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1.
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
2.
The response-spectrum mode superposition method is widely used for seismic response analyses of linear systems. In using this method, the complete quadratic combination （CQC） is adopted for classically damped linear systems and the complex complete quadratic combination （CCQC） formula is adopted for non-classically damped linear systems. However, in both cases, the calculation of seismic response analyses is very time consuming. In this paper, the variation of the modal correlation coefficients of displacement, velocity and displacement-velocity with frequency and damping ratios of two modes of interest are studied, Moreover, the calculation errors generated by using CQC and square-root-of-the-sum-of-thesquares （SRSS） methods （or CCQC and CSRSS methods） for different damping combinations are compared. In these analyses, some boundary lines for classically and non-classically damped systems are plotted to distinguish the allowed minimum frequency ratio at given geometric mean of the damping ratios of both modes if their relativity is neglected. Furthermore, the simplified method, which is a special mode quadratic combination method considering only relativity of adjacent modes in CQC method and named simplified CQC or partial quadratic combination （PQC） method for classically damped linear system, is proposed to improve computational efficiency, and the criterion for determination of how many correlated modes should be adopted is proposed. Similarly, the simplified CCQC or complex partial quadratic combination （CPQC） method for the non-classically damped linear system and the corresponding criterion are also deduced. Finally, a numerical example is given to illustrate the applicability, computational accuracy and efficiency of the PQC and CPQC methods. 相似文献
3.
The seismic analysis of structures is usually carried out considering the ground motion as fully‐correlated in space and determining the structural response by pseudo‐deterministic methods such as the response spectrum technique. Actually, the partial correlation of the seismic acceleration may influence heavily the behaviour of spatially extended structures, such as bridges, viaducts or pipelines. In order to take its partial correlation into account, the seismic ground motion is schematized as a stochastic process dependent on time and on space; the hypotheses of stationarity and homogeneity are used to obtain simple and general results. The influence of the partial correlation of the seismic ground motion on the structural response is investigated by introducing suitable Equivalent Spectra. The acceleration of the support‐points of the structure is represented by the Proper Orthogonal Decomposition (POD), defining the modes of the earthquake. The method is formulated for any kind of multi‐degree‐of‐freedom system and is applied, as a case study, to an ideal single‐storey multi‐supported frame with an axially rigid beam. In the case of two supports, the POD decouples the pseudo‐static and the dynamic contributions to the structural response. This property is preserved for structural systems with many supports, where only the lower modes of the earthquake, usually the first two POD modes, are responsible for the structural response. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
4.
目前用于结构抗震设计的反应谱仅能反映峰值反应,无法体现反应值随时间的变化。文中提出一种弹性能量半径演化谱,可反映线性单自由度体系弹性能量(即动能与弹性势能之和)随地震持时的变化,且其峰值近似等于结构峰值位移。文中给出了利用地震动演化功率谱得到该演化谱的方法并进一步发展了一种计算线性多自由度体系地震位移反应的新方法。通过两座框架结构的地震反应计算,将新方法与传统振型组合法及时程分析法的计算结果进行对比,发现对于振型稀疏结构,新方法计算结果与SRSS法接近;而对于振型密集结构,新方法计算结果较CQC法更精确,且避免了CQC法相关系数的复杂计算。 相似文献
5.
An Erratum has been published for this article in Earthquake Engng. Struct. Dyn. 2004; 33:1429. Based on structural dynamics theory, the modal pushover analysis (MPA) procedure retains the conceptual simplicity of current procedures with invariant force distribution, now common in structural engineering practice. The MPA procedure for estimating seismic demands is extended to unsymmetric‐plan buildings. In the MPA procedure, the seismic demand due to individual terms in the modal expansion of the effective earthquake forces is determined by non‐linear static analysis using the inertia force distribution for each mode, which for unsymmetric buildings includes two lateral forces and torque at each floor level. These ‘modal’ demands due to the first few terms of the modal expansion are then combined by the CQC rule to obtain an estimate of the total seismic demand for inelastic systems. When applied to elastic systems, the MPA procedure is equivalent to standard response spectrum analysis (RSA). The MPA estimates of seismic demand for torsionally‐stiff and torsionally‐flexible unsymmetric systems are shown to be similarly accurate as they are for the symmetric building; however, the results deteriorate for a torsionally‐similarly‐stiff unsymmetric‐plan system and the ground motion considered because (a) elastic modes are strongly coupled, and (b) roof displacement is underestimated by the CQC modal combination rule (which would also limit accuracy of RSA for linearly elastic systems). Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
6.
