Equivalent non‐linear single‐degree‐of‐freedom system of spatial asymmetric multi‐storey buildings in pushover procedure: theory and applications

In the present paper, the issue of the approximate definition of a new equivalent non‐linear single‐degree‐of‐freedom (NLSDF) system on spatial asymmetric reinforced concrete (r/c) tall multi‐storey buildings is presented. In order to achieve this goal, three different types of r/c systems are examined: the first type refers to multi‐storey planar r/c frames; the second type refers to asymmetric single‐storey r/c building; and the third type refers to asymmetric multi‐storey r/c buildings. The definition of the NLSDF system is mathematically derived, considering suitable dynamic loadings on the masses of each r/c system using simplified assumptions. The NLSDF system is very useful in the seismic design of the r/c systems, since it is widely used in all forms of various pushover analyses that have been published in the past. The use of the equivalent NLSDF system in combination with the inelastic design spectra can give an acceptable evaluation of the maximum required seismic floor displacement for a known design earthquake. The present paper concludes the total theory of definition of the optimum equivalent NLSDF system for the above three types of buildings that possess the required normality by the contemporary seismic codes in elevation. In order to illustrate the theory, three numerical examples are presented, respectively. The final numerical required displacement results by the use of the equivalent NLSDF system are verified and checked by non‐linear response history analyses. Copyright © 2008 John Wiley & Sons, Ltd.     

A new pushover procedure for two‐way asymmetric‐plan tall buildings under bidirectional earthquakes

Conventional pushover analyses despite of extensive applications are unable to estimate the general responses of asymmetric‐plan tall buildings because of ignoring the effects of higher modes and torsion. A consecutive modal pushover procedure is one of the recent nonlinear static pushover procedures that used to analyse the seismic response of one‐way asymmetric‐plan tall buildings under one‐directional seismic ground motions. In this paper, a modified consecutive modal pushover procedure (MCMP) has been proposed to estimate the seismic demands of two‐way asymmetric‐plan tall buildings under two horizontal components of earthquakes simultaneously. The accuracy of the MCMP procedure is evaluated using different buildings and comparing with the results of FEMA (Federal Emergency Management Agency) procedures, the practical modal pushover procedure and nonlinear time history analyses as an exact solution. The results show the proposed MCMP procedure is able to estimate the displacements and storey drifts accurately and introduces a great improvement in predicting the plastic hinge rotations. Copyright © 2013 John Wiley & Sons, Ltd.     

Identification of the mode shapes of spatial tall multi‐storey buildings due to earthquakes: the new ‘modal time‐histories’ method

In the present article, a new method is presented which attempts to identify the dynamic characteristics (eigen frequencies, eigen periods, mode shapes and modal damping ratios) of spatial asymmetric tall multi‐storey buildings through measured seismic responses (accelerations). This new method is entitled ‘method of modal time‐histories’, because its main target is to identify the modal time‐histories of accelerations that are obtained by accelerograms recorded on the points of buildings where suitable accelerometers have been installed. In the case of an earthquake, the multi‐channel local network of accelerometers records the time‐histories of the accelerations of the building. In addition, in order to have a successful outcome, the instrumentation form of the multi‐channel local network on the building can potentially play the most important role. This paper, first, presents a relevant mathematical analysis that is adapted to the instrumentation form applied to the multi‐storey buildings and, second, outlines the new method, which consists of nine steps. Finally, in order to illustrate the theory, a suitable numerical example of an instrumented asymmetric five‐storey r/c building that has been oscillated by a weak earthquake is also provided. On the one hand, the identification of the dynamic characteristics of spatial asymmetric buildings contributes to the removal of the uncertainties of building models in order to perform advanced non‐linear analyses about inherent building seismic capacity. On the other hand, this method supports the simple monitoring of a building's ‘structural integrity’. Copyright © 2010 John Wiley & Sons, Ltd.     

