Estimation of inelastic deformation demands in multistorey RC frame buildings

Estimation of peak inelastic deformation demands is a key component of any displacement-based procedure for earthquake-resistant design of new structures or for seismic evaluation of existing structures. On the basis of the results of over a thousand non-linear dynamic analyses, rules are developed for the estimation of mean and upper-characteristic peak inelastic interstorey drifts and member chord rotations in multistorey RC frame buildings, either bare or infilled in all storeys but the first. For bare frame structures, mean inelastic deformation demands can be estimated from a linear, equivalent static, or preferably multimodal response spectrum analysis with 5 per cent damping and with the RC members considered with their secant stiffness at yielding. 95 per cent characteristic values can be estimated as multiples of the mean deformations. For open-first-storey buildings, the linear analysis can be equivalent static, with the infills modelled as rigid bidiagonal struts and all RC members considered with their secant stiffness to yielding. Copyright © 1999 John Wiley & Sons, Ltd.     

Estimation of inelastic seismic deformations in asymmetric multistorey RC buildings

Four real buildings with three to six stories, strong irregularities in plan and little engineered earthquake resistance are subjected to inelastic response‐history analyses under 56 bidirectional EC8‐spectra‐compatible motions. The average chord rotation demand at each member end over the 56 response‐history analyses is compared to the chord rotation from elastic static analysis with inverted triangular lateral forces or modal response spectrum analysis. The storey‐average inelastic‐to‐elastic‐chord‐rotation‐ratio was found fairly constant in all stories, except when static elastic analysis is applied to buildings with large higher mode effects. Except for such buildings, static elastic analysis gives more uniform ratios of inelastic chord rotations to elastic ones within and among stories than modal response spectrum analysis, but generally lower than 1.0. With increasing EPA the building‐average inelastic‐to‐elastic‐chord‐rotation‐ratio decreases but scatter in the results increases. Static elastic analysis tends to overestimate the inelastic torsional effects at the flexible or central part of the torsionally flexible buildings and underestimate them at their stiff side. Modal response spectrum analysis tends to overestimate the inelastic torsional effects at the stiff or central part of the torsionally stiff buildings and underestimate them at the flexible side. Overall, for multistorey RC buildings that typically have fundamental periods in the velocity‐sensitive part of the spectrum, elastic modal response spectrum analysis with 5% damping gives on average unbiased and fairly accurate estimates of member inelastic chord rotations. If higher modes are not significant, elastic static analysis in general overestimates inelastic chord rotations of such buildings, even when torsional effects are present. Copyright © 2007 John Wiley & Sons, Ltd.     

Envelope‐based pushover analysis procedure for the approximate seismic response analysis of buildings

An envelope‐based pushover analysis procedure is presented that assumes that the seismic demand for each response parameter is controlled by a predominant system failure mode that may vary according to the ground motion. To be able to simulate the most important system failure modes, several pushover analyses need to be performed, as in a modal pushover analysis procedure, whereas the total seismic demand is determined by enveloping the results associated with each pushover analysis. The demand for the most common system failure mode resulting from the ‘first‐mode’ pushover analysis is obtained by response history analysis for the equivalent ‘modal‐based’ SDOF model, whereas demand for other failure modes is based on the ‘failure‐based’ SDOF models. This makes the envelope‐based pushover analysis procedure equivalent to the N2 method provided that it involves only ‘first‐mode’ pushover analysis and response history analysis of the corresponding ‘modal‐based’ SDOF model. It is shown that the accuracy of the approximate 16th, 50th and 84th percentile response expressed in terms of IDA curves does not decrease with the height of the building or with the intensity of ground motion. This is because the estimates of the roof displacement and the maximum storey drift due to individual ground motions were predicted with a sufficient degree of accuracy for almost all the ground motions from the analysed sets. Copyright © 2013 John Wiley & Sons, Ltd.     

基于超级单元的钢-混凝土混合结构动力特性及地震反应研究

本文提出了基于超级单元的钢框架－混凝土剪力墙结构体系动力特性及地震反应分析的一种方法，该方法考虑了混合结构体系中钢框架部分的受力和变形特点，即节点柔性（半刚性）、梁柱效应（p-δ效应）及P－△效应（以下合称P－Delta效应），推导了考虑三种因素情况下，钢框架的层间侧移刚度及钢框架－混凝土剪力墙结构体系的超级单元刚度矩阵，采用刚度法求解钢框架－混凝土混合结构周期和振型。该方法物理概念清楚，计算简便。     

