Estimation of inelastic displacement factor of soil‐shallow‐foundation MDOF systems incorporating higher modes effect

This study attempts to investigate the higher‐mode effects on the constant‐ductility inelastic displacement factors of multi‐degree‐of‐freedom (MDOF) systems considering soil‐structure interaction. These factors were computed for 12,600 two‐dimensional superstructure models of shear buildings and their corresponding equivalent single‐degree‐of‐freedom (ESDOF) systems under 26 ground motions recorded on alluvium and soft soil. An intensive parametric study was carried out for a wide range of non‐dimensional parameters, which completely define the problem. The underlying soil is considered as a homogeneous half‐space based on the concept of cone model. The higher‐mode effects were then investigated through defining the ratio of inelastic displacement factor of MDOF system to that of the corresponding ESDOF one. The influence of soil‐structure interaction key parameters, fundamental period, ductility ratio, the number of stories, and dispersion of the results are evaluated and discussed. Results indicate that as the base becomes very flexible, unlike to the fixed‐base systems, in which the defined ratios are greater than unity, using the inelastic displacement factors of ESDOF models for MDOF ones would result in a remarkable overestimation of maximum inter‐story displacement demand. A new expression is proposed to estimate the ratio of inelastic displacement factor of MDOF soil‐structure systems to that of SDOF counterpart.     

弹塑性结构的位移比谱

本文从单自由度体系弹塑性反应的计算研究人手,探讨了弹塑性结构最大位移反应与相应弹性结构的最大位移反应之间的关系,找出了有关规律。采用统计平均的方法,作出设计用的弹性位移谱及弹塑性位移比谱,从而可以在已知弹性位移的基础上,方便地求得弹塑性位移反应。本文还讨论了地面加速度峰值与结构屈服限变化对结构弹塑性最大位移反应的影响,找出了其间关系,从而使在计算弹塑性位移反应时,仅计算某一烈度区内的值即可,其他区域,可通过有关规则确定。     

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.     

Damage Identification for Hysteretic Structures Using a Mode Decomposition Method

This article investigates structural health monitoring (SHM) of multidegree of freedom (MDOF) structures after major seismic or environmental events. A recently developed hysteresis loop analysis (HLA) SHM technique has performed robustly for single degree of freedom (SDOF) and single mode dominant MDOF structures. However, strong ground motions can trigger higher vibration modes, resulting in irregular hysteresis loops and making this otherwise robust identification difficult. This study presents a new filtering tool, enabling reconstruction of single mode dominant restoring force‐displacement loops which can be readily used for HLA. The proposed filtering tool is based on a classic modal decomposition using optimized mode shape coefficients. The optimization process is carried out in a modal space and is based on decoupling frequency response spectra of interfering modes. Application of modal decomposition using the optimized mode shape coefficients allows for reconstruction of single‐mode dominant hysteresis loops, which can be effectively identified using HLA. The proposed filtering tool is validated on the reconstruction of hysteresis loops on an experimental bridge pier test structure with notable contributions from at least two modes. The results show the method eliminates the influence of all higher modes that contain significant energy content and yields the reconstruction of “smooth” single mode dominant hysteresis loops. The resulting SHM analysis on the reconstructed experimental hysteresis loops identified degradation in the elastic stiffness profiles, indicating damage within the structure and matching prior published results based on physical inspection of damage. The overall method presented increases the breadth of potential application of the HLA method and can be readily generalized to a range of MDOF structures.     

Predictive instantaneous optimal control of inelastic structures based on ground velocity

One of the challenges confronting structural engineers in structural control is to find more efficient control algorithms to ensure better and more reliable control results to protect structures against the damaging effects of destructive environmental forces. In this paper, a simple control algorithm, namely the Predictive Instantaneous Optimal Control (PIOC) algorithm, is proposed by introducing a new state space form. Different from the classical ground acceleration‐based control algorithms, this new control algorithm uses earthquake ground velocity as the input. Since the earthquake ground velocity is not at high frequency as compared with the ground acceleration, it can be predicted at certain time steps beforehand in real‐time domain with higher accuracy. This ensures the synchronous execution of the proposed PIOC algorithm with real‐time application of the control force. To capture the damaging effects during earthquake ground motions, the force analogy method is used to characterize structures responding in the inelastic domain. Numerical studies are performed to compare the structural response with and without control using both single degree of freedom and multi‐degree of freedom structural models. Results show that the PIOC algorithm is effective in reducing the structural response under earthquake excitation. Copyright © 2006 John Wiley & Sons, Ltd.     