New nonlinear anti‐seismic steel device for the increasing the seismic capacity of multi‐storey reinforced concrete frames

In order to increase the seismic capacity of multi‐storey planar reinforced concrete (r/c) frames, a new metal frictional device, which the capacity of a restricted rotation around the horizontal axis perpendicular to the vertical frame plane, is presented. The proposed steel device is joined to the four joints of the vertical floor span of the frame via four diagonal steel dual‐hinge bars. During the above restricted rotation, frictional forces develop, due to a suitable synthetic material that is inserted into the rotational frictional connections. When the horizontal relative floor displacement, between two floors, exceeds a desired specific value, then the proposed device locks and the diagonal steel bar becomes fully activated to tension, adding significant additional strength to the frame. This device is installed in a vertical floor span, but it is worth noting that the devices can be placed at floor spans that are not on the same vertical line. The nonlinear numerical (static/dynamic) analyses carried out in the present article, shows that the proposed devices contribute in increase of the lateral stiffness of the frame, the lateral strength of the frame in the inelastic area and the absorption of the inserted seismic energy. Furthermore, this device protects the diagonal steel bars from the buckling or from premature failure of compression. In addition, the proposed device is designed in a way that allows it to operate effectively under large horizontal relative floor displacements due to the cyclic dynamic loads, and can be used instead of the structural r/c walls. Copyright © 2010 John Wiley & Sons, Ltd.     

A consecutive modal pushover procedure for nonlinear static analysis of one-way unsymmetric-plan tall building structures

Seismic responses of unsymmetric-plan tall buildings are substantially influenced by the effects of higher modes and torsion. Considering these effects, in this article, the consecutive modal pushover (CMP) procedure is extended to estimate the seismic demands of one-way unsymmetric-plan tall buildings. The procedure uses multi-stage and classical single-stage pushover analyses and benefits from the elastic modal properties of the structure. Both lateral forces and torsional moments obtained from modal analysis are used in the multi-stage pushover analysis. The seismic demands are obtained by enveloping the peak inelastic responses resulting from the multi-stage and single-stage pushover analyses. To verify and appraise the procedure, it is applied to the 10, 15, and 20-storey one-way unsymmetric-plan buildings including systems with different degrees of coupling between the lateral displacements and torsional rotations, i.e. torsionally-stiff (TS), torsionally-similarly-stiff (TSS) and torsionally-flexible (TF) systems. The modal pushover analysis (MPA) procedure is implemented for the purpose of comparison as well. The results from the approximate pushover procedures are compared with the results obtained by the nonlinear response history analysis (NL-RHA). It is demonstrated that the CMP procedure is able to take into account the higher mode influences as well as amplification or de-amplification of seismic displacements at the flexible and stiff edges of unsymmetric-plan tall buildings. The extended procedure can predict to a reasonable accuracy the peak inelastic responses, such as displacements and storey drifts. The CMP procedure represents an important improvement in estimating the plastic rotations of hinges at both flexible and stiff sides of unsymmetric-plan tall buildings in comparison with the MPA procedure.     

On the applicability of pushover analysis for seismic evaluation of medium‐ and high‐rise buildings

The assumption that the dynamic performance of structures is mainly determined from the corresponding single‐degree‐of‐freedom system in pushover analysis is generally valid for low‐rise structures, where the structural behaviour is dominated by the first vibration mode. However, higher modes of medium‐ and high‐rise structures will have significant effect on the dynamic characteristics. In this paper, the applicability of pushover analysis for seismic evaluation of medium‐to‐high‐rise shear‐wall structures is investigated. The displacements and internal forces of shear wall structures with different heights are determined by nonlinear response history analysis, where the shear walls are considered as multi‐degree‐of‐freedom systems and modelled by fibre elements. The results of the analysis are compared with those from the pushover procedure. It is shown that pushover analysis generally underestimates inter‐storey drifts and rotations, in particular those at upper storeys of buildings, and overestimates the peak roof displacement at inelastic deformation stage. It is shown that neglecting higher mode effects in the analysis will significantly underestimate the shear force and overturning moment. It is suggested that pushover analysis may not be suitable for analysing high‐rise shear‐wall or wall‐frame structures. New procedures of seismic evaluation for shear‐wall and wall‐frame structures based on nonlinear response history analysis should be developed. Copyright © 2009 John Wiley & Sons, Ltd.     

An empirical relationship to determine lateral seismic response of mid‐rise building frames under influence of soil–structure interaction

