by Billy Siu Fung Cheung - University of Toronto T-Space...Billy Siu Fung Cheung Department of Civil...
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ADHESIVE BONDING OF CONCRETE-STEEL COMPOSITE BRIDGES BY POLYURETHANE ELASTOMER by Billy Siu Fung Cheung A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Civil Engineering University of Toronto © Copyright by Billy Siu Fung Cheung, 2008
Transcript of by Billy Siu Fung Cheung - University of Toronto T-Space...Billy Siu Fung Cheung Department of Civil...
ADHESIVE BONDING OF CONCRETE-STEEL COMPOSITE BRIDGES BY
POLYURETHANE ELASTOMER
by
Billy Siu Fung Cheung
A thesis submitted in conformity with the requirements
for the degree of Master of Applied Science
Graduate Department of Civil Engineering
University of Toronto
© Copyright by Billy Siu Fung Cheung, 2008
ii
ADHESIVE BONDING OF CONCRETE-STEEL
COMPOSITE BRIDGES WITH A POLYURETHANE ELASTOMER
Master of Applied Science (2008)
Billy Siu Fung Cheung
Department of Civil Engineering
University of Toronto
ABSTRACT
This thesis is motivated by the use of full-depth, precast, prestressed concrete
panels to facilitate deck replacement of composite bridges. The shear pockets required in
using convention shear stud connections, however, can cause durability problems. The
objective of this study is to investigate the possibility of eliminating the use of shear studs,
and adhesively bond the concrete and steel sections.
The feasibility of the developed polyurethane adhesive joint is defined based on
the serviceability and ultimate limit states. The joint must have sufficient stiffness that
additional deflection due to slip must not be excessive. The adhesive and bond must also
have sufficient strength to allow the development of the full plastic capacity of the
composite section. The use of the developed adhesive joint in typical composite bridges
was found to be feasible. The behaviour under live load was found to be close to a fully
composite section.
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For my family.
Mom and Dad,
your unconditional love, sacrifice, and support
have made this possible.
I love you.
Brother,
Thank you.
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ACKNOWLEDGEMENT
I would like to thank my supervisor, Professor P. Gauvreau, for his advice and
valuable comments toward this thesis. This project would not have been possible without
him. I would also like to thank Professor Birkemoe for his valuable opinions and
comments toward this thesis.
Sponsorship of BASF Canada Inc. has made this research study possible. Great
thanks go to Greg Gardin, from BASF Canada Inc., for his dedication into this project
and his help at every step of the adhesive development. Thanks also go to his lab assistant
Melody Zhang.
The assistance of the structural laboratory staff is greatly appreciated. Special
thanks go to Jimmy Susetyo and Sylvio Tam for their help at every stage of the lab work.
I would also like to thank my summer lab assistant Erica Wong for her help. Thanks also
go to Carlene Ramsay for giving me a great head start on this project. The technical help
at every step of this project from my colleagues in GB231 is also greatly appreciated.
Thanks go to my friends Mike Cavers and Jessica Wong for reading over my work.
Encouragement and understanding from all my friends are much appreciated.
Lastly, I would like to thank my family for their full support. Your love and
sacrifice have made this possible. You have been there with me through the ups and
downs. Thank you.
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TABLE OF CONTENTS
CHAPTER 1: INTRODUCTION 1 1.1. RAPID CONCRETE DECK REPLACEMENT FOR COMPOSITE BRIDGES ............................................. 1 1.2. FULL-DEPTH PRECAST CONCRETE PANELS.................................................................................. 2 1.3. SHEAR CONNECTION SYSTEM IN FULL-DEPTH PRECAST, PRESTRESSED CONCRETE PANELS....... 6 1.4. THE USE OF ADHESIVES IN BRIDGE CONSTRUCTION.................................................................... 9 1.5. OBJECTIVE AND SCOPE OF THE THESIS....................................................................................... 11 1.6. EXPERIMENTAL PROGRAM ......................................................................................................... 13 1.7. ANALYTICAL PROGRAM............................................................................................................. 13 1.8. THESIS OUTLINE ........................................................................................................................ 14
CHAPTER 2: DESIGN FACTORS FOR ADHESIVE BONDING 17 2.1. INTERACTION IN COMPOSITE BEAMS ......................................................................................... 17
2.1.1. Full and No Interaction ........................................................................................................ 17 2.1.2. Partial Interaction ................................................................................................................ 20
2.2. LIMIT STATE DESIGN ................................................................................................................. 23 2.2.1. Ultimate Limit States ............................................................................................................ 23 2.2.2. Failure Mode ........................................................................................................................ 24 2.2.3. Deflection under the Serviceability Limit State .................................................................... 25
2.3. CHARACTERIZATION OF THE LOAD - SLIP BEHAVIOUR OF A SHEAR CONNECTION..................... 26 2.4. THE CONNECTOR STIFFNESS, CONNECTION AREA STIFFNESS, AND SHEAR MODULUS .............. 28
2.4.1. Determination of the Shear Stiffness of the Connection ....................................................... 31 2.4.2. Bedding Layer....................................................................................................................... 31
2.5. ADHESIVE CONSIDERATIONS ..................................................................................................... 34 2.5.1. Material Properties .............................................................................................................. 35 2.5.2. Cure Time ............................................................................................................................. 35
2.6. POLYURETHANE ELASTOMER ADHESIVE ................................................................................... 38 2.7. CONSTRUCTION CONSIDERATION............................................................................................... 39
2.7.1. Surface Treatment................................................................................................................. 39 2.7.2. Moisture................................................................................................................................ 40 2.7.3. Temperature ......................................................................................................................... 40
2.8. SUMMARY.................................................................................................................................. 41
CHAPTER 3: LITERATURE REVIEW 43 3.1. THE DEVELOPMENT OF THE COMPOSITE STRUCTURAL LAMINATE (CSL) PLATE SYSTEM, BY
CARLETON UNIVERSITY, OTTAWA ........................................................................................................... 43
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3.2. STATIC BEHAVIOUR OF STEEL CONCRETE BEAM CONNECTED BY BONDING, BY SI LARBI ET AL.
(2006) ................................................................................................................................................... 50
3.3. EXPERIMENTAL STUDY OF BONDED STEEL CONCRETE COMPOSITE STRUCTURES, BOUAZAOUI ET
AL. (2006) ................................................................................................................................................ 58 3.4. SHEAR RESISTANCE OF A POLYURETHANE INTERFACE IN CONCRETE-STEEL COMPOSITE BEAMS,
BY RAMSAY (2007) .................................................................................................................................. 64 3.5. SUMMARY.................................................................................................................................. 66
CHAPTER 4: EXPERIMENTAL PROGRAM 67 4.1. MODIFIED PUSH-OFF TEST SPECIMENS...................................................................................... 67
4.1.1. Scope of the Experimental Program..................................................................................... 68 4.1.2. Design Consideration for the Specimens.............................................................................. 69 4.1.3. Fabrication of the Specimens ............................................................................................... 72 4.1.4. Materials............................................................................................................................... 74 4.1.5. Test Variables ....................................................................................................................... 76 4.1.6. List of Specimens and Variables........................................................................................... 81 4.1.7. Push-Out Test Setup and Instrumentation ............................................................................ 82
CHAPTER 5: TEST RESULT AND DISCUSSIONS 86 5.1. ULTIMATE LOAD AND DEFLECTION ........................................................................................... 86 5.2. RESULTS AND DISCUSSION......................................................................................................... 88
5.2.1. Series One............................................................................................................................. 88 5.2.2. Series Two ............................................................................................................................ 89 5.2.3. Series Three .......................................................................................................................... 92 5.2.4. Series Four ........................................................................................................................... 95 5.2.5. Series Five ............................................................................................................................ 97
5.3. SHEAR STIFFNESS OF THE ADHESIVE CONNECTION.................................................................. 100
CHAPTER 6: ANALYTICAL PROGRAM 102 6.1. DEGREE OF INTERACTION IN COMPOSITE BEAMS..................................................................... 103
6.1.1. Full Interaction Analysis in Composite Beams................................................................... 108 6.1.2. No Interaction Analysis in Composite Beams..................................................................... 109 6.1.3. Partial Interaction Analysis of Composite Beam by Girhammar and Gopu (1993)........... 110
6.2. COMPUTER ANALYSIS USING FRAME AND SPRING ELEMENTS ................................................. 116 6.2.1. Material Properties and Element Representation .............................................................. 117
6.3. PROBLEM DEFINITION .............................................................................................................. 119 6.4. RESULTS AND DISCUSSION – SERVICEABILITY LIMIT STATE.................................................... 121 6.5. FLEXURAL STRENGTH AT ULTIMATE LIMIT STATE .................................................................. 126
6.5.1. Rigid Plastic Analysis by Oehlers and Bradford (1995)..................................................... 126
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6.5.2. Results and Discussion – Ultimate Limit State ................................................................... 131 6.6. CRITERIA.................................................................................................................................. 132
CHAPTER 7: SUMMARY, CONCLUSION AND RECOMMENDATIONS 134 7.1. SUMMARY................................................................................................................................ 134 7.2. CONCLUSION............................................................................................................................ 135 7.3. RECOMMENDATIONS AND FUTURE WORK ............................................................................... 137
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LIST OF TABLES Table 1.1: Examples of Deck Replacement Projects with Precast Concrete Panels .......... 7
Table 1.2: Mechanical Properties of the Polyurethane Elastomer Core used in the SPS
(Minten et al., 2007)........................................................................................ 10
Table 2.1: Comparison of General Properties of Epoxy and Polyurethane...................... 36
Table 3.1: Mechanical Properties of EC-609-002/18 (after Braun, 1999) ....................... 45
Table 3.2: Tension Bond Test of the Polyurethane Elastomer Core (after Braun, 1999). 45
Table 3.3: Summary of Adhesive Push-Off Tests by Si Larbi et al. (2006)..................... 53
Table 3.4: Comparison of the Stiffness between Connectors and Bonding (after Si Larbi
et al., 2006) ..................................................................................................... 55
Table 3.5: Behaviour of the beams with different types of connection under a
concentrated load, 250KN, applied at midspan (after Si Larbi et al., 2006) .. 57
Table 3.6: Geomety of Beams Studied by Bouazaoui et al. (2006).................................. 59
Table 3.7: Comparison between Experimental Ultimate Load, F u,c and Theoretical
Ultimate Load, Fu,t .......................................................................................... 61
Table 4.2: General Properties of the Formulations of Polyurethane ................................ 76
Table 4.2: List of Specimens and Corresponding Variables............................................. 81
Table 5.1: Results from the Push-Off Tests...................................................................... 87
Table 5.2: Stiffness of Polyurethane Adhesive Joints .................................................... 101
Table 6.1: Dimensions of the Studied Composite Bridges ............................................. 121
Table 6.2: Results of the Partial Interaction Analysis..................................................... 122
