Simplified Method to Include Cumulative Damage in the Seismic Response of Single-Degree-of-Freedom Systems

In this paper a consistent method including damage criteria in the seismic response of single-degree-of-freedom systems is proposed. The method allows the determination of suitably modified strength or displacement inelastic spectra through the introduction of an equivalent damage factor p(dam) that accounts for earthquake damage potential; analogously capacity spectra could be obtained. Three types of damage indices are considered (Park and Ang index D-P&A, energy index D-E, and low-cycle fatigue index D-F) and derivation of p(dam) is pursued for all these cases. Moreover approximate simplified expressions in the function of Cosenza and Manfredi seismological I-D index, which accounts for cyclic damage potential of an earthquake, are also proposed. In this way damage capacity spectra are obtained to improve the seismic assessment of existing structures including damage effect.