In this study, to determine the elastic and inelastic structural responses of mid‐rise building frames under the influence of soil–structure interaction, three types of mid‐rise moment‐resisting building frames, including 5‐storey, 10‐storey and 15‐storey buildings are selected. In addition, three soil types with the shear wave velocities less than 600 m/s, representing soil classes C_e, D_e and E_e according to AS 1170.4–2007 (Earthquake action in Australia, Australian Standards), having three bedrock depths of 10 m, 20 m and 30 m are adopted. The structural sections are designed after conducting nonlinear time history analysis, on the basis of both elastic method and inelastic procedure considering elastic‐perfectly plastic behaviour of structural elements. The frame sections are modelled and analysed, employing finite difference method adopting FLAC2D software under two different boundary conditions: (a) fixed base (no soil–structure interaction) and (b) considering soil–structure interaction. Fully nonlinear dynamic analyses under the influence of different earthquake records are conducted, and the results in terms of the maximum lateral displacements and base shears for the above mentioned boundary conditions for both elastic and inelastic behaviours of the structural models are obtained, compared and discussed. With the results, a comprehensive empirical relationship is proposed to determine the lateral displacements of the mid‐rise moment‐resisting building frames under earthquake and the influence of soil–structure interaction. Copyright © 2012 John Wiley & Sons, Ltd.     

A consecutive modal pushover procedure for estimating the seismic demands of tall buildings

The nonlinear static procedure (NSP), based on pushover analysis, has become a favourite tool for use in practical applications for building evaluation and design verification. The NSP is, however, restricted to single-mode response. It is therefore valid for low-rise buildings where the behaviour is dominated by the fundamental vibration mode. It is well recognized that the seismic demands derived from the conventional NSP are greatly underestimated in the upper storeys of tall buildings, in which higher-mode contributions to the response are important. This paper presents a new pushover procedure which can take into account higher-mode effects. The procedure, which has been named the consecutive modal pushover (CMP) procedure, utilizes multi-stage and single-stage pushover analyses. The final structural responses are determined by enveloping the results of multi-stage and single-stage pushover analyses. The procedure is applied to four special steel moment-resisting frames with different heights. A comparison between estimates from the CMP procedure and the exact values obtained by nonlinear response history analysis (NL-RHA), as well as predictions from modal pushover analysis (MPA), has been carried out. It is demonstrated that the CMP procedure is able to effectively overcome the limitations of traditional pushover analysis, and to accurately predict the seismic demands of tall buildings.     

Pushover方法的准确性和适用性研究

Pushover方法作为一种建筑结构弹塑性地震响应的简化近似计算方法和抗震性能评价方法已得到广泛应用。但由于其理论基础不严密,其准确性需要给予必要确认,同时其适用性也应受到一定的限制。本文以逐步增量弹塑性时程方法的结果为基准,分别以一个普通6层RC框架结构和一个18层RC框架-剪力墙结构为例,对Pushover方法的准确性和适用性进行了分析研究。结果表明,Pushover方法仅适用于以第一振型为主的高度不大的结构,且应采用两种以上的侧力模式;对于高阶振型影响较大的结构,该方法的准确性较差,承载力预测显著偏低。     

钢筋混凝土框架-剪力墙结构基于位移的抗震设计方法

根据钢筋混凝土框架-剪力墙结构的特点,将其性能划分为使用良好、保证人身安全和防止倒塌三个水平,并用层间位移角限值予以量化。以作用倒三角形水平分布荷载的等截面弯剪悬臂杆的侧移曲线作为其初始侧移模式。对于使用良好性能水平,将侧移曲线上反弯点对应的楼层处的层间位移角刚好达到相应限值时的侧移曲线作为目标侧移曲线,据此计算等效单自由度体系的等效参数以及原结构的基底剪力和各质点的水平地震作用。对于保证人身安全和防止倒塌的性能水平,根据Pushover曲线与需求曲线的关系对结构予以调整,使结构满足这两个性能水平的要求。     

An improved consecutive modal pushover procedure for estimating seismic demands of multi‐storey framed buildings

An improved consecutive modal pushover (ICMP) procedure is proposed to enhance the accuracy of conventional CMP procedure for estimating seismic demands of tall buildings. It accounts for inelastic structural properties and interaction between vibration modes. The displacement increment at the roof of buildings used in each stage of pushover analyses is modified based on the displacement contribution of each mode. The performance of the proposed ICMP procedure is verified against three high‐rise frames subjected to various ground motions. The results obtained from the ICMP procedure are compared with those from the nonlinear time history analysis, conventional pushover analysis, and CMP analysis. The comparison shows the advantages of the ICMP over the other pushover procedures. It is concluded that the ICMP procedure is more accurate than the CMP procedure.     

高宝大厦巨型框筒结构静力弹塑性(Pushover)分析

将结构静力弹塑性分析与地震反应谱结合起来的Pushover方法是一种简单有效的结构抗震能力评定方法,已在我国逐渐得到推广应用.依据该法基本原理,对上海高宝大厦的巨型框筒结构进行罕遇地震下的抗震分析,得到性能点处的层剪力、层间位移角曲线和塑性铰分布.计算结果表明,该结构符合"强柱弱梁"的原则,能满足大震不倒的设防要求.     