Inelastic response of RC frame buildings with seismic isolation

A comprehensive parametric study on the inelastic seismic response of seismically isolated RC frame buildings, designed for gravity loads only, is presented. Four building prototypes, with 23 m × 10 m floor plan dimensions and number of storeys ranging from 2 to 8, are considered. All the buildings present internal resistant frames in one direction only, identified as the strong direction of the building. In the orthogonal weak direction, the buildings present outer resistant frames only, with infilled masonry panels. This structural configuration is typical of many existing RC buildings, realized in Italy and other European countries in the 60s and 70s. The parametric study is based on the results of extensive nonlinear response‐time history analyses of 2‐DOF systems, using a set of seven artificial and natural seismic ground motions. In the parametric study, buildings with strength ratio (F_y/W) ranging from 0.03 to 0.15 and post‐yield stiffness ratio ranging from 0% to 6% are examined. Three different types of isolation systems are considered, that is, high damping rubber bearings, lead rubber bearings and friction pendulum bearings. The isolation systems have been designed accepting the occurrence of plastic hinges in the superstructure during the design earthquake. The nonlinear response‐time history analyses results show that structures with seismic isolation experience fewer inelastic cycles compared with fixed‐base structures. As a consequence, although limited plastic deformations can be accepted, the collapse limit state of seismically isolated structures should be based on the lateral capacity of the superstructure without significant reliance on its inherent hysteretic damping or ductility capacity. Copyright © 2012 John Wiley & Sons, Ltd.     

约束混凝土砌块结构抗震性态研究

性态抗震设计已成为结构抗震设计的发展趋势,本文以约束混凝土砌块结构为对象,在提出约束混凝土砌块墙承载力计算公式的基础上,建立了砌块墙片的恢复力模型。对3座不同层数的典型约束混凝土砌块结构,在代表不同场地类别、不同地震动强度的输入下分别进行了动力非线性时程分析和静力非线性分析。通过计算结果的对比,讨论了2种分析方法中场地类别、地震动强度、静力非线性分析中侧力分布模式等影响,所得结论可以为用静力非线性分析估计砌块结构的抗震性能提供有益的参考依据。     

A macro-level global seismic damage model considering higher modes

For modal pushover analysis procedures, the model proposed by Ghobarah et al. (called the G model hereafter, 1999) has been extended to account for the contributions of transient higher modes to global seismic damage of structures excited by strong ground motions. The proposed model has physically and perfectly bridged the G model and the final softening model proposed by DiPasquale and Cakmak (1988). Modal damage indexes corresponding to all considered vibration modes are combined by the CQC rule or the SRSS rule. Incremental dynamic analysis (IDA) is performed on three example RC frames to validate the proposed model, and a comprehensive comparison is carried out. The demonstration indicates that the proposed model is easy to implement and reflects the influence of the transition in transient vibration periods and modes on structural damage evolution. Some limitations associated with the proposed model are also addressed. Further experimental validations are needed to improve the model in the future.     

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。     

A simplified methd of evaluating the seismic performance of buildings

This paper presents a simplified method of evaluating the seismic performance of buildings. The proposed method is based on the transformation of a multiple degree of freedom (MDOF) system to an equivalent single degree of freedom (SDOF) system using a simple and intuitive process. The proposed method is intended for evaluating the seismic performance of the buildings at the intermediate stages in design, while a rigorous method would be applied to the final design. The performance of the method is evaluated using a series of buildings which are assumed to be located in Victoria in western Canada, and designed based on the upcoming version of the National Building Code of Canada which is due to be published in 2005. To resist lateral loads, some of these buildings contain reinforced concrete moment resisting frames,while others contain reinforced concrete shear walls. Each building model has been subjected to a set of site-specific seismic spectrum compatible ground motion records, and the response has been determined using the proposed method and the general method for MDOF systems. The results from the study indicate that the proposed method can serve as a useful tool for evaluation of seismic performance of buildings, and carrying out performance based design.     

On the inelastic seismic response of asymmetric buildings under bi‐axial excitation

The elastic and inelastic seismic response of plan‐asymmetric regular multi‐storey steel‐frame buildings has been investigated under bi‐directional horizontal ground motions. Symmetric variants of these buildings were designed according to Eurocodes 3 and 8. Asymmetric buildings were created by assuming a mass eccentricity in each of the two principal directions. The torsional response in the elastic and inelastic range is qualitatively similar with the exception of the stiff edge in the strong direction of torsionally stiff buildings and the stiff edge in the weak direction of torsionally flexible buildings. The response is influenced by the intensity of ground motion, i.e. by the magnitude of plastic deformation. In the limiting case of very strong ground motion, the behaviour of initially torsionally stiff and initially torsionally flexible buildings may become qualitatively similar. A decrease in stiffness due to plastic deformations in one direction may substantially influence the behaviour in the orthogonal direction. The response strongly depends on the detailed characteristics of the ground motion. On average, torsional effects are reduced with increasing plastic deformations, unless the plastic deformations are small. Taking into account also the dispersion of results which is generally larger in the inelastic range than in the elastic one, it can be concluded that (a) the amplification of displacements determined by the elastic analysis can be used as a rough estimate also in the inelastic range and (b) any favourable torsional effect on the stiff side of torsionally stiff buildings, which may arise from elastic analysis, may disappear in the inelastic range. The conclusions are limited to fairly regular buildings and subject to further investigations. Copyright © 2005 John Wiley & Sons, Ltd.     

