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1.
Allowing flexible structures to uplift and rock during earthquakes can significantly reduce the force demands and residual displacements. However, such structures are still susceptible to large deformations and accelerations that can compromise their functionality. In this paper, we examine the dynamic response of elastic rocking oscillators and suggest that their lateral drifts and accelerations can be limited effectively by using inerter devices. To this end, we offer a detailed examination of the effects of structural flexibility on the efficiency of the proposed system. The analytical expressions governing the motion of deformable structures with base uplift are revisited to incorporate the effects of the supplemental rotational inertia. The proposed model is then used to study the structural demands of flexible rocking structures under coherent pulses as well as noncoherent real pulse-like ground motions. Our results show that combining rocking with inerters can be an efficient strategy to control the deformation and acceleration demands in uplifting flexible systems. 相似文献
2.
Tall rigid blocks are prevalent in ancient historical constructions. Such structures are prone to rocking behaviour under strong ground motion, which is recognizably challenging to predict and mitigate. Our study is motivated by the need to provide innovative nonintrusive solutions to attenuate the rocking response of historical buildings and monuments. In this paper, we examine a novel scheme that employs external resonators buried next to the rocking structure as a means to control its seismic response. The strategy capitalizes on the vibration absorbing potential of the structure-soil-resonator interaction. Furthermore, the benefits of combining the resonators with inerters in order to reduce their gravitational mass without hampering their motion-control capabilities are also explored. Advanced numerical analyses of discrete models under coherent acceleration pulses with rocking bodies of different slenderness ratios under various ground motion intensities highlight the significant vibration absorbing qualities of the external resonating system. The influence of key system parameters such as the mass, stiffness, and damping of the resonator and those of the soil-structure-resonator arrangement are studied. Finally, a case study on the evaluation of the response of rocking structures with external resonators under real pulse-like ground-motion records confirms the important reductions in peak seismic rotational demands obtained with the proposed arrangement. 相似文献
3.
A new finite element model to analyze the seismic response of deformable rocking bodies and rocking structures is presented. The model comprises a set of beam elements to represent the rocking body and zero‐length fiber cross‐section elements at the ends of the rocking body to represent the rocking surfaces. The energy dissipation during rocking motion is modeled using a Hilber–Hughes–Taylor numerically dissipative time step integration scheme. The model is verified through correct prediction of the horizontal and vertical displacements of a rigid rocking block and validated against the analytical Housner model solution for the rocking response of rigid bodies subjected to ground motion excitation. The proposed model is augmented by a dissipative model of the ground under the rocking surface to facilitate modeling of the rocking response of deformable bodies and structures. The augmented model is used to compute the overturning and uplift rocking response spectra for a deformable rocking frame structure to symmetric and anti‐symmetric Ricker pulse ground motion excitation. It is found that the deformability of the columns of a rocking frame does not jeopardize its stability under Ricker pulse ground motion excitation. In fact, there are cases where a deformable rocking frame is more stable than its rigid counterpart. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
4.
Mohammad Reza Falamarz-Sheikhabadi Mohsen Ghafory-Ashtiany 《Journal of Seismology》2012,16(4):815-827
The paper addresses the issue of researching into the engineering characteristics of rotational strong ground motion components and rotational effects in structural response. In this regard, at first, the acceleration response spectra of rotational components are estimated in terms of translational ones. Next, new methods in order to consider the effects of rotational components in seismic design codes are presented by determining the effective structural parameters in the rotational loading of structures due only to the earthquake rotational components. Numerical results show that according to the frequency content of rotational components, the contribution of the rocking components to the seismic excitation of short period structures can never be ignored. During strong earthquakes, these rotational motions may lead to the unexpected overturning or local structural damages for the low-rise multi-story buildings located on soft soil. The arrangement of lateral-load resisting system in the plan, period, and aspect ratio of the system can severely change the seismic loading of wide symmetric buildings under the earthquake torsional component. 相似文献
5.
Dynamic response analysis of solitary flexible rocking bodies: modeling and behavior under pulse‐like ground excitation 
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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
6.
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
7.
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
8.
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
9.
Predicting the rocking response of structures to ground motion is important for assessment of existing structures, which may be vulnerable to uplift and overturning, as well as for designs which employ rocking as a means of seismic isolation. However, the majority of studies utilize a single rocking block to characterize rocking motion. In this paper, a methodology is proposed to derive equivalence between the single rocking block and various rocking mechanisms, yielding a set of fundamental rocking parameters. Specific structures that have exact dynamic equivalence with a single rocking block, are first reviewed. Subsequently, approximate equivalence between single and multiple block mechanisms is achieved through local linearization of the relevant equations of motion. The approximation error associated with linearization is quantified for three essential mechanisms, providing a measure of the confidence with which the proposed methodology can be applied. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
10.
