Calculation of Ultimate Ductility Index Based on Hysteretic Energy Analysis of the Restoring Force Curve

This study proposes an energy-based framework for evaluating the seismic ductility of reinforced concrete (RC) structures using restoring force hysteresis curves. A custom-developed tool, the Damage Energy Calculation Program (DECP), is introduced to compute cumulative hysteretic energy and corresponding damage indices from experimental data. Seven methods for identifying yield displacement and yield load are examined, encompassing stiffness-based and energy-based techniques, including the conditional yield method, secant stiffness method, and double energy equivalence method. These methods are applied to a series of experimental restoring force curves (SP01 to SP10). Among them, the double energy equivalence method demonstrates the highest accuracy in capturing the yield state. Additionally, a novel ductility index based on the maximum energy envelope is proposed. Comparative analysis shows that this new index exhibits trends consistent with the double energy equivalence approach, highlighting its potential as a reliable alternative. The DECP tool significantly improves the consistency and efficiency of ductility assessment and offers practical support for energy-based damage evaluation in structural performance analysis.