gfrp-reinforced concrete guideway beams for …
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GFRP-REINFORCED CONCRETE GUIDEWAY BEAMS FOR
MONORAIL APPLICATIONS
by
Nikolaus Wootton
A thesis submitted to the Department of Civil Engineering
In conformity with the requirements for
the degree of Master of Applied Science
Queen’s University
Kingston, Ontario, Canada
(January, 2014)
Copyright © Nikolaus Wootton, 2014
ii
Abstract
Increased demand for reliable public transit is motivating new and innovative
transportation solutions. Monorail trains are quickly being established as transportation
solutions for dense urban areas, due to their unobtrusive infrastructure. To obtain
maximum value from investments made, the infrastructure is required to last longer than
typical reinforced concrete. This thesis will explore the use of glass-fibre reinforced
polymer (GFRP) bars as reinforcement in concrete guideway beams as a means of
avoiding the deterioration problems that plague steel-reinforced concrete.
This thesis includes a two part investigation: a full-scale field application of a GFRP-
reinforced concrete guideway beam (690 mm x 1,500 mm x 11,600 mm), compared to a
typical steel-reinforced beam (both installed on a 1.86 km long monorail test track); and a
laboratory study of a scaled-down version of the GFRP-reinforced beam to better predict
behaviour beyond typical service load levels.
A total of 450 test passes of a two-car monorail train were observed over the two
instrumented beams on the track. These passes were performed at vehicle loads ranging
from fully unloaded for the first testing phase, up to the maximum allowable design
service load. At each stage of testing, vehicle speeds ranged from as low as 5 km/h to as
high as 90 km/h, allowing for the dynamic behaviour of the guideway to be observed and
quantified. Deflections, strains, and cracks were recorded and compared with
code/guideline limitations as well as to numerical predictions to determine which design
tools were most effective and could predict behaviour accurately. In the laboratory, the
half-scale GFRP-reinforced beam was tested statically to failure, and the behaviour was
compared to the same modelling tools used in the field study.
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Based on the testing performed, the GFRP-reinforced concrete beams performed
satisfactorily and met all serviceability requirements, but did not perform as well as the
steel-reinforced beam (as a result of the reduced stiffness of GFRP). The use of non-
prestressed GFRP-reinforced beams should be limited to applications where spans are of
comparable length to the field study. To maintain satisfactory performance, guideway
spans significantly longer will need to continue to be design as prestressed beams.
iv
Acknowledgements
First and foremost, I’d like to express my sincere thanks to my co-supervisors, Dr. Amir
Fam, and Dr. Mark Green, for the exceptional guidance and mentorship they have
provided. The success of this research project is undeniably in great part due to the
knowledge and dedication they provided, overcoming many obstacles, large and small. I
cannot express in words how grateful I am to have been provided with this truly unique
project and learning experience.
On behalf of the Queen’s Research Team, I’d like to express my upmost gratitude to
Bombardier Transportation, and to Delbert Adams and Mark Dickson in particular, for
without them this project would never have come to fruition. Many others at BT deserve
a great deal of credit as well, from the Vehicle Testing Team who repeatedly provided us
with site-access at a moment’s notice, to those within the BT office who without having
ever met myself previously, took genuine interest in the work we were doing.
I also owe a great deal of gratitude to Anchor Concrete Products, and to Darrell Searles in
particular, for ensuring that the fabrication of our test specimens went without incident.
Additionally, I’d like to thank those in the Production Facility who spent countless hours
fastening the thousands of cable-ties for a material they had never worked with, and
walking on egg-shells to preserve our delicate instrumentation.
Paul Thrasher, Neil Porter, Bill Boulton, and the rest of the support staff within our
department also deserve a great deal of appreciation for their substantial contributions to
the fabrication, instrumentation, and computer-networking required for the testing in this
project.
v
I cannot thank my friends and colleagues enough for the last two years. From the
numerous social gatherings and recreational sports, to the trips to Anchor Concrete or the
KMTT to connect dozens of strain gauges and mounting LPs outdoors in the middle of
winter. Special thanks go to Ryan Regier, Stefano Arcovio, and Bryan Simpson for their
participation in all of the above, as well as sharing a roof with me for the majority of our
time as grad-students.
Finally, my greatest appreciation and sincerest thanks go to my family and those closest
to me. Barb & Brian Howie, Dave & Nancy Wootton, and Katie Street, your words of
encouragement and unfailing support of my pursuit of graduate studies and my path in
life have meant the world to me.
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Table of Contents
Abstract ............................................................................................................................................ ii
Acknowledgements ......................................................................................................................... iv
List of Figures ................................................................................................................................. ix
List of Tables ................................................................................................................................. xii
Chapter 1 Introduction ..................................................................................................................... 1
1.1 General ................................................................................................................................... 1
1.2 Objectives of the Research ..................................................................................................... 2
1.3 Organization of the Thesis ..................................................................................................... 3
1.4 References .............................................................................................................................. 5
Chapter 2 Literature Review ............................................................................................................ 6
2.1 Fibre-Reinforced Polymers .................................................................................................... 6
2.2 Design Codes in North America ............................................................................................ 7
2.2.1 Design Philosophy .......................................................................................................... 8
2.3 Durability ............................................................................................................................. 10
2.3.1 Environmental Effects .................................................................................................. 11
2.3.2 Mechanical Effects ........................................................................................................ 12
2.4 Shear .................................................................................................................................... 13
2.5 Crack Mitigation in Tall Members ...................................................................................... 14
2.6 Deflections and Tension Stiffening...................................................................................... 17
2.7 Hysteresis ............................................................................................................................. 18
2.8 Summary .............................................................................................................................. 19
2.9 References ............................................................................................................................ 20
Chapter 3 Full Scale Study of a GFRP-Reinforced Concrete Beam for a Monorail Guideway .... 23
3.1 Introduction .......................................................................................................................... 23
3.2 Experimental Program ......................................................................................................... 25
3.2.1 Test Specimens ............................................................................................................. 30
3.3 Experimental Results and Discussion .................................................................................. 35
3.3.1 Phase 1 .......................................................................................................................... 40
3.3.2 Phase 2 .......................................................................................................................... 43
3.3.3 Phase 3 .......................................................................................................................... 44
3.4 Numerical Modelling ........................................................................................................... 45
3.4.1 Modelling Results ......................................................................................................... 48
vii
3.4.1.1 GFRP-Reinforced Beam ........................................................................................ 48
3.4.1.2 Steel-Reinforced Beam .......................................................................................... 53
3.4.1.3 Prediction of Deflected Shapes .............................................................................. 54
3.4.1.4 Adjustments to Modelling Procedure .................................................................... 55
3.5 Comparison of Experimental Deflections with Acceptable Limits ..................................... 56
3.6 Conclusions .......................................................................................................................... 59
3.7 References ............................................................................................................................ 60
Chapter 4 Static Performance of a Laboratory-Scale Replica of a GFRP-Reinforced Concrete
Beam for a Monorail Guideway .................................................................................................... 64
4.1 Introduction .......................................................................................................................... 64
4.2 Experimental Program ......................................................................................................... 65
4.2.1 Full-Scale Beam Designs .............................................................................................. 66
4.2.2 Concrete Mix Design .................................................................................................... 69
4.2.3 Scale Factor and General Construction ......................................................................... 70
4.2.4 Scale Down Procedure .................................................................................................. 71
4.2.5 Normalized Behaviour Predictions ............................................................................... 73
4.2.6 Fabrication .................................................................................................................... 77
4.2.7 Test Setup for Half-Scale Beams .................................................................................. 78
4.2.7.1 Instrumentation ...................................................................................................... 79
4.2.8 Materials Testing .......................................................................................................... 82
4.3 Testing Results and Discussion ........................................................................................... 83
4.3.1 Service Load Ramp ....................................................................................................... 84
4.3.2 Peak Allowable Service Load (25% ffrp(ultimate)) ............................................................. 86
4.3.3 Failure Ramp ................................................................................................................. 87
4.4 Performance Evaluation ....................................................................................................... 92
4.4.1 Strain Profiles ................................................................................................................ 96
4.4.2 Deformability ................................................................................................................ 99
4.5 Conclusions ........................................................................................................................ 101
4.6 References .......................................................................................................................... 103
Chapter 5 Conclusions and Future Work ..................................................................................... 106
5.1 General ............................................................................................................................... 106
5.2 Field Study ......................................................................................................................... 107
5.3 Laboratory Study ............................................................................................................... 108
5.4 Potential Applications of GFRP-Reinforced Concrete Beams .......................................... 110
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5.5 Potential for Future Testing on Existing Guideway ........................................................... 111
Appendix A Beam Fabrication and Instrumentation Information ............................................... 112
A.1 General .............................................................................................................................. 112
A.2 Measurement Information ................................................................................................. 112
A.3 Test Beam Designs (See title blocks for identification) .................................................... 115
A.4 End Bearing Shear Friction Detail Design ........................................................................ 122
A.5 Strain Gauge Installation ................................................................................................... 123
A.6 Beam Fabrication and Casting .......................................................................................... 125
Appendix B Cracking Behaviour in Test Beams ......................................................................... 129
B.1 General .............................................................................................................................. 129
B.2 Results ............................................................................................................................... 131
Appendix C Shear Behaviour of Test Beams .............................................................................. 146
C.1 General .............................................................................................................................. 146
C.2 Testing Results .................................................................................................................. 147
C.3 References ......................................................................................................................... 151
Appendix D Concrete Materials Testing ..................................................................................... 152
D.1 General .............................................................................................................................. 152
D.2 References ......................................................................................................................... 157
ix
List of Figures
Figure 1.1: Rendering of Monorail train in future installation (Courtesy of Bombardier
Transportation) ................................................................................................................................. 2
Figure 2.1: Comparison of crack with in web for tall beams with and without skin reinforcement
....................................................................................................................................................... 17
Figure 3.1: Two-car monorail train showing loading geometry in relation to test beams ............. 27
Figure 3.2: Mid-span cross section showing instrumentation ........................................................ 29
Figure 3.3: Test beam elevation showing instrument locations ..................................................... 29
Figure 3.4: Mid-span cross sections of the steel and GFRP-reinforced guideway beams ............. 31
Figure 3.5: Assembled GFRP reinforcement cage prior to casting ............................................... 33
Figure 3.6: KMTT showing: A), steel-reinforced beam; B), GFRP-reinforced beam; and C), Test
Hut ................................................................................................................................................. 34
Figure 3.7: Two-vehicle prototype Monorail train parked on test guideway (Courtesy of
Bombardier Transportation) ........................................................................................................... 36
Figure 3.8: Summary of beam live-load deflections for all 450 passes of monorail vehicle
observed ......................................................................................................................................... 37
Figure 3.9: Summary of beam live-load curvatures for all 450 passes of monorail vehicle
observed ......................................................................................................................................... 37
Figure 3.10: Percent stiffness reduction of test beams throughout all phases................................ 38
Figure 3.11: Experimental effective moment of inertia (Ie(exp)) for all phases of testing ................ 39
Figure 3.12: Change in Phase 1 deflections with vehicle speed (a), and typical mid-span
displacement response of the un-cracked tests beams at 42 km/h (b) ............................................ 42
Figure 3.13: Live-Load vs. Mid-Span Deflection responses for test beams with predictions from
VecTor2 ......................................................................................................................................... 48
Figure 3.14: Predicted effective moment of inertia of GFRP-reinforced beam for various models
....................................................................................................................................................... 52
Figure 3.15: Experimental and predicted deflection profiles of the GFRP and steel-reinforced
beams ............................................................................................................................................. 54
Figure 3.16: Time domain responses of mid-span deflection (a & c) and acceleration (b & d) for
the test beams when subjected to AW3 loading ............................................................................ 57
Figure 3.17: Free vibration acceleration responses in the time (a &c) and frequency domain (c &
d) indicating first flexural natural frequency observed .................................................................. 59
x
Figure 4.1: Cross section designs of the full-scale Steel and GFRP-RC beams ............................ 67
Figure 4.2: GFRP bar layout in full-scale beam as built (due to supplier error) ............................ 68
Figure 4.3: Normalized responses of full-scale and half-scale GFRP RC test beam designs ........ 74
Figure 4.4: Comparison of full-scale to half-scale GFRP-reinforced beam cross section designs 77
Figure 4.5: Elevation of instrumentation placement in half-scale GFRP RC beam ...................... 81
Figure 4.6: Mid-span and shear-span section views on half-scale GFRP RC beam instrumentation
....................................................................................................................................................... 81
Figure 4.7: Half-scale GFRP-reinforced beam setup for monotonic testing.................................. 82
Figure 4.8: Responses of beam up to the scaled down service load .............................................. 85
Figure 4.9: First flexural crushing of top cover concrete at mid-span ........................................... 87
Figure 4.10: Visible buckling of side GFRP bars after rupture of top bars lead to failure ............ 89
Figure 4.11: Responses of half-scale beam until ultimate failure at 693kN .................................. 90
Figure 4.12: Behavior at crushing (a & b), top bar rupture (c) and vertical strain profiles at
various stages (d) ........................................................................................................................... 91
Figure 4.13: Predicted and experimental effective moment of inertia for the half-scale beam ..... 94
Figure 4.14: Longitudinal stress profile of tension reinforcement with observed beam cracking
patterns ........................................................................................................................................... 96
Figure 4.15: Observed cracking in mid-span region of beam at scaled service load ..................... 97
Figure 4.16: Longitudinal strain profile of compression reinforcement ........................................ 98
Figure 4.17: Large deformations in beam at first flexural crushing ............................................ 101
Figure A-1: Strain gauge installation on reinforcing bars ............................................................ 123
Figure A-2: Reinforcing bars for full-scale beams instrumented with strain gauges................... 124
Figure A-3: Wiring for internal instrumentation in full-scale GFRP-reinforced beam ............... 124
Figure A-4: Placing concrete during the casting of the full-scale beams .................................... 125
Figure A-5: Hoisting of finished beam from formwork .............................................................. 125
Figure A-6: Installing full-scale beams at the test guideway ....................................................... 126
Figure A-7: Showing deformed formwork for half-scale beams, and remedial action taken ...... 126
Figure A-8: Half-scale GFRP reinforcement cages prior to casting ............................................ 127
Figure A-9: Casting and final finish of half-scale beams ............................................................ 127
Figure A-10: Full-scale beams at test track with linear potentiometers installed ........................ 128
Figure A-11: Linear potentiometer (configured for IP 66 rating) and its IP 67 rated connection 128
Figure B-1: Measuring crack widths on the side faces of the full scale test beams ..................... 130
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Figure B-2: Comparison of crack widths for the half-scale GFRP-reinforced beam................... 131
Figure B-3: Crack Diagram of full-scale GFRP-reinforced beam (west half) ............................. 136
Figure B-4: Crack Diagram of full-scale GFRP-reinforced beam (east half) .............................. 137
Figure B-5: Crack Diagram of full-scale steel-reinforced beam (west half)................................ 138
Figure B-6: Crack Diagram of full-scale steel-reinforced beam (east half) ................................. 139
Figure B-7: VecTor2 prediction of Crack Diagram of full-scale GFRP-reinforced beam .......... 140
Figure B-8: VecTor2 prediction of Crack Diagram of full-scale steel-reinforced beam ............. 141
Figure B-9: Crack widths of half-scale beam subjected to self-weight only ............................... 142
Figure B-10: Crack widths of half-scale beam subjected to the maximum service load ............. 143
Figure B-11: VecTor2 prediction of Crack Diagram of half-scale beam subjected to self-weight
..................................................................................................................................................... 144
Figure B-12: VecTor2 prediction of Crack Diagram of half-scale beam subjected to the maximum
service load .................................................................................................................................. 145
Figure C-1: Stirrup stresses at the scaled down service load ....................................................... 149
Figure C-2: Instrumented stirrup location w.r.t. the cracks at the scaled down service load ....... 150
Figure C-3: VecTor2 prediction of vertical strains in half-scale beam showing compressive strut
..................................................................................................................................................... 150
Figure C-4: Stirrup stresses at various locations on instrumented at ultimate flexural failure .... 151
Figure D-1: Compression response of for cylinders cast from half-scale batch of concrete ....... 154
Figure D-2: Comparison of pre-peak compression models used in VecTor2 to experimental
behaviour ..................................................................................................................................... 155
Figure D-3: Compression testing of large cylinders in RIEHLE test frame ................................ 156
Figure D-4: Long term strength gain in full-scale beams' concrete ............................................. 157
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List of Tables
Table 3-1: Load definition of various occupant densities of monorail vehicles ............................ 27
Table 3-2: Material properties for reinforcement used in field-test beams .................................... 32
Table 3-3: Breakdown of three testing phases by axle load ........................................................... 36
Table 3-4: Ratio of GFRP RC mid-span deflection predictions to experimental values ............... 49
Table 3-5: Ratio of Steel RC mid-span deflection predictions to experimental values ................. 53
Table 4-1: Physical properties of full-scale and half-scale GFRP-reinforced test beams .............. 71
Table 4-2: Deformability factors based on predicted and experimental behaviour ..................... 100
Table B-1: Predicted and observed crack widths for all test specimens ...................................... 132
Table D-1: Experimental properties of large cylinders from half-scale beams ........................... 156
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Chapter 1
Introduction
1.1 General
In all parts of the world, there is a growing demand for intelligent and innovative
transportation systems. To provide these transportation solutions at acceptable costs, the
service life of its supporting infrastructure needs to increase considerably compared to
many of the reinforced concrete structures of the twentieth century. One relatively recent
method of pre-emptively combating the problem of reinforced concrete deterioration is
the use of non-ferrous reinforcements in new infrastructure. Advanced composite
materials such as fibre-reinforced polymers (FRPs) are establishing themselves as viable
alternatives to black steel reinforcement in many new-construction applications where
their non-susceptibility to corrosion can offer reduced life cycle costs by substantially
extending service life (Mufti & Neale, 2008).
The use of monorail trains on elevated guideways offers several benefits for public transit
in crowded urban areas (Xie, 2013). Figure 1.1 shows a rendering of an installation
scenario of monorail trains and their elevated infrastructure in an urban environment.
Aerial guideways (which perform the dual task of superstructure and guiding the
vehicles) allow for ease of installation and shorter construction times (compared to other
rail-style transportation). With the growing need for longer lasting transit infrastructure, it
is important to begin establishing viable alternative (corrosion resistant) structural
systems.
2
Figure 1.1: Rendering of Monorail train in future installation (Courtesy of
Bombardier Transportation)
1.2 Objectives of the Research
While many of the necessary design tools for the use of FRP in reinforced concrete are in
place, few installations have been completed at the scale discussed in this thesis, and
tested with a high degree of control and repeatability. In most cases, field studies of this
type only allow for relatively few passes of controlled vehicles because roads where the
tests take place must be closed to do so (Benmokrane et al., 2007; El-Salakawy et al.,
2003; Stallings et al., 2000).
The purpose of the field study (and supporting analysis) conducted in this thesis is to
assess the viability of using FRP reinforcing bars in the construction of a reinforced
3
concrete beam for a monorail guideway. The performance of this glass-FRP (GFRP)-
reinforced beam is compared directly to that of a steel-reinforced beam, designed for
equivalent use, so the differences in performance can be characterized quantitatively. The
main interest is the comparison of serviceability performance, and determining to what
degree does the reduced stiffness of the GFRP reinforcement impact it.
To complement the serviceability study conducted on the full-scale test beams, half-scale
GFRP-reinforced concrete beams are studied with the aim of examining the performance
of the beams up to failure. While testing of laboratory-scale GFRP beams has been
performed many times during the last 20 years, testing on replicas of the full-scale beams
increases confidence in the design (in terms of both the serviceability and ultimate limit
states). This is particularly true due to the unconventional reinforcement layout used in
the full-scale beams which could affect assumed deformability and mode of failure.
Another objective of the research is to identify numerical tools that can be used in the
design of future guideway infrastructure components. Of particular importance is
determining what combinations of tools provide a user with comprehensive, yet
decipherable information at various stages of design. Determining the most effective
application of these tools will be based on comparisons with experimental observations
made in the research.
1.3 Organization of the Thesis
Following this chapter, this thesis contains an additional four main chapters describing
the methodologies and results of the work. The thesis is presented in manuscript form
with references provided at the end of each chapter. The chapters are:
4
A literature review of the design codes and principles relevant to the design of
large FRP-reinforced concrete beams for use in monorail infrastructure.
A manuscript detailing the test program conducted for the full-scale test beams
located at the Kingston Monorail Test Track (KMTT).
A manuscript detailing the test program carried out for the half-scale test beam
lab-scale study of static performance at both service and ultimate states.
A summary of conclusions from the testing and analysis with recommendations
for areas of future work and most promising applications of the structural system
in revenue-generating installations.
Furthermore, several appendices are included after the fifth chapter, some of which
include supporting information and documentation for the research described in Chapters
3 & 4. Other appendices contain the testing and modelling results from additional areas
of interest that, although relevant, do not warrant the production of full manuscripts.
5
1.4 References
Benmokrane, B., El-Salakawy, E., El-Gamal, S., & Goulet, S. (2007). Construction and
testing of an innovative concrete bridge deck totally reinforced with glass FRP
bars: Val-Alain Bridge on Highway 20 East. Journal of Bridge Engineering,
12(5), 632-645. doi:10.1061/(ASCE)1084-0702(2007)12:5(632)
El-Salakawy, E., Benmokrane, B., & Desgagné, G. (2003). Fibre-reinforced polymer
composite bars for the concrete deck slab of Wotton Bridge. Canadian Journal of
Civil Engineering, 30(5), 861-870.
Mufti, A. A., & Neale, K. W. (2008). State-of-the-art of FRP and SHM applications in
bridge structures in Canada. Composites Research Journal, 2(2), 60-69.
Stallings, J., Tedesco, J., El-Mihilmy, M., & McCauley, M. (2000). Field performance of
FRP bridge repairs. Journal of Bridge Engineering, 5(2), 107-113.
doi:10.1061/(ASCE)1084-0702(2000)5:2(107)
Xie, Y. (2013). A modern mobility solution for urban transit with the latest generation of
the INNOVIA system. Paper presented at the Automated People Movers and
Transit Systems 2013@ Half a Century of Automated Transit-Past, Present, and
Future, 230-246.