Table 6.3: Comparison of Results from SAP2000™ and Equation 6.21. ...................... 123
Table 6.4: Results from the Rigid Plastic Analysis ........................................................ 131
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LIST OF FIGURES
Figure 1.1 A Full Depth, Precast Concrete Panels System (Figures taken from Shim et al.,
1999) ................................................................................................................. 3
Figure 1.2: Shear Pocket Design Used by Culmo (2000)................................................... 5
Figure 1.3: Conventional Mechanical Shear Connectors (Figures taken from Oehlers &
Bradford, 1995)................................................................................................. 7
Figure 1.4: a) Typical Shear Pockets; b) Cracking Between Shear Pockets (Figures taken
from Issac et. al, 1995)...................................................................................... 8
Figure 1.5: The SPS System Developed by Intelligent Engineering. 1) Steel face sheets
with thickness, t. 2 - Polyurethane Elastomer Core with Thickness h. (Figures
taken from Minten et al., 2007) ...................................................................... 10
Figure 1.6: Shenley Bridge, Quebec, Canada (Picture taken from Intelligent Engineer,
2007) ............................................................................................................... 11
Figure 2.2: Slip in a Composite Beam.............................................................................. 20
Figure 2.3: Degree of Interaction (Picture from Oehlers & Bradford, 1995) ................... 20
Figure 2.4: Cross-Section of a 50m Span Composite Bridge ........................................... 26
Figure 2.5: Standard Push-Off Test Configuration in Accordance to Eurocode ENV-
1994-1-1 (Picture from Johnson, 2004) .......................................................... 27
Figure 2.6:Typical Load-Slip Behaviour of Shear Connectors (Si Larbi et al., 2006) ..... 28
Figure 2.7: Length Used to Determine Connection Stiffness, k - a) Connector Spacing, Ls;
b) Length of Joint, Ljoint .................................................................................. 29
Figure 2.8: Shear Deformation of a Joint with Shear Modulus, G and Thickness, t. ....... 29
Figure 2.9: Bedding Layer in a Precast Panel System (Figure taken from Kim et al., 2002)
......................................................................................................................... 32
Figure 2.10: Strength Gain Behaviour of Elastocast C5039, BASF Canada (Gardin, 2007)
......................................................................................................................... 37
Figure 3.1: Composite Structural Laminate Plate System Used as the Outer Hull of the
Product Oil Tanker (Figures taken from Linder, 1995).................................. 44
Figure 3.2: a) Shear Bond Test b) Direct Tension Bond Test used by Braun (1999)...... 45
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Figure 3.3: Finite Element Models Used for the Study of Flexural Behaviour of CSL
Beams - a) Shell Element Model; b) Solid Element Model (Figures taken from
Braun, 1999) ................................................................................................... 47
Figure 3.4: Moment-Deflection Plots of the Analyses of the CSL Beam in Flexure with
Various Polyurethane Stiffness (Figures taken from Braun, 1999)................ 47
Figure 3.5: Moment Versus Mid-Span Deflection for Flexural Specimens by Funnell
(2000).............................................................................................................. 49
Figure 3.6: Push-Off Tests Conducted by Si Larbi et al. (2006), as adopted from the
Eurocode (1994).............................................................................................. 51
Figure 3.7: General Properties of the Adhesives (Figure taken from Si Larbi et al., 2006)
......................................................................................................................... 51
Figure 3.8: Average Shear Stress versus Slip from Push-Off Tests (Figure taken from Si
Larbi, 2006)..................................................................................................... 53
Figure 3.9: Failure Modes in Push-Off Tests a) Failure in Calamine; b) Failure in
Concrete (Photos taken from Si Larbi, 2006) ................................................. 54
Figure 3.10: Characteristics of Connectors (Figure taken from Si Larbi et al., 2006) ..... 54
Figure 3.11: Cross Section of the Composite Beam Studied by Si Larbi et al. (2006) .... 55
Figure 3.12: Strain Distribution at Midspan (Si Larbi et al., 2006).................................. 57
Figure 3.12: Cross-Section of the Beams Studied by Bouazaoui et al. (2006) - a) Constant
Joint Thickness; b) Varying Joint Thickness in the Transverse Direction
(FIgures taken from Bouazaoui et al., 2006) ............................................... 59
Figure 3.13: Composite Beams Studied by Bouazaoui et al. (2006) - a) Constant Joint
Thickness; b) Varying Joint Thickness in the Longitudinal Direction
(Figures taken from Bouazaoui et al., 2006)................................................ 59
Figure 3.14: Stress Distribution of Composite Section at its Plastic Capacity (Figure
taken from Bouazaoui et al., 2006).............................................................. 61
Figure 3.15: Failure Modes of Beams - a) P1 with concrete crushing; b) P2 with yielding
of steel, shearing of the adhesive joint and concrete cracking (Pictures taken
from Bouazaoui et al., 2006)........................................................................ 62
Figure 3.16: Deflection at the Midspan (Figure taken from Bouazaoui et al., 2006)....... 62
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Figure 3.17: Strain Distributions of the Section with a) Epoxy Joint; b) Polyurethane Joint
(Bouazaoui et al., 2006) ............................................................................... 63
Figure 3.18: Push-Off Specimens (Ramsay, 2007) .......................................................... 65
Figure 3.19: Debonding of the Push-Off Specimens (Ramsay, 2007) ............................. 65
Figure 4.1: Small Scale Push-Off Specimens for the Experimental Program .................. 70
Figure 4.2: Wooden Form used in the Fabrication of the Specimens............................... 71
Figure 4.3: Silicone Sealant Required to Avoid Leakage at the Joint .............................. 72
Figure 4.4: a) Setup for polyurethane pour; b) C-clamps used to tighten tubes after pour
......................................................................................................................... 73
Figure 4.5: Components of Polyurethane - a) Polyol and Chain Extender, b)
Isocyrange used in Type A ............................................................................. 75
Figure 4.6: Polyurethane Compressible Form .................................................................. 79
Figure 4.7: Experimental Test Setup ................................................................................ 82
Figure 4.8: Riehle Machine, University of Toronto ......................................................... 83
Figure 4.9: Location of LVDT.......................................................................................... 83
Figure 5.1: a) Visible Shrinkage in Specimen 1-1, b) Reduced Shrinkage in Specimen 1-3
......................................................................................................................... 88
Figure 5.2: Leakage Caused by Expansion of Polyurethane ............................................ 90
Figure 5.3: Shear Stress vs. Average Girder Displacement for Series 2. ......................... 91
Figure 5.4: Failure Surfaces of Specimen 2-1 a) Polyurethane Layer; b) Concrete Slab. 92
Figure 5.3: Improper Curing of the Polyurethane in Specimen 3-1 ................................. 93
Figure 5.6: Shear Stress vs. Average Girder Displacement for Series 3 .......................... 94
Figure 5.7: Polyurethane Layer in Specimen 3-3 with PU form ...................................... 95
Figure 5.8: Shear Stress vs. Average Displacement for Series Four. ............................... 96
Figure 5.9: Specimen 4-6 at Failure.................................................................................. 96
Figure 5.10: Shear Stress vs. Average Displacement for Series Five............................... 98
Figure 5.11: Specimen 5-1 at Failure................................................................................ 99
Figure 6.1: Length used to determine connection stiffness, k – a) Connector Spacing, Ls;
b) Length of Joint, Ljoint ................................................................................ 103
Figure 6.2: Schematic Composite Section in Partial Interaction Analysis (Picture taken
from Girhammar & Gopu, 1993) .................................................................. 107
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Figure 6.3: Uniformly Distributed Load Acting on the Composite Beam (Picture taken
from Girhammar & Gopu, 1993) .................................................................. 107
Figure 6.4: Differential Element in a Composite Beam Subjected to an Axial Load, F, and
a Uniformly Distributed Load, q(x) (Girhammar & Gopu, 1993)................ 111
Figure 6.5: Graphical Presentation of Equation 6.28 (after Wang, 1998) ...................... 115
Figure 6.6: β versus dβ /d(αL) ........................................................................................ 116
Figure 6.8: 2D SAP2000™ Model – a) A Complete Span b) Detail of the Elements.... 118
Figure 6.9: Figure 6.9: Overall Cross-Section of the Composite Bridge with 13m with
Deck Supported on four Steel beams............................................................ 120
Figure 6.10: Parameters of the Beam Studied – Thickness of Slab dc, Depth of Steel
Beam ds, Width of Flanges, wf, Thickness of web tw, and Thickness of Flanges
tf..................................................................................................................... 120
Figure 6.11: Strain Distributions of the Cross-Section at Midspan for Polyurethane Layer
Thickness of 25mm, 35mm, 45mm and 50mm – 50m-Span Design............ 124
Figure 6.12: Strain Distributions of the Cross-Section at Midspan for Polyurethane Layer
Thickness of 25mm, 35mm, 45mm and 50mm – 25m-Span Design............ 124
Figure 6.13: Relationship between the percentage increase in maximum deflection versus
shear connection stiffness, K, for 25m and 50m-span designs according to
Equation 6.21. ............................................................................................... 125
Figure 6.14: Three Possible Strain and Stress Distributions (Figures taken from Oehlers
& Bradford, 1995)......................................................................................... 128
Figure 6.15: Stresses of the Composite Section with Full Interaction at the Ultimate Limit
State Neutral Axis in the Steel Beam. (Figures taken from Oehlers & Bradford,
1995) ............................................................................................................. 130
Figure 6.16: Stresses of the Composite Section with Partial Shear Connection at the
Ultimate Limit State (Figures taken from Oehlers & Bradford, 1995)......... 130
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NOMENCLATURE Latin Symbols Ac area of concrete section
AL longitudinal area of an adhesive joint
As area of steel section
beff effective slab width
d1 distance between centroid of the concrete section to centroid of the
composite section
d2 distance between centroid of the steel section to centroid of the composite
section
dc depth of concrete slab
E Young’s Modulus
Fc force in concrete section
f’c concrete compressive strength
f’t concrete tensile strength
f’τ concrete shear strength
Fs force in steel section
Fy steel yield strength
Fult ultimate strength of a shear connector
G shear modulus
Ic moment of inertia of a concrete section
Is moment of inertia of a steel section
K stiffness of a connector
k area stiffness of a connection
L span length
Ljoint length of an adhesive joint
Lmodel spacing of frame elements used in finite element analysis
Ls center to center spacing of studs
M applied moment
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Mc moment distributed to a concrete section
Ms moment distributed to a steel section
n modular ratio
N axial force at a section
Pconcrete plastic strength of a concrete section
Ps,req required shear strength of the connection for full interaction
Pshear shear strength of connection
Psteel plastic strength of a steel section
q applied uniformly distributed load
s slip
sult slip at failure
t thickness of an adhesive joint
Tg Glass Transition Temperature
tw thickness of web of a steel girder
u horizontal displacement
V applied shear force
w deflection of a beam
w0 total deflection of a composite section with no interaction
wf total deflection of a composite section with full interaction
wjoint width of the adhesive joint in experiment
wmodel width of steel flanges of the studied beams
wp total deflection of a composite section with partial interaction
wslip deflection of a composite section due to interlayer slip
x longitudinal distance along a beam
z vertical distance along a cross section
Greek Symbols
α shear connection stiffness parameter
β partial interaction parameter
γ shear deformation of a joint
δ the mass density
xv
∆ horizontal deformation of a joint
ε strain
К curvature of a beam
η degree of shear interaction
τ shear stress
1
CHAPTER 1: INTRODUCTION
1.1. Rapid Concrete Deck Replacement for Composite Bridges
The objective of this research is motivated by the need for rapid bridge deck
replacement in rehabilitation of concrete-steel composite bridges. As the volume of
highway traffic increases, major delays due to road construction are generally not
tolerated by the public. Often bridges can only be closed during periods of low traffic or
during the nighttime and the construction work must be completed before the next
morning in order to minimize the impact to the public. The need for new methods in
rapid deck replacement has led to research studies such as that by Tadros et al. (1999),
who suggested that the reduction in reconstruction time not only can reduce the overall
cost of the project, but can also help improve public acceptance, reduce accident risk, and
yield environmental benefits. Therefore, any method to facilitate the construction time in
bridge rehabilitation projects would be desirable.