Target roof displacement of degrading moment-resisting frames

In application of the nonlinear static procedure or static pushover analysis for estimating seismic demands of building components due to an earthquake ground motion, the peak (target) roof displacement needs to be estimated so as to quantify the global seismic demand. Most of the methods for this estimation are based on using the response of an equivalent single-degree-of-freedom (SDF) system that does not explicitly account for degradation behaviour. Hence, these methods may not be suitable for use in reinforced-concrete (RC) buildings. This study proposes that the equivalent SDF system should include the effects of degradation and its degrading properties can be determined from cyclic pushover analyses. The accuracy of the proposed method is investigated by comparing the peak roof displacements of RC moment-resisting frame buildings estimated by the proposed degrading equivalent SDF systems to the ‘reference’ value determined by nonlinear response history analysis of multi-degree-of-freedom (MDF) system building models. It was found that the use of the degrading equivalent SDF systems can predict the peak roof displacement more accurately than using non-degrading, or bilinear, equivalent SDF systems, especially in the case of non-ductile RC frames with significant degradation.     

Assessment of current nonlinear static procedures for seismic evaluation of BRBF buildings

Nonlinear static procedures (NSPs) are now standard in engineering practice to estimate seismic demands in the design and evaluation of buildings. This paper aims to investigate comparatively the bias and accuracy of modal, improved modal pushover analysis (MPA, IMPA) and mass proportional pushover (MPP) procedures when they are applied to buckling-restrained braced frame (BRBF) buildings which have become a favorable lateral-force resisting system for earthquake resistant buildings. Three-, 6-, 10-, and 14-storey concentrically BRBF buildings were analyzed due to two sets of strong ground motions having 2% and 10% probability of being exceeded in 50 years. The assessment is based on comparing seismic displacement demands such as target roof displacements, peak floor/roof displacements and inter-storey drifts. The NSP estimates are compared to results from nonlinear response history analysis (NL-RHA). The response statistics presented show that the MPP procedure tends to inaccurately estimate seismic demands of lower stories of tall buildings considered in this study while MPA and IMPA procedures provide reasonably accurate results in estimating maximum inter-storey drift over all stories of studied BRBF systems.     

竖向不规则结构非线性静力推覆分析的水平侧向力研究

非线性静力分析方法可以较为简便地预估结构的弹塑性反应,但仅取常见水平侧向力分布模型并不能满足实际工程的需要,例如高振型的影响和不规则结构的特殊性。对竖向不规则结构进行非线性时程分析,建立了水平侧向力分布与结构层刚度的关系式,从而提出了一种新的水平侧向力分布形式和方法。结合几种常见的水平侧向力形式,对5种侧向刚度不规则的情况进行了推覆分析,并与时程分析结果进行了比较,结果表明该方法不但可以找到各种侧向刚度不规则结构的薄弱层而且还具有较高的精度。     

Earthquake responses of RC moment frames subjected to near‐fault ground motions

There are three objectives in this paper. The first objective is to compare the dynamic behaviour of a reinforced concrete building structure subjected to near‐fault and far‐field ground motions. A twelve‐storey and a five‐storey reinforced concrete building with moment resisting frames were selected in this study. The Chi‐Chi earthquake was selected as a first set in this study to test near‐fault earthquake characteristics. Further, another earthquake record of an event at the same site was selected to test the far‐field earthquake characteristics for comparison. Through nonlinear time history analyses, the results show that the near‐fault earthquake results in much more damage than the far‐field earthquake. The second objective of this paper is to compare the predictions for ductility demand by the nonlinear time history analyses with those obtained by the pushover analysis procedure. The third objective is to explore the parameters that will more significantly affect the the building structure's dynamic response characteristics of base shear reduction and displacement amplification. Copyright © 2001 John Wiley & Sons, Ltd.     

