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1.
This paper deals with the dynamic response of free-standing statues on the top surface of slender elastically supported cantilevers subjected to horizontal ground motion. Given that there is no link between the base of the statue and the top surface of the monolithic cantilever the statue is in equilibrium in the vertical direction under its own weight. Attention is focused on the determination of the minimum amplitude ground acceleration which leads to the rocking (overturning) instability of the statue whose mass and rotatory inertia are a priory known. It is assumed that the friction between the base of the statue and the top surface of the cantilever is sufficiently large to prevent sliding so that rocking prevails. After simulating the statue by a rigid block freely supported on the top surface of the elastically restrained monolithic cantilever, a theoretical dynamic analysis of the cantilever–rigid block system under horizontal ground motion is comprehensively presented. Two modes of overturning instability of the free standing rigid block are discussed: instability without or with impact. Criteria for overturning instability of the rigid block associated with the minimum amplitude ground acceleration which leads through the vanishing of the angular velocity to an escaped motion in the phase-plane portrait, are properly assessed. 相似文献
2.
Rocking (overturning) instability analyses of rigid blocks based on the assumption that the friction between the block and the ground is sufficiently large to exclude the effect of sliding, are reconsidered by including the effect in question. Both modes of overturning instability – without impact and after one impact – are thoroughly discussed in connection with small sliding, whose value depends on the values of kinetic (dry) friction coefficient and the external frequency excitation. Using an energy approach the analytical derivation of the nonlinear differential equations of motion of free-standing rigid blocks under one-sine ground pulse including the effect of sliding, are comprehensively established. The serious difficulties in solving this problem on one hand the change of the kinetic friction coefficient during the motion and on the other hand the reliable evaluation of the actual friction effect when rocking is included, are effectively confronted. This is achieved through a reliable approximation of an equivalent (reduced) coefficient assuming that the major part of friction takes place from the initiation of motion and terminates shortly after the onset of rocking. In cases of slender blocks closed form solutions for overturning due to simultaneous rocking–sliding without or after one impact, are conveniently derived. Among other findings, it was explored that the single block in question for small values of the external frequency (long periods of excitation) the sliding effect is beneficial (stabilizing the block), while for large values of external frequency this effect is detrimental (destabilizing the block). 相似文献
3.
The classical problem of rocking of a rigid, free-standing block to earthquake ground shaking containing distinct pulses, as is the case of near-fault earthquake motions, is revisited. A rectangular block resting on a rigid base is considered, subjected to a range of idealized single-lobe ground acceleration pulses expressed by a generalized function controlled by a single shape parameter. The problem is treated analytically in the realm of the linearized equations of motion under the assumption of slender block geometry and rocking without slipping. Peak rocking response and overturning criteria for different waveforms are presented in terms of dimensionless closed-form expressions and graphs. Two parameters are employed to this end: dimensionless pulse duration f (i.e., actual pulse duration times characteristic block frequency) and dimensionless uplift strength η (i.e., ratio of minimum required acceleration for initiation of uplift over peak pulse acceleration). The linearized response is compared analytically with the fully non-linear one using an ad hoc energy formulation leading to an approximate closed-form solution. It is shown that the non-linear equations of motion yield more stable response than their linearized counterparts. A brief discussion on scaling laws is provided. 相似文献
4.
Allowing structures to uplift modifies their seismic response; uplifting works as a mechanical fuse and limits the forces transmitted to the superstructure. However, engineers are generally reluctant to construct an unanchored structure because the system could overturn due to lacking redundancy. Using a safety factor for the design of a flat rocking foundation, ie, designing it wider, goes against the main idea of this seismic modification method as the force demand for the structure increases. We propose to extend the flat base of a rocking block with curved extensions to better protect the block from overturning, yet not prevent its uplifting. After investigating the seismic response of such rocking blocks, we extend the study to investigate the seismic response of rolling and rocking frames comprising columns with curved base extensions. The equations of motion are derived, time history analyses are performed, and rocking spectra are constructed. We draw two important conclusions: (a) the response of a class of rocking oscillators with curved base extensions is equivalent to the response of a flat-base rocking oscillators of the same slenderness, yet larger size; (b) the rotation demand on two negative stiffness rocking and rolling oscillators with the same uplifting acceleration and the same size is roughly the same as long as the rocking oscillators are not close to overturning. The above findings can serve as a basis for the rational seismic design of structures supported on rocking columns with curved bases, a system that has been used since the 1960s. 相似文献
5.
