WASHINGTON UNIVERSITY IN ST. LOUIS Department of Mechanical, Aerospace, and Structural ...

254 Pages·2008·3.58 MB·English

WASHINGTON UNIVERSITY IN ST. LOUIS
Department of Mechanical, Aerospace, and Structural Engineering

Dissertation Examination Committee:
Thomas Harmon, Chair
Shirley Dyke
Kevin Truman
Phillip Gould
Ruth Okamoto
Guy Genin
Jr-Shin Li

TOTAL STRAIN BASED BOND/SLIP AND SHEAR/FRICTION MEMBRANE
MODEL FOR FINITE ELEMENT ANALYSIS OF REINFORCED CONCRETE
by
Mi-Geum So

A dissertation presented to the
Graduate School of Arts and Sciences
of Washington University in
partial fulfillment of the
requirements for the degree
of Doctor of Philosophy

August 2008

Saint Louis, Missouri
© Copyright by
Mi-Geum So
2008
Bond/Slip and Shear/Friction R/C Model, So, Ph.D. 2008.
ABSTRACT OF THE DISSERTATION

TOTAL STRAIN BASED BOND/SLIP AND SHEAR/FRICTION MEMBRANE
MODEL FOR FINITE ELEMENT ANALYSIS OF REINFORCED CONCRETE
by
Mi-Geum So
Doctor of Philosophy in Structural Engineering
Washington University in St. Louis, 2008
Professor Thomas Harmon, Chairman

A reinforced concrete material model that includes frictional bond-slip behavior and shear friction
behavior is proposed for use in a 2D total-strain based finite element analysis. The motivation for
this model is to improve both tension stiffening behavior and shear strength and stiffness of total-
strain based models. The proposed bond/slip membrane model is based on a simplified
mechanistic concept and is capable of modeling bond/slip behavior under cyclic loading in a
smeared manner. This dissertation presents a FEA implementation of the proposed bond/slip
based material model in the OpenSees framework. The model is validated with shear wall test
results available in the literature. Another motivation for this model is to understand the
significance of crack strains so that the model can be extended to include shear friction behavior
for cracked concrete. A shear friction model is developed and implemented for 1-directional
cracking. Based on the results of the bond/slip model, the shear friction model is implemented as
a total strain based model rather than as a crack strain based model. This greatly simplifies the
implementation. This is the first FEA material model that is able to capture fundamental
shear/friction behavior by enforcing a relationship between crack slip and separation.

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Acknowledgements
The research was supported by Grant No. CMMI-0625640 from the National Science
Foundation.

Special thanks to:

Dr. Harmon, Dr. Dyke, Dr. Truman, Dr. Okamoto
Dr. Gould, Dr. Genin, and Dr. Li for serving on my committee;
Dr. Truman, the chairman of the Washington University’s MASE Department, who was
my undergraduate advisor and allowed me to pursue my studies at Washington
University;

the University of Missouri-St. Louis, which opened up an opportunity to further study in
its joint engineering program with Washington University;

Dr. Feldman, the associate dean of the UMSL-WU joint engineering program;

Dr. Stanton, Dr. Roeder, Dr. Lowes, Dr. Miller, and Dr. Arduino for inspiring lectures
and the Charles Norris fellowship at the University of Washington-Seattle.

my undergraduate advisor, Dosam Kim, a professor at Korea Maritime University, who
inspired me with his teaching, care, and support;

Taegon Kim, Joongwoo Lee, and Kabsoo Kyung, professors at Korea Maritime
University;

Daehyo Park, a professor at Han-Yang University;
Dr. Yun, an assistant professor, the University of Akron;
Dr. Hsu, the University of Houston;
the Emphrey and Bounds families for lending their help and support; and

my family and friends.

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Table of Contents

Abstract…………………………………………………………...………………..……..ii
Acknowledgements…………………………………………………………...………….iii
List of Tables….………………………………………………………………….……....ix
List of Figures……….…………………………………………………………………….x

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

1.1 Problem Definition…………………………………………………………….2
1.2 Research Objectives…………………………………………………………...4
1.3 Procedures……………………………………………………………………..5
1.4 Research Approach………………………………………………...…….……5
1.4.1 Element-Based Approach……………………………………….......6
1.4.2 FEA Model-Based Approach………………………………………..7
1.4.3 Development of Shear Stress-Strain Relationship…………………..7
1.5 Thesis Organization……………………………………………………...……8

2. Literature Review………………………………………………………………..……9

2.1 Existing Total Strain-Based Models……………………………………..…..10
2.1.1 Definition of Total-Strain Based Model……...………………..…..10
2.1.2 Evolution of Total-Strain Based Model……………………..……..11
2.1.3 Cyclic Softened Membrane Model (CSMM)………………….…..11
2.1.4 Modified Compression Field Theory (MCFT)……….........…..…..11

2.2 Comparison of CSMM and MCFT………………………………………......12
2.2.1 Analysis Method……………………….……........................……..12
2.2.2 Concrete Constitutive Model…………………………………..…..13
2.2.3 Steel Constitutive Model………………..…………………..……..15
2.2.4 Shear Models..…………………………..……………….…….…..16
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2.2.5 Summary….……………………………..……….………………...16

2.3 Evaluation of Concrete Shear Stress-Strain Relationship..…………………..16
2.3.1 Rotating vs. Fixed Crack Models………………………………….…...17
2.3.2 Four Types of Shear Stress-Strain Relationships.……...………….…...17
2.3.3 Summary……………………………,…………………………………25

