Consistency of Bond–Slip Models in Simulating the Bond between ETS-FRP Bars and Concrete and the Shear Contribution of the Strengthening System
Publication: Journal of Composites for Construction
Volume 28, Issue 4
Abstract
Predicting the shear contribution of a fiber-reinforced polymer (FRP) strengthening system in a reinforced concrete (RC) beam strengthened using the embedded through-section (ETS) method remains challenging due to the complex shear mechanisms involved. The present study proposes a new approach that analyzes the shear resistance mechanism for ETS-FRP strengthening bars by investigating their bonding behavior with concrete. First, the consistency of existing bond models and parameters for simulating the bond profile for ETS-FRP bar-to-concrete joints was studied using a simplified finite discretization method (FDM). After validation using pullout tests, the maximum bond stress, slip at peak bond stress, and slip at complete debonding were found to be consistent for all bond laws. This allows researchers and engineers to conveniently obtain suitable bond parameters for their designs. A bonding-based approach coupled with the FDM that considers various bond rules and crack compatibility for analysis of the ETS shear contribution was then developed. The proposed approach can analyze the behavior and failure progress for single ETS strengthening elements. Based on corroboration using 46 sets of beam data, the proposed method was found to more accurately predict the ETS-FRP shear contribution than current shear design models. The results of this study indicate that using the proposed method, the ETS shear resistance can be reliably estimated by applying bilinear, trapezoidal, and nonlinear bond laws considering the compatibility of nonuniform crack widths.
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Data Availability Statement
All data, models, and codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors acknowledge the resources and facilities provided by Tokyo City University.
Notation
The following symbols are used in this paper:
- Af
- cross-sectional area of the ETS-FRP bar (mm2);
- Asw
- cross-sectional area of the two-legged steel stirrup (mm2);
- a
- shear span length of the beam (mm);
- B
- parameter representing bond ductility (1/mm);
- b
- beam width (mm);
- d
- effective beam depth (mm);
- df
- ETS-FRP bar diameter (mm);
- dg
- aggregate size (mm), taken as 10 mm for all specimens;
- dsw
- steel stirrup diameter (mm);
- Ea
- elastic modulus of adhesive (MPa);
- Ef
- elastic modulus of ETS bars (MPa);
- Esw
- elastic modulus of transverse steel (MPa);
- Es
- elastic modulus of steel longitudinal reinforcement (GPa);
- concrete compressive strength (MPa);
- fct
- concrete tensile strength (MPa);
- fctm
- concrete fracture strength (MPa);
- Gf
- bond fracture energy (N/mm);
- fracture energy for concrete cracking (N/mm);
- h
- beam height (mm);
- J1
- geometry constant (mm/N);
- kp
- factor depending on prestress, taken as 1.0;
- L
- length of the beam measured from support to support (mm);
- Le
- embedment length (mm);
- Lfi
- length of the affected ETS bar (mm);
- average length of bonded region for all affected ETS bars (mm);
- LRfe
- effective length of the stress-resisting bonded region (mm);
- LRfi
- length of the stress-resisting bonded region (mm);
- Nf
- number of affected ETS bars;
- Pfi
- bonding force for the affected ETS bar (kN);
- Pf_avg
- bonding force determined by the average embedment length (kN);
- pf
- length of the perimeter of the ETS-FRP bar (mm);
- rb
- bending radius of the ETS bar (mm);
- Smθ
- shear crack spacing (mm);
- Sx_e
- effective crack spacing (mm);
- s
- slip between the ETS bar and concrete (mm);
- s1, s2, s3
- slip values for defining bond models (mm);
- scr
- crack slip (mm);
- sctrl
- slip for concrete fracture based on TR55 guidelines (mm);
- sd
- slip at complete debonding for the ETS-FRP bar–concrete bond interface (mm);
- sETS
- slip of ETS bar from concrete (mm);
- sm
- slip at peak bond stress (mm);
- sf
- ETS spacing (mm);
- ssw
- stirrup spacing (mm);
- xfi
- isf = distance from the end of the main crack plane to the end of the ith FRP bar passing the critical crack plane (mm);
- Vf
- shear contribution of ETS strengthening bars (kN);
- wci
- crack width due to concrete aggregate interlocking (mm);
- wETS
- crack width due to the ETS system (mm);
- wsw
- crack width due to stirrups (mm);
- β
- inclination of ordinary steel stirrups or ETS-FRP bars (°);
- λ
- bond constant (N/mm3);
- Δc
- displacement of the critical loading zone (mm);
- ɛ
- strain at the ETS bar–concrete interface;
- ɛfe
- effective strain in the ETS-FRP strengthening system at the ultimate stage of the beam;
- ɛf,u
- ultimate strain on ETS bars;
- ɛsw
- strain of steel stirrups;
- ɛt,avg
- average strain in flexural reinforcement;
- ρsw
- steel stirrup ratio;
- ρf
- ETS bar ratio;
- ρl
- percentage of steel longitudinal reinforcement;
- η
- reduction factor for the embedment length;
- θinitial
- initial angle of the crack (°), taken as 35° for shallow beams and 45° for deeper beams;
- θ
- angle of the crack (°);
- τ0
- bond strength for concrete fracture based on TR55 guidelines (MPa), taken as 15 MPa;
- τc
- shear stress on the crack surface (MPa);
- τm (τm_ETS)
- maximum bond stress between the ETS bar and concrete (MPa); and
- τres
- residual bond stress between the ETS bar and concrete (MPa).
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Received: Jul 22, 2023
Accepted: Feb 15, 2024
Published online: Apr 30, 2024
Published in print: Aug 1, 2024
Discussion open until: Sep 30, 2024
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