentric. The main findings are: in general, inelastic torsional response is qualitatively similar to elastic torsional response. Quantitatively, the torsional effect on the flexible side, expressed as an increase of displacements due to torsion, decreases slightly with increasing plastic deformation, unless the plastic deformations are small. The response on the stiff side generally strongly depends on the effect of several modes of vibration and on the influence of the ground motion in the transverse direction. These influences depend on the structural and ground motion characteristics in both directions. Reduction of displacements due to torsion, typical for elastic torsionally stiff structures, usually decreases with increasing plastic deformations. As an additional effect of large plastic deformations, a flattening of the displacement envelopes in the horizontal plane usually occurs, indicating that torsional effects in the inelastic range are generally smaller than in the elastic range. The dispersion of the results of inelastic torsional response analysis is generally larger than that of elastic analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

Equivalent ductility factors,taking into account low-cycle fatigue

During strong earthquakes, the deformation capacity of structures is reduced due to the cumulative damage caused by cyclic load reversals. In the paper, equivalent (reduced) ductility factors have been proposed, which take into account this effect. They are based on different failure hypotheses. Ductility reduction due to low-cycle fatigue is controlled by a dimensionless parameter γ, which is a function of dissipated hysteretic energy, maximum displacement and the natural frequency of the structural system, and which has been proved to be a relatively stable quantity in the whole period range. If approximate values for γ are used, the determination of equivalent ductility is very simple, and thus appropriate for design purposes. The formulae for equivalent ductility factors include damage indices, and permit the designer to choose acceptable level of structural damage explicitly. As an example, equivalent ductility factors have been used to construct inelastic acceleration spectra, which are proportional to strength demand, for the El Centro 1940 SOOE record. The results have been compared with the ‘exact’ spectra obtained by non-linear dynamic analysis.     

楼板及其配筋在RC框架结构实现抗震延性机制中的作用分析

总结采用梁有效翼缘来考虑楼板及配筋对"强柱弱梁"机制形成的影响的实验和数值仿真研究.基于SAP2000采用三种侧向加载模式对RC框架结构不带楼板、不带楼板考虑梁刚度放大、带楼板的三个模型进行pushover分析,对力与位移的关系曲线、塑性铰的出铰顺序以及顶点位移与层间位移等方面进行探讨.结果表明:三个模型的"强柱弱梁"...     

Displacement amplification factors for steel eccentrically braced frames

Inelastic deformation capacity of links is a factor that significantly influences design of steel eccentrically braced frames (EBFs). The link rotation angle is used to describe inelastic link deformation. The link rotation angle is generally calculated by making use of design story drifts that in turn are calculated by modifying the elastic displacements by a displacement amplification factor. This paper presents a numerical study undertaken to evaluate the displacement amplification factor given in ASCE7‐10 for EBFs and the rigid‐plastic mechanism used for calculating link rotation angles. A total of 72 EBFs were designed by considering the number of stories, the bay width, the link length to bay width ratio, and the seismic hazard level as the prime variables. All structures were analyzed using elastic and inelastic time history analyses. The results indicated that the displacement amplification factor given in ASCE7‐10 provides unconservative estimates of the story drifts. On the other hand, the rigid‐plastic mechanism provides conservative estimates of link rotations. Based on the results of the numerical study, a new set of displacement amplification factors that vary along the height of the structure and modifications to the rigid‐plastic mechanism were developed. In light of the proposed modifications, the EBFs were redesigned and analyzed using inelastic time history analysis. The results indicated that the proposed modifications provide improvements for the displacement amplification factor and link rotation angle calculation procedures. Copyright © 2014 John Wiley & Sons, Ltd.     

Inelastic response and design criteria of plan-wise asymmetric systems

The study of the torsional response of buildings in the inelastic range of behaviour is of great interest since the ability of structures to resist strong earthquakes mainly relies on their ductility and capacity for energy dissipation. Furthermore, an examination of the performance of structures during past earthquakes demonstrates that plan-asymmetric buildings suffered greater damage due to torsional response. The paper deals with this subject by analysing a model which idealizes a one-storey building with resisting elements oriented along two perpendicular directions. In addition to the parameters of the elastic behaviour, the inelastic system response depends on full yield capacity and plan-wise strength distribution. The influence of the criterion adopted for the design of resisting elements on local ductility demand and damage has been evaluated by parametric analysis. In particular, a comparison has been carried out between systems with equal design levels for all elements and systems with design levels dependent on the element location. For a given elastic behaviour and total capacity, the strength distributions in plan have been defined which minimize ductility demand and structural damage. Finally, based on these findings, responses from models designed according to several seismic codes have been compared.     