6
Chapter 2
Literature Review
Because Chapters 3 and 4 are written in the manuscript format, they contain specific
literature review for the research. This Chapter provides a general overview of important
considerations that need to be addressed when designing fibre-reinforced polymer (FRP)-
reinforced concrete beams for transit infrastructure. Specifically, the established design
guidelines will be introduced, and other design considerations discussed.
2.1 Fibre-Reinforced Polymers
FRPs are characterized as a group of composite materials comprising of high-strength
fibres, bonded by a polymer matrix. While several materials used in civil engineering
could be classified under this broad description, this thesis primarily focused on the use
of advanced composites, those of glass, carbon, or aramid fibres (or similar) in the form
of reinforcing bars or tendons for new construction in flexural members. These may be
used as either traditional internal reinforcement in reinforced concrete (or as tendons in
prestressed concrete) and typically exhibit linear elastic behaviour until failure.
Intelligent Sensing for Innovative Structures, a Canadian Network of Centres of
Excellence, has published several educational modules and design manuals for new
construction of FRP-reinforced concrete and prestressed concrete (ISIS Canada, 2007),
which may be referred to for most general inquiries. Additionally, the first three chapters
of ACI 440.1R-06 contain a great deal of information about the basic principles of
reinforcing with FRPs as well as the history of their use around the world.
7
2.2 Design Codes in North America
While various design codes exist worldwide providing guidance on the design of FRP-
reinforced concrete, this review will focus on codes and guidelines from North America.
At the time of writing, there are three main design codes/guidelines (current editions)
native to North America which are either fully dedicated, or have dedicated sections for
the design of reinforced concrete using FRPs as the primary internal reinforcement:
Design and Construction of Building Components with Fibre Reinforced
Polymers, CAN/CSA-S806 (2012)
Canadian Highway Bridge Design Code, CAN/CSA-S6-06 (2006) (Section 16)
Guide for the Design and Construction of Structural Reinforced Concrete with
FRP bars, ACI 440.1R-06 (2006)
Additionally, the Specification for Fibre-Reinforced Polymers, CAN/CSA S807 (CSA,
2010) may be referred to for guidance regarding the manufacturing process and standards
of quality for the use of FRPs in construction.
Generally, the three design codes each cover the design of FRP-reinforced concrete under
both ultimate limits states (ULS) and serviceability limit states (SLS). Much like the
design of steel-reinforced concrete, some of the relevant sectional design considerations
to the performance of FRP-reinforced concrete infrastructure at ULS include:
Flexural capacity,
Shear capacity,
Torsional capacity, and
Combined axial and flexural capacity.
8
Additional SLS requirements to ensure that the structure remains functional may include:
Limiting deflections,
Limiting crack widths,
Limiting structural vibrations.
Some requirements not specific to ULS or SLS may include:
Development length of reinforcement,
Limiting bar stress to avoid creep and/or fatigue rupture.
2.2.1 Design Philosophy
While a detailed description of the design methods for FRP-reinforced concrete is not
included in this manuscript, ISIS (2007) provides an excellent overview of the overlying
principles. That said, some of the key differences between the design of FRP-reinforced
concrete and traditional steel-reinforced concrete will be discussed here.
Because FRPs exhibit linear-elastic behaviour until ultimate failure, their design for use
in reinforced concrete differs from that of steel reinforcement (which is idealized as a
perfectly elastic/perfectly plastic bi-linear relationship). This is of particular importance
in flexural design, where at ultimate limit states, the three aforementioned design codes
all account for the non-linear plastic behaviour of their constituent materials.
Steel-reinforced concrete is preferably designed as ‘under-reinforced’, meaning that the
reinforcing steel yields, deforming plastically before the crushing of concrete in
compression occurs. This type of design undergoes large curvatures, which can be
visually observed by users as an indication of a problem before the ultimate collapse of
the structure. Ductile under-reinforced designs also absorb more energy through the
plastic deformation of materials, which is desirable in seismic design.
9
While FRP reinforcements are known for higher ultimate strengths than steel (which can
result in higher ultimate flexural capacities), design of an under-reinforced section (in this
case where FRP in tension ruptures before crushing of concrete) results in a brittle failure
mechanism with little warning. This is a highly undesirable characteristic for design, and
is accounted for in the three relevant design codes in some fashion.
CSA S806 requires that flexural members be designed as over-reinforced sections
(that is, concrete crushes before FRP in tension ruptures).
CSA S6-06 required that minimum deformability requirements be met, where
‘deformability’ replaces the concept of ductility for the case of elastic-to-failure
tensile reinforcement.
In ACI440.1R-06, the material resistance factor for FRP at ULS, φfrp, is reduced
considerably for under-reinforced sections (requiring that additional capacity be
provided to avoid sudden failure).
All three of the above design codes also allow for FRP transverse reinforcement or
stirrups for shear reinforcement. While their methods do vary considerably in terms of the
predictions of capacity, all stipulate significant reductions in tensile capacity of FRP
when bent. Currently, some bent bars may have as little as 58% of their straight bar
capacity at their bends (Ahmed et al., 2010).
Generally speaking, bend strength is determined based on functions of bend radius and
bar diameter. ACI 440.1R-06, and S6-06 both take this approach, while S806 applies a
generic factor of 0.4, which would prove to be conservative in most practical cases.
10
2.3 Durability
The durability of internal reinforcement for monorail infrastructure is of high importance
to confidently predict its useful service life. However, as composite materials have only
seen widespread use in civil structures in recent times (since the late 1980s), long term
environmental effects are difficult to quantify. Results from early research form the basis
for the reduction factors used in modern design codes. More recently, these factors have
been shown to be overly conservative (Nkurunziza et al., 2005) due to a combination of:
The database of durability testing on FRPs is ever-increasing, and encompassing
greater number of environmental variables;
Significant improvements to the mechanical and durability properties of FRPs are
being made, creating new generations of FRP bars in a relatively short time
frame.
Because little to no FRP-reinforced concrete structures greater than 50 years old exist for
study, the durability of the reinforcement is typically quantified using accelerated ageing
experimental programs. In these types of tests, the FRP bars are subjected to extreme
environmental exposure conditions at an elevated temperature for several weeks to
months. The results are then extrapolated using the Arrhenius principle to predict the
amount of time for the material to reach the observed level of degradation at ambient
temperatures, enabling a prediction of serviceable life (Nkurunziza et al., 2005).
However, much of the early accelerated durability testing performed by various
researchers was done under significantly varying conditions (type of exposure,
temperature, time, and amount of sustained loading). This was the result of the lack of a
standard test method for performing accelerating ageing tests on FRP composites for use
11
in civil infrastructure. ACI Committee 440 (Fibre-Reinforced Polymer Reinforcement) is
currently working on such a standard procedure.
To better understand the risks to the durability of FRP reinforcements (specifically
GFRP), the degradation mechanisms are first divided into: (1), degradation due to
environmental exposure; and (2), mechanical effects (such as creep and fatigue).
2.3.1 Environmental Effects
The most relevant environmental deterioration mechanisms (for an outdoor application in
transit infrastructure) are the degradation of: the glass fibres in the bar, the polymer
matrix in the bar, and the bond interface between the fibres and the matrix. These three
mechanisms can occur at varying rates (depending on exposure type and temperature),
but the resulting effects observed are (generally) the loss of stiffness and strength of the
GFRP bar. The main cause for this deterioration is the presence of moisture, combined
with high alkalinity (from the concrete).
While it is well established that the high alkalinity of concrete pore water tends to
passivate steel reinforcement (protecting it from corrosion), the same solution can
degrade the silicates in the glass fibres. Alkali-resistant glass fibres exist which
theoretically help to reduce susceptibility to alkali degradation, but their true
effectiveness is a topic of debate (Tannous & Saadatmanesh, 1999).
The chemical durability of the polymer matrix in FRP bars (which are typically
thermosetting resins) depends on the type used. It has been suggested (Dejke & Tepfers,
2001; Nkurunziza et al., 2005) that vinyl ester resins are more resistant to alkaline
environments than polyester resins used in some bars. The degradation of the fibre-matrix
12
interface can be driven by both moisture/alkali ingress as well as sustained or repeated
loading, causing swelling and/or separation of the interface (Nkurunziza et al., 2005).
2.3.2 Mechanical Effects
The primary mechanical drivers that affect durability in GFRP reinforcement are creep
due to sustained loads and fatigue due to repeated loading. However, these mechanisms
by themselves affect durability minimally at the stress levels typically seen in real
structures. The three design codes discussed previously limit the service stress levels to
approximately 25% or less of the guaranteed ultimate strength due to a combination of
safety, environmental, and serviceability factors. While creep and fatigue rupture can
occur in GFRP bars at higher stress levels, sustained load tests at serviceable stress levels
have shown minimal increases in strain (as little as 2% creep strain). In this case,
reinforcement stress was 27% of the ultimate strength, sustained for 26 weeks, with no
significant increase in strain after 72 days (Laoubi et al., 2006).
Though thermal effects on FRP-reinforced concrete due to extreme temperatures have
been (and continue to be) explored extensively, this field of study is beyond the scope of
the current project. A separate investigation would need to be done to assess the likely
risk of acute deterioration of the FRP bars as a result of a fire on the guideway, including
establishing probability and intensity of these fires.
13
2.4 Shear
The prediction of shear capacity in FRP-reinforced concrete (or even reinforced concrete
in general) is a frequently debated topic, with different codes providing an array of
methods. The three codes introduced earlier express the overall capacity of reinforced
concrete members as the summation of the contributions of concrete and transverse
reinforcement in shear (Vc and VFRP respectively). In cases where FRP used as transverse
reinforcement requires bending, the strength of the reinforcement is reduced, with
predicted capacity being proportional to the ratio of bend radius to bar diameter (rb/db)
(ACI Committee 440, 2006; CSA, 2006). S806 (CSA, 2012) implicitly reduces the tensile
capacity of FRP transverse reinforcement to 40% of straight bar strength, regardless of
other factors.
The current ACI 440.1R-06 uses a truss model capacity approach with a constant angle of
45o, evaluating Vc and VFRP based on section properties and material strengths. While this
typically provides conservative results, accuracy could be significantly improved (Ahmed
et al., 2010; Bentz et al., 2006).
Both of the current Canadian codes form the basis of their shear capacity predictions on
the Modified Compression Filed Theory (MCFT) (Vecchio & Collins, 1986). One of
purposes of the work on the MCFT was to derive expressions which could predict the
shear capacity of cracked reinforced concrete more precisely. While originally
implemented in finite element modelling, it was later simplified into a method for
calculations (reducing the number of equations from fifteen to two) which could be used
in design codes (Bentz et al., 2006). This method determines capacity based on the same
inputs as the ACI model, but also independently quantifies the “strain effect” and “size
14
effect”. Later publications by Hoult et al. (2008) on the strain effect and Bentz et al.
(2010) on the size effect showed that the MCFT accurately predicts behaviour of FRP-
reinforced concrete (despite reduced stiffness) without the addition of empirical curve-
fitting factors.
The Hoult et al. (2008) data-base shows that normalized shear stress at failure is
primarily a function of longitudinal stain, as opposed to reinforcement type. Hoult et al.
(2008) re-evaluated the strain effect term in the MCFT based on tests where mid depth
strains were significantly greater than typically observed in steel-reinforced concrete.
The implications of providing expressions which do not solely rely on empirical
adjustments for the prediction of shear capacity in FRP-reinforced concrete are that they
can be expected to provide more consistent estimations for varying conditions. As the
amount of literature and models predicting shear capacity of FRP-reinforced concrete is
ever growing, the responsibility falls to the designer to make the decision on what
methods best suit the intended application.
2.5 Crack Mitigation in Tall Members
The control of flexural crack widths are important in reinforced concrete to preserve the
aesthetic appeal (to avoid alarming users), reduce the environmental exposure of
reinforcement (to avoid degradation of both steel and FRP reinforcements), and to limit
water ingress (that can cause freeze thaw cracking). Because the ramifications of
exposing FRP reinforcements to the environment are less than that of steel (due to steel’s
susceptibility to aggressive corrosion), crack width limits are typically relaxed for FRP-
reinforced concrete. ACI440.1R-06, S806 and S6-06 (Section 16) all suggest a maximum
allowable crack width of ~0.5mm for exterior exposure (0.7 mm for indoor
15
environments). Contrarily, S6-06 (Section 8) limits cracks to 0.35 mm in steel-reinforced
members which are not exposed to de-icing salts or marine spray (and 0.25 mm if they
are exposed).
Calculation of crack width from the above codes are either implicit (S806 uses a crack
parameter, z) or explicit (ACI 440.1R-06 & S6-06).
3 AdfE
Ekz cF
f
sb (2.1)
2
2
22
sdk
E
fw cb
f
f (2.2)
smrmcb skw
where
(2.3a)
c
bcrm
dks
25.050
and
(2.3b)
2
1s
w
s
ssm
f
f
E
f (2.3c)
Equations 2.1 to 2.3 are the respective flexural crack check (either width or parameter)
for: S806; ACI 400.1R-06 & S6-06 (Section 16); and S6-06 (Section 8). In Equations 2.1
to 2.3: z is the cracking parameter (expressed in N/mm); w is the calculated crack width;
Es & Ef are the elastic moduli of steel and FRP respectively; kb is the bond coefficient of
the reinforcement (provided by the manufacturer, from testing, or conservatively
estimated); dc is the cover distance from the extreme tension face of the member to the
centroid of the reinforcing bar closest to the tension face; fF and fs are the service stresses
16
in the FRP and steel reinforcement respectively; A is the effective area of concrete in
tension per longitudinal bar; is the ratio of distance from neutral axis to extreme tension
face & neutral axis to tension reinforcement; s is the longitudinal bar spacing; c is 1.7
(when cracking is caused by load), kc is 0.5 for bending, db is the reinforcing bar
diameter, c is the ratio of area of reinforcement to effective tension area of concrete A;
and fw is the stress in the reinforcement at the time of cracking.
However, proper detailing of primary flexural reinforcement as per Equations 2.1 to 2.3
alone has been shown to be insufficient for restraining crack openings in the web of taller
beam sections (Frantz & Breen, 1980; Frosch, 2002). Due to a shear lag of the restraining
force (provided by reinforcing bars), crack widths increase (as does crack spacing)
between the level of reinforcement and the neutral axis. When side or “skin”
reinforcement is introduced in the web of the section, it serves to keep flexural cracks
from “tree branching” into fewer cracks as they propagate towards the neutral axis,
maintaining a crack pattern which is more perpendicular with the longitudinal
reinforcement (Frantz & Breen, 1980). Figure 2.1 show the typical effect of a tall
reinforced concrete beam without, and with skin reinforcement.
17
Figure 2.1: Comparison of crack with in web for tall beams with and without skin
reinforcement
Code requirements for when skin reinforcement should be used vary considerably,
because ACI 318-08 and S6-06 (Section 8) require skin reinforcement for sections taller
than 900 mm and 750 mm, respectively. Section 16 of S6-06 provides no explicit
guidance on the use of skin reinforcement for tall FRP-reinforced concrete beams. A
conservative approach would be to provide the same axial stiffness in the flexural tension
region of the beam as recommended for steel-reinforced beams (Section 8). A more
refined approach to proportioning the skin reinforcement is to follow the same procedure
as is used for the principle longitudinal reinforcement (any of Equations 2.1 to 2.3),
which has been shown to effectively predict the width of side surface cracks (Frosch,
2002).
2.6 Deflections and Tension Stiffening
While the use of FRP bars as the primary flexural reinforcement in reinforced concrete
has a significant effect on both the tension stiffening behaviour and deflections of beams,
this topic is discussed at great length within Chapters 3 and 4 and will not be repeated
here.
18
2.7 Hysteresis
To complement the experimental testing performed in this thesis, finite element models
(FEM) were created based on the three types of test beams. Because the field testing
would involve many loading phases at varying loads, high importance was placed on the
behaviour of the beams after unloading as part of the analysis. This behaviour is
important to predict precisely for field studies, as the measurements made during
experimental work do not explicitly show the strain history of the test specimens. The
highly non-linear behaviour of reinforced concrete requires that careful consideration be
given to the previous loading cycles performed.
For the service load levels considered in this thesis, the non-linear behaviour mainly
considered is the tension stiffening of the cracked reinforced concrete (as FRP is assumed
linear, and concrete remains near-linear in compression for the low stress levels
considered here). This behaviour has effects on the deflections, cracks, and strains
observed in testing. For the purposes of this thesis, the more important hysteresis factor
relates to making detailed predictions of the plastic offsets upon unloading, as opposed to
predicting the unloading/reloading behaviour after reaching a new maximum observed
strain.
In the past, individuals would assume reinforced concrete members unloaded in a linear
fashion with no plastic offsets (Palermo & Vecchio, 2003), where elements would return
to a state of zero stress or strain. The plastic offsets, which result from cracked surfaces
coming back into contact while unloading (where friction inhibits complete crack
realignment) (Palermo & Vecchio, 2003), provide a more realistic (and conservative)
estimate for the member’s condition.
19
The non-linear finite element analysis (NLFEA) was to be performed using the two-
dimensional analysis program VecTor2 (Vecchio, 2002). This program allows for the
hysteretic response to be predicted with the following models (Wong & Vecchio, 2002):
1. No offsets, with linear loading/unloading;
2. Plastic offsets, with linear loading/unloading (Vecchio, 1999);
3. Plastic offsets, with non-linear loading/unloading; and
4. Plastic offsets, with non-linear loading/unloading including cyclic decay.
The fourth model, based on the formulation by Palermo & Vecchio (2003) was chosen
for the finalized modelling of the full-scale test beams because it provided the most
consistent estimates of the observed behaviour during unloading in the laboratory-scale
testing.
2.8 Summary
The above concepts cover a broad range of considerations necessary to perform safe and
effective design of beams reinforced with FRPs, but are certainly not all-encompassing.
Great care needs to be taken when performing the design of FRP-reinforced concrete
infrastructure, particularly with respect to anticipating the severity of the structure’s
exposure to the environment. This not only includes the micro-climate the infrastructure
is constructed in, but also how the placement, design, and performance of members can
ultimately affect the rate of degradation in the reinforcement. The importance of
constantly updating design practices for FRP-reinforced concrete infrastructure with
respect to durability cannot be understated as new information becomes available in the
coming years and decades.
20
2.9 References
ACI Committee 440. (2006). Guide for the design and construction of structural concrete
reinforced with FRP bars (ACI 440.1R-06). Farmington Hills, Michigan (USA):
American Concrete Institute.
Ahmed, E. A., El-Salakawy, E. F., & Benmokrane, B. (2010). Performance evaluation of
glass fiber-reinforced polymer shear reinforcement for concrete beams. ACI
Structural Journal, 107(01)
Bentz, E. C., Massam, L., & Collins, M. P. (2010). Shear strength of large concrete
members with FRP reinforcement. Journal of Composites for Construction, 14(6),
637-646.
Bentz, E. C., Vecchio, F. J., & Collins, M. P. (2006). Simplified Modified Compression
Field Theory for calculating shear strength of reinforced concrete elements. ACI
Structural Journal, 103(4), 614.
CSA. (2006). CAN/CSA-S6-06. Canadian Highway Bridge Design Code. Mississauga,
Ontario: Canadian Standards Association.
CSA. (2010). CAN/CSA-S807-10. Specification for Fibre-Reinforced Polymers.
Mississauga, Ontario: Canadian Standards Association.
CSA. (2012). CAN/CSA-S806-12. Design and Construction of Building Components
with Fibre-Reinforced Polymers. Mississauga, Ontario: Canadian Standards
Association.
21
Dejke, V., & Tepfers, R. (2001). Durability and service life prediction of GFRP for
concrete reinforcement. Paper presented at the Proc., 5th Int. Conf. on Fiber-
Reinforced Plastics for Reinforced Concrete Structures (FRPRCS-5), 1 505-516.
Frantz, G. C., & Breen, J. E. (1980). Cracking on the side faces of large reinforced
concrete beams. Paper presented at the ACI Journal Proceedings. 77(5)
Frosch, R. J. (2002). Modeling and control of side face beam cracking. ACI Structural
Journal, 99(3)
Hoult, N., Sherwood, E., Bentz, E., & Collins, M. (2008). Does the use of FRP
reinforcement change the one-way shear behavior of reinforced concrete slabs?
Journal of Composites for Construction, 12(2), 125-133.
ISIS Canada. (2007). Reinforcing concrete structures with fibre reinforced polymers-
design manual no. 3. Manitoba: ISIS Canada Corporation.
Laoubi, K., El-Salakawy, E., & Benmokrane, B. (2006). Creep and durability of sand-
coated glass FRP bars in concrete elements under freeze/thaw cycling and
sustained loads. Cement and Concrete Composites, 28(10), 869-878.
Nkurunziza, G., Debaiky, A., Cousin, P., & Benmokrane, B. (2005). Durability of GFRP
bars: A critical review of the literature. Progress in Structural Engineering and
Materials, 7(4), 194-209.
22
Palermo, D., & Vecchio, F. J. (2003). Compression field modeling of reinforced concrete
subjected to reversed loading: Formulation. ACI Structural Journal, 100(5), 616-
625.
Tannous, F., & Saadatmanesh, H. (1999). Durability of AR glass fiber reinforced plastic
bars. Journal of Composites for Construction, 3(1), 12-19.
Vecchio, F. J. (1999). Towards cyclic load modeling of reinforced concrete. ACI
Structural Journal, 96, 193-202
Vecchio, F. (2002). VecTor2, nonlinear finite element analysis program of reinforced
concrete. University of Toronto, Toronto, ON, Canada,
Vecchio, F. J., & Collins, M. P. (1986). The Modified Compression-Field Theory for
reinforced concrete elements subjected to shear. ACI J., 83(2), 219-231.
