Effect of Transverse Reinforcement Ratios and Configurations on the Behavior of Hollow Circular Concrete Columns Reinforced with GFRP under Concentric Loading

Acknowledgments

Notation

A_b

nominal cross-sectional area of a longitudinal bar or a transverse FRP spiral/hoop, mm²;

A_cc

area of a concrete core delimited by hoop or spiral centerlines, excluding the longitudinal bar area, mm²;

A_cH

concrete cross-section area for a hollow column, mm²;

A_cS

concrete cross-section area for a solid column, mm²;

A_e

effective area of a confined concrete core, mm²;

A_frp

total area of longitudinal GFRP bars, mm²;

A_g

gross cross-sectional area of a concrete column, mm²;

D_e

effective diameter of a confined concrete core.;

D_in.

inner diameter of a hollow column, mm;

D_out.

outer diameter of a hollow column, mm;

D_s

diameter of a hoop or a continuous spiral, mm;

d_b

nominal diameter of GFRP bars and spirals, mm;

E_FRP

tensile modulus of elasticity of GFRP bars, MPa;

f_b

strength of a bent portion of GFRP bars, MPa;

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

specified compressive strength of a concrete cylinder at 28 days, MPa;

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

confined concrete strength, Mpa;

$f_{cc,\mathrm{Exp}.}^{\mathrm{\prime }}$

experimental maximum confined concrete stress, Mpa;

$f_{cc,\mathrm{Th}.}^{\mathrm{\prime }}$

theoretical confined concrete stress, Mpa;

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

in-place compressive strength of unconfined concrete, MPa;

f_fu

ultimate strength of FRP reinforcement, MPa;

f_l

confining lateral pressure, MPa;

f_y

yield strength for steel reinforcement;

k

effective length factor;

k_c

coefficient representing the efficiency of transverse reinforcement;

k_e

confinement effectiveness coefficient;

k_l

coefficient depends on concrete proprieties and lateral pressure;

k_ɛ

ratio between the average measured spiral strain to the maximum spiral tensile strain;

l_d

development length in tension of GFRP hoops, mm;

l_u

unsupported length of a column, mm;

P_bar,n1

load carried by GFRP bars at the ultimate load, kN;

P_n1

ultimate carrying load capacity, kN;

P_n2

second peak load, kN;

p_o

perimeter of continuous spirals or hoops at centerlines, mm;

P_o

nominal unconfined axial load capacity of a column, kN;

r

radius of gyration for a nominal cross section of longitudinal bars, mm;

r_b

internal radius of a bend in FRP reinforcement, mm;

s

hoop spacing or a pitch of continuous spirals, mm;

s′

clear vertical distance between a spiral’s coil and a hoop’s level, mm;

α₁

ratio of average stress in a rectangular compression block;

α_f

reduction in the compressive strength of a GFRP bar as function of its tensile strength;

Δ₁

axial deformation corresponding to the limit of elastic behavior, mm;

Δ_F

axial deformation at the reinforcement rupture, mm;

ɛ_o

theoretical concrete strain defined by Popovics (1973);

ɛ_bar,n1

average bar strain at the first peak load, mm/mm;

ɛ_c,n1

average concrete strain at the first peak load, mm/mm;

ɛ_frp2

axial compressive strain of FRP bars at the second peak load, mm/mm;

ɛ_nf,bar

average bar strain at the second peak load, mm/mm;

ɛ_sp.,n1

average spiral strain at the first peak load, mm/mm;

ɛ_sp.,n2

average spiral strain at the second peak load, mm/mm;

λ

slenderness ratio;

μ_F

ductility factor;

ρ_l

longitudinal reinforcement ratio; and

ρ_v

transverse confining reinforcement ratio.

References