Innovative Pre-Cast Cantilever Constructed Bridge Concept

7/27/2019 Innovative Pre-Cast Cantilever Constructed Bridge Concept

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INNOVATIVE PRE-CAST CANTILEVER CONSTRUCTED BRIDGE CONCEPT

by

Brent Tyler Visscher

A thesis submitted in conformity with the requirements

for the degree of Master of Applied Science

Graduate Department of Civil Engineering

University of Toronto

Copyright by Brent Tyler Visscher (2008)


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Innovative Pre-cast Cantilever Constructed Bridge Concept

Brent Tyler Visscher

Master of Applied Science

Department of Civil Engineering

University of Toronto, Canada

2008

ABSTRACT

Minimum impact construction for bridge building is a growing demand in modern urban

environments. Pre-cast segmental construction is one solution that offers low-impact, economical,

and aesthetically pleasing bridges. The standardization of pre-cast concrete sections and segments

has facilitated an improved level of economy in pre-cast construction. Through the development

of high performance materials such as high strength fibre-reinforced concrete (FRC), further

economy in pre-cast segmental construction may be realized. The design of pre-cast bridges using

high-strength FRC and external unbonded tendons for cantilever construction may provide an

economical, low-impact alternative to overpass bridge design.

This thesis investigates the feasibility and possible savings that can be realized for a single cell

box girder bridge with thin concrete sections post-tensioned exclusively with external unbonded

tendons in the longitudinal direction. A cantilever-constructed single cell box girder with a

curtailed arrangement of external unbonded tendons is examined.


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ACKNOWLEGEMENTS

This work has been partially supported by the National Science and Engineering Research

Council of Canada.

I would like to thank my supervisor Dr. Paul Gauvreau for his guidance, support, andfellowship throughout the course of this design project.

Many thanks are owed to my friends and colleagues, especially those within our bridge

engineering research group, for their helpful discussions and insightful contributions to the

development of this project: Billy Cheung, Jamie McIntyre, Kris Mermigas, Talayah Noshiravani,

Graham Potter, Carlene Ramsay, Jason Salonga, and Jimmy Susetyo. Additional thanks go out to

other graduate students who I have had the pleasure of spending time with throughout my graduate

study: Jeff Erochko, Hyungjoon Kim, Nabil Mansour, Michael Montgomery, and Lydell Wiebe.

Special thanks to Jimmy Susetyo for his generous contributions in concrete material design and for

his laboratory assistance in test specimen preparation. I would like to thank John MacDonald for

his contribution during cylinder testing.

Finally, I thank my family for their constant encouragement and support throughout this task.


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TABLE OF CONTENTS

ABSTRACT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii

ACKNOWLEGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

TABLE OF CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii

LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

1.0 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

1.1 Statement of Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Scope and Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Thesis Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.0 BACKGROUND . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

2.1 Constitutive Laws for High Performance FRC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Compressive Stress-Strain Behaviour. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.2 Tensile Stress-Strain Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Typical Modern Highway Overpass Bridge Design Currently in Ontario . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.1 Standardization of Precast Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3 Description of the Proposed Segmental Box Girder Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.4 Visual Comparison of Proposed Box Girder with Typical Slab-on-Girder Overpass . . . . . . . . . . . . . . . . . 22

2.5 Benefits and Drawbacks of the Proposed Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.5.1 Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.5.2 Drawbacks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.0 LONGITUDINAL FLEXURE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .28

3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2 Moment-Curvature Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3 Behaviour of Unbonded Tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.3.1 Reference State of Strain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.3.2 Long-Term Effective Prestress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.4 Tendon Stress Calculation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.5 Preliminary Design Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.6 Preliminary Design Methodology for Cantilever Tendons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.6.1 Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.6.2 Ultimate Moment Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3.6.3 Sizing of Cantilever Tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.7 Change in Structural System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.8 Preliminary Design Methodology for Continuity Tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50


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3.8.1 Ultimate Moment Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.8.2 Spreading of Forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.8.3 Sizing of Continuity Tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.8.4 Secondary Prestress Moment due to Continuity Tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.9 Bottom Flange Sizing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.10 Prestress Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.11 Ultimate Limit State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.12 Serviceability Limit States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

3.12.1 Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.12.2 Cracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.12.3 Global Deflection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.13 Refinement in Tendon Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.13.1 Ductility of Fibre-Reinforced Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.13.2 Deformation Capacity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.13.3 Example of Tendon Stress Increase for Negative Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.13.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.14 Global System Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3.14.1 Span-to-Depth Ratio for Constant Depth Box Girder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3.14.2 Range of Spans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.14.3 Alternative Girder Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.0 TRANSVERSE FLEXURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .78

4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.2 Typical Transverse Prestressing for Segmental Bridges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.3 Prestressing Concept for Light Weight Slab Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.3.1 Post-Tensioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804.3.2 Pretensioning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.4 Bond Strength of 15mm Pretensioning Strands in FRC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.4.1 Mechanisms of Bond . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.4.2 Development of Stress in a 15mm Pretensioning Strand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.4.3 Improvement of Bond Strength due to High Strength FRC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.5 Methods of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.5.1 Grillage Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.5.2 Frame Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.6 Comparative Study for Transverse Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.6.1 Cross Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.6.2 Material Definitions used in Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.6.3 Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

4.6.4 Deflections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

4.7 Prestress Moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

4.8 Service Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

4.9 Cross Section Design and Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4.9.1 Transverse Rib Proportions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97


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4.9.2 Web Spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

4.10 Design for Barrier Impact Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.0 SHEAR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101

5.1 Introduction to Strut-and-Tie Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.2 Funicular Load Path for Girders Prestressed with Curtailed Tendons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.3 Parallel Chord Truss Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.4 Arching Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

5.4.1 Tied Arch Model (Noshiravani, 2007) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.5 Preliminary Design Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

5.6 Opening of Joints in Segmental Bridges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.7 Design of Web Reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

5.7.1 Comparison to CAN/CSA-S6-06 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

6.0 ANCHORAGE ZONE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .125

6.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

6.2 Flow of Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

6.3 Strut-and-Tie Model for Local Spreading of Forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

6.3.1 Anchorage of External Unbonded Tendons in Slab Blisters (Wollman, 1993) . . . . . . . . . . . . . . . . . . 127

6.3.2 Design Model for External Tendon Blisters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6.4 Detailing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

6.5 Reinforcement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

7.0 FIXED END ABUTMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .138

7.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

7.2 Bras de la Plaine Bridge, France (Tanis, 2003) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

7.3 Flexible Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

7.4 Design Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

7.4.1 Preliminary Design Alternatives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

7.4.2 Recommended Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

7.5 Sizing of Flexible Piles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

7.6 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

8.0 MATERIAL UTILIZATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .145

8.1 Reference Bridges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

8.1.1 Windward Viaduct, Interstate Route H-3, Hawaii, USA (Hawaii DOT, 1991) . . . . . . . . . . . . . . . . . . 1458.1.2 Hwy 407 - Islington Avenue Underpass, Toronto, Canada (MTO, 1990) . . . . . . . . . . . . . . . . . . . . . . 147

