Table Of ContentInnovative Systems for Arch Bridges using
Ultra High-Performance Fibre-Reinforced Concrete
by
Jason Angeles Salonga
A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy
Graduate Department of Civil Engineering
University of Toronto
© Copyright by Jason Angeles Salonga (2010)
Innovative Systems for Arch Bridges using Ultra High-Performance Fibre-Reinforced Concrete
Jason Angeles Salonga
Doctor of Philosophy
Department of Civil Engineering
University of Toronto
2010
Abstract
In this thesis, new design concepts for arch bridges using ultra high-performance fibre-reinforced concrete
are developed for spans of 50 to 400 m. These concepts are light-weight and efficient, and thus have the
potential to significantly reduce the cost of construction. Lightness is achieved by the thinning of structur-
al components and the efficient use of precompression in the arch, rather than by the decrease of bending
stiffness. Using the advanced properties of the material, the design concepts were shown to reduce the
consumption of concrete in arch bridges by more than 50% relative to arches built using conventional con-
crete technology. In addition to span length, other design parameters including span-to-rise ratio and
deck-stiffening were considered, resulting in a total of seventy-two design concepts.
Other important contributions made in this thesis include: (1) the development of a simple analytical
model that describes the transition of shallow arches between pure arch behaviour and pure beam beha-
viour, (2) a comprehensive comparative study of 58 existing concrete arch bridges that characterizes the
current state-of-the-art and serves as a valuable reference design tool, and (3) the development and experi-
mental validation of general and simplified methods for calculating the capacity of slender ultra high-per-
formance fibre-reinforced concrete members under compression and bending. The research presented in
this thesis provides a means for designers to take full advantage of the high compressive and tensile
strengths of the concrete and hence to exploit the economic potential offered by the material.
ii
Acknowledgments
I would like to thank, first and foremost, Professor D. P. Gauvreau, for all the guidance and encouragement
he has given me as a supervisor, teacher, and mentor over the past five years. His passion for bridges, with
respect to their design, construction, and aesthetics has certainly been contagious and will forever be an
inspiration to me.
I would also like to thank Professor F. J. Vecchio, Professor P. C. Birkemoe, Professor S. A. Sheikh, and Pro-
fessor V. Sigrist for serving on my Ph.D. Examination Committee and for reviewing this thesis.
Financial assistance during the majority of my graduate studies was provided in large part by the Natural
Sciences and Engineering Research Council of Canada, and the University of Toronto. For this, I am
sincerely grateful.
Many others have given their time selflessly to help me along the way. Experimental work would not have
been possible without the help of my colleagues Ivan Wu, Jimmy Susetyo, Kris Mermigas, Brent Visscher,
Davis Doan, Lulu Shen, Nabil Mansour, Boyan Mihailov, James Liu, and Serguei Bagrianski, and laborat-
ory staff Joel Babbin, Renzo Bassett, Giovanni Buzzeo, and John MacDonald. I am also indebted to others
who have accompanied and helped me along the way, including: Billy Cheung, Negar Elhami Khorasani,
Jeff Erochko, Eileen Li, Jamie McIntyre, Michael Montgomery, Talayeh Noshiravani, Sandy Poon, Carlene
Ramsay, Nick Zwerling, and especially Lydell Wiebe. A special thanks is dedicated to Catherine Chen who
assisted me over two summers in compiling the database of concrete arch bridges.
Last, I thank my wife Sarah, my parents, Danilo and Elizabeth, and my siblings, Michael, Elaine, and
Rodell, for their steadfast love and support.
iii
Table of Contents
Abstract, ii
Acknowledgments, iii
Table of Contents, iv
List of Figures, x
List of Tables, xvii
List of Symbols, xix
List of Uncommon Terms, xxix
Chapter 1. Introduction, 1
1.1 Motivation, 1
1.2 State-of-the-art, 5
1.2.1 Highway girder bridges, 5
1.2.2 Pedestrian arch bridges, 7
1.2.3 Highway arch bridges, 8
1.3 Objectives and content of thesis, 12
Chapter 2. Ultra High-Performance Fibre-Reinforced Concrete, 15
2.1 Material testing at the University of Toronto, 15
2.1.1 Mix design, 17
2.1.2 Batching and casting, 17
2.1.3 Material behaviour in compression, 18
2.1.4 Material behaviour in tension, 26
2.1.5 Shrinkage behaviour of the material, 30
2.1.6 Creep behaviour of the material, 31
iv
Chapter 3. Slender Ultra High-Performance Fibre-Reinforced Concrete Columns, 32
3.1 Response of eccentrically loaded columns, 33
3.2 General analysis method, 37
3.2.1 Methodology, 37
3.2.2 Calculating moment curvature diagrams, 38
3.2.3 Calculating column deflection curves, 42
3.2.4 Calculating member capacity interaction diagrams, 46
3.2.5 Calculating load-deflection response of a given column and eccentricity of load, 52
3.3 Overview of computer program, 54
3.4 Experimental validation, 56
3.4.1 Batching, casting, and curing, 57
3.4.2 Setup and instrumentation, 57
3.4.3 Load testing and failure, 60
3.4.4 Test results and discussion, 62
3.4.5 Validation of general method, 66
3.5 Simplified design method, 69
3.5.1 Menn’s simplified design method, 69
