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On the cracking behaviour of the reinforced concrete tension chord under repeated loading

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Abstract

It is well known that repeated loads lead to increasing crack widths and deformations of reinforced concrete members. This is due to the progressive reduction of the parameters influencing the bond mechanism at the steel-concrete interface. However, current engineering methods employ severe simplifications to account for this influence, in particular to estimate values under permanent load. In this paper a model is presented to reproduce the distribution of longitudinal stresses and strains, bond stresses and relative slips along the crack spacing of a reinforced concrete tie with number of cycles. The model allows for a better understanding of the mechanical degradation sources affecting the evolution of tension-stiffening contribution. On the one hand, a cyclic degradation law is introduced to affect the local bond-slip behaviour. On the other hand, the mechanical damage of concrete is also introduced in the analysis. A parametric study is reported to show the role played by the different sources of degradation. Finally, the model capabilities are employed to analyse own experimental results.

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Abbreviations

A s :

Area of the rebar

A c,eff :

Effective concrete area

A c,eff,min :

Effective concrete area under minimum load

b :

Parameter to define the cyclic rate of the relative slip

c :

Parameter to define the cyclic degradation of the effective concrete area

E c :

Concrete modulus of deformation

E s :

Steel modulus of deformation

F :

Load

F cr :

Cracking load

F max :

Maximum load

F min :

Minimum load

f c :

Concrete compressive strength

f ct :

Concrete tensile strength

f C–Tct,res :

Residual tensile strength of concrete in a compression–tension fatigue test

f T–Tct,res :

Residual tensile strength of concrete in a tension–tension fatigue test

K :

Stiffness of the unloading and reloading branches of the bond-slip model

k N :

Increase of the slip due to N load cycles

l :

Width of the reinforced concrete tie

l b,unl :

Unloaded transfer length

m :

Tension-stiffening parameter

N :

Number of load cycles

n :

Ratio between modulus of elasticity of steel and concrete

s :

Relative slip between the concrete and the reinforcement

s 0 :

Static relative slip

s 1 :

Relative slip that corresponds to the bond strength

s red1 :

Relative slip that corresponds to the reduced bond strength

s 2 :

Relative slip that corresponds to the end of the horizontal line of the static bond-slip envelope

s 3 :

Relative slip that corresponds to the residual bond strength

s n :

Relative slip at the section halfway between cracks

s r :

Crack spacing

U s :

Perimeter of the rebar

w :

Crack width

w max :

Maximum crack width

w min :

Minimum crack width

x :

Distance from the section halfway between cracks to an arbitrarily chosen section

β2 :

Tension-stiffening parameter of EC2

β t :

Tension-stiffening parameter of MC90

ΔN :

Increment of the number of cycles

ε c :

Concrete strain

ε s :

Steel strain

εs,I :

Steel strain at state I

εs,II :

Steel strain at state II

εs,crack :

Steel strain at the crack

ε sm :

Average steel strain

ε cm :

Average concrete strain

Φ:

Diameter of the rebar

ρ:

Steel reinforcement ratio with respect to the effective concrete area

σ c :

Concrete stress

σ s :

Steel stress

σs,max :

Maximum steel stress at the crack

σs,min :

Minimum steel stress at the crack

τ :

Bond stress

τ f :

Negative frictional bond strength

τ red f :

Reduced negative frictional bond strength

τ max :

Bond stress under maximum load

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Acknowledgement

Financial support provided by the Universidad Politécnica de Madrid (Spain) through the program for doctoral researchers is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Continuum Mechanics and Structures, E.T.S. Ingenieros de Caminos, Canales y Puertos, Universidad Politécnica de Madrid, Av. Profesor Aranguren s/n, 28040, Madrid, Spain

    Carlos Zanuy, Luis Albajar & Pablo de la Fuente

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  1. Carlos Zanuy
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  2. Luis Albajar
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  3. Pablo de la Fuente
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Correspondence to Carlos Zanuy.

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Zanuy, C., Albajar, L. & de la Fuente, P. On the cracking behaviour of the reinforced concrete tension chord under repeated loading. Mater Struct 43, 611–632 (2010). https://doi.org/10.1617/s11527-009-9516-9

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