Numerous structures uplift under the influence of strong ground motion. Although many researchers have investigated the effects of base uplift on very stiff (ideally rigid) structures, the rocking response of flexible structures has received less attention. Related practical analysis methods treat these structures with simplified ‘equivalent’ oscillators without directly addressing the interaction between elasticity and rocking. This paper addresses the fundamental dynamics of flexible rocking structures. The nonlinear equations of motion, derived using a Lagrangian formulation for large rotations, are presented for an idealized structural model. Particular attention is devoted to the transition between successive phases; a physically consistent classical impact framework is utilized alongside an energy approach. The fundamental dynamic properties of the flexible rocking system are compared with those of similar linear elastic oscillators and rigid rocking structures, revealing the distinct characteristics of flexible rocking structures. In particular, parametric analysis is performed to quantify the effect of elasticity on uplift, overturning instability, and harmonic response, from which an uplifted resonance emerges. The contribution of stability and strength to the collapse of flexible rocking structures is discussed. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
11.
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
12.
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
13.
To achieve rational and precise seismic response predictions of large span spatial structures(LSSSs),the inherent non-uniformity and multidimensionality characteristics of earthquake ground motions should be properly taken into consideration.However,due to the limitations of available earthquake stations to record seismic rotational components,the effects of rocking and torsional earthquake components are commonly neglected in the seismic analyses of LSSSs.In this study,a newly developed method to extract the rocking and torsion components at any point along the area of a deployed dense array from the translational earthquake recordings is applied to obtain the rotational seismic inputs for a LSSS.The numerical model of an actual LSSS,the Dalian International Conference Center(DICC),is developed to study the influences of multi-support and multidimensional excitations on the seismic responses of LSSSs.The numerical results reveal that the non-uniformity and multidimensionality of ground motion input can considerably affect the dynamic response of the DICC.The specific degree of influence on the overall and local structural displacements,deformations and forces are comprehensively investigated and discussed. 相似文献
14.
The seismic ground rotations are important with respect to spatial structural models, which are sensitive to the wave propagation. The rotational ground motion can lead to significant increasing of structural response, instability and unusual damages of buildings. Currently, the seismic analyses often take into account the rocking and torsion motions separately using artificial accelerograms. We present an exact analytical method, proposed by Nazarov [15] for computing of three rotational accelerograms simultaneously from given translational records. The method is based on spectral representation in the form of Fourier amplitude spectra of seismic waves, corresponding to the given three-component translational accelerogram. The composition, directions and properties of seismic waves are previously determined in the form of a generalized wave model of ground motion. It is supposed that seismic ground motion can be composed by superposition of P, SV, SH- and surface waves. As an example, the dynamic response analysis of 25-story building is presented. Here recorded (low-frequency) and artificial (high-frequency) accelerograms were used; each of them includes three translational and three rotational components. In this structural analysis, we have clarified primarily conditions under which rotational ground motion should be taken into account. Next, we have calculated three rotational components of seismic ground motion. Then they were taken as additional seismic loads components for further seismic analysis of the building. Note, soil–structure interaction (SSI) is not considered in this study. For computing, we use the special software for structural analyses and accelerogram processing (FEA Software STARK ES and Odyssey software, Eurosoft Co., Russia). It was developed and is used in engineering practice in the Central Research Institute of Building Constructions (TsNIISK, Moscow, Russia). 相似文献
15.
The three‐dimensional behavior of inverted pendulum cylindrical structures during earthquakes 下载免费PDF全文
下载免费PDF全文 《地震工程与结构动力学》2017,46(14):2261-2280
In order to use rocking as a seismic response modification strategy along both directions of seismic excitation, a three‐dimensional (3D) rocking model should be developed. Since stepping or rolling rocking structural members out of their initial position is not a desirable performance, a rocking design should not involve these modes of motion. To this end, a model that takes the aforementioned constraint into account needs to be developed. This paper examines the 3D motion of a bounded rigid cylinder that is allowed to uplift and sustain rocking and wobbling (unsteady rolling) motion without sliding or rolling out of its initial position (i.e., a 3D inverted pendulum). Thus, the cylinder is constrained to zero residual displacement at the end of its 3D motion. This 3D dynamic model of the rocking rigid cylinder has two DOFs (three when damping is included), making it the simplest 3D extension of Housner's classical two‐dimensional (2D) rocking model. The development of models with and without damping is presented first. They are simple enough to perform extensive parametric analyses. Modes of motion of the cylinder are identified and presented. Then, 3D rocking and wobbling earthquake response spectra are constructed and compared with the classical 2D rocking earthquake response spectra. The 3D bounded rocking earthquake response spectra for the ground motions considered seem to have a very simple linear form. Finally, it is shown that the use of a 2D rocking model may lead to unacceptably unconservative estimates of the 3D rocking and wobbling seismic response. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
16.
