iv 

 

TABLE OF CONTENTS

ABSTRACT……………………………………………………………………. ii

ACKNOWLEDGEMENT……………………………………………............ iii

TABLE OF CONTENTS……………………………………………………… iv

LIST OF FIGURES………..……………………………………......................ix

LIST OF TABLES……………………………………………………………. xi

NOTATION……………………………………………………………………. x

CHAPTER I

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

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

1.2. Research Significance……………………………………………………… 4

1.3. Problem Statements ………………………………………………………. 5

1.4. Research Objectives……………..…………………………………………. 5

1.5. Limitations …………………………………………………………………. 6

CHAPTER II

THEORETICAL REVIEW …………………………………........................... 7

2.1. Introduction ………………………………………………………………... 7

2.2. Material Properties for Seismic Resistance………………………………… 8

2.2.1. Unconfined Concrete……………………………………………... 8

2.2.2. Confined Concrete………………………………………………... 8

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2.3. Moment Curvature Analysis ……………………………………………...... 10

2.3.1. Moment Curvature Sectional Analysis …………………………... 10

2.4. Concrete Stress-strain models ……………………………………………... 11

2.4.1. Mander et al model ………............................................................. 11

2.4.2. Fafitis et al model………………………………………………… 13

2.4.3. Sheikh et al model………………………………………………... 14

2.5. Stress-strain model for non-prestressed steel……………….......... 16

2.6. The Modified Compression Field Theory………………………………...... 19

2.6.1. Introduction…………………………………................................. 19

2.6.2. Important Aspects of MCFT……………………………………... 19

2.6.2.1. Equilibrium Conditions………………………………… 20

2.6.2.2. Geometric Conditions………………………………….. 22

2.6.2.3. Stress-strain relationship curves…………………...…… 23

2.7. Ductility Requirement……………………………………………………… 25

2.7.1. Ductility Demand Criteria………………………………………... 25

2.7.2. Strain Ductility…………………………………………………... 26

2.7.3. Curvature Ductility……………………………………………….26

2.7.4. Displacement Ductility……………………………………….......27

CHAPTER III

RESEARCH METHODOLOGY…………………………………………….. 29

3.1. Introduction …………………………………………………………........... 29

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3.2. Data Collection …………………………………………………………….. 29

3.3. Research Methods …………………………………………………………. 30

3.4. Xtract Overview………………………………………................................ 32

3.4.1. Creating a New Project…………………………………………. 32

3.4.2. Viewing Results………………………………………………… 36

3.4.3. Plotting Results and Exporting Data……………………………. 37

3.5. Response 2000……………………………………………………………… 37

3.5.1. Input files…………………………………………………………. 38

3.5.2. Loading and Member Properties…………………………………. 39

3.5.2.1. Loading…………………………………………………. 39

3.5.2.2. Full Member Properties……………………………........ 39

3.5.3. Analysis and Interpretation………………………………….......... 39

3.5.4. Response 2000 9-Plots General…………………………………... 41

3.5.4.1. Cross section……………………………………............. 41

3.5.4.2. Longitudinal Strain………………………....................... 41

3.5.4.3. Transverse Strain……………………………………….. 41

3.5.4.4. Crack Diagram………………………………………….. 42

3.5.4.5. Shear Strain ……………………………………………. 42

3.5.4.6. Shear Stress ……………………………………………. 42

3.5.4.7. Principal Compressive Stress…………………………... 42

3.5.4.8. Shear on the Crack……………………………………… 43

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3.5.4.9. Principal Tensile Stress………………………………… 43

CHAPTER IV

NUMERICAL APPLICATION ……………………………………………… 44

4.1. Introduction ………………………………………………………………... 44

4.2. Model Descriptions ………………………………………………………... 44

4.3. Strength and Ductility………………………………………………………. 47

4.4. Deformed Shape …………………………………………………………… 50

CHAPTER V

RESULTS AND DISCUSSION ……………………………………………… 51

5.1. Introduction ………………………………………………………………... 51

5.2. Moment Curvature Analyses……………………………………………….. 51

5.3. Analysis of Models ……………………………………………………….. 52

5.3.1. Beam B1-F7 ……………………………………………………… 52

5.3.2. Beam B18-F5…………………………………………………….. 53

5.3.3. Beam B22-F7…………………………………………………….. 55

5.3.4. Beam B50-F7 …………………………………………………….. 56

5.3.5. Beam B58-F7…………………………………………………….. 58

5.3.6. Beam B40-F7…………………………………………………….. 59

5.3.7. Beam B42-F7…………………………………………………….. 60

5.3.8. Beam B23-F7…………………………………………………….. 61

5.3.9. Beam B20-F7…………………………………………………….. 63

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5.3.10. Beam B45-F7…………………………………………………… 64

