Abstract
A method is presented to find upper and lower bounds of the probability that a simple structure will fail under a random loading of earthquake type. The structure considered is a one-story building treated as a system of mass, spring and dashpot with single-degree of freedom. The failure is assumed to occur when the absolute value of the displacement of the mass exceeds a critical value. The present method leads to evaluation of lengthy integrals which, however, can be performed numerically with an electronic digital computer and produces the upper and lower bound close enough at least for the order estimation of the probability.
