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1.
A procedure is presented to determine new modal combination rules (both CQC and SRSS) for non‐classically damped structures. The procedure presented in this paper does not need the solution of any complex eigenvalue problem, in contrast to other methods found in the literature. Thus, the modal combination rules presented here are easily applicable, even by those engineers who are unaccustomed to using complex algebra. Moreover, these formulations show the further advantage of requiring the response spectra only for the target damping ratio value. So the use of approximated formulae, necessary for passing from the response spectrum with the target damping ratio value to other ones, is avoided. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

2.
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   

3.
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   

4.
A generalized pushover analysis (GPA) procedure is developed for estimating the inelastic seismic response of structures under earthquake ground excitations. The procedure comprises applying different generalized force vectors separately to the structure in an incremental form with increasing amplitude until a prescribed seismic demand is attained for each generalized force vector. A generalized force vector is expressed as a combination of modal forces, and simulates the instantaneous force distribution acting on the system when a given response parameter reaches its maximum value during dynamic response to a seismic excitation. While any response parameter can be selected arbitrarily, generalized force vectors in the presented study are derived for maximum interstory drift parameters. The maximum value of any other response parameter is then obtained from the envelope of GPAs results. Each nonlinear static analysis under a generalized force vector activates the entire multi‐degree of freedom effects simultaneously. Accordingly, inelastic actions develop in members with the contribution of all ‘instantaneous modes’ in the nonlinear response range. Target seismic demands for interstory drifts at the selected stories are calculated from the associated drift expressions. The implementation of the proposed GPA is simpler compared with nonlinear response history analysis, whereas it is less demanding in computational effort when compared with several multi‐mode adaptive nonlinear static procedures. Moreover, it does not suffer from the statistical combination of inelastic modal responses obtained separately. The results obtained from building frames have demonstrated that GPA is successful in estimating maximum member deformations and member forces with reference to the response history analysis. When the response is linear elastic, GPA and response spectrum analysis produce identical results. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

5.
A procedure for incorporating record‐to‐record variability into the simplified seismic assessment of RC wall buildings is presented. The procedure relies on the use of the conditional spectrum to randomly sample spectral ordinates at relevant periods of vibration. For inelastic response, displacement reduction factors are then used to relate inelastic displacement demand to the spectral displacement at the effective period for single‐degree‐of‐freedom systems. Simple equations are used to convert back and forth between multi‐degree‐of‐freedom RC wall buildings and equivalent single‐degree‐of‐systems so that relevant engineering demand parameters can be obtained. Consideration is also given to higher‐mode effects by adapting existing modal combination rules. The proposed method is applied to several case study buildings, showing promising results in the examination of inter‐storey drift ratio and shear forces. The proposed method captures the variation in the distribution of structural response parameters that occurs with variations in structural configuration, intensity, engineering demand parameter of interest and site characteristics. Discussion is provided on possible ways to improve the accuracy of the procedure and suggestions for additional future work. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

6.
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   

7.
An envelope‐based pushover analysis procedure is presented that assumes that the seismic demand for each response parameter is controlled by a predominant system failure mode that may vary according to the ground motion. To be able to simulate the most important system failure modes, several pushover analyses need to be performed, as in a modal pushover analysis procedure, whereas the total seismic demand is determined by enveloping the results associated with each pushover analysis. The demand for the most common system failure mode resulting from the ‘first‐mode’ pushover analysis is obtained by response history analysis for the equivalent ‘modal‐based’ SDOF model, whereas demand for other failure modes is based on the ‘failure‐based’ SDOF models. This makes the envelope‐based pushover analysis procedure equivalent to the N2 method provided that it involves only ‘first‐mode’ pushover analysis and response history analysis of the corresponding ‘modal‐based’ SDOF model. It is shown that the accuracy of the approximate 16th, 50th and 84th percentile response expressed in terms of IDA curves does not decrease with the height of the building or with the intensity of ground motion. This is because the estimates of the roof displacement and the maximum storey drift due to individual ground motions were predicted with a sufficient degree of accuracy for almost all the ground motions from the analysed sets. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