Conventional technology can be improved to minimize the construction time in
composite bridge rehabilitations by modifying both the bridge deck system and the
girder-to-deck connection system (Tadros et al., 1999). Typically bridge decks are
designed using cast-in-place concrete according to well established standards such as the
Canadian Highway Bridge Design Code (CAN-CSAS6-06). Provided that time is not a
constraint on the projects, cast-in-place concrete bridge decks are often promising
solutions since adjustments can be easily made in the field to achieve the required
geometry or profile. However, in projects where time is a constraint, alternative bridge
deck designs that utilize full-depth precast concrete slabs as an alternative to cast-in-place
2
concrete could provide a great potential to reduce the construction time. This,
unfortunately, leads to potential durability problems because conventional shear
connectors cannot be well adapted to the use of precast concrete panels. Openings in the
precast panels, called shear pockets or shear blockouts, are required so connectors can be
welded on site after the panels have been placed properly onto the girders. The shear
pockets would then be filled with a grouting material to form a sound mechanical shear
connection. Not only can the numerous pours for the shear pockets cause extensive
delays, these shear pockets can also create vulnerable areas that are prone to durability
problems, which could result in premature deterioration of the concrete bridge decks.
This research study investigates an alternate connection method to connect
concrete panels to steel girders by adhesively bonding to enhance the technology in rapid
concrete deck replacement for steel-concrete composite bridges.
1.2. Full-Depth Precast Concrete Panels
In concrete-steel composite bridges, the replacement of concrete decks can be
facilitated by using full-depth precast panels. An example of a full-depth precast,
prestressed concrete deck panel system is shown in Figure 1.1. As shown, a composite
section consists of a concrete deck, which can be precast or cast in-situ, and the concrete
deck is supported by steel beams. In the case where precast panels are used, prestressing
of the panels is usually recommended (Issa et al., 1995) to ensure that the transverse
joints between the panels are sealed. Traditionally, the concrete deck is connected to the
steel beams through mechanical shear connectors, such as the commonly used headed
shear studs shown in Figure 1.1. For a cast-in-place concrete deck, the concrete is poured
directly onto the headed studs that would have be welded to the steel beams, however, the
3
use of a precast concrete deck require openings called shear pockets, shown in Figure 1.1,
which must be grouted after the placement of the panels in order for the deck and the
beams to act compositely. Lastly, a gap created by rubber strips along the edge of the top
flanges of the steel beam is usually present to provide geometric tolerances, and this gap
is usually referred as the haunch if the concrete deck is cast-in-place, and is referred as
the bedding layer if the concrete deck is precast.
As discussed in the research study by Culmo (2000), the use of precast panels
avoids the extensive curing periods and eliminates the time consuming and labour
intensive formwork installation required for cast-in-place concrete, hence making rapid
overnight deck construction feasible.
Figure 1.1 A Full Depth, Precast Concrete Panels System (Figures taken from Shim et al., 1999)
Efficient implementation of full-depth precast concrete panels in bridge deck
reconstruction has been well documented. In the investigation performed by the Illinois
Department of Transportation rehabilitation program (Issa et al. 1995), the authors
presented the findings from the inspection of selected bridges in the United States that
were rehabilitated with full-depth precast, prestressed concrete panels. The field
4
investigation led to the conclusion that, in general, the use of precast concrete panels in
replacing deteriorated bridge decks can be efficient and economical. Although not all the
bridges inspected were performing at a satisfactory level, recommendations were made in
the study outlining the appropriate detailing required to avoid the durability problems
encountered, which includes leaking at the transverse joints and spalling and cracking of
the concrete decks between shear pockets. In general, Issac et al. (1995) recommended
that the precast panels should be post-tensioned longitudinally to secure all the joints to
prevent leakage. Secondly, a sufficient amount of transverse prestressing should also be
provided to avoid cracking of the deck during handling of the units. A waterproof
membrane system and an overlay are also essential to keep the deck in a good condition.
The shear keys should be designed to ease the grouting process and to take into account
potential irregularities.
With the intention to advance its bridge rehabilitation technology, the Connecticut
Department of Transportation also investigated the use of full-depth precast concrete
slabs in two bridge rehabilitation projects that required a rapid deck replacement system
(Culmo, 2000). At the initial stage of the investigation, Culmo (2000) studied a design
that required only night closures of the bridge with days opened to traffic. This, however,
was considered problematic because firstly, both the bridges that needed deck
replacement were composite, and the removal of the existing deck would be time
consuming because of the existing shear connectors. Therefore, only a small portion of
the bridge could be removed and replaced in each night closure. Secondly, when only a
portion of the bridge deck could be replaced each night, a construction joint between the
old and new slabs could be present when the bridge re-opened to public traffic. This open
5
joint would be a non-composite section and Culmo (2000) discovered that the steel
girders would be stressed beyond allowable limits from the full dead and live load that
would act on it during the normal traffic periods. These concerns have led to the
development of a deck system that required precast, prestressed full-depth concrete
panels so it would be possible for the rehabilitation work to be completed in a weekend
closure. A typical span layout consists of concrete panels that were 2400mm wide and
200mm thick, which could provide adequate room for the post-tensioning ducts. The
shear pockets, as shown in Figure 1.2, were spaced at 600mm center-to-center and two to
four welded studs could be placed in each pocket. The transverse joints between the
panels were sealed by a high-strength non-shrink grout, which was allowed to set before
the panels were post-tensioned together. The two bridge decks were still in excellent
condition five years after the replacement, therefore the author concluded that the
solution was viable.
Figure 1.2: Shear Pocket Design Used by Culmo (2000)
The abovementioned research projects have demonstrated that the use of full-
depth precast concrete panels can be a promising solution to rapid bridge deck
replacement projects with only weekend closures and minimal impact to the public.
Furthermore, the high quality control inherent to the fabrication of the precast panels
6
under plant conditions is another advantage that warrants it as an excellent alternative to
cast-in-place concrete decks. Culmo (2000) discussed that the use of precast concrete
panels requires considerations of the variable field conditions and tolerances in both the
original structures and the new components. To ensure that the concrete panels could fit
together on-site, they need to be fabricated with accurate geometry. This requires high
quality control, which includes proper curing of the concrete to avoid excess shrinkage.
Proper curing is easier to achieve under plant conditions compared to casting in-situ
because the moisture and temperature can be controlled and monitored. Since durability
of the concrete greatly depends on the curing, therefore, concrete deck panels fabricated
under plant conditions can be more durable than concrete decks that are cast-in-situ of
which the curing conditions greatly depends on the field conditions. In addition to
projects discussed by Culmo (2000) and Issac et al. (1995), other examples of deck
replacement projects that used precast concrete panels are summarized in Table 1.1.
1.3. Shear Connection System in Full-Depth Precast, Prestressed Concrete Panels
In conventional composite bridge construction, the concrete slab and the steel
girders are connected through conventional mechanical shear connectors, such as channel
or bar connectors and most commonly, welded headed shear studs, as shown in Figure
1.3. In practice, if the concrete was cast in-situ, the headed studs would be welded onto
the steel girders prior to the concrete pour. However, when precast panels have been used
in the past, shear pockets, which are openings in the panels as shown in Figure 1.2, were
required for the shear studs to be welded on site. Since the grout is poured in-situ under
7
Table 1.1: Examples of Deck Replacement Projects with Precast Concrete Panels
Name of Bridge Year of
Construction or Reconstruction
Type of Bridge Total Length (m)
Tappan Zee Bridge, New York 2006 Steel Truss, Slab-on-Girders 4800
Jacques Cartier Bridge, Montreal, Canada 2001 Slab-on-Girders
or Floor Truss 2700
Chulitna River Bridge, Alaska 1992 Slab-on-Girders 241
Burlington Bridge, Iowa 1992 Cable-Stayed 324
Interstate 84-Connecticut Route 8 Interchange, Waterbury, Connecticut 1989 Slab-on-Girders 213
Batchellerville Bridge, New York 1982 Slab-on-Girders 937
Seneca Bridge, Illinois 1986 Steel Truss 460
Dublin 0161 Bridge, Ohio 1986 Concrete Arch 162
Clark Summit Bridge, Pennsylvania 1980 Slab-on-Girders 496
Figure 1.3: Conventional Mechanical Shear Connectors (Figures taken from Oehlers & Bradford, 1995)
8
field conditions after the concrete decks are prestressed, these shear pockets can create
vulnerable areas at which durability problems could occur. The corners of rectangular
shear pockets, for example, could promote stress concentration, which could result in
cracking of the concrete deck at areas between the shear pockets. In fact, many of the
bridges investigated in the research study by Issa et al. (1995) showed signs of cracking
and spalling problems in the concrete that were initiated by the shear pockets, as shown
in Figure 1.4.
a. b.
Figure 1.4: a) Typical Shear Pockets; b) Cracking Between Shear Pockets (Figures taken from Issac et. al, 1995)
This problem with the current practice of connecting precast concrete bridge deck
panels to steel girders is the primary motivation of this thesis. This research study
investigates an alternative way to connect the concrete to steel by using a polyurethane
adhesive to avoid the need for shear pockets required for headed shear stud connections.
9
1.4. The Use of Adhesives in Bridge Construction
The use of adhesive materials in bridge construction has become more common as
new technology for construction and materials are introduced to bridge designs and
rehabilitation. With the introduction of precast segmental bridge construction, for
example, epoxy resins have been used as a sealant at the transverse joints between the
precast concrete segments. Research studies that investigated the strengthening of
concrete or steel structures by adhesively bonding fibre-reinforced polymer
reinforcement or steel plates to the beams or columns are also well documented (Example:
Tumialan et al., 2002; Triantafillou, 1998). The use of adhesives, however, as a shear
connector in composite structures is less common. It was not until recent years that
experimental investigations have been conducted to connect materials that act
compositely through adhesive bonding.
Application of adhesives in bridge construction has greatly evolved with the
introduction of Sandwich Plate System (SPS), which was jointly developed by BASF and
Intelligent Engineering (Excell, 2004). The SPS, shown in Figure 1.5, composed of two
steel plates bonded to a polyurethane elastomer core, was first introduced in the marine
industry to replace the conventional outer hull in double hull oil tankers to eliminate
fatigue and corrosion problems caused by steel stiffening plates. Since polyurethane has a
wide range of achievable stiffness (a Young’s Modulus ranging from 20MPa to 2300
MPa) and the SPS is light in weight (approximately 1100 kg/m3) (Funnell, 2000), the
application of the system has been extended to civil engineering projects including bridge
deck replacements. Table 1.2 summarizes the properties of the polyurethane elastomer
core used in the SPS system.
10
The Shenley Bridge in Quebec, Canada, shown in Figure 1.6, was one of its first
applications in bridge construction (Farmer, 2006). The prefabricated SPS deck plates
were bolted together and to the steel girders and the system was designed to act
compositely. Other bridge projects that used the SPS system include the deck
replacement of the Lennoxville Bridge in Quebec, Canada and the deck strengthening of
the Schönwassenpark Bridge in Krefeld, Germany (Intelligent Engineering, 2007). The
developer of the SPS system continues to investigate the possibility for other applications
in civil engineering projects with either the existing or a modification of the SPS system
(Excell, 2004).
