Toppling of Computer‐Type Equipment under Base Excitation

Dimentberg, M. F.; Lin, Yuanzheng; Zhang, Ruichong

doi:10.1061/(asce)0733-9399(1993)119:1(145)

Cited by 37 publications

(23 citation statements)

References 12 publications

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“…Although the rocking response of free-standing blocks has been the subject of several investigators [see references Zhang and Makris (2001)], the rocking response of anchored blocks has received limited attention. Dimentberg et al (1993), following a probabilistic approach, concluded that, under a white-noise excitation, anchored blocks with elastic restrainers are much more stable than free-standing blocks. Herein the rocking stability of anchored blocks is revisited following a deterministic approach and it is shown that there is a finite frequency range where the conclusion of Dimentberg et al (1993) does not hold.…”

Section: Introductionmentioning

confidence: 99%

“…Dimentberg et al (1993), following a probabilistic approach, concluded that, under a white-noise excitation, anchored blocks with elastic restrainers are much more stable than free-standing blocks. Herein the rocking stability of anchored blocks is revisited following a deterministic approach and it is shown that there is a finite frequency range where the conclusion of Dimentberg et al (1993) does not hold.…”

Section: Introductionmentioning

confidence: 99%

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Rocking Response of Anchored Blocks under Pulse-Type Motions

2001

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This paper examines the transient rocking response of anchored blocks subjected to physically realizable horizontal pulse-type motion. Restrainers with elastic-brittle and elastic-plastic behavior are considered. Under one-sine pulse, anchored blocks can overturn with two distinct modes of overturning: (1) by exhibiting one impact; and (2) without exhibiting any impact. It is found that restrainers are more efficient in preventing overturning of small slender blocks subjected to low frequency pulses. This study uncovers that, although for most of the frequency range anchored blocks survive higher accelerations than free-standing blocks, there is a finite frequency range where the opposite happens. This paper examines this counterintuitive behavior and explains the destructive effect that increased strength and increased ductility of restrainers have on the rocking stability of rigid structures when excited by certain ground motions.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Rocking Response of Anchored Blocks under Pulse-Type Motions

2001

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“…[9][10][11]). This noise model, which is also used here in the Melnikov and Markov analyses, provides a good approximation when the noise correlation time is much shorter than the system relax time [15].…”

Section: Direct Numerical Simulationmentioning

confidence: 99%

“…As for randomly excited systems, PDFs are widely used to depict response characteristics [9][10][11]. In this study, the PDFs are demonstrated to be a unified measure for both perturbed and unperturbed chaotic responses.…”

Section: Foguel Alternative Theoremmentioning

confidence: 99%

“…By approximating the impact-induced energy dissipation by viscous damping and assuming no overturning under weak noise perturbations, an approximate stationary solution of the probability density function (PDF) was obtained. Another probabilistic analysis on the stochastic rocking response was carried out by Dimentberg et al [11]. The base excitations were modelled as white noise in both horizontal and vertical directions, and both free-standing and anchored objects were considered.…”

Section: Introductionmentioning

confidence: 99%

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Deterministic and stochastic analyses of chaotic and overturning responses of a slender rocking object

Lin

Yim

1996

Nonlinear Dyn

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The relationship between chaos and overturning in the rocking response of a rigid object under periodic excitation is examined from both deterministic and stochastic points of view. A stochastic extension of the deterministic Melnikov function (employed to provide a lower bound for the possible chaotic domain in parameter space) is derived by taking into account the presence of random noise. The associated Fokker-Planck equation is derived to obtain the joint probability density functions in state space. It is shown that global behavior of the rocking motion can be effectively studied via the evolution of the joint probability density function. A mean Poincar6 mapping technique is developed to average out noise effects on the chaotic response to reconstruct the embedded strange attractor on the Poincar~ section. The close relationship between chaos and overturning is demonstrated by examining the structure of the invariant manifolds. It is found that the presence of noise enlarges the boundary of possible chaotic domains in parameter space and bridges the domains of attraction of coexisting responses. Numerical results consistent with the Foguel alternative theorem, which discerns asymptotic stabilities of responses, indicate that the overturning attracting domain is of the greatest strength. The presence of an embedded strange attractor (reconstructed using the mean Poincar6 mapping technique) indicates the existence of transient chaotic rocking response.

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Sliding fragility of block‐type non‐structural components. Part 1: Unrestrained components

López-García

Soong

2002

Earthq Engng Struct Dyn

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SUMMARYMotivated by the development of performance-based design guidelines with emphasis on both structural and non-structural systems, this paper focuses on seismic vulnerability assessment of block-type unrestrained non-structural components under sliding response on the basis of seismic inputs speciÿed by current seismic codes. Two sliding-related failure modes are considered: excessive relative displacement and excessive absolute acceleration. It is shown that an upper bound for the absolute acceleration response can be assessed deterministically, for which a simple yet completely general equation is proposed. In contrast, fragility curves are proposed as an appropriate tool to evaluate the excessive relative displacement failure mode. Sample fragility curves developed through Monte-Carlo simulations show that fragility estimates obtained without taking into account vertical base accelerations can be significantly unconservative, especially for relatively large values of the coe cient of friction. It is also found that reasonable estimates of relative displacement response at stories other than the ground in multistorey buildings cannot in general be obtained by simply scaling the ground acceleration to the peak acceleration at the corresponding storey. Failure modes considered in this study are found to be essentially independent of each other, a property that greatly simpliÿes assessment of conditional limit states.

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Toppling of Computer‐Type Equipment under Base Excitation

Cited by 37 publications

References 12 publications

Rocking Response of Anchored Blocks under Pulse-Type Motions

Rocking Response of Anchored Blocks under Pulse-Type Motions

Deterministic and stochastic analyses of chaotic and overturning responses of a slender rocking object

Sliding fragility of block‐type non‐structural components. Part 1: Unrestrained components

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