Wong, P., & Vecchio, F. (2002). VecTor2 and FormWorks user’s manual. University of
Toronto
23
Chapter 3
Full Scale Study of a GFRP-Reinforced Concrete Beam for a Monorail
Guideway
3.1 Introduction
In order to help avoid exorbitant costs due to either replacement or upgrading of transit
infrastructure, advanced materials for reinforced concrete are gaining prevalence in new
construction. One such method to combat the problem of steel reinforcement corrosion
directly is to replace it with some form of non-ferrous reinforcement. Typically, the
deterioration observed in bridges is driven by the use of de-icing salts. In the case of
elevated light rail or monorail infrastructure, different mechanisms are the primary
concern. Previous works (Bertolini et al., 2007; Kai et al., 2011) have shown that, in the
presence of stray direct current, corrosion of reinforcing steel embedded in concrete can
occur at accelerated rates. This poses a risk to monorail infrastructure where vehicles are
powered by direct currents travelling through electrified rails mounted on either side of
the guideway beams.
In this study, fibre reinforced polymer (FRP) bars are used internally in a reinforced
concrete beam for monorail transit infrastructure. While FRPs are well established for
their non-susceptibility to corrosion and high ultimate tensile strength, their design is
typically limited by serviceability considerations because of their markedly reduced
stiffness compared to steel.
The test program consists of two instrumented reinforced concrete beams (11.6m long
each) which were part of a 1.86 km monorail test track. Of these test beams, one was
24
reinforced with glass-FRP (GFRP) bars, while the other was reinforced with steel bars
(equivalent to the remainder of the test guideway). By placing the beams in succession of
one another, the performance of the GFRP-reinforced beam was directly compared to that
of a typical reinforced concrete beam. While the primary purpose of this test track was to
test and certify a newly developed monorail vehicle, this study was performed during the
vehicle testing to evaluate the performance of the GFRP-reinforced concrete beam for
this system. This approach allowed not only for a side-by-side comparison of the two
beams, but also for repeatable, controlled loading of the beams. Additionally, the
parameters of vehicle weight and speed were varied to observe the system under all
service conditions. This is in contrast to typical field highway bridge studies, where only
a small number of passes are often observed due to cost of road closure time.
Thus far, a great deal of research has been conducted on the performance of GFRP-
reinforced concrete beams at the lab-scale level to evaluate static performance. Similarly,
several studies have been conducted on full scale bridge decks reinforced with FRP.
Currently however, little previous work exists on full scale applications where FRP is
used as the primary reinforcement for the superstructure of elevated guideways.
Because this monorail infrastructure system must perform to stringent serviceability
limits, the study will monitor the beams internally and externally to compare their
behaviour not only to the relevant design codes, but also to limits imposed by the vehicle
manufacturer because the structural performance inevitably affects vehicle component
service-life.
25
3.2 Experimental Program
Since the guideway must function for purposes other than this study, the beams must
conform to the relevant design codes for safety and serviceability. As such, the beams
were designed by a third party consulting firm, and met the requirements of the CHBDC
(Canadian Highway Bridge Design Code), S6-06 (CSA, 2006). Additionally, the cross-
sectional dimensions of the beams were constrained by the shape of the monorail
vehicles, and their length by handling restrictions. While not a true highway bridge,
designing the guideway using S6-06 is advantageous in that guidance is provided for the
design of both steel and FRP reinforced concrete, avoiding compatibility issues with
respect to loading and resistance factor calibration (Gilstrap et al., 1997). Therefore,
rather than comparing the performance of the two structural systems based on equivalent
section properties, an evaluation is made of both designs’ ability to meet the required
serviceability limits.
As planning of the study was done in conjunction with the initial construction of the
guideway, the location of the test beams was selected such that they could experience the
highest speeds permitted by the monorail vehicles. Thus, the location of the beams was
chosen to be on a straight section of the guideway (avoiding lateral loading), immediately
before the initiation of a high speed curve, approximately mid-way along the open circuit
track. As the monorail test vehicle may travel in both directions at high speed, the GFRP-
reinforced concrete beam was arbitrarily chosen as the first of the beams to be crossed in
the forward direction. All beams on the guideway were simply supported by 1350 mm
diameter reinforced concrete piers, extending to bedrock. Because the test guideway did
not cross any other infrastructure or obstacles, it was unnecessary to elevate the beams by
26
a substantial amount, resulting in the soffit of the two test beams being located
approximately 400mm above grade, thereby decreasing the difficulty in applying
deflection measuring instruments.
Instrumentation (both internal and external) was monitored by a Vishay Micro-
Measurements System 7000 data acquisition system, located within a small shed,
adjacent to the test guideway. For safety and convenience reasons, this data acquisition
system was then made accessible from the internet, so that data collection could be
controlled from a remote location. The following types of data were collected:
reinforcement strain, as measured by strain gauges bonded to reinforcing bars
prior to the casting of test beams;
beam deflection (both live and residual), as measured by linear potentiometers
(LPs) placed between the beams and a poured concrete slab located beneath the
beams;
internal temperature (four locations per beam), as measured by thermocouples
(TCs) to help interpret thermal effects in other collected data during test sessions
over extended durations.
Because of the high speeds that the monorail vehicles would travel, the data collection
was performed at 100 Hz (higher frequencies were also attempted, but they limited
possible data collection time due to the excessive file size of collected data). Vehicle test
sessions were monitored at speeds from below 10 km/h, to a maximum speed of
approximately 90 km/h, for all Axle Wheel (AW-) loading scenarios. For a revenue-
generating installation of this vehicle system, anticipated service speed is 80 km/h.
27
Each car of the test vehicles used two axles (single load bearing wheel with rubber tire set
per axle). Table 3-1 indicates the various axle loading scenarios covered in this study.
Table 3-1: Load definition of various occupant densities of monorail vehicles
Load Designation Axle Load (kN)
AW0 75.0
AW1 81.4
AW2 125.3
AW3 139.6
AW0 loading represents a fully unloaded vehicle, while AW3 loading corresponds to the
maximum allowable service load per axle, as limited by the load rating of the tires. AW1
and AW2 loading are intermediate load levels corresponding to various passenger
densities (passengers/m2) inside the passenger compartment of the vehicles. Figure 3.1
shows the geometry of the two-car automated monorail vehicle system in relation to the
guideway beams.
Figure 3.1: Two-car monorail train showing loading geometry in relation to test
beams
28
Note that the true span of the beams in Figure 3.1 is 11,300 mm. For the two-car system
studied, the most critical flexural loading occurs when the rear axle for the forward car
and front axle of the rearward car approach the centre of the beams. For the case of two
moving and equal concentrated loads applied to the simply supported beams, the
maximum elastic bending moment, Mmax, can be expressed as:
2
max22
al
l
PM (3.1)
where: P = point load (each); l = unsupported length of the beam; a = distance between
point loads. The maximum bending moment (and consequently, the theoretical
reinforcement stress), occurs at the position of the forward point load, when it is a
distance a/4 past mid-span. Subsequent elastic analysis done in SAP 2000 determined
that the maximum deflection would be located at mid-span.
The aforementioned instrumentation was placed strategically, according to this structural
analysis so that the maximum strains and deflections could be observed during testing.
Figure 3.2 shows the cross-sectional layout chosen for all instrumentation, which is
similar for both the steel and GFRP-reinforced beams. Figure 3.3 shows the elevation of a
test beam with instruments placed along its length.
29
Figure 3.2: Mid-span cross section showing instrumentation
Figure 3.3: Test beam elevation showing instrument locations
30
While strain gauges were also installed on the transverse reinforcement in the end
quarters of both beams, they were not used in this particular study because the beams
were not designed to be shear critical, nor did any of the analysis suggest that significant
strains would be observed in these regions. Additionally, gauges were installed in the
mid-span region on the web reinforcing bars but were not used in this study due to
limited data collection space.
3.2.1 Test Specimens
Both the steel and GFRP-reinforced beams were designed to conform to the requirements
of the CHBDC (CSA, 2006) based on Sections 8 and 16 of the Code respectively. Figure
3.4 shows cross sections of the two test beams illustrating the reinforcement as specified
at mid-span. Additional information on the design and fabrication of the beams may be
found in Appendix A.
31
Figure 3.4: Mid-span cross sections of the steel and GFRP-reinforced guideway
beams
Because the longitudinal web reinforcement significantly contributes to the flexural
capacities in both beams, the amount of reinforcement cannot be described in condensed
format in terms of a reinforcement ratio (ρ) as is often done. Table 3-2 contains the
relevant material properties assumed in the design of the reinforcement for both the steel
and GFRP-reinforced beams. Bar strength certification tests were performed by the
manufacturer, characterizing the behaviour of the GFRP, and the results provided with
the shipment of bars. The information provided did not contain all bar types used for the
test beam, therefore the published mechanical properties were used instead for analysis to
maintain consistency.
32
Table 3-2: Material properties for reinforcement used in field-test beams
Steel #7 HM GFRP #6 LM Bent GFRP
Cross Section Area (mm2) All 388 285
True Bar Diameter (mm) - 22.4 18
Yield Strength (MPa) 400 - -
Tensile Strength Straight
(MPa)
- 1059 510
Tensile Strength Bent (MPa) - - 290
Modulus of Elasticity (GPa) 200 62.6 42.9
Ultimate Elongation (%) - 1.7% 0.7%
The control beam was reinforced with steel provided by the pre-cast manufacturer, with
varying diameters of longitudinal reinforcement for compression, web, and tension zones.
Transverse reinforcement was provided by overlapping “U” steel stirrups for the majority
of the beam, and closed steel stirrups within 500mm of either end (to resist end-bearing
failure). The ends of the longitudinal bars were bent into “L” hooks to help develop their
capacity near the end of the beams.
The GFRP-reinforced beam used a symmetrical reinforcing scheme (equal bars in
extreme compression and tension zones), with all longitudinal bars being #7 (22 mm
diameter) “high modulus” (HM) bars. Transverse reinforcement was provided by
overlapping “U” stirrups throughout. The mid-span section of the GFRP-reinforced beam
used #6 (19 mm diameter) “low modulus” (LM) bent stirrups while the end sections use
#8 (25 mm diameter) LM (spacing reduced to 150 mm on-centre). Similar to the steel-
reinforced beam, the longitudinal GFRP bars were also hooked at the ends. This was
accomplished by lap-splicing “L” shaped bars at either end of the longitudinal bars which
extended beyond the basic development length for the spliced portion. Since the end
33
bearing sections of beams were not a focus of the study, their design and material
properties are not discussed in any further detail.
The two test beams were fabricated and cast by the same pre-caste manufacturer that
constructed the remainder of the test guideway. Reinforcing cages were tied in an
assembly jig to ensure repeatability in the fabrication process. This was done once the
necessary bars were instrumented with strain gauges by the authors. To ensure tolerances
were maintained, the cages were cast in the same steel formwork as the remainder of
straight track beams. Figure 3.5 shows the instrumented GFRP reinforcement cage
immediately prior to placement in formwork and subsequent casting.
Figure 3.5: Assembled GFRP reinforcement cage prior to casting
34
While the majority of the guideway beams were fabricated using a 50 MPa self-
compacting concrete mixture (allowing faster turn-around time for the repetitive
fabrication process), the test beams were cast using a 20 MPa (nominal compressive
strength) mixture. This was a result of early analysis showing that the high strength
concrete would not allow the beams to crack under service loads. Having an un-cracked
beam would have severely reduced the significance of data collected. The 20 MPa mix
(which had an average compressive strength of 25 MPa after 56 days) was selected to
increase the probability that flexural cracking would occur so that measurable strains
could be observed in the reinforcement under service loads. Beams were cast upside-
down so that a textured form liner could create the necessary friction surface for the
monorail vehicles to travel on. Following casting and a two week curing period, the
beams were moved and installed at the guideway site. Figure 3.6 shows the two
instrumented test beams installed at the test track adjacent to the instrumentation hut.
Figure 3.6: KMTT showing: A), steel-reinforced beam; B), GFRP-reinforced beam;
and C), Test Hut
The beams were installed by anchoring the steel end bearing plates (cast into the
concrete) to reinforced concrete piers (which were cast into soil and anchored to
35
bedrock). Rectangular elastomeric bearing pads were located between the pier and end
bearing plates. The bearing plates on each beam (one end slotted to allow translation
while other is essentially pinned) were intended to provide simply supported end
conditions. No expansion joint mechanism was provided at the ends of the beams, but
rather a 5mm (nominal) gap was left between beams to allow for thermal
expansion/contraction and dimensional tolerances.
3.3 Experimental Results and Discussion
During a four month testing period, 450 passes of a two-vehicle monorail train were
observed and recorded over the test beams, organized into three phases. These passes
varied significantly in both travelling speed as well vehicle loads (simulating various
occupant densities). Figure 3.7 shows the two-car monorail train (while stationary) on the
test guideway and Table 3-3 shows how the three phases of testing were segmented by
different axle loadings (order is chronological left-to-right).
36
Figure 3.7: Two-vehicle prototype Monorail train parked on test guideway
(Courtesy of Bombardier Transportation)
Table 3-3: Breakdown of three testing phases by axle load
Phase 1 Phase 2 Phase 3
Axle Load AW0 AW0/AW3 AW2 AW3 AW0 AW3 AW2 AW0
Passes 79 53 17 28 57 86 79 41
Figure 3.8 shows the summary of beam deflections at mid-span (also indicating what
loads were applied), and Figure 3.9 shows the mid-span section curvatures (as determined
by strain gauges on both top and bottom reinforcing bars) for all 450 passes observed
during testing.
37
Figure 3.8: Summary of beam live-load deflections for all 450 passes of monorail
vehicle observed
Figure 3.9: Summary of beam live-load curvatures for all 450 passes of monorail
vehicle observed
0 50 100 150 200 250 300 350 400 450
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Run Number
Mid
Span D
eflection
Phase 3 Phase 2Phase 1
AW0
AW0/AW3
AW2
AW3 AW0 AW3 AW2 AW0
GFRP Beam
Steel Beam
0 50 100 150 200 250 300 350 400 4500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Run Number
Curv
atu
re (
rads/k
m)
GFRP
Steel
38
The first 79 passes were performed with both monorail vehicles in an “empty” state or
“AW0” loading conditions (see Table 3-1). This phase (Phase 1) began with the test
beams being in a flexurally un-cracked state as confirmed by both visual observations for
flexural cracks as well as comparison of measured deflections to elastic predictions of un-
cracked reinforced concrete. Figure 3.10 shows the change in stiffness of the beams,
relative to their un-cracked stiffness, where a similar softening trend is observed.
Figure 3.10: Percent stiffness reduction of test beams throughout all phases
Phase 2 of field testing was completed with the forward monorail car remaining unloaded
(AW0), and the rear car loaded to AW3. Fifty-three passes were observed in this
configuration, with the first evidence of flexural cracking occurring in the first few
passes. While deflections in the steel-reinforced beam remained largely unchanged for
this second phase, the stiffness in the GFRP-reinforced beam decreased noticeably during
these 53 passes of AW0/AW3 loading.
0 50 100 150 200 250 300 350 400 4500.0
0.2
0.4
0.6
0.8
1.0
Run Number
Fra
ction o
f O
rigin
al S
tifn
ess
AW
0
AW
0/A
W3
AW
2
AW
3
AW
0
AW
3
AW
2
AW
0
GFRP
Steel
39
Phase 3 was subdivided into six sub-phases where, in each case, the two vehicles were
loaded equally (as opposed to Phase Two where only the rearward car was loaded). When
the higher axle loads were tested, the steel-reinforced beam exhibited a similar stiffness
reduction trend over time as the GFRP-reinforced beam.
As the beams underwent flexural cracking, the apparent stiffness was reduced to
approximately 43% and 57% of the original un-cracked stiffness (for GFRP and steel-
reinforced beams respectively) in the first 200 passes. By the end of the test program of
450 passes, the stiffness in the beams appeared to have stabilized to 38 % and 50 % of the
un-cracked stiffness for the GFRP and steel-reinforced beams respectively. Figure 3.11
expresses the change in stiffness in the test beams as the experimentally derived effective
moment of inertia, Ie(exp) (based on the observed modulus of elasticity of 26,500 MPa).
Figure 3.11: Experimental effective moment of inertia (Ie(exp)) for all phases of testing
0 50 100 150 200 250 300 350 400 4500.0
0.4
0.8
1.2
1.6
2.0
Run Number
Effective M
om
ent of In
ert
ia (
x10 11m
m4)
AW
0
AW
0/A
W3
AW
2
AW
3
AW
0
AW
3
AW
2
AW
0
Ie GFRP
Ie Steel
40
In Figure 3.8 to Figure 3.11, the outlying steel-reinforced beam point (test pass 435) is
due to the vehicle not fully crossing the beam, but rather stopping with only one vehicle
axle present on the beam before changing directions. Also in Figure 3.8 to Figure 3.11,
there appears to be greater variability in the GFRP beam behaviour. This apparent
increased variability is likely a scaling effect. The deflections and curvatures in the
GFRP-reinforced beam are much larger than those of the steel-reinforced beam, and any
variability is amplified. Examining the AW3 loading stage, the difference between
maximum and minimum deflection observed was determined to be 9.3% and 9.5% of the
mean values for the GFRP and steel-reinforced beams respectively. Furthermore, the
relative standard deviation (standard deviation as a percentage of the mean values) was
2.3% for both the GFRP and steel-reinforced beams. The variability in behaviour was
most likely caused by changes in number of occupants or on-board equipment during
vehicle testing.
The following sections will outline the observations of each Phase separately. Note that
AW1 loading was not observed during any of the field testing.
3.3.1 Phase 1
The observed behaviour of the test beams during Phase 1 carried little significance in
terms of providing comparison between the two reinforcement types. The two beams
exhibited comparable deflections, with magnitudes between 0.9 and 1.0mm. The mean
difference between mid-span deflections of the two beams was determined as 0.009 mm,
with a standard deviation of 0.02 mm, and maximum difference for any single pass of
0.06 mm. Since the typical linearity (accuracy) of the linear potentiometers used to
41
measure deflection was 0.075 mm, the difference in deflections between the two beams
was measurably insignificant.
While the deflections were almost the same in the two test beams, the curvatures showed
greater differences. On average, the GFRP-reinforced beam had 42% more curvature than
the steel-reinforced beam for Phase 1. Based on a prediction of elastic curvature for a
completely un-cracked beam (Ψ = 7.53 x 10-8
mm-1
, based on gross section properties),
the steel-reinforced beam was still exhibiting un-cracked behaviour at this point (Ψaverage
= 6.65 x 10-8
mm-1
), whereas the GFRP beam was starting to crack (Ψaverage = 9.44 x 10-8
mm-1
) based on the difference in observed curvatures. One possible explanation for this
difference could be that the first flexural cracks were initiated at the gauge locations in
the GFRP-reinforced beam, allowing for greater strains at these discrete points. If only a
few small cracks were present at this stage of loading, the overall beam would still appear
to behave as if fully un-cracked in terms of deflection measurements.
To verify the idea that the beams were generally deflecting in an un-cracked manner, a
SAP2000 structural analysis was performed. Using the un-cracked section and stiffness
properties of the beams (where the beam model is comprised of six identical beam
elements), a “monorail” vehicle was defined using the AW0 loading, and an analysis
performed at various speeds to ascertain the additional dynamic deflection. This was
done by performing a time-history based analysis, where dynamic response is predicted
using the modal properties (frequencies and mode shapes) determine in SAP2000
simultaneously, and idealizes the vehicle as a moving force (as opposed to a mass with
inertial effects). The loading for the SAP2000 model was discretized at 100 Hz (same as
the data sampling frequency).
42
For the first half of Phase 1, the maximum vehicle speed was limited to 50km/h for safety
reasons. During these tests, no evidence of stiffness changes occurred in either beam, and
the mid-span deflections corresponded closely to numerical predictions made in
SAP2000 for the load travelling across the un-cracked concrete beams (see Figure
3.12(b)). The final tests for Phase 1 however, included passes up to 90km/h. In these
passes, consistently larger deflections can be observed in both beams, possibly due to the
surface roughness of the beams (which cannot be modelled in SAP2000), which could
potentially increase the observed dynamic impact. Figure 3.12(a) shows the predicted
dynamic SAP2000 time-history analysis deflections with respect to changes in vehicle
speed, compared to the observed mid-span deflections. A reduction in beam stiffness (due
to cracking) is not thought to have caused the increase in mid-span deflection, as the
residual deflections did not changed any appreciable amount after the test.
Figure 3.12: Change in Phase 1 deflections with vehicle speed (a), and typical mid-
span displacement response of the un-cracked tests beams at 42 km/h (b)
0 15 30 45 60 75 900.8
0.9
1.0
1.1
1.2
Vehicle Speed (km/h)
Max D
elfection (
mm
)
SAP 2000 Prediction
a)"Low" Speed Tests
"High" Speed Test
0 1 2 3-1.2
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
Time (seconds)
Mid
-Span D
elfection (
mm
)
b)
Monorail Train(AW0)
SAP 2000
43
3.3.2 Phase 2
The second phase of testing was performed with the forward vehicle of the two-car
monorail train unloaded (AW0) and the rearward car fully loaded (AW3). While a
symmetrical loading scenario would have been preferable, the changes in loading
scenarios were governed purely by vehicle testing at the time. However, this intermediate
loading stage allowed for the observation of the progressive change in stiffness as both
beams underwent gradual flexural cracking. Vehicle speeds ranged again between quasi-
static (~4 km/h), and approximately 90km/h. During this phase, 53 passes of the train
were observed, all within a three day period. Although total loading acting on the beam
increased by 43%, peak live-load mid-span deflections of the steel and GFRP-reinforced
beams increased to a maximum of 2.4mm & 1.6mm or by 50% & 125% (when compared
to the final passes of Phase 1) respectively. However, this change in deflection was not
entirely abrupt. The first passes at this load level resulted in the GFRP beam deflecting
only 12% more than its steel counterpart. During Phase 2, the deflections of the steel-
reinforced beam remained relatively constant, while the GFRP beam underwent
significant flexural softening during the same period. The delayed flexural cracking of
the steel-reinforced beam may have been due to its larger predicted transformed (un-
cracked) moment of inertia (approximately 8% larger than the un-cracked transformed
moment of inertia for the GFRP-reinforced beam). The same behaviour was observed in
the curvature data from the tests to an even higher degree (see Figure 3.9). Based on the
first and last passes of Phase 2, the maximum deflection per pass increased from 1.6 mm
to 2.4 mm (49%) without a change in vehicle loading. Similarly, the curvature of the
GFRP beam increased from 0.17 radians/km to 0.45 radians/km (an increase of 170%).
