Method to Identify Stress–Strain Relationship of FRP-Confined Concrete under Eccentric Load

Data Availability Statement

Acknowledgments

Notation

A

area of cross section;

A_Δc

incremental compression area of cross section in ɛ_c < ξ < ɛ_c + Δɛ_c;

A_Δt

incremental tension area of cross section in ɛ_t + Δɛ_t < ξ < ɛ_t;

b

breadth of rectangular section;

c

distance from the extreme compression face to the neutral axis;

E_f

elastic modulus of the FRP jacket;

E_l

confinement stiffness in the lateral direction;

E₁, E₂, f₁, η

parameters in the stress–strain model of Zhou and Wu (2012);

f

stress of concrete at strain ξ;

f_c

concrete stress at the extreme compression face;

${\overline{f}}_c$

mean stress in the range of ɛ_c < ξ < ɛ_c + Δɛ_c;

f_co

concrete compressive strength;

f_l

confinement stress at ɛ_fu;

f_o

transition stress defined by the stress–strain models of FRP-confined concrete;

${\overline{f}}_t$

mean stress in the range of ɛ_t + Δɛ_t < ξ < ɛ_t;

f(ξ)

stress function with respect to strain;

h

depth of cross section;

i

index of iteration;

k

curvature of cross section;

M

bending moment with respect to the neutral axis;

$M_I^{\mathrm{Int}}$

bending moment by integration with respect to the neutral axis for the section in ɛ_t < ξ < ɛ_c, using Eq. (35);

$M_{I,\mathrm{sd}}^{\mathrm{Int}}$

bending moment by integration with respect to the neutral axis for the shaded section shown in Fig. 6;

$M_{I,\mathrm{usd}}^{\mathrm{Int}}$

bending moment by integration with respect to the neutral axis for the unshaded section in the middle region in Fig. 6;

M*

bending moment with respect to the centroid of section;

m_o

M/(bh²);

N

axial force;

$N_I^{\mathrm{Int}}$

axial force by integration for the range of ɛ_t < ξ < ɛ_c, using Eq. (31);

$N_{I,\mathrm{sd}}^{\mathrm{Int}}$

axial force by integration for the shaded region in Fig. 6;

$N_{I,\mathrm{usd}}^{\mathrm{Int}}$

axial force by integration for the unshaded region in Fig. 6;

(N_smoothed, M_smoothed, ɛ_c,smoothed, ɛ_t,smoothed)

corresponding smoothed point of (N_unsmoothed, M_unsmoothed, ɛ_c,unsmoothed, ɛ_t,unsmoothed);

(N_unsmoothed, M_unsmoothed, ɛ_c,unsmoothed, ɛ_t,unsmoothed)

particular point in the data set;

n

number of data point from a set of data;

n_o

N/(bh);

R

radius of circular section;

r

depth of centroid to the extreme compression face;

t_f

thickness of the FRP jacket;

X₊

distance from the y-axis to the positive boundary;

X₋

distance from the y-axis to the negative boundary;

$X_{+}^{\mathrm{\prime }}$

distance from the y-axis to the positive boundary after a load increment;

$X_{-}^{\mathrm{\prime }}$

distance from the y-axis to the negative boundary after a load increment;

x

distance from a point to the y-axis;

y

distance from the neutral axis to a fiber;

y_c

distance from the neutral axis to the extreme compressive face;

y_t

distance from the neutral axis to the extreme tension face;

α

random independent variable;

β_smoothed

smoothed β_unsmoothed;

β_unsmoothed

dependent variable with respect to α;

ɛ_c

strain at the extreme compression face;

${\overline{\epsilon }}_c$

strain where ${\overline{f}}_c$ locates;

ɛ_cc

location of centroid of f(ξ) distribution in the region (ɛ_c, ɛ_c + Δɛ_c);

ɛ_fu

ultimate tensile strain of FRP;

ɛ_o

transition strain defined by the stress–strain models of FRP-confined concrete;

ɛ_t

strain at the extreme tension face;

${\overline{\epsilon }}_t$

strain where ${\overline{f}}_t$ locates;

ɛ_tc

location of centroid of f(ξ) distribution in the region of (ɛ_t + Δɛ_t, ɛ_t); and

ξ

strain of concrete at location x.

References