8.2 Concrete Consumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

8.3 Mild Reinforcing Steel Utilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

8.4 Longitudinal Post-Tensioning Utilization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

8.5 Transverse Post-Tensioning Utilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

8.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

9.0 CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .155


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9.1 Longitudinal Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

9.2 Transverse Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

9.3 Shear Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

9.4 Anchorage Zone Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

9.5 Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

9.6 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

10.0 REFERENCES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159

APPENDIX A - DESIGN DRAWINGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .164

APPENDIX B - MATERIAL TESTING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .175

APPENDIX C - CAN/CSA-S6-06 SHEAR PROVISIONS . . . . . . . . . . . . . . . . . . . . . . . .178

CURRICULUM VITAE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .180


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LIST OF FIGURES

2.0 BACKGROUND ..................................................................................................................7

Figure 2-1. Variation in modulus of elasticity with the ultimate compressive strength of concrete............... 8

Figure 2-2. Compressive stress-strain relationship for nominal 80MPa FRC test specimens and simplified

model ...................................................................................................................................... 9

Figure 2-3. Photo of intensively cracked compression cylinder after failure and significant post-peakstraining ................................................................................................................................ 10

Figure 2-4. a) Dogbone-shaped specimen: dimensions and sensors, b) test set-up of the uniaxial tensile test,

showing the front side of the specimen (adapted from Habel et al., 2006) .............. ............ 11

Figure 2-5. Tensile stress-strain relationship for nominal 80MPa FRC test specimens and simplified model:12

Figure 2-6. Typical slab-on-girder highway underpass built in Markham, Ontario on Highway 407.

Photograph courtesy of Scott Steves, 2006............... ................ ............. ................ .............. . 13

Figure 2-7. Recommended girder spacing with respect to span length for standard CPCI precast I-girders

(adapted from CPCI, 1996)....... .............. ............... ............... ............... ............... ............... ... 14

Figure 2-8. Plan and elevation view of a possible cantilever-constructed overpass bridge.......................... 16

Figure 2-9. Cross section and details of the constant depth box girder shown in Figure 2-8 ....................... 17

Figure 2-10. Typical standard segment components of proposed box girder concept.................................. 18

Figure 2-11. Top flange supported by steel struts, a) example shown of Shibakawa Viaduct, Japan (photo

courtesy of Takashi Kosaka, 2006), b) rendering of proposed 90m overpass structure ....... 19

Figure 2-12. Second Severn Bridge, a) total external unbonded prestressing tendons, b) cantilever

construction showing bulkhead face of segment with no continuous bonded steel across the

joint and no internal bonded tendons (adapted from Mizon, 1997).............. ............... ......... 20

Figure 2-13. Possible tendon arrangement shown for half the span (symmetrical about span centreline)... 21

Figure 2-14. Numbering scheme for segment labels..................................................................................... 22

Figure 2-15. Rendered perspective views on typical highway overpass construction using precast CPCI

girders (left) and proposed cantilever-constructed single cell box girder (right) as seen on an

overcast day....... ................ ............... .............. ................ .............. ............... ............... ........... 23

Figure 2-16. Deck cross sections for a) two-span precast CPCI girder overpass and b) proposed cantilever-

constructed single cell box girder. ........................................................................................ 23

Figure 2-17. Visual slenderness attained through shadow casting for a superstructure with a a) small deck

overhang and b) large deck overhang. ............... .................. .............. ............... .............. ...... 25

Figure 2-18. Collapse slab-on-girder bridge after being struck by tractor-trailer (adapted from El-Tawil,

2005) ..................................................................................................................................... 26

Figure 2-19. Elevation (1:2500 scale) showing the result of elevating the overpass road grade.................. 27

3.0 LONGITUDINAL FLEXURE..........................................................................................28

Figure 3-1. Idealization of box cross section for analysis of longitudinal flexure........................................ 29

Figure 3-2. Internal lever arm from tendon elevation to the compression flange, a) for a continuously guidedtendon, b) for a tendon attached only at discrete locations........... ................ ............... ......... 30

Figure 3-3. Strain Distribution at ultimate limit state (adapted from Naaman, 2006) .................................. 31

Figure 3-4. Material strains due to equilibrium in the reference state and in the ultimate state ................... 31

Figure 3-5. Family of moment-curvature responses for a specific cross section and varying prestress force

assuming a concentric prestress .............. ............... ............... ............... ............... ............... ... 35

Figure 3-6. Iterative method behaviour for tendon stress calculation for a) girder impending plastic hinging,

b) girder experiencing plastic hinging ................. ................ .............. ............... .............. ...... 36

Figure 3-7. Iterative method solution for obtaining tendon stress by incrementing applied load................. 37


9/197ix

Figure 3-8. Typical segment cross section .................................................................................................... 40

Figure 3-9. Comparison of live load models defined in CAN/CSA-S6-06 .................................................. 41

Figure 3-10. ULS bending moments on continuous girder........................................................................... 42

Figure 3-11. Cantilever prestress concepts for haunched and constant depth girders .................................. 44

Figure 3-12. Preliminary ULS demand and capacity for cantilever PT........................................................ 45

Figure 3-13. Layout of cantilever tendons .................................................................................................... 46

Figure 3-14. Redistribution of forces through concrete creep due to change in structural system (adapted fromPodolny et al., 1982)............................................................................................................. 48

Figure 3-15. Time-dependent creep coefficient assuming t0= 28 days, a) for 75 year period, b) for 5 year

period ............. .............. ................ .............. ............... .............. ............... .............. ................ . 49

Figure 3-16. Sectional forces due to prestressing with top and bottom tendons........................................... 51

Figure 3-17. Moment development length, la, due to anchorage of continuity tendon (adapted from Menn,

1990) ..................................................................................................................................... 52

Figure 3-18. Required moment development length for a girder post-tensioned with unbonded tendons... 53

Figure 3-19. Layout of continuity tendons.................................................................................................... 54

Figure 3-20. Preliminary ULS demand and capacity for continuity tendons................................................ 55

Figure 3-21. Secondary prestress moment due to prestressed continuity tendon ......................................... 57Figure 3-22. Ultimate state of stress for section with undersized bottom flange.......................................... 59

Figure 3-23. Appropriately sized bottom flange thickness for negative bending at ULS............................. 59

Figure 3-24. Primary prestress force distribution.......................................................................................... 61

Figure 3-25. Girder response for varying prestress force.............................................................................. 63

Figure 3-26. Girder response at ULS (half span shown)............................................................................... 64

Figure 3-27. Girder response at SLS (half span shown) ............................................................................... 66

Figure 3-28. Stress-strain response of FRC and typical normal-weight concrete......................................... 68

Figure 3-29. FRC comparison for total moment-curvature response in negative bending........................... 69

Figure 3-30. Plastic hinging in negative moment regions............................................................................. 70

