PSI - Issue 64

Emanuele Gandelli et al. / Procedia Structural Integrity 64 (2024) 685–692 Emanuele Gandelli / Structural Integrity Procedia 00 (2019) 000 – 000

688

4

Table 1. Case- study beams’ properties.

unit [kg/m] [m4] , [GPa] , [MPa] , [GPa] , , [MPa] , , [MPa] , [GPa] , , [MPa] , , [MPa] [kN]

parameter

beam-1

beam-2

mass per unit length

586

563

inertia moment

0.0190

0.0176

concrete C50/60 elastic modulus concrete C50/60 compression strength rebars B450C elastic modulus (Φ8 / Φ12) rebars B450C yielding strength (Φ8 / Φ12) rebars B450C ultimate strength (Φ8 / Φ12)

36.2 61.2

35.8 75.5

196.9 532.8 635.3 202.4 1783 1947

196.9 / 196.2 532.8 / 525.8 635.3 / 641.3

strands S15 elastic modulus strands S15 yielding strength strands S15 ultimate strength prestressing internal action

202.4 1783 1947

960

0÷1130

3. Detection of shear cracks This section presents the results of dynamic identification tests conducted on beam-1 in both virgin and damaged conditions. Fig. 3-a,b shows the cracking pattern of the damaged beam, obtained by the "Digital Image Correlation ” (DIC) technique. The cracks were obtained by applying a vertical load of 800 kN, with the load point located 2.2 m from one support. This loading configuration, featuring an a/d ratio of about 2.8, generated diagonal shear cracks. Dynamic identifications in virgin and damaged conditions involved the recording of environmental vibrations (i.e., "white noise") and their processing using the "Frequency Domain Decomposition ” (FDD), implemented by the Authors in MatLab framework (MathWorks, 2024). This technique allowed the determination of the natural frequencies and mode shapes of the beam (Brincker and Ventura, 2015). The objective of this investigation was twofold: (1) verify whether, through variations in the fundamental frequencies, it is possible to detect damages associated to shear cracks; (2) evaluate if, analysing the variations of the modal components, it is possible to localize the damage. In both virgin and damaged conditions, ambient vibrations were recorded using five piezoelectric accelerometers (Wilcoxon model 731A) uniformly distributed along the top flange. Cantilever sections of the beam beyond the two supports were not instrumented, as considered unnecessary for the purposes. The acquisitions were performed at a frequency of 600 Hz with the beam unloaded (i.e., supporting only its own weight). Evaluating the frequency associated to the primary peak of the first singular value line (SVL1) in the virgin condition (f 1 =31.25 Hz) shows that it closely matches the fundamental frequency (f 1 =31.45 Hz) calculated by modal analysis by means of the FEM software Telaio2D (Gelfi, 2008) . The slight discrepancy ∆f=0.20 Hz, (i.e., 0.64%) could result from various factors, such as small errors in the measurement of the beam weight or the actual distance between supports. However, more significant results arise from comparison of the beam's SVL1 in virgin and damaged conditions and comparison of the relative modal shapes associated with their peaks. The presence of an extensive shear crack pattern, extending approximately 3.3 m from the support, results in a significant decrease in the fundamental frequency of the beam (i.e., ∆ = , − = − . , where , = . represents the "damaged frequency"). Furthermore, a disparity is observed between the two mode shapes calculated via FDD: in the virgin condition, the fundamental mode (see Fig. 4-a) perfectly matches the one calculated by the FEM software Telaio2D (Gelfi, 2008); on the contrary, in the damaged condition discrepancies are noted in the modal components associated with accelerometers No. 1 and No. 2 located above the cracked region of the beam (see Fig. 4-b). Evaluating the "Modal Assurance Criterion ” (MAC), i.e., a synthetic index varying between 0 and 1 that allows evaluating the similarity of two mode shapes (Allemang et al., 1982), between the mode frequency of the virgin beam and the damaged beam results in a relatively high value of 0.996. Nevertheless, a visual examination of the graphs makes it possible to identify the location of the shear cracks responsible for the decrease in natural frequency. This observation becomes particularly pertinent considering potential in situ applications such as continuous monitoring of multi-span