# Effect of Bond-Slip on Dynamic Response of FRP-Confined RC Columns with Non-Linear Damping
## 1 Introduction  
FRP (Fiber Reinforced Polymer) materials have been widely used in various civil engineering fields due to their superior properties such as light weight, high strength, and corrosion resistance [1; 2; 3; 4], especially in some seismic strengthening of concrete structures [5; 6; 7]. FRP-confined reinforced concrete (FRP-C RC) columns show superior seismic performance [8; 9; 10; 11; 12]. In recent years, many static behavior studies on subjects such as axial compression performance and various calculation models of FRP-confined concrete have been conducted. [PERSON] et al. [13] assessed the performances of 88 existing prediction models by establishing a test database of 730 FRP-confined concrete cylinders tested under monotonic axial compression, and indicated [PERSON] and [PERSON] 2003 model [14] as one of the top performing models. Nevertheless, in the dynamic analysis of FRP-confined concrete, to simplify the engineering calculation, the damping coefficient is generally defined as a constant [15]. For instance, [PERSON] et al. [16] and [PERSON] et al. [17] adopted the constant damping ratio of concrete materials in studying the seismic performance of FRP-confined concrete columns. To the best of the author's knowledge, there are few researches on nonlinear damping of FRP-C RC materials. [PERSON] et al. [18] conducted an experimental and numerical investigation to study the cyclic behavior and the energy dissipation of CFRP-confined square RC columns. [PERSON] and [PERSON] [19] simulated the hysteretic behaviors of two tested FRP-confined circular columns and proposed a six parameter stress-dependent damping model. Based on a damping-stress relation, [PERSON] et al. [20] developed an iterative scheme forthe computations of the non-linear damping and dynamic response of FRP-C RC columns at any given harmonic exciting frequency. In fact, as a composite material, the damping and energy dissipation mechanism of FRP-C RC materials are very complex. A constant damping ratio can't truly represent the complex damping characteristics of actual structures. In addition, it is unreliable if the damping ratio of the FRP-C RC composite structure is still the same as that of ordinary concrete structure. In conclusion, it is necessary to further explore the damping and dynamic characteristics of FRP-C RC materials and structures. On the other hand, there are many failure modes of FRP-C RC members under loading, including \"premature\" tensile failures of FRP jacket studied by [PERSON] et al. [21], concrete cover spalling, reinforcement buckling described by [PERSON] et al. [22], and bond-slip stated by [PERSON] and [PERSON] [23], in addition to the bearing capacity failure. [PERSON] et al. [24] have presented an analytical model to directly evaluate the FRP strain efficiency factor as the strain ratio between the effective FRP hoop strain at failure and the flat coupon test outcomes. However, this paper focuses on capturing the bond slip due to strain penetration along fully anchored bars into FRP-confined concrete columns footings and assumes that FRP fails when hoop strain in the jacket reaches its ultimate tensile strain determined according to flat coupon tests. The bond-slip between steel bar and concrete has influences on cyclic performance of reinforced concrete (RC) structures [25; 26; 27]. The research of [PERSON] et al. [28; 29] indicated that the deformation component associated with bar slippage in elements with plain bars may contribute to 80-90% of the elements' overall deformability. For a reinforced concrete column subjected to seismic load, localized inelastic deformation easily occurs at the column foot where the stress gradient is higher, due to reinforcement slip. This slip results from strain penetration along a portion of the fully anchored bars into the adjoining concrete members [30].