44
Deflections comparable to predictions were not achieved in the GFRP until many passes
had been made over the track. This is an important consideration for field testing where
observations are made at speed, because typically only a handful of passes are observed.
Data from as many passes as possible should be acquired to provide greater confidence in
the results. This is particularly true when field tests are conducted on a new or newly
repaired structure.
In Figure 3.11, there is a gap in the effective moment of inertia between Phases 2 and 3
for both the steel and GFRP-reinforced beams. This was due to testing of the monorail
train (believed to be configured to AW2 loading) taking place without data being
acquired. It was not possible to obtain data for all passes of the monorail train because
testing schedules were occasionally revised on short notice.
3.3.3 Phase 3
The final phase of the experimental field testing program consists of the remaining 318
passes of the total 450 passes. While this phase uses six different vehicle loadings, both
vehicles are loaded equally in each case. AW2 and AW3 both represent progressively
higher load levels that had not previously travelled over the beam. This allowed for the
progressive stiffness degradation to be observed in incremental steps before returning to
lower load levels.
During the AW2 and AW3 loading portions, a similar progressive softening trend was
observed in both the steel and GFRP-reinforced beams as for the GFRP observed in
Phase 2. Based on the number of passes completed to date, it was not possible to
determine to a high degree of certainty at what point the beam deflections would stabilize
(in the short term).
45
3.4 Numerical Modelling
In addition to the field testing, numerical analysis was conducted based on models
created for the two test beams. The program Response 2000, or R2k (Bentz & Collins,
1998), was used for the initial modelling and comparison to code-determined values. As a
sectional analysis program, R2k (based on the Modified Compression Field Theory (F. J.
Vecchio & Collins, 1986)) provides detailed output of behaviour for reinforced concrete
sections. While user-friendly (requiring minimal numerical modelling experience to use),
certain limitations exist in Response, such as the inability to define complex or
asymmetric loading scenarios when performing a full member analysis (which it
accomplished by numerically integrating multiple sectional analyses together based on
the simple loading geometry). For this reason, a two-dimensional non-linear finite
element analysis (NLFEA) using the program VecTor2 (Vecchio, 2002) was used as
well. VecTor2 allows the user to define a greater number of material parameters as well
as to choose from a library of material behaviour models and is specifically tailored for
the NLFEA of reinforced concrete. Additionally, VecTor2 allows the user to define
multiple load cases, allowing for the isolation of live loading effects while still
accounting for the self-weight effects (which for the large test beams, contributes
significantly to overall loading), making it easier to compare to observed behaviour in the
field. Finally, VecTor2 also allows the inclusion of a cyclical damage (hysteresis) model.
In the final iteration of the FEM, the non-linear (with plastic offsets) model was used
(Palermo & Vecchio, 2003). For the purpose of this study, it allows for the residual
deflections and strains to be predicted after unloading of the beams at each of the load
stages. This is useful for comparing the post-cracking live load deflections observed in
46
the test beams if residual deflections in the test beam were not known (such as when
performing a field study on a previously cracked reinforced concrete beam).
For the beta version of VecTor2 used, there is a limitation imposed on the maximum
number of nodes and elements (5200 and 6000 respectively). While using smaller
elements is ideal for increasing the precision of NLFEA, elements should be sized
practically, with the heterogeneity of concrete in mind. By eliminating the rotational
degree of freedom at mid-span, only half the beam needs to be modelled based on
symmetry (so long as the loading is chosen to be symmetrical). While the true moving
load results in the maximum bending moments being slightly off-centre, the difference in
magnitude was determined to be negligible when compared to an idealized four-point
bending case (<<1% difference in peak live-load bending moment). As a result, the
beams are modelled in VecTor2 with a nominal concrete element (rectangular) size of
58mm x 58mm with a maximum aspect ratio of 1.5, optimized for the beam dimensions
and reinforcement layouts. Other nominal sizes resulted in non-uniformity of element
size aspect ratio in certain regions of the mesh, due to the location of reinforcement
elements. The rectangular elements used are plane stress (membrane) elements with eight
degrees of freedom (DOF): two translational DOFs (one in each of the “x” and “y”
directions) at each of the four nodes. Because the reinforcement is not evenly distributed
throughout the beam, truss elements are used for all longitudinal and transverse
reinforcement. Truss elements are have two nodes with two translational DOFs at each
node. Alternatively, a “smeared” reinforcement can be applied the rectangular concrete
elements. Due to the relatively low load levels the beams experienced, a “reinforcement
truss” was expected to allow for more precise analysis results due to the localized effects
47
of the reinforcement (particularly with respect to effects of tension stiffening and crack
sizes). It was found that using the “reinforcement truss” in VecTor2 for these beam
models would lose convergence as load was increased well past service levels, regardless
of the magnitude of the loading increment. For this reason, discussion of the VecTor2
modelling results in this Chapter are limited to the prescribed service load levels.
Concrete material properties were determined based on materials testing performed on
concrete cylinders cast during beam fabrication (see Appendix A). Reinforcement
properties used in the model are those provided by the manufacturer, listed in Table 3-2.
The end of the beam is “supported” by a node with the vertical translation degree of
freedom restrained. All elements on the centreline of the beam are restrained against
horizontal translation, effectively restraining this section from any rotation (allowing
analysis of half the beam by symmetry). Two load cases are defined; one which applies a
constant gravity load to the rectangular concrete elements, the other applies load in 1 kN
increments to the various axle loads shown in Table 3-1.
48
3.4.1 Modelling Results
Figure 3.13 shows the experimental load vs. mid-span deflections of the two test beams
compared to the predictions made in VecTor2. Note that, in this figure, the marker sizes
(radii) for experimental values are sized to correspond with maximum linearity
(accuracy) error in deflection measurements. Experimental values shown are the
maximum observed deflections for a given axle load. Additionally, as the test beams
were subjected to their own self-weight prior to the installation of LPs, the offset in
experimental deflections at zero axle load is based on the predicted elastic deflection for
the un-cracked concrete beam.
Figure 3.13: Live-Load vs. Mid-Span Deflection responses for test beams with
predictions from VecTor2
3.4.1.1 GFRP-Reinforced Beam
Predictions from VecTor2 show general agreement with the experimental mid-span
deflections of the GFRP-reinforced beam (Table 3-4 shows the pred/experimental for
several predictions, including VecTor2). While VecTor2 over-predicts the peak
0 1 2 3 4 5 6 7 8 90
30
60
90
120
150GFRP Beam Deflections
Mid-Span Deflection (mm)
Axle
Load (
kN
)
AW0
AW0/AW3
AW2
AW3Vector 2
Experimental
0 1 2 3 4 5 6 7 8 90
30
60
90
120
150Steel Beam Deflections
Mid-Span Deflection (mm)
Axle
Load (
kN
)
AW0
AW0/3
AW2
AW3Vector 2
Experimental
49
deflections in the beam at each axle load stage, the consistency in the error suggests that
material properties should be re-evaluated (for example GFRP stiffness from the
manufacture could be understated). Predicted residual deflections after unloading from
each load stage prove to be highly variable, depending on which cyclical damage model
is chosen for VecTor2. Likewise, small changes in the concrete tensile strength used in
VecTor2 have significant effects on predicted deflections at these low load levels.
Table 3-4: Ratio of GFRP RC mid-span deflection predictions to experimental
values
Δpred/Δexp
Loading ISIS ACI 440 Branson Faza &
Ganga Rao
Bischoff S806 VecTor2
AW0 7.06 4.59 0.88 5.12 0.90 4.24 1.18
AW0/AW3 4.35 3.42 0.95 3.25 1.99 3.52 1.14
AW2 3.78 3.06 0.91 2.84 1.91 3.15 1.19
AW3 2.84 2.38 0.79 2.17 1.61 2.46 1.06
To complement the analysis done in VecTor2, several other models (using an effective
moment of inertia approach) for deflection are used to predict the mid-span deflection of
the GFRP-reinforced beam. Though more models exist in the literature, the six chosen
provide a variety of predictions, and are derived on different rationales. Some are
empirically derived based on databases of beam tests, while others are derived rationally
by integrating curvatures and including the effects of tension stiffening. Table 3-4 shows
the ratio of predicted to observed peak deflection for all load cases for the each of the
following equations:
50
Intelligent Sensing for Innovative Structures (ISIS Canada, 2007)
crt
a
cr
cr
crt
e
IIM
MI
III
2
5.01
(3.2)
ACI 440.1R-06 (ACI Committee 440, 2006)
gcr
a
crgd
a
cre II
M
MI
M
MI
33
1 (3.3a)
where
15
1
fb
f
d
(3.3b)
Unmodified Branson’s equation (Branson & Metz, 1963)
3
)(
a
crcrgcre
M
MIIII
(3.4)
Faza & Ganga Rao (1992)
)(
)(
158
23
Broansonecr
Bransonecr
eII
III
(3.5)
Bischoff (2007)
2
11
a
cr
g
cr
cre
M
M
I
I
II (3.6)
51
S806-12 (CSA, 2012)
333
max 184324 L
L
I
I
L
a
L
a
IE
PL g
g
cr
crc
(3.7)
In Equations 3.2 to 3.7, Ie is the calculated effective moment of inertia; Icr is the cracked
moment of inertia of the section; Ig is the un-cracked moment of inertia; Im is the
modified moment of inertia; It is the transformed, un-cracked moment of inertia; Mcr is
the cracking moment of the beam; and Ma is the applied moment. Note that the method
proposed in Equation 3.7 explicitly determines the deflection, and not the effective
moment of inertia. Equation 3.7 is specific to a four-point bending loading geometry,
where L represents the un-cracked length of the shear span a. The mid-span deflection is
then given by Equation 3.8 (in this case, a is the entire shear span, not just the un-cracked
portion):
)43(24
22
max aLIE
Pa
ec
(3.8)
Note that Equation 3.4 is also the approach used in the A23.3-04 design code, Design of
Concrete Structures (CSA, 2004); however it will simply be referred to as Branson’s
approach hereafter. While Branson’s equation provides better accuracy in this case,
Bischoff’s method would be preferable in design where deflection control is the limiting
serviceability concern (erring on the side of conservatism). The accuracy of Branson’s
method may not be the case for other beams. The ISIS (2007), S806, ACI 440 (2006),
and Faza & Ganga Rao (1992) all greatly over-predict the post-cracking deflections, until
much higher loads, when Ie approaches Icr. It is evident, that these models does not
correctly account for tension stiffening with this type of beam However, other studies
52
have shown (Al-Sunna et al., 2012; Baena et al., 2011; Kara & Ashour, 2012; Mousavi &
Esfahani, 2012) that the modified forms of Branson’s original equation can perform well
in many cases, however their accuracy remains dependent on the reinforcement ratio. As
aforementioned, the types of cross sectional reinforcement designs used in the test beams
are difficult to describe with a reinforcement ratio, requiring all flexural properties to be
determined from a strain compatibility approach.
Bischoff (2007) suggests a different contributing factor, which is the ratio of un-cracked
to cracked beam stiffness (Ig/Icr). This leads to the development of a more rational
approach to determining an effective moment of inertia (based on tension stiffening
models, rather than being empirically developed), which is not specific to either steel or
GFRP-reinforced concrete, nor explicitly on the reinforcement ratio. In the case of this
study where the test beam exhibits a high Ig/Icr ratio of 8.5, it is suggested that this
method is the most reliable.
Figure 3.14: Predicted effective moment of inertia of GFRP-reinforced beam for
various models
0
20
40
60
80
100
Vehicle Loading
I e/I
g (
%)
AW0
AW0/AW3AW2
AW3
Branson
Bischoff
ACI 440 ISIS
Icr
Experimental Stiffness
53
Figure 3.14 shows the predicted effective moment of inertia for Equations 3.2, 3.3, 3.4,
3.6, and Icr for the loading range relevant to the test beams. For Equations 3.2 and 3.3, the
predicted stiffness reduces to less than 20% of the un-cracked stiffness after an additional
5% of loading. In contrast, Bischoff’s and Branson’s (which is assumed un-conservative)
reduce to 62% and 90% respectively in the same loading range. These results would
suggest agreement with Bischoff’s (2007) conclusion that, to properly account for the
reduced stiffness of FRP reinforced concrete beams, the ratio of Ig/Icr is a more critical
factor than the reduced material stiffness of FRP when compared to steel.
3.4.1.2 Steel-Reinforced Beam
VecTor2 predictions of load-displacement behaviour for the steel-reinforced beam
(Figure 3.13) show excellent agreement with the experimental results for AW0,
AW0/AW3, and AW2 loading (Table 3-5 shows the pred/experimental for multiple
predictions, including VecTor2). However, these 3 stages all occur within the earliest
onset of flexural cracking. As the loading is increased to AW3, the observed deflections
far exceed the predicted behaviour. Similarly, the residual deflections after reaching
AW3 loading and deflection when performing passes at AW0 thereafter are significantly
underestimated.
Table 3-5: Ratio of Steel RC mid-span deflection predictions to experimental values
Δpred/Δexp
Loading Branson Bischoff VecTor2
AW0 0.87 0.88 0.99
AW0/AW3 1.22 1.57 1.02
AW2 1.13 1.45 0.99
AW3 0.88 1.11 0.79
54
For comparison, both Branson’s and Bischoff’s effective moment of inertia models are
applied to the steel-reinforced test beam, and their ratios of predicted to observed
deflection are compared in Table 3-5. As is the case for the GFRP-reinforced beam,
Branson’s equation un-conservatively predicts deflection at AW3 (pred/experimental of
0.79), while Bischoff’s model makes an acceptably conservative estimate.
3.4.1.3 Prediction of Deflected Shapes
The deflected profiles of the test beams were also compared to predictions made in
VecTor2. As was the case with peak deflections at various load stages described above,
VecTor2 over-predicts the deflection of the GFRP-reinforced beam at all measurement
points (for all loadings), while under-predicting the deflections in the steel-reinforced
beam at AW3 loading. Figure 3.15 shows the observed deflected shape of the test beams
(average of 10 passes at each load stage) and the corresponding VecTor2 predictions.
Figure 3.15: Experimental and predicted deflection profiles of the GFRP and steel-
reinforced beams
0 1/4 1/2 1/4 0-5.5
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
Relative Distance Along Beam
Beam
Liv
e L
oad D
eflection (
mm
) AW0
AW0/AW3
AW2
AW3
GFRP Beam Steel Beam
Observed Deflection
Vector 2
55
3.4.1.4 Adjustments to Modelling Procedure
As mentioned earlier, the two main factors contributing to the accuracy (or lack thereof)
of the NLFEA predictions were the material properties, and the material models. Ideally,
all material attributes would be verified by experimental testing prior to modelling,
however, this is not possible for design and some material properties are predicted from
more characteristic values (such as predicting concrete stiffness from concrete cylinder
compressive strength). While all constituent material properties need not be determined
explicitly for the purpose of finite element modelling, it is recommended that direct
tensile tests of the plain concrete be performed (split cylinder tests will over-predict
tensile capacity) in addition to cylinder compressive strength tests, if accuracy of
deflection predictions is a high priority. This is particularly important when attempting to
model behaviour during the early onset of flexural cracking, because small changes to the
assumed tensile strength have larger effects on both the cracking load and early tension
stiffening. Additionally, the tensile strength of the concrete can be reduced considerably
by shrinkage restraint (by the reinforcement) during curing (Bischoff, 2008). As such,
two valuable additions in materials testing would be to perform direct tensile strength
tests on the chosen concrete mix as well as to quantify the unrestrained shrinkage strain
of the concrete from the time of casting until testing. The tensile strength of concrete
elements could then be estimated by combining the results from the direct tensile test,
and that determined from Bischoff’s shrinkage-compensated tensile strength.
56
3.5 Comparison of Experimental Deflections with Acceptable Limits
Design guidelines such as the S806 and ACI 440.1R-06 provide generalized approaches
on determining the short term deflections for both steel and FRP reinforced concrete
members. However, limitations on deflections for maintaining serviceability are largely
left up to the designer and depend greatly on the intended application. In the monorail
guideway tested in this study, a limit on deflection was imposed based on displacement to
span ratio. In this case, deflections of up to l/800 (equating to 14.5mm) were deemed
permissible by the client. This is also the same general limitation used in the American
Association of State Highway and Transportation Officials Load and Resistance Factor
Design’s Bridge Design Specifications (AASHTO, 2008). As shown in the results, peak
deflections in both the steel and GFRP-reinforced beams meet this requirement (with
peak service deflections being 6.17mm and 8.44mm respectively as shown in Figure
3.13).
However, the CHBDC also provides guidance on limiting static deflections of members
to better control superstructure vibrations. This limit, places the main emphasis on
user/pedestrian comfort by implicitly limiting the acceleration response of the member.
The check requires the prediction of static deflections, and the natural frequency of the
first flexural mode of vibration (fn1).
57
Figure 3.16: Time domain responses of mid-span deflection (a & c) and acceleration
(b & d) for the test beams when subjected to AW3 loading
Figure 3.16 shows the time domain deflection and acceleration responses (determined
using forward finite-difference approximate derivatives of the displacement data) for the
GFRP [(a) & (b)] and steel-reinforced beam [(c) and (d)] for a sample pass using AW3
loading. Accelerometers were not used in data acquisition due to the limited number of
channels available. It should be noted that two possible sources of error in the
experimental derivation of the acceleration signal could be:
the error present in the mid-span deflection signal that was used to derive the
acceleration signal; and
the need to perform a sensitivity analysis on the time-step size used in the
derivation of the acceleration signal.
Peak accelerations occur during unloading immediately after the point of peak deflection
and are determined as 1.51m/s2 and 1.71m/s
2 for the GFRP and steel-reinforced beams
0 1 2 3
-4
-2
0
Time (Seconds)
Deflection (
mm
)
max
:4.61
a)
GFRP
0 1 2 3
-1
0
1A
max:1.51
Accele
ration (
m/s
2)
Time (s)
b)
GFRP
0 1 2 3-4
-3
-2
-1
0
Time (Seconds)
Deflection (
mm
)
max
:3.29
c)
Steel
0 1 2 3
-1
0
1
Amax
:1.71
Accele
ration (
m/s
2)
Time (s)
d)
Steel
58
respectively. Using the predicted stiffness of the test beams from VecTor2, the SAP2000
predicted peak accelerations are 1.39 m/s2 and 0.75 m/s
2 for the GFRP and steel-
reinforced beams respectively. The observed (derived) accelerations are above the upper
allowable limit for pedestrian bridges (1.5m/s2) stipulated in the CHBDC. Although the
guideway is not open to pedestrian use (the exception being emergencies), vertical
accelerations should be limited to avoid causing discomfort to passengers while riding
inside the vehicle. Quantifying this limit would be the work of a future vehicular-
dynamic interaction study.
Figure 3.17 shows the time domain acceleration free vibration response, and the
frequency domain analysis of the acceleration response of the two test beams for the
same pass as used in Figure 3.16. Using the Fast Fourier Transform (FFT) algorithm, the
first flexural natural frequencies, fn1, were determined to be 13.5Hz and 15.0Hz (from the
peaks of the FFT) for the GFRP and steel-reinforced beams respectively (compared to the
SAP2000 predictions of 11.7 Hz and 14.5 Hz for the GFRP and steel-reinforced beams
respectively). Because the Nyquist frequency of the sampled data was 50 Hz (one half the
sampling frequency), the relatively low frequency of data sampling was sufficient to
observe the first flexural natural frequencies of the test beams. Additionally, the modal
damping ratios were determined to be 5.4% and 7.7% of critical damping for the GFRP
and steel-reinforced beams respectively. These damping ratios, determined using the
logarithmic decrement method, are in the typical range expected for reinforced concrete
beams (Tilly, 1977).
59
Figure 3.17: Free vibration acceleration responses in the time (a &c) and frequency
domain (c & d) indicating first flexural natural frequency observed
3.6 Conclusions
Based on the experimental study and the numerical analyses performed, the following
conclusions and recommendations are made with respect to the use of GFRP-reinforced
concrete guideway beams for monorail infrastructure.
Considerably larger strains and curvatures can be observed in the GFRP-
reinforced beam compared to the steel-reinforced beam, despite using a
considerably larger total area of longitudinal reinforcement in the case of GFRP.
Compared to the steel-reinforced beam, slightly larger short-term deflections were
found in the GFRP-reinforced beam, but they were still well under the allowable
limit of l/800.
Some predictive models for beam deflection based on an effective moment of
inertia approach greatly under-predict GFRP stiffness, specifically in the early
post-cracking stages. Bischoff’s model performs best as a design equation for
0 0.4 0.8 1.2 1.6 2-1
-0.5
0
0.5
1
Time (s)
Acce
lera
tio
n (
m/s
2) c)
Steel
0 0.4 0.8 1.2 1.6 2-1
-0.5
0
0.5
1
Time (s)
Acce
lera
tio
n (
m/s
2) a)
GFRP
0 5 10 15 20 25 30 350
0.02
0.04
0.06
0.08
Frequency (Hz)
|Y(f
)|
fn1steel
:15.04Hzd)
Steel
0 5 10 15 20 25 30 350
0.01
0.02
0.03
0.04
Frequency (Hz)
|Y(f
)|
fn1GFRP
:13.48Hzb)
GFRP
60
both the steel and GFRP-reinforced beams, making accurate and conservative
predictions by considering the large Ig/Icr ratio.
More value can be obtained in performing more complex numerical analyses of
members, in addition to required capacity calculations, to help ensure a higher
probability that all serviceability requirements are met while maintaining efficient
reinforcement design.
