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1.
Ernesto Heredia‐Zavoni 《地震工程与结构动力学》2011,40(11):1181-1196
The complete Square‐Root‐of‐Sum‐of‐Squares (c‐SRSS) modal combination rule is presented. It expresses the structural response in terms of uncoupled SDOF modal responses, yet accounting fully for modal response variances and cross‐covariances. Thus, it is an improvement over the classical SRSS rule which neglects contributions from modal cross‐covariances. In the c‐SRSS rule the spectral moments of the structural response are expressed rigorously in terms of the spectral moments of uncoupled modal responses and of some coefficients that can be computed straightforwardly as a function of modal frequencies and damping, without involving the computation of cross‐correlation coefficients between modal responses. An example shows an application of the c‐SRSS rule for structural systems with well separated and closely spaced modal frequencies, subjected to wide‐band and narrow‐band excitations. Comparisons with response calculations using the SRSS and the Complete Quadratic Combination rules are given and discussed in detail. Based on the c‐SRSS rule a response spectrum formulation is introduced to estimate the maximum structural response. An example considering a narrow‐band excitation from the great Mexico earthquake of September 19, 1985, is given and the accuracy of the response spectrum formulation is examined. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
2.
The existing rules for combining peak response to individual components of ground motion are evaluated. The response values re to two horizontal components of ground motion estimated by four multicomponent combination rules—SRSS‐, 30%‐, 40%‐ and simplified‐SRSS‐rules—are compared with the critical response, rcr, obtained by the CQC3‐rule, which takes into account the direction of the principal ground components with respect to the structural axes and provides the largest response over all possible seismic incident angles. The following results are obtained in the first part of the paper and are valid for any elastic structure and any earthquake design response spectrum: For realistic values of the ratio γ of the design spectra for the two principal components of ground motion the SRSS‐rule estimate lies between 0.79rcr and 1.00rcr, the Simplified‐SRSS‐rule estimate lies between 1.00rcr and 1.26rcr, the 40%‐rule estimate lies between 0.99rcr and 1.25rcr, and the 30%‐rule estimate lies between 0.92rcr and 1.16rcr. None of the multicomponent combination rules account for the increase in response of systems if the vibration periods of the two modes that contribute most to the response to the x‐ and y‐components of ground motion are close to each other. Evaluated in the second part of the paper is the accuracy of the multicomponent combination rules in estimating the response of a range of one‐storey systems with (a) symmetrical plan and (b) unsymmetrical plan, and of two multistorey buildings. The SRSS‐rule underestimates the response by up to 16% and the other three rules overestimate it by up to 18%. Although these errors appear to be smaller than the many approximations inherent in structural design, they can be eliminated with very little additional computation by using an explicit formula for the critical response based on the CQC3 rule. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
3.
The responses, re, given by several multicomponent combination rules used in seismic codes for determining peak responses to three ground motion components are evaluated for elastic systems and compared with the critical response rcr; this is defined as the largest response for all possible incident angles of the seismic components and obtained by means of the CQC3‐rule when a principal seismic component is vertical, or the GCQC3‐rule when it departs from the vertical direction. The combination rules examined are the SRSS‐, 30%‐, 40%‐ and IBC‐rules, considering different alternatives for the design horizontal spectrum. Assuming that a principal seismic component is along the vertical direction, the upper and lower bounds of the ratio re/rcr for each combination rule are determined as a function of the spectral intensity ratio of the horizontal seismic components and of the responses to one seismic component acting alternately along each structural axis. Underestimations and overestimations of the critical response are identified for each combination rule and each design spectrum. When a component departs from the vertical direction, the envelopes of the bounds of the ratio re/rcr for each combination rule are calculated, considering all possible values of the spectral intensity ratios. It is shown that the inclination of a principal component with respect to the vertical axis can significantly reduce the values of re/rcr with respect to the case when the component is vertical. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
4.