Inelastic earthquake spectra

This paper presents a procedure for computing inelastic design spectra in terms of yield displacement. The procedure results in substantial computational savings as compared to the current procedures for computing the inelastic spectra in terms of displacement ductility. The proposed method is used to obtain inelastic design spectra for alluvium and rock. The results for alluvium are compared to those from the Newmark and Hall,¹⁰ Riddell and Newmark¹² and Lai and Biggs⁴ studies. The findings indicate that for given ductility and frequency one may de-amplify the elastic response or reduce the elastic forces more for a structure on rock than for a structure on alluvium. A technique is presented so that the inelastic design spectrum can be scaled to any desired yield displacement and acceleration. An example is presented to illustrate how the proposed inelastic spectra can be used to compute the required ductility for a given system.     

Inelastic spectra for infilled reinforced concrete frames

In two companion papers a simplified non‐linear analysis procedure for infilled reinforced concrete frames is introduced. In this paper a simple relation between strength reduction factor, ductility and period (R–µ–T relation) is presented. It is intended to be used for the determination of inelastic displacement ratios and of inelastic spectra in conjunction with idealized elastic spectra. The R–µ–T relation was developed from results of an extensive parametric study employing a SDOF mathematical model composed of structural elements representing the frame and infill. The structural parameters, used in the proposed R–µ–T relation, in addition to the parameters used in a usual (e.g. elasto‐plastic) system, are ductility at the beginning of strength degradation, and the reduction of strength after the failure of the infills. Formulae depend also on the corner periods of the elastic spectrum. The proposed equations were validated by comparing results in terms of the reduction factors, inelastic displacement ratios, and inelastic spectra in the acceleration–displacement format, with those obtained by non‐linear dynamic analyses for three sets of recorded and semi‐artificial ground motions. A new approach was used for generating semi‐artificial ground motions compatible with the target spectrum. This approach preserves the basic characteristics of individual ground motions, whereas the mean spectrum of the whole ground motion set fits the target spectrum excellently. In the parametric study, the R–µ–T relation was determined by assuming a constant reduction factor, while the corresponding ductility was calculated for different ground motions. The mean values proved to be noticeably different from the mean values determined based on a constant ductility approach, while the median values determined by the different procedures were between the two means. The approach employed in the study yields a R–µ–T relation which is conservative both for design and performance assessment (compared with a relation based on median values). Copyright © 2004 John Wiley & Sons, Ltd.     

Additional seismic inelastic deformation caused by structural asymmetry

Using a single mass monosymmetric model, this paper examines the additional seismic inelastic deformations and displacement caused by structural asymmetry of the model. Stiffness eccentricity and resistance eccentricity are used as measures of asymmetry in the elastic and inelastic range respectively. Seven ways of specifying strength distribution among resisting elements are considered, including code provisions from Canada, Mexico, New Zealand and the United States. These specifications are related t o the model resistance eccentricity. It is shown that when torsional shears are included in the strength design of the elements, the structure in general will have small resistance eccentricity, even if it has large stiffness eccentricity in the elastic range. For structures which are designed with allowance for torsional shears, the ductility demands on the elements are similar to those when the structure is symmetrical. However, the edge displacements can be up to three times that if the system is symmetrical. This finding has significant implications in evaluating adequate separation between buildings to avoid the pounding problem during earthquakes.     

Direct displacement-based seismic design of steel eccentrically braced frame structures

This paper details a direct displacement-based design procedure for steel eccentrically braced frame (EBF) structures and gauges its performance by examining the non-linear dynamic response of a series of case study EBF structures designed using the procedure. Analytical expressions are developed for the storey drift at yield and for the storey drift capacity of EBFs, recognising that in addition to link beam deformations, the brace and column axial deformations can provide important contributions to storey drift components. Case study design results indicate that the ductility capacity of EBF systems will tend to be relatively low, despite the large local ductility capacity offered by well detailed links. In addition, it is found that while the ductility capacity of EBF systems will tend to reduce with height, this is not necessarily negative for seismic performance since the displacement capacity for taller EBF systems will tend to be large. To gauge the performance of the proposed DBD methodology, analytical models of the case study design solutions are subject to non-linear time-history analyses with a set of spectrum-compatible accelerograms. The average displacements and drifts obtained from the NLTH analyses are shown to align well with design values, confirming that the new methodology could provide an effective tool for the seismic design of EBF systems.     

双向地震动作用的拟等延性系数谱

首先建立了以强度折减系数表述的恢复力特性满足二维屈服面模型的理想弹塑性单质点系统(它在2个相互垂直的主轴方向上分别具有水平平动自由度)在双向地震动作用下的归一化运动方程。然后引入单向地震动作用下等延性系数的强度折减系数谱,给出了双向地震动作用的拟等延性系数谱(定义为系统分别承受双向和单向地震动作用,在同一主轴方向上的最大位移反应之比)最后通过硬土场地10组双向地震动记录拟等延性系数谱的统计平均结果,分析了结构周期、位移延性系数和阻尼等因素对谱值及结构双向地震反应的影响。结果表明,双向地震动作用与单向地震动作用相比主要增加结构较长周期方向的最大位移反应。若在基于位移的抗震设计中降低结构较短周期方向的设计位移延性系数,可在一定程度上降低双向地震动的不利影响。因定义的谱为比值形式,阻尼对其影响不大。     

