Rigid body spring network modeling of the tension stiffening of FRP-strengthened RC members

Tension stiffening behavior of post-cracking concrete is an important phenomenon which has been extensively studied for reinforced concrete structures. Although externally bonded fibre reinforced polymer (FRP) composites are widely used for strengthening existing RC structures, it remains unclear to what extent the tension stiffening of post-cracking concrete is quantitatively influenced by the addition of FRP composites, as a result of the bond between the FRP and the concrete substrate. This paper presents a rigid body spring networks (RBSN) model, by which the tension stiffening behavior of concrete in FRP-strengthened RC tensile members was investigated. A two-parameter fracture energy-based model was deployed to represent the bond-slip behavior of the FRP-to-concrete interface. The reliability of the RBSN model was verified through comparisons with previous test results. Further parametric analysis has been conducted to investigate how the bond properties and the end anchorage conditions for the FRP-to-concrete interface influence the tension stiffening behavior of postcracking concrete. 1 GENERAL INTRODUCTION The use of externally bonded fibre reinforced polymer (FRP) composites (e. g. in a sheet/ plate form) to strengthen existing reinforced concrete (RC) structures has gained widespread acceptance in recent years. A significant characteristic of FRP-strengthened RC members is that they usually fail due to premature debonding at the FRP-to-concrete interface. Previous researchers have pursued an accurate debonding strength prediction model for FRP composites in FRP-strengthened RC members (e.g. early work by Wu and Niu 2000, fib 2001 and Teng et al. 2002). Work has also taken place to improve the debonding strength of FRP composites by optimizing the bond configurations, such as (1) the use of near surface mounted FRP reinforcement (De Lorenzis and Nanni 2001); (2) the use of a ductile adhesive bonding or a new type of fibre sheet geometry (Dai et al. 2005a, 2009); and (3) a combination of adhesive bonding and mechanical fasteners (Wu et al. 2009). The bond between FRP composites and concrete substrates influences the ultimate limit state (USL) of FRP-strengthened RC members. Research in recent years has led to a good understanding of the local bond mechanism at the FRP-to-concrete interface. The local bond behavior has also been correlated with the macro debonding behavior of FRP-strengthened RC members, both in flexure and in shear, based upon an empirical approach (e.g. Teng et al. 2002), a fracture mechanics-based approach (e.g. Gunes et al. 2009), an analytical approach (e.g. Dai et al. 2008), or a finite element (FE) approach (e.g. Niu and Wu 2005), with the aim of achieving a refined ultimate limit state (ULS) design. The bond between FRP composites and concrete substrates also influences the serviceability limit state (SLS) of FRP-strengthened RC members, in terms of concrete crack widths, member stiffness and member deformation. It is well known that, in RC structures, taking account of the tension stiffening effect, which results from the bond slip between steel reinforcement and the surrounding concrete, produces more accurate RC member deformation predictions. By now only a limited amount of analytical work (Ferretti and Savoia 2003; Sato and Vecchio 2003) dealt with the fundamental interactions occurring between concrete, steel reinforcement and FRP composites at the FRP-to-concrete and the steel reinforcement-to-concrete bond interfaces. It remains unclear to what extent the tension stiffening of cracked concrete is influenced by the addition of FRP, due to the bond between the FRP and the concrete substrate. This paper presents a two dimensional (2D) rigid body spring networks (RBSN) model for the analysis of the tension stiffening behavior of FRP-strengthened RC members. A fracture energy-based non-linear interfacial model, representing the behavior of the bond between the FRP and the concrete substrate, is incorporated into the program. Upon the validation of the 2D RBSN program, the effects of the bond properties of the FRP–to-concrete interface on the cracking and tension stiffening behavior of concrete and the full-range structural responses of FRP-strengthened RC members were further investigated. 2 RBSN MODELING FOR FRP-STRENGTHENED RC MEMBERS