The interaction of elasticity and rocking in flexible structures allowed to uplift

SummaryThe rocking response of a rigid, freestanding block in two dimensions typically assumes perfect contact at the base of the block with instantaneous impacts at two distinct, symmetric rocking points. This paper extends the classical two-dimensional rocking model to account for an arbitrary number of rocking points at the base representing geometric interface defects. The equations of motion of this modified rocking system are derived and presented in general terms. Energy dissipation is modeled assuming instantaneous point impacts, yielding a discrete angular velocity adjustment. Whereas this factor is always less than unity in the classical model, it is possible for this factor to exceed unity in the presented model, yielding a finite increase in the angular velocity at impact and a markedly different rotational response than the classical model predicts. The derived model and the classical model are numerically integrated and compared to the results of recent shake table tests. These comparisons show that the new model significantly enhances agreement in both peak angular displacement and motion decay. The equations of motion and the energy dissipation of the presented model are further investigated parametrically considering the size of the defect, the number of rocking points, and the aspect ratio and size of the block. | INTRODUCTIONThe original motivation for studying freestanding and rocking structures stems from the observed overturning of small, slender structures compared to the apparent stability of certain larger, slender structures following strong earthquake excitations. 1 More recently, motivation has shifted to the intentional design of rocking structures in an effort to harness their inherent energy dissipation and self-centering mechanisms (e.g., Ref [ 2 ], and references therein). Additionally, the class of freestanding and rocking structures includes water towers, gravestones, nuclear radiation shields, mechanical and electrical equipment, and culturally significant statues and columns. Since many of these components are critical to a facility's post-earthquake functionality or are culturally significant, accurate prediction of the seismic response is necessary.The well-known and broadly utilized classical rocking model was introduced in the pioneering work of Housner. 1 This rocking model considers a two-dimensional, symmetric, rectangular, rigid block that oscillates about two rocking points at its base atop a rigid foundation. The model further assumes that there is sufficient friction to prevent sliding and that the block transitions smoothly between rocking points through an inelastic impact with conservation of angular momentum. The response of this block is modeled as a set of piecewise equations of motion and an instantaneous reduction of angular velocity at the moment of impact. This velocity reduction is typically known as a coefficient of restitution and is strictly a function of geometry

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“…In addition, the rotation is bounded on one side only for the extreme rocking points, as noted in Equation 10.…”

Section: Equations Of Motionmentioning

confidence: 99%

Rocking bodies with arbitrary interface defects: Analytical development and experimental verification

Wittich

Hutchinson

2017

Earthq Engng Struct Dyn

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“…On the contrary, the footings of the model RA stayed in position and therefore rocking was developed by that model with partial lateral sliding of the column tips into the grooves of the footings. During the large amplitude earthquakes and low frequency earthquake, the time-historey accelerations suggest an out of phase storey profile, which if combined with the existence of the impacts, it further suggests the development of an uplifted mode of vibration [18,30], driven by the input motion frequencies.…”

Section: Test-1 Eq-2mentioning

confidence: 99%

A Centrifuge Investigation of Two Different Soil-Structure Systems With Rocking and Sliding on Dense Sand

Pelekis¹,

Madabhushi²,

Jong³

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…However, few computational models exist for modeling the response of deformable rocking bodies (e.g. [9], [10], [11], [12], [13], [14], [15], [16], [17]). Most of these studies, though, consider the rocking base to be rigid, take into account the stress nonlinearity only across the rocking interface or make simplifications regarding the stress distribution near the contact area.…”

Section: Introductionmentioning

confidence: 99%

A New Computational Approach for the Rocking Response of Deformable Bodies Considering Material Nonlinearity

Avgenakis¹,

Psycharis²

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. An increasing interest in the use of rocking members in earthquake resistant structural systems has been observed in recent years. The benefits of such members include the limitation of the damage, re-centering capabilities and reduction of seismic forces transmitted to the rest of the structure due to a yield-like response.Despite the importance of such members, few models able to describe the response of flexible rocking members in structural systems realistically can be found in literature, since most of the research focuses on the response of rigid bodies or ignores the stress nonlinearity near the contact area, which is considered crucial to the accurate determination of the rocking response of deformable rocking bodies. A new macro-element formulation for elastic rocking members has been proposed by the authors in previous papers which is able to take into account this stress nonlinearity, producing results which are very close to the ones produced by conventional finite element programs.Rocking members in structural systems are expected to behave inelastically for large seismic excitations. In this paper, the macroelement presented previously by the authors, which considered the element material to be elastic, is extended to also take material nonlinearity into account. The effect of the nonlinear stress distribution across the rocking interface on the member displacements is determined and approximate formulas for their determination are included in the macro-element formulation. The results produced by the macro-element with the inelastic material are finally compared to the ones of conventional finite element codes, showing very good agreement between the results of the two methods.

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The interaction of elasticity and rocking in flexible structures allowed to uplift

Cited by 139 publications

References 18 publications

Rocking bodies with arbitrary interface defects: Analytical development and experimental verification

Rocking bodies with arbitrary interface defects: Analytical development and experimental verification

A Centrifuge Investigation of Two Different Soil-Structure Systems With Rocking and Sliding on Dense Sand

A New Computational Approach for the Rocking Response of Deformable Bodies Considering Material Nonlinearity

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