Consistency of Bond–Slip Models in Simulating the Bond between ETS-FRP Bars and Concrete and the Shear Contribution of the Strengthening System

Data Availability Statement

Acknowledgments

Notation

A_f

cross-sectional area of the ETS-FRP bar (mm²);

A_sw

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);

d_f

ETS-FRP bar diameter (mm);

d_g

aggregate size (mm), taken as 10 mm for all specimens;

d_sw

steel stirrup diameter (mm);

E_a

elastic modulus of adhesive (MPa);

E_f

elastic modulus of ETS bars (MPa);

E_sw

elastic modulus of transverse steel (MPa);

E_s

elastic modulus of steel longitudinal reinforcement (GPa);

$f_c^{\mathrm{\prime }}$

concrete compressive strength (MPa);

f_ct

concrete tensile strength (MPa);

f_ctm

concrete fracture strength (MPa);

G_f

bond fracture energy (N/mm);

$G_f^c$

fracture energy for concrete cracking (N/mm);

h

beam height (mm);

J₁

geometry constant (mm/N);

k_f

model factor, taken as 1.0 for 440.1R-17 (ACI 2017) and 7/8 for JSCE (2007);

k_p

factor depending on prestress, taken as 1.0;

L

length of the beam measured from support to support (mm);

L_e

embedment length (mm);

L_fi

length of the affected ETS bar (mm);

$\overline{L_{fi}}$

average length of bonded region for all affected ETS bars (mm);

L_Rfe

effective length of the stress-resisting bonded region (mm);

L_Rfi

length of the stress-resisting bonded region (mm);

N_f

number of affected ETS bars;

P_fi

bonding force for the affected ETS bar (kN);

P_{f_avg}

bonding force determined by the average embedment length (kN);

p_f

length of the perimeter of the ETS-FRP bar (mm);

r_b

bending radius of the ETS bar (mm);

S_mθ

shear crack spacing (mm);

S_{x_e}

effective crack spacing (mm);

s

slip between the ETS bar and concrete (mm);

s₁, s₂, s₃

slip values for defining bond models (mm);

s_cr

crack slip (mm);

s_ctrl

slip for concrete fracture based on TR55 guidelines (mm);

s_d

slip at complete debonding for the ETS-FRP bar–concrete bond interface (mm);

s_ETS

slip of ETS bar from concrete (mm);

s_m

slip at peak bond stress (mm);

s_f

ETS spacing (mm);

s_sw

stirrup spacing (mm);

x_fi

is_f = distance from the end of the main crack plane to the end of the ith FRP bar passing the critical crack plane (mm);

V_f

shear contribution of ETS strengthening bars (kN);

w_ci

crack width due to concrete aggregate interlocking (mm);

w_ETS

crack width due to the ETS system (mm);

w_sw

crack width due to stirrups (mm);

β

inclination of ordinary steel stirrups or ETS-FRP bars (°);

λ

bond constant (N/mm³);

Δ_c

displacement of the critical loading zone (mm);

ɛ

strain at the ETS bar–concrete interface;

ɛ_fe

effective strain in the ETS-FRP strengthening system at the ultimate stage of the beam;

ɛ_f,u

ultimate strain on ETS bars;

ɛ_sw

strain of steel stirrups;

ɛ_t,avg

average strain in flexural reinforcement;

ρ_sw

steel stirrup ratio;

ρ_f

ETS bar ratio;

ρ_l

percentage of steel longitudinal reinforcement;

η

reduction factor for the embedment length;

θ_initial

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;

τ_c

shear stress on the crack surface (MPa);

τ_m (τ_{m_ETS})

maximum bond stress between the ETS bar and concrete (MPa); and

τ_res

residual bond stress between the ETS bar and concrete (MPa).

References