Flexural Capacity of Fiber-Reinforced Polymer-Confined Concrete Column–Ring Beam Exterior Joints under Low Cyclic Loading

Acknowledgments

Notation

A_bs

cross-sectional area of the longitudinal tensile reinforcement;

A_r

cross-sectional area of a single ring reinforcement;

A_rs

total area of the ring beam ring reinforcement;

A_sv

cross-sectional area of a single limb of a ring beam stirrup;

$a_s^{\mathrm{\prime }}$

distance between the longitudinal reinforcement resultant point and concrete edge;

b

ring beam width;

b_b

section width of the frame beam;

b_rb

effective width of the failure surface;

D

damage index;

dE

incremental dissipated hysteretic energy;

F_k

tension of longitudinal reinforcement in the frame beams;

F_rh

horizontal tension in the ring reinforcement at the junction of the ring beam and frame beam;

F_sr

radial tension in the stirrups at the junction of the ring beam and frame beam;

F_sv

vertical tension in the stirrups at the junction of the ring beam and frame beam;

$F_k^{\mathrm{\prime }}$

compressive longitudinal reinforcement in the frame beams;

$F_{rh}^{\mathrm{\prime }}$

pressure in the ring reinforcement at the junction of the ring beam and frame beam;

$F_{rh}^c$

estimated horizontal tension in the ring reinforcement at the junction of the ring beam and frame beam;

$F_{sv}^c$

estimated vertical tension in the stirrups at the junction of the ring beam and frame beam;

f_c

axial compressive strength of concrete;

f_yrs

yield strength of the ring reinforcement;

f_yv

yield strength of ring beam stirrups;

h

height of the ring beam;

h₀

effective section height of the ring beam;

h_b

effective height of the ring beam section;

l_r

distance between the resultant points of tension and compression ring reinforcement;

M_j

flexural bearing capacity of the ring beam joint;

$M_j^c$

estimated flexural capacity of PCRBEJs;

$M_j^t$

test data flexural capacity of PCRBEJs;

M_k

design value of the frame beam end bending moment;

M_rc

flexural capacity of concrete at the flexural failure surface at the junction of the ring beam and frame beam;

M_rh

flexural capacity formed by the horizontal tension and pressure in the ring reinforcement at the junction of the ring beam and frame beam;

M_v

flexural capacity generated by the radial tension and vertical tension in the stirrups at the junction of the ring beam and frame beam;

M_vr

flexural capacity generated by the radical stirrups of the ring beam;

M_vv

flexural capacity generated by the vertical stirrups of the ring beam;

M_y

calculated yield strength;

n

axial compression ratio;

P

vertical load on the frame beam end;

P_cr

cracking load;

P_m

peak load;

R₀

calculated radius (the average of R_c and R_j);

R_c

radius of PVC-CFRP-confined concrete columns;

R_j

radius of ring beam joints;

R_x

uniform reaction force of the PVC tube to the ring beam;

R_y

uniform vertical reaction force of ring reinforcement;

S_ABCD

area of the hysteresis loop;

S_AC

horizontal projection length of the main crack extending to the side of the ring beam at the junction of the ring beam and frame beam;

s_f

CFRP strip spacing;

S_OEC

triangular area enclosed by curves of OEC;

S_OFA

triangular area enclosed by curves of OFA;

x

height of compression zone at the failure surface;

x_i

distance between the ith ring reinforcement and the inner surface of the ring beam;

Δ

corresponding vertical displacement;

Δ_y

yield displacement;

α₀

central angle;

α₁

reduction factor of concrete strength;

α_v

calculation coefficient;

β

non-negative parameters;

γ_H

distance among the ring beam stirrups in a circumferential direction;

${\gamma }_1^i$

non-uniform adjustment coefficients corresponding to the first failure modes;

${\gamma }_2^i$

non-uniform adjustment coefficients corresponding to the second failure modes;

δ_M

maximum deformation under seismic load;

δ_u

ultimate deformation under monotonic load;

${\overline{\epsilon }}_{rs}$

average strain in the ring reinforcement at the junction of the ring beam and frame beam;

ɛ_b

strain in the frame beam longitudinal reinforcement at specified positions;

ɛ_r

strain in the ring reinforcement at specified positions;

ɛ_rs

ring reinforcement strain in each layer at the junction of the ring beam and frame beam;

ɛ_s

strain in the ring beam stirrups at specified positions;

θ₁

included angle between the line formed by the frame beam edge passing through the ring beam center and frame beam axis;

θ₂

angle between main cracks on the ring beam surface and the axis of the frame beam;

θ₃

angle between the straight line (OD) and axis of the frame beam;

ξ_ef

equivalent viscous damping ratio;

ρ_b

frame beam longitudinal reinforcement ratio;

ρ_r

ring beam reinforcement ratio;

ω_rs

yield nonuniformity coefficient of ring reinforcement; and

ω_ss

yield nonuniformity coefficient of ring beam stirrups.

References