Figure 1.5: The SPS System Developed by Intelligent Engineering. 1) Steel face sheets with thickness,
t. 2 - Polyurethane Elastomer Core with Thickness h. (Figures taken from Minten et al., 2007)
Table 1.2: Mechanical Properties of the Polyurethane Elastomer Core used in the SPS (Minten et al., 2007)
Density ∆ = 1150 kg/m3
Young’s Modulus E = 874 MPa
Shear Modulus G = 285 MPa
f’c = 18 MPa, at ε = 0.2% Compressive Strength
f’cu = 32 MPa, at ε = 10 %
ft = 16.1 MPa, at ε = 0.2% Tensile Strength
ftu = 33.9 MPa at ε = 32%
Shear Strength fτ = 18 MPa
11
Figure 1.6: Shenley Bridge, Quebec, Canada (Picture taken from Intelligent Engineer, 2007)
1.5. Objective and Scope of the Thesis
The main objective of this research study is to investigate the feasibility of
adhesively bonding precast concrete deck panels and steel girders using a polyurethane
elastomer. The target application of the study is the rapid replacement of concrete decks
in concrete-steel composite bridges. The use of full-depth precast, post-tensioned
concrete slabs connected to steel girders is assumed. The concrete is assumed to have a
compressive strength, f’c, of approximately 45 MPa and the steel girders are assumed to
have an yield strength, Fy, of 350 MPa. The adhesive is assumed to replace conventional
headed stud connections, and act as the conventional bedding layer that has normally
been filled with a mortar material. Kim (2002) suggested that the minimum thickness of
should be at least 25 mm, which is the typical thickness of the bedding layer that could
provide sufficient construction tolerance under field conditions.
12
This research study is designed to:
1) Establish the criteria to define the feasibility of bonding concrete to steel with a
polyurethane adhesive as the shear connector in composite bridges through an
analytical program. The criteria to be established will be based on the following:
a) Under the serviceability limit state, the adhesive joint must have
sufficient stiffness to minimize additional deflection due to interlayer
slip.
b) Under the ultimate limit state, the adhesive bond must be strong
enough to allow the full development of the plastic capacity of the
concrete and the steel sections.
2) Develop a formulation of the polyurethane adhesive and an adhesive joint
configuration that could be used to meet the abovementioned criteria through an
experimental program.
3) Study the influence of the pouring methods, the different formulations of the
polyurethane elastomer, the curing time of the elastomer, the temperature of the
specimens during the pour of the elastomer, and the different surface treatments
on the bonding of the adhesive layer to the concrete and steel surfaces.
4) Investigate the feasibility of bonding concrete decks to steel beams in composite
bridges using the polyurethane elastomer developed in the experimental program
based on the criteria established.
13
1.6. Experimental Program
The experimental part of the research involved the use of a commonly used shear
connection test, called the push-off test, to investigate the use of a polyurethane elastomer
to adhesively bond concrete to steel. Nineteen small-scale push-off tests were conducted
with the goal to investigate the influence of several factors on the bond strength of the
polyurethane and substrates. The factors examined included the pouring method of the
adhesive layer, the surface treatment of the concrete slabs and the steel girders, the
characteristics of the polyurethane adhesive, and the temperature of the specimens at the
time when the polyurethane layer is poured. The second goal of the experimental
program was to characterize the load-slip behaviour of the shear connection. The stiffness
of the shear connections was then determined from the results of the push-off tests and
the values were used in the analytical part of the study.
1.7. Analytical Program
The analytical part of the research involved the use of a partial interaction
analysis that was outlined by Girhammar and Gopu (1993), which provides analytical
solutions that describe the behaviour of a simply supported composite beam with partial
shear connection. The analysis is then compared to a computer model designed with
program SAP2000™, which was used to study the overall effect of the shear deformation
in the polyurethane layer on the deflection of a composite bridge. Perfect bond is
assumed between the polyurethane and the concrete interface, as well as the polyurethane
and the steel interface. A parametric study that examined the effects of varying the
thickness of the adhesive layer and the stiffness of the polyurethane elastomer to the
deflection of the bridge was conducted. The relationship between the span lengths and the
14
stiffness of the shear connection was also examined. A rigid plastic analysis outlined by
Oehlers and Bradford (1995) was used to study the behaviour of the composite sections
under the ultimate limit state. The results were used to determine if the polyurethane
adhesive bond developed in the experimental program had sufficient strength to be used
as the shear connection in composite bridges. A list of criteria used to define the
feasibility of adhesively bonded shear connection was established based on analyses
under the serviceability and the ultimate limit state.
1.8. Thesis Outline
Chapter 1 of this report has provided an introduction to rapid deck replacement of
bridge decks to minimize public disruption during bridge rehabilitation constructions.
The chapter has also described the advantages in using full-depth precast, prestressed
concrete panels in rapid deck replacement and the potential problems of using headed
shear studs with the precast panels. Various applications of adhesives in composite
bridges have also been presented. Lastly, the experimental and analytical programs of the
research study have been outlined.
Chapter 2 outlines the general design considerations necessary in composite
bridges. The standard push-off test used to determine the load-slip behaviour of a shear
connection is described. This is followed by a discussion of the considerations regarding
to the selection of an adhesive suitable for the purpose of this research study. The chapter
concludes with an outline of construction requirements specific to the use of the selected
adhesive.
Chapter 3 begins with a discussion of the series of research of the composite
structural laminate plate system by Carleton University that inspired the design of the
15
adhesively bonded shear connection developed in this study. An overview of two recent
research studies that investigated concrete and steel composite structures connected by
adhesive bonding is then provided. Lastly, the research study conducted by Ramsay
(2007) is summarized.
Chapter 4 describes the experimental program, including a description of the
specimens and their fabrication, a description of the test set-up, an outline of the testing
procedures, and an explanation of the variables that could affect the bond strength at the
polyurethane to concrete and polyurethane to steel interfaces.
Chapter 5 provides the results of the experimental program, including the stress-
slip behaviour of each specimen, the estimation of the stiffness of the polyurethane
adhesive connection, the shear strength of the adhesive bond, and the description of the
failure modes and surfaces.
Chapter 6 describes the analytical model of concrete-steel composite bridges that
use the polyurethane elastomer adhesive as the shear connection. An overview of the
analyses involved in studying composite beams with full, partial and no interaction is
provided. The numerical solutions to the partial interaction analysis described by
Girhammar and Gopu (1993) are outlined. Adhesively bonded composite sections with
polyurethane layer ranging from 25mm to 50m and span lengths of 25m, 50m, and 75m
were analyzed under the serviceability limit state. The chapter continues with the
analyses of the composite sections under ultimate limit state based on the rigid plastic
analysis as described by Oehlers and Bradford (1995). Lastly, a list of criteria that defines
the feasibility of the polyurethane adhesive bond was established.
16
Chapter 7 concludes the thesis with a brief summary of the results obtained from
the experimental and analytical program. The feasibility of using the polyurethane
adhesive as a mean of shear connection based on the results of the experimental program
and the criteria established from the analytical program are discussed. Finally,
recommendations for future research are provided.
17
CHAPTER 2: DESIGN FACTORS FOR ADHESIVE BONDING
One of the main reasons in assembling concrete and steel in composite bridges is
to combine the high compressive strength of concrete and the high tensile strength of
steel to create a stiffer and stronger structure (Bouazaoui et al., 2006). To ensure that the
two components are connected properly, the connection must be capable of transferring
the loads between the concrete and the steel. This chapter begins with a discussion of the
interaction in composite beams. The limit state designs that have to be considered will
then be discussed and a set of criteria based on these requirement will be proposed. The
standard push-off test used to characterize a shear connection is then described. The
different stiffness parameters used to characterize a shear connection will then be defined.
The chapter continues with a discussion of the field requirements that are specific to the
use of adhesives in construction. A comparison of the relevant properties of two typical
adhesive materials that can be used as a shear connection: an epoxy and polyurethane will
be given. The chapter concludes with a description of the design considerations that is
specific to the use of polyurethane in adhesively bonded connections.
2.1. Interaction in Composite Beams
2.1.1. Full and No Interaction
The degree of shear interaction of the concrete slab and steel girder in composite
bridges is dependent on the stiffness and strength of the shear connectors. Often the
degree of shear connection, denoted by η, is expressed as:
18
,
shear
s req
PP
η =
where Pshear is the ultimate strength of the shear connection and Ps, req is the connection
strength required to allow the concrete and steel sections of a composite beam to attain
their plastic strength under ultimate loading. This will be discussed further in the
analytical program in Chapter 6.
Figure 2.1: Cross Section of a Composite Beam
One of the most important behaviours that designers must consider when
designing for service loads is the deflection of the beam, which is a function of the
overall stiffness of the composite section. The stiffness of the shear connection also
influences the degree of interaction between the composite components, which in turns
affects the overall deflection of the beam. The two limiting cases for this interaction are
when no shear connection is provided and when the connection is very stiff. Consider a
composite cross-section shown in Figure 2.1. When no connection is provided, a case in
which the beam is referred to as non-composite and there is no interaction between the
19
concrete and steel sections, the concrete slab and the steel girder act independently and
share the loads applied to the structure proportional to their stiffness. The bending
stiffness of a non-composite section can be described as:
( ) c c s soEI E I E I= + Eq. 2.1
where (EI)o denotes the non-composite stiffness and EcIc and EsIs are the bending
stiffness of the concrete slab and steel girder respectively. On the contrary, when the
shear connection is very stiff, the beam is referred to as being fully composite with a
perfect bond between the concrete and steel sections, and there is full interaction between
the two sections. When the beam has a perfect bond, the assumption that plane sections
remain plane is valid and the bending stiffness of the fully composite section can be
calculated by transforming the concrete slab into an equivalent steel section according to
the modular ratio, n, which is the ratio of the Young’s modulus of concrete, Ec, to that of
steel, Es. This can be done by determining the effective width, beff, which can be
calculated by dividing the width of the concrete slab, b, by the modular ratio. The
bending stiffness of the section with full interaction, (EI)f, can then be estimated by this
equivalent section of steel as:
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛+++= 2
22
1
3
12dAIdA
dbEEI ssc
ceffsf Eq. 2.2
20
2.1.2. Partial Interaction
In reality, it is difficult to achieve either of the limiting cases: there will always be
some frictional forces between the two materials even if the two materials are not
connected, and if they are connected, the connectors will never be completely rigid.
There will always be relative horizontal movement, or slip, between the two materials as
they deflect under bending, as shown schematically in Figure 2.2. A composite beam that
cannot attain full interaction is said to have partial interaction. The strain distributions of
a beam with full, partial, and no interaction under bending are shown in Figure 2.3.
Figure 2.2: Slip in a Composite Beam
Figure 2.3: Degree of Interaction (Picture from Oehlers & Bradford, 1995)
21
A perfect bond is characterized by a linear strain distribution across the section with no
change in the strain at the concrete-steel interface. As seen from Figure 2.3, the strain ε at
any distance z from the bottom of the steel can be described as (Si Larbi et al., 2006):
ε(z)= εs + z К Eq. 2.3
where εs is the strain at the top fibre of the steel girder, К is referred to as the curvature of
the beam, and z is the vertical distance along the cross-section. A partial interaction
between two composite materials is characterized by linear strain distributions across
each of the section, with a difference in strain across the interface, which is usually
referred to as the slip strain, denoted by dsdx , where s is the slip between the two
components and x is the longitudinal distance along the beam. Since the slip is sometimes
denoted by ∆u, the slip strain can also be denoted by 'u∆ .
