• Earthquakes and Structures
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• v.23 no.2
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• pp.169-181
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• 2022

To research the dynamic response of the high-rise structure under the rocking ground motion, which we believed that the effect cannot be ignored, especially accompanied by vertical ground motion. Theoretical analysis and shaking table seismic simulation tests were used to study the response of a high-rise structure to excitation of a H-V-R ground motion that included horizontal, vertical, and rocking components. The use of a wavelet analysis filtering technique to extract the rocking component from data for the primary horizontal component in the first part, based on the principle of horizontal pendulum seismogram and the use of a wavelet analysis filtering technique. The dynamic equation of motion for a high-rise structure under H-V-R ground motion was developed in the second part, with extra P-△ effect due to ground rocking displacement was included in the external load excitation terms of the equation of motion, and the influence of the vertical component on the high-rise structure P-△ effect was also included. Shaking table tests were performed for H-V-R ground motion using a scale model of a high-rise TV tower structure in the third part, while the results of the shaking table tests and theoretical calculation were compared in the last part, and the following conclusions were made. The results of the shaking table test were consistent with the theoretical calculation results, which verified the accuracy of the theoretical analysis. The rocking component of ground motion significantly increased the displacement of the structure and caused an asymmetric displacement of the structure. Thus, the seismic design of an engineering structure should consider the additional P-△ effect due to the rocking component. Moreover, introducing the vertical component caused the geometric stiffness of the structure to change with time, and the influence of the rocking component on the structure was amplified due to this effect.

• Earthquakes and Structures
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• v.7 no.6
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• pp.1187-1221
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• 2014

The uplifting and rocking of slender, free-standing structures when subjected to ground shaking may limit appreciably the seismic moments and shears that develop at their base. This high-performance seismic behavior is inherent in the design of ancient temples with emblematic peristyles that consist of slender, free-standing columns which support freely heavy epistyles together with the even heavier frieze atop. While the ample seismic performance of rocking isolation has been documented with the through-the-centuries survival of several free-standing ancient temples; and careful post-earthquake observations in Japan during the 1940's suggested that the increasing size of slender free-standing tombstones enhances their seismic stability; it was George Housner who 50 years ago elucidated a size-frequency scale effect that explained the "counter intuitive" seismic stability of tall, slender rocking structures. Housner's 1963 seminal paper marks the beginning of a series of systematic studies on the dynamic response and stability of rocking structures which gradually led to the development of rocking isolation-an attractive practical alternative for the seismic protection of tall, slender structures. This paper builds upon selected contributions published during this last half-century in an effort to bring forward the major advances together with the unique advantages of rocking isolation. The paper concludes that the concept of rocking isolation by intentionally designing a hinging mechanism that its seismic resistance originates primarily from the mobilization of the rotational inertia of its members is a unique seismic protection strategy for large, slender structures not just at the limit-state but also at the operational state.

• Structural Engineering and Mechanics
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• v.18 no.3
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• pp.343-362
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• 2004

Rocking response of rigid bodies with rectangular footprint, freely standing on horizontal rigid plane is studied analytically. Bodies are subjected to simulated single component of horizontal earthquakes. The effect of baseline correction, applied to simulated excitations, on the rocking response is first examined. The sensitiveness of rocking motion to the details of earthquakes and geometric properties of rigid bodies is investigated. Due to the demonstrated sensitivity of rocking response to these factors, prediction of rocking stability must be made in the framework of probability theory. Therefore, using a large number of simulated earthquakes, the effects of duration and shape of intensity function of simulated earthquakes on overturning probability of rigid bodies are studied. In the case when a rigid body is placed on any floor of a building, the corresponding probability is compared to that of a body placed on the ground. For this purpose, several shear frames are employed. Finally, the viability of the energy balance equation, which was introduced by Housner in 1963 and widely used by nuclear power industry to estimate the rocking stability of bodies, is evaluated. It is found that the equation is robust. Examples are also given to show how this equation can be used.

• Journal of Mechanical Science and Technology
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• v.16 no.9
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• pp.1040-1053
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• 2002

This research deals with the influence of nonlinearities associated with impact and sliding upon the rocking behavior of a rigid block, which is subjected to two-dimensional horizontal and vertical excitation. Nonlinearities in the vibration were found to depend strongly on the effect of the impact between the block and the base, which involves an abrupt reduction in the system's kinetic energy. In particular, when sliding occurs, the rocking behavior is substantially changed. Response analysis using a non-dimensional rocking equation was carried out for a variety of excitation levels and excitation frequencies. The chaos responses were observed over a wide response region, particularly, in the cases of high vertical displacement and violent sliding motion, and the chaos characteristics appear in the time histories, Poincare maps, power spectra and Lyapunov exponents of the rocking responses. The complex behavior of chaotic response, in phase space, is illustrated by the Poincare map. The distribution of the rocking response is described by bifurcation diagrams and the effects of sliding motion are examined through the several rocking response examples.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.04a
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• pp.169-176
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• 1997

In this study, vertical ground motion effects on rocking response of free standing structure are investigated. Based on the mathematical model, computer program is developed using Kutta's Fourth-Order Method. Using the program, several parametric studis are performed to predict the effects of vertical ground motion. From the results of this study, it can be found that the vertical ground motion may overturn the structure which is stable under the horizontal ground motion, stabilize the structure which overturns due to horizontal ground motion alone, and delay the time of overturning of the structure or greatly reduce the rocking of the structure. It is concluded that the effect of vertical ground motion on the rocking response of free standing structure is apparently not systematic.

