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.     

平面不规则结构非弹性扭转地震反应研究进展

不规则建筑结构在侧向地震荷载作用下由于质量中心和刚度中心的不重合导致平扭耦联反应的发生,使得结构构件的变形需求分布在结构平面内并不一致,从而产生附加的强度和变形需求。尽管不规则建筑结构在地震作用下的扭转问题一直受到研究学者的关注和研究,并取得了很多显著的成果,但仍然存在着一些争议,有待于继续深入研究。本文从结构的分析模型、影响参数及地震动输入等方面回顾总结了平面不规则建筑结构在地震作用下非弹性扭转的研究进展,结合当前的研究工作指出今后研究的发展方向。     

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.     

Inelastic torsion of multistorey buildings under earthquake excitations

The inelastic earthquake response of eccentric, multistorey, frame‐type, reinforced concrete buildings is investigated using three‐ and five‐storey models, subjected to a set of 10, two‐component, semi‐artificial motions, generated to match the design spectrum. Buildings designed according to the EC8 as well as the UBC‐97 code were included in the investigation. It is found that contrary to what the simplified one‐storey, typical, shear‐beam models predict, the so‐called ‘flexible’ side frames exhibit higher ductility demands than the ‘stiff’ side frames. The substantial differences in such demands between the two sides suggest a need for reassessment of the pertinent code provisions. This investigation constitutes one of the first attempts to study the problem of inelastic torsion by means of realistic, multistorey inelastic building models. Additional studies with similar or even more refined idealizations will certainly be required to arrive at definite results and recommendations for possible code revisions. Copyright © 2005 John Wiley & Sons, Ltd.     

Pseudodynamic response of torsionally unbalanced two‐storey test structure

Two one‐way eccentric, two‐storey, one‐by‐one‐bay reinforced concrete (RC) structures are pseudodynamically tested under unidirectional ground motions. Theoretical considerations about the effect of torsional coupling on modal periods and shapes agree with modal results of the test structure, considering member stiffness is equal to the secant stiffness to yielding in skew‐symmetric bending. Modal periods of such an elastic structure are in fair agreement with effective periods inferred from the measured response at the beginning of a test of a thoroughly cracked structure and at the end of the test. A time‐varying stiffness matrix and a non‐proportional damping matrix fitted to the test results may be used to reproduce the measured response approximately by modal superposition and identify the role of the four time‐varying modes. Flexible side columns sustained very large drift demands simultaneously in the two transverse directions and suffered significant but not heavy, damage at lap‐splices. RC‐jacketing of the flexible side columns practically eliminated the static eccentricity between the floor centres of twist and mass as well as the torsional response. Inelastic time‐history analysis with point‐hinge member models, using as elastic stiffness the secant stiffness to yielding and neglecting post‐ultimate‐strength cyclic degradation of resistance in members with plain bars and poor detailing, predicted fairly well the response until the peak displacements and member deformations occurred. After that, it underestimated displacement peaks and the lengthening of the apparent period and missed the gradual drifting of the response towards a permanent offset. Copyright © 2007 John Wiley & Sons, Ltd.     

Effects of supplemental viscous damping on inelastic seismic response of asymmetric systems

This paper investigates the effects of supplemental viscous damping on the seismic response of one‐storey, asymmetric‐plan systems responding in the inelastic range of behaviour. It was found that addition of the supplemental damping reduces not only deformation demand but also ductility and hysteretic energy dissipation demands on lateral load resisting elements during earthquake loading. However, the level of reduction strongly depends on the plan‐wise distribution of supplemental damping. Nearly optimal reduction in demands on the outermost flexible‐side element, an element generally considered to be the most critical element, was realized when damping was distributed unevenly in the system plan such that the damping eccentricity was equal in magnitude but opposite in algebraic sign to the structural eccentricity of the system. These results are similar to those noted previously for linear elastic systems, indicating that supplemental damping is also effective for systems expected to respond in the inelastic range. Copyright © 2001 John Wiley & Sons, Ltd.     

A review of reference models for assessing inelastic seismic torsional effects in buildings

This paper reviews the various forms of reference model adopted for studies that evaluate inelastic seismic torsional effects and assess their implications for building design. Both qualitative and quantitative comparisons are presented. The importance of selecting an appropriate reference model is in accordance with the above aims is emphasised. It is found that variations in the reference models adopted in analyses of inelastic seismic torsional effects may lead to significant differences in the results obtained and, hence, to the conclusions drawn from such studies. It is demonstrated that accidental torsional effects, as incorporated in code design provisions, result in significant changes to the distribution of element strengths and the inelastic response behaviour of symmetric and generalised torsionally balanced reference models. Such changes should be considered when employing such models to evaluate the ineslatic response of torsionally unbalanced building systems.     

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。     

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.     

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.     