框架——剪力墙结构的静力弹塑性分析研究

静力弹塑性方法作为一种评价结构抗震性能和计算结构弹塑性变形的简化方法,近年来得到了广泛应用。但由于传统的定侧力模式的静力弹塑性方法只考虑第一振型,无法反映高层建筑结构的高阶振型影响。为考虑高阶振型的影响,Chopra在振型分解反应谱组合法的基础上,提出了MPA方法。本文首先讨论了应用MPA方法需注意的问题,然后用一个18层钢筋混凝土框架—剪力墙结构为算例,以逐步增量弹塑性时程分析结果为基准,对传统定侧力模式静力弹塑性方法和MPA方法的分析结果进行了对比研究。结果表明,相比于定侧力模式静力弹塑性分析结果,MPA方法的分析结果更接近弹塑性时程分析结果。     

Seismic analysis of asymmetric multistorey buildings including foundation interaction and P-Δ effects

This paper presents a method of seismic analysis of three-dimensional asymmetric multistorey buildings founded on flexible foundations. The building-foundation system considered in this study is a linear elastic N-storey asymmetric building with a rigid footing resting on the surface of a linear elastic soil half-space. The method of analysis also includes the P-Δ effects, in which the additional overturning moment and torsional moment at each storey due to P-Δ effects have been replaced by fictitious lateral forces and torques. The whole system has 3N + 5 displacement degrees-of-freedom. The necessary governing equations have been developed considering the three motions of each floor and the five motions of the whole building. Recognizing that the superstructure alone admits classical normal modes, the governing equations of the floors are first uncoupled in terms of footing displacements using the mode superposition method. Substitution of structural deformations, in combination with the dynamic soil-structure interaction force-displacement relationships into the governing equations of the whole system results in five integro-differential equations for footing displacements, which are then solved by numerical step-by-step time history analysis. The floor displacement responses, storey shears, storey torque, etc., are obtained by back substitution of footing accelerations into the relevant governing equations. As a demonstration of the method of analysis and in order to obtain the soil-structure interaction effects, P-Δ effects, and the eccentricity effects, a 10-storey asymmetric building on soft soil was subjected to El Centro 1940 earthquake excitations. The results show that the soft soil conditions increase the lateral deflections, but reduce the twists, storey shears and torques. Increasing eccentricity increases the floor twists and storey torques, however, it does not modify the lateral deflections at the centre of mass, and the total storey shears. The significance of P-Δ effects along with soil-structure interactions on the response of this building has also been discussed.     

Incremental dynamic collapse analysis of RC core‐wall tall buildings considering spatial seismic response distributions

Despite wide‐ranging studies on fragility analysis and collapse safety assessment of short to medium‐rise reinforced concrete (RC) structures, a new interest in the topic is still valuable and even necessary for tall RC buildings. This study aims at establishing fragility relationships as well as collapse probability of high‐rise RC core‐wall buildings under maximum considered earthquake ground motions. This study is carried out in a probabilistic framework on a case study of a fully 3‐dimensional numerical model developed to simulate seismic behavior of a 42‐story building having a RC core‐wall system. Proposing planar and vertical distributions of ductility and damage indices, the incremental dynamic analysis, and the multi‐direction nonlinear static (pushover) analyses were employed to reach the research goal. Median collapse‐level capacities were defined in terms of seismic responses (e.g., ductility/damage indices) as well as several intensity measures by employing statistical analyses and cumulative density functions. Available and acceptable collapse margin ratios were next estimated to quantify collapse safety at maximum considered earthquake shaking level. On an average basis, the statistics indicated 9%–10% and 5%–6% collapse probability of the building subjected to near‐ and far‐field ground motions, respectively.     

Seismic fragility relationships of reinforced concrete high‐rise buildings

A complete methodology is presented for the seismic fragility assessment of reinforced concrete high‐rise buildings. The key steps of the methodology are illustrated through an example of the fragility assessment of an existing 54‐story building with a dual core wall system. The set of rigorously derived probabilistic fragilities are the first published for high‐rise reinforced concrete buildings. The inelastic nonlinear dynamic analyses for the fragility assessments are made using a simplified lumped‐parameter model that was derived from highly detailed FE models using genetic algorithms. New definitions for performance limit states were based on the results of detailed pushover analyses of a distributed inelastic nonlinear finite element model that includes shear–flexure–axial interaction effects. To develop the fragility relationships, 1800 dynamic response history analyses were conducted. This study considered uncertainty in structural material values as well as in seismic demand. Thirty strong motion records were selected for use in the analyses that would produce an appropriate range in structural response characteristics due to variation in magnitude, distance and site condition. The overall approach is generic and can be applied to developing computationally efficient and probabilistically‐based seismic fragility relationships for reinforced concrete high‐rise buildings of different configurations. Copyright © 2007 John Wiley & Sons, Ltd.