Floor Spectra of MDOF Nonlinear Structures

In this article, the influence of nonlinear behavior of multiple degree of freedom (MDOF) primary structures on floor response spectra is investigated by means of simple structural models. The cases of shear beam type as well as of capacity-designed plane frames were studied. It is shown that, in general, but not always, nonlinearity of the primary structure has a beneficial effect on floor spectra. However, higher mode response may be amplified due to nonlinear behavior. The issue of a one story structure exhibiting torsionnal response has also been addressed and some important properties are highlighted.     

DUCTILITY REDUCTION FACTOR OF MDOF SHEAR-BUILDING STRUCTURES

In this paper, the results of recent studies on inelastic seismic response of MDOF shear-building structures are presented. In the last few decades, the concept of response modification factor R has been introduced and developed to account for inelastic nonlinear behaviour of structures under earthquakes. In this paper, an attempt has been made to adjust and extend this concept through introducing a modifying factor R _T . This factor is used for dynamic analysis of MDOF structures, including the calculation of inelastic response spectra. Sensitivity analysis was carried out to identify the parameters that have influence on R _T . It has been demonstrated that R _T is predominantly a function of number of stories, and accordingly a relationship has been suggested. Finally, an approximate approach has been developed for evaluating the seismic strength and ductility demands of MDOF structures.     

COMPLEX MODE SUPERPOSITION ALGORITHM FOR SEISMIC RESPONSES OF NON-CLASSICALLY DAMPED LINEAR MDOF SYSTEM

This paper deals with a complex mode superposition method for the seismic responses of general multiple degrees of freedom (MDOF) discrete system with complex eigenvectors and eigenvalues. A delicate general solution, completely in real value form, for calculat-ing seismic time history response of the MDOF system which cannot be uncoupled by normal modes, is deduced based on the algorithms of the complex superposition method. This solution comprises of two parts which are in relation to the Duhamel integration to sine and cosine function respectively. The related term of the Duhamel integration to sine function is actually the displacement response of the oscillator with corresponding modal frequency and the damping ratio. The other can be transferred into a combina-tion of the displacement and velocity responses of the same oscillator. In order to meet the practical needs of seismic design based on code design spectra for various kinds of structures equipped by viscous dampers, the complex complete quadratic combination (CCQC) method is deduced following similar procedures such as the well-known CQC method, in which a new modal velocity correlation coefficient, together with a new modal displacement-velocity correlation coefficient are involved besides the modal displacement correlation coefficient in normal CQC formula. The new algorithm of CCQC is not only as concise as that of the normal CQC but also has explicit physical meaning. The results obtained from complex mode superposition approaches are discussed and verified in some examples through step by step integration computation under a prescribed earth-quake motion input. From these examplary analyses, it may be pointed that the CCQC algorithm normally yields conservative outcome and that the forced mode uncoupling approach has good approximation even the discussed examplary structures are strongly non-proportional.     

PERFORMANCE-BASED SEISMIC RESPONSE OF FRAME STRUCTURES INCLUDING RESIDUAL DEFORMATIONS. PART II: MULTI-DEGREE OF FREEDOM SYSTEMS

The role of residual deformations when evaluating the performance of multi-storey frame structures subjected to ground motion is investigated in this paper. The limitations of damage indices available in the literature, either based on ductility, energy dissipation or a combination of both, in capturing such a significant aspect of the seismic response of frame structures are discussed. The concept of residual deformations as a critical complementary indicator to cumulative damage, introduced in a companion paper (Part I) for single-degree-of-freedom (SDOF) systems, is herein extended to multi-degree-of-freedom (MDOF) frame systems. The seismic performance of multi-storey frame structures, either representative of new designed or existing structures, is investigated, focusing on the response in terms of residual deformations. Residual deformations are shown to be sensitive to the hysteretic rule adopted, to the system inelastic mechanism as well as to the seismic intensity. The influence of higher modes and P-Δ effects on the final residual deformations is addressed. A combination of maximum drift and residual drift in the format of a performance matrix is used to define the system's global performance levels and is then extended to a framework for an alternative performance-based seismic design and assessment approach.     