• Earthquakes and Structures
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• v.15 no.3
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• pp.243-251
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• 2018

The dynamic responses of a rocking wall-moment frame (RWMF) with a post-tensioned cable are investigated. The nonlinear equations of motions are developed, which can be categorized as a single-degree-of-freedom (SDOF) model. The model is validated through comparison of the rocking response of the rigid rocking wall (RRW) and displacement of the moment frame (MF) against that obtained from Finite Element analysis when subjected ground motion excitation. A comprehensive parametric analysis is carried out to determine the seismic performance factors of the RWMF systems under near-fault trigonometric pulse excitation. The horizontal displacement of the RWMF system is compared with that of MF structures without RRW, revealing the damping effect of the RRW. Frame displacement spectra excited by trigonometric pulses and recorded earthquake ground motions are constructed. The effects of pulse type, mass ratio, frame stiffness, and wall slenderness variations on the displacement spectra are presented. The paper shows that the coupling with a RRW has mixed results on suppressing the maximum displacement response of the frame.

• Earthquakes and Structures
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• v.22 no.6
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• pp.597-608
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• 2022

One of the most important parameters affecting nonlinearsoil-structure interaction, especially rocking foundation, is the vertical factor of safety (F.S_v). In this research, the effect of F.S_v on the behavior of rocking foundations was experimentally investigated. A set of slow, cyclic, horizontal loading tests was conducted on elastic SDOF structures with different shallow foundations. Vertical bearing capacity tests also were conducted to determine the F.S_v more precisely. Furthermore, 10% silt was mixed with the dry sand at a 5% moisture content to reach the minimum apparent cohesion. The results of the vertical bearing capacity tests showed that the bearing capacity coefficients (N_c and N_γ) were influenced by the scaling effect. The results of horizontal cyclic loading tests showed that the trend of increase in capacity was substantially related to the source of nonlinearity and it varied by changing F.S_v. Stiffness degradation was found to occur in the final cycles of loading. The results indicated that the moment capacity and damping ratio of the system in models with lower F.S_v values depended on soil specifications such cohesiveness or non-cohesiveness and were not just a function of F.S_v.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.7
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• pp.1242-1246
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• 2016

Heel rocking phase in gait cycle is from initial contact to forefoot contact. The purpose of this study was to investigate the effect of age on heel rocking time. Seven young women ($21.9{\pm}1.5yrs$) and seven elderly women ($74.1{\pm}6.7yrs$) participated in this study. Subjects wore the shoes equipped with pressure sensors and walked along 10 m walkway at comfortable speeds. Stride time, stance time, and heel rocking time were compared between groups. Stride time was not different between groups (p=0.087). Stance time was longer (p<0.001) but heel rocking time was shorter in the elderly than in the young (p<0.001). The shorter heel-rocking time in elderly women indicates less efficient shock-absorption in the heel-rocking phase, which might be related to the abnormal control and/or reduced performance of ankle dorsiflexors.

• Journal of the Earthquake Engineering Society of Korea
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• v.19 no.6
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• pp.293-302
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• 2015

ASCE 4 requires that a hard stop be built around the seismic isolation system in nuclear power plants. In order to maintain the function of the isolation system, this hard stop is required to have clearance-to-stop, which should be no less than the 90th-percentile displacements for 150% Design Basis Earthquake (DBE) shaking. Huang et al. calculated clearance-to-stop by using a Latin Hypercube Sampling technique, without considering the rocking behavior of the isolated structure. This paper investigates the effects on estimation of clearance-to-stop due to 1) rocking behavior of the isolated structure and 2) sampling technique for considering the uncertainties of isolation system. This paper explains the simplified analysis model to consider the rocking behavior of the isolated structure, and the input earthquakes recorded at Diablo Canyon in the western United States. In order to more accurately approximate the distribution tail of the horizontal displacement in the isolated structure, a modified Latin Hypercube Sampling technique is proposed, and then this technique was applied to consider the uncertainty of the isolation system. Through the use of this technique, it was found that rocking behavior has no significant effect on horizontal displacement (and thus clearance-to-stop) of the isolated structure, and the modified Latin Hypercube Sampling technique more accurately approximates the distribution tail of the horizontal displacement than the existing Latin Hypercube Sampling technique.

• Structural Engineering and Mechanics
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• v.22 no.3
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• pp.293-310
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• 2006

In seismic prone areas it is possible to meet very different objects (equipment components, on shelf artefacts, simple architectural elements) that can be modelled as a rigid body rocking on a rigid foundation. The interest in their behaviour can have different reasons: seismological, in order to estimate the ground motion intensity, or more strictly mechanical, in order to limit the response severity and to avoid overturning. The behaviour of many rigid bodies subjected to twenty wide ranging acceleration recordings is studied here. The response of the blocks is described using kinematic and energy parameters. A condition under which a so called scale effect is tangible is highlighted. The capacity of the signals to produce overturning is compared to different ground motion parameters, and a good correlation with the Peak Ground Velocity is unveiled.