More comprehensive limits should be considered for tolerable beam vibration
with respect to user comfort when pedestrian use of the infrastructure is not a
practical concern. Future work could include an investigation studying the
monorail system’s vehicle-beam dynamic interaction to experimentally verify
modelling tools for future infrastructure and/or vehicle suspension design.
3.7 References
AASHTO, L. (2008). Bridge design specifications, customary US units, with 2008
interim revisions. American Association of State Highway and Transportation
Officials, Washington, DC,
ACI Committee 440. (2006). Guide for the design and construction of structural concrete
reinforced with FRP bars (ACI 440.1R-06). Farmington Hills, Michigan (USA):
American Concrete Institute.
Al-Sunna, R., Pilakoutas, K., Hajirasouliha, I., & Guadagnini, M. (2012). Deflection
behaviour of FRP reinforced concrete beams and slabs: An experimental
investigation. Composites Part B: Engineering, 43(5), 2125-2134.
61
Baena, M., Turon, A., Torres, L., & Miàs, C. (2011). Experimental study and code
predictions of fibre reinforced polymer reinforced concrete (FRP RC) tensile
members. Composite Structures, 93(10), 2511-2520.
Bentz, E. C., & Collins, M. P. (2000). RESPONSE-2000: Reinforced concrete sectional
analysis using the Modified Compression Field Theory
Bertolini, L., Carsana, M., & Pedeferri, P. (2007). Corrosion behaviour of steel in
concrete in the presence of stray current. Corrosion Science, 49(3), 1056-1068.
Bischoff, P. (2007). Deflection calculation of FRP reinforced concrete beams based on
modifications to the existing Branson equation. Journal of Composites for
Construction, 11(1), 4-14.
Branson, D. E., & Metz, G. A. (1963). Instantaneous and time-dependent deflections of
simple and continuous reinforced concrete beams Department of Civil
Engineering and Auburn Research Foundation, Auburn University.
CSA. (2004). CAN/CSA-A23.3-04. Design of Concrete Structures. Mississauga, Ontario:
Canadian Standards Association.
CSA. (2006). CAN/CSA-S6-06. Canadian Highway Bridge Design Code. Mississauga,
Ontario: Canadian Standards Association.
CSA. (2012). CAN/CSA-S806-12. Design and construction of building components with
Fibre-Reinforced Polymers. Mississauga, Ontario: Canadian Standards
Association.
62
Faza, S. S., & Ganga Rao, H. V. S. (1992). Pre- and post-cracking deflection behaviour
of concrete beams reinforced with fiber-reinforced plastic rebars. Proceedings of
the First International Conference on the use of Advanced Composite Materials in
Bridges and Structures (ACMBSI), Montreal. 151-60.
Gilstrap, J., Burke, C., Dowden, D., & Dolan, C. (1997). Development of FRP
reinforcement guidelines for prestressed concrete structures. Journal of
Composites for Construction, 1(4), 131-139.
ISIS Canada. (2007). Reinforcing concrete structures with fibre reinforced polymers-
design manual no. 3. Manitoba: ISIS Canada Corporation.
Kai, W., Quan-shui, W., Meng-cheng, C., & Li, X. (2011). Corrosion fatigue of
reinforced concrete in the presence of stray current. Paper presented at the
Electric Technology and Civil Engineering (ICETCE), 2011 International
Conference On, 1133-1136.
Kara, I. F., & Ashour, A. F. (2012). Flexural performance of FRP reinforced concrete
beams. Composite Structures, 94(5), 1616-1625.
Mousavi, S., & Esfahani, M. (2012). Effective moment of inertia prediction of FRP-
reinforced concrete beams based on experimental results. Journal of Composites
for Construction, 16(5), 490-498.
63
Palermo, D., & Vecchio, F. J. (2003). Compression field modeling of reinforced concrete
subjected to reversed loading: Formulation. ACI Structural Journal, 100(5), 616-
625.
Tilly, G. (1977). Damping of highway bridges: A review. Paper presented at the
Proceeding of a Symposium on Dynamic Behavior of Bridges at the Transport
and Road Research Laboratory, Crowthorne, Berkshire, England, May 19, 1977.
(TRRL Rpt. 275 Proceeding)
Vecchio, F. (2002). VecTor2, nonlinear finite element analysis program of reinforced
concrete. University of Toronto, Toronto, ON, Canada,
Vecchio, F. J., & Collins, M. P. (1986). The modified compression-field theory for
reinforced concrete elements subjected to shear. ACI J., 83(2), 219-231.
64
Chapter 4
Static Performance of a Laboratory-Scale Replica of a GFRP-
Reinforced Concrete Beam for a Monorail Guideway
4.1 Introduction
Reinforced concrete structures in North America are subjected to some of the harshest
exposure conditions, from rapid freezing and thawing cycles, to the de-icing salts used on
many forms of transportation infrastructure. Composite materials have been introduced
for rehabilitation of in-service structures, and also in new construction. However, their
application in new construction has raised some important questions. While the strength
of fibre reinforced polymer (FRP)-reinforced concrete members is well understood, other
areas of concern can be identified in terms of serviceability.
Where serviceability requirements of steel-reinforced concrete members are often met
with a design governed by the ultimate capacity, FRP-reinforced members often violate
the same serviceability requirements while satisfactorily resisting the structural loading.
This has prompted the suggestion that the serviceability requirements for steel-reinforced
concrete members are not directly transferable for use in the design of FRP-reinforced
concrete (Alsayed, 1998). Not only can the accuracy of calculated behaviour suffer, but
also the logical basis for limitations on certain parameters may need to be altered.
The following sections outline the experimental program conducted to evaluate the
performance of half-scale glass-FRP (GFRP)-reinforced concrete beams to be used in the
construction of elevated monorail transit infrastructure. This study aims to provide a
better understanding of the static performance of GFRP-reinforced concrete flexural
65
members. Chapter 3 contains the results from a pilot study completed where a full-scale
GFRP-reinforced concrete beam was instrumented and compared to a steel-reinforced
beam used for a test guideway for a newly developed monorail train.
4.2 Experimental Program
Much of the work completed on FRP-reinforced concrete to date has been comprised of
parametric studies done at the lab scale, where certain material or design parameters are
varied for a large series of test specimens. This study is different in that the primary focus
is the evaluation of beams built to the relevant design standards. In Chapter 3, two full-
scale beams were compared (one GFRP-reinforced and one steel-reinforced) where the
point of equivalency between the two was the serviceability criteria that must be satisfied.
The half-scale portion of testing described herein examines the behaviour of members
with equivalent behaviour (scaled down) as the full size GFRP-reinforced beam installed
at the test track.
Due to the full scale beams being required to satisfactorily perform their duties on a test
guideway for many years, they are designed to satisfy the requirements of the Canadian
Highway Bridge Design Code (CHBDC), S6-06 (CSA, 2006), and were designed by a
third party structural consultant. While the full-sized beams contain several details
important to their design, the main focus will be on their behaviour in flexure (with
minimal focus on shear).
66
4.2.1 Full-Scale Beam Designs
Constructed of simply supported reinforced (non-prestressed) concrete beams laid end to
end (approximate dimensions 11,600x690x1500mm with 11,300 mm unsupported span),
the monorail test guideway is 1.86 km long with two instrumented test beams (one steel-,
one GFRP-reinforced) being located close to the mid-point of the guideway. Choosing
beams at the midpoint of the track allows for the highest allowable vehicle speeds to be
achieved for testing. This section design has a relatively low span to depth ratio (7.53).
As the beam dimensions are limited by both shipping constraints as well as the geometric
design of the monorail vehicle’s undercarriage, design alterations were not possible to
create more favourable test specimens (for example flanged or prestressed sections).
Figure 4.1 shows the cross sections of the two full-scale test beams installed on the
monorail test track as they were designed (dimensions are in mm). The steel-reinforced
beam uses an asymmetrical longitudinal reinforcement arrangement with four 30M bars
making up the primary flexural reinforcement, and four 25M bars for the top. Skin
reinforcement in the web of the beam is provided by eight rows of two 20M bars, mostly
to minimize the growth of flexural cracks in the side faces of the beam (Frantz & Breen,
1980).
67
Figure 4.1: Cross section designs of the full-scale Steel and GFRP-RC beams
The GFRP-reinforced beam was designed as symmetrically reinforced, using only #7
bars throughout (six bars top and bottom, with 14 rows of two bars in the web). However,
two errors resulted in the beam differing from the intended design. The first issue was a
typographical error on the structural drawing used for the purchase order of the
reinforcement. While the intention was that all longitudinal bars in the GFRP beam
would be #7 high modulus (HM) bars, one plan view of the beam showed #8HM bars in
the top row of reinforcement. This went unnoticed, and #8HM bars were delivered for the
top of the beam. The second issue was the delivery of a mixture of #8 low modulus (LM)
and #7HM bars for the remaining flexural reinforcement. In this nomenclature system,
LM refers to a modulus of elasticity between 40 and 45 GPa and HM refers to a modulus
of 60 to 65 GPa (as reported by the manufacturer). No information is provided by the
manufacturer to indicate what differences exist between the two product lines to result in
the change in stiffness, as the fibre volume fraction is reported as the same in both cases.
One potential explanation is the misrepresentation of bar sizes to change the apparent
68
strength and stiffness. From measuring the diameter of #8LM and #7HM bars and
comparing these to material data provided by the manufacturer, it is possible that the
apparent increase in stiffness of the HM bar is due to the fact that it is much larger than
stated (~25 mm measured diameter as opposed to the reported 22 mm), rather than
having inherently stiffer glass fibres or matrix. Should this be the case, the #8LM and
#7HM bars would have roughly equivalent mechanical properties in terms of strength and
stiffness when their actual diameter and cross sectional areas are used in calculations.
Figure 4.2 shows the layout of longitudinal reinforcement for the full-scale GFRP beam
as it was built compared to the intended design. The effects of this change on the
intended performance of the GFRP-reinforced guideway beam are minimal. However, all
analysis and numerical modeling (including the scale down procedure for the half-scale
beam) were modified to reflect the change in bar layout. To avoid confusion all further
discussion will not include mention of this alternating arrangement of reinforcement,
although it is implied in all analyses.
Figure 4.2: GFRP bar layout in full-scale beam as built (due to supplier error)
69
4.2.2 Concrete Mix Design
To reduce construction cost and time, all beams for the test guideway were fabricated by
a local pre-cast manufacturer. In order to maintain an acceptable turnaround time for the
beam production phase, concrete with relatively high compressive strength (~50 MPa at
28 days) was used for the “production” beams. This ensured that the beams would have
reach sufficient capacity as to be removed from their formwork the following day (~17
MPa), without risk of flexural cracking under their own self-weight. However, this high
concrete strength (in conjunction with the low span-to-depth ratio described earlier)
would have likely resulted in the beams undergoing little or (possibly) no flexural
cracking under full service load of the monorail train (based on the predicted flexural
cracking moment of the section at full service load (CSA, 2012)). These high strengths of
test beams would greatly diminish the value of data retrieved from testing, as only the
strains and deflections of un-cracked concrete would be observed.
To mitigate this risk, a lower strength mix (to be provided by a separate ready-mix
supplier) was used for the instrumented test beams, targeting a cylinder compressive
strength (f’c) of 20 MPa. Two trial mixes were sampled, a 20 MPa mix and a 17 MPa
mix. Because quality control of the 17 MPa batch proved to be an issue (due to the high
water to cement ratio), the 20 MPa mix was chosen. This mix showed an average
cylinder compressive strength of 25 MPa for both the trial mix and the mix used in
casting the full-scale test beams. Due to the mix design being proprietary, no further
details were provided, other than the nominal aggregate size of 19mm.
70
4.2.3 Scale Factor and General Construction
To mitigate size scaling effects, the half-scale beams were proportioned to the maximum
size (weight) permissible to be tested in the testing laboratory (as limited by the overhead
crane). The chosen scale-down factor of 2.15 was based on not exceeding the 3-ton
capacity of the crane, where the density of the concrete was determined from the concrete
mix used in the full-scale beams. Table 4-1 shows the dimension of both the full-scale
beams (GFRP and steel-reinforced) compared to the scaled down GFRP versions. Both
the full and half-scale beams use pultruded sand-coated GFRP bars for their longitudinal
and transverse reinforcement. The transverse reinforcement (closed stirrups) is made by
two overlapping ‘U’ bent bars, as the manufacturing process limits the number and types
of bends possible for pultruded GFRP. Also, use of overlapping ‘U’ stirrups greatly
simplifies the fabrication of the reinforcement cage when compared to using traditional
closed stirrups, as stirrups do not have to be slipped over the ends of the beam.
In order to prevent end bearing failure (shear friction failure, as the supports are very
close to the ends), both the full-scale and half-scale GFRP beams have special end details
designed for them. However, due to space constraints, the full and half-scale beams use
different types of details to provide this resistance. Because the performance of the beams
close to their supports is not a focus in the study, this change is deemed acceptable and
ensures adequate end bearing capacity (see Appendix A).
71
Table 4-1: Physical properties of full-scale and half-scale GFRP-reinforced test
beams
Full-Scale Half-Scale
Base Width, b 690 320 mm
Height, h 1500 700 mm
Depth to Bottom Reinforcement, d 1428 656 mm
Long. Bar Size #7 HM #4 HM -
Long. Bar Area 388 127 mm2
Cylinder Strength, f'c 22 32 MPa
4.2.4 Scale Down Procedure
To analyze the full-scale and proposed half-scale designs (evaluating them for equivalent
normalized behaviour), a variety of approaches were taken to predict their behaviour,
including:
simple design equations as per CSA S6-06, the Canadian Highway Bridge Design
Code; and CSA S806-02/S806-12, Design and Construction of Building
Components with Fibre-Reinforced Polymers (CSA, 2002; CSA, 2012) ;
numerical sectional analysis program Response 2000, or, R2k (Bentz & Collins,
1998), based on the Modified Compression Field Theory (MCFT) (Vecchio &
Collins, 1986);
non-linear finite element analysis program VecTor2 (Vecchio, 2002).
Once the beam dimensions were chosen based on the scale factor of 2.15, reinforcement
was then proportioned for the half-scale beam based on normalizing the bar area and
stiffness of the full scale beam design. Due to the magnitude of the scale reduction, it was
not possible to simply reduce the number of reinforcing bars while maintaining the same
size bars (#7/#8) of the full scale beam. It is further recognized that bar strength varies
with size due to the changes in shear lag effect (Kocaoz et al., 2005). This is complicated
72
further by the full-scale beam having a mixture of low modulus and high modulus bars.
As it was intended that the full-scale beam would use one size of bar, the half-scale beam
would be designed to use one bar size throughout the longitudinal reinforcement.
Having determined approximately the number and size of bars required to yield similar
normalized behaviour as the full-scale beams, trial designs for half-scale beams were
created and their normalized responses in flexure and shear were compared to the full-
scale beam. Comparison of beam behaviour was chosen to be mainly the normalized
moment-curvature and normalized shear force-shear strain responses, and to a lesser
extent, the normalized moment-bar stress and stirrup strain at ultimate. Moment,
curvature, and shear force are normalized based on cross-section dimensions as shown in
Equations 4.1, 4.2, and 4.3 respectively, while shear strain is already a dimensionless
quantity.
2*dbMMn (4.1)
dn * (4.2)
vn db
VV*
(4.3)
Where M, Ψ, and V are the bending moment, section curvature, and shear force
respectively, and Mn, Ψn, and Vn are the normalized values. As for section properties, b is
the beam width, and d is the effective depth (or shear depth in the case of dv) of the
section. As the beams contain many rows of reinforcement, the effective depth is defined
as the distance from the extreme compression fibre to the centre of the bottom row of
longitudinal reinforcing bars.
73
During this highly iterative process, small changes were made to cover, stirrup size,
stirrup spacing, number of longitudinal bars, and size of longitudinal bars to produce a
best-fit candidate for a half-scale design. Normalized moment-curvature response is
predicted for the sections assuming pure flexure (i.e. at the mid-span region of highest
moment (constant between point loads) and no shear). The two beams’ responses in shear
are predicted at the critical location for shear, as recommended by Bentz (2000) and
(Hoult et al., 2008), at the location dv away from the applied load (towards the support).
This would be the most likely location for the initiation of the failure crack in a shear
critical beam.
4.2.5 Normalized Behaviour Predictions
After performing more than twenty major iterations and several minor changes, a final
candidate was chosen based on the optimization of normalized behaviour matching to the
full-scale beam and constructability of the new half-scale beams. Other potential
candidates (based on quality of fit of behaviour) were not chosen based on their bar
spacing being too small for concrete placement purposes. Figure 4.3(a) and Figure 4.3(b)
show the normalized moment-curvature and shear force-stirrup strain responses for the
chosen half-scale GFRP-reinforced beam design. It is important to note that the following
predictions of behaviour for both the full and half-scale beams are made using the actual
concrete cylinder strengths of 25 MPa, rather than the design value of 20 MPa. While
both beams were cast using the same mix design from the same ready-mix distributor, 28
day average cylinder strengths were significantly greater for the half-scale beams (cast 12
months after the full-scale) at 32 MPa. Much of the over-strength seen in the half-scale
74
beam design in the following normalized responses could be attributed to this difference
in concrete strength.
Figure 4.3: Normalized responses of full-scale and half-scale GFRP RC test beam
designs
In Figure 4.3, the flexural responses shown are terminated when the concrete
compressive strain reaches 0.0035 in the extreme compression fibre (as per S6-06). Post-
cracking normalized stiffness for the half-scale design agrees well with the prediction of
full-scale behaviour. The flexural stiffness of the two designs (slope of the moment-
curvature plots) varies by only 1.8%. However, the half-scale is offset in terms of
absolute stiffness (magnitude of normalized moment for given normalized curvature).
This is caused by not being able to reduce the half-sale beam’s concrete cover to the
reinforcement, as limited by the concrete aggregate size of 19 mm, in addition to the
higher f’c. The result is that effective depth to overall height ratio differs for the full and
0 0.005 0.01 0.015 0.020
1000
2000
3000
4000
Normalized Curvature (*d)
Mo
me
nt
(M/b
*d2) a)
0 5 10 150
500
1000
1500
2000
Shear Strain, (mm/m)
Sh
ea
r F
orc
e (
V/b
*d)
b)
0 200 400 600 8000
1000
2000
3000
4000
Longitudinal Bar Stress (MPa)
Mo
me
nt
(M/b
*d2) c)
0 1 2 3 4 50
H/4
H/2
3H/4
H
Strirrup Strain (mm/m)
Cro
ss S
ectio
n H
eig
ht
d)
75
half-scale beams (cracking moment governed by h, while post-cracking behaviour
governed by d).
A portion of the slight over-strength observed in the half-scale beam in Figure 4.3(b)
could be attributed to the much lower bending moment to shear force ratio (M/V) in the
half-scale design, which in the four-point bending case is proportional to the shear span
length. As R2k calculates the contribution of concrete to shear capacity (Vc) using the
MCFT, it is affected significantly by changes in longitudinal strain. As a result of the
scale-down, M/V values are 2.9 and 1.43 for the full-scale and half-scale beams,
respectively (as taken from the critical section in shear, dv away from the loading point).
This decreases the expected longitudinal strain (at mid-depth in the section) at failure,
increasing the normalized shear stress that can be carried by the concrete. As the main
focus of the study is the beams performance in flexure, ensuring that the scaled down
beam has the properly proportioned constant moment region was prioritized.
Figure 4.3(c) and Figure 4.3(d) show normalized responses for longitudinal
reinforcement bar stress and stirrup strain in both the full and half-scale beam designs.
While the longitudinal bar stress of the two beam designs show good agreement, the half-
scale beam design again exhibits a slight over-strength as a result of the increased
concrete compressive strength. In neither cases of the full or half beams do the
longitudinal bars reach their guaranteed tensile strain before flexural crushing of the
concrete (bottom longitudinal bars in both beams are at approximately 62% of their
guaranteed rupture strain). Stirrup stress was not compared in this case as the elastic
moduli of stirrups used in the full and half-scale beams differed considerably
(approximately 45 and 55 GPa, respectively) due to a change in the manufacturing
76
process during the time between fabrication of the full and half-scale beams. The
distribution of stirrup strain (along the cross sectional height of the beam) shown in
Figure 4.3(d) are taken from the section dv away from the load point, and again at the
flexural failure load. As seen in Figure 4.3(d), comparable strains in the stirrups at the
critical location match closely for the ultimate flexural load.
Based on the general agreement in normalized behaviour for the sectional responses
described above, the half-scale beam design was approved. All longitudinal reinforcing
bars were chosen to be size #4HM with #3 standard modulus (StdM) “U” shaped stirrups
(overlapping), spaced at 125mm on-centre. Like the full-scale beam, the longitudinal bars
are developed at their ends with “L” hooks for all bottom bars, as well as every other side
bar. Top bars do not have ‘L’ hooks at their ends. Figure 4.4 shows the cross sections (as
designed) for both the full and half-scale GFRP-reinforced beams (dimensions in mm).
Table 4-1 contains the mechanical properties of the sand coated, pultruded GFRP bars
used for the construction of the full and half-scale beams. Appendix A contains the
fabrication drawings for the two identical half-scale GFRP beams, including concrete
cover and the end bearing region design.
77
Figure 4.4: Comparison of full-scale to half-scale GFRP-reinforced beam cross
section designs
4.2.6 Fabrication
The two half-scale beams were fabricated by the same pre-caster as the full-scale test
beams. Like the full-scale beams, the GFRP bars were instrumented in the lab for quality
control purposes (23 strain gauges per beam internally), then shipped for assembly.
Assembly of the reinforcing cage was done by tying the bars with plastic cable (zip) ties.
This resulted in the end bearing plates being the only ferrous material in the beam.
Steel formwork was constructed by the pre-cast manufacturer which would be used to
pour both beams at the same time. They were to be cast on their side (as per the pre-
casters suggestion), to reduce the height of the formwork, which avoided the risk of
deforming the forms during casting due to the increased hydrostatic pressure.