A SIMPLE METHOD FOR ANALYSIS OF SLIDING STRUCTURES CONSIDERING VARIATIONS OF FRICTION COEFFICIENT

In this paper, the responses of multidegree of freedom (MDOF) structures on sliding foundations, subjected to harmonic or random base motions, are investigated taking into consideration the variations of friction forces. The variation of friction force is a consequence of variation of friction coefficient, which depends on such parameters as relative velocity and the existing pressure. Modelling of the friction force under the foundation raft is accomplished by using a fictitious rigid link with a rigid-perfectly plastic material. This results in identical equations of motion for the sliding structure, both in the sliding and nonsliding (stick) phases and considerably decreases the required number of time steps for the nonlinear analysis. Since the force in the link is of constant value, to consider the varying friction force, a compensatory force, which is the difference between the exact friction force and the constant force in the rigid link, is applied to the foundation raft. A model of variable friction coefficient for Teflon-steel interfaces is used for the assessment of the method and the results are compared with existing literature, through which, the capability of the method is illustrated. It is shown that by using exact model of friction lower values for the superstructure responses are predicted compared with those obtained by using Coulomb friction model. Furthermore the effect of the stiffness of the structure on the differences between the results of the two models is also studied.     

Definition of Seismic Input for Out-of-Plane Response of Masonry Walls: I. Parametric Study

Response of masonry walls to out-of-plane excitation is a complex, yet inadequately addressed theme in seismic analysis. The seismic input expected on an out-of-plane wall (or a generic “secondary system”) in a masonry building is the ground excitation filtered by the in-plane response of the walls and the floor diaphragm response. More generally, the dynamic response of the primary structure, which can be nonlinear, contributes to the filtering phenomenon. The current article delves into the details and results of several nonlinear dynamic time-history analyses executed within a parametric framework. The study addresses masonry structures with rigid diaphragm response to lateral loads. The scope of the parametric study is to demonstrate the influence of inelastic structural response on the seismic response of secondary systems and eventually develop an expression to estimate the seismic input on secondary systems that explicitly accounts for the level of inelasticity in the primary structure in terms of the displacement ductility demand. The proposed formulation is discussed in the companion article.     

A Nonlinear Frame Test Structure with Repeatable Behavior for Experimental Dynamic Response History Investigation

This article describes a novel, small-scale nonlinear beam-column connection and an associated six-story frame test structure for the experimental dynamic response investigation of multi-story buildings subjected to earthquake loading. The objective is to create a re-configurable, reusable experimental platform on which several aspects of nonlinear dynamic response can be investigated through successive, exhaustive testing under suites of earthquake records. Static and dynamic calibration tests demonstrate excellent test-to-test repeatability of four structure configurations. These results confirm that the properties of each configuration (period, strength, energy dissipation) remain invariant, thus allowing future experimental investigations (e.g., of peak engineering demands) under earthquake loading.     

YIELDING OSCILLATOR UNDER TRIANGULAR GROUND ACCELERATION PULSE

An analytical solution is presented for the response of a bilinear inelastic simple oscillator to a symmetric triangular ground acceleration pulse. This type of motion is typical of near-fault recordings generated by source-directivity effects that may generate severe damage. Explicit closed-form expressions are derived for: (i) the inelastic response of the oscillator during the rising and decaying phases of the excitation as well as the ensuing free oscillations; (ii) the time of structural yielding; (iii) the time of peak response; (iv) the associated ductility demand. It is shown that when the duration of the pulse is long relative to the elastic period of the structure and its amplitude is of the same order as the yielding seismic coefficient, serious damage may occur if significant ductility cannot be supplied. The effect of post-yielding structural stiffness on ductility demand is also examined. Contrary to presently-used numerical algorithms, the proposed analytical solution allows many key response parameters to be evaluated in closed-form expressions and insight to be gained on the'response of inelastic structures to such motions. The model is evaluated against numerical results from actual near-field recorded motions. Illustrative examples are also presented.     

Design Methodology for Seismic Upgrading of Substandard Reinforced Concrete Structures

This article presents a design methodology for seismic upgrading of existing reinforced concrete (RC) buildings. The methodology is based on the modification of the deflected shape of the structure so as to achieve a near-uniform distribution of interstorey drift along the building height, thereby eliminating damage localization. Yield Point Spectra are utilized for the definition of demand and a direct displacement-based design approach is implemented. The fundamental steps of the method are described in detail, including a systematic evaluation of assumptions and limitations. A full-scale tested structure is used as a case study for assessment and verification of the proposed methodology. Alternative retrofit scenarios are set according to target response and performance levels. The role of the target deflected response shape and its influence on the outcome of the retrofit strategy is investigated. The viability of the alternative retrofit scenarios is studied for different ground motions including near-fault earthquake records.     

