Calculation of response spectra from strong-motion earthquake records

A numerical method for computing response spectra from strong-motion earthquake records is developed, based on the exact solution to the governing differential equation. The method gives a three to four-fold saving in computing time compared to a third order Runge-Kutta method of comparable accuracy. An analysis also is made of the errors introduced at various stages in the calculation of spectra so that allowable errors can be prescribed for the numerical integration. Using the proposed method of computing or other methods of comparable accuracy, example calculations show that the errors introduced by the numerical procedures are much less than the errors inherent in the digitization of the acceleration record.