PSI - Issue 47

Umberto De Maio et al. / Procedia Structural Integrity 47 (2023) 469–477 Author name / Structural Integrity Procedia 00 (2019) 000–000

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Table 2. Modal Assurance Criterion (MAC) for the investigated damage levels refers to the undamaged configuration L1’. L0’L0’ 1.0000 0.0127 0.0000 0.0010 0.0127 1.0000 0.0241 0.0045 0.0000 0.0241 1.0000 0.0977 0.0010 0.0045 0.0977 1.0000 L0’L7’ 0.9969 0.0085 0.0000 0.0008 0.0214 0.9947 0.0160 0.0012 0.0000 0.0250 0.9963 0.1506 0.0012 0.0011 0.0853 0.9823

L0’L8’

L0’L1’

0.9963 0.0224 0.0000 0.0012

0.0082 0.9938 0.0254 0.0011

0.0000 0.0159 0.9960 0.0862

0.0008 0.0010 0.1582 0.9787

1.0000 0.0132 0.0000 0.0010

0.0126 0.9999 0.0252 0.0040

0.0000 0.0224 0.9999 0.0933

0.0009 0.0046 0.1072 0.9995

L0’L9’

L0’L2’

0.9957 0.0231 0.0000 0.0012

0.0077 0.9921 0.0265 0.0011

0.0000 0.0157 0.9954 0.0883

0.0009 0.0012 0.1532 0.9778

0.9994 0.0163 0.0000 0.0011

0.0115 0.9986 0.0267 0.0023

0.0000 0.0180 0.9986 0.0856

0.0007 0.0051 0.1249 0.9956

L0’L10’

L0’L3’

0.9916 0.0276 0.0000 0.0014

0.0043 0.9706 0.0282 0.0006

0.0000 0.0149 0.9870 0.0896

0.0011 0.0016 0.1336 0.9548

0.9989 0.0179 0.0000 0.0011

0.0106 0.9970 0.0260 0.0015

0.0000 0.0167 0.9977 0.0837

0.0007 0.0049 0.1331 0.9933

L0’L11’

L0’L4’

0.9939 0.0254 0.0000 0.0013

0.0062 0.9840 0.0278 0.0011

0.0000 0.0160 0.9929 0.0904

0.0009 0.0013 0.1413 0.9722

0.9983 0.0190 0.0000 0.0011

0.0098 0.9955 0.0246 0.0010

0.0000 0.0163 0.9971 0.0832

0.0007 0.0039 0.1404 0.9899

L0’L12’

L0’L5’

0.9893 0.0307 0.0001 0.0014

0.0024 0.9546 0.0241 0.0003

0.0001 0.0108 0.9844 0.0949

0.0014 0.0034 0.1124 0.9534

0.9979 0.0197 0.0000 0.0012

0.0092 0.9952 0.0243 0.0010

0.0000 0.0165 0.9964 0.0813

0.0008 0.0023 0.1472 0.9861

L0’L6’

0.9974 0.0206 0.0000 0.0012

0.0088 0.9951 0.0245 0.0010

0.0000 0.0160 0.9964 0.0842

0.0008 0.0017 0.1469 0.9846

4. Conclusions In the present work, an innovative numerical model for the investigation of the crack-induced degradation of vibration characteristics in FRP-plated RC elements has been presented. In particular, proper traction-separation laws adapted for the cycling loading conditions, have been developed in order to capture all complex non-linear phenomena induced by the load application. The results of the static analysis show the ability of the proposed model to predict the structural behavior of FRP-strengthened elements, being able to accurately capture one of the principal failure mechanisms, i.e. debonding phenomena. The vibration frequency analysis, together with their crack-induced degradation, highlights the positive effect of the reinforcement system in the early load levels limiting the opening of the main cracks. Finally, the MAC establishes a correlation between the mode shapes and shows that no particular deviations from the undamaged configurations are present before the yielding point, emphasizing the stiffening effect provided by the FRP plate.