Free Rocking of Prismatic Blocks

Abstract

This paper investigates both experimentally and theoretically the free rocking of a prismatic block supported by a stationary , horizontal foundation: the block is tilted, almost to the point of overturning, and released from this position. It is shown that the standard mathematical model for this problem is often inaccurate. A critical review of the implicit assumptions behind the standard model reveals that the free-rocking response of short blocks depends crucially on bouncing after each impact; out-of-plane effects are significant in very short blocks. The response of slender blocks is found to be easier to predict. Rocking has been observed during earthquakes in structures that consist of fairly rigid, unbonded elements, e.g. stacks of graphite blocks in nuclear reactors. and ancient Greek columns, and also in slender structures with foundations unable to resist uplift.

Oscillations Control of Rocking-Block-Type Buildings by the Addition of a Tuned Pendulum

“…The main issue investigated in this and other earlier studies [3][4][5][6][7][8][9][10][11] was the performance and the overturning of a rigid body against the base motion dynamics, for example, an earthquake, assuming the block to be a building model. The work by Housner was devoted to the explanation of the collapse of many bulky structures during the catastrophic Chilean earthquake of May 1960.…”

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

“…Indeed, for stocky blocks, say µ = 1, 3, bouncing was shown to occur, and the response was seen to be very sensitive to the restitution coefficient value [20]. For these blocks, such as cubes, a two-dimensional or three-dimensional bouncing model is therefore required.…”

“…They noticed discrepancies of the restitution coefficients' values between experimental and analytical results. A relevant contribution was also given by Lipscombe and Pellegrino [20], who conducted four free rocking tests on steel blocks with µ = 1, 2, 4, 8, colliding on a steel base. The blocks, initially tilted almost to the point of overturning and then released, exhibited values of restitution coefficients ranging between 0.88 and 0.93, although it was respectively e H = 0.25, 0.70, 0.91, 0.98 (given by Equation (3)) for the mentioned µ values.…”

Rocking and Sliding of Unanchored Bodies Subjected to Seismic Load According to Conventional and Nuclear Rules

“…The Equations (1) or (2) were derived under the assumption that rocking and sliding motions do not occur at the same time. The equations of motion for a simultaneous occurrence of rocking and sliding motion are given in [2], [10], [19] and [22].…”

“…In other cases the body will perform complicated kinds of motion like bouncing or jumping. Further attempts to understand the impact and the motion after the impact are given in [9], [10], [16] and [21]. The Equations (1) or (2) were derived under the assumption that rocking and sliding motions do not occur at the same time.…”