Prediction of Concrete Cover Separation in Reinforced Concrete Beams Strengthened with FRP

Acknowledgments

Notation

A_st

longitudinal steel tensile reinforcement area (mm²);

A_sv

cross-section area of stirrups (mm²);

A_sw

cross-section area of the shear stirrups (mm²);

a

shear span (mm);

a_L

fictitious shear span (mm);

a_f

distance between the support and the end of the strip (mm);

b

width of the section (mm);

b_c

width of the section (mm);

b_p

width of the FRP soffit plate (mm);

b_v

effective web width (mm);

b_w

width of the section (mm);

d

effective depth of the section (mm);

d_s

effective depth of the section (mm);

d_v

effective shear depth (mm);

E_c

elastic modulus of the concrete (N/mm²);

E_p

elastic modulus of the FRP (N/mm²);

EI_c,0

flexural rigidity of the cracked section without an FRP soffit plate (N/mm²);

EI_c,p

flexural rigidity of the cracked section with an FRP soffit plate (N/mm²);

E_sv

elastic modulus of the stirrups (N/mm²);

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

mean compressive cylinder concrete strength (N/mm²);

f_sy

mean yield strength of stirrups (N/mm²);

f_sy.f

yield strength of the shear stirrups (N/mm²);

f_ywd

yield strength of the shear stirrups (N/mm²);

I_F

second moment of the area of the cracked section transformed to concrete in the case of FRP (mm⁴);

I_P

second moment of the area of the cracked section transformed to concrete in the case of replacing FRP with steel (mm⁴);

k

dimensionless factor;

k_v

factor relating to the degree of shear retention of cracked concrete which is determined following AS 5100.5 (AS 2017a);

L

unplated length of the beam (mm);

S_F

first moment of the area of the cracked section transformed to concrete in the case of FRP (mm³);

S_P

first moment of the area of the cracked section transformed to concrete in the case of replacing FRP with steel (mm³);

s

spacing of the shear stirrups (mm);

s_v

spacing between internal stirrups (mm);

t_p

thickness of the FRP soffit plate (mm);

V_ccs

shear force to initiate CCS failure (N);

V_p

contributions of the FRP soffit plate (N);

V_Rd

shear force at the termination point of the FRP plate (N);

V_Rd,c,fe

shear force required to initiate CCS (N);

V_Rd,c

shear capacity for members not requiring shear reinforcement following EN 1992-1-1 (CEN 2004) (N);

V_Rd,s

shear strength of the RC section including shear reinforcement following BS EN 1992-1-1 (CEN 2004) (N);

V_uc

concrete contribution to shear strength (N);

V_us

contribution of the internal shear steel reinforcement to the shear capacity of the specimen (N);

V_us

steel contribution to shear capacity (N);

W

widths of FRP (mm);

W_m

width of epoxy mortar (mm);

z

inner lever arm (mm);

α_E

dimensionless parameter;

α_flex

dimensionless parameter;

α_t

dimensionless parameter;

${\alpha }_{\omega }$

dimensionless parameter;

γ_c

partial factor for concrete;

Δτ_MOD

modification proposed by the authors (N/mm²);

ɛ_v,e

strain in the steel shear reinforcement;

η

factor equal to 1.4 when designing against all end-debonding failure modes and 1.5 when designing against CCS failure only;

θ_v

angle between the concrete compression strut and the longitudinal axis of the member;

θ

angle between the concrete compression strut and the beam longitudinal axis perpendicular to the shear force;

$\overline{\lambda }$

modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normal weight concrete of the same compressive strength;

ρ_s

longitudinal steel reinforcement ratio;

τ_PES

plate-end shear strength (N/mm²);

τ_Rd

fiber-end shear strength (N/mm²);

τ_Rd

mean nominal maximum shear stress (N/mm²); and

τ

original shear strength according to ACI 318 (ACI 2019) (N/mm²).

References