Experimental and Theoretical Development of Load–Moment Interaction Diagrams of Circular Hollow GFRP-Reinforced Concrete Bridge Columns

Data Availability Statement

Acknowledgments

Notation

A_b

nominal cross-sectional area of the longitudinal GFRP bar and spiral, mm²;

A_ce

effective area of the circular compressive concrete segment, mm²;

A_frp

total area of the longitudinal GFRP bars, mm²;

A_g

cross-sectional area of a concrete column, mm²;

A_ΔF

area under the load–axial deformation response corresponding to the ultimate axial deformation at reinforcement rupture using the trapezoidal rule;

A_Δ1

area corresponding to the limit of the elastic behavior on the ascending part using the trapezoidal rule;

a

depth of the ERSB, mm;

c

neutral-axis distance, mm;

D_in.

inner diameter of the hollow column, mm;

D_out.

outer diameter of the hollow column, mm;

d

distance from the concrete surface on the compression side to the centroid of the outermost bars on the tension side, mm;

d_b

nominal diameter of the GFRP bars, mm;

d_bar

diameter of the circle passing through the centers of the longitudinal GFRP bars, mm;

d_c

depth of the longitudinal bars at row level c on the compression side relative to the extreme concrete fiber, mm;

d_t

depth of the longitudinal bars at row level t on the tension side relative to the extreme concrete fiber, mm;

d_sp

nominal diameter of the GFRP spirals, mm;

E_c

modulus of elasticity of the concrete, MPa;

E_c

modulus of elasticity of steel, MPa;

E_FRP

tensile modulus of elasticity of the FRP bars: E_BFRP for basalt bars; E_CFRP for carbon bars; and E_GFRP for glass bars, MPa;

$E{I}_{\sec }$

secant flexural stiffness, N.mm²;

e

load eccentricity, mm;

e/D_out.

eccentricity-to-outer diameter ratio;

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

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

f_fu

ultimate strength of the FRP reinforcement, MPa;

f_y

yield strength of the steel reinforcement, MPa;

I_g

gross moment of inertia, mm⁴;

K_n

normalized axial force factor;

k

effective length factor;

l_u

unsupported length of the column, mm;

M_n

ultimate carrying bending moment capacity, kN.m;

M_n1

primary bending moment obtained from the initial load eccentricity, kN.m;

M_n2

secondary bending moment obtained from the second-order effect, kN.m;

N_bar

total number of longitudinal bars;

P_conc.

ultimate load-carrying capacity for concentric columns, kN;

P_e

ultimate load-carrying capacity for eccentric columns, kN;

P_n

ultimate load-carrying capacity, kN;

P_o

nominal pure axial force (taken by $P_o=0.85{\alpha }_1{f}_c^{\mathrm{\prime }}(A_g-A_{\mathrm{frp}})$), kN;

P_n,cons.

ultimate load-carrying capacity for Scenario 2 considering bar compressive strength, kN;

P_n,Dis.

ultimate load-carrying capacity for Scenario 1 disregarding bar compressive strength, kN;

R_n

normalized bending moment factor;

r

radius of gyration of the nominal cross section of the longitudinal bars, mm;

r_bar

radius of the circle passing through the centers of the longitudinal GFRP bars, mm;

r_in.

inner radius of the hollow column, mm;

r_out.

outer radius of the hollow column, mm;

s

pitch of continuous spirals, mm;

x_c

clear concrete cover measured from the transverse reinforcement, mm;

${\overline{y}}_{ce}$

distance between the centroid of the concrete segment on the compression side and the centroid of the concrete cross section (Point O), mm;

α₁

ratio of average stress of the ERSB to the specified concrete strength;

β₁

ratio of the distance from the neutral axis to the extreme tension fiber to the distance from the neutral axis to the center of the tensile reinforcement;

δ_L,mid.

midheight lateral displacement at peak load, mm;

${\epsilon }_c$

experimental compressive strain in the outermost longitudinal GFRP bars at a certain load level, mm/mm;

${\epsilon }_t$

experimental tensile strain in the outermost longitudinal GFRP bars at a certain load level, mm/mm;

${\epsilon }_o$

theoretical concrete strain defined by Popovics (1973);

${\epsilon }_{cu}$

ultimate concrete strain, mm/mm;

${\epsilon }_{fd}$

ultimate design tensile strain of the GFRP bars, mm/mm;

${\epsilon }_{\mathrm{frp},c}$

compressive strain in the longitudinal bars at level c;

${\epsilon }_{\mathrm{frp},t}$

tensile strain in the longitudinal bars at level t;

${\epsilon }_{fu}$

ultimate tensile strain in the straight GFRP bars, mm/mm;

λ

slenderness ratio;

ρ_l

longitudinal reinforcement ratio;

ρ_T

transverse confining reinforcement ratio;

μ_F

ductility index; and

ψ_exp.

experimental curvature, rad/m.

References