8.
In the conventional seismic design of high‐rise reinforced concrete core‐wall buildings, the design demands such as design shear and bending moment in the core wall are typically determined by the response spectrum analysis procedure, and a plastic hinge is allowed to form at the wall base to limit the seismic demands. In this study, it is demonstrated by using a 40‐story core‐wall building that this conventional approach could lead to an unsafe design where the true demands—the maximum inelastic seismic demands induced by the maximum considered earthquake—could be several times greater than the design demands and be unproportionately dominated by higher vibration modes. To identify the cause of this problem, the true demands are decomposed into individual modal contributions by using the uncoupled modal response history analysis procedure. The results show that the true demands contributed by the first mode are reasonably close to the first‐mode design demands, while those contributed by other higher modes are much higher than the corresponding modal design demands. The flexural yielding in the plastic hinge at the wall base can effectively suppress the seismic demands of the first mode. For other higher modes, however, a similar yielding mechanism is either not fully mobilized or not mobilized at all, resulting in unexpectedly large contributions from higher modes. This finding suggests several possible approaches to improve the seismic design and to suppress the seismic demands of high‐rise core‐wall buildings. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

9.
A generalized multi‐mode pushover analysis procedure was developed for estimating the maximum inelastic seismic response of symmetrical plan structures under earthquake ground excitations. Pushover analyses are conducted with story‐specific generalized force vectors in this procedure, with contributions from all effective modes. Generalized pushover analysis procedure is extended to three‐dimensional torsionally coupled systems in the presented study. Generalized force distributions are expressed as the combination of modal forces to simulate the instantaneous force distribution acting on the system when the interstory drift at a story reaches its maximum value during seismic response. Modal contributions to the generalized force vectors are calculated by a modal scaling rule, which is based on the complete quadratic combination. Generalized forces are applied to the mass centers of each story incrementally for producing nonlinear static response. Maximum response quantities are obtained when the individual frames attain their own target interstory drift values in each story. The developed procedure is tested on an eight‐story frame under 15 ground motions, and assessed by comparing the results obtained from nonlinear time history analysis. The method is successful in predicting the torsionally coupled inelastic response of frames responding to large interstory drift demands. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

10.
The accuracy of the three‐dimensional modal pushover analysis (MPA) procedure in estimating seismic demands for unsymmetric‐plan buildings due to two horizontal components of ground motion, simultaneously, is evaluated. Eight low‐and medium‐rise structures were considered. Four intended to represent older buildings were designed according to the 1985 Uniform Building Code, whereas four other designs intended to represent newer buildings were based on the 2006 International Building Code. The median seismic demands for these buildings to 39 two‐component ground motions, scaled to two intensity levels, were computed by MPA and nonlinear response history analysis (RHA), and then compared. Even for these ground motions that deform the buildings significantly into the inelastic range, MPA offers sufficient degree of accuracy. It is demonstrated that PMPA, a variant of the MPA procedure, for nonlinear systems is almost as accurate as the well‐known standard response spectrum analysis procedure is for linear systems. Thus, for practical applications, the PMPA procedure offers an attractive alternative to nonlinear RHA, whereby seismic demands can be estimated directly from the (elastic) design spectrum. In contrast, the nonlinear static procedure specified in the ASCE/SEI 41‐06 Standard is demonstrated to grossly underestimate seismic demands for some of the unsymmetric‐plan buildings considered. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

