Response spectra of one-degree undamped elastic systems for earthquakes in Turkey

Abstract

At first, various methods of obtaining the response spectrum of a single-degree-of-freedom systems for earthquake ground motion, are studied and compared to find the best method for obtaining the most accurate results. Various sample calculations indicated that The Runge-Kutta- Gill method for the solution of differential equations by numerical integration usually gives relatively more accurate results. Subsequently, using this method, a computer program is developed in order to obtain the maximum values of relative displacement, velocity and acceleration of a single-degree-of-freedom system subject to the ground acceleration of a given earthquake motion. Since, no ground acceleration-time curves are available in Turkey, an approximate method is introduced to obtain the ground accelerationtime curves from the ground velocity-time records. March 28, 1968 Alaşehir Earthquake is taken as an example and the response spectra for this earthquake is obtained for relative displacements, velocities and accelerations. Further, approximated spectral values of displacements, velocities and accelerations are related to each other on the basis of the circular frequency of vibrations of the systems.