A novel modeling approach for the seismic response assessment of rocking frames is presented. Rocking frames are systems with columns that are allowed to fully, or partially, uplift. Despite the apparent lack of a mechanism to resist lateral forces, they have a remarkable capacity against earthquake loading. Rocking frames are found in old structures, for example, ancient monuments, but it is also a promising design concept for modern structures such as bridges or buildings. The proposed modeling can be implemented in a general-purpose structural analysis software, avoiding the difficulties that come with the need of formulating and solving specifically tailored differential equations, or the use of detailed computational models. Different configurations of a rocking portal frame problem are examined. The model is based on rigid, or flexible, beam elements that describe the members of the frame. Negative-stiffness rotational springs are smartly positioned at the rocking interfaces in order to simulate the rocking restoring moment, while the mass and the rotational moment of inertia are considered either lumped or distributed. Both the cases of rigid and flexible piers/columns are discussed, while it is shown that frames with restrained columns can be considered in a straightforward manner. A simple alternative based on an equivalent oscillator that follows the generalized rocking equation of motion is also investigated. The efficiency and the accuracy of the proposed modeling is demonstrated with the aid of carefully chosen case studies. 相似文献
17.
Marios Apostolou George Gazetas Evangelia Garini 《Soil Dynamics and Earthquake Engineering》2007,27(7):642-654
The rocking of rigid structures uplifting from their support under strong earthquake shaking is investigated. The structure is resting on the surface of either a rigid base or a linearly elastic continuum. A large-displacement approach is adopted to extract the governing equations of motion allowing for a rigorous calculation of the nonlinear response even under near-overturning conditions. Directivity-affected near-fault ground motions, idealized as Ricker wavelets or trigonometric pulses, are used as excitation. The conditions under which uplifting leads to large angles of rotation and eventually to overturning are investigated. A profoundly nonlinear rocking behavior is revealed for both rigid and elastic soil conditions. This geometrically nonlinear response is further amplified by unfavorable sequences of long-duration pulses in the excitation. Moreover, through the overturning response of a toppled tombstone, it is concluded that the practice of estimating ground accelerations from overturning observations is rather misleading and meaningless. 相似文献
18.
By now, it is well known that long‐period surface waves can induce resonant response in high‐rise buildings, in particular those located in sedimentary basins. Rayleigh wave passage has been reported to induce rocking motion at the base of the buildings which can increase displacement demands significantly. However, the building behavior to base rocking has not been extensively studied because commercially available instruments do not record rotational components of ground motion, and thus, rocking time histories have not been available to the analysts. In a recent study, we proposed an effective method for estimating the rocking associated with Rayleigh waves, which takes into account their frequency‐dependent phase velocities. In the present work, we select a number of recorded seismic motions which include surface waves on sedimentary basins from recent well‐recorded earthquake events. Then, we proceed to identify and extract the recorded surface waves by using the technique mentioned above. Using realistic soil‐structure analytical models that have been proposed in the published literature for high‐rise buildings, we study their response to Rayleigh waves as they respond to both translational and rocking motions. Of particular interest is to compare the response of such structures with and without the presence of rotational motions due to surface waves. Using the roof displacement and the building interstory drift as response quantities, our results indicate that demands are controlled by rotational (rocking) motions associated with Rayleigh waves. 相似文献
19.
20.
An effort is made to examine the properties of rotational (torsional and rocking) ground motions using Chiba dense array data. The Chiba array system, located 30 km east of Tokyo, Japan, is composed of 15 boreholes with separation distances varying from 5 to 320 m. This provides a unique opportunity to examine the characteristics of rotational components. For this purpose, 17 events are considered and rotational ground motions are evaluated using spatial derivatives of translational ones. The effects of seismological parameters and separation distances between stations on properties of rotational motions are examined, showing a sudden increase in rotational motions for the earthquakes with large magnitude or PGA and decrease of these motions with increasing separation distance. While the duration of torsional motion is found to be larger than translational ones, there is no significant difference between durations of rocking and vertical motions. The effects of separation distance and earthquake magnitude on rotational response spectra are also investigated. The normalized rotational response spectra are found to be strongly affected by separation distance. The spectral ratios of rotational and translational motions are not linearly proportional to period as suggested by the previous studies. Finally, the torsional motion is predicted from translation ones for different separation distances at the site. The comparison of the predicted and the calculated torsional motions reveals a weak estimation in close separation distances (<30m) and satisfactory predictions in other cases. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献