An answer to an important controversy and the need for caution when using simple models to predict inelastic earthquake response of buildings with torsion

This paper presents evidence that the extension of conclusions based on the widely used simplified, one story, eccentric systems of the shear‐beam type, to actual, nonsymmetric buildings and consequent assessments of the pertinent code provisions, can be quite erroneous, unless special care is taken to match the basic properties of the simplified models to those of the real buildings. The evidence comes from comparisons of results obtained using three variants of simplified models, with results from the inelastic dynamic response of three‐ and five‐story eccentric buildings computed with detailed MDOF systems, where the members are idealized with the well‐known plastic hinge model. In addition, a convincing answer is provided on a pertinent hanging controversy: For frame‐type buildings, designed in accordance with the dynamic provisions of modern codes (such as EC8 or IBC2000), which allow reduced shears at the stiff edge due to torsion, the frames at the flexible sides are the critical elements in terms of ductility demands. Copyright © 2009 John Wiley & Sons, Ltd.     

Seismic behavior of asymmetric RC wall buildings: principles and new deformation‐based design method

The seismic design of multi‐story buildings asymmetric in plan yet regular in elevation and stiffened with ductile RC structural walls is addressed. A realistic modeling of the non‐linear ductile behavior of the RC walls is considered in combination with the characteristics of the dynamic torsional response of asymmetric buildings. Design criteria such as the determination of the system ductility, taking into account the location and ductility demand of the RC walls, the story‐drift demand at the softer (most displaced) edge of the building under the design earthquake, the allowable ductility (ultimate limit state) and the allowable story‐drift (performance goals) are discussed. The definition of an eccentricity of the earthquake‐equivalent lateral force is proposed and used to determine the effective displacement profile of the building yet not the strength distribution under the design earthquake. Furthermore, an appropriate procedure is proposed to calculate the fundamental frequency and the earthquake‐equivalent lateral force. A new deformation‐based seismic design method taking into account the characteristics of the dynamic torsional response, the ductility of the RC walls, the system ductility and the story‐drift at the softer (most displaced) edge of the building is presented and illustrated with an example of seismic design of a multi‐story asymmetric RC wall building. Copyright © 2005 John Wiley & Sons, Ltd.     

一类多层偏心结构的地震反应研究

本文用空间的两向抗侧力体系振动模型对五层结构分别分析了首层偏心,中间层偏心,顶层偏心和均匀偏心等不同偏心情况下的弹性地震反应规律,研究了静力偏心距,结构的基本平动周期,平扭频率比,非激励方向的平动频率等对结构的名义基底剪力和偏心层构件的最大剪力系数的影响。     

Effect of site amplification on inelastic seismic response

The available models for eff ective periods of site and structure are reviewed in context of frequency tuning in the inelastic seismic response of soil-structure system. The eff ect of seismic intensity and ductility demand, on the eff ective periods, is investigated, and inelastic site amplifi cation is shown to be strongly correlated to the normalized eff ective period. Two non-dimensional parameters, analogous to the conventional site amplifi cation factors in codes, are defi ned to quantify the inelastic site amplifi cation. It is shown that the inelastic site amplifi cation factor (i.e. ratio of constant ductility spectral ordinates at soil site to those at rock outcrop) is able to represent the site eff ects more clearly, as compared to the inelastic site amplifi cation ratio (i.e. ratio of inelastic spectral ordinates at soil site to the corresponding elastic spectral ordinates at rock outcrop). Further, the peak in the amplifi cation factor corresponding to the eff ective site period diminishes rapidly with increasing ductility demand.     

An alternative approach for the seismic rehabilitation of existing RC buildings using seismic isolation

Usually, buildings with seismic isolation are designed to comply with an operational building performance level after strong earthquakes. This approach, however, may limit the use of seismic isolation for the seismic rehabilitation of existing buildings with low lateral strength or substandard details, because it often requires invasive strengthening measures in the superstructure or the use of expensive custom‐made devices. In this paper, an alternative approach for the seismic rehabilitation of existing buildings with seismic isolation, based on the acceptance of limited plastic deformations in the superstructure under strong earthquakes, is proposed and then applied to a real case study, represented by a four‐storey RC frame building. Nonlinear response‐time histories analyses of an accurate model of the case‐study building are carried out to evaluate the seismic performances of the structure, comparing different rehabilitation strategies with and without seismic isolation. Initial costs of the intervention and possible (future) repair costs are then estimated. Based on the results of this study, values of the behavior factor (i.e. response modification factor) higher than those adopted in the current codes for base‐isolated buildings are tentatively proposed. Copyright © 2015 John Wiley & Sons, Ltd.     

Effect of orthogonal inplane structural elements on inelastic torsional response

The elastic torsional stiffness of a structure has important influence on the seismic response of an asymmetric structure, both in the elastic and inelastic range. For elastic structures it is immaterial whether the stiffness is provided solely by structural elements in planes parallel to the direction of earthquake or by a combination of such elements in parallel and orthogonal planes. The issue of how the relative contribution of structural elements in orthogonal planes affects the torsional response of inelastic structures has been the subject of continuing study. Several researchers have noted that structural elements in orthogonal planes reduce the ductility demands in both the flexible and stiff edge elements parallel to the earthquake. Some have noted that the beneficial effect of structural elements in orthogonal planes is more pronounced when such elements remain elastic. These issues are further examined in this paper through analytical studies on the torsional response of single-storey building models. It is shown that, contrary to the findings of some previous studies, the torsional response of inelastic structures is affected primarily by the total torsional stiffness in the elastic range, and not so much by whether such stiffness is contributed solely by structural elements in parallel planes or by such elements in both parallel and orthogonal planes. Copyright © 1999 John Wiley & Sons, Ltd.     

