An Intensity Measure for Seismic Input Energy Demand of Multi-Degree-of-Freedom Systems

Nonlinear dynamic analyses are performed to compute the maximum relative input energy per unit mass for 21 multi-degree-of-freedom systems (MDOF) with preselected target fundamental periods of vibration ranging from 0.2 to 4.0 s and 6 target inter-story ductility demands of 1, 2, 3, 4, 6, 8 subjected to 40 the earthquake ground motions. The efficiency of the several intensity measures as an index for damage potential of ground motion in MDOF systems are examined parametrically. To this end, the dispersion of normalized input energy by different intensity measures have been evaluated and compared. Results of this study show that using all intensity measures will result in a significant discrepancy in input energy spectra of MDOF systems, which are in most cases larger than 0.5 and even can take the value of 1.9 for some cases. This signifies that the evaluated intensity measures may not suitable for MDOF systems. A dimensionless intensity measure as a normalized energy index is proposed for MDOF systems subjected to far-fault earthquakes. It was demonstrated that the proposed normalized input energy values have smaller dispersion compared to those of the other indices for MDOF systems with all ranges of period and ductility ratio used.