The Momentum-Balance Method in Earthquake Engineering

Abstract

During an earthquake the shaking of the ground imparts movement to structures which are then stressed by the resulting inertia forces. When the structure is a dam, it experiences additional earthquake forces from the water in the reservoir. The horizontal motion of the ground does not impart movement to the water so the dam accelerates into and away from the water and experiences dynamic water pressures. The first analysis of this problem was by H. M. Westergaard, Professor of Theoretical and Applied Mechanics at the University of Illinois, his paper [1] appearing in the 1933 Transactions of the American Society of Civil Engineers. In the 1920's when Boulder Dam was being designed, Westergaard was a Visiting Scientist at the Bureau of Reclamation and became jnterested in this practical earthquake engineering problem. His paper elicited numerous discussions, also printed in the 1933 ASCE Transactions, and an especially interesting discussion was contributed by Theodore Von Karman, Professor of Aeronautics at the California Institute of Technology. Essentially the same result that Westergaard obtained by means of a series solution of a partial differential equation was deduced by Karman using a remarkably simple momentum-balance method. Although Karman's method was mathematically simple, some steps in the analysis appeared to be inexplicable. The method might be said to be an example of Operational Mechanics which, like Operational Mathematics, involves operations that, give the desired result without it being understood why they do so. It is the purpose of this paper to give a rational explanation of the momentum-balance method.

Files

Additional details