Energy-based seismic demand of multi-storey structures under pulse-like and non pulse-like ground motions

Assessing seismic demand is a critical task in energy-based seismic design, as it depends on both ground motion characteristics and structural hysteretic properties. In recent years, growing attention has been devoted to demand evaluation through energy-related parameters, such as the equivalent number of yielding excursions ( n y e ), particularly following the integration of energy-based approaches in the second-generation Eurocode drafts. Despite this interest, existing studies often rely on a limited number of structural typologies and ground motion records, with many focusing exclusively on SDOF systems. This work aims to bridge this gap by evaluating n y e for MDOF structures through an extensive investigation of diverse structural configurations and a broad ground motion database. Specifically, this study investigates the cyclic seismic demand on multi-storey buildings subjected to 898 far-field records and 262 near-fault pulse-like records. The analyzed structures range from two to six storeys, with fundamental periods between 0.3 s and 1.5 s, and different hysteretic material models. The paper proposes two original formulations to estimate a global, system-level, n y e parameter to be used within energy-based design frameworks alongside storey-level demands. The variability of this global parameter is extensively discussed by investigating its sensitivity to ground motion characteristics and by comparing MDOF results with their SDOF counterparts. The results show that median estimates remain quite stable and consistent with the literature, whereas the recorded dispersions are noteworthy. Furthermore, the practical utility of these descriptors is demonstrated: their integration enables a significantly more accurate estimation of strength reduction factors compared to the traditional Equal Displacement Approximation. Overall, the findings underscore the importance of n y e for the development of energy-based methodologies and highlight the central role of uncertainty characterization in its estimation for future regulatory and code applications.