The dynamics of an elastic structure coupled with a rocking wall

Makris, Nicos; Aghagholizadeh, Mehrdad

doi:10.1002/eqe.2838

Cited by 56 publications

(48 citation statements)

References 33 publications

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“…The coupling of a bending and a rocking member has several applications; eg, a rocking wall in a moment frame can be used to suppresses the dynamic response of the SDOF oscillator. Makris and Aghagholizadeh investigated the dynamic response of a SDOF rigidly connected with a rocking wall as shown in Figure A, and they also studied the case of having an inelastic SDOF instead . According to Figure A, the SDOF oscillator has mass m s , stiffness k , and damping c and is connected with a rectangular rocking wall via a rigid link (arm) with length L .…”

Section: Rocking Systemsmentioning

confidence: 99%

Seismic response assessment of rocking systems using single degree‐of‐freedom oscillators

Diamantopoulos

Fragiadakis

2019

Earthq Engng Struct Dyn

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Summary A new modeling for the seismic response assessment of free‐standing, rigid or flexible, pure rocking systems is presented. The proposed modeling is based on equivalent single degree‐of‐freedom (SDOF) oscillators that can be implemented with common engineering software or user‐made structural analysis codes. The SDOF models adopted use beam elements that are connected to a nonlinear rotational spring with negative stiffness that describes the self‐centering capacity of the rocking member. The loss of energy at impact is treated with an “event‐based” approach consistent with Housner's theory. Different variations pertinent to rigid blocks are first presented, and then the concept is extended to the flexible case. The implementation of the method requires some minor programming skills, while thanks to the versatility of the finite element method, it is capable to handle a variety of rocking problems. This is demonstrated with two applications: (a) a vertically restrained block equipped with an elastic tendon and (b) a rigid block coupled with an elastic SDOF oscillator. The accuracy and the efficiency of the proposed modeling is demonstrated using simple wavelets and historical ground motion records.

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Section: Rocking Systemsmentioning

confidence: 99%

Seismic response assessment of rocking systems using single degree‐of‐freedom oscillators

Diamantopoulos

Fragiadakis

2019

Earthq Engng Struct Dyn

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“…From the identity, cos 2 ψ + sin 2 ψ = 1, one concludes that the horizontal displacement, u of the SDOF oscillator is related to the horizontal displacement x of the center of mass of the rotating wall via the expression:

\frac{u}{L} = 1 + \frac{x}{L} - \sqrt{1 - \frac{v^{2}}{L^{2}} .}

In this paper, the coupling arm is assumed to be long enough so that v 2 / L 2 is much smaller than unity ( v 2 / L 2 < < 1), and in this, case u = x . A recent study by Makris and Aghagholizadeh on the response of an elastic oscillator coupled with a rocking wall showed that the effect due to a shorter coupling arm is negligible.…”

Section: Dynamics Of a Yielding Oscillator Coupled With A Vertically mentioning

confidence: 96%

Earthquake response analysis of yielding structures coupled with vertically restrained rocking walls

Aghagholizadeh

Makris

2018

Earthq Engng Struct Dyn

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Summary This paper investigates the inelastic response of a yielding structure coupled with a vertically restrained rocking wall. The paper first derives the nonlinear equations of motion of a yielding oscillator coupled with a vertically restrained rocking wall, and the dependability of the one‐degree of freedom idealization is validated against the nonlinear time‐history response analysis of a well‐known nine‐story moment‐resisting steel frame that is coupled with a stepping, vertically restrained rocking wall. While, the coupling of weak building frames with rocking walls is an efficient strategy that controls inelastic deformations by enforcing a uniform interstory‐drift distribution, therefore, avoiding mid‐story failures, the paper shows that even for medium‐rise buildings the effect of vertical tendons on the inelastic structural response is marginal, with the exception of increasing the vertical reactions at the pivoting points of the rocking wall. Accordingly, the paper concludes that for medium‐rise to high‐rise buildings, vertical tendons in rocking walls are not beneficial.

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“…It is noteworthy that the use of rocking systems has emerged in the last few years as an efficient way to reduce seismic damage [20] and different solutions are available for coupling the frame and the external pinned rocking structures [21,22]. The rocking tower considered in this study has been employed for the seismic design of new constructions and for retrofitting existing buildings [23,24] by using a patented technical solution [25].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Seismic Analysis and Comparison of Alternative External Dissipative Systems

Gioiella

Tubaldi

Gara

et al. 2018

Shock and Vibration

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This paper deals with the seismic retrofit of existing frames by means of external passive dissipative systems. Available in different configurations, these systems allow high flexibility in controlling the structural behaviour and are characterized by some feasibility advantages with respect to dissipative devices installed within existing frames. In particular, this study analyzes and compares the performances of two external solutions using linear viscous dampers. The first is based on the coupling of the building with an external fixed-based steel braced frame by means of dampers placed horizontally at the floor levels. The second is an innovative one, based on coupling the building with a "dissipative tower," which is a steel braced frame hinged at the foundation level, and activating the dampers through its rocking motion. The effectiveness of the two solutions is evaluated and compared by considering a benchmark existing reinforced concrete building, employing a stochastic dynamic approach, under the assumption of linear elastic behaviour for the seismic performance evaluation. This allows efficiently estimating the statistics of many response parameters of interest for the performance assessment and thus carrying out extensive parametric analyses for different properties of the external systems. The study results provide useful information regarding the design and the relative efficiency of the proposed retrofit solutions.

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The dynamics of an elastic structure coupled with a rocking wall

Cited by 56 publications

References 33 publications

Seismic response assessment of rocking systems using single degree‐of‐freedom oscillators

Seismic response assessment of rocking systems using single degree‐of‐freedom oscillators

Earthquake response analysis of yielding structures coupled with vertically restrained rocking walls

Stochastic Seismic Analysis and Comparison of Alternative External Dissipative Systems

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