Flexural Behavior and Design of Ultrahigh-Performance Concrete Beams Reinforced with GFRP Bars

Data Availability Statement

Acknowledgments

Notation

A_f

area of tensile FRP reinforcements;

a

shear span;

b

beam width;

c_b

depth of the neutral axis;

c₀

depth between the neutral axis and the position where ${\epsilon }_{c0}$ is located;

d

effective depth;

E_c

elastic modulus of UHPC;

E_el

elastic energy;

E_tot

total energy;

f_cr

cracking tensile strength of UHPC;

f_cu

compressive strength of UHPC;

f_f

tensile stress in FRP;

f_fu

ultimate tensile strength of FRP;

f_tu

ultimate tensile strength of UHPC;

h

depth of the beam section;

I_cr

transformed moment of inertia of the cracked section;

I_g

gross moment of inertia of uncracked section;

I_e

effective moment of inertia;

L

clear span;

l_f

length of steel fiber;

M_a

applied bending moment;

M_cr

cracking moment;

M_cr,pred

predicted cracking moment;

M_n

maximum moment;

M_n,pred

predicted maximum moment;

M_u

ultimate moment;

P

applied load;

V_f

steel fiber volume fraction;

y_t

distance from neutral axis to extreme tension fiber;

σ

stress in UHPC;

ɛ

strain in UHPC;

${\epsilon }_{\mathrm{cf}}$

UHPC strain at the extreme compression fiber of the section;

${\epsilon }_{\mathrm{cu}}$

ultimate compressive strain of UHPC;

${\epsilon }_{c0}$

UHPC compressive strain at which the compressive strength is reached;

${\epsilon }_f$

tensile strain in FRP;

${\epsilon }_{\mathrm{fu}}$

ultimate tensile strain of FRP;

ɛ_t,cr

cracking tensile strain of UHPC;

ɛ_t,loc

localization strain of UHPC;

ɛ_t,lim

UHPC tensile strain at which the tensile stress is reduced to zero;

Δ

midspan deflection;

Δ_cr

cracking deflection;

Δ_peak

deflection corresponding to the maximum capacity;

Δ_s

service deflection;

Δ_s,pred

predicted service deflection;

Δ_u

ultimate deflection;

μ_e

energy-based ductility index;

ζ

plastic influence coefficient;

ρ

flexural reinforcement ratio;

ρ_b

balanced reinforcement ratio;

ρ_min

minimum FRP reinforcement ratio required to ensure progressive failure; and

γ

factor that depends on the boundary conditions and the type of applied load.

References