Flexural Performance and Design of Concrete Beams Reinforced with BFRP and Steel Bars

Data Availability Statement

Acknowledgments

Notation

A_f

area of tensile FRP bars;

A_s

area of tensile steel bars;

a

shear span;

b

width of the cross section;

c

distance from the extreme compression fiber to the neutral axis;

d

depth from the extreme compression fiber to the centroid of longitudinal reinforcements;

d_c

thickness of the concrete cover measured from the tension face to the center of the closest bar;

d_f

depth from the extreme compression fiber to the center of the tensile FRP bars;

d_s

depth from the extreme compression fiber to the center of the tensile steel bars;

d_t

depth from the extreme compression fiber to the centroid of the extreme layer of tension reinforcements;

E_c

elastic modulus of concrete;

E_f

elastic modulus of tensile FRP bars;

E_s

elastic modulus of tensile steel bars;

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

cylinder compressive strength of concrete and equal to 0.8f_cu;

f_cu

cubic compressive strength of concrete;

f_f

tensile stress of FRP bars at failure of the beam;

f_fu

ultimate tensile strength of FRP bars;

f_y

yielding tensile strength of steel bars;

h

total depth of the beam;

I_cr

moment of inertia of the cracked section;

I_e

effective moment of inertia;

I_g

gross moment of inertia;

k_b

bond coefficient that accounts for the bond degree between FRP bars and the surrounding concrete;

k_cr

ratio of c to d after cracking;

L

clear span of the beam;

L_g

distance from one end of the member to the point where M = M_cr;

M_a

applied moment;

M_cr

cracking moment;

M_cr,exp

experimental cracking moment;

M_cr,pre

cracking moment predicted by equations;

M_n

nominal flexural strength;

M_n,exp

experimental flexural strength;

M_n,pre

nominal flexural strength predicted by equations;

M_u

ultimate moment;

M_y

yielding moment;

n_f

ratio of E_f to E_c;

n_s

ratio of E_s to E_c;

P

applied load;

s

spacing of tensile bars;

w_l

crack width at the lower layer, which is at the level of the tensile FRP bars;

w_max

maximum crack width at the bottom;

w_u

crack width at the upper layer, that is, at the level of the tensile steel bars;

y_t

distance from the centroidal axis of the gross section, ignoring reinforcements, to the tension face;

α₁

ratio of the average concrete stress to the concrete strength;

β

ratio of the distance between the neutral axis and the tension face to the distance between the neutral axis and the center of the tensile reinforcements;

β₁

ratio of the depth of the equivalent rectangular stress block to the depth of the neutral axis;

γ

parameter that accounts for the variation in stiffness along the member length;

Δ_cr

deflection at cracking;

Δ_exp

experimental deflection;

Δ_m

midspan deflection;

Δ_pred

predicted deflection;

Δ_u

deflection at the ultimate state;

Δ_y

deflection at yielding;

δ_max

maximum midspan deflection;

ɛ_cu

ultimate compressive strain of concrete;

ɛ_f

tensile strain of FRP bars;

η₁

1−I_cr/I_g;

λ

modifier that considers the reduced tensile-to-compressive strength of lightweight concrete compared with normal weight concrete, and should be taken as 1.0 for normal-weight concrete, 0.85 for sand-lightweight concrete, and 0.75 for all-lightweight concrete;

ρ_f

reinforcement ratio of tensile FRP bars;

ρ_f,b

balanced reinforcement ratio in which concrete crushing and the rupture of FRP bars occur synchronously;

ρ_s

reinforcement ratio of tensile steel bars;

ρ_s,b

balanced reinforcement ratio in which concrete crushing and the yielding of steel bars occur synchronously;

ρ_sf,f

reinforcement ratio for hybrid-RC members and equal to f_y/f_fu · ρ_s + ρ_f; and

ρ_sf,s

reinforcement ratio for hybrid-RC members and equal to ρ_s + E_f/E_s · ρ_f.

References