Mechanisms of Control in Emergent Interorganizational Networks

The delegation of decision‐making capacity from one actor to another—known variously as authority or control—is a central phenomenon of organizational sociology. Despite its theoretical and practical significance, however, the dynamics of control within disrupted settings (such as disasters) remain poorly understood. Here, we shed light on this question by a reexamination of historical data on multiorganizational disaster response networks, using recently developed statistical methods for robust inference from error‐prone informant reports. Specifically, we test competing hypotheses about the relationship of control during the response process to the structure of interorganizational communication. We find that both the realized and normative response hierarchies are likely shaped by coordination among both nonadjacent alters and along indirect channels. Our results suggested that the communication structure of these networks is consistent with a control at a distance model of command. This article makes a substantial contribution to understanding the role of network structure in the emergence of control between organizations in disrupted settings. Additionally, our innovative approach to network inference will guide researchers in dealing with error‐prone data in their own research on policy networks.     

A New Proposed Passive Mega-Sub Controlled Structure and Response Control

It is still a serious challenge for structural engineers to effectively reduce the seismic responses of tall and super tall buildings to further improve these structural safeties. In order to solve this problem, in this article a new kind of structural configuration, named passive mega-sub controlled structure (PMSCS), is presented, which is constructed by applying the structural control principle into structural configuration itself, to form a new structure with obvious response self-control ability, instead of employing the conventional method. In the analysis of PMSCS the equations of motion of the seismically excited system are developed, based on a realistic analytical model of the complete mega-structural system. Expressions of the displacement and acceleration response of the structure, resulting from simulated earthquake ground motions represented by stationary and nonstationary random processes, are derived. These responses are then determined for both the PMSCS and its conventional mega-sub structure (MSS) counterpart, whose configuration was modeled after the traditional mega-frame that was used in the construction of the Tokyo City Hall. A parametric study of the structural characteristics that influence the response control effectiveness of the PMSCS is presented and discussed. The region over which these structural characteristics yield the optimum seismic response control of the PMSCS is identified and serves as a very useful design tool for practitioners. The study illustrates that the proposed PMSCS offers an effective means of controlling the seismic displacement and acceleration response of tall/super-tall mega-systems. It also overcomes shortcomings exhibited in earlier proposed mega-sub controlled structural configurations.     

Considering Soil-Nonlinearity Effect on Seismic Performance Evaluation of Structures based on Pushover Analysis

According to the most of current seismic codes, nonlinear soil behavior is commonly ignored in seismic evaluation procedure of the structures. To contribute on this matter, a pushover analysis method incorporating the probabilistic seismic hazard analysis (PSHA) is proposed to evaluate the effect of nonlinear soil response on seismic performance of a structure. The PSHA outcomes considering soil nonlinearity effect is involved in the analysis procedures by modifying the site-specific response spectrum. Results showed that incorporation of nonlinear soil behavior leads to an increase in displacement demand of structures which should accurately be considered in seismic design/assessment procedure. Results of implemented procedure are confirmed with the estimated displacement demand including soil-structure interaction (SSI).     

古代石塔地震安全性评价研究——以清净化城塔为例

本文采用反应谱分析法对西黄寺清净化城塔进行了地震安全性分析,找出其薄弱环节,得出对其结构抗震安全性评价有价值的结论。目前的反应谱分析多般基于线弹性应力应变模型,但结构一旦出现开裂,结构的应力应变关系将是非线形性的,若求解开裂结构的位移和应力,反应谱分析不再适用。但反应谱分析结果能够帮助分析人员找出结构的薄弱环节,判断结构在关键部位是否会出现裂缝以及其定性地判定裂缝开展的程度。从这个意义上讲,反应谱分析对结构的抗震分析具有重要的作用。     

Multiperiod migration patterns: the timing and frequency of household responses

"The structure of intertemporal patterns of household migration responses is empirically examined. The findings indicate that migration decisions are often related to changes in household conditions in both prior as well as following periods, are dependent on the duration of household status characteristics (e.g., marital status) and not just their presence at any point in time, and finally that migration response in any particular period very often differs among households as a result of differences in the underlying structure of migration frequency behavior. These findings suggest that inferences based on comparisons of household migration responses over only a single period of time are incomplete, possibly to the point of being misleading." The study is based on a calculation of "the distribution of migration patterns between 1976 and 1979 for a sample of 4,739 households in the [U.S.] Michigan Panel Survey on Income Dynamics (PSIC)."     