The use of uniform hazard spectra which have the same probability of exceedance at different frequencies has been proposed for the future version of the National Building Code of Canada. Commonly used combination rules to estimate the peak responses of multi‐degree‐of‐freedom (MDOF) systems are the square root of sum of squares rule and the complete quadratic combination rule. However, the probability that the peak response of a MDOF system exceeds the one estimated by using these rules with the peak modal responses from the uniform hazard spectra cannot be inferred directly. The assessment of the probability of exceedance of the peak response of MDOF systems is presented by considering that the uncertainty in seismic excitation due to all potential earthquakes can be lumped in the power spectral density function of the ground acceleration with uncertain model parameters. This probability is evaluated based on the random vibration of linear systems and the first‐order reliability method. It is found that the under‐ or over‐estimations are less than about 5 or 10% if the modal contributions are not within 10–90% of, or not within 20–80% of, the absolute sum of the effective modal peak responses, respectively. Otherwise, severe under‐ or over‐estimation could result. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
5.
A response spectrum method for dynamic analysis of linear structures subjected to multicomponent seismic input is developed. The method is based on elementary concepts of stationary random vibration and assumes the existence of a set of principal directions along which components of ground motion are uncorrelated. Modal combination rules in terms of ground response spectra are developed for the mean and standard deviation of peak responses and for rootmean-square responses. These rules account for correlations between modal responses of the structure, as well as correlations between the input components. When the position of principal directions is unknown, two alternative rules are proposed: one uses the direction which is most critical for the response quantity of interest, and the other considers the direction as a random variable. The proposed method is simple for practical implementation and gives more accurate results than other existing methods. 相似文献
6.
A method is presented for generating floor response spectra for aseismic design of equipment attached to primary structures. The method accurately accounts for tuning, interaction and non-classical damping, which are inherent characteristics of composite oscillator-structure systems. Modal synthesis and perturbation techniques are used to derive the modal properties of the composite system in terms of the known properties of the structure and the oscillator. Floor spectra are generated directly in terms of these derived properties and the input ground response spectrum using modal combination rules that account for modal correlations and non-classical damping. The computed spectra, in general, are considerably lower than conventional floor response spectra due to the effect of interaction. They provide more realistic and economical criteria for design of equipment. The method is accurate to the order of perturbation and is computationally efficient, as it avoids time-history analysis and does not require numerical eigenvalue evaluation of the composite oscillator-structure system. The results of a parametric study demonstrate the accuracy of the method and illustrate several key features of floor response spectra. 相似文献
7.
The spatial variability of seismic ground motion is an important aspect for the earthquake resistant design of extended facilities. A modified response spectrum model, which addresses the problem of multiply supported structures subjected to imperfectly correlated seismic excitations, has already been developed (see References 1 and 2). The present paper proposes a modal combination rule for the case of non-uniform seismic input, which would be used together with the modified response spectrum model in order to compute physical responses. This rule, which accounts for modal cross-correlations, is an extension to an existing rule for the case of uniform seismic motions. It modifies the existing modal cross-correlation coefficients through a correction factor which depends on structural properties and on the characteristics of the wave propagation phenomenon. Finally, some practical considerations on the theoretical development are addressed. They aim at suggesting reasonable simplifications which render the modal combination rule more appealing for engineering purposes. The proposed practical combination rule is validated through a numerical experiment which also characterizes the effect of non-uniform seismic input on modal cross-correlation. 相似文献
8.