Figure 3-31. 90m span with midspan hinge when load is close to failure.................................................... 71

Figure 3-32. Stresses in unbonded tendons for curtailed prestressing. a) change in tendon stresses during

construction due to the addition of segments and post-tensioning, b) change in tendon stresses

due to the application of increasing uniform load until failure.......... ............... ............... ..... 72

Figure 3-33. Ultimate behaviour for a continuous girder using unbonded draped tendons (adapted from

Muller et al., 1990) ............................................................................................................... 73

Figure 3-34. Material consumption for varying span/depth ratios................................................................ 74

Figure 3-35. Concept comparison of haunched girder and constant depth girder elevation......................... 76

4.0 TRANSVERSE FLEXURE ..............................................................................................78

Figure 4-1. Possible pretensioning arrangement........................................................................................... 82

Figure 4-2. Bond mechanisms between FRC and 15mm pretensioning strand (adapted from Chao, 2006) 83

Figure 4-3. Idealized strand stress profile in a pretensioned strand under applied load (adapted from Kahn,

2002) ..................................................................................................................................... 83

Figure 4-4. Generalized frame element properties for grillage analysis (adapted from Menn, 1990).......... 87

Figure 4-5. 3-dimensional grillage model..................................................................................................... 88

Figure 4-6. Comparison of top flange thicknesses of AASHTO-PCI-ASBI standard box girder examples

(adapted from Prestress/Precast Concrete Institute, 1997) ............. .............. ............... ......... 90

Figure 4-7. Cross section dimensions for typical segment............................................................................ 91


10/197x

Figure 4-8. Assumed stress-strain material properties for investigation of transverse stiffness................... 91

Figure 4-9. Live load models for transverse load analysis............................................................................ 92

Figure 4-10. Vertical slab deflection envelope due to live load, AASHTO-PCI-ASBI box girder .............. 93

Figure 4-11. Edge beam stiffening ................................................................................................................ 93

Figure 4-12. Vertical slab deflection envelope due to live load of proposed box girder: a) thin slab stiffened

with transverse ribs only, b) thin slab stiffened with transverse ribs and longitudinal edge

beam............... ............... ............... .............. ............... .............. .............. ............... ................ . 94

Figure 4-13. Moment distribution due to non-concentric prestress applied at the transfer length ............... 95

Figure 4-14. Total transverse bending moments for transverse flexure........................................................ 96

Figure 4-15. SLS top slab stress ranges at the extreme fibre due to service loading.................................... 97

Figure 4-16. Longitudinal section for a typical segment .............................................................................. 98

Figure 4-17. Web spacing requirements........................................................................................................ 99

Figure 4-18. Truss model for basis of barrier reinforcement ........................................................................ 99

Figure 4-19. PL-2 barrier detail for impact loading.................................................................................... 100

5.0 SHEAR..............................................................................................................................101

Figure 5-1. 45 degree truss model (adapted from Ritter, 1899) .................................................................. 102Figure 5-2. Possible truss models for girders with unbonded and bonded prestressing steel (adapted from

Gauvreau, 1993).......... ............... ............... .............. ................ .............. ............... ............... 102

Figure 5-3. Alternative girder designs to resist applied load Q .................................................................. 104

Figure 5-4. Effect of prestress arrangement on funicular compression chord ............................................ 105

Figure 5-5. Funicular shape of compression spine for continuous cantilever girder with curtailed tendons106

Figure 5-6. Strut-and-tie model for a fully prestressed flanged section. a) simplified model; b) through d)

detailed model of web, top flange and bottom flange, respectively (adapted from Schlaich et

al., 1989) ............................................................................................................................. 108

Figure 5-7. Variable angle truss model (adapted from Collins et al., 1997) ............................................... 109

Figure 5-8. Arch spreading of forces for a rectangular section (adapted from Schlaich et al., 1989) ........ 110

Figure 5-9. Comparison of tied arch model for a rectangular section and a flanged section (adapted from

Noshiravani, 2006)...... ............... .............. ............... .............. ................ .............. ................ 112

Figure 5-10. Girder dimensions (adapted from Noshiravani, 2007) ........................................................... 113

Figure 5-11. Girder cross section and web reinforcement (adapted from Noshiravani, 2007)................... 113

Figure 5-12. Tied arch model for load stage corresponding to flexural cracking (adapted from Noshiravani,

2007) ................................................................................................................................... 113

Figure 5-13. Tied arch model for load stage corresponding to ULS (adapted from Noshiravani, 2007) ... 114

Figure 5-14. Crack pattern and alternative parallel chord model for load stage corresponding to flexural

cracking............................................................................................................................... 115

Figure 5-15. Crack pattern and alternative parallel chord model for load stage corresponding to ULS .... 116

Figure 5-16. Truss model for shear design. a) fully prestressed state for continuous beam; b) modified modelto account for flange decompression (formation of plastic hinge) .............. .............. ......... 117

Figure 5-17. Prestress forces applied to truss model in Figure 5-16 for each applied anchorage force ..... 117

Figure 5-18. Incorrect hanger reinforcement model for shear stresses crossing an open joint (adapted from

Virlogeux, 1993) ................................................................................................................. 118

Figure 5-19. ULS Combination 1 maximum shear demands...................................................................... 119

Figure 5-20. ULS transverse steel demand and chosen capacity ................................................................ 120

Figure 5-21. Web reinforcement ................................................................................................................. 120


11/197xi

Figure 5-22. Shear panel tests for normal reinforced concrete and FRC concrete (adapted from Susetyo,

2007) ................................................................................................................................... 122

Figure 5-23. Shear parameter predictions according to CAN/CSA-S6-06................................................. 123

6.0 ANCHORAGE ZONE.....................................................................................................125

Figure 6-1. Top and bottom corner anchorage blisters................................................................................ 126

Figure 6-2. Flow of forces at an intermediate anchorage............................................................................ 127

Figure 6-3. Strut-and-tie model for corner blister (Adapted from Wollman, 1993) ................................... 129

Figure 6-4. Strut-and-tie model for corner blister satisfying static equilibrium; a) 3d isometric view, b) front

view, c) side elevation............... ............... .............. ............... .............. ................ .............. .. 130

Figure 6-5. Jack clearances necessary for installation (adapted from VSL, 2007)..................................... 132

Figure 6-6. Minimum anchorage eccentricities to box girder corner.......................................................... 132

Figure 6-7. Anchorage blister lengths ......................................................................................................... 133

Figure 6-8. Strut-and-tie anchorage model for a bottom tendon................................................................. 133

Figure 6-9. Tension ties linking deviation force to box reinforcement (adapted from Beaupre et al., 1990)134

Figure 6-10. Flow of forces for different reinforcement details ................................................................. 135

Figure 6-11. Anchorage zone reinforcement for critical 19 strand bottom tendon..................................... 136

7.0 FIXED END ABUTMENT .............................................................................................138

Figure 7-1. Bras de la Plaine Bridge, Reunion Island, France (adapted from Tanis, 2003) ....................... 139

