Effect of Internal Stirrups on the Eccentric Compression Behavior of FRP-Confined RC Columns Based on Finite-Element Analysis

Acknowledgments

Notation

A

cross-sectional area of the column;

A_s

cross-sectional area of longitudinal reinforcement;

A_sh

cross-sectional area of transverse reinforcement;

c

concrete cover thickness;

D

column diameter;

d_a

maximum aggregate size;

d_h

transverse steel diameter;

d_l

longitudinal steel diameter;

d_s

dimension between centerlines of perimeter hoops;

E_c

elastic modulus of concrete;

E_f

elastic modulus of FRP jacket in hoop direction;

E_s

elastic modulus of reinforcement;

E₂

slope of linear second segment of stress–strain curve;

e₀

initial load eccentricity;

e_a

additional load eccentricity;

e_max

maximum eccentricity;

f

midheight lateral deflection;

f_co

compressive strength of unconfined concrete;

f_cc

ultimate axial stress of concrete;

$f_{cc}^{*}$

peak axial stress of concrete under a given constant confining pressure;

f_ls,y

effective confining pressure from transverse reinforcement;

f_t

concrete tensile strength;

f_y

yield strength of longitudinal reinforcement;

f_yh

yield strength of transverse reinforcement;

G_F

fracture energy of concrete;

k_e

confinement effectiveness coefficient;

l₀

effective length of the column;

N_u

ultimate axial load;

n_l

number of longitudinal reinforcement;

n_f

number of FRP layers;

R

radius of the column section;

r_s

distance from the column center to the centers of the longitudinal reinforcement;

S₃₃

axial compressive stresses in the stress contour legend;

s

center to center spacing between stirrups;

s′

clear vertical spacing between stirrups;

t_f

thickness of FRP jacket;

w_cr

crack opening displacement at the complete release of stress or fracture energy;

w_t

crack opening displacement;

2πα

angel corresponding to the depth of equivalent stress block;

α₁

mean stress factor for concrete;

σ_c

axial stress of concrete at compression face;

σ_l

confinement pressure;

σ_t

tensile stress of concrete;

σ_mid

middle principal stress of concrete;

σ_min

minimum principal stress of concrete;

ɛ_co

unconfined concrete compressive strain at peak stress;

${\epsilon }_{cc}^{*}$

concrete axial strain at peak stress under a given constant confining pressure;

ɛ_c

axial compressive strain of concrete;

ɛ_cu

ultimate axial strain of concrete;

ɛ_f

rupture strain of FRP jacket from coupon test;

ɛ_l

lateral strain;

ɛ_s

steel strain;

ɛ_t

axial tensile strain of concrete;

ɛ_y

yield strain of reinforcement;

ɛ_h,rup

FRP hoop rupture strain;

θ

angle from x-axis;

ρ_cc

ratio of cross-sectional area of the longitudinal steel reinforcement to area of core concrete;

ρ_f

confinement stiffness ratio between FRP and transverse reinforcement;

ρ_K

FRP confinement stiffness ratio;

ρ_s

transverse reinforcement ratio;

ρ_ɛ

ratio of ɛ_h,rup to ɛ_co;

λ

column slenderness ratio;

ζ₁

factor that clarify the effect of axial load level on the curvature at balanced failure;

ζ₂

factor that clarify the effect of slenderness on the curvature at balanced failure; and

Δf_cs

increase in the intercept stress due to transverse steel confinement.

References