Evaluation of site‐dependent constant‐damage design spectra for reinforced concrete structures

An investigation on the validity of the conventional design approach known as constant displacement ductility is carried out. The hysteretic behaviour described by the Modified Takeda model is taken to represent the characteristics of reinforced concrete structural systems. The results presented in the form of seismic damage spectra indicate that the conventional design approach may not be valid because cumulative damage is excessively high. The inelastic design spectra based on the constant‐damage concept are proposed in terms of simplified expressions. The expressions are derived from constant‐damage design spectra computed by non‐linear response analysis for SDOF systems subjected to ground motions recorded on rock sites, alluvium deposits, and soft‐soil sites. The proposed expressions, which are dependent on the local soil conditions, are functions of target seismic damage, displacement ductility ratio and period of vibration. The seismic damage of structures that have been designed based on this new design approach is also checked by a design‐and‐evaluation approach. The results are found to be satisfactory. Copyright © 2004 John Wiley & Sons, Ltd.     

Isoductile strengths and strength reduction factors of elasto‐plastic SDOF systems subjected to simple waveforms

The inelastic response of elasto‐plastic SDOF oscillators subjected to 24 simple waveforms was studied. The waveforms contain linear, quadratic, sinusoidal, and triangular acceleration components that repeat for not more than several cycles. Similarities and differences in oscillator response characteristics are presented, organized by a characteristic period. The strengths and corresponding strength reduction factors required for constant ductility responses are discussed. Response data are compared with expectations based on the concepts of equal energy, equal displacement, and preservation of force. Limitations on the applicability of the equal energy concept are identified. Copyright © 2001 John Wiley & Sons, Ltd.     

剪切型结构的抗震强度折减系数研究

为了研究剪切型结构抗震强度需求的变化规律,本文基于单自由度体系的非线性时程分析,研究了不同场地条件下延性折减系数与位移延性系数和结构自振周期的关系;采用修正等效单自由度体系位移延性折减系数的方法,研究了剪切型多自由度体系的延性折减系数;以基于中国建筑抗震规范设计的代表不同抗震能力要求的RC框架结构为分析对象,通过静力弹塑性分析,研究了RC框架结构的体系超强能力。分析结果表明场地类别、位移延性水准和结构振动周期对单自由度体系的延性折减系数有显著的影响;多自由度体系的抗震延性折减系数明显比其相应的等效单自由度体系的抗震延性折减系数小;RC框架结构的超强系数一般随结构楼层数的增加而减小,随抗震设防烈度的增大而减小,内框架的超强系数比边框架的超强系数大。     

Comparison of displacement coefficient method and capacity spectrum method with experimental results of RC columns

For the performance‐based seismic design of buildings, both the displacement coefficient method used by FEMA‐273 and the capacity spectrum method adopted by ATC‐40 are non‐linear static procedures. The pushover curves of structures need to be established during processing of these two methods. They are applied to evaluation and rehabilitation of existing structures. This paper is concerned with experimental studies on the accuracy of both methods. Through carrying out the pseudo‐dynamic tests, cyclic loading tests and pushover tests on three reinforced concrete (RC) columns, the maximum inelastic deformation demands (target displacements) determined by the coefficient method of FEMA‐273 and the capacity spectrum method of ATC‐40 are compared. In addition, a modified capacity spectrum method which is based on the use of inelastic design response spectra is also included in this study. It is shown from the test specimens that the coefficient method overestimates the peak test displacements with an average error of +28% while the capacity spectrum method underestimates them with an average error of ‐20%. If the Kowalsky hysteretic damping model is used in the capacity spectrum method instead of the original damping model, the average errors become ‐11% by ignoring the effect of stiffness degrading and ‐1.2% by slightly including the effect of stiffness degrading. Furthermore, if the Newmark–Hall inelastic design spectrum is implemented in the capacity spectrum method instead of the elastic design spectrum, the average error decreases to ‐6.6% which undervalues, but is close to, the experimental results. Copyright © 2003 John Wiley & Sons, Ltd.     

INELASTIC SEISMIC RESISTANCE OF REINFORCED CONCRETE STACK-LIKE STRUCTURES

A method is presented to quantify the inelastic seismic resistance of reinforced concrete stack-like structures by non-linear earthquake analysis. The deformed configuration of stack is idealized as an assemblage of beam elements and actual stress–strain relationships of concrete and reinforcing steel are used to evaluate element matrices. Repeated non-linear analyses are performed by gradually increasing the intensity of acceleration time histories to a level where collapse of the stack is observed in primary stresses. The set of time histories thus obtained are then used to define the ultimate intensity of ground motion that the stack can sustain if inelastic deformations are permitted. A procedure is presented to quantify the difference between inelastic seismic resistance and elastic seismic resistance in terms of displacement ductility capacity factors. For seismic design using available inelastic resistance, values of curvature ductility factor demand for the cross-sections of stacks are also presented. © 1997 by John Wiley & Sons, Ltd.