Damage to the formwork (cause unknown) prior to casting resulted in the half-scale
beams being out of dimension, and out of square (by as much as 10 mm). Appendix A
78
contains photographs from the fabrication of the half-scale beams, including images of
the deformed formwork and the methods used to mitigate the problem.
4.2.7 Test Setup for Half-Scale Beams
The first of the half-scale beams was to be tested monotonically to failure, with complete
unloading planned to occur at two intervals. These points of interest would be;
the maximum vehicle service load (normalized), and
the maximum allowable service stress in the reinforcement as per CSA S806.
Unloading at these two load levels would allow for the per-cycle stiffness to be
experimentally determined. The stiffness at the normalized service load (planned to
simulate AW3 vehicle loading in the full-scale beam) is of particular importance, as it
will be compared to deflections and stiffness observed in the full-scale beam.
Additionally, this load will also be used for the cyclical load testing of the second half-
scale GFRP-reinforced beam.
After performing the first two loading cycles, the beam would be loaded to failure, in
order to observe the failure mechanism(s) and compare the true ultimate load and
deflection to various predictions made (based on both design codes and numerical
analysis).
A 2000 kN MTS 440 servo-hydraulic controlled actuator was chosen to test the beam.
This system would allow for experiments to be completed in either a load control or
stroke control. For the first beam (monotonic test), the beam would be tested in stroke
control, at a rate of one millimetre per minute (1mm/min). Future testing of the second
half-scale beam (long term cyclic test) would be performed under load control cycles at
the service load. The test was performed in four-point bending using a steel load-
79
spreading beam to distribute the actuator load to two points. It should be noted that an
idealized four-point bending case differs slightly from the full-scale moving load case
(where the location of maximum moment would be underneath the axle closer to mid-
span when the axles are shifted one quarter of the distance between them from being
centered on the beam). However, the difference in peak bending moment (as shown by
SAP 2000 moving-load analysis) was shown to be small (1.4% less in the four-point
bending case). Therefore, symmetry in the loading was preferred for simplicity, and
comparison to numerical models.
During the test, the stroke (and load) would be held periodically (for one or two minutes)
to observe and mark the propagation of cracks on the side of the beam. This would be
done at roughly 10 kN load intervals (as measured by the load cell attached to the
actuator) from observation of the first flexural crack to about 200 kN, and then every
20kN thereafter (subject to change based on the rate of crack propagation). Photographs
would be taken at each load stage to track the propagation of cracks, however, the layout
of the MTS 440 frame did not allow for full side view (elevation) photos to be taken
during the test.
4.2.7.1 Instrumentation
The half-scale GFRP beams were internally instrumented with 23 electric resistance
strain gauges at various locations, as well as one surface concrete strain gauge applied at
the top (compression) face of the beam, at mid-span (bonded after casting). The majority
of internal gauges were located to observe the flexural behaviour of the beam in great
detail within the constant moment region. At mid-span, gauges were placed on all the
bottom bars, on an alternating pattern on the side bars, and on two out of four of the top
80
bars. This allowed for a detailed strain profile to be developed, with some redundancy in
the event that some of the gauges fail during fabrication or testing.
To help develop the strain profile longitudinally, gauges were also placed on one bottom
bar at the load point (i.e. at the boundary between the shear span and the constant
moment region) and at the location dv away from load point (towards the support), where
dv is 590 mm. A gauge was also placed on a top bar at the location dv away from the load.
While predictions showed that the designed half-scale beam (like the full-scale) was not
shear-critical, it was decided to instrument stirrups at the critical point (dv away from the
load point) to observe strains in the stirrups in the unlikely event that they exceed
strength limitations and fail. Strain gauges were applied to the middle of the bend of the
stirrup, and then at ¼ and ½ of the overall beam height along the stirrup.
Seven linear potentiometers (LPs) were used to measure the displacement of the beam at
various locations. LPs were placed at:
Mid-span (one on either side of the beam),
Quarter-spans (one at each),
Eighth-spans from supports (one at each), &
One measuring lateral displacement of the beam as measured on the side face at
the top of the beam (at mid-span).
Figure 4.5 and Figure 4.6 show the layouts of the instrumentation (strain gauges and LPs)
in elevation and section views respectively.
81
Figure 4.5: Elevation of instrumentation placement in half-scale GFRP RC beam
Figure 4.6: Mid-span and shear-span section views on half-scale GFRP RC beam
instrumentation
Because the beam supports were quite rigid (large steel plates directly in contact with
concrete), LPs were not used to track support-settlement displacements. Figure 4.7 shows
the beam setup in the MTS 440 frame prior to testing. Acquisition of data was performed
82
with a Vishay Micro-Measurements System 7000 unit recording at a rate of 1Hz (logging
all channels simultaneously, scanning at 10 Hz).
Figure 4.7: Half-scale GFRP-reinforced beam setup for monotonic testing
4.2.8 Materials Testing
Prior to testing the beam, tests were performed on numerous concrete cylinders cast from
the same batch as the half-scale GFRP beams (results of which are presented in Appendix
D). These would be used to re-calibrate the numerical models before testing of the beam.
These were both tests on small (100 mm diameter by 200 mm tall) cylinders to determine
compressive strength (f’c, as per ASTM C39M) and large (150 mm diameter by 300 mm
tall) cylinders to determine the modulus of elasticity.
As aforementioned, the mix design was to be the same as that used for the full-scale
beams (which resulted in a compressive strength of 22 MPa), however, the batch used in
83
the half-scale tests resulted in strengths significantly higher, with f’c being 32 MPa on
average of the 4 large cylinders tested to failure (no cylinder was less than 31.45 MPa).
Based on CSA S6-06, the elastic modulus would be predicted as 26,430 MPa (Cl.
8.4.1.7), however, the average experimental modulus of elasticity (as per ASTM C649M-
10) was 30,009 MPa (13.5% higher).
The observed over-strength in the half-scale batch of concrete is likely due to the
incorrect amount of water used in the batch. While the mix design is proprietary to the
ready-mix company, they did provide some information for quality assurance purposes,
including a maximum water to cement (w/c) ratio of 0.7 (by mass).
As detailed mechanical properties are published for the FRP reinforcing bars by the
manufacturer, material testing was not performed on them. Additionally, certifications
tests were performed by the manufacturer for the production run of the bars, and the
results provided at the time of shipping.
4.3 Testing Results and Discussion
The monotonic testing of the half-scale beam was completed in 4 stages (or ramps) over
the course of two days. The beam was unloaded completely at:
The scaled-down maximum vehicular service load
The maximum allowable service in GFRP reinforcement as per CSA S6-06 (Cl.
16.8.3)
An actuator load of 370 kN (to provide more insight to residual deflections and
concrete hysteresis)
Final ramp to ultimate failure.
84
As aforementioned, loading of the beam was held periodically while inspections of the
crack propagation could be made and marked on the side face of the beam.
4.3.1 Service Load Ramp
Based on the predicted normalized moment-curvature responses for the full and half-
scale GFRP beam designs, a scaled-down service load (as measured by the actuator) of
106 kN was selected as the first load ramp, based on equivalent reinforcement stress as
the full-scale beam at maximum service loads. Figure 4.8 shows the following responses
along with the numerical predictions from R2k and VecTor2:
a) Load-deflection
b) Moment-reinforcement strain
c) Moment-curvature
d) Deflection profile at the service load.
For the VecTor2 predictions of (scaled) service load behaviour, the beam was modelled
with rectangular plane stress elements with 8 DOFs for concrete regions with truss
elements (4 DOFs) for the GFRP reinforcing bars. Rectangular element dimensions were
25 mm x 25mm for the half-scale service load model. The modelling approach was
similar to that used with the full-scale beam presented in Chapter 3. As described in
Chapter 3, the element size was selected to allow modelling of discreet reinforcement
bars.
85
Figure 4.8: Responses of beam up to the scaled down service load
Initially, numerical predictions underestimated the post cracking deflections due to an
overestimation of the cracking strength of the beams. At relatively low load levels, the
accuracy of predicted responses have shown to be highly sensitive to small changes in the
tensile strength of the concrete f’t. Figure 4.8 shows the second iteration of numerical
predictions which include a reduction of the predicted tensile strength of the concrete
(f’t), as per the method described by Bischoff (2001). For the revised predictions, the
concrete tensile strength is reduced due to the restrained shrinkage of the beam. As the
unrestrained shrinkage of the concrete mix was not included in materials testing, and
estimation of the shrinkage had to be made. Using the provisions of CSA S6-06, the
unrestrained shrinkage strain was predicted to be approximately 1x10-4
mm/mm. Then,
based on the elastic modulus of the reinforcement and concrete, and the reinforcing ratio
0 2 4 6 80
30
60
90
120
Mid-Span Deflection (mm)
Actu
ato
r Load (
kN
)
a)
0 400 800 1200 16000
30
60
90
120
Mid-Span Average Strain ()
Bendin
g M
om
ent
(kN
m)
b)
0 0.5 1 1.5 2 2.5 30
20
40
60
80
100
120
Curvature (rad/km)
Bendin
g M
om
ent
(kN
m)
c)
0 1/8 1/4 3/8 1/2 5/8 3/4 7/8 1-8
-6
-4
-2
0
Relative Distance Along Span
Dis
pla
cem
ent
(mm
)
d)
86
(all longitudinal reinforcement in this case), the analytical expression derived by Bischoff
(Equation. 4.4 below) can be used to predict the reduction in concrete tensile strength.
n
nEf csh
c
1 (4.4)
In Equation 4.4, fc is the reduction in concrete tensile strength to be applied, εsh is the
unrestrained shrinkage strain of the concrete, Ec is the modulus of elasticity of the
concrete, n is the modular ratio (EFRP/Ec), and ρ is the reinforcement ratio (total
longitudinal reinforcement area/total cross section area).
Mid-span deflection at the scaled-down service load was 6.61 mm, or approximately
equal to the allowable limit of L/800, indicating that a higher service load may not be
advisable for this beam configuration.
4.3.2 Peak Allowable Service Load (25% ffrp(ultimate))
A loading ramp of the test beam was performed to assess the condition of the member
approximately at the maximum allowable service stress as per S6-06. To reduce the
possibility of creep rupture or fatigue rupture of the FRP reinforcement (due to sustained
or cyclic loading), S^-06 limits the maximum allowable stress due to service loads to one
quarter the guaranteed ultimate strength of the bar (0.25*ffrp(ultimate)), which corresponded
to an applied load of approximately 240 kN. Upon performing this ramp, the total mid-
span beam deflection reached 23.16 mm or ~L/227. This far exceeds the imposed
deflection limit for the intended use of the beam, which is L/800, or 6.6 mm.
87
4.3.3 Failure Ramp
Following the ramp to 370kN (with no significant change in behaviour), the beam was
loaded to failure. The marking of cracks was performed periodically until the actuator
load reached 450kN, after which it was deemed unsafe to approach the beam. Testing
continued until first flexural crushing of the top layer of concrete occurred at a load of
584kN, after which the load dropped by nearly 50 kN. Figure 4.9 shows the mid-span
region of the beam after first flexural crushing of the concrete cover has taken place.
Figure 4.9: First flexural crushing of top cover concrete at mid-span
After the loss of the top cover concrete, the beam continued to carry load linearly to
693kN, at which point one of the top longitudinal bars failed causing the load to drop by
~10kN. This was almost immediately followed by the crushing of the remaining three
longitudinal bars in quick succession, associated with a drop in load to 553kN. It was
88
agreed that the beam would not carry anymore load now that it had suffered a brittle
failure, and unloading of the beam began at a rate of 1mm/min. After 1 minute of
unloading, the load on the beam had reduced to 447kN, and then the beam suffered
another brittle failure. The cause of this failure appeared to be the rupture of two stirrups
in the top of the beam, due to large hoop-stresses they carried to confine the concrete
core. This sudden release of energy caused complete collapse of the confined concrete
core to occur at mid-span, with the remaining longitudinal bars holding the two halves of
the beam together (the total load had now dropped to 87kN). Figure 4.10 shows the
constant moment region of the beam after failure in the top longitudinal bars had
occurred. While the buckled top longitudinal bars are obscured by the spreader beam in
Figure 4.10, the buckled skin reinforcement can be easily observed.
89
Figure 4.10: Visible buckling of side GFRP bars after rupture of top bars lead to
failure
Figure 4.11 shows the same responses as Figure 4.8, extended for the entirety of the
monotonic test. In Figure 4.11(a), first flexural crushing of the cover concrete is clearly
visible which occurred well above the assumed crushing strain of concrete (the peak
concrete compressive strain was observed to be ~0.0044). Figure 4.11(d) shows the
displacement profile of the beam at the time of first flexural crushing (584 kN). For
predictions to ultimate loads, the VecTor2 model was changed from a discrete
reinforcement truss to a smeared reinforcement model. The mesh size remains the same
as the model used for (scaled) service loads, but now longitudinal and shear
reinforcement are modelled within the rectangular elements. In each of the 4 responses
shown, predictions from R2k and Vector2 agree well up to and even past first flexural
90
crushing, generally providing slightly conservative estimates. Neither model however
was able to predict that the beam would carry an additional 18.6% of its load after first
crushing, but rather predict modest increases in capacity of (606kN VecTor2 and 560
R2k) 7.8% and 5.3% for VectTor2 and R2k, respectively. As both programs are two-
dimensional analysis programs, the effects of confinement from the bars are not
accounted for.
Figure 4.11: Responses of half-scale beam until ultimate failure at 693kN
Figure 4.12(a) and Figure 4.12(b) show the top surface concrete strains and the top GFRP
reinforcing bars, respectively, and additionally indicate the point of first flexural crushing
of the cover concrete (as determined by a combination of visual observation, drop in load,
and a drop in concrete surface strain). As seen in Figure 4.12(a), this occurs at close to a
strain of 0.0045; well past the assumed crushing strain of 0.0035, but significant non-
0 25 50 75 100 125 1500
200
400
600
Mid-SpanDeflection (mm)
Actu
ato
r Load (
kN
)
a)
0 0.4 0.8 1.2 1.6 2
x 104
0
200
400
600
Bottom Reinforcement Strain ()
Bendin
g M
om
ent
(kN
m)
b)
0 5 10 15 20 25 30 35 400
200
400
600
Curvature (rads/km)
Bendin
g M
om
ent
(kN
m)
c)
0 1/8 1/4 3/8 1/2 5/8 3/4 7/8 1-100
-75
-50
-25
0
Relative Distance Along Beam
Dis
pla
cem
ent
(mm
)
d)584 kN
91
linearity of the beam response (a reduction in stiffness) occurs immediately prior to this.
The applied load then increased linearly (without further partial failures) until the onset
of the final failure at 693 kN.
Figure 4.12: Behavior at crushing (a & b), top bar rupture (c) and vertical strain
profiles at various stages (d)
The peak strain observed in the top GFRP bars at ultimate failure was 11,875 με
(0.011875), or 3.39 times the assumed crushing strain of the concrete. At this point, it is
uncertain if the concrete core (meaning the concrete inside the reinforcement cage) was
fully subjected to this strain and contributing significantly to the increased capacity.
Alternatively, it is proposed that while a small portion of the residual capacity is provided
by the remaining concrete in compression, the majority could have been provided by the
reinforcing cage itself acting as a plane truss, where the concrete core served to restrain
the GFRP bars against buckling (the eventual failure mechanism).
Figure 4.12(c) shows the load-deflection response of the beam close to ultimate failure.
Point (1) in the figure indicates rupture of the first top GFRP bar (associated with an
-5 -4 -3 -2 -1 00
150
300
450
600
Actu
ato
r L
oad
(kN
)
Concrete Strain (mm/m)
a) First Flexural Crushing
-12 -9 -6 -3 00
150
300
450
600
Actu
ato
r L
oad
(kN
)
Top Longitudinal Bar Strain (mm/m)
b)
First Flexural Crushing
130 135 140 145 150 155 160550
600
650
700
750
Mid-SpanDeflection (mm)
Actu
ato
r L
oad
(kN
)
c)(1)
(2)
-10 -5 0 5 10 15 200
150
300
450
600
Be
am
He
ight
(mm
)
Reinforcement Strain (mm/m)
d)
106kN
240kN
567kN
693kN
92
approximate10 kN drop in load). Point (2) occurs after a small increase in displacement,
with rupture of the remaining three top GFRP bars, and a very abrupt drop in load.
Figure 4.12(d) shows the longitudinal strain profile across the height of the half-scale
beam for various load stages. At the ultimate load (693kN), the maximum tensile strain is
observed to be over 2% (the minimum guaranteed failure strain for the GFRP bars as
provided by the manufacturer), however no tension reinforcement failure occurred in this
beam. Conversely, the stain in the top compression bars is ~1.2% at the point of rupture.
4.4 Performance Evaluation
While the two numerical analyses presented on this first load ramp do satisfactorily
predict behaviour, they require more effort to perform than typical design-code based
analyses. Therefore, more basic predictions are also made of the load-deflection response
and compared to the experimental data, using the following expressions for deflection
calculations:
Un-modified Branson’s equation (Branson & Metz, 1963)
3
)(
a
crcrgcre
M
MIIII (4.5)
Bischoff (2007)
2
11
a
cr
g
cr
cre
M
M
I
I
II
(4.6)
93
Faza and Ganga Rao (1992)
)(
)(
158
23
Bransonecr
Bransonecr
mII
III
(4.7)
ACI 400.1 R-06 (ACI Committee 440, 2006)
gcr
a
crgd
a
cre II
M
MI
M
MI
33
1
Where:
(4.8a)
15
1
fb
f
d
(4.8b)
CSA S806-12 (same as S806-02) (CSA, 2012)
333
max 184324 L
L
I
I
L
a
L
a
IE
PL g
g
cr
crc
(4.9)
ISIS (2007)
crt
a
crcr
crte
IIM
MI
III
2
5.01
(4.10)
In Equations 4.5 to 4.10: Ie is the effective moment of inertia; Icr is the cracked moment
of inertia of the section; Ig is the un-cracked moment of inertia; Im is the modified
moment of inertia; It is the transformed, un-cracked moment of inertia; Mcr is the
cracking moment of the beam; and Ma is the applied moment. Note that the method
proposed in S806 explicitly determines the deflection, and not the effective moment of
94
inertia. Equation 4.9 is specific to a four-point bending loading geometry, where L
represents the un-cracked length of the shear span a.
In the previous chapter, derivation of Bischoff’s (2007) rational prediction model based
on revised tension stiffening approaches (which is neither specific to steel or GFRP-
reinforced concrete) was discussed. This model provided the most accurate estimation of
deflections for the full-scale GFRP Beam, and made predictions of comparable error to
Branson’s equation (~10%) for the steel-reinforced beam as well. Figure 4.13 shows the
application of Equations 4.6 to 4.10 to predict the effective moment of inertia (Ie) for the
half-scale GFRP compared to the experimentally determined Ie.
Figure 4.13: Predicted and experimental effective moment of inertia for the half-
scale beam
Not surprisingly, Bishoff’s method again provides the closest estimation to the observed
behaviour. As was the case with the full-scale beam, the unmodified Branson’s equation
greatly overstates stiffness, and Equations 4.7 to 4.10 under-predict stiffness at the
95
scaled-down service load (106 kN). It is worth noticing that although the predicted
deflections at this service load would be highly dependent on choice of model, all models
(and observed behaviour) have converged closely to Icr at 50% higher load than service.
The high un-cracked to cracked stiffness ratio of the beam results in a very small tension
stiffening region after cracking, and stiffness quickly reduces close to fully cracked
levels. Due to the strict deflection limits imposed for the intended use, more
comprehensive analysis (such as VecTor2) should be used to confirm similar predictions
during detailed design.
Additionally, Figure 4.13(a) shows that at an applied moment of ~53% of the moment at
first flexural crushing, the experimental stiffness reduces to levels below the predicted
cracked section stiffness. The reduced stiffness is likely due to the non-linearity of
concrete in compression close to peak stress (as opposed to a reinforcement or bond
softening mechanism). Based on materials testing performed on cylinders cast from the
mixed used in the test beam (Appendix D), peak cylinder stress, f’c, occurs approximately
at a strain of 0.0021 (peak strain, εp), with non-linear behaviour beginning before that. As
such, use of these deflection predictions should be limited to well below εp to stay within
the linear (or near-linear) elastic range of the concrete, such as a maximum allowable
compressive strain of 0.0015 (or less).
Pre-cracking stiffness is well below the predicted stiffness for the un-cracked case. A
possible cause of this could be that the first flexural crack initiated well before
predictions due to a combination of shrinkage restraint and creep and the beam was
sitting unsupported for many weeks.
96
4.4.1 Strain Profiles
Cracking as a serviceability requirement for FRP reinforced concrete monorail
infrastructure may not carry the same importance as peak deflection, due to the
reinforcement’s non-susceptibility to corrosion (often accelerated by water ingress).
However the appearance of numerous large cracks could be discomforting to users, and
could result in other long term durability issues (Laoubi et al., 2006). Figure 4.14 shows
observed and predicted (VecTor2) tensile reinforcement stress profiles at the four load
stages. Additionally, the observed cracking patterns are included under each of the four
sub-plots, and the actuator load indicated.
Figure 4.14: Longitudinal stress profile of tension reinforcement with observed
beam cracking patterns
0 1350 2700 4050 5400
0
25
50
75
100
106.12kN
Distance Along Beam (mm)
Rein
forc
em
ent S
tress (
MP
a)
a)
0 1350 2700 4050 5400
0
100
200
300
400
247.96kN
Distance Along Beam (mm)
Rein
forc
em
ent S
tress (
MP
a)
b)
0 1350 2700 4050 5400
0
200
400
600
376.9 kN
Distance Along Beam (mm)
Rein
forc
em
ent S
tress (
MP
a)
c)
0 1350 2700 4050 5400
0
200
400
600
800
1000
567.08kN
Distance Along Beam (mm)
Rein
forc
em
ent S
tress (
MP
a)
d)
97
Figure 4.14(a) shows the peak FRP stress at the service load (average of 4 bottom bars) is
100.22 MPa, or ~7.6% of the guaranteed ultimate strength of the reinforcement. Stress at
the loading point in the right end (as viewed in the diagram) is much less (only 13.5 MPa)
due to the reduced amount of cracking in this region. At the scaled down service load,
cracks extend close to the predicted (cracked) neutral axis depth of 113mm and while
numerous, are barely visible to the eye. Figure 4.15 shows the observed cracks at mid-
span of the half-scale beam during testing at the scaled down service load (cracks are
highlighted for easier visibility). Note that the location of flexural cracks appear to
coincide with the location of stirrups.