Figure 7-2. Ballasted abutment of Bras de la Plaine Bridge (adapted from Tanis, 2003)........................... 139

Figure 7-3. Counterweight abutment concept (superseded)........................................................................ 141

Figure 7-4. Tie-down abutment concept (superseded)................................................................................ 142

Figure 7-5. Proposed conceptual abutment design...................................................................................... 143

8.0 MATERIAL UTILIZATION .........................................................................................145

Figure 8-1. Partial elevation view of Windward Viaduct (adapted from Hawaii DOT, 1991) ................... 146Figure 8-2. Typical cross section of Windward Viaduct (adapted from Hawaii DOT, 1991)..................... 146

Figure 8-3. Post-tensioning arrangement for typical span of Windward Viaduct (adapted from Hawaii DOT,

1991) ................................................................................................................................... 147

Figure 8-4. General arrangement of Islington Avenue Underpass (adapted from MTO, 1990) ................. 148

Figure 8-5. Typical cross section of Islington Avenue Underpass (adapted from MTO, 1990) ................. 148


12/197xii

LIST OF TABLES

2.0 BACKGROUND ..................................................................................................................7

Table 2-1. Reference concrete mix quantities (Susetyo, 2007)....................................................................... 9

Table 2-2. Simplified constitutive law for the nominal 80Mpa stress-strain behaviour used in analysis..... 12

3.0 LONGITUDINAL FLEXURE..........................................................................................28Table 3-1. Procedure for calculating the stress in an unbonded tendon due to girder deflections................ 34

Table 3-2. Procedure for calculating uniform applied load corresponding to a desired tendon stress.......... 37

Table 3-3. Estimation of dead load for typical segment................................................................................ 40

Table 3-4. Estimation of superimposed dead load for typical segment ........................................................ 40

Table 3-5. Preliminary prestressing scheme for cantilever tendons based on ultimate capacity .................. 46

Table 3-6. Calculation of long-term bending moment redistribution............................................................ 50

Table 3-7. Preliminary prestressing scheme for continuity tendons based on ultimate capacity.................. 54

Table 3-8. Secondary prestress moment calculation ..................................................................................... 56

Table 3-9. Tendon unit sizes (15mm strands) used for cantilever post-tensioning ....................................... 70

6.0 ANCHORAGE ZONE.....................................................................................................125

Table 6-1. Area of steel required for local spreading reinforcement for top tendons (in mm2).................. 137

Table 6-2. Area of steel required for local spreading reinforcement for bottom tendons (in mm2) ........... 137

8.0 MATERIAL UTILIZATION .........................................................................................145

Table 8-1. Concrete consumption for one span of the Windward Viaduct (Hawaii DOT, 1991) ............... 149

Table 8-2. Concrete consumption for Islington Avenue Underpass (MTO, 1990) ..................................... 149

Table 8-3. Concrete consumption for proposed cantilever box girder........................................................ 149

Table 8-4. Mild reinforcing steel utilization for one span of the Windward Viaduct (Hawaii DOT, 1991)150

Table 8-5. Mild reinforcing steel utilization for Islington Ave Underpass (MTO, 1990)........................... 151

Table 8-6. Mild reinforcing steel utilization for proposed box girder.........................................................151

Table 8-7. Post-tensioning utilization for one span of the Windward Viaduct (Hawaii DOT, 1991) .........152

Table 8-8. Post-tensioning utilization for Islington Ave. Underpass (MTO, 1990).................................... 152

Table 8-9. Post-tensioning utilization for proposed cantilever box girder.................................................. 152

Table 8-10. Transverse prestressing steel utilization for one span of the Windward Viaduct (Hawaii DOT,

1991) ................................................................................................................................... 153

Table 8-11. Transverse prestressing steel utilization for Islington Avenue Underpass (MTO, 1990) ........ 153

Table 8-13. Relative material consumption of proposed box girder...........................................................154

Table 8-12. Transverse prestressing steel utilization for proposed box girder............................................ 154


13/197xiii

LIST OF SYMBOLS

Ap area of unbonded prestressing steel

Aps area of prestressing strand

As area of bonded steel

b width of compression flange

bbf width of bottom flange

bc concrete width function for idealized cross section

btf width of top flange

c distance from neutral axis to extreme compression fibre

d depth of cross section; centre-to-centre distance between tension and compression

piles

db diameter of bonded steel

dp distance from centroid of prestressing steel to extreme compression fibre

dv effective shear depth taken as the greater of 0.9d or 0.72h (CSA 23.3-04)

e eccentricity of prestressing steel

eb continuity tendon eccentricity from girder axis

Ec compressive modulus of elasticity of concrete

Ep elastic modulus of prestressing steel

Et

tensile modulus of elasticity of concrete

et cantilever tendon eccentricity from girder axis

fc stress in concrete

Fc force in concrete

fc cylinder compressive strength of concrete

fci initial concrete strength at transfer

long-term effective prestress

fps stress in bonded prestressing strand

fpu ultimate stress of prestressing steel

fpy yield stress of prestressing steel

fse effective stress in bonded pretensioning steel after losses

fsi stress in bonded prestressing strand just prior to transfer

fsy yield stress of bonded reinforcing steel

ft dogbone tensile strength of concrete

fp


14/197


15/197xv

Ptot total prestress force of unbonded tendons for top and bottom prestressing steel

q uniform load

Q applied load

Qu applied load corresponding to the ultimate state

tbf thickness of bottom flange

ttf thickness of top flange

uf average flexural bond stress of pretensioning strand

V shear

Vc shear resistance attributed to concrete

Vf factored shear demand

Vs shear resistance attributed to transverse reinforcement

w width of web; uniform dead load

x coordinate along longitudinal axis of girder

y elevation in cross section (where bottom fibre elevation is y = 0)

yclo cantilever tip deflection at closure

midspan deflection of continuous system due to long-term creep

ratio of the average stress in compression block to the specified concrete strength

live load factor

prestress load factor

ratio of the depth of compression block to the neutral axis depth

girder deflection

centre-to-centre spacing of transverse ribs

change in beam length due to prestress, dead load, and applied load

elongation of unbonded prestressing steel relative to initial prestress

initial change in beam length due to prestress and dead load

increase in tendon force due to girder deformations

loss in prestress due to superimposed dead load

increase in prestress due to superimposed dead load

change in strain in prestressing steel relative to strain due to initial prestress

