NORMALIZED ENERGY-BASED METHODS TO PREDICT THE SEISMIC DUCTILE RESPONSE OF SDOF STRUCTURES

In this paper, normalization procedures for simple rectangular pulse a nd sine-wave ground excitations are proposed. Normalized hysteretic en ergy spectra are then developed for a simple SDOF system subjected to these simple excitations, and studied to determine how the seismic ine lastic cyclic response is expressed in these spectra. The influence of damping on these spectra is also investigated. It is found that the s elected energy normalization methods, one using maximum ground velocit y square and structural mass as a normalization basis, the other using structural yield strength and displacement, both produce useful dimen sionless energy values. Then, the applicability of these simple normal ization methods is studied for systems subjected to real earthquakes. Prediction of hysteretic energy using the previously derived pulse spe ctra is attempted statistically by considering earthquakes as a sequen ce of equivalent rectangular pulses. It is found that the normalized p redicted hysteretic energy can be easily obtained for actual earthquak e excitations by: firstly, converting these earthquakes into equivalen t pulses; secondly, summing the values read for each pulse from the no rmalized hysteretic energy spectra constructed for simple rectangular pulse or sine wave excitations; and finally, adjusting the total value s by ratio spectra or equations statistically calibrated against a num ber of real earthquake records. This simple and rapid procedure allows direct and reliable prediction of hysteretic energies without the nee d to resort to complex and time-consuming step-by-step nonlinear inela stic time-history analyses.