Estimation of seismic drift and ductility demands in planar regular X‐braced steel frames

This paper summarizes the results of an extensive study on the inelastic seismic response of X‐braced steel buildings. More than 100 regular multi‐storey tension‐compression X‐braced steel frames are subjected to an ensemble of 30 ordinary (i.e. without near fault effects) ground motions. The records are scaled to different intensities in order to drive the structures to different levels of inelastic deformation. The statistical analysis of the created response databank indicates that the number of stories, period of vibration, brace slenderness ratio and column stiffness strongly influence the amplitude and heightwise distribution of inelastic deformation. Nonlinear regression analysis is employed in order to derive simple formulae which reflect the aforementioned influences and offer a direct estimation of drift and ductility demands. The uncertainty of this estimation due to the record‐to‐record variability is discussed in detail. More specifically, given the strength (or behaviour) reduction factor, the proposed formulae provide reliable estimates of the maximum roof displacement, the maximum interstorey drift ratio and the maximum cyclic ductility of the diagonals along the height of the structure. The strength reduction factor refers to the point of the first buckling of the diagonals in the building and thus, pushover analysis and estimation of the overstrength factor are not required. This design‐oriented feature enables both the rapid seismic assessment of existing structures and the direct deformation‐controlled seismic design of new ones. A comparison of the proposed method with the procedures adopted in current seismic design codes reveals the accuracy and efficiency of the former. Copyright © 2007 John Wiley & Sons, Ltd.     

Evaluation of residual drift demands in regular multi‐storey frames for performance‐based seismic assessment

This paper summarizes results of a comprehensive analytical study aimed at evaluating the amplitude and heightwise distribution of residual drift demands in multi‐storey moment‐resisting frames after earthquake excitation. For that purpose, a family of 12 one‐bay two‐dimensional generic frame models was subjected to an ensemble of 40 ground motions scaled to different intensities. In this investigation, an inelastic ground motion intensity measure was employed to scale each record, which allowed reducing the record‐to‐record variability in the estimation of residual drift demands. The results were statistically processed in order to evaluate the influence of ground motion intensity, number of stories, period of vibration, frame mechanism, system overstrength, and hysteretic behaviour on central tendency of residual drift demands. In addition, a special emphasis was given to evaluate the uncertainty in the estimation of residual drift demands. Results of incremental dynamic analyses indicate that the amplitude and heightwise distribution of residual drift demands strongly depends on the frame mechanism, the heightwise system structural overstrength and the component hysteretic behaviour. An important conclusion for performance‐based assessment is that the evaluation of residual drift demands involves significantly larger levels of uncertainty (i.e. record‐to‐record variability) than that of maximum drift demands, which suggests that this variability and corresponding uncertainty should be explicitly taken into account when estimating residual drift demands during performance‐based seismic assessment of frame buildings. Copyright © 2006 John Wiley & Sons, Ltd.     

Evaluation of predictors of non‐linear seismic demands using ‘fishbone’ models of SMRF buildings

Predictors (or estimates) of seismic structural demands that are less computationally time‐consuming than non‐linear dynamic analysis can be useful for structural performance assessment and for design. In this paper, we evaluate the bias and precision of predictors that make use of, at most, (i) elastic modal vibration properties of the given structure, (ii) the results of a non‐linear static pushover analysis of the structure, and (iii) elastic and inelastic single‐degree‐of‐freedom time‐history analyses for the specified ground motion record. The main predictor of interest is an extension of first‐mode elastic spectral acceleration that additionally takes into account both the second‐mode contribution to (elastic) structural response and the effects of inelasticity. This predictor is evaluated with respect to non‐linear dynamic analysis results for ‘fishbone’ models of steel moment‐resisting frame (SMRF) buildings. The relatively small number of degrees of freedom for each fishbone model allows us to consider several short‐to‐long period buildings and numerous near‐ and far‐field earthquake ground motions of interest in both Japan and the U.S. Before doing so, though, we verify that estimates of the bias and precision of the predictor obtained using fishbone models are effectively equivalent to those based on typical ‘full‐frame’ models of the same buildings. Copyright © 2003 John Wiley & Sons, Ltd.     

