Investigation on the Impact Response of Concrete Beams Reinforced with Hybrid Steel–BFRP Bars

Acknowledgments

Notation

A_f

area of the BFRP reinforcement;

A_s

area of the steel reinforcement;

D

double-layer reinforcement concrete beam;

d

damage variable for concrete;

E

modulus of elasticity of materials;

E₀

initial modulus of elasticity of concrete;

E_fB

elastic modulus of BFRP reinforcement;

E_fB

static modulus of BFRP reinforcement;

E_fB,dyn

dynamic modulus of BFRP reinforcement;

E_P

plastic hardening modulus of steel reinforcement;

E_t

plastic tangent modulus of steel reinforcement;

f₀

frequency of an undamaged member;

f₁

frequency of a damaged member;

f_c

compressive strength of concrete;

f_cm

mean compressive strength of concrete;

f_fd

design tensile strength of the BFRP reinforcement;

f_fu

ultimate stress of the BFRP reinforcement;

f_fu,dyn

dynamic tensile strengths of BFRP reinforcement;

f_t

tensile strength of concrete;

f_u

ultimate stress of the BFRP and steel reinforcement;

f_y

yield strength of the steel reinforcement;

f_y

yield stress of steel reinforcement;

f_y,dyn

dynamic yield stress of the steel reinforcement;

G_f

fracture energy of concrete;

I

BFRP bars placed inside;

O

BFRP bars placed outside;

S

single-layer reinforcement concrete beam;

t

development time of impact process;

w₁

critical displacement of concrete;

α

proportion of the BFRP reinforcement area;

β

hardening parameter of steel reinforcement;

ɛ₀

yield strain of steel reinforcement;

${\dot{\epsilon }}_0$

compressive strain rates of concrete;

${\dot{\epsilon }}_0$

static tensile strain rates of concrete;

${\epsilon }_{c0}$

compressive strain of concrete;

${\dot{\epsilon }}_{c0}$

static compressive strain rates of concrete;

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

elastic strain of concrete;

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

plastic strains of concrete;

${\epsilon }_{\mathrm{eff}}$

equivalent plastic strain of steel reinforcement;

${\dot{\epsilon }}_f$

strain rates of BFRP reinforcement;

${\epsilon }_{fu}$

ultimate strain of the BFRP reinforcement;

${\dot{\epsilon }}_s$

strain rate of steel reinforcement;

${\epsilon }_t$

strain of BFRP reinforcement;

${\dot{\epsilon }}_{t0}$

static tensile strain rates of concrete;

${\epsilon }_{t0}$

tensile strains of concrete;

${\epsilon }_u$

ultimate strain of the BFRP and steel reinforcement;

ρ

density of materials;

σ_f

stress of BFRP reinforcement;

σ_c,dyn

dynamic compressive strength of concrete;

σ_c0

ultimate compressive tresses of concrete;

σ_t

tensile stress of concrete;

σ_t,dyn

dynamic tensile strength of concrete;

σ_t0

ultimate tensile stress of concrete; and

ν

Poisson’s ratio of materials.

References