H形断面钢筋混凝土立体剪力墙的非线性动力响应分析

为了建立统一的动力响应分析模型,本文以NUPEC振动台试验的H形断面钢筋混凝土立体剪力墙为研究对象进行了三维非线性有限元动力响应分析。根据分析结果与试验结果的比较可知,在RC剪力墙到达最大承载力之前由简化模型和一般模型得到的动力响应特性与试验结果吻合较好,荷载-变形关系能很好模拟试验结果。但是,最大承载力之后,由于混凝土开裂、损伤、劣化的急剧发展,较难模拟混凝土开裂、裂缝的开闭及滑移等非线性特性,分析得到的加速度衰减较慢、位移响应较小。基于上述研究成果探讨并提出了进一步改善非线性有限元动力响应分析精度的建议。     

The ductility reduction factor in the seismic design of buildings

This paper presents new trends in the relationship between the ductility reduction factor and the ductility demand in the seismic design of buildings. A total of 4860 inelastic time-history analyses were carried out to study this relationship using 60 single-degree-of-freedom models excited by an ensemble of 81 earthquake accelerogram records from around the world. The asymmetrical distribution of the results highlighted the inaccuracies associated with assuming a normal distribution simply described by the mean and standard deviation to represent the data. A probability of exceedence approach has been used based on counting the number of occurrences the ductility demand exceeds a specified level. The ductility reduction factors developed in this study are consistent with other studies in the long-period range but are different in the short-period range. The ductility reduction factor for very short period buildings of limited ductility has been found to be greater than previously predicted. © 1998 John Wiley & Sons, Ltd.     

Seismic reliability analysis of buildings with torsional eccentricities

A study is presented of the influence of stiffness and strength eccentricities on the inelastic torsional response of buildings under the action of two simultaneous orthogonal horizontal ground motion components. Asymmetric buildings were obtained from their respective symmetric systems and were characterized by their stiffness and strength torsional eccentricities in both orthogonal directions. Based on the results of inelastic response of both building types (symmetric and asymmetric), the seismic reliability functions are determined for each system, and their forms of variation with different global system parameters are evaluated. Illustrative examples are presented about the use of this information for the formulation of seismic design criteria for in‐plan asymmetric multistory systems, in order to attain the same reliability levels implicit for symmetric systems designed in accordance with current seismic design codes. Copyright © 2014 John Wiley & Sons, Ltd.     

利用等位移原则估计高层结构的非弹性地震反应(二)

通过高层结构弹性和非弹性地震时程反应分析,研究了两者的位移反应关系。结果表明：结构在不同地震作用下非弹性总位移角反应的平均值与弹性反应十分接近,基本符合等位移原则,可以用后者分析结果直接估计前者;结构最大层间位移角反应的平均值在弱和中等非线性阶段亦与弹性反应十分接近,在强非线性阶段则大于弹性反应,经数据拟合,初步提供了一个在此阶段由弹性最大层间位移角反应估计非弹性反应的近似公式。     

钢筋混凝土框架结构抗震超强系数分析

基于我国建筑抗震规范要求设计的14栋代表不同抗震特征要求的多高层规则钢筋混凝土框架,通过静力弹塑性分析详细地评估了框架结构的体系超强能力。分析中采用与抗震规范等效静力地震作用效应分布模式相同的单调递增侧向荷载,以二维平面框架为分析对象。分析结果表明地震分区对超强系数的影响较大;有填充墙框架比无填充墙框架的超强能力明显要大;内框架的超强能力比外框架的超强能力大;超强系数随框架楼层数的增加而减小。     

Further development of a multimodal pushover analysis procedure for seismic assessment of bridges

An improvement is first suggested to the modal pushover analysis (MPA) procedure for bridges initially proposed by the writers (Earthquake Engng Struct. Dyn. 2006; 35 (11):1269–1293), the key idea being that the deformed shape of the structure responding inelastically to the considered earthquake level is used in lieu of the elastic mode shape. The proposed MPA procedure is then verified by applying it to two actual bridges. The first structure is the Krystallopigi bridge, a 638 m‐long multi‐span bridge, with significant curvature in plan, unequal pier heights, and different types of pier‐to‐deck connections. The second structure is a 100 m‐long three‐span overpass bridge, typical in modern motorway construction in Europe, which, although ostensibly a regular structure, is found to exhibit a rather unsymmetric response in the transverse direction, mainly due to torsional irregularity. The bridges are assessed using response spectrum, ‘standard’ pushover (SPA), and MPA, and finally using non‐linear response history analysis (NL‐RHA) for a number of spectrum‐compatible motions. The MPA provided a good estimate of the maximum inelastic deck displacement for several earthquake intensities. The SPA on the other hand could not predict well the inelastic deck displacements of bridges wherever the contribution of the first mode to the response of the bridge was relatively low. Copyright © 2009 John Wiley & Sons, Ltd.     

