Flexural Strength and Serviceability of GFRP-Reinforced Lightweight Self-Consolidating Concrete Beams

Acknowledgments

Notation

A_f

area of tension FRP bars (mm²);

$A_f^{\mathrm{\prime }}$

area of compressive FRP bars (mm²);

a

depth of the equivalent rectangular stress block (mm);

a_s

shear span (mm);

b

beam width (mm);

c

distance from the extreme compression fiber to the neutral axis (mm);

c_c

clear concrete cover (mm);

d

distance from the compression face of the concrete to the center of the tension FRP bars (mm);

d_c

distance from the center of the tension bars to the tension face of the concrete (mm);

d′

distance from the compression face of the concrete to the center of the compressive FRP bars (mm);

E_c

modulus of elasticity of concrete (MPa);

E_c-exp

experimental modulus of elasticity of concrete (MPa);

E_f

modulus of elasticity of tension FRP bars (MPa);

$E_f^{\mathrm{\prime }}$

modulus of elasticity of compressive FRP bars (MPa);

E_s

modulus of elasticity of steel bars (MPa);

${\epsilon }_f^{\mathrm{\prime }}$

strain in compressive FRP bars;

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

specified compressive strength of concrete (MPa);

f_f

stress in tension FRP bars (MPa);

$f_f^{\mathrm{\prime }}$

stress in compressive FRP bars (MPa);

f_fs

stress level induced in FRP bars at service loads (MPa);

f_fu

ultimate strength of tension FRP bars (MPa);

h₁

distance from the neutral axis to the center of bar location closest to it (mm);

h₂

distance from the neutral axis to the center of the tension bars (mm);

I_cr

cracking moment of inertia (mm⁴);

I_e

effective moment of inertia (mm⁴);

I_e-exp

experimental value of the effective moment of inertia (mm⁴);

I_g

gross moment of inertia (mm⁴);

I_t

moment of inertia of uncracked section transformed to concrete (mm⁴);

J

deformability factor (called overall performance factor for CSA S6-19, CSA 2019a);

k_b

bond-dependent coefficient;

L

clear span (mm);

L_g

distance from support to point where M_a is M_cr (mm);

M_a

maximum moment in member at stage deflection (kN · m);

M_c

moment at a concrete strain of 0.001 (kN · m);

M_cr

cracking moment (kN · m);

M_cr-exp

experimental cracking moment (kN · m);

M_cr-pred

predicted cracking moment from equations (kN · m);

M_n

nominal moment capacity (kN · m);

M_n-exp

experimental moment capacity (kN · m);

M_n-pred

predicted moment capacity from equations (kN · m);

M_ult

ultimate moment capacity (kN · m);

P

applied concentrated load (kN);

P_exp+self

recorded applied load plus the magnitude of the equivalent load due to the self-weight of the tested beam (kN);

${\rho }_f^{\mathrm{\prime }}$

reinforcement ratio of compressive FRP bars;

s_max

maximum allowable bar spacing for flexural-crack control (mm);

t

height of a beam (mm);

w_cr

maximum permissible crack width (mm);

w_cr-exp

measured crack width (mm);

w_cr-pred

predicted crack width from equations (mm);

y_t

distance from the centroidal axis of the cross section (including the reinforcement) to the extreme fiber in tension;

α

reduction factor;

α_b

bond-dependent coefficient equal to 0.5;

α₁

ratio of average stress in rectangular compression block to the specified concrete strength;

β

reduction factor;

β_d

reduction factor;

β₁

ratio of the depth of rectangular compression block to the depth of the neutral axis;

ϕ_c

resistance factor for concrete;

ϕ_f

resistance factor for FRP;

γ

reduction factor;

γ_c

concrete density (kg/m³);

ɛ_cu

ultimate strain in concrete;

ɛ_f

strain in tension FRP bars;

ɛ_Fu

ultimate strain of FRP bars;

λ

concrete density reduction factor;

ρ_f

longitudinal reinforcement ratio of tension FRP bars;

ρ_fb

balanced reinforcement ratio of FRP bars;

ρ_s

longitudinal reinforcement ratio of steel bars;

δ

deflection (mm);

δ_exp

immediate midspan deflection (included deflection from self-weight of beam) (mm);

δ_pred

predicted deflection from equations (mm);

ψ_c

curvature at a concrete strain of 0.001; and

ψ_ult

ultimate curvature.

References