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1.
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   

2.
A new hybrid ductile‐rocking seismic‐resistant design is proposed which consists of a code‐designed buckling‐restrained braced frame (BRBF) that yields along its height and also partially rocks on its foundation. The goal of this system is to cost‐effectively improve the performance of BRBFs, by reducing drift concentrations and residual deformations, while taking advantage of their large ductility and their reliable limit on seismic forces and accelerations along a building's height. A lock‐up device ensures that the full code‐compliant lateral strength can be achieved after a limited amount of column uplift, and supplemental energy dissipation elements are used to reduce the rocking response. This paper outlines the mechanics of the system and then presents analyses on rocking frames with both ductile and elastic braces in order to highlight the large higher mode demands on elastic rocking frames. A parametric study using nonlinear time‐history analysis of BRBF structures designed according to the proposed procedure for Los Angeles, California is then presented. This study investigates the system's seismic response and the effect of different energy dissipation element properties and allowable base rotation values before the lock‐up is engaged. Finally, the effect of vertical mass modeling on analysis results was investigated. These studies demonstrated that the hybrid ductile‐rocking system can in fact improve the global peak and residual deformation response as well as reduce brace damage. This enhanced performance could eliminate the need for expensive repairs or demolition that are otherwise to be expected for conventional ductile fixed base buildings that sustain severe damage.  相似文献   

3.
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   

4.
Rocking column-foundation system is a new design concept for bridges that can reduce overall seismic damage, minimize construction and repair time, and achieve lower cost in general. However, such system involves complex dynamic responses due to impacts and highly nonlinear rocking behavior. This study presents a dimensionless regression analysis to estimate the rocking and shaking responses of the flexible column-foundation system under near-fault ground motions. First, the transient drift and rocking responses of the system are solved numerically using previously established analytical models. Subsequently, the peak column drifts and uplift angles are derived as functions of ground motion characteristics and the geometric and dynamic parameters of column-foundation system in regressed dimensionless forms. The proposed response models are further examined by validating against the numerical simulations for several as-built bridge cases. It is shown that the proposed model not only physically quantifies the influences of prominent parameters, but also consistently reflects the complex dynamics of the system. The seismic demands of rocking column-foundation system can be realistically predicted directly from structural and ground motion characteristics. This can significantly benefit the design of bridges incorporating this new design concept.  相似文献   

5.
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   

6.
The seismic behaviour of a wide variety of structures can be characterized by the rocking response of rigid blocks. Nevertheless, suitable seismic control strategies are presently limited and consist mostly on preventing rocking motion all together, which may induce undesirable stress concentrations and lead to impractical interventions. In this paper, we investigate the potential advantages of using supplemental rotational inertia to mitigate the effects of earthquakes on rocking structures. The newly proposed strategy employs inerters, which are mechanical devices that develop resisting forces proportional to the relative acceleration between their terminals and can be combined with a clutch to ensure their rotational inertia is only employed to oppose the motion. We demonstrate that the inclusion of the inerter effectively reduces the frequency parameter of the block, resulting in lower rotation seismic demands and enhanced stability due to the well-known size effects of the rocking behaviour. The effects of the inerter and inerter-clutch devices on the response scaling and similarity are also studied. An examination of their overturning fragility functions reveals that inerter-equipped structures experience reduced probabilities of overturning in comparison with uncontrolled bodies, while the addition of a clutch further improves their seismic stability. The concept advanced in this paper is particularly attractive for the protection of rocking bodies as it opens the possibility of nonlocally modifying the dynamic response of rocking structures without altering their geometry.  相似文献   

7.
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   

8.
Some spread footing foundations from real retrofitting practices in Taiwan were extended to be uneconomically large due to the restriction of foundation uplift regulated in the design code. Although rocking mode of spread footings induced from foundation uplift is not favorable in current design code, recent studies have shown that the rocking of a spread footing may have a beneficial effect on the dynamic performance of piers by reducing the earthquake forces that can be transmitted to the pier base. This implies that the plastic deformation that occurs at the pier's plastic zone can be decreased and as a result the ductility demand of piers can possibly be reduced. In order to gain a better understanding of the structural behavior related to rocking and to clarify that if the widening and strengthening of the foundations to limit the rocking mechanism of spread footing is necessary for the retrofitting work, a series of preliminary rocking experiments were performed. A total of three circular reinforced concrete columns with spread footing foundations were tested. Using pseudo‐dynamic tests and a cyclic loading test, these columns were subjected to different levels of earthquake accelerations, including a near field ground motion. The results of the tests and the rocking behavior of the footings are discussed in this paper. From the benchmark test, the difference between the response behavior of a rocking base and a fixed base foundation was highlighted. By comparing the experimental responses of the retrofitted column with the responses of the original one, the effect of the rocking mechanism on the ductility demand and strength demand of the columns was also identified. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

