• Structural Engineering and Mechanics
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• 제73권3호
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• pp.303-317
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• 2020

In this study an innovative rocking zipper braced frame (RZBF) is proposed to overcome the deficiencies of common concentrically braced frames. RZBF is an improved rocking concentrically braced frame which is based on combination of rocking behavior and zipper columns. The base rocking joints and post-tensioned bars provide rocking response and restoring force, respectively. Also, zipper columns distribute the unbalance force over the frame height and reduce the damage concentration. To evaluate seismic performance of RZBF, a comparison study is carried out considering concentrically braced frame, zipper braced frame, rocking concentrically braced frame and RZBF. Thereby, a suite of non-linear time history analyses had been performed on four different types of archetypes with four, six, eight, ten and twelve stories. Frames were designed and non-linear time history analyses were conducted in OpenSees. To compare the seismic behavior of the archetypes, roof drifts, residual roof drifts, story drifts, the forces of first and top story braces, PT bars forces, column uplift and base shears were taken in to consideration. Results illustrate that using RZBF, can reduce the damage due to reduced residual drifts. Zipper columns enhance the seismic performance of rocking systems. As the number of stories increase in the RZBF systems, larger top story braces were needed. So the RZBF system is applicable on low and midrise buildings.

• Earthquakes and Structures
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• 제15권3호
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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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• 제25권4호
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• pp.269-282
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• 2023

This study investigates a rocking seismic isolation (RSI) system as a seismic protection measure against narrow-band ground-motions generated by earthquakes. Structures supported over RSIs are considered capable of reducing the lateral demands and damage of the main structural system through lifting and rocking. This lifting and rocking during earthquake activity is provided by free-standing columns. A single-degree-of-freedom (SDOF) system supported on a RSI system is subjected to narrow-band seismic motions and its response is compared to an analog system without RSI. The comparison is then extended to reinforced concrete linear frames with and without RSI; three-bay frames with 11 and 17 storeys are considered. It is found that the RSI systems significantly reduce acceleration and displacement demands in the main structural frames, more noticeably if the first structural mode dominates the response and for ratios of the predominant frequency of the ground motion to the predominant frequency of the main frame near one. It is also found that the RSI system is more effective in reducing lateral accelerations and displacements of the main structure when the aspect ratio, b/h, and size, R, of the free-standing columns decrease, although the rocking stability of the RSI system is also reduced.

• Earthquakes and Structures
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• 제23권2호
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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.

• Journal of Mechanical Science and Technology
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• 제17권9호
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• pp.1249-1260
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• 2003

This present work focuses on the influence of nonlinearities associated with impact on the rocking behavior of a rigid body block subjected to a two-dimensional excitation in the horizontal and vertical directions. The nonlinearities in rocking system are found to be strongly dependent on the impact between the block and the base that abruptly reduces the kinetic energy. In this study, the rocking systems of the two types are considered : The first is an undamped rocking system model that disregards the energy dissipation during the impact and the second is a damped rocking system, which incorporates energy dissipation during the impact. The response analysis is carried out by a numerical method using a non-dimensional rocking equation in which the variations in the excitation levels are considered. Chaos responses are observed over a wide range of parameter values, and particularly in the case of large vertical displacements, the chaotic characteristics are observed in the time histories, Poincare sections, the power spectral density and the largest Lyapunov exponents of the rocking responses. Complex behavior characteristics of rocking responses are illustrated by the Poincare sections.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 1997년도 춘계 학술발표회 논문집 Proceedings of EESK Conference-Fall 1997
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• pp.107-114
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• 1997

A dynamic fluid-structure-soil interaction analysis method is developed to investigate the effects of rocking motion on the seismic response of the 3-D flexible rectangular liquid storage tanks founded on the deformable ground. The governing equation of 3-D rectangular tanks subjected to the translational and rocking motions is obtained by Rayleigh-Ritz method. The dynamic stiffness matrix of the rigid surface foundation resting on the surface of a stratum are calculated by hyperelement method. The seismic responses of a 3-D flexible tank model founded on the deformable ground is calculated by combining the governing equation of the structural motion with the dynamic stiffness matrix of the rigid surface foundation.

• Earthquakes and Structures
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• 제7권6호
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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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• 제22권3호
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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.

• Structural Engineering and Mechanics
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• 제23권3호
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• pp.293-308
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• 2006

This paper presents a complete and consistent formulation to study the seismic response of a free-standing ship supported by an arrangement of n keel blocks which are all located in a dry dock. It is considered that the foundation of the system is subjected to both horizontal and vertical in plane excitation. The motion of the system is classified in eight different modes which are Rest (relative), Sliding of keel blocks, Rocking of keel blocks, Sliding of the ship, Sliding of both keel blocks and the ship, Sliding and rocking of keel blocks, Rocking of keel blocks with sliding of the ship, and finally Sliding and rocking of keel blocks accompanied with sliding of the ship. For each mode of motion the governing equations are derived, and transition conditions between different modes are also defined. This formulation is based on a number of fundamental assumptions which are 2D idealization for motion of the system, considering keel blocks as the rigid ones and the ship as a massive rigid block too, allowing the similar motion for all keel blocks, and supposing frictional nature for transmitted forces between contacted parts. Also, the rocking of the ship is not likely to take place, and the complete ship separation from keel blocks or separation of keel blocks from the base is considered as one of the failure mode in the system. The formulation presented in this paper can be used in its entirety or in part, and they are suitable for investigation of generalized response using suitable analytical, or conducting a time-history sensitivity analysis.

• Structural Engineering and Mechanics
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• 제73권4호
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• pp.447-454
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• 2020

Seismic isolation technology has a wide application to protect bridges from earthquake damage, a new designed bridge pier with seismic isolation are provided for railways in seismic regions of China. The pier with rocking isolation is a self-centering system under small and moderate earthquakes, and the unbonded prestressed tendons are used to prevent overturning under strong earthquakes. A numerical model based on pseudo-static testing results is presented to evaluate the seismic performance of isolation bridge piers, and is validated by the shaking table test. It is found that the rocking response and the loss of prestressing for the bridge pier increase with the increase of earthquake intensity. Besides, the intensity and spectral characteristics of input ground motion have great influence on displacement of the top and bottom of the bridge pier, while have less influence on the bending moment of the pier bottom. Experimental and numerical results show that the rocking-isolated piers presented in this study have good seismic performance, and it provides an alternative way for the railway bridge in the regions with high occurrence of earthquakes. Therefore, we provide the detailed procedures for seismic design of the rocking-isolated bridge pier, and a case study of the seismic isolation design with rocking piers is carried out to popularize the seismic isolation methods.