The peak dynamic responses of two mathematical models of a fifteen-storey steel moment resisting frame building subjected to three earthquake excitations are computed by the response spectrum and time history methods. The models examined are: a ‘regular’ building in which the centres of stiffness and mass are coincident resulting in uncoupled modes with well-separated periods in each component direction of response; and an ‘irregular’ building with the mass offset from the stiffness centre of the building causing coupled modes with the translational modes having closely spaced periods. Four response spectrum modal combination rules are discussed and are used to predict the peak responses: (1) the square root of the sum of the squares (SRSS) method; (2) the double sum combination (DSC) method; (3) the complete quadratic combination (CQC) method; and (4) the absolute sum (ABS) method. The response spectrum results are compared to the corresponding peak time history values to evaluate the accuracy of the different combination rules. The DSC and the CQC methods provide good peak response estimates for both the regular and irregular building models. The SRSS method provides good peak response estimates for the regular building, but yields significant errors in the irregular building response estimates. The poor accuracy in the irregular building results is attributable to the effects of coupled modes with closely spaced periods. It is concluded that the DSC and CQC methods produce response estimates of equivalent accuracy. Both methods are recommended for general use. In addition to the DSC and CQC rules, the SRSS method is recommended for systems where coupled modes with closely spaced periods do not dominate the response. 相似文献
9.
The modal combination rules commonly used in response spectrum analyses implicitly assume that the peak factor associated with the response quantity of interest is equal to the peak factors of the contributing modal responses. In this paper, we examine the validity of this assumption and demonstrate that it causes the modal combination rules to over‐represent the contribution of the higher modes of vibration to the total response and under‐represent the contribution of the lower modes. Consequently, a response‐spectrum‐based analysis can yield a biased estimate for the peak value of a response quantity when two or more well‐separated modal frequencies make significant contributions to the total response. To correct this potential bias in response‐spectrum‐based estimates, we develop a procedure for estimating the peak factors that is suitable to the response spectrum analysis calculations commonly used in the current design practice. Examples are presented to demonstrate the proper use and potential impact of the proposed procedure. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
10.
This paper presents an efficient procedure to determine the natural frequencies, modal damping ratios and mode shapes for torsionally coupled shear buildings using earthquake response records. It is shown that the responses recorded at the top and first floor levels are sufficient to identify the dominant modal properties of a multistoried torsionally coupled shear building with uniform mass and constant eccentricity even when the input excitation is not known. The procedure applies eigenrealization algorithm to generate the state‐space model of the structure using the cross‐correlations among the measured responses. The dynamic characteristics of the structure are determined from the state‐space realization matrices. Since the mode shapes are obtained only at the instrumented floor (top and first floors) levels, a new mode shape interpolation technique has been proposed to estimate the mode shape coefficients at the remaining floor levels. The application of the procedure has been demonstrated through a numerical experiment on an eight‐storied torsionally coupled shear building subjected to earthquake base excitation. The results show that the proposed parameter identification technique is capable of identifying dominant modal parameters and responses even with significant noise contamination of the response records. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
11.
Dynamic characteristics of structures — viz. natural frequencies, damping ratios, and mode shapes — are central to earthquake‐resistant design. These values identified from field measurements are useful for model validation and health‐monitoring. Most system identification methods require input excitations motions to be measured and the structural response; however, the true input motions are seldom recordable. For example, when soil–structure interaction effects are non‐negligible, neither the free‐field motions nor the recorded responses of the foundations may be assumed as ‘input’. Even in the absence of soil–structure interaction, in many instances, the foundation responses are not recorded (or are recorded with a low signal‐to‐noise ratio). Unfortunately, existing output‐only methods are limited to free vibration data, or weak stationary ambient excitations. However, it is well‐known that the dynamic characteristics of most civil structures are amplitude‐dependent; thus, parameters identified from low‐amplitude responses do not match well with those from strong excitations, which arguably are more pertinent to seismic design. In this study, we present a new identification method through which a structure's dynamic characteristics can be extracted using only seismic response (output) signals. In this method, first, the response signals’ spatial time‐frequency distributions are used for blindly identifying the classical mode shapes and the modal coordinate signals. Second, cross‐relations among the modal coordinates are employed to determine the system's natural frequencies and damping ratios on the premise of linear behavior for the system. We use simulated (but realistic) data to verify the method, and also apply it to a real‐life data set to demonstrate its utility. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
12.
