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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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.

Fig. 3. Load-deflection curves for loading and unloading processes represented through a red solid line and red dotted lines, respectively.

3.3. Dynamic analysis The dynamic analyses have involved the study of the degradation of the natural vibration frequencies as the damage level increases. A linearized eigenvalue problem has been carried out by performing the analysis of small amplitude free oscillations superimposed on the last point of each unloading path, for all the nine damage scenarios considered. The results have been compared with the ones taken from the literature (Hamad et al., 2015). The dynamic response performed at different load levels shows a reduction of the natural frequencies as the load level increases mainly induced by the evolution of damage phenomena in the tested structure. With reference to Fig. 4 (a), the degradation of the frequencies of the proposed model at different load levels doesn’t follow the frequencies behavior of the control beam test results. This is due to the non-linearities present in a cracked vibrating beam, so due to the opening and closing of the crack. To consider this non-linear behavior of the beam, in the literature it’s proposed an effective natural frequency calculated as a combination of the natural frequency for crack open configuration and natural frequency for crack closed configuration. This is called Bilinear frequency, and it was proposed by (Chati et al., 1997):

1 2 2 i i     

(13)

 

i

1

2

i

i

where 1 i  and 2 i  are the natural frequencies for crack open and crack closed configurations, respectively, for each mode shape. In Fig. 4 (b) it is shown the trend of the bilinear frequency obtained by Eq. 13. This trend does not show good agreement between the experimental results and the numerical ones of the proposed model. The divergence between the results depends on the fact that Eq. 13 was obtained for a reinforced concrete beam in which only one crack was located, whereas in the numerical model analyzed the damage scenario has multiple diffuse cracks.