FRP Strips Externally Bonded to Quasi-Brittle Substrates: Discussions and Advances of Open Research Topics

Data Availability Statement

Acknowledgments

Notation

A_f

cross-sectional area of the FRP strip used in the RC beam;

b

width of the substrate in a single-lap specimen;

b_b

brick length;

b_f

width of the FRP strip;

d_G

depth of the centroid of the concrete layer measured from the top of the RC beam;

d_n

depth of the neutral axis from the top of the RC beam;

E_c

elastic modulus of concrete;

E_f

elastic modulus of the composite strip;

F

force applied to an RC beam in a four-point bending test (Fig. 12);

F_f

maximum force in the composite strip of full-scale RC beams strengthened in flexure with FRP;

$f_t^{\mathrm{\prime }}$

tensile strength of concrete;

G_F

interfacial fracture energy;

$G_F^b$

fracture energy of the FRP–brick interface;

$G_F^m$

fracture energy of the FRP–mortar interface;

$G_F^{P_{\mathrm{deb}}}$

fracture energy computed directly from experimental P_deb;

g

global slip in a single-lap test;

g_K

global slip at Point K of the load response of a single-lap test (Fig. 9);

g₁

global slip corresponding to P_deb;

g₂

global slip corresponding to the P(g) curve plateau;

$\overline{g}$

generic global slip in a single-lap test, with $\overline{g}\le g_1$;

H

height of the RC beam cross section;

k

ratio of the bending moments at two consecutive cracked cross sections in an RC beam;

L_eff

effective bond length;

$L_{\mathrm{eff}}^b$

effective bond length of the FRP–brick interface;

L_eff,i

value of L_eff for a certain substrate named substrate i, with i = 1, 2, …, 5;

M₁

bending moment in the concrete layer of the RC beam;

M_t

bending moment at the cross section of the RC beam;

N_c(z)

resultant force in concrete (compression) at coordinate z for the RC beam (Fig. 12);

N_f(z)

resultant force in the FRP composite at coordinate z for the RC beam (Fig. 12);

N_f,A

force in the FRP composite at coordinate z_A for the RC beam;

N_f,B

force in the FRP composite at coordinate z_B for the RC beam;

N_L

FRP axial force at the LCCS in the RC beam;

${\overline{N}}_L$

maximum value of N_L;

N_R

FRP axial force at the RCCS in the RC beam;

${\overline{N}}_R$

maximum value of N_R;

N_s(z)

resultant force in steel rebars at coordinate z for the RC beam (Fig. 12);

N₀

force in the FRP composite at coordinate z_f for the RC beam;

P

applied load in a single-lap test;

P_deb

plateau load, load-carrying capacity, or bond capacity in a single-lap test;

$P_{\mathrm{deb}}^b$

plateau load for the FRP–brick interface in a single-lap test;

P_deb,i

value of P_deb for a certain substrate named substrate i, with i = 1, 2, …, 6;

P_max

maximum load in a single-lap test;

P_PT

periodically transferred load at the FRP–masonry interface in a single-lap test;

$P^{*}$

maximum load (global slip-controlled test) in a single-lap test;

$P_{\mathrm{deb}}^{\mathrm{theor}}$

theoretical bond capacity in a single-lap test;

q

applied load on the RC beam;

s

interfacial slip used as an alternative notation to s_y;

s₀

slip corresponding to τ_max;

s_A

interfacial slip at coordinate z_A for the RC beam;

s_B

interfacial slip at coordinate z_B for the RC beam;

s_f

slip corresponding to τ = 0;

s_fi

value of s_f for a certain substrate, named substrate i, with i = 1, 2, …,6;

s_i

slip at the FRP–substrate interface when the CML is τ_i(s), with i = 1, 2, …, 6;

s_L

slip at the LCCS in the RC beam;

s_R

slip at the RCCS in the RC beam;

s_y

slip at the FRP–substrate interface;

t_f

thickness of the FRP strip;

u

displacement measured on the external surface of the FRP as an alternative notation to u_y;

u_y

displacement measured on the external surface of the FRP;

w

crack opening (Mode I softening curve of concrete);

w_P

crack opening at Point P in Fig. 15(a);

x

reference axis orthogonal to the fibers in the plane of the interface in direct shear test specimens;

y

reference axis in the fiber direction in the plane of the interface in direct shear test specimens;

y₀

coordinate that identifies the beginning of the finite-length STZ (toward the free end);

y₁

coordinate that identifies the end of the finite-length STZ (toward the loaded end);

y_ji

coordinate that identifies the location of the mortar joint, with i = 1, 2, …,4 (Fig. 6);

z

longitudinal reference axis for beams;

z_A

coordinate of Cross section A of an RC beam;

z_B

coordinate of Cross section B of an RC beam;

z_f

coordinate at the end of the debonded part of the FRP strip;

z₁

coordinate that identifies the beginning of a segment that includes a flexural crack in an RC beam (Fig. 12);

z₂

coordinate that identifies the end of a segment that includes a flexural crack in an RC beam (Fig. 12);

γ

shear strain (Fig. 7);

γ_xy

shear strain in the FRP strip due to the width effect (Fig. 10);

ΔL

elongation of a concrete tensile specimen;

Δs_i

difference of slips corresponding to the beginning and end of the mortar joint (Fig. 6), with i = 1, 2;

Δz

distance between two consecutive cracks in the FRP-strengthened RC beam;

δ

deflection of an RC beam in a four-point bending test (Fig. 12);

$\epsilon$

longitudinal strain of the FRP stip, used as an alternative notation to ${\epsilon }_y$;

${\epsilon }_c$

longitudinal strain in concrete in tension;

${\epsilon }_{c,P}$

strain in concrete bulk at Point P in Fig. 15(a);

ɛ_i

FRP strain when the CML is τ_i(s), with i = 1, 2, …,6;

${\epsilon }_y$

longitudinal strain of the FRP stip;

ζ

variable that identifies a location along the bonded length, defined as $\zeta =y\sqrt{\phi /\psi }$;

$\mathit{\ell }$

bonded length of the FRP strip;

${\mathit{\ell }}_d$

length of debonded FRP strip;

ξ

length of the STZ when the shear stress transfer is not fully established;

σ

axial stress in the FRP strip, used as an alternative notation to σ_y;

σ_c

axial stress in concrete in a tension test;

σ_c,P

axial stresses in concrete bulk at Point P in Fig. 15(a);

σ_t

normal stresses at the FRP–substrate interface;

σ_y

axial stress in the FRP strip;

τ

shear stress at the FRP–substrate interface, used as an alternative notation to τ_zy;

τ₀

shear stress corresponding to s = 0 when the first part of Condition C2 is satisfied;

τ_i

shear stress at the FRP–substrate interface for a certain substrate named substrate i, with i = 1, 2, … 6;

τ_max

maximum shear stress in the CML;

τ_zy

shear stress at the FRP–substrate interface;

φ

positive scalar number [Eq. (14)];

χ

curvature of the RC beam;

ψ

positive scalar number [Eq. (14)]; and

Ω

area between the FRP–brick and FRP–mortar CMLs corresponding to the slips at the beginning and end of the mortar joint.

References