PSI - Issue 66

Umberto De Maio et al. / Procedia Structural Integrity 66 (2024) 459–470 Author name / Structural Integrity Procedia 00 (2025) 000–000

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4. Conclusions In this work, a finite element model, based on the coupled damage-plasticity approach, is proposed to analyze the degradation of dynamic properties of reinforced concrete beams subjected to progressive damage. In particular, the model is first employed to simulate the structural response, in terms load carrying capacity and crack patterns, of reinforced concrete beams and then used to detect the damage magnitude and location by using available dynamic damage indicators. Moreover, a formula that combines the frequencies obtained during the loading and unloading phases has been proposed. Specifically, the proposed formula calculates the dynamic properties, in terms of the natural vibration frequencies of RC beams with diffuse damage and multiple cracks, using two simplified parameters. These parameters have been evaluated by employing the mean squared error (MSE) and the ordinary least squares (OLS) as objective functions. The obtained quasi-static structural response is in good agreement with the experimental one reported in (Hamad et al., 2015) in terms of both loading curve and multiple crack propagation, exhibiting the typical trilinear behavior of the RC beam under loading condition and residual plastic deformation in the unloading crack paths. For high values of damage two different slopes have been observed. They are related to the combined effect of the concrete plasticity and the partial contact between crack faces which cannot completely close due to the presence of aggregates and the sliding phenomena occurring at concrete/rebar interface. Subsequently, the damage detection procedure is performed by using the Modal Curvature (MC) and the Modal Assurance Criterion (MAC) and considering the optimized natural frequencies. Because the values of the diagonal coefficients of the MAC matrix (MACii) deviate more from the unit value as the damage level increases, we can observe that the correlation between the mode in the undamaged configuration and that relating to the damaged configuration decreases as the level of damage increases. Finally, we can state that the proposed numerical procedure can be employed as valuable tool to predict and detect damage in the RC structural elements thanks to its precision and comprehensiveness guaranteed by the experimental findings and mathematical models. Acknowledgements Andrea Pranno gratefully acknowledges financial support from the Italian Ministry of Education, University and Research (MIUR) under the PON 2014-2020 Action IV.4 – Rep. No. 1062 of 10/08/2021. References Avci, O., Abdeljaber, O., Kiranyaz, S., Hussein, M., Gabbouj, M., Inman, D.J., 2021. 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