多维地震输入下首都机场航站楼T3反应谱分析 总被引：2，自引：0，他引：2
首都机场航站楼(T3)下部为混凝土和钢混合框架,上部为复杂的双曲面形双层扁网壳,长960 m,宽780 m,为超大体量大跨度复杂空间钢结构体系。本文采用SAP2000有限元软件,对其进行了单维和多维地震输入下的反应谱分析,研究了单维和多维地震输入对构件内力、节点位移和地震总剪力的影响;研究了多维地震输入下地震响应值与按规范地震组合公式计算所得地震响应值的关系;研究了模态提取数目和质量参与系数的关系,CQC法中参与组合的模态数目与结构地震响应的关系。研究表明,采用振型分解反应谱法时,模态频率越高,对结构内力的影响越小,对于对结构影响较小的高频模态,可以忽略其对结构的影响;根据单维和多维地震反应的对比分析,对超大跨度复杂钢结构宜进行三维地震输入的反应谱分析。另外,本文提出了一种新的地震效应组合方法,可替代多维地震反应分析,并弥补现行规范的不足。 相似文献
7.
This paper presents a response spectrum analysis procedure for the calculation of the maximum structural response to three translational seismic components that may act at any inclination relative to the reference axes of the structure. The formula GCQC3, a generalization of the known CQC3‐rule, incorporates the correlation between the seismic components along the axes of the structure and the intensity disparities between them. Contrary to the CQC3‐rule where a principal seismic component must be vertical, in the GCQC3‐rule all components can have any direction. Besides, the GCQC3‐rule is applicable if we impose restrictions to the maximum inclination and/or intensity of a principal seismic component; in this case two components may be quasi‐horizontal and the third may be quasi‐vertical. This paper demonstrates that the critical responses of the structure, defined as the maximum and minimum responses considering all possible directions of incidence of one seismic component, are given by the square root of the maximum and minimum eigenvalues of the response matrix R , of order 3×3, defined in this paper; the elements of R are established on the basis of the modal responses used in the well‐known CQC‐rule. The critical responses to the three principal seismic components with arbitrary directions in space are easily calculated by combining the eigenvalues of R and the intensities of those components. The ratio rmax/rSRSS between the maximum response and the SRSS response, the latter being the most unfavourable response to the principal seismic components acting along the axes of the structure, is bounded between 1 and √(3γa2/(γa2 + γb2 + γc2)), where γa?γb?γc are the relative intensities of the three seismic components with identical spectral shape. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
8.
Naohiro Nakamura 《地震工程与结构动力学》2006,35(2):217-231
In order to perform time history earthquake response analyses with consideration to both the dynamic soil–structure interaction and the non‐linear behaviour of the structure, it is important to transform the soil impedance in the frequency domain to the impulse response in the time domain. In this paper, a new transform method with high practicality is proposed. First, the formulation of the proposed transform method is described. Next, the validity of the method is examined using an example problem whose impulse response is analytically obtained. Then, the impedance of the rigid foundation on 2‐layered soil is transformed to the time domain, and the characteristics of the impulse response are investigated. Finally, time history earthquake response analyses of a structure on the soil using the obtained impulse response are carried out. The validity and the efficiency of the proposed method are confirmed through these investigations. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
9.
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
10.
In this paper, an analytical method is proposed to determine the dynamic response of 3‐D rectangular liquid storage tanks with four flexible walls, subjected to horizontal seismic ground motion. Fluid–structure interaction effects on the dynamic responses of partially filled fluid containers, incorporating wall flexibility, are accounted for in evaluating impulsive pressure. The velocity potential in which boundary conditions are satisfied is solved by the method of separation of variables using the principle of superposition. The impulsive pressure distribution is then computed. Solutions based on 3‐D modeling of the rectangular containers are obtained by applying the Rayleigh–Ritz method using the vibration modes of flexible plates with suitable boundary conditions. Trigonometrical functions that satisfy boundary conditions of the storage tank such that the flexibility of the wall is thoroughly considered are used to define the admissible vibration modes. The analysis is then performed in the time domain. Moreover, an analytical procedure is developed for deriving a simple formula that evaluates convective pressure and surface displacements in a similar rigid tank. The variation of dynamic response characteristics with respect to different tank parameters is investigated. A mechanical model, which takes into account the deformability of the tank wall, is developed. The parameters of such a model can be obtained from developed charts, and the maximum seismic loading can be predicted by means of a response spectrum characterizing the design earthquake. Accordingly, a simplified but sufficiently accurate design procedure is developed to improve code formulas for the seismic design of liquid storage tanks. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
11.