Assuming that there is no uplift between the concrete slab and steel girder, the
curvatures of both sections will be the same, as shown by the following. Consider the
case when the beam is fully composite and the bending stiffness of the section is (EI)f as
calculated from Equation 2.2, the applied moment, M, distributed to each section is:
⎟⎟⎠
⎞⎜⎜⎝
⎛=
f
ccc EI
IEMM)(
Eq. 2.4
( )
s ss
f
E IM MEI
⎛ ⎞= ⎜ ⎟⎜ ⎟
⎝ ⎠ Eq. 2.5
where, c sM M M= + Eq. 2.6
The curvature in each component can be calculated by:
22
cc
cc IE
M=κ Eq. 2.7
ss
ss IE
M=κ Eq. 2.8
Substituting Equations 2.4 and 2.5 into Equations 2.6 and 2.7, it can be shown that:
f
sc EIM
)(=== κκκ Eq. 2.9
As will be seen in Chapter 6, this assumption is relevant because many of the
numerical solutions developed to analyze the behaviour of composite beams with partial
interaction are based on the assumption that there is no uplift between the components
and the curvatures of the components are the same (Example: Newmark et al., 1951;
Girhammer and Gopu, 1993).
The guideline in the Canadian Highway Bridge Design Code (CAN/CSA-S6-06)
is designed for headed stud connections and there is no guideline proposed for adhesive
connection. An adhesive connection is continuous as opposed to the discrete shear stud
connections, and the slip in a composite beam bonded by an adhesive would be dictated
by the overall shear deformation of the adhesive joint as opposed to the stiffness of the
individual connectors. Therefore, the adhesive joint must have the required shear stiffness
to ensure that a sufficient interaction between the concrete slab and the steel girder can be
attained. Unfortunately, the current guideline does not provide a clear deflection limit that
is directly related to the flexural stiffness of a bridge, but rather the deflection limit is
based on its dynamic behaviour, namely the vibration of the bridge. Therefore, a set of
criteria must be proposed in order to determine the minimum allowable connection
stiffness for an adhesive bond. The following sections will discuss the required limit state
23
designs, and general criteria required to determine the feasibility of the adhesive bond
connections will be proposed.
2.2. Limit State Design
While understanding the composite interaction between the concrete slab and the
steel girder is important, limit states relevant to the design of an adhesive as the shear
connection in composite bridges must also be considered. This section discusses the
design factors relevant to the use of adhesive in bonding concrete slab to steel girders in
composite bridges.
2.2.1. Ultimate Limit States
As discussed by Keller & Gürtler (2005), the current design method for concrete-
steel composite bridges requires that global failure in the beam at ultimate limit state to
occur before the failure of the deck-to-girder connection. This suggests that in adhesively
connected composite beams, the shear strength and the bond strength should be high
enough to allow the concrete slab to crush and the steel girder to yield at failure. As will
be outlined in detail in the discussion of the analytical program in Chapter 6, the shear
connection must have sufficient strength to transfer the forces between the concrete slab
and the steel girder under ultimate limit state in a plastic analysis.
As demonstrated in the analytical program in Chapter 6, the maximum
longitudinal shear stress encountered at the shear connection of simply supported
composite bridges with spans ranging from 25m to 75m and concrete strength ranging
from 25MPa to 55 MPa is found to be less than 3MPa. Although this value greatly
depends on the actual design of the beam, it correlates well with the results and
24
conclusion by Si Larbi et al. (2000), who had advised that the adhesive used in as the
shear connection of composite bridges should be able to resist a longitudinal stress of at
least 3 MPa.
2.2.2. Failure Mode Generally the failure mode in any structure at ultimate limit state should be as
ductile as possible to avoid sudden catastrophic failure. As already mentioned, the failure
of composite bridges should not happen at the connection because bond failures tend to
be brittle, therefore, the adhesive connection must be able to provide sufficient bond
strength so that the concrete slab crushes and the steel yields prior to the shear failure at
the connection. In the case where the failure occurs at the connection, the adhesive joint
should have sufficient ductility to allow visible plastic deformation at ultimate load
before failure. The two different failure modes are demonstrated by the study of
Bouazaoui et al. (2006), where two different adhesively bonded shear connections in
composite bridges were compared. Generally, the beam with the stiffer adhesive and
sufficient bond strength failed with crushing of concrete and yielding of steel, whereas
the beam with a softer adhesive and insufficient bond strength failed in a ductile manner,
with visible vertical deflection and failure started with the shearing of the adhesive layer
followed by the cracking of concrete and buckling of the top steel flange.
In addition, adhesive joints are usually weak against stresses normal to the
bonding surface (Adderley, 1988), usually referred as the tearing or peeling stress, and
failure in this manner is usually brittle due to a quick propagation of the stress along the
failure interface, therefore, tearing stress on the adhesive joint should be avoided.
25
2.2.3. Deflection under the Serviceability Limit State Deflection of a beam under bending is dictated by the sectional stiffness, EI,
which is in turn a function of the stiffness of the shear connection. Similar to the slip, the
maximum deflection of a composite beam under bending is highest when no shear
connection is provided between the concrete slab and the steel girder, and is lowest when
the two materials are perfectly bonded together. This suggests that in a bonded
composite beam with partial interaction, the deflection can be reduced by choosing a
stiffer adhesive material. As will be further discussed in Chapter 6, the closed-form
analytical solutions derived by Girhammar and Gopu (1993) suggest that the
displacement of a beam with partial interaction is the sum of the deflection of the
corresponding fully composite section, wf and the deflection caused by slip between the
two materials, ws. It is important to choose an adhesive material and design the adhesive
joint to minimize additional deflection due to the interlayer slip between the sections. The
deflection limits set by the Canadian Highway Bridge Design Code (CAN/CSA-S6-06)
are based on the vibration of the bridge, and the code does not have a clear guideline that
directly relates deflection limits to the stiffness of the bridge. As a result, the criteria
necessary to determine the minimum allowable stiffness of the adhesive connection to
avoid excessive deflection due to slip are also unclear. This research study proposes a
criterion by limiting the additional deflection due to interlayer slip relative to the overall
deflection of the bridge with perfect bond connection.
The criterion can be determined by first examining the increase of the deflection
of a bridge with no interaction compared to the same design with full interaction.
Consider the composite cross-section, shown in Figure 2.4, for a 50m span bridge. The
26
geometry is based on the typical designs of composite bridges with a span to depth ratio
of approximately 1 to 28. Under any given load, if the design is non-composite, the
bridge would deflect 130% more than that of the corresponding fully composite section.
Based on this deflection range, this study proposes that the maximum additional
deflection of a composite bridge with partial interaction allowed shall be less than 20% of
the overall deflection of the bridge with full interaction. If the additional deflection due to
the interlayer slip exceeds this 20% limit, further investigation that is beyond the scope of
this thesis is required.
Figure 2.4: Cross-Section of a 50m Span Composite Bridge
2.3. Characterization of the Load - Slip Behaviour of a Shear Connection
In order to determine the structural performance of a composite beam, the
behaviour of the connection under shear loading should be characterized. A common
method, called the push-off test, has been developed to characterize the behaviour of
conventional mechanical connections under shear stresses. A standard push-off test
recommended by the Eurocode ENV-1994-1-1 is shown in Figure 2.5. The push-off test
27
consists of a steel I-girder connected to two concrete slabs by the shear connectors under
consideration. The girder is then loaded under a constant load and the slip between the
steel and the concrete is measured. The result of a push-off test is a characterization of
the load-slip behaviour of the shear connection. Typical load-slip plots are shown in
Figure 2.6. Important information about the shear connection, such as the shear stiffness
in the elastic range and the ultimate shear strength, can be determined from the load-slip
plot. As shown from the plot, the shear connectors can be classified, based on the
Eurocode, as rigid or ductile depending on the slip they allowed at ultimate load. The
results can be used, for example, to validate results in a full composite beam test or an
analytical model.
Figure 2.5: Standard Push-Off Test Configuration in Accordance to Eurocode ENV-1994-1-1 (Picture from Johnson, 2004)
28
Figure 2.6:Typical Load-Slip Behaviour of Shear Connectors (Si Larbi et al., 2006)
2.4. The Connector Stiffness, Connection Area Stiffness, and Shear Modulus
Since the degree of interaction in a composite section is directly related to the
stiffness of the connection, one of the most important values that can be obtained from a
load-slip plot is the connection stiffness. The connection stiffness can be expressed in
terms of the stiffness of the connector, K [N/mm], as determined from the push-off test,
or sometimes the connection area stiffness, k [N/mm2]. As shown in Figure 2.6, K can be
obtained from the push-off test by determining the slope of the load-slip curve, and the
stiffness value is unique to the configuration and geometry of the shear connection used
in the push-off test. When the stiffness of the individual connectors is required to be
distributed along the length of the beam, the area stiffness, k, is often used. This allows
designers to, in the case of the conventional stud connections, simplify analyses by
assuming a continuous connection as opposed to connectors at discrete locations
(Girhammer & Gopu, 1993). As a result, the continuous nature of adhesively bonded
29
connections allows the use of the connection area stiffness in their analyses. Consider the
headed stud connection and the adhesive joint connection as shown in Figure 2.7, where
Ls is the spacing between the connection, and Ljoint is the length of the adhesive joint. The
area stiffness of the connection can be calculated by:
L jointL s
a. b. Figure 2.7: Length Used to Determine Connection Stiffness, k - a) Connector Spacing, Ls; b) Length of Joint, Ljoint
1) In the case with mechanical shear connectors:
sL
Kk = Eq. 2.10
where Ls is the spacing between the shear connectors, or:
2) In the case with adhesively bonded joint:
intjoL
Kk = Eq. 2.11
D
g
Figure 2.8: Shear Deformation of a Joint with Shear Modulus, G and Thickness, t.
30
The shear modulus of an adhesive used in a bonded connection can also be determined
from the connection stiffness, K. Consider the adhesive joint shown in Figure 2.8. The
shear load, V, and the shear deformation, γ, can be related by:
γLA
VG = Eq. 2.12
where AL is the area of the joint. For small shear deformation, γ, the following
relationship can be assumed:
t∆
=γ Eq. 2.13
where t is the thickness of the joint and ∆ is the horizontal deformation, therefore,
VK =∆
Eq. 2.14
GAVt
=∆ Eq. 2.15
Since the connection stiffness, K, can be related to V and ∆ by,
VK =∆
Eq. 2.16
Substituting, K can be related to G as:
GAKt
= Eq. 2.17
Equation 3.5 can be used to either determine the shear modulus of the adhesive material
from the results obtained in a push-off test or, if the shear modulus of the adhesive is
known, the stiffness of a bonded connection can be estimated.
31
2.4.1. Determination of the Shear Stiffness of the Connection
The behaviour of composite beams at the serviceability limit states greatly
depends on the stiffness of the shear connection. However, most studies usually use the
push-off test to determine the shear strength of the connector and are less interested in
determining the stiffness of the connector (Wang, 1998). The reasons for this is because
designs of composite bridges connected with conventional shear studs usually assume
perfect bond, therefore, designer are mainly concerned with the ultimate strength of the
connectors. In spite of the numerous investigations conducted on shear connectors, the
definition of the shear stiffness is not unified among researchers and scholars, especially
when the load-slip behaviour of the shear connection is nonlinear (Wang, 1998). If the
shear connector is rigid with a linear elastic range in the load-slip curve, the connection
stiffness can usually be defined as the tangent stiffness of the plot. This assumption,
however, would not be valid if the connector is ductile with nonlinear load-slip behaviour.
Although there is not a general agreement of where the secant tangent should be
measured from, Oehlers and Coughlan (1986) have studied the load-slip plots of 116
push-tests and derived that the Ksecant can be taken at a load of 0.5Fult, where Fult is the
strength of the connector based on the push-off test. In the study by Si Larbi et al. (2000),
the secant tangent is taken as 0.6Fult according to the Eurocode.
