NEWMARK'S FORMULA FOR ESTIMATING SLIDING DISPLACEMENT OF AN UNANCHORED BODY SUBJECTED TO EARTHQUAKE EXCITATION

摘要

A free standing rigid body under the action of base excitation can move in many different ways. In this study, the sliding response of a body placed on a horizontal base which undergoes a one-dimensional horizontal motion is considered. In 1965, Newmark gave a simple formula to determine the sliding distance of a free-standing 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 are 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.