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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Fig. 1. Traction-separation laws for Mode I (a) and Mode II (b) fracture processes.

During the unloading stage, in order to allow the effect of the partial contact between crack faces, induced by the presence of aggregates in concrete phase, the following expression of the cohesive normal stress has been introduced:   0 0 0 for for c p p p n n n n n n c n p n n n n K t K                  , (3) c n K is the normal tangent stiffness computed by an adaptive formulation when an inversion in the sign of the cohesive stresses, from tensile to compressive during the unloading phase, is registered:   0 1 1 p n n n c n K K K        , (4) where the scalar parameter  , set as 225 after the calibration procedures performed on experimental works (Hamad et al., 2015; Reinhardt, 1984), reduces the initial normal stiffness 0 n K as the damage increases. The interpenetration phenomenon between the cohesive elements is prevented through a contact constraint that is active when the displacement reaches the limit value of: 3. Investigation of the crack-induced degradation of vibration characteristics in FRP-strengthened RC beam The static and dynamic behavior of an FRP-plated RC beam has been investigated by employing the numerical model explained in Section 2. The setup of the test, the geometry, and the boundary conditions are reported in Fig. 2. Concrete with a Young’s Modulus of 40.3 GPa, taken from (Hamad et al., 2015) like all material's properties, has been used. The tensile and compressive strengths are 2.1 MPa and 36.5 MPa, respectively. Steel rebars with a Young’s modulus of 210 GPa are employed. In particular, 6 mm plain bars with a yield strength of 393.6 MPa have been used in the compressive side of the specimen and for the shear stirrups, while 10 mm ribbed bars with a yield strength of 490 MPa have been placed in the tension side of the beam. The external reinforcement system is made of a carbon FRP (CFRP) plate of 0.44 mm bonded at the bottom side of the reinforced concrete beam, by a 2 mm thick epoxy where 0   0 p c n n K K K   p n c n n , (5)