Estimating Sliding Displacement of an Unanchored Body Subjected to Earthquake Excitation

Abstract

A freestanding rigid body under the action of base excitation can move in many different ways. In this study, the sliding response of a body is considered. The body is placed on a horizontal base that undergoes a one-dimensional horizontal motion. In 1965, Newmark (1965) gave a simple formula to determine the sliding distance of a freestanding body subjected to a single rectangular acceleration pulse of short duration at the base. The objective of this study is to see if this formula can be applied to estimate the sliding displacement of a body under the action of real earthquakes. Newmark's formula calls for the maximum velocity of the base which information is usually not directly available. To make use of the response spectrum commonly available to the engineers, Newmark's formula is first re-derived and expressed in terms of the maximum displacement of the base, which can be determined from the absolute displacement response spectrum in low frequency range. An ensemble of 75 real earthquakes is then employed, the equation of sliding motion is solved numerically and the average of the maximum sliding displacement of the body relative to the base is computed. The computed displacement is then compared with that obtained by Newmark's formula. This is done for a body placed on the ground as well as on the floors of a building. It is shown that Newmark's formula can be used if an adjustment factor, as suggested in this study, is applied. Key words: earthquake, sliding, unanchored body

Building contents sliding demands in elastically responding structures

“…Choi and Tung [16] investigated sliding displacement of an unanchored body on a flat surface subject to earthquake loading. They first re-derived Newmark's 1965 formula, and expressed in term of maximum displacement rather than velocity as used by Newmark.…”

“…These include investigations into block sliding response to earthquake motions [13][14][15][16][17][18][19][20][21][22][23][24], derivation of formulations and criteria for rigid bodies sliding due to base excitation [21,[25][26][27], and in-field analyses of sliding rock blocks [28][29][30][31][32]. Also, many observations of contents sliding and falling off shelves have been obtained from the 1976 San Fernando, the 1989 Loma Prieta, the 1994 Northridge, and the recent Canterbury earthquakes [33][34][35][36].…”

Estimation of Peak Ground Acceleration from Horizontal Rigid Body Displacement: A Case Study in Port-au-Prince, Haiti

“…The displacement of a rigid body subjected to horizontal accelerations was first investigated by Newmark (1965). Choi and Tung (2001) re-derived this formula in terms of the displacement response spectrum. A small number of forensic studies, that is, analysis of observed displacement to infer PGA, have been done.…”

The response of a two-degree-of-freedom dynamic sliding system subjected to uni-directional horizontal dynamic and seismic excitations

“…One of the important design parameters in base isolation schemes utilizing sliders is the sliding displacement. Choia and Tung [13] performed a parametric study on the sliding displacement using many earthquake records. The sliding displacement response will be particularly studied and discussed in this paper.…”