Inelastic seismic response of one-way plan-asymmetric systems under bi-directional ground motions

The static design requirements of some seismic codes, such as the Eurocode 8 and—in most cases—the Uniform Building Code, to allow for the effects of earthquake excitation acting in a direction other than the principal axes of the structure do not apply to one-way asymmetric systems. Therefore, with some exceptions, no specific provisions are considered for such systems to cover effects of structural asymmetry on the behaviour of elements located along the symmetric system direction. Aimed towards fulfilling this need, in this paper, a wide parametric study of the inelastic response of one-way asymmetric systems designed according to Uniform Building Code is carried out, considering two-component earthquake excitations. The analyses show that the maximum ductility demands on elements aligned along the asymmetric system direction are very close to, and even lower than, those obtained for symmetric reference systems. Conversely, the symmetric direction elements undergo significantly larger inelasticity than if they were located in symmetric reference systems. Subsequently, the overstrength needed by the symmetric direction elements to prevent such additional ductility demands for several stiffness and plan configurations is quantified. It is concluded that one-way asymmetry should be considered by seismic codes as an intrinsic system property, thus implying that specific provisions should be included for designing elements located along the symmetric system direction, in addition to those currently subscribed to design the asymmetric direction elements. © 1998 John Wiley & Sons, Ltd.     

Assessment of seismic design response factors of concrete wall buildings

To verify the seismic design response factors of high-rise buildings, five reference structures, varying in height from 20- to 60-stories, were selected and designed according to modern design codes to represent a wide range of concrete wall structures. Verified fiber-based analytical models for inelastic simulation were developed, considering the geometric nonlinearity and material inelasticity of the structural members. The ground motion uncertainty was accounted for by employing 20 earthquake records representing two seismic scenarios, consistent with the latest understanding of the tectonic setting and seismicity of the selected reference region (UAE). A large number of Inelastic Pushover Analyses (IPAs) and Incremental Dynamic Collapse Analyses (IDCAs) were deployed for the reference structures to estimate the seismic design response factors. It is concluded that the factors adopted by the design code are adequately conservative. The results of this systematic assessment of seismic design response factors apply to a wide variety of contemporary concrete wall buildings with various characteristics.     

Damage response of multistorey r/c buildings with different structural systems subjected to seismic motion of arbitrary orientation

In the present study the combined influence of seismic orientation and a number of parameters characterizing the structural system of Reinforced Concrete (R/C) buildings on the level of expected damages are examined. For the purposes of the above investigation eight medium‐rise buildings are designed on the basis of the current seismic codes. The structural characteristics examined are the ratio of the base shear received by the structural walls, the ratio of horizontal stiffness in two orthogonal directions and the structural eccentricity. Then, the buildings are analyzed by nonlinear time response analysis using 100 bidirectional earthquake ground motions. The two horizontal accelerograms of each ground motion are applied along horizontal orthogonal axes, forming 72 different angles with the structural axes. The structural damage is expressed in terms of the Park and Ang damage index. The results of the analyses revealed that the damage level of the buildings is strongly affected by the incident angle of the ground motion. The extent at which the orientation of the seismic records influences the damage response depends on the structural system and the distance of the record to the fault rupture. As a consequence, the common practice of applying the earthquake records along the structural axes can lead to significant underestimation of structural damage. Also, it was shown that the structural eccentricity can significantly differentiate the seismic damage level, as well as the impact of the earthquake orientation on the structural damage. Copyright © 2015 John Wiley & Sons, Ltd.     

Seismic code analysis of multi-storey asymmetric buildings

Static torsional provisions in most seismic codes require that the lateral force at each floor level be applied at some distance from the reference centre at that floor. However, codes do not specify how to determine the locations of these centres. As a result, several different definitions of the reference centres are being used to implement the code analysis. This investigation examined how the results using various reference centres differ and which of these centres would lead to results that are in agreement with those of dynamic analysis. For this purpose three different buildings ranging form torsionally stiff to torsionally flexible were analysed. It was shown that for the class of buildings studied in this investigation that although the locations of the reference centres were quite different, the results were very similar and nearly independent of the reference centre. Comparison of results calculated from static code equivalent lateral force procedures and results from dynamic response spectrum analyses showed that the static code procedures led to design forces very close (flexible wall) or slightly conservative (stiff wall) when compared to the dynamic analysis for the torsionally stiff building. However, the static code procedures significantly underestimated the design forces of the stiff walls and significantly overestimated the design forces of the flexible walls for the torsionally flexible buildings. © 1998 John Wiley & Sons, Ltd.