strain

bottom fibre strain

ultimate strain of concrete

initial longitudinal strain in concrete at level of prestressing steel

y

1

L

P

1

b

lcp

lcp lp0

lp0

P

P

Pdl

p

b

'c

c0


16/197xvi

average initial strain in concrete due to prestress and dead load

strain caused by concrete stress fc

strain in concrete at level of prestressing steel

ultimate compressive strain

strain in prestressing steel

initial strain in prestressing steel

top fibre strain

cracking strain of fibre-reinforced concrete

strain of concrete at mid depth of member

girder slope; angle of principle compressive stress in the web; angle of force

resultant trajectory for arching shear

angle of compression force in slabs due to anchorage bursting forces

angle of compression force in anchorage blister projected onto flange

angle of compression force in anchorage blister projected onto web

coefficient of friction

fully redistributed concrete stress

bottom fibre stress

concrete actual stress at time of closure

concrete stress obtained assuming entire structure is built simultaneously on

falsework

stress in prestressing steel

long-term effective prestress

top fibre stress

curvature

resistance factor for concrete

resistance factor for prestressing steel

resistance factor for steel

cantilever tip rotation at closure

c0 avg,

cf

cp

cu

P

P0

t

't

x

b

fw

b

clo

fa l

p

p

t

c

p

s

clo


17/197

1

1.0 INTRODUCTION

In modern urban environments, providing increased capacity on existing roadways and bridges

is a significant challenge. Engineers are faced with several demanding factors including tightconstruction scheduling, the maintenance of traffic in highly travelled corridors, and the creation

of structures that enhance the urban landscape. Precast segmental construction is one solution that

can provide aesthetically pleasing structures that can be erected on difficult construction sites. By

the method of match-cast precasting, segments can be fabricated and prepared off-site and erected

rapidly with minimal effect on traffic.

Traditional methods of bridge construction over high-volume highways generally require lane

closures, traffic delays, and in some cases total road closures and traffic detours. Faced with agrowing economy and increased need for traffic flow reliability, minimum impact construction and

rapid erection for bridge building is becoming more crucial especially in the dense urban

environment. This necessity is realized not only for commuter traffic but also industries that rely

on just-in-time delivery. In Europe, new technologies have been implemented exclusively for the

purpose of fast erection in order to minimize impact of construction. Recent implementations of

fast construction in Ontario has been the use of full-width precast panels for overpass bridge

construction over Highway 401 in the Municipality of Chatham-Kent (Rapoport, 2006), and the

recent use of a self-propelled modular transporter for replacement of an overpass bridge on

Highway 417 in Ottawa (Tinkess, 2007). The implementation of new rapid bridge building

technology in Ontario is a testament to the increasing need of new construction methods for fast,

low-impact construction.

New opportunities for efficient and aesthetically pleasing designs exist through the

development of high performance materials such as high strength concrete. Due to the low water-

to-cement ratio made possible by the inclusion of water reducing admixtures, high strength

concrete exhibits favourable design properties such as higher ultimate stress and stiffer modulus of

elasticity. The impact on design due to these improved material properties is the ability to create

more elegant structural designs that make better use materials through the use of thinner sections

that result in light weight solutions. The increased stiffness of new materials allows engineers to

design more slender shapes that add to the aesthetic transparency of the structure.


18/1972

Light weight girders with thin sections for prestressed concrete structures can be made possible

through the use of external unbonded tendons. Flange and web sections with large amounts of

internal bonded steel generally require a significant amount of concrete clear cover solely for the

purpose of durability and corrosion protection. This sacrificial layer of concrete is necessary to

protect the bonded tendons from environmental exposure, but it is not designed as an efficient use

of materials from a strength perspective. By removing the tendons from the concrete section, the

concrete thickness may be reduced to make more efficient use of concrete material, while reducing

the overall weight of the superstructure.

1.1 Statement of Problem

A new minimum-impact solution for rapid highway overpass construction is desired which

makes efficient use of high-performance concrete and external unbonded tendons. The use of

external unbonded tendons in prestressed concrete structures allows for the minimization of

concrete consumption, reduction in dead load due to thinner cross sections, and simplified

construction.

The cantilever method is one type of segmental construction that is self-supporting as it allows

erection of the bridge from the fixed end with no interference with the ground below and no

requirement for falsework. This method is attractive for minimum impact highway overpass

construction since it allows the bridge to be built overhead of the traffic with no requirement for

equipment and machinery below the bridge. For prestressed concrete cantilever-constructed

bridges, cantilever tendons are traditionally designed as internally bonded within the top flange.

Flange thickness is governed by the space required for tendons inside the concrete section, and the

minimum reinforcing steel required for adequate crack control and durability.

Through the development of high-performance materials such as high strength fibre-reinforced

concrete (FRC), improved mechanical properties have been observed to allow engineers greater

possibilities for the design of prestressed concrete structures. Of interest are the benefits to be

gained by the adaptation of high strength FRC and unbonded tendons for use with precast

segmental structures. Quality control of concrete is maximized for precasting in comparison to

cast-in-place concrete, as it is fabricated, cast and cured in a controlled environment. The use of

high strength FRC in combination with external unbonded tendons in concrete structures appears

to be a complimentary pairing of materials as external tendons allow for the minimization of


19/1973

concrete consumption and high strength concrete allows for large precompression stresses from

external prestressing.

Precast segmental cantilevered-construction using exclusively external unbonded tendons with

no continuous reinforcing steel is traditionally not done in standard practice. One rare example of

the use of total external unbonded tendons for precast segmental cantilever construction is theSecond Severn Bridge across the River Severn between England and Wales. Although the use of

total external unbonded prestressing for this bridge was primarily due to a Government durability

requirement, this design also simplified deck unit production and enabled thinner webs and flanges

(Mizon, 1997). Extending the use of external unbonded tendons to cantilever construction

potentially provides an opportunity for designers to erect medium span overpass bridges faster, off

the right-of-way, with little or no interference with traffic demands.

1.2 Scope and Objective

The purpose of this study is to develop and validate a design concept using a new application

of external unbonded tendons intended for rapid overpass bridge construction requiring a low-

impact construction technique.

The objectives of this study are as follows:

develop valid design assumptions for consideration of the proposed bridge type

determine the global member response of the superstructure under serviceability and ultimatelimit states

incorporate the use of high performance (80MPa characteristic compressive strength) fibre-

reinforced concrete (FRC) for the design of thin sections to reduce dead load and minimize

reinforcing steel

validate the use of external unbonded tendons as a new application in segmental cantilevered

construction

The member response investigated for this study examines explicitly the effects of longitudinal

flexure, longitudinal shear and transverse flexure due to the force effects of dead load, live load,

and prestress.

Several actions have not been considered explicitly within the scope of this thesis. These

effects include: a) thermal action, b) torsional loads, and c) combined effects of moment, shear, and

torsion. These effects are important to the final design and for the full understanding of structural

behaviour, and could possibly have an impact on the proposed design concept. Future work is


20/1974

necessary for the complete validation of the superstructure concept. In addition, the primary focus

of this thesis has been on the design and development of the superstructure system for a light

weight box girder design using high strength FRC. The design and development of the substructure

system is briefly discussed but a detailed design of the substructure is beyond the scope of this

work.