A new spatial coherence model and analytical coefficients for multi-support response spectrum combination 总被引：1，自引：0，他引：1
In this paper, a new spatial coherence model of seismic ground motions is proposed by a fi tting procedure. The analytical expressions of modal combination (correlation) coeffi cients of structural response are developed for multi-support seismic excitations. The coeffi cients from both the numerical integration and analytical solutions are compared to verify the accuracy of the solutions. It is shown that the analytical expressions of numerical modal combination coeffi cients are of high accuracy. The results of random responses of an example bridge show that the analytical modal combination coeff icients developed in this paper are accurate enough to meet the requirements needed in practice. In addition, the computational effi ciency of the analytical solutions of the modal combination coeff icients is demonstrated by the response computation of the example bridge. It is found that the time required for the structural response analysis by using the analytical modal combination coeffi cients is less than 1/20 of that using numerical integral methods. 相似文献
13.
大跨度钢桁架转换层结构的竖向地震反应分析 总被引：1，自引：1，他引：0
对某一带钢桁架转换层的复杂高层结构进行了有限元建模,分别采用振型分解反应谱法、时程分析法和《建筑抗震设计规范》(GB50011-2001)的设计反应谱法对大跨高位钢桁架转换层结构的竖向地震响应进行了分析.对采用振型分解反应谱法计算此类结构响应时所要选取的振型数及振型组合方法进行了探讨,并对规范采用10％的重力荷载代表值... 相似文献
14.
The classical response spectrum method continues to be the most popular approach for designing base‐isolated buildings, therefore avoiding computationally expensive nonlinear time‐history analyses. In this framework, a new method for the seismic analysis and design of building structures with base isolation system (BIS) is formulated and numerically validated, which enables one to overcome the main shortcomings of existing techniques based on the response spectrum method. The main advantages are the following: first, reduced computational effort with respect to an exact complex‐valued modal analysis, which is obtained through a transformation of coordinates in two stages, both involving real‐valued eigenproblems; second, effective representation of the damping, which is pursued by consistently defining different viscous damping ratios for the modes of vibration of the coupled BIS‐superstructure dynamic system; and third, ease of use, because a convenient reinterpretation of the combination coefficients leads to a novel damping‐adjusted combination rule, in which just a single response spectrum is required for the reference value of the viscous damping ratio. The proposed approach is specifically intended for design situations where (i) the dynamic behaviour of seismic isolators can be linearised and (ii) effects of nonproportional damping, as measured by modal coupling indexes, are negligible in the BIS‐superstructure assembly. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
15.
An analysis is made of the coupled lateral-torsional response of a partially symmetric single-storey building model to horizontal translatory earthquake excitation. Interest centres on the evaluation of realistic estimates for two equivalent static actions (a shear and a torque) which account for the worst dynamic consequences of torsional unbalance. The results substantiate the findings of previous investigations which have given rise to the belief that strong modal coupling and severely coupled lateral and torsional responses are possible even in nominally symmetric buildings. The response of the model is assumed to be linearly elastic and viscously damped. In a preliminary analysis the equations of motion are solved using the modal analysis technique and the conditions necessary for full modal coupling are ascertained. Then by employing the design spectrum concept, together with suitably conservative procedures for combining the modal maxima, dimensionless forms of the equivalent static actions are evaluated as functions of two independent parameters. The final results are furnished by modified square root of the sum of the squares (SRSS) combination functions which take account of the spacing between the translational and torsional frequencies. Examples at the end of the paper illustrate the practical significance of the work. 相似文献
16.
The square root of the sum of the squares (SRSS) procedure and its modified forms are often used to obtain seismic design response. The design inputs for such procedures are usually defined in terms of pseudo velocity or acceleration response spectra. Erroneous results have been obtained with these existing SRSS procedures, especially in the calculation of responses where high frequency effects dominate. Here an alternative SRSS procedure is developed using the so-called mode acceleration approach of structural dynamics. The design input in this procedure is defined in terms of relative acceleration and relative velocity spectra. The relative spectra can be related to pseudo spectra. For a given number of modes to be included in the analysis the new SRSS rule proposed here will reduce the error due to the so-called ‘missing mass’ effect and predict a more accurate response value than the rules which use pseudo spectra as input, for systems either with or without dominant high frequency mode effects. 相似文献
17.