2.4.2. Bedding Layer
Most of the current design codes for composite bridges are based on
investigations done on cast-in-place concrete decks with headed shear studs, and do not
apply specifically to full-depth precast concrete decks (Kim et al., 2002). When the
32
concrete deck is cast-in-place, there is often a gap between the steel beams and the
concrete deck, called the haunch, which is usually filled with concrete. In the case where
the deck is precast, this gap is referred to as a bedding layer, as shown in Figure 2.9. The
bedding layer is necessary in construction with precast concrete decks in order to provide
tolerance for changes in the dimensions of the steel girders due to field splices,
cambering, and other geometric variations. The adhesive bond connection being
developed in this research study eliminates the use of headed studs and uses a
polyurethane adhesive joint to act as the bedding layer.
Figure 2.9: Bedding Layer in a Precast Panel System (Figure taken from Kim et al., 2002)
Kim et al. (2002) studied the influence of the bedding layer on the strength of the
shear connection in full-depth precast decks and discovered that as the bedding layer
thickness increases, the slip in the connection also increases. The reason for this is
because the thin and unreinforced bedding layer has a lower compressive strength
compared to the concrete deck, and stress concentrations at the shear studs would cause
33
cracking of the mortar, hence allowing a larger deformation of the shear studs. Although
shear studs would not be present in an adhesively bonded system, the adhesive layer
would also be a more flexible layer compared to the concrete deck and the steel girder.
As the thickness of the adhesive joint increases, the shear deformation in the layer would
increase under a given load since the stiffness of the layer is a function of its thickness.
This can be shown by considering the deformed joint shown in Figure 2.8 again. Recall,
from Equation 2.15 that:
GAVt
=∆
Therefore, Equation 2.15 shows that the shear deformation ∆ is proportional to
the thickness of the joint. It is therefore necessary to determine the bedding layer
thickness that could provide the field tolerance required, but at the same time as thin as
possible to avoid the reduction in the overall stiffness of the structure. The thickness of
the bedding layer required usually depends on the configuration of the bridge and the
geometric tolerance required, but in practice the thickness is usually around 20 to 40mm
(Kim et al., 2002; Shim et al., 2001).
34
2.5. Adhesive Considerations
The selection of an adhesive suitable for structural purposes requires
consideration of the strength of the adhesive, its stiffness, the temperature required for
proper curing, and the sensitivity to field conditions such as moisture and contamination.
In addition, the adhesive selected for the use in rapid bridge rehabilitation must also be
able to develop sufficient strength in a short time when the bridge reopens to traffic after
the construction. One class of adhesives that can be used for structural applications is the
thermosets – a class of adhesive that sets by a chemical reaction, since they are capable of
resisting high sustained loading (Adderley, 1988). Two commonly used thermosets in
civil engineering applications are the epoxy and the polyurethane.
Epoxy adhesives consist of an epoxy resin combined with a hardener. The
versatility in its formulation allows a wide range of application. Though epoxies can
provide good thermal, environmental and creep resistance, these adhesives tend to have
long curing time and low toughness (Adderley, 1988). The application of epoxy in civil
engineering projects such as bridge rehabilitation, concrete beam strengthening, and
composite bridge construction has been well documented (Hänsch, 1978; Bouazaoui et
al., 2006).
Polyurethane is a two-part adhesive that cures quickly at ambient temperature.
Polyurethane has been successfully applied to civil engineering applications such as the
sandwich plate system (Linder, 1995; Braun 1999; Funnell 2000), which was first
developed for ship outer hulls and then was adapted to bridge deck replacements, as will
be discussed in the literature review in Chapter 3. The following sections will provide a
35
comparison of the properties of epoxy and polyurethane and explain why polyurethane is
considered more suitable for rapid deck replacement.
2.5.1. Material Properties
Unlike steel and other common materials, properties of the adhesives are not
standardized since the adhesive can be customized to achieve a wide range of properties
depending on the usage. Table 2.1 presents a comparison of the general properties of
epoxy and polyurethane gathered from different sources including data from various
research studies and data provided by BASF Canada Inc., who is the industrial partner in
this study. The values presented in Table 2.1 are only provided as a comparison between
the two adhesives and the values can vary according to the actual formulations of the
adhesives. Generally, it can be concluded that polyurethane is relatively less stiff than
epoxy and is a more ductile material.
2.5.2. Cure Time
As discussed by Adderley (1988), one of the concerns in using epoxy is the long
setting time. The setting time can be defined as the point at which the adhesive solidifies.
The different components of the adhesive will continue to react and the adhesive will
gradually gain its strengths over time. The study by Issa et al. (1995) stated that the
epoxy resin used in filling the shear pockets during the rehabilitation of the Amsterdam
Interchange Bridge that used precast full-depth concrete panels required up to 2 hours to
set and in the case when the same resin is used as a sealant in the transverse keys, the
setting time took up to 5 hours due to the low mass of material in the thin joint. A study
36
Table 2.1: Comparison of General Properties of Epoxy and Polyurethane
Epoxy Polyurethane
Young’s Modulus, E (MPa) 12300 1 45 - 2200 3
Shear Modulus, G (MPa) 4580 1 15 – 700 3
Tensile Strength, Fu (MPa) 19.5 1 9.2 - 704
Elongation at Failure (%) 16 1 300 4
Poisson’s Ratio 0.34 1 0.49 3
Pot Life (min) 90 5 2 - 13 4
Bond Strength – Concrete to Steel (MPa) 18 5 5.51
Note: 1. From Si Larbi et al. (2006) 2. From Issac et al. (1998) 3. From Braun (1999) 4. From Hepburn (1992) 5. From SIKA 30 Technical Data Sheet (2007)
by Li et al. (2000) that investigated the strengthening of concrete beams with adhesively
bonded steel plates used an epoxy resin that required a minimum curing time of 20 hours.
In addition to the long setting time, the strength gain of an epoxy adhesive is also slow.
After 24 hours of curing at 15 oC, an epoxy could only gain approximately 20% of its full
shear strength (SIKA, 2007). The long curing time, however, permits the application of
the epoxy adhesive without any special machinery.
On the contrary, the polyurethane is characterized by its fast setting time. For
example, one of the formulations of polyurethane developed for this research study has a
setting time of only 13 minutes (Gardin, 2007). Furthermore, polyurethane generally
gains strength relatively faster than an epoxy resin. Figure 2.10 shows the flexural
strength development of the Elastocast 5039, formulated by BASF Canada Inc. for this
37
research. As shown on the plot, the flexural stffiness of the polyurethane reaches
approximately 750 MPa after 4 hours of curing, which is 55% of its designed stiffness
and after 24 hours of curing, the polyurethane reaches approximately 83% of its full
strength.
Flexural Stiffness vs. Time
0200400600800
1000120014001600
0 25 50 75 100 125 150 175 200
Hours of Cure
Flex
ural
Stif
fnes
s, M
Pa
Figure 2.10: Strength Gain Behaviour of Elastocast C5039, BASF Canada (Gardin, 2007)
Although both an epoxy and polyurethane could be a suitable adhesive as the
shear connector in composite bridges in terms of their strengths, the fast curing time and
quick strength gain of polyurethane makes it a better choice in rapid deck replacement.
The long setting time of epoxy would become impractical when the window of
construction time is only six to eight hours in a night closure.
The remaining sections of this chapter will focus the discussion on using
polyurethane as the adhesive for bonding concrete decks to steel girders in composite
bridges.
38
2.6. Polyurethane Elastomer Adhesive
Prior to further discussion of the design considerations necessary for the use of
polyurethane, a brief description of its chemical properties and processing procedures is
necessary. In general, polyurethane elastomer is a polymer of which the chemical
structure consists of three main building blocks: a polyol, an isocyanate, and a chain
extender (Hepburn, 1992). The physical and mechanical properties of the polyurethane
elastomer are dependent on the properties related to these three building blocks, which
dictates the flexibility of the chain segments, the entanglement of the chains, and the
forces between the chains. The unusual higher strength, hardness, modulus and
elongation at failure of polyurethane compared to most elastomers are a result of the long
polyurethane chains that contain large number of polar groups that are free to align
themselves to form strong physical and chemical bonds (Hepburn, 1992). These bonds
prevent the chains from sliding over each other under an applied stress, therefore,
yielding a high modulus and a high strength.
A common method in processing and manufacturing polyurethane involves the
pre-mixing of the polyol and chain extender, which results in a resin that will be mixed
together with the isocyanate and injected in the mould. This is referred to as the Reaction
Injection Moulding (RIM) or Liquid Injection Moulding (LIM). This method requires
accurate consideration of the temperature, pressure and moisture content of the materials
for the proper formation of the polyurethane. This was the method used in the pilot
testing conducted by Ramsay (2007), but the pressure of the injection might have caused
turbulence in the polyurethane that resulted in foaming and improper bonding of the
39
polyurethane to the concrete and steel. In this study, the resin and the isocyanate were
hand-mixed for two minutes to address this problem.
2.7. Construction Consideration
Since no mechanical connection is provided between the two composite
components, it is important that the polyurethane adhesive can develop its required
strength under field conditions. The setting of polyurethane is a chemical reaction and is
very sensitive to variables such as the presence of contaminants at the bonding surfaces,
presence of moisture in the uncured state of the adhesive, and the temperature during the
cure. This section briefly provides a guideline to address these issues under the field
conditions.
2.7.1. Surface Treatment
One essential condition for good bond development is a contaminant-free surface.
Any form of contaminant – oil, grease, dust, metal corrosion product or release agents
can cause an improper bonding between the adhesive and the adherends. Sandblasting of
the steel girder preceded and followed by a solvent wash can easily remove any
contaminants that could cause bonding problem (Adderley, 1988). A primer and other
additives, such as a wetting or foaming agent, can also be used to enhance the bond at the
steel interface (Gardin, 2007).
40
2.7.2. Moisture
Uncured polyurethane is very sensitive to the presence of moisture (Adderley,
1988). The moisture content must be strictly controlled before the mixing the components.
A moisture content of less than 0.07% is desirable for a satisfactory processing (Hepburn
1992). An increase in moisture content can affect all of the structural properties, namely
up to a 40% decrease in tensile strength. It is necessary to make sure that the materials are
relatively dry when the polyurethane is applied. This also means that the concrete panels
must be air dried after reaching the necessary compressive strength under standard moist
curing. Furthermore, the moisture content of the two components, the resin and the
isocyanate, must also be monitored closely before and during the mixing to ensure proper
curing of the polyurethane.
2.7.3. Temperature
The working temperature of the adhesive material should be above -450C, below
which the chemical structure of the polyurethane would change and would fail in a brittle
manner. During the processing of the polyurethane, the adherends must be heated to a
temperature of at least 40 oC for the proper curing of the adhesive. The reason for this is
because the formation of the polyurethane is an exothermic reaction and substrates at a
lower temperature would act as a heat sink, which would result in an inconsistent curing
of the polyurethane because the reaction rates of the different chemical components
change with temperature. Although this might only be practical for construction in the
summer or in locations with a hot climate, the scope of this research is to develop a
feasible adhesive connection under ideal lab conditions. Further development of the
41
formulation and special treatment of the substrates are needed for applications in lower
temperatures, which would usually involve the addition of a catalyst to facilitate the
reactions of the components.
2.8. Summary
The effects of the slip on the overall stiffness of the structure requires that the
selected adhesive must have sufficient shear stiffness to ensure that the shear deformation
in the adhesive joint will not significantly increase the deflection of the bridge at service
loads. This study proposes two limit state criteria:
1) At serviceability limit state:
The additional deflection of a composite bridge with partial interaction between
the concrete and steel shall not exceed 20% of the overall deflection of its design with
full interaction. This proposed value will be examined in the analytical component of this
study in Chapter 6. If the additional deflection exceeds this limit, further investigation
that is beyond the scope of this project is needed.
