PSI - Issue 64

Francesco Focacci et al. / Procedia Structural Integrity 64 (2024) 1557–1564 Francesco Focacci / Structural Integrity Procedia 00 (2019) 000–000

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the described procedure starts from the attempt values cross-sections. Therefore, n -1 values of

1 2 1 n d d ,d ,...,d − = of the positions of the CRR at the cracked j N ∆ can be associated with the n -1 values of j d and the n -1 functions

(

)

1 2 j n N N d ,d ,...,d − ∆ =∆ can be defined. The correct positions d cj ( j =2,3,.. n ) of the CRR at at any load step (i.e., for any s M ) by solving the n -1 equations c cn N N d ,d ,...,d ∆ =∆ = , 1 2 1 j , ,...n = − . The described procedure can be then applied with the correct CRR positions to determine the profiles of slip, axial force, and rotation, and λ associated with any s M . The profiles ( ) M s s z , ( ) sM N z , and ( ) M s z ϕ corresponding to the attainment of ε t for the beam with thee cracks are shown in Fig. 3e, whereas Fig. 3f shows the profiles obtained for the beam with 19 cracks. Fig. 3b shows the load response obtained by integrating the rotation profile at each load step. Each load drop of the load response corresponds to the formation of two further cracks. 3. Conclusion In this paper, an analytical model was proposed to study the load response of a concrete beam strengthened in flexure with an externally bonded FRP composite. The occurrence of concrete cracking was considered by assuming concrete tensile linear behavior up to the cracking strain. Furthermore, the FRP-concrete bond behavior was accounted for considering an interface cohesive material law previously proposed in the literature. Details regarding the analytical solution for the concrete first crack, three cracks, and n cracks were provided. The profiles of the FRP concrete slip, FRP axial force, and cross-section rotation corresponding to different load values, and the evolution of the cracking process were provided. The results obtained showed that the model represents a promising and useful tool to investigate the FRP-concrete debonding process in real-scale strengthened beams. References Ahmed, O., Van Gemert, D., and Vandewalle, L., 2001. Improved model for plate-end shear of CFRP strengthened RC beams, Cement and Concrete Composites, Special Issue on Theme Analysis, 23(1), 3–19. Barnes, R., and Fidell, J., 2006. 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Shear transfer along FRP-concrete interface in flexural members, Doboku Gakkai Ronbunshu, 2000(662), 231–45. Yang, J., Haghani, R., Blanksvärd, T., and Lundgren, K., 2021. Experimental study of FRP-strengthened concrete beams with corroded reinforcement, Construction and Building Materials, 301, 124076. 1 j cj z z = are determined ( ) 2 3 0 j j c