1.3 Thesis Structure

This document consists of 9 chapters. Chapter 1 introduces the topic and establishes the design

motivation for using high performance concrete and external unbonded tendons for the application

of rapid highway bridge construction. Chapter 2 presents background information on material

properties and the proposed structural system for discussion. Chapter 3 describes the behaviour of

unbonded tendons in a system with curtailed prestressing and the design for longitudinal flexure of

the proposed bridge. Chapter 4 discusses the motivation for minimizing the thickness of the top

flange and provides a feasible solution for transverse bending using a thin top flange and transverse

pretensioning. Chapter 5 presents a variation of design models for the analysis of shear behaviour

in concrete structures prestressed with unbonded tendons, and provides the design for shear for the

proposed bridge. Chapter 6 describes the importance of anchorages for girders prestressed with

external tendons, and provides the design developed for anchorage reinforcement. Chapter 7

briefly discusses a design concept for a substructure design. Chapter 8 reviews the material

consumption for the proposed bridge and compares the material consumption of other

conventionally constructed bridge designs. Conclusions for this work are summarized in Chapter

9.

Chapter 2 begins by describing the benefits of FRC and the improved constitutive laws that are

distinctive of the material. The results of a mini experimental study are presented and used for the

basis of a simplified design model for the behaviour of high strength FRC in compression. Typical

highway overpass bridges are discussed and the proposed alternative solution is described and

compared.

Chapter 3 first describes the flexural response of concrete girders prestressed with unbonded

tendons and convenient analysis techniques for the preliminary design of girders. For concrete

girders that are prestressed under the action of self-weight, a reference state of strain is described

that corresponds to the deformations of the girder after jacking. To begin the design process,

conservative preliminary design assumptions are described for the state of stress of the unbonded


21/1975

tendons. Following this, the design methodology for cantilever tendons is discussed for a

preliminary estimate of tendon arrangement. The change in structural system due to closure of the

span is discussed and an estimation for long-term redistribution of forces is presented. The design

methodology for continuity tendons is then presented and the effect of the tendon layout on

secondary prestress moments is described. Based on the designed prestress loads, the bottom

flange of the girder is designed for negative bending at the support. The girder behaviour is then

analyzed under factored loads at the ultimate limit state, and unfactored loads for seviceability

performance. Following this, a refinement in tendon stress at the ultimate limit state is investigated

to improve the economy of prestress strand consumption. Finally, the effect of span-to-depth ratio

of the proposed box girder is presented, and a practical range of spans for the proposed box girder

is identified.

Chapter 4 describes the design challenges of satisfying prestress requirements for the thin top

slab in transverse bending due applied vertical loads and prestress forces. The design assumption

of small concrete covers is addressed. The chosen pre-tensioning prestress system is justified based

on the available studies that demonstrate the improved bond strength characteristics between high

strength FRC and 15mm pretensioning strands. The method of analysis to determine the live load

distribution of forces is described. A comparative study between the proposed box girder and an

AASHTO-PCI-ASBI standard box girder (Precast/Prestressed Concrete Institute, 1997) is then

carried out for the validation of the thin top flange design in transverse bending on the basis of

maximum allowable deflections. The deflections and computed stress ranges of the top flange at

service loads is shown for the final design. Finally, a design detail for a proposed PL-2 barrier

defined in the CAN/CSA S6-06 (Canadian Standards Association, 2006) is presented for the

resistance of impact loads.

Chapter 5 begins with a discussion on strut-and-tie models and the description of the funicular

load path in a prestressed girder with curtailed unbonded prestressing tendons. Various approaches

to shear design are discussed based on alternative decompositions of the funicular load path in

concrete structures. A parallel chord model is discussed and the variable angle parallel chord model

used in the CAN/CSA-S6-06 shear provisions is described. Based on the results of a previous

study, an arching model by Noshiravani (2007) is described and compared to the parallel chord

model. For the proposed box girder, a parallel chord model is decided to be most appropriate to

describe the flow of forces in the box girder to transfer vertical loads. The proposed girder is then


22/1976

analyzed for the shear demands based on CAN/CSA-S6-06 load configurations. Finally, the design

for web reinforcement is presented based on the parallel chord model.

Chapter 6 begins with a discussion of anchorages for prestressed concrete girders with external

unbonded tendons. The fundamentally different flow of forces within the anchorage zone for an

unbonded tendon is then described in comparison to the anchorage zone of an internal tendon. Athree-dimensional strut-and-tie model is developed for the design of reinforcement required to

anchor an external unbonded tendon at a corner blister. Possible reinforcement detailing based on

the developed truss model is proposed to enable the required flow of forces.

Chapter 7 briefly describes a conceptual abutment design for the proposed bridge. The

abutment must: a) adequately provide anchorage of all cantilever prestressing, b) resist large fixed

end moments due to negative flexure of the superstructure, and c) provide longitudinal flexibility

to allow for thermal movements since the proposed bridge is designed to be monolithic at the

midspan with no expansion joints. A detailed analysis of substructure behaviour is beyond the

scope of this work, however.

Chapter 8 first describes two reference bridges which are used to determine the material

utilization of conventional construction in comparison to the proposed box girder bridge. One

reference bridge is representative of traditional cantilever construction, and the other reference is

representative of a typical highway overpass structure in Ontario. Concrete usage, mild steel

reinforcement utilization, longitudinal prestressing and transverse prestressing steel consumption

quantities are compared.

Chapter 9 concludes with a summary of findings for the design components investigated within

this study. Recommendations for the design of cantilever-constructed bridges prestressed with

unbonded tendons are provided. Advantages of using thin concrete sections with unbonded

tendons are described, and the disadvantages are identified. Necessary future work is discussed for

the full validation of the proposed design concept.


23/197

7

2.0 BACKGROUND

This chapter begins by discussing the behaviour of fibre-reinforced concrete (FRC) under axial

compression and axial tension. The results of a small experimental program are presented andbriefly discussed for test specimens fabricated with nominal 80MPa strength concrete, similar to

the concrete intended for design. A simple stress-strain model is developed for the FRC specimens

tested which will be used for the behaviour of concrete throughout the work of this study.

Following this, conventional highway overpass bridge construction using precast components is

described and a description of the proposed bridge concept using precast segments is presented. A

visual comparison of the proposed bridge to a conventional overpass is made to evaluate the

aesthetic qualities of the proposed bridge. Finally, benefits and drawbacks of the proposed bridge

concept are identified.

2.1 Constitutive Laws for High Performance FRC

2.1.1 Compressive Stress-Strain Behaviour

The innovation of material technology has introduced a widespread variety of high

performance concrete materials that have improved mechanical properties over traditional 35MPa

concrete mix designs. High performance concretes (HPC) range to approximately 100MPa and

ultra-high-performance fibre-reinforced concrete (UHPFRC) can be as high as 200MPa. Research

programs have been carried out in many countries to study the behaviour high performance

concrete, leading to significant changes to design codes in several countries. (Paultre et al., 2003).