2) At ultimate limit state:
The adhesively bonded connection must also have sufficient shear strength to
allow the concrete deck and steel girder to develop their full plastic capacity under
ultimate loading. Based on the criteria determined from the analytical component that
will be discussed in Chapter 6 of this study, the adhesive bond should be able to resist a
minimum stress of 3MPa under the ultimate limit state.
A comparison between epoxy and polyurethane shows that the use of
polyurethane is more appropriate in rapid deck rehabilitation. The experimental program
42
in this research study, conducted in association with the BASF Canada Group, was
designed to develop and characterize a formulation of polyurethane elastomer adhesive
that will satisfy the criteria under the serviceability and ultimate limit states.
43
CHAPTER 3: LITERATURE REVIEW
The chapter begins with a discussion of the series of research studies by Carleton
University in Ottawa (Linder, 1995; Braun, 1999; Funnell, 2006) on the composite
structural laminate (CSL) plate system that inspired the development of the adhesive
shear connection discussed in this study. This is followed by a brief summary of two
recent research studies, one by Si Larbi et al. (2006) and one by Bouazaoui et al (2006),
which investigated steel-concrete composite beams connected by bonding. Lastly, the
pilot study conducted by Ramsay (2007) at the University of Toronto on using a
polyurethane adhesive as a shear connection in concrete-steel composite beams is
outlined.
3.1. The Development of the Composite Structural Laminate (CSL) Plate System, by Carleton University, Ottawa
An extensive series of research studies under taken at the Carleton University in
Ottawa investigated a new sandwich plate system called the composite structural
laminate (CSL) plate system, which consists of two steel plates bonded to a polyurethane
elastomer core (Linder, 1995; Braun, 1999; Funnell, 2000). This system was developed to
replace the conventional outer hull in double hull oil tankers in order to eliminate steel
stiffening plates, which were the major causes for fatigue and corrosion problems. The
system that was investigated is shown in Figure 3.1.
The initial investigation in this series of research studies conducted exploratory
tests of the system to determine its behaviour and to determine a plastic core material
44
appropriate for such system (Linder, 1995). The study conducted by Braun (1999)
involved an experimental program to test the design philosophy of the system and to
Figure 3.1: Composite Structural Laminate Plate System Used as the Outer Hull of the Product Oil Tanker (Figures taken from Linder, 1995)
develop, with an industrial partner, a polyurethane elastomer formulation that was
suitable for maritime structures. Lastly, Funnell (2000) conducted large scale experiment
on the CSL system based on the results from Braun (1999).
The polyurethane elastomer used was the EC-609-002/18 developed by
Elastogran to attain a minimum required modulus of 275MPa at a maximum temperature
of 100oC. The properties of EC-609-002/18 is provided in Table 3.1. Shrinkage must also
be controlled to ensure the integrity of the bond between the steel plates and the core.
Braun (1999) suggested that flocculates such as calcium carbonate or 5% to 10% of air
entrainment could be used to control the shrinkage provided that they do not significantly
reduce the strength and stiffness of the material. The direct shear and direct tension bond
45
Table 3.1: Mechanical Properties of EC-609-002/18 (after Braun, 1999)
Mechanical Properties Measurements Units Test Procedure
Hardness 70 Shore D DIN 53 505
Tensile Strength 22.7 MPa DIN 53 504
Elongation at Fracture 26 % DIN 53 504
Young’s Modulus 517 MPa DIN 53 497
Table 3.2: Tension Bond Test of the Polyurethane Elastomer Core (after Braun, 1999)
Test Bond Strength, MPa
-40oC 7.24 20 oC 7.68 Shear 60 oC 6.45 -40oC 6.06 20 oC 4.18 Tension 60 oC 3.72
a. b.
Figure 3.2: a) Shear Bond Test b) Direct Tension Bond Test used by Braun (1999)
46
test used in the study by Braun (1999) are shown in Figure 3.2 a and b, respectively. The
results of the bond tests at -40oC, 20oC, and 60oC are shown in Table 3.2. Generally,
Braun (1999) found that the values obtained from the direct tension tests were not
representative of the actual bond strengths because the additional shear stress at the
corners of the polyurethane-steel plate interface due the poisson affect would cause
peeling of the elastomer core from the steel plates and result in a sudden bond failure.
In addition to the experimental analysis, Braun (1999) also performed numerical
analyses to accurately describe the flexure and in-plane compressive behaviours of the
plate system. Figure 3.3 shows schematically the finite element models used by Braun
(1999), who suggested that the system should be designed so that the section could reach
the plastic moment capacity of the plates without local failure, namely debonding with a
local buckling of the plates. The beams studied have a total length of 2m and width of
200mm, and the CSL plate system is composed of two 10mm plates with a 50mm
polyurethane elastomer core. The plates were modeled assuming perfect bonding
between the materials and plane section would remain plane. The results, shown in
Figure 3.4, are presented in moment – mid-span deflection plots, of which the moment
was expressed as a ratio of the plastic capacity of the steel plates. The two dotted lines
represent the elastic and the plastic capacity of 33.8 kN-m and 44.02 kN-m, respectively.
Due to the non-linear behaviour of the polyurethane core, the stiffness of the beam
reduces gradually, as opposed to a significant loss in stiffness as expected from a regular
steel beam. As can be seen from Figure 3.4, the maximum moment capacity of the
sections was dictated by the plastic capacity of the steel plates without any local failures.
47
Figure 3.3: Finite Element Models Used for the Study of Flexural Behaviour of CSL Beams - a) Shell
Element Model; b) Solid Element Model (Figures taken from Braun, 1999)
Figure 3.4: Moment-Deflection Plots of the Analyses of the CSL Beam in Flexure with Various
Polyurethane Stiffness (Figures taken from Braun, 1999)
48
The analysis showed that the systems would become more flexible as the Young’s
modulus decreased due to an increase in shear deformation of the polyurethane core.
Lastly, the maximum transverse shear stress was found to be approximately 8.5 MPa,
therefore, a minimum bond strength of 8.5 MPa must be provided to avoid a brittle bond
failure. The preliminary numerical analyses conducted by Braun (1999) had provided
insights into the minimum bond strength and the minimum modulus of the elastomer
required for the sandwich plate system to reach its full plastic capacity at failure, in both
flexure and compression. These results were used and compared in the next phase of the
experimental program conducted by Funnell (2000).
Funnell conducted a large-scale experimental program that tested the CSL plate
system in flexure and in-plane compression to verify the numerical models that were
developed in the previous phases of the research. The expected behaviour of the beams
were calculated based on an equivalent section of steel, which was basically the two
plates separated by an equal distance from the centroid of the section since the modular
ratio of the polyurethane to steel is minimal (approximately 0.0032). Therefore, the
flexural moment capacity of the specimens would be equal to the plastic capacity of the
steel plates. The results of the tests are shown in Figure 3.5. Funnell (2000) encountered
premature failures in flexure caused by unexpected torsional effects due to the test setup,
which added to the expected shear stresses at the interface causing debonding of the steel
plates. The tests were modified and the experiment results for the remaining specimens
generally agreed with the analyses from the numerical study by Braun (1999). Therefore,
Braun’s model predicted the results well with tests-to-predict ratio of around 0.98 and
0.96 for flexural stiffness and plastic moment capacity, respectively. The maximum
49
Figure 3.5: Moment Versus Mid-Span Deflection for Flexural Specimens by Funnell (2000)
transverse shear stress value measured during the tests was 5.1 MPa, which was lower
than the bond strength of 8.5 MPa.
Funnell (2000) concluded in the research study that the developed elastomer met
the design specifications for maritime structures. The techniques in the finite element
analysis models established by Braun (1999) were also verified. Therefore, the series of
research studies undertaken at the Carleton University has successfully designed a
sandwich plate system, of which the flexural and in-plane compressive behaviour can be
accurately described by numerical models.
The series of research on the CSL system by Carleton University sets an
encouraging precedent of implementing polyurethane into structural systems. This
extensive series of research studies has also provided an example to the necessary
analyses necessary to determine and define the feasibility of a structural system that usesf
an adhesive bond as a mean of shear connection. The system, which is now named the
50
Sandwich Plate System (SPS), has been well adopted in the maritime, as well as civil
engineering applications (Farmer, 2006).
3.2. Static Behaviour of Steel Concrete Beam Connected by Bonding, by Si Larbi et al. (2006)
The research study by Si Larbi et al. (2006) examined adhesive connections in
steel-concrete composite highway bridges. Two types of adhesives for the shear
connections were investigated: epoxy mixed with silica sand and polyurethane. The
study included an experimental component and an analytical component. The
experimental component involved push-off tests of the adhesive connections, as shown in
Figure 3.6, and the results were verified with computer models of the specimens. The
analytical component involved computer modeling of steel-concrete composite beams
with either conventional headed stud connections or adhesively bonded shear connections.
The different types of connections were compared in terms of the deflection, slip, strain,
and stress of the computer models in the analysis.
Si Larbi et al. (2006) examined the effects of the types of resins, the thickness of
bonding joints, and the surface treatments in the experimental part of the study. The
details of the parameters are summarized in Table 3.3 and the properties of the adhesives
used in the study are shown in Figure 3.7. As can be seen, the epoxy had a higher
51
Figure 3.6: Push-Off Tests Conducted by Si Larbi et al. (2006), as adopted from the Eurocode (1994)
Figure 3.7: General Properties of the Adhesives (Figure taken from Si Larbi et al., 2006)
ultimate strength, Fu, and was much stiffer compared to the polyurethane, which had a
lower strength but a larger elastic deformation. Tg is defined as the Glass Transition
Temperature, under which the properties adhesive will change and it will fail in a brittle
52
manner. High strength concrete with 28 days compressive strength of 67 MPa was used
in the push-off tests to prevent tensile and shear failures in the concrete. The steel girder
were 300mm sections cut from an HEA 100 rolled beam with a yield strength of 235
MPa. The adhesive was allowed to cure for 7 days at 20 oC to allow full polymerization
of the materials. The concrete slabs were sandblasted an hour before the bonding, and the
steel girders were either washed once by acetone, a solvent used to eliminate the
contaminants at the steel surfaces, or sandblasting followed by an acetone wash and a
primer dump, a chemical agent that is used to enhance the bonding between the
polyurethane and steel. A 1mm layer of calamine was applied to the surface of the steel
after sandblasting to aid the bonding of the adhesive to the steel surface. The results of
the push-off tests are shown in Table 3.3 and Figure 3.8. The specimen with the 3mm
thick polyurethane joint was deemed unsuccessful because of the unexpected failure that
happened at the interface due to an incomplete bonding. The reason was not clear but Si
Larbi et al. (2006) related the problem to the high fluidity of the polyurethane
formulation used that prevented it to bond properly when the thickness is higher.
Failures in the other specimens were cohesive, meaning it was a material failure that
happened in the adherends. The cohesive failure happened either in the 1mm calamine
layer or in the concrete, as shown in the Figures 3.9. The ultimate shear stress averaged
between 5.0 to 5.9 MPa. Though the ultimate shear stress depended only slightly on the
parameters examined, the stiffness of the connections varied greatly between 12 to 46
MN/mm, with epoxy connections being twice to four times more stiff than those of the
polyurethane.
