A Strut-and-Tie Model for Predicting the Shear Strength of Exterior Beam–Column Joints Strengthened with Fiber-Reinforced Polymers

Data Availability Statement

Notation

A_fh

area of horizontal FRP (mm²);

A_fv

area of vertical FRP (mm²);

A_jh

area of transverse reinforcement (stirrup) in the joint region (mm²);

A_jv

area of the column intermediate reinforcement (mm²);

A_sb

area of the top and bottom reinforcement of the beam (mm²);

A_st

cross-sectional area of tensile beam reinforcement (mm²);

A_strut

effective area of the diagonal strut (mm²);

b_b

beam width (mm);

b_c

column width (mm);

b_j

effective joint width (mm);

C_strut

compression force in the diagonal strut (N);

d_b

beam internal lever arm (mm);

E_f

tensile modulus of elasticity of FRP (MPa);

f₁

principal tensile stress at the mid-depth of the joint (MPa);

f_ce

effective compressive strength of the concrete in a strut (MPa);

f_yb

yield strength of beam reinforcement (MPa);

f_yh

yield strength of transverse reinforcement (stirrup) in the joint region (MPa);

f_yv

yield strength of the column intermediate reinforcement (MPa);

$f^{\mathrm{\prime }}{c}_{}$

specified compressive strength of concrete (MPa);

H_b

beam depth (mm);

H_c

column depth (mm);

k

nondimensional function;

L_b

beam length (mm);

L_c

total column height (mm);

N_c

axial force acting on the column (N);

n_fh

number of FRP layers;

n_p

number of joint panel sides strengthened in shear with FRP systems in the plane of the load;

n_str

number of strips on the joint panel;

R_d

ratio of the joint shears resisted by the diagonal mechanism;

R_h

ratio of the joint shears resisted by the horizontal mechanism;

R_v

ratio of the joint shears resisted by the vertical mechanism;

T

tensile force resulting from the beam longitudinal (N);

t_f

thickness of the FRP reinforcement (mm);

V_b

maximum recorded shear force on the beam (N);

V_h,strut

contribution of the concrete diagonal strut mechanism to horizontal joint shear strength (N);

V_jh

horizontal joint shear strength (N);

V_jh,EXP

experimental horizontal joint shear strength (N);

V_jh,STM

strut-and-tie model horizontal joint shear strength (N);

V_jv

vertical joint shear strength (N);

V_th

contribution of horizontal mechanism to the joint shear strength (N);

V_tv

contribution of vertical mechanism to the joint shear strength (N);

V_u

design shear force (N);

W_b

depth of the compression zone in the beam (mm);

W_c

depth of the compression zone in column (mm);

W_s

diagonal strut width (mm);

W_fh

horizontal FRP width (mm);

W_fv

vertical FRP width (mm);

W_str

strip width (mm);

x

distance of the column edge beyond the edge of the beam (mm);

y_f

FRP strength reduction factor;

α₁

angle of direction of horizontal FRP relative to the horizon;

α₂

angle of direction of vertical FRP relative to the horizon;

β_c

strut-and-node confinement modification factor;

β_s

strut coefficient or concrete softening coefficient;

γ

bond factor;

γ_h

fraction of horizontal shear transferred by the horizontal tie with the absence of the vertical tie;

γ_v

fraction of vertical shear carried by the vertical tie with the absence of the horizontal tie;

Δf₁

principal tensile stress corresponding to the FRP contribution to the shear strength (MPa);

δ_c

correction factor for the diagonal mechanism;

δ_h

correction factor for the horizontal mechanism;

δ_v

correction factor for the vertical mechanism;

${\delta }_h^{\mathrm{FRP}}$

correction factor for the horizontal mechanism for FRP-strengthened joints;

${\delta }_s^{\mathrm{FRP}}$

correction factor for the diagonal mechanism for FRP-strengthened joints;

${\delta }_v^{\mathrm{FRP}}$

correction factor for the vertical mechanism for FRP-strengthened joints;

ɛ_fe

effective strain in FRP reinforcement;

θ

inclination angle of the diagonal compression strut;

θ₁

inclination angle of the flat strut;

θ₂

inclination angle of the steep strut;

λ

bond factor which depends on the bond behavior of beam reinforcement;

ν_jh

net horizontal shear stress at mid-depth of the joint core (MPa);

σ_c

column axial stress (MPa);

ϕ_v

shear strength reduction factor;

Ψ

nondimensional function;

ω_b

beam reinforcement index;

ω_h

horizontal reinforcement index; and

ω_v

vertical reinforcement index.

References