A fuzzy–random analysis model for seismic performance of framed structures incorporating structural and non‐structural damage

Past earthquake experiences indicate that most buildings designed in accordance with modern seismic design codes could survive moderate‐to‐strong earthquakes; however, the financial loss due to repairing cost and the subsequent business interruption can be unacceptable. Designing building structures to meet desired performance targets has become a clear direction in future seismic design practice. As a matter of fact, the performance of buildings is affected by structural as well as non‐structural components, and involves numerous uncertainties. Therefore, appropriate probabilistic approach taking into account structural and non‐structural damages is required. This paper presents a fuzzy–random model for the performance reliability analysis of RC framed structures considering both structural and non‐structural damages. The limit state for each performance level is defined as an interval of inter‐storey drift ratios concerning, respectively, the non‐structural and structural damage with a membership function, while the relative importance of the two aspects is reflected through the use of an appropriate cost function. To illustrate the methodology, herein the non‐structural damage is represented by infill masonry walls. The probabilistic drift limits for RC components and masonry walls from the associated studies are employed to facilitate the demonstration of the proposed model in an example case study. The results are compared with those obtained using classical reliability model based on single‐threshold performance definition. The proposed model provides a good basis for incorporating different aspects into the performance assessment of a building system. Copyright © 2005 John Wiley & Sons, Ltd.     

Behavior of moment‐resisting frame structures subjected to near‐fault ground motions

Near‐fault ground motions impose large demands on structures compared to ‘ordinary’ ground motions. Recordings suggest that near‐fault ground motions with ‘forward’ directivity are characterized by a large pulse, which is mostly orientated perpendicular to the fault. This study is intended to provide quantitative knowledge on important response characteristics of elastic and inelastic frame structures subjected to near‐fault ground motions. Generic frame models are used to represent MDOF structures. Near‐fault ground motions are represented by equivalent pulses, which have a comparable effect on structural response, but whose characteristics are defined by a small number of parameters. The results demonstrate that structures with a period longer than the pulse period respond very differently from structures with a shorter period. For the former, early yielding occurs in higher stories but the high ductility demands migrate to the bottom stories as the ground motion becomes more severe. For the latter, the maximum demand always occurs in the bottom stories. Preliminary regression equations are proposed that relate the parameters of the equivalent pulse to magnitude and distance. The equivalent pulse concept is used to estimate the base shear strength required to limit story ductility demands to specific target values. Copyright © 2004 John Wiley & Sons, Ltd.     

基于地震易损性的框架结构的优化方法

给出了一种框架结构地震易损性优化的准则算法．根据优化准则构造了一种修改设计变量的格式,提出了设计方案可行性调整的方法并推导了计算公式,给出了优化算法的计算步骤,并通过一个算例阐述了这种算法的应用。     

Strengthening of moment‐resisting frame structures against near‐fault ground motion effects

Near‐fault ground motions with forward directivity are characterized by a large pulse. This pulse‐like motion may cause a highly non‐uniform distribution of story ductility demands for code‐compliant frame structures, with maximum demands that may considerably exceed the level of code expectations. Strengthening techniques for multi‐story frame structures are explored with the objective of reducing maximum drift demands. One option is to modify the code‐based SRSS distribution of story shear strength over the height by strengthening of the lower stories of the frame. The modified distribution reduces the maximum story ductility demand, particularly for weak and flexible structures. However, this strengthening technique is less effective for stiff structures, and is almost ineffective in cases in which the maximum demand occurs in the upper stories, i.e. strong and flexible structures. As an alternative, the benefits of strengthening frames with elastic and inelastic walls are evaluated. The effects of adding walls that are either fixed or hinged at the base are investigated. It is demonstrated that strengthening with hinged walls is very effective in reducing drift demands for structures with a wide range of periods and at various performance levels. Wall inelastic behavior only slightly reduces the benefits of strengthening with hinged walls.Copyright © 2004 John Wiley & Sons, Ltd.     

