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Materials and Structures

, 51:139 | Cite as

Analytical bond strength of deformed bars in concrete due to splitting failure

  • Feng XuEmail author
  • Zhimin Wu
  • Weiwei Li
  • Weiqing Liu
  • Shuguang Wang
  • Dongsheng Du
Original Article
  • 171 Downloads

Abstract

The bond behavior of deformed bar in concrete is important for the design and analysis of concrete structures, especially with insufficient concrete cover or confinement. This paper presents an analytical solution for the bond strength of deformed bar in concrete due to the splitting failure of concrete cover. A hypothesis of the equivalent elastic deformation field is proposed to approximate the deformation within the inner cracked concrete, while a linear crack profile is assumed to formulate the width of fictitious cracks. In conjunction with a realistic softening relationship, the analytical solutions of the internal pressure and bond strength are then derived for the splitting failure. The comparisons between the analytical predictions and the extensive experimental results demonstrate that the presented analytical model is capable of predicting the bond capacity with good accuracy. Finally, the influences of geometric and material parameters on the prediction results are examined, and an expression for the required bonded or splice length is suggested for design applications.

Keywords

Reinforced concrete Deformed bars Bond strength Splitting failure Analytical solution 

List of symbols

As

Cross-section area of reinforcing bar

c

Thickness of concrete cover

c1, c2

Material constants for softening relationship

d

Diameter of reinforcing bar

e

Radial distance from the fictitious crack front to the circle of rebar

Ec

Elastic modulus of concrete

Es

Elastic modulus of reinforcing bar

ft

Tensile strength of concrete

fy

Yielding strength of reinforcing bar

l0

Critical bonded length for short bonded specimen

lb

Bonded/splice length

n

Number of fictitious cracks

p

Radial internal pressure

pmax

Maximum radial internal pressure

\(p_{\text{r}}^{\text{e}}\)

Radial internal pressure at boundary between cracked and uncracked parts

r

Random radial distance to the circle of rebar

Rc

Outer radius of concrete cover

Rs

Inner radius of concrete cover (radius of reinforcing bar)

ur

Radial deformation of inner cracked concrete

\(u_{\text{r}}^{\text{cal}}\)

Calculated radial deformation of inner cracked concrete

\(u_{\text{r}}^{\text{e}}\)

Radial deformation at boundary between cracked and uncracked parts

w

Width of fictitious crack

w0

Crack width when the cohesive stress is zero

wm

The crack width at the rebar-concrete interface

α

Inclination angle of bond action

γ

Reduction coefficient considering the effect of bonded length

Δθ

Circumferential deformation of the inner cracked concrete

\(\Delta_{{_{\theta } }}^{{R_{s} }}\)

Circumferential deformation of the cracked concrete at the bar-concrete surface

εcr

Strain of concrete at tensile strength

εr

Radial strain of concrete

εθ

Circumferential strain of concrete

νc

Poisson’s ratio of concrete

σr

Radial stress in the outer elastic concrete

σ(w)

Cohesive stress across the fictitious crack in the inner cracked concrete

σθ

Circumferential stress in the outer elastic concrete

\(\sigma_{\theta }^{e}\)

Circumferential stress at boundary between cracked and uncracked parts

τ

Longitudinal bond stress

τmax

Maximum bond stress

Notes

Funding

This study is funded by the National Basic Research Program of China (973 Program) with Grant No. 2011CB013801 and the National Natural Science Foundation of China with Grant No. 51308285. The financial supports from the Natural Science Foundation of Jiangsu Province with Grant No. BK20130943, Natural Science Foundation for College and University in Jiangsu Province with Grant No. 13KJB560004 and the China Scholarship Council (CSC) with Grant No. 201508320041 are also greatly acknowledged.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© RILEM 2018

Authors and Affiliations

  1. 1.College of Civil EngineeringNanjing Tech UniversityNanjingPeople’s Republic of China
  2. 2.State Key Laboratory of Coastal and Offshore EngineeringDalian University of TechnologyDalianPeople’s Republic of China

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