An extensive study of a simple method for estimating the response spectrum based on a simulated spectrum

Abstract

A simple method to simulate the response spectrum is proposed and developed. The response spectrum of the single-degree-of-freedom system shows generally multi-peaks at ground predominant periods. The simulated response spectrum of a building and a building-appendage structure system is made a standard. It is statistically computed using the theory of random vibration assuming earthquake motion with a single ground predominant period. Based on the fact that the simulated response spectrum for two ground predominant periods fits well with the spectrum for the earthquake motion, it is proposed that the simulated response spectrum can also be given by adequate summation of the standard spectrum, which is carried out by the method of square root of sum of squares. This makes it possible to simulate the spectrum which has generally plural ground predominant periods. This was virtually impossible using the statistical computation. It is shown that the method is generally applicable to multi-degree-of-freedom building systems and appendages. This means that if the average response spectrum for a single-degree-of-freedom at a site is given, the so-called floor response spectrum can be estimated from the standard spectrum.