A modal pushover analysis procedure to estimate seismic demands for unsymmetric‐plan buildings

An Erratum has been published for this article in Earthquake Engng. Struct. Dyn. 2004; 33:1429. Based on structural dynamics theory, the modal pushover analysis (MPA) procedure retains the conceptual simplicity of current procedures with invariant force distribution, now common in structural engineering practice. The MPA procedure for estimating seismic demands is extended to unsymmetric‐plan buildings. In the MPA procedure, the seismic demand due to individual terms in the modal expansion of the effective earthquake forces is determined by non‐linear static analysis using the inertia force distribution for each mode, which for unsymmetric buildings includes two lateral forces and torque at each floor level. These ‘modal’ demands due to the first few terms of the modal expansion are then combined by the CQC rule to obtain an estimate of the total seismic demand for inelastic systems. When applied to elastic systems, the MPA procedure is equivalent to standard response spectrum analysis (RSA). The MPA estimates of seismic demand for torsionally‐stiff and torsionally‐flexible unsymmetric systems are shown to be similarly accurate as they are for the symmetric building; however, the results deteriorate for a torsionally‐similarly‐stiff unsymmetric‐plan system and the ground motion considered because (a) elastic modes are strongly coupled, and (b) roof displacement is underestimated by the CQC modal combination rule (which would also limit accuracy of RSA for linearly elastic systems). Copyright © 2004 John Wiley & Sons, Ltd.     

离散单元法在框架结构地震反应分析中的应用

将离散单元法应用于框架结构的地震反应分析,并建立了框架结构的离散单元计算模型。在数值求解过程中,本文采用同步动态松弛法确立与求解结构单元平衡关系,避免了动态松弛法由于路径相关性所造成的误差。本文编制了框架结构地震反应时程分析程序,并以一实际结构为例,进行了时程分析。算例表明,本文所提出的方法简单、有效,为工程结构地震反应分析提供了新的思路与方法。     

Advanced frame element for seismic analysis of masonry structures: model formulation and validation

This paper presents a masonry panel model for the nonlinear static and dynamic analysis of masonry buildings suitable for the seismic assessment of new and existing structures. The model is based on an equivalent frame idealization of the structure and stems from previous research on force‐based frame elements. The element formulation considers axial, bending, and shear deformations within the framework of the Timoshenko beam theory. A phenomenological cyclic section law that accounts for the shear panel response is coupled, through equilibrium between shear and bending forces along the element, with a fiber‐section model that accounts for the axial and bending responses. The proposed panel model traces with a low computational burden and numerical stability the main aspects of the structural behavior of masonry panels and is suitable for analyses of multi‐floor buildings with a relatively regular distribution of openings and with walls and floors organized to grant a box‐like behavior under seismic loads. The model capabilities are validated though analyses of simple unreinforced masonry panels and comparisons with published experimental results. The model accuracy is strongly dependent on the fiber and shear constitutive laws used. However, the formulation is general, and laws different from those employed in this study are easily introduced without affecting the model formulation. Copyright © 2015 John Wiley & Sons, Ltd.     

施工缝对框架结构抗震性能影响的数值分析

为研究施工缝对框架结构抗震性能的影响,利用提出的施工缝模型,基于OPENSEES平台建模进行静力非线性分析和非线性动力时程分析。通过对比整浇框架与带缝框架的顶点最大位移、层间位移角、塑性铰出现和分布规律等明确施工缝对框架结构的抗震性能的影响程度。结果表明,施工缝使框架结构的变形和层间位移角显著增大,并且使8、9度区框架结构的层间位移角分布发生改变;施工缝使柱端更易出现塑性铰,更易发生"强梁弱柱"的破坏模式;在高烈度区,施工缝的影响比较显著,如果忽略其影响,将会高估框架结构的抗震性能。     

基于性能的框架结构抗震设计研究

对国内外基于性能的抗震设计研究成果进行了较系统的综述与分析,研究表明,基于性能的抗震设计能够对结构在未来可能地震作用下的性能进行有效的控制,使破坏和损失限定在可接受的范围内。在此基础上,本文还初步提出了钢筋混凝土框架结构基于延性的抗震设计建议。     

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.     

Multiobjective optimization for performance‐based seismic design of steel moment frame structures

The performance‐based seismic design of steel special moment‐resisting frame (SMRF) structures is formulated as a multiobjective optimization problem, in which conflicting design criteria that respectively reflect the present capital investment and the future seismic risk are treated simultaneously as separate objectives other than stringent constraints. Specifically, the initial construction expenses are accounted for by the steel material weight as well as by the number of different standard steel section types, the latter roughly quantifying the degree of design complexity related additional construction cost; the seismic risk is considered in terms of maximum interstory drift demands at two hazard levels with exceedance probabilities being 50% and 2% in 50 years, respectively. The present formulation allows structural engineers to find an optimized design solution by explicitly striving for a desirable compromise between the initial investment and seismic performance. Member sizing for code‐compliant design of a planar five‐story four‐bay SMRF is presented as an application example using the proposed procedure that is automated by a multiobjective genetic algorithm. Copyright © 2004 John Wiley & Sons, Ltd.     

