PSI - Issue 64

Tahreer M. Fayyad et al. / Procedia Structural Integrity 64 (2024) 708–715 Tahreer M. Fayyad / Structural Integrity Procedia 00 (2019) 000–000

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reinforced concrete flexural specimens and predict the equivalent damage stage, it was used to explain the behaviour of the test beam and the different failure stages. The theory of the behaviour states that a considerable increase in the crack mouth opening occurs during the softening stage while the first stage of the cracking process is primarily associated with crack propagation. Damage state description where vibration tests were done based on the DIC analysis and the IFBM are summarised in Table 2. As described in Section 2.3, 100 individual rubber hammer tests were conducted. For each test, 300 sampling points, roughly equivalent to 0.6 seconds of midspan accelerations, were recorded using the Sensor-E. The built-in function, ‘fft’, was used to compute the Power Spectral Density (PSD) versus frequency spectrum. The results of beam the beam C45_0.6_2 are shown in Fig. 7(a) and Fig. 7(c). Distributions of the extracted frequencies for healthy and damaged beam are presented in Fig. 7(b) and Fig. 7(d), respectively. Average frequencies for those 100 tests are calculated and presented in Fig. 7 as well, as highlighted in vertical dash-dotted lines in Fig. 7(b) and Fig. 7(d), giving frequencies of 133.17 Hz, and 115.84 Hz, respectively. The results of test beams are summarised in Table 2.

(a) (d) Fig. 7. (a) PSD Results of healthy beam C45_0.6_2 from Sensor-E located at 1/2 span; (b) frequency distribution of healthy beam; (c) PSD Results for damaged beam C45_0.6_2 from Sensor-E located at 1/2 span; (d) frequency distribution of damaged beam. Table 2. Results Beam notation Damage state based on DIC analysis (b) (c)

Frequency of healthy beam

Frequency of damaged beam

C45_0.3_2

133.17

115.84

0.8 relative crack length at unstable crack growth phase “rotation phase”, crack opening of 3 mm 0.6 relative crack length at unstable crack growth phase “rotation phase”, crack opening of 2 mm Full development of the crack. The beam almost completely failed 0.2 relative crack length at stable crack growth stage “propagation phase”

C45_0.5_2

133.52

111.47

C60_0.3_2

134.32

88.57

C60_0.5_2

134.08

123.19

Table 2 clearly demonstrates that the frequency of the beam decreases as damage progresses. This decrease is modest yet apparent in the early stages of crack propagation (beam C60_0.5_2). The reduction in frequency values becomes significantly noticeable in the critical stage of crack propagation, the rotation phase, where the crack shows an opening with a relatively constant crack length (C45_0.3_2, C45_0.5_2). The frequency values decrease substantially when the beam reaches the final failure phase. This indicates that combining the results of Digital Image Correlation (DIC) for defining the crack geometry with frequency measurements provides more precise information about the state of structures as they begin to sustain damage. 4. Conclusions In this paper, the investigation into lightly reinforced concrete beams, combining Digital Image Correlation (DIC) and dynamic frequency measurements, has produced noteworthy results. Significantly, it was observed that the frequency of a beam subjected to damage changes markedly during crack propagation phase, particularly in the