© 2022 Sari and Manuel.Background: The intensity of ground shaking and the demand on structures during earthquakes have been generally characterized using parameters such as peak ground acceleration as well as strength-based parameters such as response spectrum ordinates (e.g., spectral acceleration), which represent the maximum amplitude of shaking for structures with specified natural period and damping values. Methods: It has long been recognized that to assess the demands on structures during earthquakes, one might employ an energy-based approach (as an alternative to the more common strength-based one), especially when there is an interest in assessing the damage potential of ground motions. The study focuses on the correlation between Ground Motion Parameters (GMPs) and structural damage indicators for reinforced concrete frames. The relationship between ground motion intensity and structural damage is of primary concern in seismic regions. Here, we consider GMPs that are strength-based (such as spectral acceleration, Sa) and energy-based (such as input energy-equivalent acceleration, Ai, and absorbed energy-equivalent acceleration, Aa), as defined in the study. In order to evaluate Ground Motion Parameters (GMPs) for efficiency, power-law format regression studies of damage measures (DM) on each GMP are utilized. Results: The general objective of this paper is to investigate if energy-based parameters can correlate well with structural damage. Thus, power-law formats in regression of damage on GMP are considered. In regression studies of this type, a lower standard deviation of the damage measure given the value of the ground motion parameter (GMP) is considered an indication of a stronger correlation between that damage measure and the corresponding ground motion parameter. Conclusion: These extensive regression studies are carried out for both low-rise and high-rise reinforced concrete buildings. Conclusions are discussed following these analyses.