Shake table tests of stiff, unattached, asymmetric structures

Abstract

SUMMARYStiff, unattached structures are highly vulnerable to damage and failure during an earthquake, as evidenced following numerous past events. This class of structures encompasses a wide range of objects and systems such as electrical transformers, radiation shields, office furniture, and marble statues. The vulnerability of these objects is exacerbated when it is highly asymmetric and unattached. Although a number of studies have focused on rigid blocks, few have concentrated on blocks with asymmetric geometries. In an effort to better understand the implications of asymmetries, an extensive shake table testing campaign including more than 150 tests was conducted. These tests incorporate a systematic variation of the mass eccentricities of stiff, unattached structures. The primary modes of rocking, sliding, and twisting as well as interactive modes were recorded for the duration of numerous earthquake motions. The magnitude and direction of response are experimentally correlated with the geometric variations in the various models. These tests indicate that even for symmetric structures with uniaxial shaking, multiple modes and three-dimensional responses are probable. Furthermore, certain asymmetric geometries exhibited both increased rocking (and overturning) as well as increased sliding when compared with their symmetric counterparts. A final aspect of this study compared the free rocking response of symmetric and asymmetric structures to classical, two-dimensional rocking analysis. While the theoretical values for the coefficient of restitution yielded a significant overestimation in the simulation (up to ≈90%), reduced coefficients greatly improved the performance of the model.

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

“…20 During fabrication of the tower specimen, a marble slab was wet-bonded with concrete at the base, resulting in a mild warp of the slab. As a result, the tower specimen did not have two distinct rocking points and exhibited a "wobble" mode during low-amplitude shaking, as detailed in Ref [ 17 ]. A general overview of the specimen is shown in Figure 3, as well as detailed images of the warped interface highlighting the regions that were in contact.…”

“…While the testing was part of a much larger campaign focused on the seismic response of asymmetric freestanding structural systems, only the free-rocking tests are described herein. 17 The experimental setup consisted of (i) a stiff, freestanding steel tower structure with moveable weight plates and marble base and (ii) marble bolted to a uniaxial shake table that formed the interface with the tower specimen.…”

“…While previous studies have highlighted the importance of the value of the coefficient of restitution at impact (e.g., Refs [ 13,[15][16][17][18] ]), few have analyzed the effect of geometric interface defects, which result in multiple rocking points and an increased number of impact events. Such studies have been limited with the exception of a recent experiment by Purvance et al, 8 in which three boulders incorporating jagged bases were tested on a shake table to the point of overturning.…”

Rocking and Kinematic Approaches for Rigid Block Analysis of Masonry Walls: State of the Art and Recent Developments

“…These bumps change the evolution of motion as more impacts occur; the modified equations of motion are proposed in [23]. Recent experimental tests observed relevant results on the evaluation of the coefficient of restitution and motion decay [24][25][26][27]. It was shown how the interface material strongly influences the dissipation in the free rocking behavior.…”

Dynamic Response of a Rigid Slab Supported by Four Rigid Cylinrical Rocking and Wobbling Columns

“…Indeed, a simple freestanding rocking block has been systematically studied for more than five decades both when the block is assumed rigid [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] and when it assumed deformable [27][28][29][30][31][32][33][34][35][36][37]. Small scale experiments have been also performed [38][39][40][41][42][43][44][45][46][47][48][49][50][51]. It has been proven that structures that rock inplane (2d rocking) have remarkable dynamic stability.…”