The damped cable system for seismic protection of frame structures — Part II: Design and application

The complementary sections of the studies carried out on the damped cable system, whose experimental and numerical characterization and assessment analyses are described in the companion paper, are presented herein. The first section includes a criterion for a preliminary evaluation of the section area of cables, the second branch stiffness of spring‐dampers and the mutual installation preload, and suggestions for a simplified nonlinear dynamic computation of the damping coefficient of dissipaters. A second section follows, aimed at evaluating the influence of cable layout on damped cable system performance. A numerical enquiry is developed on a four‐story and an eight‐story RC plane frame, to assess their seismic response for several shapes of cables, and determine what geometrical configurations are the best performing ones. In the third section, a demonstrative application of the protective system, represented by the seismic retrofit of a hospital building with RC structure, is offered. The characteristics of the system designed for this case study, including locations, dimensions, layouts, and technical installation details of cables and spring‐dampers, are illustrated, and the improvement of seismic performance as compared with the original conditions, is finally assessed. Copyright © 2011 John Wiley & Sons, Ltd.     

Evaluation of collapse resistance of RC frame structures for Chinese schools in seismic design categories B and C

According to the Code for Seismic Design of Buildings (GB50011-2001), ten typical reinforced concrete (RC) frame structures, used as school classroom buildings, are designed with different seismic fortification intensities (SFIs) (SFI=6 to 8.5) and different seismic design categories (SDCs) (SDC=B and C). The collapse resistance of the frames with SDC=B and C in terms of collapse fragility curves are quantitatively evaluated and compared via incremental dynamic analysis (IDA). The results show that the coll...     

Development and modeling of a frictional wall damper and its applications in reinforced concrete frame structures

A wall‐type friction damper is newly proposed in this paper to improve the performance of reinforced concrete (RC) framed structures under earthquake loads. Traditionally, the damper was generally invented as a brace‐type member. However, it has been seen to cause problems in the RC frame structures in that concrete is apt to be damaged in the connection regions of the RC member and the brace‐type damper under earthquake loads. The proposed wall‐type damper has an advantage in the retrofit of RC structures. The system consists of a Teflon® slider and a RC wall. The damper is also designed to control normal pressures acting on a frictional slider. The numerical applications show that the proposed damper can be effective in mitigating the seismic responses of RC frame structures and reducing the damage to RC structural members. Copyright © 2004 John Wiley & Sons, Ltd.     

RC框架结构薄弱层的层间位移可靠度水平考察

讨论了钢筋混凝土框架结构层间极限变形角的近似概率特性,考察了大震作用下20余幢钢筋混凝土框架结构薄弱层的层间位移可靠度水平,从而为直接基于位移可靠度的抗震设计中层间目标位移可靠度的确定提供了一定依据。     

钢筋混凝土框架结构直接基于位移的抗震设计

直接基于位移的抗震设计方法是对基于力的抗震设计方法的重大改进。按此方法进行设计时,需要解决的关键问题是确定结构的目标位移和相应的侧移模式。提出用框架梁节点截面屈服时的位移作为目标位移,并推导了层间屈服位移的计算公式;然后用结构近似的第一振型曲线作勾其侧移模式,对层间屈服位移进行修正。算例表明,本方法计算结果合理。     

The dynamic response of seabed anchored floating tunnels under seismic excitation

In this paper a procedure for analysing the seismic response of seabed anchored floating tunnels is presented. The first step of the research was the development of an ‘ad hoc’ finite element for modelling the behaviour of anchor elements, with particular reference to the problem of transverse oscillations under time varying axial loads. The element was subsequently inserted in a step‐by‐step procedure for the numerical analysis of non‐linear response to multiple‐support seismic input; the procedure encompasses simplified modelling of fluid–structure and soil–structure interaction effects. An example of an application is given concerning two 4680 m long floating tunnels with different seabed profiles. Copyright © 2000 John Wiley & Sons, Ltd.