Analytical damage models provide a way to have an index to create a single measure that fairly represents the damage sustained under seismic loading in reinforced concrete structures. Damage indices are important tools to quantify the consequences of a structural decision. A damage model is proposed for reinforced concrete elements. The model yields a damage index at a point in the time history for the load on the element, based on the predicted monotonic response from the point in time to

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... re. The model takes into account the parameters that describe the hysteretic behavior: stiffness degradation, strength deterioration, and ultimate displacement reduction. The model is cumulative and it combines energy, ductility, and low-cycle accumulation. The model is based on the work needed to fail the element monotonically after it experiences cyclic loading and takes the energy under the monotonic load-deformation envelope for the virgin state of the element as a reference capacity. The model modifies the ultimate displacement that the element can achieve, due to low-cycle accumulated damage at the longitudinal reinforcement using the Coffin-Manson rule in combination with Miner's hypothesis. Most of this study is applied specifically to reinforced concrete columns and column-like elements, but the application is also demonstrated for a coupling beam in a coupled shear wall system. A layers analysis program is written to predict the monotonic force-displacement envelope based on plane sections remaining plane, accounting for concrete confinement, elastic shear deformation, elastic and inelastic flexural deformation, and bond slip deformation. The proposed model is applied to 12 bridge columns tested by others. The proposed model gave a realistic prediction o f the damage throughout the loading cycles for the test specimens investigated. The results are also compared to two existing damage models; the Park and Ang (1985) and the low-cycle damage model by Mander and Cheng (1995). An experimental test for a full-scale c [...]