This paper attempts to study the response of equipment items attached to torsional buildings supported by elastic bearings under earthquake excitations. To account for the effect of torsion and translation, each storey of the building is modelled with two degrees of freedom, one for translation and the other for torsion. The equipment is assumed to be so light that it affects slightly the vibration modes of the primary structure to which it is attached. Modal synthesis results obtained by the perturbation technique together with the CQC procedure are compared with those from a complete eigenvalue analysis. Using the present semi-analytical approach, the key parameters that govern the equipment and structure responses can be easily identified. In the numerical studies, it is confirmed that the response of the equipment and the building to which it is mounted, can be effectively reduced through installation of the base isolators. The optimal point for mounting the equipment is the one where the equipment remains undisplaced during vibration of the tuned mode. © 1998 John Wiley & Sons, Ltd. 相似文献
12.
The objective of this work was to assess the significance of the values of damping obtained applying the half‐power bandwidth method to the frequency response records of the steady‐state response of a system that does not possess real modes either because the damping matrix does not satisfy the orthogonality condition or because its parameters are functions of frequency. A multi‐degree of freedom system with real modes and different types of damping is considered first. A two degree of freedom system with an arbitrary damping matrix, a rigid mass on an elastic foundation subjected to vertical and coupled horizontal/rocking vibrations, and a single degree of freedom model of a building accounting for inertial soil structure interaction effects are considered next in more detail. The results show that the predictions of the method, when applicable compare very well with those provided by approximate formulae and procedures used in practice. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
13.
It is well-known that the application of the Square-Root-of-Sum-of-Squares (SRSS) method in seismic analysis for combining modal maxima can cause significant errors. Nevertheless, this method continues to be used by the profession for significant buildings. The purpose of this note is to present an improved technique to be used in place of the SRSS method in seismic analysis. A Complete Quadratic Combination (CQC) method is proposed which reduces errors in modal combination in all examples studied. The CQC method degenerates into the SRSS method for systems with well-spaced natural frequencies. Since the CQC method only involves a small increase in numerical effort, it is recommended that the new approach be used as a replacement for the SRSS method in all response spectrum calculations. 相似文献
14.
This paper examines higher mode effects in systems where the ductile mechanism for seismic design is the base moment‐rotation response. The modal properties of flexural and shear beams with uniform mass and elasticity and with a variable amount of base rotational restraint are derived. As the base fixity is released, the first mode becomes the rigid body rotation of the beam about the base, but the higher modes change much less, particularly for the shear beam model. Most response quantities that are of interest in the seismic design of typical mid‐rise buildings are controlled by the first two lateral modes, except at locations along the height where the second mode contributes little. However, the third and higher lateral modes are more significant for high‐rise buildings. Based on the theory of uniform cantilever shear beams, expressions are developed to avoid the need for a modal analysis to estimate the overturning moment, storey shear, and floor acceleration envelopes. Considering the measured response from the shake table testing of a large‐scale eight‐storey controlled rocking steel braced frame, the proposed expressions are shown to be of similar or better accuracy to a modified modal superposition technique, which combines the higher mode response from an elastic modal analysis with the response associated with achieving the maximum base overturning moment according to an inverted triangular load distribution. Because the proposed method uses only parameters that are available at the initial design stage, avoiding the analysis of a structural model, it is likely to be especially useful for preliminary design. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
15.
An analytical study of the seismic response of typical base isolated structures mounted on rubber bearings is presented. Isolated buildings are liable to have closely spaced lower modes of vibration with small eccentricity between centres of mass and rigidity. The isolated structure is modelled as a rigid deck with lumped masses supported on axially inextensible elastomeric rubber bearings. This simplified system has three degrees of freedom (dof), two translations and one rotation in the horizontal plane. The Green's functions for the displacement response of the 3 dof system are derived for both undamped and damped cases with small and large eccentricities. The small eccentricity case is taken from a specific isolated building, while the large eccentricity case arises from the 5 per cent accidental eccentricity which is required by various seismic codes. An interaction equation for normalized displacements is established for an idealized flat velocity spectrum or hyperbolic acceleration spectrum. An isolated building on rubber bearings would have its fundamental period fall into this range of a design spectrum. Numerical results for the specific building subjected to the El Centro earthquake of 1940 are presented. Both the time history and the response spectrum modal superposition analysis were performed. In the response spectrum analysis, the Complete Quadratic Combination (CQC) showed superiority over the Square Root of the Sum of Squares (SRSS) in estimating maximum responses. It is concluded that the effect of torsional coupling on the transient response of base isolated structures is insignificant, due to the combined effect of the time lag between the maximum translational and torsional responses and the influence of damping in the isolation system which for elastomeric bearings can be as high as 8 to 10 per cent. 相似文献
16.