Numerical and comparative study of earthquake intensity indices in seismic analysis

Elastoplastic and time‐dependent analysis of seismic structures has become a major analysis technique in popularly accepted performance‐based seismic design. However, the primary difficulty in using this technique is the lack of a unified criterion in the selection of various intensity indices of ground motions. Various earthquake factors influencing the elastoplastic response of seismic structures are highly sophisticated. Hence, it is vitally important to choose an appropriate and comprehensive earthquake intensity index to achieve an accurate correlation with the structural performance. In this study, a total of 30 earthquake intensity indices published in the literature are reviewed and are evaluated through correlation analysis based on 60 ground motion records. Examined herein is the correlation between existing earthquake intensity indices and the seismic responses of elastoplastic single degree‐of‐freedom and multi degree‐of‐freedom systems. The characteristics and applicability of such indices are also discussed in some detail, based on which appropriate earthquake intensity indices are recommended. Copyright © 2011 John Wiley & Sons, Ltd.     

Strength reduction factor for MDOF soil–structure systems

In most of the seismic design provision, the concept of strength reduction factor has been developed to account for inelastic behavior of structures under seismic excitations. Most recent studies considered soil–structure interaction (SSI) in inelastic response analysis are mainly based on idealized structural models of single degree‐of‐freedom (SDOF) systems. However, an SDOF system might not be able to well capture the SSI and structural response characteristics of real multiple degrees‐of‐freedom (MDOF) systems. In this paper, through a comprehensive parametric study of 21600 MDOF and its equivalent SDOF (E‐SDOF) systems subjected to an ensemble of 30 earthquake ground motions recorded on alluvium and soft soils, effects of SSI on strength reduction factor of MDOF systems have been intensively investigated. It is concluded that generally, SSI reduces the strength reduction factor of both MDOF and more intensively SDOF systems. However, depending on the number of stories, soil flexibility, aspect ratio and inelastic range of vibration, the strength reduction factor of MDOF systems could be significantly different from that of E‐SDOF systems. A new simplified equation, which is a function of fixed‐base fundamental period, ductility ratio, the number of stories, structure slenderness ratio and dimensionless frequency, is proposed to estimate strength reduction factors for MDOF soil–structure systems. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance test of a tuned liquid mass damper for reducing bidirectional responses of building structures

In this study, a tuned liquid mass damper (TLMD) was proposed to reduce bidirectional responses of building structures, and its control performance was experimentally evaluated. The proposed TLMD with only one device body reduces bidirectional responses of building structures by behaving as a TMD and a TLCD in the weak and strong axial directions of a building floor plan, respectively. First, the control performance of a TLMD mounted on a scale‐downed single‐degree‐of‐freedom building model was experimentally evaluated by exciting this system with an actuator. Then, the real‐time hybrid shaking table testing method (RTHSTTM) was performed to assess the control efficiency of the total system by adopting the TLCD and the building model as the experimental and numerical parts, respectively. It was confirmed by comparing uncontrolled and controlled testing results that the proposed TLMD can be applied to reduce the responses in both the weak and strong directions of building structures. Also, the results from RTHSTTM showed that the performance of TLMD‐controlled building structure can be accurately evaluated by this method only using a TLMD as the experimental part. Copyright © 2008 John Wiley & Sons, Ltd.     

基于概率的单自由度体系震后残余变形计算

准确预测结构的震后残余变形,对于结构震后性能控制及建立考虑可修复性的抗震设计方法具有重要意义。通过对不同参数的双线性单自由度（SDOF）体系分别在100条标准地震动输入下弹塑性地震反应的统计分析,研究了模型参数和地震动不确定性对SDOF体系残余变形和最大弹塑性变形的影响;建立了双线性SDOF体系震后残余变形的概率计算模型。结果表明：不同地震动输入下SDOF体系的残余变形与最大弹塑性变形之比（dR/dm）存在明显的离散性,且离散程度与结构的刚度比、自振周期、相对屈服荷载系数及峰值地面加速度相关;dR/dm的统计分布规律服从对数正态分布,基于该分布函数建立的计算模型可对给定超越概率条件和地震水平下SDOF体系的震后残余变形进行预测。通过典型算例分析认为,可以采用所建议的模型进行SDOF体系震后残余变形分析及可修复性评估。     

Direct displacement‐based design of steel‐braced reinforced concrete frames

This study investigates a direct displacement‐based design procedure for dual system structures composed of reinforced concrete frames and steel bracings. In this procedure, in order to establish the design displacement profile before any analysis, strength proportions between bracings and frames are assigned. By using the displacement profile and damping characteristics of the structural components, the structure can be represented as an equivalent single‐degree‐of‐freedom system. The effective period and secant stiffness of the structure are then calculated, and finally, after the base shear was computed, the design process can be implemented. Structures with 4, 8 and 12 stories have been designed using this methodology, and in order to validate it, seven accelerograms have been used for nonlinear time‐history analysis of the above structures. The results demonstrate the efficiency of this procedure. Copyright © 2012 John Wiley & Sons, Ltd.     