Figure 4.15: Observed cracking in mid-span region of beam at scaled service load
In each of the four load ramps examined, VecTor2 satisfactorily predicts the longitudinal
stress profiles in the bottom tensile reinforcement. At the point of first flexural crushing,
98
the maximum observed stress in the GFRP is 1038 MPa, or 79% of the guaranteed
minimum tensile strength, which suggests that the design is over-reinforced by a
satisfactory margin for deformability purposes.
Figure 4.16 shows the longitudinal strain profiles in the top compression reinforcement at
the peak load of the four load ramps completed in the study. In all four cases, the
prediction from VecTor2 agrees well with the experimental observation, right up until the
onset of first flexural crushing of the top cover concrete. At this point, the model predicts
an abrupt increase in strain (cut off in Figure 4.16(d)), signifying that the top concrete in
this region is crushed and no longer contributing to the flexural capacity.
Figure 4.16: Longitudinal strain profile of compression reinforcement
0 1350 2700 4050 5400
-0.3
-0.2
-0.1
0106.12kN
Distance Along Beam (mm)
Longitudunal S
train
(m
m/m
)
a)
0 1350 2700 4050 5400
-0.8
-0.6
-0.4
-0.2
0247.96kN
Distance Along Beam (mm)
Longitudunal S
train
(m
m/m
)
b)
0 1350 2700 4050 5400
-1.6
-1.2
-0.8
-0.4
0376.9 kN
Distance Along Beam (mm)
Longitudunal S
train
(m
m/m
)
c)
0 1350 2700 4050 5400-4
-3
-2
-1
0567.08kN
Distance Along Beam (mm)
Longitudunal S
train
(m
m/m
)
d)
99
4.4.2 Deformability
As ductility, by definition, is not an inherent property of FRP reinforced concrete, a
deformability factor (D.F.) can be used to describe beam performance. While steel-
reinforced concrete beams can undergo large amounts of curvature after yielding of steel
(under-reinforced section), FRP reinforced concrete can also provide the desired
curvatures at failure due to the non-linearity of concrete in an over-reinforced case. Two
deformability factors will be discussed:
As required for design by S0-06 (CSA, 2006);
cc
UltimateUltimate
M
MFD
..
(4.12)
And by:
Newhook et al. (2002)
ServiceService
UltimateUltimate
M
MFD
..
(4.13)
In the S6-06 equation, Mc and ψc are the bending moment and curvature (respectively)
calculated for an extreme concrete compressive strain of 0.001. Table 4-2 shows the
bending moments, curvatures, and deformability factors for the half-scale GFRP-
reinforced concrete beam from the experimental data, and numerical predictions. In the
case of the experimental data, ‘ultimate’ was considered to be at first flexural crushing of
the top cover concrete, and not at the ultimate load capacity. This was chosen because the
observed ultimate capacity is not functional capacity. While the structure would remain
intact past first flexural crushing, in a monorail guideway application, loss of the top
concrete would not allow transit of the monorail train.
100
Table 4-2: Deformability factors based on predicted and experimental behaviour
Multimate ψultimate Mservice ψservice Mc ψc Deformability Factor
Definition (kNm) (rads/km) (kNm) (rads/km) (kNm) (rads/km) Newhook
(2002) CHBDC (2006)
Experimental 588.8 32.35 125 3.07 212.7 7.25 49.6 12.4
R2K 569 30.39 125 2.91 232 7.72 47.5 9.6
VecTor2 557.1 27.28 125 2.88 250.7 8.68 42.2 7.0
*S6-06 512.1 23.78 125 5.48 201.6 8.84 17.8 6.8
For the designed beam, where the peak service load is an unusually small fraction of the
ultimate load, Equation 4.13 yields a very high deformability factor of 49.6 for the
experimental case. Based on the relatively small loading applied to the beam, the
deformability factor used in the CHBDC (which yields a D.F. of 12.4 for the
experimental case) is much more conservative and may be a better representation of
deformations of the section design. The observed deformability using the CHBDC
equation is still much greater than the minimum allowable of 4, chosen based on steel-
reinforced beams typically exhibiting the same minimum deformability (CSA, 2006).
Figure 4.17shows the half-scale GFRP-reinforced concrete beam deforming visibly at the
point of first flexural crushing. At ultimate buckling of the compression bars, the
deformations had increased another 50% of those seen in Figure 4.17, and the
experimental deformability factor (based on S6-06) would increase further to 19.2.
101
Figure 4.17: Large deformations in beam at first flexural crushing
4.5 Conclusions
While additional testing is needed to verify the long term cyclic performance of GFRP-
reinforced concrete beams for elevated transit infrastructure, some important conclusions
can be made with respect to their static performance.
As designed, the beams will currently satisfy the serviceability requirements of
deflection and cracking (see Appendix B for cracking study) based on anticipated
vehicle loads.
The beams exhibit similar flexural capacity to code (S6-06) predictions of
ultimate capacity, as defined by the first flexural crushing of top cover concrete
As expected, the beam was flexure-critical, with many closely spaced cracks.
Locations of flexural cracks appear to be initiated by the placement of stirrups.
102
A combination of closely spaced longitudinal bars in the web face of the beam
and top of the beam, and closely spaced stirrups provided significant confinement
to the concrete core. This allowed for significant additional load carrying capacity
(~19%) after first flexural crushing of the beam, until the buckling of the top
reinforcing bars resulted in failure. However, this confinement effect and
contribution of FRP bars in compression does not necessarily transfer directly to
the full-scale beam. More modelling on the confining mechanisms occurring and
the load carrying capacity of FRP bars in compression would have to be
performed before the additional capacity could be factored into useful design
capacity at ultimate limit states. The implications of this increased capacity would
be minimal, as serviceability requirements will almost certainly govern for GFRP
reinforce concrete monorail infrastructure.
Considering the two methods of predicting deformability of FRP reinforced
concrete, the equation prescribed in S6-06 is more conservative in this case as the
anticipated service loads are exceptionally low for this size of member. In either
case, the beam far exceeds requirements for deformability as determined by
several numerical predictions, and assisted by the experimental observations.
Post cracking stiffness of the beam can be satisfactorily predicted using
Bischoff’s (2007) method. Other predictions found in literature, including the two
codes (ACI440 and S806), greatly under-predict post-cracking stiffness. While
conservative, they would not lead to the most cost-effective design.
In all cases, the numerical predictions of the sectional analysis program Response
2000 and the Non-Linear Finite Element Analysis of reinforced concrete program
103
VecTor2 provided excellent predictions of all aspects of behaviour, exceeding the
accuracy of code predictions in almost every case. The behaviour of members can
be studied in much greater detail than code-type equations allow for, with a
marginal increase in effort. As VecTor2 requires considerable more modelling
skill on the user’s part, R2k would be the more preferable preliminary design tool,
where VecTor2 could be used for more detailed analysis.
4.6 References
ACI Committee 440. (2006). Guide for the design and construction of structural concrete
reinforced with FRP bars (ACI 440.1R-06). Farmington Hills, Michigan (USA):
American Concrete Institute.
Alsayed, S. H. (1998). Flexural behaviour of concrete beams reinforced with GFRP bars.
Cement and Concrete Composites, 20(1), 1-11.
Bentz, E. C., & Collins, M. P. (2000). RESPONSE-2000: Reinforced concrete sectional
analysis using the Modified Compression Field Theory
Bischoff, P. (2007). Deflection calculation of FRP reinforced concrete beams based on
modifications to the existing Branson equation. Journal of Composites for
Construction, 11(1), 4-14.
Bischoff, P. H. (2001). Effects of shrinkage on tension stiffening and cracking in
reinforced concrete. Canadian Journal of Civil Engineering, 28(3), 363-374.
104
Branson, D. E., & Metz, G. A. (1963). Instantaneous and time-dependent deflections of
simple and continuous reinforced concrete beams Department of Civil
Engineering and Auburn Research Foundation, Auburn University.
CSA. (2002). CAN/CSA-S806-02. Design and Construction of Building Components
with Fibre-Reinforced Polymers. Mississauga, Ontario: Canadian Standards
Association.
CSA. (2006). CAN/CSA-S6-06. Canadian Highway Bridge Design Code. Mississauga,
Ontario: Canadian Standards Association.
CSA. (2012). CAN/CSA-S806-12. Design and Construction of Building Components
with Fibre-Reinforced Polymers. Mississauga, Ontario: Canadian Standards
Association.
Faza, S. S., & Ganga Rao, H. V. S. (1992). Pre- and post-cracking deflection behaviour
of concrete beams reinforced with fiber-reinforced plastic rebars. Proceedings of
the First International Conference on the use of Advanced Composite Materials in
Bridges and Structures (ACMBSI), Montreal. 151-60.
Frantz, G. C., & Breen, J. E. (1980). Cracking on the side faces of large reinforced
concrete beams. Paper presented at the ACI Journal Proceedings. 77(5)
Hoult, N., Sherwood, E., Bentz, E., & Collins, M. (2008). Does the use of FRP
reinforcement change the one-way shear behavior of reinforced concrete slabs?
Journal of Composites for Construction, 12(2), 125-133.
105
ISIS Canada. (2007). Reinforcing concrete structures with Fibre Reinforced Polymers-
design manual no. 3. Manitoba: ISIS Canada Corporation.
Kocaoz, S., Samaranayake, V. A., & Nanni, A. (2005). Tensile characterization of glass
FRP bars. Composites Part B: Engineering, 36(2), 127-134.
Laoubi, K., El-Salakawy, E., & Benmokrane, B. (2006). Creep and durability of sand-
coated glass FRP bars in concrete elements under freeze/thaw cycling and
sustained loads. Cement and Concrete Composites, 28(10), 869-878.
Newhook, J., Ghali, A., & Tadros, G. (2002). Concrete flexural members reinforced with
Fiber Reinforced Polymer: Design for cracking and deformability. Canadian
Journal of Civil Engineering, 29(1), 125-134.
Vecchio, F. (2002). VecTor2, nonlinear finite element analysis program of reinforced
concrete. University of Toronto, Toronto, ON, Canada,
Vecchio, F. J., & Collins, M. P. (1986). The Modified Compression-Field Theory for
reinforced concrete elements subjected to shear. ACI J., 83(2), 219-231.
106
Chapter 5
Conclusions and Future Work
5.1 General
The following is a summary of recommendations from the two experimental programs.
Limitations of the structural system in its present form are discussed and suggestions for
possible implementation are made. Finally, areas of mutually beneficial study which
could be initiated in the near future are discussed that may be performed using much of
the existing instrumentation and testing equipment on the Kingston Monorail Test Track.
The GFRP-reinforced guideway beam, in its current form, met all serviceability criteria
in the field study, when subjected to 450 passes of a monorail train. The GFRP-reinforced
beam was also shown to have less flexural stiffness than its steel-reinforced counterpart,
showing larger deflections and strains at equivalent load levels. Accurately predicting
serviceability behaviour of the two full-scale beams proved to be difficult with the use of
the models typically used in design codes. An investigation found methods which yielded
satisfactorily accurate (and conservative) results for both beams. In all cases, computer
numerical modelling consistently determined the best estimates of the beams’ responses
as well as providing additional insight. Results from testing the half-scale GFRP-
reinforced beam to failure were consistent with expectations. This suggests that in a full-
scale application, the beams’ failure mode would be the desirable flexural compression
mode, exhibiting substantial deformability beforehand. While this GFRP-reinforced beam
design could be a viable alternative at equivalent (or shorter) spans, serviceability criteria
would not likely be met at longer span lengths (requiring members to be prestressed).
107
5.2 Field Study
Despite using a substantially greater area of reinforcement, the GFRP-reinforced beam
exhibited larger strains and deflections than were observed for the comparable beam
reinforced with steel. The short term stains measured during field testing on the guideway
were considerably larger in the GFRP-reinforced beam than in the steel-reinforced beam,
although the stresses in the reinforcing bars were comparable. The tensile strength
advantage of GFRP reinforcing bars over steel is shown to be somewhat irrelevant
because the peak stress carried by the reinforcement is only approximately7% of its
ultimate strength, whereas steel uses approximately 22% of its nominal capacity at the
service load levels investigated.
Recorded deflections of the two instrumented guideway beams were within the specified
limit of one eight-hundredth the span length. However, the stiffness of the GFRP-
reinforced beam deteriorated noticeably faster as vehicle loading was increased
throughout the test program. The predictions of deflections using the design code
equations yielded highly unsatisfactory results, under-predicting the stiffness of the
GFRP-reinforced beam by a substantial amount. Furthermore, the standard Branson’s
equation was also ineffective at modelling the post-cracking stiffness of the steel-
reinforced beam, yielding un-conservative estimates at some loading stages. Several other
predictive models for the post-cracking effective moment of inertia were investigated,
with Bischoff’s (2007) method providing the most consistent results for both the GFRP
and steel-reinforced beams. It is suggested that the success of this method is due to its
more rational approach of predicting the change from gross section to fully cracked
section properties, as opposed to modifying existing approaches with empirical fits.
108
While use of the “hand calculation” approaches provided suitable estimates of behaviour
(considering the time required to complete them), more detailed numerical analysis is
truly required to increase the confidence that the design will meet all serviceability
requirements. In the majority of cases, the predictions made using the sectional analysis
software Response 2000, and the non-linear finite element analysis program VecTor2
were more accurate when compared to experimental results, and they provided a far
greater amount of detail and insight. Use of these two tools form a well-rounded design
approach where one program can be used for proportioning, with reduced effort or input
(Response 2000) and a more refined analysis completed thereafter, requiring greater
modelling skill and completion time (VecTor2).
5.3 Laboratory Study
To better understand the performance of GFRP-reinforced concrete beams for monorail
applications at conditions exceeding service load levels, a laboratory scale beam was
fabricated and tested. This beam was designed to have comparable normalized behaviour
in flexure and shear to the GFRP-reinforced beam used in the field study, with analysis
using the modelling tools Response 2000 and VecTor2. Design code predictions of
strength, ductility, and deflections were made to evaluate their effectiveness for this
application.
The beam was tested statically, completing multiple loading and unloading cycles before
being tested monotonically to failure. As designed, the beam failed in flexural-
compression and at comparable ultimate conditions as predicted by the code equations.
The beam exhibited considerable deformability at the point of first flexural crushing of
the top cover concrete (defined as the functional ultimate capacity), exceeding the code
109
predictions by a significant margin. After the top cover concrete crushed (no longer
contributing to flexural capacity), the beam carried an additional 19% of the crushing
load (and deforming considerably more) before reaching ultimate failure. This un-
anticipated capacity was likely the result of the close longitudinal reinforcement and
stirrup spacing providing confinement to the concrete core, which allowed the beam to
deform to strain levels well beyond the unconfined capacity of concrete. The subsequent
ultimate failure mode was a compressive rupture of the top row of reinforcement (at
approximately half the tensile strain capacity of the bars) combined with a tensile rupture
of the stirrups at the bend location in the top of the beam. Despite this significant and
unpredicted increase in load carrying capacity, it does not represent functional capacity,
because at these high load levels, all serviceability criteria are violated, and the top
concrete surface on which the vehicle is intended to travel is no longer present.
The observed post cracking stiffness of the beam (like the beams in the Field Study) is
not modelled to suitable accuracy with the design code equations. However, the method
proposed by Bischoff (2007) restores a degree of precision to the “hand calculations”.
Again, the predictions made using the more advanced numerical modelling techniques,
Response 2000 and VecTor2, provide greater insight and agreement with observed
behaviour.
Cracking patterns were also observed in all test specimens (see Appendix B) and
compared to both design code equations and the numerical models. While the numerical
models would suggest cracks approaching or exceeding the specified limits, the observed
cracks are smaller because the close stirrup spacing induces more closely spaced cracks.
110
Closely spaced stirrups in combination with properly proportioned side face
reinforcement restrained crack widths at all heights within the beams to acceptable levels.
5.4 Potential Applications of GFRP-Reinforced Concrete Beams
Based on the testing and modelling performed on the full and half-scale beams, all of the
serviceability requirements have been met for the maximum service loading stipulated.
However, the results also show that the steel-reinforced beams out-perform the GFRP-
reinforced beams at service load levels with respect to deflections (potentially the most
critical aspect of study). For a revenue-generating application, the short spans required to
maintain the serviceable performance of the GFRP-reinforced beam design would likely
be undesirable (and uneconomical) for the majority of guideway beams. Similar
limitations would apply to the steel–reinforced beam, which certainly cannot be
lengthened to spans of two or three times the current length without consequence to
serviceability. For spans longer than 12 m, prestressing/post-tensioning will likely
continue to be a more effective structural system. In areas where short spans can be used
economically, GFRP certainly has the potential to provide an economical alternative
solution. For longer spans, a fully or partially prestressed beam design can be made
which incorporates GFRP as transverse and passive longitudinal reinforcement to meet
requirements at ultimate limit states. If the removal of all ferrous internal is desired,
revenue-generating guideway beams may be prestressed with carbon-FRP (CFRP). This
possibility however, would require extensive investigation because prestressing with
CFRP is certainly not yet commonplace in industry.
111
5.5 Potential for Future Testing on Existing Guideway
While the current phase of testing has concluded on the Kingston Monorail Test Track,
new testing programs could be performed with relative ease using the existing
instrumentation and network infrastructure. As the instrumented GFRP-reinforced beam
at the KMTT is one of the few permanent full-scale application s of this structural system
available to monitor long term, great value could be obtained by monitoring the beam
periodically in the coming years for changes in behaviour. This could provide valuable
insight to the true levels of degradation occurring in GFRP-reinforced concrete, as
opposed to the accelerated aging tests commonly used to quantify these effects. An area
of mutual benefit would be the study of structural-vehicular dynamic interaction as the
monorail vehicle passes over the instrumented test beams. This would be a unique
opportunity to experimentally quantify vibrations in an instrumented vehicle and
guideway beam simultaneously under repeatable and controlled conditions. Such work
could be used to calibrate numerical models used in the design of both the guideway
structure as well as vehicle components to reduce wear and increase component service
life and user comfort.
112
Appendix A
Beam Fabrication and Instrumentation Information
A.1 General
The following Appendix shows images of several important steps in the fabrication of the
test beams used in the research. Information regarding the selection of instruments and
supporting equipment is included.
A.2 Measurement Information
Linear Potentiometers were model MLS 130/50/R/P manufactured by Penny &
Giles and were configured with a protective sleeve providing an IP 66 rating.
o Guaranteed Linearity (accuracy): 0.125 mm (0.25% of stroke)
o Typical Linearity (accuracy): 0.075 mm (0.15% of stroke)
o Observed Linearity (accuracy): 0.055mm (maximum error obtained in
calibration)
o Resolution (precision): Infinite, but limited by digital data acquisition
system
Connectors were TE Connectivity Sensor Connectors, P/N 1838275-3 (female)
and 1838274-3 (male) and were IP 67 rated.
Wire used for the linear potentiometers was Delco Wire P/N 36904 which
includes: four 24 AWG conductors (two twisted pairs), PVC conductor insulation,
aluminum shield (shielding all four conductors) with drain wire, and a PVC
jacket. Twisted pairs combined with foil shielding were provided for noise
113
rejection in signal processing. Individual foil shields for each twisted pair would
have been preferable, but desired wire (Delco Wire P/N 33673), was no longer in
production.
Strain gauges for full-scale beams were Vishay Micro-Measurements foil gauges
P/N CEA-06-250UW-350.
o Gauges use 350 ohm resistance which allow for higher voltage excitations
without causing excessive self-heating (potential source of error as it
changes the apparent gauge factor). Higher voltage excitations reduce
presence of signal noise due to electro-magnetic interference (EMI).
o Gauges use a self-temperature-compensation (STC) value typical for
applications on steel or concrete (which have similar coefficient of linear
thermal expansion, or CLTE). Although GFRP has a different CLTE, the
difference was minimal, and consistency in gauge model was selected as
preferable for the two full-scale beams.
Strain gauge wire for the full-scale beams was Vishay Micro-Measurements P/N
326-DSV which included: three 26 AWG conductors, twisted conductors with
braided shielding (for noise rejection), and PVC conductor insulation and jacket.
o Connections for strain gauge wires between the beam and the
instrumentation hut were made inside a sealed junction box mounted to
the beams. Connections were made using 25 –pin D-Subminiature
connectors, shielded from EMI with TE Connectivity Cable Clamps (P/N
5745833-1).
114
Strain gauges for half-scale GFRP test beams’ reinforcement were Vishay Micro-
Measurements foil gauges P/N CEA-05-250UW-350.
o Use an STC number more preferable to the CLTE of GFRP
Strain gauges for half-scale GFRP test beams’ top compression face were Vishay
Micro-Measurements foil gauges P/N N2A-06-20CBW-350.
o ~50 mm gauge length, better for concrete surfaces.
Strain gauge wire for the half-scale GFRP-reinforced beams was Vishay Micro-
Measurements P/N 326-DTV which included: three 26 AWG twisted conductors,
and PVC conductor insulation .
o Shielding was not deemed necessary for the half-scale beams as they were
to be tested in the lab and no significant sources of EMI were located
within close proximity to the test set-up.
