PSI - Issue 64

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

1558

2

(2003), Yang et al. (2021)), as well as to improve the axial capacity and ductility of members mainly subjected to compressive loads (Rousakis et al. (2007)). In general, failure of concrete members strengthened with EB FRP occurs due to composite debonding within a thin layer of concrete (Carloni (2014)). The debonding process was studied using direct and indirect shear tests (Ahmed et al. (2001), Wu and Jiang (2013)), which were then modeled using analytical and numerical approaches (Salomoni et al. (2011)). Single- and double-lap direct shear tests were largely used due to their simplicity (Bizindavyi and Neale (1999)). Indirect small-scale bending tests were also proposed to study the debonding process under loading conditions close to those of the real strengthened member (Barnes and Fidell (2006)). Among analytical and numerical models, cohesive interface approaches were proposed to model the debonding process (Wang (2007)). Single- and double-lap shear tests and small-scale bending tests allow to study the debonding process considering a single substrate discontinuity that represents a concrete crack. However, the debonding process in real-scale beams strengthened in flexure is characterized by multiple cracks that affect the bond behavior (Rosenboom and Rizkalla (2008)). Several models were proposed to describe the debonding process in a flexurally strengthened RC beam. Some models focus on the maximum force transferable at the FRP-concrete interface between two consecutive cracks (Teng et al. (2006), Finckh and Zilch (2012), Federation Internationale du Beton (2019), Focacci et al. (2024)). However, the application of these models requires the preliminary evaluation of the crack distance. In this paper, the load response of a concrete beam strengthened in flexure with an externally bonded FRP composite is studied using an analytical model. A similar model was proposed in (Wu and Niu (2000), Niu and Wu (2001)), where a linear relationship between the interfacial slip and the shear stress was introduced or a limited number of cracks was considered. In the proposed model, the concrete is considered brittle, i.e., its tensile behavior is considered linear until cracking, whereas the composite is considered linear elastic. The bond relationship between the concrete and FRP is modeled using a contact cohesive approach that relates the interface slip with the corresponding shear stress (Dai et al. (2006)). The profiles of the FRP-concrete slip, FRP axial force, and cross-section rotation corresponding to different loads applied to the beam, and the evolution of the cracking process are obtained. The model represents a useful tool to investigate the relationship between the bond capacity of FRP-concrete interfaces with a single crack and that observed in real-scale strengthened beams. 2. Analytical model 2.1. Equations of the model The model refers to a composite beam with the longitudinal axis along the z -direction (Fig. 1a). The composite beam comprises two layers, namely, the concrete beam and the composite reinforcement. The internal forces (axial force N , shear force V , and bending moment M ) of the concrete beam and composite reinforcement are denoted with the subscripts 1 and 2, respectively, whereas subscript t is adopted for the internal forces of the composite beam, which are related to the applied load q ( z ) via equilibrium equations. The beam is subjected to the load q ( z )= λ q 0 ( z ), where q 0 ( z ) is a given function that defines the load distribution and the load multiplier λ determines its amplitude. q 0 ( z ) may represent a load per unit length or a system of concentrated forces. The shear force V 2 and the bending moment M 2 of the composite layer are neglected and the axial force N t is zero for the composite beam. The equivalence condition of the internal forces on the composite beam and the internal force of the elements is (Fig. 1b and c)

(

)

1 t G M M N H d = + − 2

(1)

0

1 t V V =

N N + =

1

2

where d G is the distance of the centroid of the concrete cross-section from the extrados of the beam. Since N 2 =- N 1 , the symbol N will be employed to identify N 2 =- N 1 (a positive value of N corresponds to a tensile force in the reinforcement and a compression force in the concrete beam, Fig. 1d). The slip s ( z ) at the interface between the concrete beam and the reinforcement is defined as: ( ) ( ) ( ) = − f c s z u z u z (2)