An analytical model of a deformable cantilever structure rocking on a rigid surface: development and verification 
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下载免费PDF全文 This paper extends previously developed models to account for the influence of the column and the foundation masses on the behavior of top‐heavy deformable elastic cantilever columns rocking on a rigid support surface. Several models for energy dissipation at impact are examined and compared. A novel Vertical Velocity Energy Loss model is introduced. Rocking uplift and overturning spectra for the deformable elastic cantilever model excited by sinusoidal ground motions are constructed. The effects of non‐dimensional model parameter variations on the rocking spectra and the overturning stability of the model are presented. It is shown that the remarkable overturning stability of dynamically excited large cantilever columns is not jeopardized by their deformability. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
6.
This paper examines the rocking response and stability of rigid blocks standing free on an isolated base supported: (a) on linear viscoelastic bearings, (b) on single concave and (c) on double concave spherical sliding bearings. The investigation concludes that seismic isolation is beneficial to improve the stability only of small blocks. This happens because while seismic isolation increase the ‘static’ value of the minimum overturning acceleration, this value remains nearly constant as we move to larger blocks or higher frequency pulses; therefore, seismic isolation removes appreciably from the dynamics of rocking blocks the beneficial property of increasing stability as their size increases or as the excitation pulse period decreases. This remarkable result suggests that free‐ standing ancient classical columns exhibit superior stability as they are built (standing free on a rigid foundation) rather than if they were seismically isolated even with isolation system with long isolation periods. The study further confirms this finding by examining the seismic response of the columns from the peristyle of two ancient Greek temples when subjected to historic records. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
7.
Loizos Papaloizou Petros Komodromos 《Soil Dynamics and Earthquake Engineering》2009,29(11-12):1437-1454
In this paper, the dynamic behavior of multi-drum columns and colonnades with epistyles under earthquake excitations is examined through planar numerical simulations. A specialized software application, developed utilizing the discrete element methods (DEM), is used to investigate the influence of certain parameters on the seismic response of such multi-body structural systems. First, this custom-made software is extensively validated by comparing the computed responses of various problems, such as sliding, rocking and free vibration dynamics of rigid bodies, with the corresponding analytical solutions. Then, the developed software is used to study the influence of the frequency content and amplitude of the ground motions on the columns and colonnades, as well as the geometric characteristics of these structures. Parameters such as the number of drums that assemble each column and the number of columns of a colonnade appear to be defining parameters that affect the seismic response of colonnades with epistyles. For ground motions with relatively low predominant frequencies, rocking is the dominant effect in the response, while with the increase of the excitation frequency the response becomes even more complex involving both sliding and rocking phenomena. The numerical simulations show that earthquakes with relatively low predominant frequencies seem to endanger both standalone columns and colonnades with epistyles more than earthquakes with higher predominant frequencies. 相似文献
8.
The present study explores analytically the concept of rocking isolation in bridges considering for the first time the influence of the abutment-backfill system. The dynamic response of rocking bridges with free-standing piers of same height and same section is examined assuming negligible deformation for the substructure and the superstructure. New relationships for the prediction of the bridge rocking motion are derived, including the equation of motion and the restitution coefficient at each impact at the rocking interfaces. The bridge structure is found to be susceptible to a failure mode related to the failure of the abutment-backfill system, which can occur prior to the well-known overturning of the rocking piers. Thus, a new failure spectrum is proposed called Failure Minimum Acceleration Spectrum (FMAS) which extends the overturning spectrum put forward in previous studies, and it differs in principle from the latter. The comparison with the dynamic response of bridges modelled as rocking frames without abutments reveals not only that seat-type abutments and their backfill have a generally beneficial effect on the seismic performance of rocking pier bridges by suppressing the free rocking motion of the frame system, but also that the simple frame model cannot capture all salient features of the rocking bridge response as it misses potential failure modes, overestimating the rocking bridge's safety when these modes are critical. 相似文献
9.