I. N. Psycharis J. V. Lemos D. Y. Papastamatiou C. Zambas C. Papantonopoulos 《地震工程与结构动力学》2003,32(13):2063-2084
A numerical study of the seismic behaviour of a proposed restoration of the Parthenon Pronaos is presented. The column‐architrave classical structure was represented by a discrete element model, with the assumption of rigid blocks and frictional joints. Time domain analyses were performed, considering the geometric and material non‐linear behaviour at the joints. The deformation and failure modes of drum columns subject to seismic excitations of various types and intensities were analysed. The adverse influence of drum imperfections on structural safety was examined. A proposal of reinforcement with titanium connections was analysed, and it was found that architrave connections generally improve the response by decreasing the permanent displacements, while titanium dowels between the column drums do not improve significantly the behaviour and in some cases they may be unfavourable to the safety of the structure. Copyright 2003 John Wiley & Sons, Ltd. 相似文献
17.
An efficient approach is proposed for analysing the non-stationary random responses of complex structures located in an evolutionary inhomogeneous stochastic field. The approach is a kind of complete CQC method because the cross-correlation terms both between the participant modes and between the ground joint excitations are included in the response calculations. The effect of the loss of coherency between ground joints is also taken into account. For non-proportionally damped structures with many degrees of freedom, the order of the equations of motion can be reduced by using only real modes while structural non-stationary random responses can still be computed conveniently and accurately. © 1997 by John Wiley & Sons, Ltd. 相似文献
18.
The influence of stochastic kinematic interaction (SKI) on structural response is investigated in this paper. The SKI is evaluated through a computational model based on the boundary element method (BEM) formulated in the frequency domain. The singular integrals required in the computation of BEM are evaluated in a closed form. It is assumed that the foundation input motion (FIM) is the result of the superposition of many plane, stationary, correlated stochastic SH‐, P‐ and SV‐waves travelling within a homogeneous viscoelastic soil at different angles. The results obtained indicate that the effect of SKI on the foundation response is qualitatively similar to that of wave passage. Both effects involve a reduction of translational components of the response at intermediate and high frequencies and creation of a rotational response component at intermediate frequencies, which decreases at high frequencies. While, it is found that the SKI decreases the maximum response of structures built on embedded rigid strip foundations excited by SH‐ and P‐waves, it increases the maximum response for SV‐waves, except when the natural frequency of the structure is less than 0.5 Hz and for short structures excited by shallowly incident SV‐waves. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
19.
A first-order formulation to analyze the dynamic response of layered soil profiles is presented as an alternative to the widely used second-order thin-layer method by the direct stiffness approach, including an efficient simulation of the underlaying elastic half-space. In contrast to the thin-layer method where response is expressed through a combination of second-order propagation modes, the proposed procedure uses first-order modal parameters that have the capacity to provide a good approximation in the complete wave number domain k, including the exact stiffness values for k=0 and k→∞, thus justifying its designation of doubly-asymptotic. This feature allows obtaining the exact soil profile response for static loads, while the proposed treatment of the elastic half-space reproduces naturally the radiation condition without a need of artificial damping. The capacity of the proposed formulation to solve elastodynamic problems is assessed by comparing its results with those of exact solutions available in the literature, and numerical solutions of rigid disks supported on the surface of different soil profiles. 相似文献
20.
Nonparametric techniques for estimation of wave dispersion in buildings by seismic interferometry are applied to a simple model of a soil–structure interaction (SSI) system with coupled horizontal and rocking response. The system consists of a viscously damped shear beam, representing a building, on a rigid foundation embedded in a half‐space. The analysis shows that (i) wave propagation through the system is dispersive. The dispersion is characterized by lower phase velocity (softening) in the band containing the fundamental system mode of vibration, and little change in the higher frequency bands, relative to the building shear wave velocity. This mirrors its well‐known effect on the frequencies of vibration, i.e. reduction for the fundamental mode and no significant change for the higher modes of vibration, in agreement with the duality of the wave and vibrational nature of structural response. Nevertheless, the phase velocity identified from broader band impulse response functions is very close to the superstructure shear wave velocity, as found by an earlier study of the same model. The analysis reveals that (ii) the reason for this apparent paradox is that the latter estimates are biased towards the higher values, representative of the higher frequencies in the band, where the response is less affected by SSI. It is also discussed that (iii) bending flexibility and soil flexibility produce similar effects on the phase velocities and frequencies of vibration of a building. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献