Experimental Investigation of Short and Slender Rectangular Concrete Columns Reinforced with GFRP Bars under Eccentric Axial Loads

Acknowledgments

Notation

A_f

cross-sectional area of longitudinal FRP reinforcement;

A_fc

area of GFRP bars in the compression side;

A_ft

area of GFRP bars in the tensile side;

A_g

gross cross-sectional area of concrete;

A_st

cross-sectional area of longitudinal steel reinforcement;

d₁

centroid of bars in the compression side;

d₂

centroid of bars in the tensile side;

d_C

distance between the neutral axis and the resultant of the internal compressive forces of concrete;

d_fc

distance between the neutral axis and the centroid of the compressive GFRP bars;

d_ft

distance between the neutral axis and the centroid of the tensile GFRP bars;

e₀

initial eccentricity;

E_c

modulus of elasticity of concrete;

E_f

modulus of elasticity of FRP bars;

E_fc

modulus of elasticity of GFRP bars in compression;

E_ft

modulus of elasticity of GFRP bars in tension;

E_s

modulus of elasticity of steel rebars;

EI

effective stiffness;

EI_D

experimental flexural stiffness corresponding to design strength (when the concrete reaches the design strain of 0.003 mm/mm per ACI 318-19);

EI_GC

experimental flexural stiffness corresponding to crushing of GFRP bars in compression;

EI_i

calculated stiffness based on the ith equation provided in Table 6 (i 1–10);

EI_peak

experimental flexural stiffness corresponding to the peak load;

EI_SP

experimental flexural stiffness corresponding to concrete spalling;

F_C

resultant of internal forces of concrete in compression;

F_fc

internal force of GFRP bars in compression;

F_ft

internal force of GFRP bars in tension;

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

compressive strength of concrete;

$f_{fcu}^{\mathrm{\prime }}$

ultimate crushing strength of GFRP bars in compression;

$f_{ftu}^{\mathrm{\prime }}$

ultimate rupture strength of GFRP bars in tension;

$f_y^{\mathrm{\prime }}$

yield strength of steel rebars;

h

width of column cross section;

I_f

moment of inertia of all GFRP bars in the concrete column;

I_g

moment of inertia of gross cross section of concrete (chamfers are excluded);

I_s

moment of inertia of all steel bars in the concrete column;

k

effective length factor (unbraced length) of the concrete columns;

l

length of the column;

M

bending moment (M P × (e₀ + Δ));

M_C

internal moment resistance due to compressive concrete;

M_CC

bending moment corresponding to concrete crushing;

M_D

experimental moment at the design load (when the concrete reaches the design strain of 0.003 mm/mm at the furthest concrete fiber in compression);

M_{D_1st}

experimental first-order moment calculated at the design load;

M_fc

internal moment resistance due to compressive GFRP bars;

M_ft

internal moment resistance due to tensile GFRP bars;

M_GC

bending moment corresponding to crushing of GFRP bars in compression;

M_u

moment capacity of the specimens at their peak load;

M_ult

ultimate factored moment;

M_{u_1st}

experimental first-order moment calculated at the peak load;

n

modular ratio (the ratio of modulus of elasticity of GFRP bars to concrete);

P

axial load;

P_CC

axial load corresponding to concrete crushing;

P_cr

critical buckling load;

P_D

design load (when the concrete reaches the design strain of 0.003 mm/mm at the furthest concrete fiber in compression);

P_GC

axial load corresponding to crushing of GFRP bars in compression;

P_o

nominal axial strength at zero eccentricity;

P_u

axial capacity of the specimens at their peak load;

P_ult

ultimate factored load;

r

radius of gyration;

Δ

lateral displacement at midspan;

δ

moment magnification factor;

Δ_axial

axial displacement of the specimens at their peak load;

Δ_CC

lateral displacement corresponding to concrete crushing;

Δ_GC

lateral displacement corresponding to crushing of GFRP bars in compression;

Δ_lateral

lateral displacement of the specimens at their peak load;

δ_calc

calculated moment magnification factor;

δ_test

experimental moment magnification factor;

ɛ_CC,c

compressive strain of GFRP bar in compression side corresponding to crushing of concrete;

ɛ_fc

strain of GFRP bars in compression;

ɛ_fcu

ultimate crushing strain of GFRP bars in compression;

ɛ_ft

strain of GFRP bars in tension;

ɛ_ftu

ultimate rupture strain of GFRP bars in tension;

ɛ_GC,c

compressive strain of GFRP bars in the compression side corresponding to crushing of GFRP bars in compression;

ɛ_peak,c

compressive strain of GFRP bars in the compression side corresponding to the peak load;

ɛ_y

yield strain of steel rebars;

λ

slenderness ratio;

ρ

reinforcement ratio; and

ψ

curvature of the column at the midsection.

References