Rocking isolation has been increasingly studied as a promising design concept to limit the earthquake damage of civil structures. Despite the difficulties and uncertainties of predicting the rocking response under individual earthquake excitations (due to negative rotational stiffness and complex impact energy loss), in a statistical sense, the seismic performance of rocking structures has been shown to be generally consistent with the experimental outcomes. To this end, this study assesses, in a probabilistic manner, the effectiveness of using rocking isolation as a retrofit strategy for single-column concrete box-girder highway bridges in California. Under earthquake excitation, the rocking bridge could experience multi-class responses (eg, full contacted or uplifting foundation) and multi-mode damage (eg, overturning, uplift impact, and column nonlinearity). A multi-step machine learning framework is developed to estimate the damage probability associated with each damage scenario. The framework consists of the dimensionally consistent generalized linear model for regression of seismic demand, the logistic regression for classification of distinct response classes, and the stepwise regression for feature selection of significant ground motion and structural parameters. Fragility curves are derived to predict the response class probabilities of rocking uplift and overturning, and the conditional damage probabilities such as column vibrational damage and rocking uplift impact damage. The fragility estimates of rocking bridges are compared with those for as-built bridges, indicating that rocking isolation is capable of reducing column damage potential. Additionally, there exists an optimal slenderness angle range that enables the studied bridges to experience much lower overturning tendencies and significantly reduced column damage probabilities at the same time. 相似文献
10.
Dynamic response analysis of solitary flexible rocking bodies: modeling and behavior under pulse‐like ground excitation 下载免费PDF全文
下载免费PDF全文 Results obtained for rigid structures suggest that rocking can be used as seismic response modification strategy. However, actual structures are not rigid: structural elements where rocking is expected to occur are often slender and flexible. Modeling of the rocking motion and impact of flexible bodies is a challenging task. A non‐linear elastic viscously damped zero‐length spring rocking model, directly usable in conventional finite element software, is presented in this paper. The flexible rocking body is modeled using a conventional beam‐column element with distributed masses. This model is verified by comparing its pulse excitation response to the corresponding analytical solution and validated by overturning analysis of rocking blocks subjected to a recorded ground motion excitation. The rigid rocking block model provides a good approximation of the seismic response of solitary flexible columns designed to uplift when excited by pulse‐like ground motions. Guidance for development of rocking column models in ordinary finite element software is provided. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
11.
Previous studies have suggested that rocking vibration accompanied by uplift motion might reduce the seismic damage to buildings subjected to severe earthquake motions. This paper reports on the use of shaking table tests and numerical analyses to evaluate and compare the seismic response of base‐plate‐yielding rocking systems with columns allowed to uplift with that of fixed‐base systems. The study is performed using half‐scale three‐storey, 1 × 2 bay braced steel frames with a total height of 5.3 m. Base plates that yield due to column tension were installed at the base of each column. Two types of base plates with different thicknesses are investigated. The earthquake ground motion used for the tests and analyses is the record of the 1940 El Centro NS component with the time scale shortened by a factor of 1/√2. The maximum input acceleration is scaled to examine the structural response at various earthquake intensities. The column base shears in the rocking frames with column uplift are reduced by up to 52% as compared to the fixed‐base frames. Conversely, the maximum roof displacements of the fixed and rocking frames are about the same. It is also noted that the effect of the vertical impact on the column associated with touchdown of the base plate is small because the difference in tensile and compressive forces is primarily due to the self‐limiting tensile force in the column caused by yielding of the base plate. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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13.