All strain gauges were environmentally protected (where the primary concern was
water ingress) using a two stage process.
o First step was the application of a clear poly-urethane coating (product
name “M-Coat A”, manufactured by Vishay Micro-Measurements) to the
gauge, soldered connections, and the area immediate surrounding the
gauge.
o After curing, the second step was the liberal application of an automotive
room temperature vulcanizing (RTV) silicon rubber gasket maker as an
additional coating (product name “Ultra Black” manufactured by
Permatex) to the gauge and its wires (up to a distance of 50 mm from the
gauge). This second coating is primarily used as protection against
115
physical damage for the gauge and its soldered connections. In tests
performed by the author on several adhesives and sealants, this product far
outperformed others in terms of durability, but more importantly, in its
adhesion to the reinforcing bar.
A.3 Test Beam Designs (See title blocks for identification)
116
117
118
119
120
121
122
A.4 End Bearing Shear Friction Detail Design
123
A.5 Strain Gauge Installation
Figure A-1: Strain gauge installation on reinforcing bars
124
Figure A-2: Reinforcing bars for full-scale beams instrumented with strain gauges
Figure A-3: Wiring for internal instrumentation in full-scale GFRP-reinforced
beam
125
A.6 Beam Fabrication and Casting
Figure A-4: Placing concrete during the casting of the full-scale beams
Figure A-5: Hoisting of finished beam from formwork
126
Figure A-6: Installing full-scale beams at the test guideway
Figure A-7: Showing deformed formwork for half-scale beams, and remedial action
taken
127
Figure A-8: Half-scale GFRP reinforcement cages prior to casting
Figure A-9: Casting and final finish of half-scale beams
128
Figure A-10: Full-scale beams at test track with linear potentiometers installed
Figure A-11: Linear potentiometer (configured for IP 66 rating) and its IP 67 rated
connection
129
Appendix B
Cracking Behaviour in Test Beams
B.1 General
The cracking behaviour of beams to be used in transit guideways is an important
serviceability concern. While it is uncommon (and un-economical) for reinforced (non-
prestressed) concrete beams to remain un-cracked when subjected to design service loads,
excessive cracking may pose other problems. Apart from the aesthetic concerns, where
users may be uncomfortable with the sight of large cracks (even if there is no reduction in
ultimate capacity), cracks in reinforced concrete members can allow ingress of unwanted
substances. Ingress of water can lead to freeze thaw damage, accelerated corrosion of
steel reinforcement (which can be aggravated further if chlorides are present), and
degradation of GFRP reinforcement. For these reasons, the cracking behaviour of the
full-scale and half-scale test beams was observed and compared to various predictions to
determine the accuracy of the predictions, as well as to assess the cracked condition of
the beams qualitatively.
For both the full-scale and half-scale beams, crack widths were measured using a
Monogram Industries Optical Micrometer (Model 966A). This tool is typically used for
measuring crack (or scratch) depth (where it is accurate to 0.0002”). For this application,
it was fitted with a reticle (comparator) eyepiece, allowing for width measurements to be
taken. The comparator had a field of view of 0.040” (~1 mm) and accuracy of 0.001”
(~0.025 mm). This method requires a user to have arms-length access to the beam, which
would greatly complicate measurements performed on an in service monorail guideway
130
due to the elevation of the beams. Figure B-1 shows an assistant performing a crack
width measurement on the field beams.
Figure B-1: Measuring crack widths on the side faces of the full scale test beams
The observed cracks were then compared to predictions, namely:
Design codes [S6-06 (CSA, 2006), ACI 440.1R-06 (ACI Committee 440, 2006),
and S806-12 (CSA, 2012)], and
Numerical models [VecTor2 (Vecchio, 2002), and Response 2000 (R2k) (Bentz
& Collins, 1998)].
The numerical models allowed for the comparison of the cracking patterns (spacing and
height of cracks) as well as the widths. Comparisons of predicted to observed crack
widths were done in greater detail for the half-scale beam, as measurements could be
131
made at the scaled service load. This was not possible for the full-scale test beams
however, as safety requirements would not allow for personnel to be present at the test
beams during operation of the monorail vehicles. Note that crack widths were not
calculated using Response 2000 for the case of self-weight only, as the program analyses
the section monotonically and does not include the ability to predict unloading scenarios.
B.2 Results
Figure B-2 shows the numerical model prediction of crack widths compared to the
observed cracks in the half-scale GFRP-reinforced beam at the maximum (scaled down)
service load. In this figure, both the maximum observed and the average (as determined
from the cracks in the constant moment region only) crack widths are shown across the
height of the beam.
Figure B-2: Comparison of crack widths for the half-scale GFRP-reinforced beam
132
Table B-1 shows the various predictions of crack widths for the three test beams
compared to the observed values.
Crack Width (mm)
Specimen GFRP Beam Steel Beam Half-Scale GFRP
Loading Dead Full Service Dead Full Service Dead Full Service
S806 0.16 0.43 0.11 0.28 0.03 0.18
S6-06 & ACI 440.1 0.12 0.31 - - 0.04 0.31
Largest Observed 0.31 - 0.38 - 0.15 0.30
Average Observed @ Reinforcement 0.18 - 0.17 - 0.10 0.22
Table B-1: Predicted and observed crack widths for all test specimens
While VecTor2 and R2k over predict both the average and maximum crack width
profiles, their error can likely be attributed to the difference in crack spacing when
compared to the experimental observations. As the crack width can be conceptualized as
the difference between the strain in the reinforcement and in the concrete, integrated over
the distance between cracks (MacGregor et al., 1997), accurately predicting crack spacing
is crucial to determining crack width.
B
A
crcr dxw (1)
Where:
(B-A) is the crack spacing, and
r & c are the strain in the reinforcement and concrete respectively.
In the case of the half-scale GFRP-reinforced beam, flexural cracks in the constant
moment region appear to be initiated at the location of stirrups (~129 mm on centre). As
VecTor2 and R2k predict crack spacing as 197 mm and 210 mm respectively at the
bottom reinforcement level (in the predominately flexural region), their estimates for
crack width would be much closer to the observed widths if crack spacing was a
133
parameter within the control of the user. Furthermore, R2k predicts significantly larger
crack spacing at the boundary of the effective area in tension of the bottom
reinforcement. This abrupt change is likely due to the reduction in axial stiffness in the
mid-section region. In testing however, the skin reinforcement appears resist the “tree
branching” effect as cracks remained predominantly vertical and of uniform height up to
the scaled service load.
Figure B-3 to Figure B-6 show the cracking patterns (with widths indicated in mm) of the
two full-scale test beams subjected to self-weight only. The crack measurements shown
were taken after the beams had been subjected to the maximum design service load
(AW3) from the monorail vehicles. It should be noted that the full-scale test beams
exhibited significant shrinkage cracking, which often made it difficult to define the
endpoint of flexural cracks when being marked on the beams. Figure B-7 and Figure
B-8show the VecTor2 NLFEA predictions of crack widths for the full-scale test beams
subjected to self-weight only (after being unloaded from AW3). Figure B-9 and Figure
B-10show the observed cracking patterns on the half-scale GFRP-reinforced beams
subjected to self-weight (after unloading from the scaled down maximum service load),
and peak service load (scaled down) respectively. Figure B-11 and Figure B-12show the
VecTor2 NLFEA predictions of crack widths for the half-scale GFRP beams subjected to
self-weight, and peak service load (scaled down) respectively.
As the measurements of cracks for the full-scale beams could not be made at service
loads, measurements taken from the effects of self-weight only can be compared to the
VecTor2 model as a calibration tool, determining any reasonable cause for doubt in the
FEM predictions at maximum service load (such as erroneous crack spacing).
134
In all test beam specimens, the widest cracks are (as expected) typically located near the
bottom tension reinforcement. The skin reinforcement present in each case appears to
restrain crack growth at locations between the bottom row of reinforcement and the
neutral axis, as linearly decreasing crack widths were observed. In two instances on the
full-scale GFRP beam however, larger crack widths were recorded at approximately 400
mm from the bottom of the beam. Due to the presence of significant shrinkage cracking,
it cannot be concluded that these larger cracks are the result of insufficient skin
reinforcement (although it remains a possibility) in the side faces of the beam.
As the observations show, the magnitude of crack widths can be highly variable in a
given specimen, with widths ranging from crack to crack on the order of 100% or more.
In the Full Scale test beams, the largest observed crack widths are approximately double
the average, while in the Half Scale beam, there is an approximate 50% increase. This
inherent variability of crack width is the primary reason many of the design guidelines
have switched their cracking requirement from explicitly calculating crack widths to
instead calculating a “cracking parameter”, z (MacGregor et al., 1997).
Based on the observations of the three test beams, the numerical models produced
satisfactory and conservative estimates of crack width and spacing. Like other
serviceability concerns discussed in Chapters 3 and 4, the accuracy of numerical models
is heavily dependent on small changes in the tension stiffening behaviour of the beams.
In the specific case of cracking patterns, more accurate results in modelling would be
obtained if the crack spacing could be better controlled, as in each case, the observed
cracks in test specimens appear to be initiated by the stirrups, and are not only affected by
the relative size of the member and distribution of longitudinal reinforcement. With
135
respect to the magnitude of cracks observed at service loads in the half-scale beam, the
maximum widths are below the limits in any of the codes investigated, mostly due to the
close crack spacing initiated by the stirrups. While the distribution of longitudinal
reinforcement is the main factor identified by the Codes for limiting crack widths, it is
worth including that stirrup spacing (when stirrups are used) should be spaced closely to
help decrease crack spacing (and crack widths as a result).
136
Fig
ure
B-3
: C
rack
Dia
gra
m o
f fu
ll-s
cale
GF
RP
-rei
nfo
rced
bea
m (
wes
t h
alf
)
137
Fig
ure
B-4
: C
rack
Dia
gra
m o
f fu
ll-s
cale
GF
RP
-rei
nfo
rced
bea
m (
east
half
)
138
Fig
ure
B-5
: C
rack
Dia
gra
m o
f fu
ll-s
cale
ste
el-r
ein
forc
ed b
eam
(w
est
half
)
139
Fig
ure
B-6
: C
rack
Dia
gra
m o
f fu
ll-s
cale
ste
el-r
ein
forc
ed b
eam
(ea
st h
alf
)
140
Fig
ure
B-7
: V
ecT
or2
pred
icti
on
of
Cra
ck D
iagram
of
full
-sca
le G
FR
P-r
ein
forc
ed b
eam
141
Fig
ure
B-8
: V
ecT
or2
pred
icti
on
of
Cra
ck D
iagram
of
full
-sca
le s
teel
-rei
nfo
rced
bea
m
142
Fig
ure
B-9
: C
rack
wid
ths
of
half
-sca
le b
eam
su
bje
cted
to s
elf-
wei
gh
t on
ly
143
Fig
ure
B-1
0:
Cra
ck w
idth
s of
half
-sca
le b
eam
su
bje
cted
to t
he
ma
xim
um
ser
vic
e lo
ad
144
Fig
ure
B-1
1:
VecT
or2
pre
dic
tion
of
Cra
ck D
iagra
m o
f h
alf
-sca
le b
eam
su
bje
cted
to s
elf-
wei
gh
t
145
Fig
ure
B-1
2:
VecT
or2
pre
dic
tion
of
Cra
ck D
iagra
m o
f h
alf
-sca
le b
eam
su
bje
cted
to t
he
maxim
um
ser
vic
e lo
ad
146
Appendix C
Shear Behaviour of Test Beams
C.1 General
As mentioned in the body of the thesis (Chapters 3 and 4), the test beams studied in this
thesis were not designed to be shear critical, that is, where a shear failure would govern
their ultimate load carrying capacity. However, both the full-scale and half-scale test
beams were instrumented to monitor strains in the reinforcement in potentially shear
critical areas. In the full-scale study, data acquisition limitations did not allow for
information to be collected in the field on shear behaviour. In the static half-scale beam
test however, strains were collected from a number of points at two stirrup locations (in
the shear critical locations as defined by (Bentz & Collins, 1998).
While studying the shear behaviour of the half-scale beam is not as valuable as observing
a shear-critical beam, some insight can still be provided:
It creates experimental data which can be compared to the previously developed
numerical models, and verify their accuracy; and
Investigate the observation of Bentz et al. (2010) that by distributing the flexural
reinforcement into multiple layers, reduces the transverse strain in the in the lower
portion of the section for this type of beam.
While both of the above focus areas could prove useful, it is the second point which may
have larger implications to design. It was observed (Bentz et al., 2010) that by placing the
longitudinal reinforcement in several rows (rather than concentrating it in the very bottom
of the beam) would result in reduced transverse strain at the bottom of the beam. This
147
strain would then increase when moving up through the section, resembling the quadratic
shear stress distribution observed in homogenous, elastic beams. The importance of this
is that the peak strains no longer occur near the weakest point in the transverse
reinforcement, the bend. Unlike steel, the manufacturing of bent FRP bars markedly
reduces their strength at the bend locations, often cutting it in half (or more). Current
design codes in North America (S6-06, ACI 440.1R-06, and S806-12) require the
designer to design for this reduced strength (either explicitly as in S6-06 and ACI 440.1,
or implicitly in S806), resulting in reduced design efficiency.
Currently, a more effective method of providing transverse reinforce than bent FRP
stirrups has not become widely accepted, though some attempts have been made such as
the use of short headed-anchor GFRP bars cast vertically in the beam (Johnson & Sheikh,
2013). While an innovative solution, the pullout capacity of the headed anchor provided
similar capacity in shear as the current method of bent stirrups. In the same study, beams
using the headed bars as transverse reinforcement also failed in flexure much sooner than
beam using stirrups. Similar to the laboratory tests performed in Chapter 4, the stirrups
provided significant confinement via hoop stresses after flexural crushing of the cover
concrete, greatly increasing the deformability of the beam.
C.2 Testing Results
Having established that there is potential to increasing the cost effectiveness of shear
design in beams (as the cost/m of bent FRP bars is considerably higher than straight bars)
by using smarter design, there is a major obstacle which is the current design codes.
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Figure C-1 shows the stresses at various locations on the stirrup (locations indicated on
figure). In this figure, two curves are plotted for each of the sub-figures a through c, one
for each of the two instrumented stirrups (one at either critical location for shear). In all
three sub-figures, a changing in stiffness at an applied shear-force of approximately 35
kN likely indicates the initiation of the first crack near flexural crack near the stirrup.
Figure C-1(a) is particularly interesting, as one of the stirrup bends (end of beam in
Figure C-2(b) is shown to go into tension (as initially expected), while the other (end of
beam in Figure C-2(a) goes briefly into tension before quickly going into compression
during the unloading of the beam from the scaled-down service load. Upon examining the
VecTor2 NLFEA prediction of vertical strains in the region of the instrumented stirrup
bend, the area is predicted to be on the boundary of a narrow compressive strut region of
the beam (see Figure C-3) at the scaled down service load. This is a trivial finding
however, as the magnitude of the compressive strain is approximately equal to the
precision of the VecTor2 model. The difference in observed behaviour between the
instrumented stirrup bends in either end of the beam can likely be attributed to the slight
difference in angle at which the cracks in Figure 2 intercept the stirrups.
Figure C-4 shows the response of the instrumented stirrup in the “E” end for all load
stages (some “A” end strain gauges were damaged during testing). Again, the bend of the
stirrup (Figure 3a) is in compression (~20MPa) until just before the first flexural crushing
of the top cover concrete in the midspan region. After this, the bend takes on some tensile
strain, up to a maximum of 122 MPa (“E” end stirrup). The stirrup stress at the quarter-
height and mid-heights are subjected to more than double the stress at the bend (267 MPa
and 296 MPa respectively, again in the “E” end stirrup), however at these locations, it is
149
expected that the stirrup’s full bar strength (for straight portion) can contribute to
capacity. Therefore, these results support the notion that distributing the flexural
reinforcement in multiple layers can reduce the vertical strains in the bottom of the
beam’s cross section, where the reduced bend strength of the GFRP stirrup would
otherwise limit shear capacity.
Figure C-1: Stirrup stresses at the scaled down service load
-20 0 20 40 600
10
20
30
40
50
60
Sh
ea
r F
orc
e (
kN
)
Stirrup Stress (MPa)
a)
-20 0 20 400
15
30
45
60
Sh
ea
r F
orc
e (
kN
)
Stirrup Stress (MPa)
b)
0 20 40 600
15
30
45
60S
hea
r F
orc
e (
kN
)
Stirrup Stress (MPa)
c)
150
“A” End of Beam
“E” End of Beam
Figure C-2: Instrumented stirrup location w.r.t. the cracks at the scaled down
service load
Figure C-3: VecTor2 prediction of vertical strains in half-scale beam showing
compressive strut
151
Figure C-4: Stirrup stresses at various locations on instrumented at ultimate
flexural failure
C.3 References
Bentz, E. C., & Collins, M. P. (1998). RESPONSE-2000: Reinforced concrete sectional
analysis using the Modified Compression Field Theory
Bentz, E. C., Massam, L., & Collins, M. P. (2010). Shear strength of large concrete
members with FRP reinforcement. Journal of Composites for Construction, 14(6),
637-646.
Johnson, D. T., & Sheikh, S. A. (2013). Performance of bent stirrup and headed glass
fibre reinforced polymer bars in concrete structures1. Canadian Journal of Civil
Engineering, 40(11), 1082-1090.
-30 0 30 60 90 1200
70
140
210
280
350
Sh
ea
r F
orc
e (
kN
)
Stirrup Stress (MPa)
*Note: Gage placed on outside of stirrup bend
a)
0 75 150 225 3000
100
200
300
Sh
ea
r F
orc
e (
kN
)
Stirrup Stress (MPa)
b)
0 75 150 225 3000
100
200
300
Sh
ea
r F
orc
e (
kN
)
Stirrup Stress (MPa)
c)
152
Appendix D
Concrete Materials Testing
D.1 General
To predict behavior and calibrate models of the beams tested in this research, various
forms of concrete materials strength testing were performed. This included compression
testing on cylinders cast from the concrete batches at the time of beam casting, as well as
split-cylinder and modulus of rupture tests (to characterize tensile behaviour).
Compressive strength tests conforming to ASTM C39/C39M-12, Standard Test Method
for the Compressive Strength of Cylindrical Concrete Specimens (ASTM, 2012), were
performed on “small” concrete cylinders (100 mm x 200 mm) for both the half and full-
scale beams’ concrete batches. In addition to numerous small concrete cylinder
compression tests, “large” cylinders (150 mm x 300 mm) were tested in compression to
experimentally determine the Young’s Modulus of the half-scale mix design. The testing
procedure of the large cylinders conformed to ASTM C469/C469-10 (ASTM, 2010b),
Standard Test Method for Static Modulus of Elasticity and Poisson’s Ratio of Concrete in
Compression.
These tests also allowed for the comparison of various materials models available in the
non-linear finite element analysis program used in the study, VecTor2, to the
experimental pre and post-peak compression behaviour. All of the material models
compared in VecTor2 corresponded well with the experimental data, and based on the
‘best fit”, the Popovics pre and post-peak compression models were chosen for finite
element modelling purposes. Figure D-1 and Figure D-2 shows the observed compressive
153
behaviour for the four cylinders cast from the half-sale beam’s concrete compared to
some of the material models available in VecTor2. Figure D-3 shows the apparatus for
determining the modulus of elasticity of concrete cylinders conforming to ASTM C469.
The results of these cylinder tests are shown in Table D-1, where the modulus of
elasticity was determined to be 30,000 MPa, and compressive strength was 32 MPa
(occurring at a peak strain of 0.0021). Note that in ASTM C469, Young’s Modulus is
rounded to the nearest 200 MPa and is determined as the chord modulus of two points:
The stress at 40% of peak compressive strength, &
The stress at a compressive strain of 50 (= 5x10-5
mm/mm).
For tensile characterization of the concrete used in the full scale mix, both split-cylinder
tests and modulus of rupture tests were performed (in accordance with ASTM
C496/C496M-11 (ASTM, 2011) and ASTM C78/C78M-10) (ASTM, 2010a). Direct
tensile tests were not performed as no apparatus was immediately available. Split-
cylinder tests were performed on “small” cylinders (100 mm diameter, 200 mm height)
and purpose-built formwork was used to cast the modulus of rupture beams (150 mm
width, 150 mm height, 500 mm long, & 450 mm span). The experimental tensile
capacities were 1.76 MPa and 4.11 MPa (average of all specimens) for the splitting
tensile strength and modulus of rupture respectively. The split cylinder tests were
performed 28 days after casting, while the modulus of rupture tests were done 112 days
after casting. It was decided to wait an extended period of time to test the modulus of
rupture specimens so that effects of long term strength gain of concrete could be
accounted for. Figure D-4 shows the strength gain in the concrete used for the full-scale
beams over time based on “small” cylinder compression tests. Tests were performed at
154
14, 21, 28, 56, and 112 days after casting, with no significant strength gains after the 58
days (peak strength of ~ 25MPa). Determining the long term strength gain was critical, as
the full-scale beams were not tested in the field until 16 months after installation at the
test track.
Figure D-1: Compression response of for cylinders cast from half-scale batch of
concrete
155
Figure D-2: Comparison of pre-peak compression models used in VecTor2 to
experimental behaviour
156
Figure D-3: Compression testing of large cylinders in RIEHLE test frame
Property Cyl. 1 Cyl. 2 Cyl. 3 Cyl. 4 Mean
Ec by ASTM (MPa) 30057 29027 30897 30057 30009
Rounded Ec (MPa) 30000 29000 30800 30000 30000
Peak Strain, εp (+/- 0.0003) 0.0020 0.0021 0.0023 0.0020 0.0021
Peak Stress f'c (MPa) 31.5 32.6 32.5 31.7 32.1
Stress at εcu=0.0035 (MPa) 26.2 29.4 29 26.9 27.9
Table D-1: Experimental properties of large cylinders from half-scale beams
157
Figure D-4: Long term strength gain in full-scale beams' concrete
D.2 References
ASTM. (2010a). Test method for flexural strength of concrete (using simple beam with
third-point loading) ASTM International.
ASTM. (2010b). Test method for static modulus of elasticity and poissons ratio of
concrete in compression ASTM International.
ASTM. (2011). Test method for splitting tensile strength of cylindrical concrete
specimens ASTM International.
ASTM. (2012). Test method for compressive strength of cylindrical concrete specimens
ASTM International.