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Cyclic behaviors of reinforced concrete beam-column joints with debonded reinforcements and beam failure: experiment and analysis

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Abstract

It was experimentally validated that partially debonded high-strength longitudinal reinforcement can provide strong self-centering capacity to minimize residual deformation, and greatly mitigate seismic damage of column. To continuously investigate the influence of partially debonded longitudinal rebars (PDLR) of column and beam on seismic behaviors of beam-column joint assembly, three interior and three exterior joint specimens were fabricated to subject to cyclic lateral loading. It was showed experimentally that joint specimens with PDLRs in both beams and columns had slighter seismic damages, smaller stiffness and energy dissipating ratios, better ductility compared with joint specimens without PDLRs in the beams. Furthermore, the lateral load of joint specimens without PDLRs in the beams decreased from lateral drift of about 4.0%–5.0% due to much crushing and spalling of concrete in the compressive zones of the beams. Whereas, joint specimens with PDLRs in the beams had continuously increased lateral load until lateral drift up of 10.0%. An analytical approach was derived to evaluate the lateral behavior of beam-column joint assembly which can considering joint deformation and steel bond slip. The proposed approach can reasonably predict the lateral behaviors of joint specimens with or without PDLRs. Analytical results indicate that approximately 70% of total deformation of joint specimens with PDLRs in both beams and columns is contributed by slippage deformation of the beams, whereas, that contribution ratio of the other joint assembly specimens is only 30%.

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Abbreviations

A st :

Total area of tensile steel rebar

A sc :

Total area of compressive steel rebar

A si :

Total area of longitudinal reinforcement layer i

BI :

Beam reinforcement index (= ρb × fyb)/fc)

B 1 , B 2 :

Resultant carried by compressive concrete of beam section

b :

Width of cross-section

b j :

Effective width of joint

b b :

Width of beam section

b c :

Width of column section

C 1, C 2 :

Resultant carried by compressive concrete of column section

d b :

Diameter of reinforcing bar

E s :

Young’s modulus of steel

E si :

Young’s modulus of longitudinal reinforcement layer i

e :

Eccentricity

E n :

Dissipated energy at each lateral loading cycle

f c :

Measured concrete compression strength of cylinder according to material test

f y :

Yield stress of steel

f yb :

Yield stress of beam reinforcement

f yj :

Yield stress of joint transverse reinforcement

f u :

Ultimate stress

f s :

Stress of tension longitudinal bar

f st :

Resultant forces of tensile longitudinal rebars in a structural section

f sc :

Resultant forces of compressive longitudinal rebars in a structural section

H :

Lateral force resisted by the lateral actuator

h :

Height of cross-section

h eq :

Energy dissipation damping ratio

h c :

Height of column section

h b :

Height of beam section

h 0 :

Effective height of cross-section

JI :

Joint transverse reinforcement index (= ρj × fyj)/fc)

JPR :

Factor for in-plane geometry, 1.0 for interior, 0.588 for exterior and 0.323 for knee joints

JPRU :

Factor with 5/6 reduction to JPR

k e :

Enhanced ratio of moment capacity of cross-section

K i :

Secant stiffness of beam-column joint assembly at lateral loading cycle i

L :

Shear span length

L c :

Shear span of column

L b :

Shear span of beam

l pd :

Designed length of partially debonded steel rebar

l p :

Length of plastic hinge of column

M n :

Moment capacity of cross-section

M c :

Moment resisted by column section

M b :

Moment resisted by beam section

m :

Eccentricity between the beam centerline and the column centroid exceeds bc/8, m = 0.3, other cases, m = 0.5

N′ :

Axial load computed by using Eq. (2)

N :

Axial load applied to cross-section

N c :

Axial load carried by concrete

N s :

Axial load carried by longitudinal reinforcements

n :

Axial load ratio

P my :

Yield flexural strength capacity of beam

R :

Lateral drift

R peak :

Measured lateral drift at Vpeak

R ja :

Total lateral drift of beam-column joint assembly

R cf :

Lateral drift due to flexural deformations of column

R bf :

Lateral drift due to flexural deformations of beam

R cs :

Lateral drift due to slip deformations of column

R bs :

Lateral drift due to slip deformations of beam

R f :

Lateral drift due to flexural deformation (Rcf or Rbf)