An analytical model of a deformable cantilever structure rocking on a rigid surface: experimental validation 下载免费PDF全文
下载免费PDF全文 This paper describes an experimental program to examine the dynamic response of deformable cantilevers rocking on a rigid surface. The primary goal of the tests is to verify and validate a dynamic rocking model that describes the behavior of these structures. The benchmark response data was obtained from shaking‐table tests on deformable rocking specimens with different natural vibration frequencies and different aspect ratios excited by analytical pulses and recorded ground motions. The responses computed using the model are found to be in good agreement with the benchmark test results. Widely used impact, restitution and damping assumptions are revisited based on the experiment results and the analytical model findings. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
14.
The overturning fragilities of symmetric and asymmetric freestanding blocks, ranging in height from 0.54 to 3.6 m and with height‐to‐width ratios ranging from 2.1 to 6.6, are determined numerically. A probabilistic formulation regularizes the overturning responses when exposed to earthquake‐like random‐vibration waveforms. The peak amplitude of the forcing excitation (peak ground acceleration or PGA) is parameterized as a function of the block size, block shape, overturning probability, and either the PGA normalized peak ground velocity (PGV/PGA), spectral acceleration at 1 s (Sa(1)/PGA), or spectral acceleration at 2 s (Sa(2)/PGA). These later intensity measures are correlated with the duration of the predominant acceleration pulse. The overturning fragilities are compared with shake table experiments using blocks ranging in height from ～0.2 to 1.2 m and with height‐to‐width ratios ranging from ～2 to 10. Excitations utilized in the shake table experiments include recordings of the 1979 Imperial Valley, 1985 Michoacan, 1999 Duzce, 1999 Chi‐Chi, and 2002 Denali Earthquakes along with synthetic waveforms. The overturning fragilities accurately represent the overturning responses of blocks with simple basal contact conditions. Objects with multiple rocking points, such as precariously balanced rocks, are more fragile than predicted. Nondestructive tilting tests are used to account for blocks with complex basal contact conditions, demonstrating that these blocks overturn similarly to more slender blocks with simple contact conditions. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
15.
A freestanding rigid block subjected to base excitation can exhibit complicated motion described by five response modes: rest, pure rocking, pure sliding, combined sliding-rocking, and free flight. Previous studies on the dynamics of a rocking block have assumed that the block does not interact with neighboring objects. However, there are many applications in which the block may start or come in contact with an adjacent boundary during its motion, for example, a bookcase or cabinet colliding with a partition wall in an earthquake. This paper investigates the dynamics of a sliding-rocking block considering impact with an adjacent wall. A model is developed in which the base and wall are assumed rigid, and impact is treated using the classical impulse and momentum principle. The model is verified by comparing its predictions in numerical simulations against those of an existing general-purpose rigid-body model in which impact is treated using a viscoelastic impact model. The developed model is used to investigate the effects of different parameters on the stability of a block subjected to analytical pulse excitations. It is found that wall placement (left or right) has a dominant effect on the shape of the overturning acceleration spectra for pulse excitations. In general, decreasing the gap distance, base friction coefficient, and wall coefficient of restitution enhance the stability of the block. Similar observations are made when evaluating the overturning probability of a block using earthquake floor motions. 相似文献
16.
Lydell Wiebe Constantin Christopoulos Robert Tremblay Martin Leclerc 《地震工程与结构动力学》2013,42(7):1069-1086
This paper presents the results of 56 large‐amplitude shake table tests of a 30% scale eight‐storey controlled rocking steel frame. No significant damage or residual deformations were observed after any of the tests. The frame had four possible configurations on the basis of combinations of two higher mode mitigation mechanisms. The first mitigation mechanism was formed by allowing the upper section of the frame to rock, so as to better control the mid‐height overturning moment. The second mitigation mechanism was formed by replacing the conventional first‐storey brace with a self‐centering energy dissipative (SCED) brace, so as to better control the base shear. The mechanisms had little effect during records where higher mode effects were not apparent, but they substantially reduced the shear and overturning moment envelopes, as well as the peak floor accelerations, during more demanding records. The reduction in storey shears led to similarly reduced brace force demands. Although the peak force demands in the columns were not reduced by as much as the frame overturning moments, using an upper rocking joint allowed the column demands to be estimated without the need to assume a lateral force distribution. The tests demonstrated that multiple force‐limiting mechanisms can be used to provide better control of peak seismic forces without excessive increases in drift demands, thus enabling more reliable capacity design. These results are expected to be widely applicable to structures where the peak seismic forces are significantly influenced by higher mode effects. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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18.