9.
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   

10.
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   

11.
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   

12.
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   

13.
Though rocking shallow foundations could be designed to possess many desirable characteristics such as energy dissipation, isolation, and self-centering, current seismic design codes often avoid nonlinear behavior of soil and energy dissipation beneath foundations. This paper compares the effectiveness of energy dissipation in foundation soil (during rocking) with the effectiveness of structural energy dissipation devices during seismic loading. Numerical simulations were carried out to systematically study the seismic energy dissipation in structural elements and passive controlled energy dissipation devices inserted into the structure. The numerical model was validated using shaking table experimental results on model frame structures with and without energy dissipation devices. The energy dissipation in the structure, drift ratio, and the force and displacement demands on the structure are compared with energy dissipation characteristics of rocking shallow foundations as observed in centrifuge experiments, where shallow foundations were allowed to rock on dry sandy soil stratum during dynamic loading. For the structures with energy dissipating devices, about 70–90% of the seismic input energy is dissipated by energy dissipating devices, while foundation rocking dissipates about 30–90% of the total seismic input energy in foundation soil (depending on the static factor of safety). Results indicate that, if properly designed (with reliable capacity and tolerable settlements), adverse effects of foundation rocking can be minimized, while taking advantage of the favorable features of foundation rocking and hence they can be used as efficient and economical seismic energy dissipation mechanisms in buildings and bridges.  相似文献   

14.
Controlled rocking steel frames have been proposed as an efficient way to avoid the structural damage and residual deformations that are expected in conventional seismic force resisting systems. Although the base rocking response is intended to limit the force demands, higher mode effects can amplify member design forces, reducing the viability of the system. This paper suggests that seismic forces may be limited more effectively by providing multiple force‐limiting mechanisms. Two techniques are proposed: detailing one or more rocking joints above the base rocking joint and providing a self‐centring energy dissipative (SCED) brace at one or more levels. These concepts are applied to the design of an eight‐storey prototype structure and a shake table model at 30% scale. A simple numerical model that was used as a design tool is in good agreement with frequency characterization and low‐amplitude seismic tests of the shake table model, particularly when multiple force‐limiting mechanisms are active. These results suggest that the proposed mechanisms can enable better capacity design by reducing the variability of peak seismic force demands without causing excessive displacements. Similar results are expected for other systems that rely on a single location of concentrated nonlinearity to limit peak seismic loads. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

15.
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   

16.
Prediction of displacement demand to assess seismic performance of structures is a necessary step where nonlinear static procedures are followed. While such predictions have been well established in literature for fixed-base structures, fewer bodies of researches have been carried out on the effect of rocking and uplifting of shallow foundations supported by soil, on such prediction. This paper aimed to investigate the effect of soil structure interaction on displacement amplification factor C1 using the beam on nonlinear Winkler foundation concept. A practical range of natural period, force reduction factors, and wide range of anticipated behavior from rocking, uplifting and hinging are considered and using thousands nonlinear time history analysis, displacement amplification factors are evaluated. The results indicate that the suggested equations in current rehabilitation documents underestimate displacement demands in the presence of foundation rocking and uplift. Finally, using regression analyses, new equations are proposed to estimate mean values of C1.  相似文献   

17.
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   

18.
The effects of transient foundation uplift on the earthquake response of flexible structures are investigated. The structural idealization chosen in this study is relatively simple but it incorporates the most important features of foundation uplift. In its fixed base condition the structure itself is idealized as a single-degree-of-freedom system attached to a rigid foundation mat which is flexibly supported. The flexibility and damping of the supporting soil are represented by a Winkler foundation with spring-damper elements distributed over the entire width of the foundation. Based on the response spectra presented for several sets of system parameters, the effects of foundation-mat uplift on the maximum response of structures are identified. The influence of earthquake intensity, structural slenderness ratio, ratio of foundation mass to structural mass, foundation flexibility and p-δ effects on the response of uplifting structures is also investigated.  相似文献   

19.
Strong shaking of structures during large earthquakes may result in some cases in partial separation of the base of the structure from the foundation. A simplified problem of this type, the dynamic response of a rocking rigid block allowed to uplift, is examined here. Two foundation models are considered: the Winkler foundation and the much simpler ‘two-spring’ foundation. It is shown that an equivalence between these two models can be established, so that one can work with the much simpler two-spring foundation. Simple solutions of the equations of motion are developed and simplified methods of analysis are proposed. In general, uplift leads to a softer vibrating system which behaves non-linearly, although the response is composed of a sequence of linear responses. As a result the apparent rocking period increases with the amount of lift-off. The corresponding apparent ratio of critical damping decreases, in general, with the amplitude of the response. Compared to the case without lift-off, the response of the system may increase or decrease because of the uplift, depending on the excitation and the parameters of the system.  相似文献   

20.
Unlike conventional seismic resisting systems, rocking core-moment frame (RCMF) combinations as low-damage assemblies are being developed to mitigate, or even eliminate structural damage and residual deformations following a severe earthquake. Despite extensive studies on the performance of specific rocking cores, dynamic characteristics and strength demands of a generic RCMF have not been addressed. By utilizing cantilever beam analogy, the current article proposes a modal analysis method to formulate RCMF demands. The proposed model and obtained analytical charts provide a manual method for rapid study and preliminary design of low- to mid-rise RCMFs with relatively uniform properties over the height. An extensive parametric study investigates the effects of rocking core base-fixity and frame-to-core stiffness on demand values. An independent computer analysis verifies the validity and accuracy of the proposed formulas. Findings show significant higher-mode effects in several RCMF combinations.  相似文献   

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