R s :

Lateral drift due to slip deformation (Rcs or Rbs)

T c1 ,T c2 :

Resultant tensile forces of longitudinal rebars of columns

T b1 ,T b2 :

Resultant tensile forces of longitudinal rebars of beams

u :

Bond strength of steel rebar

V :

Shear force

+ V i,max :

Positive lateral force at lateral loading cycle i

− V i,max :

Negative lateral force at lateral loading cycle i

V n :

Nominal shear resistant capacity of joint

V b :

Shear force resisted by beam section

V c :

Shear force resisted by column section

V peak :

Average measured peak lateral force

v j,h :

Shear stress of joint in the transverse direction

v j,v :

Shear stress of joint in the longitudinal direction

v j :

Horizontal shear stress calculated according to the Kim and LaFave model

W e1 :

Equivalent area of positive half of loop

W e2 :

Equivalent area of negative half of loop

X n :

Neutral depth of compressive zone of concrete

X nc :

Neutral depth of column section

y i :

Distance of longitudinal reinforcement layer i to the most out end of cross-section

ε y :

Yield strain

Ψ :

Elongation ratio steel

Δ :

Displacement at the loading point of column

+ Δ i,max :

Lateral displacement at + Vi,max

− Δ i,max :

Lateral displacement at − Vi,max

ϕ :

Curvature of column section in hinge region

ε s :

Tensile strain of longitudinal rebar at beam-column intersection

ε si :

Strain of longitudinal reinforcement layer i

ε c :

Any concrete strain at the most out fiber

ε cb :

Any concrete strain at the most out fiber of beam section

ε cc :

Any concrete strain at the most out fiber of column section

ε c0 :

Concrete strain at peak stress

σ(ε c ) :

Concrete stress at any strain εc

γ j :

Shear strain of joint

γ n :

Factor accounting for the effect of geometry in-plane

П :

Factor of power function of neutral depth

Г :

Factor of power function of neutral depth

α γt :

= (JPRU)2.1 is the parameter for describing in-plane geometry

α t :

Parameter for describing in-plane geometry: 1.0 for interior connections, 0.7 for exterior connections, and 0.4 for knee connections

β :

Coefficient of equivalent neutral depth of compressive zone of concrete

β t :

Parameter for describing out-of-plane geometry: 1.0 for subassemblies with zero or one transverse beam, and 1.18 for sub-assemblies with two transverse beams

β γt :

Parameter for describing out-of-plane geometry (1.0 for subassemblies with zero or one transverse beam, and 1.4 for subassemblies with two transverse beams)

η t :

= (1 − e/bc)0.67, describes joint eccentricity (1.0 for no eccentricity)

η γt :

= (1 − e/bc)0.6, describes joint eccentricity (1.0 for no eccentricity)

ρ b :

Beam reinforcement ratio

ρ j :

Volumetric joint transverse reinforcement ratio in the direction of loading

θ :

Lateral drift angle of specimen

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Acknowledgements

The research reported herein was supported by the National Natural Science Foundation of China (Project No: 51708288).

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  1. Guangdong Provincial Key Laboratory of Durability for Marine Civil Engineering, College of Civil and Transportation Engineering, Shenzhen University, Shenzhen, 518000, Guangdong Province, China

    J. H. Wang

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Appendix

Appendix

AIJ standard-prescribed equations to evaluate the yield flexural strength (Pmy) of general concrete beams are written as follows (AIJ 2010):

$$P_{my} = \frac{{0.9A_{st} f_{y} h_{0} }}{L}$$
(19)

ACI-ASCE code was used to calculate the nominal shear strength of beam-column joint (ACI-ASCE 2002):

$$\begin{aligned} & V_{n}^{{}} = 0.083\gamma_{n} \sqrt {f_{c} } b_{j} h_{c} \\ & b_{j} = Min\left( {b_{c} ,\frac{{b_{b} + b_{c} }}{2},b_{b} + \sum {\frac{{mh_{c} }}{2}} } \right) \\ \end{aligned}.$$
(20)

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Wang, J.H. Cyclic behaviors of reinforced concrete beam-column joints with debonded reinforcements and beam failure: experiment and analysis. Bull Earthquake Eng 19, 101–133 (2021). https://doi.org/10.1007/s10518-020-00974-1

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