预应力混凝土结构非线性地震反应分析

本文针对预应力混凝土与普通混凝土不同的受力特点,提出了适合于分析预应力混凝土结构抗震性能的非线性有限元模型。模型首先将混凝土结构离散为杆单元,然后对各杆单元按分层组合原理分成许多混凝土层、预应力钢筋层和普通钢筋层,计算混凝土分层单元、预应力钢筋和普通钢筋的应力和应变,最后,根据钢筋与混凝土之间的粘结－滑移关系高速钢筋变形,根据混凝土弹性模量调整结构及杆单元变形,通过对普通混凝土构件和三个预应力混凝     

Analytical modelling of near‐source pulse‐like seismic demand for multi‐linear backbone oscillators

Nonlinear static procedures, which relate the seismic demand of a structure to that of an equivalent single‐degree‐of‐freedom oscillator, are well‐established tools in the performance‐based earthquake engineering paradigm. Initially, such procedures made recourse to inelastic spectra derived for simple elastic–plastic bilinear oscillators, but the request for demand estimates that delve deeper into the inelastic range, motivated investigating the seismic demand of oscillators with more complex backbone curves. Meanwhile, near‐source (NS) pulse‐like ground motions have been receiving increased attention, because they can induce a distinctive type of inelastic demand. Pulse‐like NS ground motions are usually the result of rupture directivity, where seismic waves generated at different points along the rupture front arrive at a site at the same time, leading to a double‐sided velocity pulse, which delivers most of the seismic energy. Recent research has led to a methodology for incorporating this NS effect in the implementation of nonlinear static procedures. Both of the previously mentioned lines of research motivate the present study on the ductility demands imposed by pulse‐like NS ground motions on oscillators that feature pinching hysteretic behaviour with trilinear backbone curves. Incremental dynamic analysis is used considering 130 pulse‐like‐identified ground motions. Median, 16% and 84% fractile incremental dynamic analysis curves are calculated and fitted by an analytical model. Least‐squares estimates are obtained for the model parameters, which importantly include pulse period T_p. The resulting equations effectively constitute an R ? μ ? T ? T_p relation for pulse‐like NS motions. Potential applications of this result towards estimation of NS seismic demand are also briefly discussed. Copyright © 2016 John Wiley & Sons, Ltd.     

Establishment of performance‐based seismic design factors for precast concrete floor diaphragms

This paper presents an analytical study used to establish design factors for a new seismic design methodology for precast concrete floor diaphragms. The design factors include diaphragm force amplification factors Ψ and diaphragm shear overstrength factors Ω_v. The Ψ factors are applied to the ASCE7‐05 diaphragm design forces to produce diaphragm design strengths aligned to different performance targets. These performance targets are based on diaphragm detailing choices, and include: (i) elastic diaphragm behavior or (ii) limiting inelastic deformation demand on the diaphragm reinforcement (connectors between precast units or reinforcing bars in a topping slab) to within their reliable deformation capacities. The Ω_v factors provide overstrength relative to the diaphragm bending strength for capacity protection against shear failure. The analytical study was performed by conducting nonlinear time history analyses of a simple evaluation structure, of which the dimensions and structural properties were varied. The analytical model used in the study is constructed and calibrated on the basis of extensive physical testing. The analytically obtained values of the diaphragm design factors are presented as functions of the geometric and structural properties of the building. The design factors presented here have been verified through evaluation of a set of realistic precast prototype structures. The diaphragm design methodology is currently in the codification process. Copyright © 2015 John Wiley & Sons, Ltd.     

截面中部配置型钢的混凝土剪力墙抗震性能研究

本文通过试验研究了型钢混凝土(SRC)剪力墙的抗震性能,对16个试件进行了低周反复加载试验,得到了这些构件的延性比;研究了高宽比等参数对型钢混凝土剪力墙抗震性能的影响。在试验中,研究了在中部配置型钢的型钢混凝土剪力墙,结果表明这种新型的型钢混凝土剪力墙具有更好的抗震性能。在试验的基础上,本文建立了型钢混凝土剪力墙恢复力骨架曲线的数学模型,为分析高层结构的非线性地震反应分析提供了基础数据。