TENSION STIFFENING MODEL FOR REINFORCED CONCRETE BASED ON BOND STRESS SLIP RELATION

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TENSION STIFFENING MODEL FOR REINFORCED CONCRETE BASED ON BOND STRESS SLIP RELATION

Abstract

Tension stiffening is a structural property of reinforced concrete that refers to the contribution of concrete between cracks to the overall stiffness of the member. In assessing the strength of reinforced concrete sections the tension in the concrete is usually ignored because it contributes little to member strength. However it provides an important contribution to the performance of members at service loads. Tension stiffening can be modeled at the stress-strain level by use of a post-peak degrading modulus of elasticity as first proposed by the first author in 1971. This paper proposes and evaluates a method to evaluate the post-peak parameters of the tension stiffening model based on bond characteristics between concrete and steel.

 

 

 

 

 

 

 

 

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Table of contents

Chapter 1 INTRODUCTION……………………………………………………………….………1

1.1           Background…………………………………………………………………………1

1.2           Objective and Scope………………………………………………………………..2

Chapter 2 LITERATURE REVIEW……………………………………………………………….3

2.1      Tension Stiffening Mechanism……………………………………………………….3

2.2       Steel-concrete Bond…………………………………………………………………6

2.3       Tension Stiffening Models…………………………………………………………..6

2.4       Finite Element Models………………………………………………………………8

2.5       Harajli’s Bond Stress-slip Model……………………………………………………9

2.6       Summary…………………………………………………………………………..10

Chapter 3 DEVELOPMENT OF ANALYTICAL MODELS……………………………………11

3.1       Introduction…………………………………………………………………………11

3.2      Algorithm…………………………………………………………………………..11

3.3      Two-dimensional Simplification……………………………………………………20

3.4       Bond Link Element…………………………………………………………………21

3.5       Mesh and Cracks……………………………………………………………………25

3.6       Example Application of the Model…………………………………………………27

Chapter 4 BEEBY AND SCOTT TEST SPECIMEN……………………………………………..38

4.1      Develop Tension Stiffening Model………………………………………………….38

4.2      Strain Distribution along the Steel Bar……………………….……………………..49

Chapter 5 APPLICATION OF THE MODEL……………………………………………………53

5.1      Introduction……………………………………………….………………..……….53

5.2      Comparison with CEB Model……………………………………………………….53

5.3      Effect of Varying Reinforcement Ratio…………………………………………….57

Chapter 6 SUMMARY CONLUSIONS AND RECOMMENDATIONS……………………….57

6.1      Summary……………………………………………………………………………57

6.2      Conclusion………………………………………………………………………….57

6.3      Recommendations…………………………………………………………………..58

References……………………………………………………………………………………….59

Appendix Bond-slip Relation Chart………………………………………………………………61

 

 

 

 

 

Chapter 1 Introduction

1.1 Background

Reinforced concrete members have been widely use for structural purposes. Tension stiffening refers to tension carrying ability of concrete between cracks, contributing to the stiffness of a reinforced concrete member before the reinforcement yields. If concrete is assumed to carry tension between the cracks only, the reinforcement carries the entire axial load at the crack location. The rigidity of the reinforced member affects the performance of a reinforced member in terms of deflection and crack control.

Concrete cracks when the tensile stress limit is exceeded. Cracking causes a softening behavior in plain concrete. As cracking progresses, concrete loses its stiffness at a relatively high rate. However, this softening behavior is counteracted by the steel reinforcing bars in the tension zone of concrete. The tensile stress in concrete gradually decreases as cracking develops.

The propagation of cracks is a complicated phenomenon that depends on the interaction between concrete and reinforcement and plays an important role in the analysis of concrete structures. This thesis investigates the development of a tension stiffening model based on bond stress-slip relationships that for can be used in smeared cracking finite element analysis.

 

 

1.2 Objective and Scope

The objective and scope of this study is to investigate the behavior of concrete between cracks considering bond stress-slip relationships to develop tension stiffening models for reinforced concrete. Tension stiffening models are needed to simulate post-cracking behavior of reinforced concrete which is important for evaluating serviceability and in particular, deflection control.

This objective will be achieved within the scope of the following tasks:

  1. Literature review
  2. Development of analytical models to trace the development of cracking in axially loaded prisms and the effect on overall stiffness.
  3. Evaluation of the analytical models using available experimental data
  4. Comparison with the CEB tension stiffening model and study of the effect of reinforcement ratio

Development of conclusions and recommendations.

 

TENSION STIFFENING MODEL FOR REINFORCED CONCRETE BASED ON BOND STRESS SLIP RELATION

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