Design codes are continually evolving documents using a consistent philosophy and the latest

research results, often reflecting the prior state of the art and tradition of the country of origin

(Paultre et al., 2003). However, because concrete is a heterogeneous material without standardized

mixture designs, the compressive stress-strain responses of different concrete mixtures exhibit

significant scatter (Graybeal, 2007). As a result, the empirical definitions of compressive stiffness

of HPC is not entirely consistent among design codes. A comparison of elastic modulus code

definitions and recent results of some researchers are displayed in Figure 2-1below.


24/1978

Figure 2-1. Variation in modulus of elasticity with the ultimate compressive strength of concrete

While these design values for elastic stiffness are useful for the calculation of structural

behaviour at the serviceability limit state, very little information is available in the literature that

discusses the post-peak descending branch of FRC. The post peak behaviour is important since it

has a considerable effect on the flexural ductility of a member at the ultimate limit state. Due to the

large amount of scatter in the elastic stiffness constitutive laws, and the lack of information

published on the compressive post-peak response of FRC, compression cylinder tests were

performed to develop a full range stress-strain material model for use in the analysis of the

proposed design.

A concrete mix design was adapted from Susetyo (2007) for a nominal 80MPa FRC containing

1.5% hooked steel fibre volume ratio. The reference concrete mix design is outlined in Table 2-1.

Two compression cylinder specimens were tested for the basis of the simplified stress-strain model

shown in Figure 2-2. The average peak stress was observed to be 74.5MPa, and the average

uncracked elastic modulus was observed to be 43680MPa. A more thorough description of the

experimental program is given in Appendix B. The compression cylinder test results were

compared with a previous study by Chao et al. (2006), who performed cylinder tests for a 75MPaFRC mortar matrix containing no coarse aggregate and 1% steel fibres, and found there was good

agreement in the results. The curves are comprised of a stiff initial ascending branch, followed by

a ductile post-peak descending branch.

0

00001

00002

00003

0000400005

00006

00007

00008

00009

00108060402

80Mpa concrete strengthintended for design

Ec[MPa]

fc[MPa]

Graybeal 2007 (fc 200MPa)

CHBDC 2006 (fc 85MPa)

ACI 1992 (fc 83MPa)

ACI 2005 (fc 40MPa)

Ma et al. 2004 (fc 200MPa)

CEB-FIP 1990 (fc 88MPa)

CSA 2004 (fc 80MPa)

CSA 2004 (fc 40MPa)


25/1979

Figure 2-2. Compressive stress-strain relationship for nominal 80MPa FRC test specimens and simplified model

The presence of fibres in the concrete matrix provides excellent confinement which facilitates

the sustained compressive stresses after concrete crushing and allows for significant ductility in the

post-peak response. Figure 2-3displays a failed FRC compression cylinder after the test. Even

after significant post-peak straining, the concrete remains intact and very little spalling from the

surface is observed. The resistance to spalling not only contributes to the strength of FRC at the

ultimate limit state, but it also provides an important benefit for durability of structures as it

improves the performance for frost resistance during freeze-thaw cycles (Xu et al., 1998).

Table 2-1. Reference concrete mix quantities (Susetyo, 2007)

Material Measured Unit Quantity Equivalent Volume

HSF Cement kg 600 0.191

Sand (SSD) kg 1133 0.419

10mm limestones (SSD) kg 802 0.292

Water L 162 0.162

Water Reducer mL 4200 -

Superplasticizer mL 9600 -

Entrapped Air 0.02

Total Volume m3 1.083

0

01

02

03

04

05

06

07

08

09

001

800.0700.0600.0500.0400.0300.0200.0100.00

Chao (2006)

UofT testscompression modeldeveloped for design

# specimens tested = 2E

avg= 43680 MPa

c avg

= 0.00209 mm/mmf

c avg= 74.6 MPa

fc[MPa]

c[mm/mm]


26/19710

Figure 2-3. Photo of intensively cracked compression cylinder after failure and significant post-peak straining

2.1.2 Tensile Stress-Strain Behaviour

Since fibre-reinforced concrete exhibits a more ductile tension stress-strain response in

comparison to the brittle nature of normal concrete, the standard ASTM C496 cylinder splitting

test is insufficient to measure the tensile response of FRC. In lieu of the ASTM C496 test,

deformation-controlled dogbone-shaped test specimens loaded in uniaxial tension have been

performed by previous researchers to provide a tensile stress-strain relationship of FRC. Susetyo

(2007) performed a dogbone tension test on the nominal 80MPa FRC similar to the test set-up by

Habel et al. (2006), shown in Figure 2-4below.


27/19711

Figure 2-4. a) Dogbone-shaped specimen: dimensions and sensors, b) test set-up of the uniaxial tensile test, showingthe front side of the specimen (adapted from Habel et al., 2006)

The result of the dogbone tension test performed by Susetyo (2007) is presented in Figure 2-5.

The FRC mix design predominantly exhibits tension softening following the occurrence of the first

crack. In general, the formation and opening of one primary crack dominates the post-cracking

response due to the relatively low fibre ratio of 1.5%. Although tension stiffening behaviour is

possible for some FRC mix designs (which generally requires a larger amount of fibres), an

increased consumption of steel fibres to achieve this behaviour is not necessary or economical for

the application of FRC in precast segmental construction. For either dry joints or epoxy joints

between precast units, there is no embedment length of fibres across the joint; therefore, the

smeared tension behaviour of FRC can not be relied upon at the joint interface undergoing flexural

tension forces. For epoxied joints, a brittle tensile behaviour would be expected that is related to

the cracking strength of the concrete, with no contribution of the fibres since internal equilibrium

of tension stresses in the fibres can not be established at the joint. Thus, the inclusion of steel fibres

in the concrete mix is included predominantly for the benefit of controlling plastic shrinkagecracking which replaces typical temperature and shrinkage reinforcement.

Sivakumar (2007) has provided a study which indicates that for a high strength 60MPa silica

fume cement, the inclusion of only 0.5% steel fibres reduces the plastic shrinkage cracking by 49%

compared to the same mix with no fibres. Some hybrid mix designs including steel fibres and

polyester fibres provided a better reduction in shrinkage cracking by 95% while maintaining

a) b)

100

5050

100

5050

100

100

200

LVDT

U4

Front Back

specimen

depth = 50mm

U4 - deformation transducers

LVDT - linear variable differential transformer


28/197


29/19713

2.2 Typical Modern Highway Overpass Bridge Design Currently in Ontario

Since the 1950s, prestressed concrete bridges have become increasingly popular, and

comprise about two-thirds of all bridges with spans between 18 and 36m (Lounis et al., 1997). The

precast concrete I-girder system represents about 50% of all prestressed concrete bridges built up

until the early 1990s (Dunker et al., 1992). Precast I-girder systems have expanded their use evenfurther in the last thirty years through the concept of spliced girders to extend the span capability

(Rabbat et al., 1999; CPCI, on-line). Although transportation equipment and available cranes

limited the length of precast pretensioned girders to around 34m in the 1960s, precast I-girders

now can be fabricated and transported in lengths of 40m to 50m and weights up to 75 to 90 tonnes

(CPCI, on-line). The standardization of girder sections has led to simplified designs, speed of

construction, and resulted in economy (Rabbat et al., 1999).