3.5.2 Simplified method for the design of slender members, 75
v
Chapter 4. Statical Analysis of Arch Bridges, 82
4.1 Relevant literature, 82
4.2 Definition of structural system, 84
4.3 Comparison of three-hinged, two-hinged, and fixed arches, 85
4.3.1 Flexural buckling of arches, 86
4.3.2 Setting the shape of the arch, 89
4.3.3 Response of arches to nonuniform, vertical loads, 91
4.3.4 Effects of restrained deformation on arches, 96
4.3.5 Other load cases, 98
4.4 Structural response of fixed arch systems, 98
4.4.1 Simplified statical system, 99
4.4.2 Force method for non-shallow arches, 107
4.4.3 Force method for shallow arches, 110
4.4.4 Flexural buckling of shallow arches, 118
4.4.5 Second-order analysis: geometric nonlinearity, 120
4.4.6 Second-order analysis: material nonlinearity, 123
4.4.7 Fixed system moments, 126
4.5 Critical load combinations, 127
4.5.1 Long-term loads, 130
4.5.2 Short-term loads, 134
4.5.3 Second-order analysis of combined long and short-term loads, 135
4.5.4 Maximum sectional forces at quarter-points, 138
4.6 Summary of arch analysis, 140
4.7 Critique of Billington’s arch stress analysis, 144
vi
Chapter 5. Comparative Study of 58 Concrete Arch Bridges, 153
5.1 Objective and utility, 153
5.2 Database of concrete arch bridges, 156
5.2.1 Sources of information, 156
5.2.2 Acceptance criteria, 157
5.2.3 Drawing database, 158
5.2.4 Recorded data, 160
5.3 Trends in recorded data and geometric ratios, 165
5.3.1 Geographic location, 166
5.3.2 Methods of construction, 167
5.3.3 Structural depths of arches and decks, 171
5.3.4 Moments of inertia of arches, decks, and columns, 174
5.3.5 Arch slenderness ratios, 179
5.3.6 Span-to-rise ratios, 180
5.3.7 Modified slenderness ratios, 184
5.3.8 Equivalent slab thickness, 187
5.3.9 Historical evolution, 189
5.3.10 Horizontal reactions caused by dead load, 190
5.3.11 Effects of combined dead and live loads, 191
5.4 Summary of observed trends, 194
vii
Chapter 6. New Concepts for Arch Bridges, 197
6.1 Parametric design study, 198
6.1.1 Loads, load factors, and material resistance factors, 201
6.1.2 Longitudinal proportioning of self-stiffened arch systems, 205
6.1.3 Longitudinal proportioning of deck-stiffened arch systems, 207
6.1.4 Longitudinal proportioning of partially deck-stiffened arch systems, 210
6.1.5 Wall slenderness, 212
6.1.6 Proportioning of spandrel columns, 215
6.2 Preliminary design concepts, 217
6.2.1 Parametric design solutions, 217
6.2.2 Sample design calculations including shear, 227
6.2.3 Concept 80, 228
6.3 Discussion of design concepts, 237
6.3.1 Proportions of self-stiffened arch concepts, 237
6.3.2 Proportions of deck-stiffened arch concepts, 239
6.3.3 Proportions of partially deck-stiffened arch systems, 240
6.3.4 Design interaction diagrams, 241
6.3.5 Proportions of spandrel columns, 243
6.3.6 Material efficiency, 243
6.3.7 Distribution of concrete volume, 245
6.3.8 System slenderness and shallowness, 247
6.3.9 Structural demands, 252
6.3.10 Summary of results and conclusions, 257
6.4 Recommendations, 259
viii
Chapter 7. Conclusions and Summary, 266
7.1 Conclusions, 266
7.2 Material behaviour, 269
7.3 Sectional behaviour, 271
7.4 Slender column behaviour, 273
7.5 Arch system behaviour, 275
7.6 Trends observed from existing concrete arch bridges, 280
7.7 Innovative systems for concrete arches, 282
References, 288
Appendices, 294
A. Integrated Database of Concrete Arch Bridges, 295
B. Details of Computer Program QULT, 299
C. Slender Column Drawings, 305
D. Design Calculations for Concept 80, 315
Curriculum Vitae, 335
ix
List of Figures
Figure 1-1. Flow of forces and sectional forces in arches and beams, 2
Figure 1-2. Construction of Sandö Bridge (top) and Colorado River Bridge (bottom), 3
Figure 1-3. Cross-section of ultra high-performance fibre-reinforced concrete girder used in Virginia Bridge, 6
Figure 1-4. Sun-Yu Pedestrian Bridge, 7
Figure 1-5. Reinforcement-free micro-anchorage detail, 8
Figure 1-6. Elevation, cross-section, and joint detail views of WILD Bridge concept, 9
Figure 1-7. Bakar Bridge concept, 10
Figure 1-8. Bridge concept for a 1000 m crossing, 11
Figure 2-1. Mortar mixer and concrete bucket, 18
Figure 2-2. Load versus displacement data of cylinders from Set 1, tested 27 days after casting, 19
Figure 2-3. Load versus displacement data of cylinder from Set 2, tested 60 days after casting, 19
Figure 2-4. Ultra high-performance fibre-reinforced concrete cylinder at failure, 22
Figure 2-5. Compressive strength versus age of concrete after casting, 23
Figure 2-6. Material model in compression, 24
Figure 2-7. Tangent modulus of elasticity versus compressive strength of tested cylinders, 25
Figure 2-8. Modulus of rupture test setup and load-displacement results, 26
Figure 2-9. Material model in tension, 28
Figure 2-10. Shrinkage strains as a function of days after casting, 30
Figure 2-11. Creep strain of an untreated ultra high-performance fibre-reinforced concrete specimen over time, 31
Figure 3-1. Structural model for eccentrically loaded columns, 33
Figure 3-2. Load deflection and sectional response of a slender column given different analytical assumptions, 35
Figure 3-3. Contours of equal curvature and corresponding moment-curvature diagrams, 40
x
Description:4.5.4 Maximum sectional forces at quarter-points, 138 Elevation, cross-section, and joint detail views of ILD Bridge concept, 9 Precast, segmental canti-. 1.
