Seismic Response of a Yielding Structure Coupled with a Rocking Wall

Summary A design procedure for seismic retrofitting of concentrically and eccentrically braced frame buildings is proposed and validated in this paper. Rocking walls are added to the existing system to ensure an almost uniform distribution of the interstorey displacement in elevation. To achieve direct and efficient control over the seismic performance, the design procedure is founded on the displacement‐based approach and makes use of overdamped elastic response spectra. The top displacement capacity of the building is evaluated based on a rigid lateral deformed configuration of the structure and on the ductility capacity of the dissipative members of the braced frames. The equivalent viscous damping ratio of the braced structure with rocking walls is calculated based on semi‐empirical relationships specifically calibrated in this paper for concentrically and eccentrically braced frames. If the equivalent viscous damping ratio of the structure is lower than the required equivalent viscous damping ratio, viscous dampers are added and arranged between the rocking walls and adjacent reaction columns. The design internal forces of the rocking walls are evaluated considering the contributions of more than one mode of vibration. The proposed design procedure is applied to a large set of archetype braced frame buildings and its effectiveness verified by nonlinear dynamic analysis.

Section: Application To Case Studiessupporting

confidence: 89%

Section: Investigated Structuressupporting

confidence: 88%

Seismic retrofitting of braced frame buildings by RC rocking walls and viscous dampers

Barbagallo

Bosco

Marino

et al. 2018

“…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

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.

“…17 Further analytical evidence to the first-mode dominated response is offered in Qu et al 18 and also shown in a recent paper. 19 These results together with additional evidence by other investigators were recently evaluated in Grigorian and Grigorian, 20 and it was concluded that a moment resisting frame FIGURE 1 Yielding single-degree-of-freedom oscillator coupled with a vertically restrained stepping rocking wall coupled with a rocking wall can be categorized as a single-degree-of-freedom (SDOF) system. Accordingly, in this study, we adopt the SDOF idealization shown in Figure 1.…”

Section: Introductionmentioning

confidence: 79%

“…The motivation for coupling of a moment‐resisting frame with a strong rocking wall is to primarily enforce a uniform distribution of interstory drifts; therefore, the first mode of the frame becomes dominant as was first indicated in the seminal paper by Alavi and Krawinler . Further analytical evidence to the first‐mode dominated response is offered in Qu et al and also shown in a recent paper . These results together with additional evidence by other investigators were recently evaluated in Grigorian and Grigorian, and it was concluded that a moment resisting frame coupled with a rocking wall can be categorized as a single‐degree‐of‐freedom (SDOF) system.…”

Section: Introductionmentioning

confidence: 83%

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

Aghagholizadeh

Makris

2018

Self Cite

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.