Since slab-on-girder bridges represents such a large proportion of bridges of short to medium

spans, precast slab-on-girder bridges will be regarded as a typical highway overpass design for

comparison to the proposed precast segmental box girder design. Both of these systems are precast

and are comparable in terms of low impact of construction solutions. A visual example of a typical

modern slab-on-girder structure is shown in Figure 2-6. This bridge depicts a typical continuous

two-span overpass structure supported by a centre pier in the median of the highway. The

abutments have parallel wingwalls oriented parallel to the axis of the bridge. A concrete parapet

lines the edges of the deck slab along the length of the bridge and continues to the furthest extents

of the wingwalls.

Figure 2-6. Typical slab-on-girder highway underpass built in Markham, Ontario on Highway 407. Photographcourtesy of Scott Steves, 2006.


30/19714

To maximize economy, bridge girder sections have been standardized as it provides a basis for

consistency and allows for the multiple reuse of standard forms for several bridge projects (Figg,

1997). The Canadian Precast/Prestressed Concrete Institute (CPCI) provides a range of standard

sections that are available in Canada. A suggested range of spans is provided for the use of each

standard section and a recommended transverse girder spacing is provided in relation to the girder

span length (shown in Figure 2-7). Although this recommendation is given only as a guideline, it

provides engineers with a launching point in which to form a slab-on-girder bridge concept.

Figure 2-7. Recommended girder spacing with respect to span length for standard CPCI precast I-girders (adaptedfrom CPCI, 1996)

In addition to precast concrete girder sections being standardized, the design of slab-on-girder

bridges are also somewhat standardized as they must conform to several geometric constraints for

evaluation using the Simplified Method of Analysis detailed in the CAN/CSA-S6-06 (cl. 5.6.1, cl.

5.7.1). As the Simplified Method outlines an empirical approach to provide safe designs for a wide

range of span lengths and bridge widths, the design of bridges using these methods in general

produces conservative designs.

2.2.1 Standardization of Precast Components

Following the standardization of precast I-girder sections, an evolution for prestressed precast

concrete applications emerged in 1997 for standardized segmental bridge construction (Rabbat et

al., 1999). The AASHTO-PCI-ASBI Segmental Box Girder Standards provided a new product for

grade separations and interchange bridges for span lengths up to 61m (Freyermuth, 1997). Two

families of standard box girder sections exist: one intended for span-by-span construction, and

another intended for cantilever construction. The standard box girder for span-by-span

construction, which has a maximum intended span of 45.7m, exhibits thinner flanges since all post-


31/19715

tensioning steel is comprised of external unbonded tendons. The standard box girder for cantilever

construction has thicker top and bottom flange components to incorporate the internal bonded

cantilever and continuity post-tensioning tendons and a thicker web since cantilevering can achieve

longer spans.

Segmental spans can be erected very quickly, typically in a few days, minimizing disruption oftraffic (Figg, 1997). For bridge projects intended for the standard precast box girders, it is generally

anticipated that segments are erected by crane (Freyermuth, 1997). The large amount of work that

can be done off site under a controlled environment is favourable as it reduces the amount of on-

site construction time and permits the best curing conditions for the concrete to achieve a higher

standard of durability. Quality control can be maintained as segments fabricated with high-quality

precast concrete can be erected during non-peak traffic hours when disruption of traffic is kept to

a minimum.

The recommended minimum concrete strength for the standard segmental sections is 34MPa.

In some cases, concrete with a greater compressive strength can be used; however, no changes to

the standard AASHTO-PCI-ASBI cross sectional dimensions and cross sectional thicknesses can

be made to exploit the full potential and economy of high-strength concrete mix designs. These

standard sections have been developed for the application of traditionally reinforced normal

concrete mixes. For the application of high-performance FRC and total external unbonded post-

tensioning, a new structural section, respecting the inherent advantages of FRC, needs to be

developed to achieve economical designs and efficient use of the material.

2.3 Description of the Proposed Segmental Box Girder Concept

The proposed bridge system for precast segmental cantilever construction is a constant depth

single cell box girder with a span-to-depth ratio of 25:1. The box girder cross section is designed

to have thin flanges and thin webs to make efficient use of high-strength concrete and to reduce

dead load of the superstructure. The maximum bridge span considered for this study is 90m for

practical and visual considerations. As a practical consideration, the maximum depth of the girder

segments should be limited to accommodate ease of transportation which is constrained by

standard vertical clearances for existing overpass structures. As a visual consideration, the depth

of the girder should be limited to maintain a reasonable level of slenderness for the design. At a

25:1 span-to-depth ratio, a 90m span length corresponds to a girder depth of 3.6m.


32/19716

For the transportation of tall segments, a low-boy trailer is necessary which has a lowered

section of the trailer to reduce the top of the bed to within 610mm of the roadway surface (Precast/

Prestressed Concrete Institute, 1997). The minimum vertical clearance provided under highway

bridges in Ontario is 4.7m for existing structures and 4.8m for new structures (Ontario Ministry of

Transportation, 2002). The barrier walls of the precast segments are intended to be cast-in-place

after the cantilever structure has been closed; therefore, the 3.6m deep girder may be transported

along any major highway in Ontario with a minimum vertical clearance of 490mm for protruding

reinforcing steel for the cast-in-place barrier wall.

A conceptual plan and elevation of the proposed cantilever girder concept for the longest span

considered of 90m is shown in Figure 2-8. The girder is erected segmentally from the abutments,

and each cantilevered segment during construction is post-tensioned to the structure with

permanent external unbonded post-tensioning tendons. The typical precast segment length is 3m

to accommodate standard traffic lane widths for delivery of segments. The minimum vertical

clearance provided over traffic lanes is 5000mm, which is consistent with standard policy for new

structures over roadways for this bridge type (Ontario Ministry of Transportation, 2002) and a

700mm construction tolerance has been provided for safety during construction. The 90m

mainspan is continuous across the abutment face and the short 15m sidespan is ballasted by backfill

material to maintain rotational restraint at the abutment face and to prevent uplift of the backspan.

Figure 2-8. Plan and elevation view of a possible cantilever-constructed overpass bridge


33/19717

Assuming the overpass bridge structure services an arterial undivided urban roadway, the

minimum side clearance from the edge of the travelled way to the face of the barrier is 2.0m

(Ontario Ministry of Transportation, 2002). The arrangement of traffic lanes intended for the box

girder bridge consists of two centrally located lanes with a width of 3.6m each, two exterior

shoulders with a width of 2.0m each, and an allowance for traffic barriers with a width of 400mm

each. Therefore, the total cross sectional width of the top flange considered for this design is 12.0m

(shown in Figure 2-9). As there is no thickness requirement t

Documents

Innovative Pre-Cast Cantilever Constructed Bridge Concept