The result of a theoretical study on the rocking response of rigid blocks subjected to sinusoidal base motion is presented. The study indicates that, for a given excitation amplitude and frequency, a rigid block can respond in several different ways. Based on analysis, the regions of different classes of steady state symmetric response solutions are mapped on the excitation amplitude-frequency parameter space. The steady state response solutions (both harmonic and subharmonic) are classified into two classes, out-of-phase and in-phase with respect to the excitation. Only out-of-phase solutions are found to be stable. A parametric study shows that steady rocking response amplitude is highly sensitive to the size of the block and the excitation frequency in the low frequency range. It is relatively insensitive to the excitation amplitude and the system's coefficient of restitution of impact. For two blocks of the same aspect ratio and coefficient of restitution subjected to the same excitation, the larger block always responds in smaller amplitude than the smaller block. Computer simulation is carried out to study the stability of the symmetric steady state response solutions obtained from analysis. It is found that as the excitation frequency is decreased beyond the boundary of stable symmetric response, the response becomes unsymmetric where the mean amplitude of oscillation is non-zero. Further decrease in excitation frequency beyond the stable unsymmetric response boundary causes instability in the form of overturning. 相似文献
19.
The rocking response of large flexible structures to earthquakes 总被引：1，自引：0，他引：1
The rocking response of structures subjected to strong ground motions is a problem of ‘several scales’. While small structures are sensitive to acceleration pulses acting successively, large structures are more significantly affected by coherent low frequency components of ground motion. As a result, the rocking response of large structures is more stable and orderly, allowing effective isolation from the ground without imminent danger of overturning. This paper aims to characterize and predict the maximum rocking response of large and flexible structures to earthquakes using an idealized structural model. To achieve this, the maximum rocking demand caused by different earthquake records was evaluated using several ground motion intensity measures. Pulse-type records which typically have high peak ground velocity and lower frequency content caused large rocking amplitudes, whereas non-pulse type records caused random rocking motion confined to small rocking amplitudes. Coherent velocity pulses were therefore identified as the primary cause of significant rocking motion. Using a suite of pulse-type ground motions, it was observed that idealized wavelets fitted to velocity pulses can adequately describe the rocking response of large structures. Further, a parametric analysis demonstrates that pulse shape parameters affect the maximum rocking response significantly. Based on these two findings, a probabilistic analysis method is proposed for estimating the maximum rocking demand to pulse-type earthquakes. The dimensionless demand maps, produced using these methods, have predictive power in the near-field provided that pulse period and amplitude can be estimated a priori. Use of this method within a probabilistic seismic demand analysis framework is briefly discussed. 相似文献
20.
This paper characterizes the ability of natural ground motions to induce rocking demands on rigid structures. In particular, focusing on rocking blocks of different size and slenderness subjected to a large number of historic earthquake records, the study unveils the predominant importance of the strong‐motion duration to rocking amplification (ie, peak rocking response without overturning). It proposes original dimensionless intensity measures (IMs), which capture the total duration (or total impulse accordingly) of the time intervals during which the ground motion is capable of triggering rocking motion. The results show that the proposed duration‐based IMs outperform all other examined (intensity, frequency, duration, and/or energy‐based) scalar IMs in terms of both “efficiency” and “sufficiency.” Further, the pertinent probabilistic seismic demand models offer a prediction of the peak rocking demand, which is adequately “universal” and of satisfactory accuracy. Lastly, the analysis shows that an IM that “efficiently” captures rocking amplification is not necessarily an “efficient” IM for predicting rocking overturning, which is dominated by the velocity characteristics (eg, peak velocity) of the ground motion. 相似文献