5.4. Discussion Analysis Results……………………………………………… 65

CHAPTER VI

CONCLUSION AND RECOMMENDATION …………………………….... 70

6.1. Conclusions ………………………………………………………………... 70

6.2. Recommendations for future work ………………………………………… 71

REFERENCES ………………………………………………………………...72

APPENDIX A: ICSBE 2010 Technical Paper, entitled: Strength and Ductility

Demand of Reinforced Concrete Structural Members

APPENDIX B: Certificate as Presenter International Conference on Sustainable

Built Environment 2010

APPENDIX C: Project Assignment Letters

APPENDIX D: The Grove Architectural and Structural Data

APPENDIX E: XTRACT analysis results

APPENDIX F: Response 2000 analysis results

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LIST OF FIGURES

1.1. The Grove Condominium and Hotel………………………………………. 2

2.1. Effectively confined core for rectangular hoops reinforcement.................... 9

2.2. Mander et al model……………………………………………………….... 12

2.3. Stress-strain models by different researchers……………………………… 16

2.4. The stress-strain relationship model for steel by Park and Paulay………… 17

2.5. Stress-strain relationship for non-prestressed reinforcing steel…………… 18

2.6. The Modified Compression Field theory…………………………………... 20

2.7. Membrane Element in MCFT……………………………………. ………. 20

2.8. Average strains in cracked element….…………………………………….. 22

2.9. MCFT stress-strain relationship curves……………………………………. 23

2.10. Typical load displacement relationship…………………………………… 25

2.11. Definition of curvature ductility…………………………………………. 27

3.1. Flow diagram final project…………………………………………………. 31

3.2. Xtract section design template page……………………………………….. 33

3.3. Xtract stress-strain materials section ………………………………………. 34

3.4. Reinforcement stress-strain curves input ………………………………….. 35

3.5. Xtract analysis overview …………………………………………………... 36

3.6Concrete cross section page. ………………………………………………. 38

3.7. Full member response 2000 results page ………………………………….. 40

4.1. Beam at yield and ultimate condition ……………………………………… 47

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4.2. Moment-curvature relations by Pam et al …………………………………. 49

4.3. Xtract concrete beam section analysis …………………………………….. 50

5.1. Cross Section of Beam B1-F7 …………………………………………….. 52

5.2. Moment curvature relationships of Beam B1-F7 …………………………. 52

5.3. Cross section of Beam B18-F5 ……………………………………………. 54

5.4. Moment curvature relationships of B18-F5………………………………... 54

5.5. Cross section of Beam B22-F7 ……………………………………………. 56

5.6. Moment Curvature curves of Beam B22-F7… …………………………… 56

5.7. Cross section of Beam B50-F7…………………………………………….. 57

5.8. Moment curvature relationships of Beam B50-F5………………………… 58

5.9. Cross Section of B58-F7…………………………………………………… 57

5.10. Moment curvature plot of B58-F7………………………………………… 59

5.11. Cross section of B40-F7 …………………………………………………. 60

5.12. Moment curvature plot of B40-F5………………………………………… 60

5.13. Cross section of B42-F7………………………………….......................... 61

5.14. Moment-curvature relationships of B42-F7……………………………… 61

5.15. Cross section of B23-F7………………………………………………….. 62

5.16. Moment-curvature relationships of beam B23-F7………………………... 63

5.17. Cross section of B20-F5………………………………………………….. 63

5.18. Moment-curvature relationships of B20-F5……………………………… 64

5.19. Cross section of B45-F7………………………………………. 65

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5.20. Moment-curvature relationships of B45-F7………………….. 65

5.21. Confined concrete Mander et al model 1988…………………. 67

5.22. Confined concrete model Popovics et al……………………… 67

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LIST OF TABLES

Table 4.1.Details of Beams …………………………………… 54

Table 5.1. Results of analysis………………………………….. 68

 

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NOTATION

Ac Area of concrete

A Stress block depth

b Width of section

C Compressive force

D Total Depth of section

ds Effective depth of the concrete section

dn Depth to the Neutral Axis

Ec Mean value of the modulus of elasticity of concrete at 28 days

fc ′ Compressive strength of concrete

fcf ′ Characteristic flexural tensile strength

fcu Cube compressive strength of concrete

fy Yield Strength of Steel

fsty Yield strength of stirrups

Mcr The bending moment causing cracking of the section

s Stirrup spacing

T Tensile steel force (T=Ast x fy)

xy Depth to the neutral axis from the extreme compression fibre

a/d Shear span to effective depth ratio

α1, β1 Rectangular Stress Block Parameters (α1 =k1k3, β1=k2)

 

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µ Ductility factor

εsy Yield strain for steel

εy Yield Strain

εcu Ultimate concrete strain

Фu Ultimate curvature

Фy Yield curvature (Фy= εy/d-xy)

∆ Deflection at mid-span ρ Density of concrete, in kg/m3, taken as 2400 kg/m3

η Correction factor to determine the modulus of elasticity for high strength

concrete.