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TIME-DEPENDENT DAMAGE BASED TENSION STIFFENING IN REINFORCED CONCRETE

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TIME-DEPENDENT DAMAGE BASED TENSION STIFFENING IN REINFORCED CONCRETE

ABSTRACT

 

Deflection control is an important criterion for design of reinforced concrete structures. Deflection control becomes critical for lightly reinforced members. Behavior of concrete members at service load levels involves complex interactions of cracking, creep, shrinkage and bond between concrete and embedded reinforcing bars. The creep and shrinkage phenomena are well established but the deterioration of tension stiffening with time is not fully understood. Current tension stiffening models consider short term effects of cracking. The primary focus of this research is to examine the effect of time on tension stiffening.

An analytical model is developed to examine the time-dependent effects of creep, shrinkage and bond on tension stiffening. The model is evaluated by comparison with the available experimental data. The sensitivity of the model to various parameters is examined through parametric study. The results of the research can be extended to flexural members for incorporation in design.

 

 

 

TABLE OF CONTENTS

List of Figures  ………………………………………………………………………………………………. v

List of Tables ………………………………………………………………………………………………… vi

Acknowledgements ………………………………………………………………………………………… vii

Chapter 1 Introduction ……………………………………………………………………………………. 1

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

1.2 Problem Statement ……………………………………………………………………………… 2

1.3 Objective & Scope ……………………………………………………………………………… 2

Chapter 2 Literature Review ……………………………………………………………………………. 4

2.1 Time dependent deformation ……………………………………………………………….. 4

2.1.1 Creep Function …………………………………………………………………………. 5

2.1.2 Shrinkage Function ……………………………………………………………………. 7

2.2 Tension Stiffening Models ………………………………………………………………….. 8

2.2.1 ACI 318 …………………………………………………………………………………… 10

2.2.2 CEB MODEL …………………………………………………………………………… 11

2.2.3 Scanlon and Murray Model ………………………………………………………… 13

2.2.4 Lin & Scordelis Model ………………………………………………………………. 14

2.2.5 Damjanic & Owen model …………………………………………………………… 15

2.3 Tensile Strength of Concrete ……………………………………………………………….. 17

2.3.1 Split Cylinder Test (ASTM C 496) ……………………………………………… 17

2.3.2 Flexure Test (ASTM C78 or C293) ……………………………………………… 18

2.4 Decay of tension stiffening with time ……………………………………………………. 18

2.4.1 Creep in Tension ……………………………………………………………………….. 19

2.4.2 Shrinkage in Tension …………………………………………………………………. 202.4.3 Bond Deterioration ……………………………………………………………………. 22

Chapter 3 Method of Analysis …………………………………………………………………………. 24

3.1 Development of Algorithm – Axial Prism ……………………………………………… 24

3.1.1 Assumptions …………………………………………………………………………….. 24

3.1.2 Material Properties ……………………………………………………………………. 25

3.1.3 Computation of strain ………………………………………………………………… 26

3.1.4 Computation of stresses ……………………………………………………………… 29

3.1.5 Introduction of Tension Stiffening ………………………………………………. 31

3.1.6 Methodology …………………………………………………………………………….. 333.2 Development of Matlab Code & Time Step Analysis ……………………………… 33Chapter 4 Validation of Results ……………………………………………………………………….. 36

4.1 Test Setup …………………………………………………………………………………………. 364.2 Comparison of Results ………………………………………………………………………… 37

Chapter 5 Parametric Studies …………………………………………………………………………… 43

5.1 Input Parameters ………………………………………………………………………………… 43

5.2 Study Results …………………………………………………………………………………….. 46

5.2.1. Sensitivity to the Numbers of Time-steps ……………………………………. 47

5.2.2. Reinforcement Ratio, ρg ……………………………………………………………. 48

5.2.3. Compressive strength of concrete,  f ‘c ………………………………………… 53

5.2.4. Ultimate Creep Coefficient, Cu …………………………………………………… 56

5.2.5. Ultimate Shrinkage Strain, εshu …………………………………………………… 58

5.2.6. Tension Stiffening Parameter, β …………………………………………………. 61

5.2.7. Strength reduction factor, α ……………………………………………………….. 64

5.2.8. Strength Reduction Parameter α & Tension Stiffening Parameter, β .. 67

5.2.9. Cracking Load, Pcr ……………………………………………………………………. 70

Chapter 6 Conclusions & Recommendations …………………………………………………….. 73

6.1. Conclusions ……………………………………………………………………………….. 73

6.2. Recommendations ………………………………………………………………………. 74

 

References ………………………………………………………………………………………………. 76

 

Appendix A  Matlab Code ………………………………………………………………………… 79

A.1. Program for calculating tension stiffening stress-strain curve ………….. 79

A.2. Program for calculating total strain ………………………………………………. 80

Chapter 1 

 

Introduction

1.1 Background

Deflection control is an important criterion for design of reinforced concrete members. Deflection control considerations largely dominate lightly reinforced members. With the use of high strength material, construction of thinner slabs with longer spans is made possible leading to need of a reliable calculation of deflection.  Assessment of effect of tension stiffening is important for calculating deflection in lightly reinforced members.

The term “tension stiffening” refers to the contribution of concrete between cracks to the overall stiffness of a member due to bond between concrete and steel reinforcement. The primary focus of this research is to examine the effect of time on tension stiffening. Current tension stiffening models consider short term effects of cracking. However, concrete in the tensile zone between cracks is subjected to creep and shrinkage effects as well as breakdown of bond over time. An analytical model is developed including these effects and results are compared with available experimental data.

1.2 Problem Statement

An analytical model is needed to examine the time-dependent effects of creep, shrinkage, and bond degradation on tension stiffening. Such a model is useful in understanding the behavior of tension zones in reinforced concrete members when subjected to long term sustained loads.

1.3 Objective & Scope

The objective of the research was to develop an analytical model for time dependent deformations in reinforced concrete members considering the combined effect of creep, shrinkage and tension stiffening.

The following tasks were conducted to achieve the objective:

  1. Literature review was conducted on tension stiffening models.
  2. A method of analysis was developed to calculate time dependent deformations in cracked tension zones of reinforced concrete members. The analysis procedure includes effects of creep and shrinkage in the tension zone. The tension stiffening model for short term loading was extended to include sustained load effects. Analytical results were validated using available experimental data.
  3. A parametric study was conducted to determine the effect of different conditions on time dependent deformation.

Recommendations are made for additional research required to extend the model to flexural members and provide a theoretical basis for long term multipliers for deflection control considering the time dependent nature of tension stiffening.

TIME-DEPENDENT DAMAGE BASED TENSION STIFFENING IN REINFORCED CONCRETE

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