2.4 Suggested Improvements………………………………...…………………..26
2.4.1 Geometry Dependent Tension Stiffening and
Crack Closing Models……………………………………………….....26
2.4.2 Inclusion of Frictional Resistance and
Bond-Slip Behavior……………………………………………………29
2.4.3 Poisson’s Effect (Growth Effect)……...…………………………….…30
2.4.4 Concrete Crack Strain………….……...……………………………….30
2.4.5 Net Shear……………………….……...…………………………….…32
2.4.6 Panels under Various Cyclic Loading Conditions……………………..33

2.5 Future Research Direction (Ties to Research Objectives)..………………….33

3. Assessment of Existing 2D Total Strain Membrane Models...…………………….34

3.1 Introduction……….……………………………………………………….…35
3.1.1 Definitions………………………………………………………….36

3.2 Tension Stiffening Behavior……..……………………………………….….38
3.2.1 Analytical Reinforcing Steel Model…………………………….…39
3.2.2 Estimated Tension Stiffening Model from
Experimental Results……………..…………………………….….41

3.3 Discussions and Conclusions………………………………………….……..44

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4. Formulation of a Bond-Slip Membrane Model……..……………….…………..…51

4.1 New Features…………...………………………………………….………...52
4.1.1 Bonded and Slip Regions………………..………………….……...52
4.1.2 Unbonded Length Factor………………......................….………...54
4.1.3 Bond/Slip Friction………………………………………….……....56
4.1.4 Concrete Expansion Strain...…………………………………….....58
4.1.5 Concrete Crack Strain...…………………………………………....58
4.1.6 Concrete Contact Stress……………………………………….…...60

4.2 Analysis Procedure…………………………………..……………….……...61
4.3 Comparison of Predictions and Experimental Results……………………….63
4.4 Conclusions…………………………………….………………………….....69

5. Development of a Platform for Implementation of 2D Nonlinear
Material Model in the OpenSees Interface………………………………………...70

5.1 Introduction…………………………………………………………….…….71
5.2 Approaches………...…………………………………………….…………..72
5.2.1 OpenSees Website..………………………………………….…….73
5.2.2 Visual C++ Software……………………………............................73
5.2.3 Tcl Editor…………………………………………..........................73
5.2.4 Plotting Tool…………………………………….............................73

5.3 Background…………………………….…..…………………………….…..73
5.3.1 OpenSees…………………………………………...........................73
5.3.2 Existing 2D Reinforced Concrete Material Model...........................75

5.4 A New Nonlinear 2D Material Model……………………………...………..75
5.4.1 New Fixed-Crack R/C Material Model: Theory..……………….....76
5.4.2 Existing Uniaxial Material Models………...………………….…...80
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5.4.3 New ND Material Model……….…………………………….……84
5.4.4 Methodology: Adding a New Multi-Dimensional
Material, NDMaterial…………………………………………...….87

5.5 Shear Wall Analysis……………..……..………………………………….....94
5.5.1 Model Description (SW4)…......…………………………………...94
5.5.2 Analysis Results (SW4)………..….…….………………………..104
5.5.3 Analysis and Results (PCA Wall B2)………………………….....106

5.6 Conclusions and Recommendations..............................................................109

6. FEA Implementation/Verification of a 2D Membrane
Bond-Slip Model…………………………………………….……………………...110
6.1 Introduction..………………..………………...……………………………111
6.2 FEA Formulation……….…..………………...……………………………114
6.2.1 Effect of Bond/Slip on Behavior of a Reinforced
Concrete Shear Wall ……………………………………………..114
6.2.2 Stress-Strain Relationship: Concrete …...……………….....….....115
6.2.3 Stress-Strain Relationship: Steel …………………….…......….....119
6.2.4 Stress-Strain Relationship: Combined (Reinforced Concrete).......120
6.2.5 Significance of Separating Crack Strain.........................................123

6.3 FEA Verification……………………………………………………………124
6.3.1 FEA Model and Analysis Method……..….…….………………..125
6.3.2 Comparison of Predictions and Experimental Results.…..…….…126
6.3.3 Computed Crack Strains..….………………….……………….…128

6.4 Discussion……. ……………………………………………………………130
6.5 Conclusions…………………………………………………………………131

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7. Shear-Friction Membrane Model………….……………….……………………...132
7.1 Shear-Friction Concept..………………………...……………………….…133
7.2 Introduction……………………...……………………………………….…134
7.3 Formulation……………………...……………………………………….…137
7.3.1 Effective Concrete Strain....…...………………….........................138
7.3.2 Maximum and Minimum Shear Stresses.…….…………………..141
7.3.3 Secant Stiffness Matrix…….………………….……………….…143

7.4 Verification of 1-Directional Shear Friction Membrane Model……………148
7.4.1 Procedures…………….......…...……………………………….....148
7.4.2 Results and Discussions………………...…….…………………..149

7.5 Comparison of Analytical and Experimental Results………………………154
7.6 Conclusions…………………………………………………………………157

8. Summary and Conclusions………...……………………………………………....158
8.1 Summary……………………………………………………………………159
8.2 Conclusions…………………………………………………………………160
8.3 Future Research……...……...………………………………………...……162

Appendix A – Notations and Figures Used in Comparing MCFT and CSMM..………165
Appendix B – ‘Model BS’ Source Code…………………….………………………....180
Appendix C – Tcl Input File for SW4……………………………………………….....216
References………………………………………………………………………………231

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