Nonlinear Structural Response to Low-Cut Filtered Ground Acceleration Records

Ground acceleration records obtained from instruments in the field are often filtered to reduce noise in both low and high frequency bands before being used for structural response analyses. The structural analysis using a filtered acceleration record may elongate the fundamental period of a structure which will potentially lead to an underestimation of the nonlinear response.

The nonlinear response of single-degree-of-freedom systems to low-cut filtered ground acceleration records is investigated. Based on the results of this study, a simple criterion for selecting ground acceleration records for seismic response analyses is proposed to avoid underestimating the nonlinear structural response.     

Application of an Extended Bouc-Wen Model in Seismic Response Prediction of Unbonded Fiber-Reinforced Isolators

The focus of this article is on seismic-response prediction of Stable Unbonded-Fiber Reinforced Elastomeric Isolators (SU-FREIs). The lateral load-displacement of a SU-FREI can be characterized with a gradual softening that is followed by stiffening. An extended Bouc-Wen Model is developed to simulate the response behavior of SU-FREIs under seismic events. To examine the accuracy of model, the response of a base isolated structure to different input earthquakes were simulated and compared with the results of a previous shake table study. Results of this study indicate that the proposed Bouc-Wen Model is robust and reasonably accurate in seismic analysis of SU-FREIs.     

An Improved Displacement-Based Adaptive Pushover Procedure for the Analysis of Frame Buildings

The main purpose of this article is to develop an alternative adaptive pushover method in which multiple inelastic response spectra proportional to the instantaneous ductility ratio of the structure are employed to reflect the actual energy dissipation characteristic of the structure at a given deformation level. Based on the proposed methodology, two load patterns are independently applied to the structure and the envelope of the demand values is computed. The obtained results demonstrate that the proposed method provides improved predictions of the peak interstory and total drift profiles of the structure.     

DESIRABLE STRENGTH DISTRIBUTION FOR ASYMMETRIC STRUCTURES WITH STRENGTH-STIFFNESS DEPENDENT ELEMENTS

Recent studies have shown that for many reinforced concrete lateral force-resisting elements (LFRE) stiffness is dependent on strength, and as a result strength assign-ment to these elements would affect both the strength and stiffness distributions in a structure. As a consequence, stiffness distribution cannot be considered known prior to strength assignment. This implies that in assigning strength to LFRE, the designer has the ability not only to prescribe the strength distribution, but also indirectly control the stiffness distribution in the structure. In this paper, a study is made on the seis-mic performance of a number of single-story structures to reconfirm that the “balanced CV-CR location” criterion, previously suggested by the writers, constitutes a desirable strength/stiffness distribution for minimising torsional response of asymmetric reinforced concrete structures.     

Seismic Evaluation of Tall Buildings Using a Simplified but Accurate Analysis Procedure

A simplified analysis procedure for evaluating the nonlinear seismic responses of tall reinforced concrete (RC) buildings is examined in this study. It is called the Uncoupled Modal Response History Analysis (UMRHA) procedure. It can be viewed as an extended version of the classical modal analysis procedure, where the nonlinear response of each vibration mode is first computed, and they are later on combined into the total response of the structure. The procedure requires the knowledge of the modal hysteretic behavior, which can be obtained from a cyclic modal pushover analysis. The responses of four tall buildings in Bangkok to distant large earthquakes are computed by this procedure and compared with those obtained from the Nonlinear Response History Analysis (NLRHA) procedure. These four buildings have different heights—varying from 20 to 44 stories, different configurations of floor plan, and different arrangement of RC walls. The comparison shows that the UMRHA procedure is able to accurately compute the story shears and story overturning moments, floor accelerations, and inter-story drifts of all these tall buildings. The required computational effort is also extremely low compared to that of the NLRHA procedure. Moreover, since the UMRHA procedure computes the response of each individual vibration mode, it provides more understanding and insight into the complex nonlinear seismic responses of these tall buildings.