Supplemental damping could mitigate the earthquake‐induced damage in buildings with asymmetric plan, known to be more vulnerable to damage than comparable symmetric‐plan buildings. This investigation aims to improve the understanding of how and why planwise distribution of fluid viscous dampers (FVDs) influences the response of linearly elastic, one‐storey, asymmetric‐plan systems. Starting with vibration mode shapes, we predict this influence on the modal damping ratios, and in turn on the individual modal responses and the total response. These predictions are confirmed by the computed responses, which demonstrated that the reduction in earthquake response of the system achieved by supplemental damping is strongly influenced by its planwise distribution, which is characterized by four parameters. Identified are asymmetric distributions of supplemental damping that are more effective in reducing the response compared to symmetric distribution. The percentage reduction achieved by a judiciously selected asymmetric distribution can be twice or even larger compared to symmetric distribution. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
18.
Interval complete quadratic combination rule for the response spectrum analysis of buildings with accidental eccentricity 
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下载免费PDF全文 The accidental torsion, caused by several sources of structural uncertainties, gets the elastic response of a building different from that computed. To take into account of these uncertainties, building codes impose the introducing in every storey of the buildings an artificial eccentricity, called accidental, as a fraction of the plan dimension. Because, according to building codes, the accidental eccentricity can mathematically be expressed as a modification of the mass matrix, it follows that each mass modifications require new dynamic analyses that could be cumbersome from a numerical point of view. This paper proposes a new combination rule to obtain in closed form the maximum responses of structures with mass modification by the response spectrum analysis (RSA) without solving any further eigenproblem. In particular, the proposed procedure, based on the application to the RSA of the interval perturbation method, leads to an extension of the classical complete quadratic combination rule to the analysis of structural systems with uncertain‐but‐bounded parameter. In particular, for structural systems with accidental eccentricity, the proposed approach allows to directly evaluate the worst condition for the structural elements with a single RSA. This very remarkable result is obtained by adopting a new modal combination rule, here called interval complete quadratic combination. Numerical results evidence a very good accuracy of the interval complete quadratic combination for single‐storey buildings as well as for the analyzed multistorey buildings. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
19.
An extensive programme of full-scale ambient vibration tests has been conducted to measure the dynamic response of a 542 m (centre span of 274 m) cable-stayed bridge—the Quincy Bayview Bridge in Illinois. A microcomputer-based system was used to collect and analyse the ambient vibration data. A total of 25 modal frequencies and associated mode shapes were identified for the deck structure within the frequency range of 0–2 Hz. Also, estimations were made for damping ratios. The experimental data clearly indicated the occurrence of many closely spaced modal frequencies and spatially complicated mode shapes. Most tower modes were found to be associated with the deck modes, implying a considerable interaction between the deck and tower structure. No detectable levels of motion were evident at the foundation support of the pier. The results of the ambient vibration survey were compared to modal frequencies and mode shapes computed using a three-dimensional finite element model of the bridge. For most modes, the analytic and experimental modal frequencies and mode shapes compare quite well, especially for the vertical modes. Based on the findings of this study, a linear elastic finite element model appears to be capable of capturing much of the complex dynamic behaviour of the bridge with very good accuracy, when compared to the low-level dynamic responses induced by ambient wind and traffic excitations. 相似文献
20.
The dynamic response of a single span cable due to a travelling seismic excitation is studied in this paper. The influence of propagation time between the supports is investigated in detail. The importance of considering both vertical and longitudinal equations of motion in the analysis is highlighted. The results indicate the considerable influence of the time-lagged support motions on the cable dynamic tension. A modal combination rule based on the response spectrum method is developed to arrive at the peak estimates of the cable response. Some significant aspects of cable behaviour, especially under horizontal support motion, are discussed. 相似文献