11.
Civil engineering structures are often subjected to multidirectional actions such as earthquake ground motion, which lead to complex structural responses. The contributions from the latter multidirectional actions to the response are highly coupled, leading to a MIMO system identification problem. Compared with single‐input, multiple‐output (SIMO) system identification, MIMO problems are more computationally complex and error prone. In this paper, a new system identification strategy is proposed for civil engineering structures with multiple inputs that induce strong coupling in the response. The proposed solution comprises converting the MIMO problem into separate SIMO problems, decoupling the outputs by extracting the contribution from the respective input signals to the outputs. To this end, a QR factorization‐based decoupling method is employed, and its performance is examined. Three factors, which affect the accuracy of the decoupling result, including memory length, input correlation, and system damping, are investigated. Additionally, a system identification method that combines the autoregressive model with exogenous input (ARX) and the Eigensystem Realization Algorithm (ERA) is proposed. The associated extended modal amplitude coherence and modal phase collinearity are used to delineate the structural and noise modes in the fitted ARX model. The efficacy of the ARX‐ERA method is then demonstrated through identification of the modal properties of a highway overcrossing bridge. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

12.
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   

13.
This paper focuses on slab vibration and a horizontal‐vertical coupling effect observed in a full‐scale 5‐story moment frame test bed building in 2 configurations: isolated with a hybrid combination of lead‐rubber bearings and cross‐linear (rolling) bearings, and fixed at the base. Median peak slab vibrations were amplified—relative to the peak vertical shake table accelerations—by factors ranging from 2 at the second floor to 7 at the roof, and horizontal floor accelerations were significantly amplified during 3D (combined horizontal and vertical) motions compared with 2D (horizontal only) motions of comparable input intensity. The experimentally observed slab accelerations and the horizontal‐vertical coupling effect were simulated through a 3D model of the specimen using standard software and modeling assumptions. The floor system was modeled with frame elements for beams/girders and shell elements for floor slabs; the insertion point method with end joint offsets was used to represent the floor system composite behavior, and floor mass was finely distributed through element discretization. The coupling behavior was partially attributed to the asymmetry of the building that was intensified by asymmetrically configured supplemental mass at the roof. Horizontal‐vertical coupled modes were identified through modal analysis and verified with evaluation of floor spectral peaks.  相似文献   

14.
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   

15.
This paper investigates the seismic response of tall cantilever wall buildings subjected to pulse type ground motion, with special focus on the relation between the characteristics of ground motion and the higher‐modes of response. Buildings 10, 20, and 40 stories high were designed such that inelastic deformation was concentrated at a single flexural plastic hinge at their base. Using nonlinear response history analysis, the buildings were subjected to near‐fault seismic ground motions and simple closed‐form pulses, which represented distinct pulses within the ground motions. Euler–Bernoulli beam models with lumped mass and lumped plasticity were used to model the buildings. The response of the buildings to the closed‐form pulses fairly matched that of the near‐fault records. Subsequently, a parametric study was conducted for the buildings subjected to three types of closed‐form pulses with a broad range of periods and amplitudes. The results of the parametric study demonstrate the importance of the ratio of the fundamental period of the structure to the period of the pulse to the excitation of higher modes. The study shows that if the modal response spectrum analysis approach is used — considering the first four modes with a uniform yield reduction factor for all modes, and with the square root of sum of squares modal combination rule — it significantly underestimates bending moment and shear force responses. A response spectrum analysis method that uses different yield reduction factors for the first and the higher modes is presented. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

16.
High force‐to‐volume extrusion damping devices can offer significant energy dissipation directly in structural connections and significantly reduce seismic response. Realistic force levels up to 400 kN have been obtained experimentally validating this overall concept. This paper develops spectral‐based design equations for their application. Response spectra analysis for multiple, probabilistically scaled earthquake suites are used to delineate the response reductions due to added extrusion damping. Representative statistics and damping reduction factors are utilized to characterize the modified response in a form suitable for current performance‐based design methods. Multiple equation regression analysis is used to characterize reduction factors in the constant acceleration, constant velocity, and constant displacement regions of the response spectra. With peak device forces of 10% of structural weight, peak damping reduction factors in the constant displacement region of the spectra are approximately 6.5 ×, 4.0 ×, and 2.8 × for the low, medium, and high suites, respectively. At T = 1 s, these values are approximately 3.6 ×, 1.8 ×, and 1.4 ×, respectively. The maximum systematic bias introduced by using empirical equations to approximate damping reduction factors in design analyses is within the range of +10 to ?20%. The seismic demand spectrum approach is shown to be conservative across a majority of the spectrum, except for large added damping between T = 0.8 and 3.5 s, where it slightly underestimates the demand up to a maximum of approximately 10%. Overall, the analysis shows that these devices have significant potential to reduce seismic response and damage at validated prototype device force levels. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