Approximate modal analysis of multistory symmetrical buildings with restricted inelasticity

Simplified capacity curves are presented for modal decomposition of multistory inelastic cantilever bents. These structural systems are uniform over the height and plasticity is assumed to be restricted into the beams, since significant rotation ductility factors may be attained in these members without loss of strength. The approximate method of modal decomposition of multistory inelastic bents is based on the concept that the total response may be obtained from the contributions of equivalent nonlinear single‐degree‐of‐freedom (SDOF) modal systems, in combination with the technique of modal superposition. In particular, the contribution of the first mode equivalent inelastic SDOF system is examined, since its modal contribution is of higher importance. The response of such SDOF systems basically depends on their capacity curve, which may be formulated by using the dynamic properties (frequency, effective modal mass and mode shape) of the initially elastic bent, as well as the corresponding properties of the bent when the entire set of coupling beams is assumed to be yielded. The procedure is presented for plane cantilever bents, but it can be easily extended to symmetrical structural systems composed of different types of inelastic bents. Its application is illustrated by means of a 10‐story inelastic coupled‐wall bent subject to a strong earthquake motion, equal to 1·5× El Centro N–S ground excitation, and the results compare well with those obtained from a step‐by‐step nonlinear time history analysis of the discrete member model. Copyright © 2007 John Wiley & Sons, Ltd.     

An alternative approach for assessing eccentricities in asymmetric multistory buildings. 2. Inelastic systems

The approximate method, presented in the companion paper, for assessing modal eccentricities of elastic multistory buildings with simple eccentricity is extended in systems composed by elastoplastic resisting bents. Following the technique of the aforementioned paper for computing modal properties of such buildings by means of an equivalent single‐story system composed of elastic elements, modal capacity curves of these systems may also be drawn when the resisting elements are defined by a bilinear force–displacement (characteristic) curve. The procedure for constructing element‐characteristic curves is based on the methodology presented by the author in an earlier paper, and modal capacity curves of the equivalent single‐story system may be drawn by performing a non‐linear pushover analysis using the inertia force eccentricity of each mode of this system. Therefore, base shears and their eccentricities for the first two modes of vibration of multistory inelastic buildings can be determined as in real one‐story non‐linear systems. The method is illustrated in a 10‐story partial symmetric building, having along the direction of the ground motion three identical, inelastic, coupled wall bents. The structure is analyzed for a strong ground motion, equal to 1·5 × El Centro earthquake excitation, and the results are compared with those obtained from a step‐by‐step non‐linear time history analysis of the discrete member model. Copyright © 2007 John Wiley & Sons, Ltd.     

基础转动结构随机风振响应分析的复模态法

对多自由度基础转动结构随机风振响应问题进行了系统研究。针对用上部结构第一振型展开所得方程为非经典阻尼和非对称结构以及脉动风谱为非有理分式风谱情况 ,用线性滤波过程生成脉动风谱 ,用复模态和扩阶法进行解耦 ,获得了等效风谱对应的以第一振型表示的结构响应解析解 ,对单自由度体系 ,此解即为结构响应精确解。该方法可用于带TMD或TLD结构的风振分析和优化设计。     

Empirical evaluation of ductility factors for the special steel moment‐resisting frames in view of soil condition

It is well known that the response modification factor (R) takes into account the ductility, over‐strength, redundancy and damping of structural systems. The ductility factor has played an important role in seismic design, as it is a key component of R. In this study, the ductility factors (R_μ,MDOF) of special steel moment‐resisting frames are calculated by multiplying the ductility factor of single degree of freedom (SDOF) systems (R_μ,SDOF) with the multi‐degree of freedom (MDOF) modification factors (R_M). The ductility factors (R_μ,SDOF) of SDOF systems are computed from non‐linear dynamic analysis undergoing different levels of displacement ductility demands and periods when subjected to a large number of recorded earthquake ground motions. To compute the R_μ,SDOF, a group of 1,860 ground motions recorded from 47 earthquakes were considered. R_M factors are proposed to account for the MDOF systems, based on previous studies. A total of 108 prototype steel frames were designed to investigate the ductility factors, considering design parameters such as the number of stories (4, 8 and 16), framing systems (perimeter frames and distributed frames), failure mechanisms (strong column‐weak beam and weak column‐strong beam), soil profiles (S_A, S_C and S_E in Uniform Building Code 1997) and seismic zone factors (Z = 0·075, 0·2, and 0·4 in UBC 1997). The effects of these design parameters on the R_μ,MDOF of special steel‐moment‐resisting frames were investigated. Copyright © 2009 John Wiley & Sons, Ltd.     

Stochastic seismic collapse and reliability assessment of high‐rise reinforced concrete structures

To provide knowledge beyond the conventional engineering insights, attention in this work is focused on a comprehensive framework for the stochastic seismic collapse analysis and reliability assessment of large complex reinforced concrete (RC) structures. Three key notions are emphasized: the refined finite element modeling and analysis approach towards structural collapse, a physical random ground motion model, and an energy‐based structural collapse criterion. First, the softening of concrete material, which substantially contributes to the collapse of RC structures, is modeled by the stochastic damage constitutive model. Second, the physical random ground motion model is introduced to quantitatively describe the stochastic properties of the earthquake ground motions. And then the collapse‐resistance performance of a certain RC structure can be systematically evaluated on the basis of the probability density evolution method combining with the proposed structural collapse criterion. Numerical results regarding a prototype RC frame‐shear wall structure indicate that the randomness from ground motions dramatically affects the collapse behaviors of the structure and even leads to entirely different collapse modes. The proposed methodology is applicable in better understanding of the anti‐collapse design and collapse prediction of large complex RC buildings.     

Effects of hysteretic model on seismic demands: consideration of near‐fault ground motions

This paper summarizes the results of a study that is to evaluate the structural response attributes of near‐fault ground motion. Ground motion recordings from the Chi‐Chi earthquake are used as inputs to the structural system. An improved nonlinear hysteretic model, based on the experimental study, was used to calculate the response of the single degree‐of‐freedom inelastic system. Comparison of the results of analysis with traditional elastic–perfect plastic mode calculations was made. Discussions on the inelastic design spectrum, particularly the code‐specified base shear coefficients, using the improved nonlinear hysteretic model incorporated with the near‐fault input ground motion are made. Copyright © 2002 John Wiley & Sons, Ltd.     

弹性多自由度系统地震输入能量的研究

本文介绍了基于能量抗震设计方法的基本思路和基本概念。根据振型分解法推导了弹性多自由度系统与单自由度系统弹性地震输入能量间的关系。研究表明,N个自由度弹性系统的地震输入能量可表示为N个弹性单自由度系统弹性输入能量的线性组合,组合系数与多自由度系统的振型和质量分布有关。通过时程分析算例,以Eleentro波输入验证了这种方法的正确性。算例结果表明,对于自由度较多的系统,可以只取前几阶振型计算即可得到足够精确的结果。     

An introduction to the structural design of rocking wall‐frames with a view to collapse prevention,self‐alignment and repairability

The purpose of this article is to present a new method of analysis for the structural design of pin‐supported rocking wall‐moment frames with supplementary devices and post‐tensioned stabilizers. The function of the wall is to prevent soft story failure, impose uniform drift and provide support for the supplementary equipment. The proposed methodology lends itself well to several seismic design strategies, ranging from severe damage avoidance, to collapse prevention, to structural self‐alignment and repairability. Repairability means avoiding major damage to columns and foundations. The success of the resulting solutions is due to the single degree of freedom behavior of the combined system and the fact that its overall performance is not significantly affected by minor changes in the stiffness of the wall. The sensitivity of the response to wall rigidity is addressed by comparing the maximum elastic slope of the wall with a fraction of the specified uniform drift. The limitations of rocking wall‐moment frames, as viable lateral resisting systems, have been addressed. Several worked examples have been presented to provide insight and technical information that may not be readily available from electronic output. The proposed solutions are exact within the bounds of the theoretical assumptions and are ideally suited for manual as well as spreadsheet computations. Copyright © 2015 John Wiley & Sons, Ltd.     

ISCS method for the performance‐based seismic design of vertically irregular reinforced concrete frame structures

The procedure to obtain the inelastic demand curves for the multi‐degree‐of‐freedom system, composed of inter‐story shear versus inter‐story displacement curve is introduced. The demand curves are established by using mode spectrum method, and the dynamical characteristic of structure under different earthquake hazard levels is taken into account. The relation of structure performance object and displacement ductility is adopted to deduce the relation of structure performance object and inter‐story demand curve. Therefore, the inter‐story demand curves take into account the inelastic behavior of structure under earthquake action adequately. Then, considering the seismic responding characteristic and the capacity curve of the frame structure, a new method named Inter‐Story Capacity Spectrum (ISCS) is put forward for the performance‐based seismic design of vertically irregular frame structures. Examples are presented to demonstrate the applicability and the utility of the proposed method. It is concluded that the new method can control the inter‐story drift, the order and position of hinges of vertically irregular structures under different earthquake hazard levels. Comparing with time‐history analysis method, it leans to safe and is superior to direct displacement‐based design method. Copyright © 2011 John Wiley & Sons, Ltd.