17.
Load‐dependent Ritz (LDR) vectors are used in conjunction with the multiple‐support response spectrum (MSRS) combination rule for analysis of structures subjected to spatially varying earthquake ground motions. The LDR vector approach for MSRS analysis is motivated by the fact that LDR vectors in general are more accurate and computationally simpler than eigenvectors in mode superposition analysis, and because many researchers and engineers are using LDR vectors in linear structural dynamic analysis. Mode truncation rules for the original MSRS method are modified to apply to LDR vectors. Two methods for selecting LDR vectors for multicomponent MSRS analysis are introduced. Idealized models of two real bridges with differing structural characteristics are used to investigate the accuracy and efficiency of the two LDR‐MSRS methods in comparison with results obtained by the original MSRS method as well as an extended version that accounts for the static contribution of truncated modes. The results show that the LDR‐MSRS method is generally more accurate than the original MSRS method and at least as accurate as the extended MSRS method. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

18.
The CQC rule for modal combination is extended to include the quasi-static contribution of truncated modes and the effects of input narrow-bandedness and cut-off frequency. A simple measure of the error in approximating a high-frequency modal response by its quasi-static contribution is derived. The extended rule is applicable to structures with high-frequency modes and to seismic inputs which may not be regarded as wide band. Numerical examples demonstrate the significance of input bandwidth and cut-off frequency on modal cross-correlation coefficients, and on the error resulting from truncation of high-freqeuncy modes.  相似文献   

19.
An improvement is suggested to the direct displacement‐based design (DDBD) procedure for bridges to account for higher mode effects, the key idea being not only the proper prediction of a target‐displacement profile through the effective mode shape method (wherein all significant modes are considered), but also the proper definition of the corresponding peak structural response. The proposed methodology is then applied to an actual concrete bridge wherein the different pier heights and the unrestrained transverse displacement at the abutments result in an increased contribution of the second mode. A comparison between the extended and the ‘standard’ DDBD is conducted, while further issues such as the proper consideration of the degree of fixity at the pier's top and the effect of the deck's torsional stiffness are also investigated. The proposed methodology and resulting designs are evaluated using nonlinear response‐history analysis for a number of spectrum‐compatible motions. Unlike the ‘standard’ DDBD, the extended procedure adequately reproduced the target‐displacement profile providing at the same time a good estimate of results regarding additional design quantities such as yield displacements, displacement ductilities, etc., closely matching the results of the more rigorous nonlinear response‐history analysis. However, the need for additional iterations clearly indicates that practical application of the proposed procedure is feasible only if it is fully ‘automated’, that is, implemented in a software package. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

20.
A statistical analysis of the peak acceleration demands for nonstructural components (NSCs) supported on a variety of stiff and flexible inelastic regular moment‐resisting frame structures with periods from 0.3 to 3.0 s exposed to 40 far‐field ground motions is presented. Peak component acceleration (PCA) demands were quantified based on the floor response spectrum (FRS) method without considering dynamic interaction effects. This study evaluated the main factors that influence the amplification or decrease of FRS values caused by inelasticity in the primary structure in three distinct spectral regions namely long‐period, fundamental‐period, and short‐period region. The amplification or decrease of peak elastic acceleration demands depends on the location of the NSC in the supporting structure, periods of the component and building, damping ratio of the component, and level of inelasticity of the supporting structure. While FRS values at the initial modal periods of the supporting structure are reduced due to inelastic action in the primary structure, the region between the modal periods experiences an increase in PCA demands. A parameter denoted as acceleration response modification factor (Racc) was proposed to quantify this reduction/increase in PCA demands. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

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