53
Table 3.3: Summary of Adhesive Push-Off Tests by Si Larbi et al. (2006)
Resin Surface Treatment
Joint Thickness
(mm) Failure Mode
Ultimate Average
Load (kN)
Ultimate Average
Shear stress (MPa)
Tangent Bonding Stiffness
(MN/mm)
Acetone 1.2 Cohesive in Calamine 104 5.2± 0.3 46
Corumdum + Primer 1.2 Cohesive in
Concrete 118 5.9± 0.1 47 Epoxy
Corumdum + Primer 3 Cohesive in
Concrete 110 5.5± 0.1 23
Acetone 0.2 Cohesive in Calamine 100 5.2± 0.0 11
Corumdum + Primer 0.2 Cohesive in
Concrete 104 5.2± 0.3 12 Polyurethane
Corumdum + Primer 3 Interface 7 0.3± 0.1 -
Figure 3.8: Average Shear Stress versus Slip from Push-Off Tests (Figure taken
from Si Larbi, 2006)
54
a. b.
Figure 3.9: Failure Modes in Push-Off Tests a) Failure in Calamine; b) Failure in Concrete (Photos taken from Si Larbi, 2006)
Figure 3.10: Characteristics of Connectors (Figure taken from Si Larbi et al., 2006)
Two shear stud connections were compared to the adhesively connections bonded
by polyurethane and epoxy, respectively. The load-slip behaviour of the shear stud
connections is shown in Figure 3.10. The shear connectors were classified as rigid,
ductile and semi-ductile depending on the slips at their ultimate stress, sult. The
connection stiffness, k, used in the numerical analysis was calculated based on the
tangent stiffness, Ktangent of the connectors, as shown in Figure 3.10, divided by a spacing
55
of 150mm. The stiffness values were then compared to those of the bonded connections,
which can be calculated by dividing the tangent stiffness values obtained from the push-
off tests by the length of the adhesive bond of the specimens. The stiffness values are
shown in Table 3.4. Generally, the stiffness of the adhesive bond connection is
comparable to that of a rigid headed stud connection.
Table 3.4: Comparison of the Stiffness between Connectors and Bonding (after Si Larbi et al., 2006)
Connection Rigid Connector
Semi-Rigid
Connector
Ductile Connector
Epoxy 1.2mm
Epoxy 3mm
Polyurethane 0.2mm
k (MN/m2) 16000 3333 2000 37600 18400 8800
Figure 3.11: Cross Section of the Composite Beam Studied by Si Larbi et al. (2006)
The cross-section of the 5m beam studied by Si Larbi et al. (2006) is shown in
Figure 3.11. The numerical analysis used was based on a model that provided closed-
form solutions to the behaviour of a composite beam by taking into account the interlayer
slip between the concrete and steel sections. The model was designed to analyze
composite beams connected by mechanical connectors, and the stiffness of the connectors
56
was assumed to be distributed uniformly along the length of the beam. The bonded
connections were compared to two ductile stud arrangements, with two rows of 19mm
diameter studs, 80mm in height and spaced at 150mm or 450mm. The connections were
also compared to the case where there was no slip between the concrete deck and the
steel beam, often referred to as a perfect bond where the assumption of plane sections
remain plane remains valid. The strain distributions at the mid-span of the composite
beams with the different connection configurations are shown in Figure 3.12, and the
corresponding stress values are presented in Table 3.5. The value k shown in Table 3.5
corresponds to the connection area stiffness, as discussed in Chapter 2. As can be seen
from the strain distributions, the adhesively bonded connections were very stiff compared
to those of the conventional studs that the slips at the interfaces of the bonded
connections were less than 5% of those in headed studs. In fact, both bonded connections
had a linear distribution of strains, which is characteristic to a perfect bond. The computer
analysis also showed that the maximum shear stress at the bonding interface remained
lower than 3 MPa and the yielding of the steel girder occurred before failure at the joint.
This indicates that the bond was strong enough to allow the development of the full
plastic strength of the steel section at ultimate limit state.
The study by Si Larbi et al. (2000) has provided insights into the behaviour of
adhesively bonded composite sections under loading. Although the stiffness of the
adhesive joint greatly depends on the thickness of the joint and the nature of the adhesive,
the study suggested that an adhesive bond can be very stiff that the interlayer slip
between the concrete and steel sections can be ignored. Si Larbi et al. (2000) also
suggested that adhesively bonded connection must be able to resist a longitudinal shear
57
stress of at least 3MPa, which will be verified in the analytical program of the current
study in Chapter 6.
Figure 3.12: Strain Distribution at Midspan (Si Larbi et al., 2006)
Table 3.5: Behaviour of the beams with different types of connection under a concentrated load, 250KN, applied at midspan (after Si Larbi et al., 2006)
Studs, spa. = 450 mm
Studs, spa. = 150mm
Bonding PU
t = 0.2mm
Bonding Epoxy
t = 1.2 mm
Perfect Bond
(no slip)
k (MPa) 667 2000 88000 376000 infinity
Deflection (mm) 9.9 8.4 7.6 7.6 7.5
σc,top (MPa) -17.0 -16.9 -16.8 -16.8 -16.8
σc,bottom (MPa) 2.1 -0.5 -3.9 -3.9 -4.2
σs,top (MPa) -131.1 -86.4 -34.4 -29.6 -25.1
Mid-Span
σs,bottom(MPa) 256.6 246.2 234.1 232.9 231.9
Slip (µm) 470 167 4 1 0 Extremity Shear Stress
(MPa) - - 2.2 2.4 -
58
3.3. Experimental Study of Bonded Steel Concrete Composite Structures, Bouazaoui et al. (2006)
The research study by Bouazaoui et al. (2006) involved an experimental analysis
of adhesively bonded steel-concrete composite beams. They explained that the use of an
adhesive material to replace conventional shear studs can: 1) Eliminate stress
concentration at the connections; 2) Create a lighter structure; 3) Protect the steel girder
from corrosion; and 4) Allow the use of precast concrete slabs instead of cast-in-place
concrete.
Similar to the experiment by Si Larbi et al. (2006), the study investigated two
different adhesives: an epoxy with a Young’s Modulus of 12300 MPa and a polyurethane
elastomer with a Young’s Modulus of 80 MPa. The effects of two parameters on the
overall structural performance of composite beams were examined: 1) The characteristics
of the adhesives; 2) The variable thickness of the adhesive joint in the transverse and
longitudinal directions, as demonstrated in Figure 3.12b and 3.13b. The beam sections
that were used in the experiment are shown in Figure 3.12. Four beams were tested in the
study: Three connected with the epoxy adhesive; and one with the polyurethane adhesive.
Of the three connected with the epoxy adhesive, one had variable thickness from 3 to
5mm in the transverse direction (Figure 3.12b) and the other from 3 to 7mm in the
longitudinal direction (Figure 3.13b). Table 3.6 summarizes the geometry of the beams
studied by Bouazaoui et al. (2006).
59
Table 3.6: Geomety of Beams Studied by Bouazaoui et al. (2006)
Beam Transverse Thickness Longitudinal Thickness Adhesive
P1 Constant – 3 mm Constant – 3mm Epoxy
P2 Constant – 3 mm Constant – 3 mm Polyurethane
P3 Constant – 3 mm Varies – 3mm to 5mm Epoxy
P4 Varies – 3mm to 7mm Constant – 3mm Epoxy
/
a. b.
Figure 3.12: Cross-Section of the Beams Studied by Bouazaoui et al. (2006) - a) Constant Joint Thickness; b) Varying Joint Thickness in the Transverse Direction (FIgures taken from Bouazaoui et al., 2006)
a. b.
Figure 3.13: Composite Beams Studied by Bouazaoui et al. (2006) - a) Constant Joint Thickness; b) Varying Joint Thickness in the Longitudinal Direction (Figures taken from Bouazaoui et al., 2006)
60
The beams in the tests were compared in terms of the failure mode, the ultimate
deflection at midspan, the strains in the concrete and steel at midspan, the relative slip
between the concrete slab and the steel beam, and the ultimate load. The theoretical
ultimate load was calculated based on the plastic capacity of the beams, which was
calculated assuming that:
a) The steel and concrete reach their maximum strength
b) The entire steel beam section has yielded, with stresses equal to the yield
stress, Fy.
c) The entire concrete section has a uniform compressive stress of 0.85f’c,
which is the plastic capacity of concrete.
d) The plane section remains plane for the entire cross-section.
e) The tensile strength of the concrete can be neglected.
The stress distribution and the corresponding forces in the concrete and steel, Fc
and Fs, at the cross-section at its plastic capacity are illustrated in Figure 3.14. In this
study, Bouazaoui et al. (2006) designed the cross-sections to maximize the shear stress at
the adhesive layer to allow the development of the maximum compressive strength of the
concrete slab and the maximum tensile strength of the steel girder, therefore, the plastic
neutral axis should be situated right below the concrete section in the steel top flange.
The plastic moment capacity could then be determined by taking moment of all the forces
in the cross- section.
61
Figure 3.14: Stress Distribution of Composite Section at its Plastic Capacity (Figure taken from
Bouazaoui et al., 2006)
Table 3.7: Comparison between Experimental Ultimate Load, F u,c and Theoretical Ultimate Load, Fu,t
Composite Beam Fu,c (kN) Fu,t (kN) , ,
,
*100u c u t
u c
F FF
⎛ ⎞−⎜ ⎟⎜ ⎟⎝ ⎠
P1 238 206 13.4 P2 185 206 -11.4 P3 246 206 16.3 P4 219 206 5.9
The results of experimental beams and the theoretical beams are shown in Table
3.7. In general, the three epoxy connected beams had similar behaviour despite the
irregularities in the thickness of the joint. Figures 3.15 and 3.16 show the failure modes
and the ultimate deflection of the beams, respectively. The beams with the epoxy joint
were stiffer and the failure modes were always brittle with steel yielding and concrete
crushing, as shown in Figure 3.15a. The beam connected by the polyurethane adhesive,
however, was significantly more flexible with a greater vertical deflection and a greater
shear deformation in the joint, as shown in Figure 3.15b. The ultimate load of the beam
62
a. b.
Figure 3.15: Failure Modes of Beams - a) P1 with concrete crushing; b) P2 with yielding of steel, shearing of the adhesive joint and concrete cracking (Pictures taken from Bouazaoui et al., 2006)
Figure 3.16: Deflection at the Midspan (Figure taken from Bouazaoui et al., 2006)
connected by the polyurethane adhesive was 11% less than the theoretical ultimate load
due to the lower strength of the adhesive. This suggests that the ultimate strength of the
adhesively bonded composite beams greatly depends on the strength of the adhesive bond.
The beams with the epoxy connection were found to have a linear strain
distribution with no slip between the concrete and steel, while the cross-section with the
polyurethane adhesive experienced an interlayer slip between the concrete slab and the
steel beam, as shown in Figure 3.17.
63
The above review of the study by Bouazaoui et al., (2006) suggests that the
behaviour of the adhesively bonded composite section greatly depend on the stiffness of
the adhesive and the strength of the adhesive bond. The experimental results demonstrate
that the connections bonded with an epoxy, a stiffer adhesive, had lower deflection at
failure, but the failures were always brittle. The epoxy connections had sufficient bond
strength that allowed the concrete and steel sections to reach their plastic strength at
failure. In the case where the connections were bonded with polyurethane, the deflection
at failure was higher, but the connection did not have sufficient bond strength to allow the
full development of the plastic strength of the concrete slabs and the steel beams, that is,
it had a bond strength that was lower than the plastic capacity of the concrete or the steel
section, which resulted in a reduction of the ultimate flexural strength of the section.
a. b.
Figure 3.17: Strain Distributions of the Section with a) Epoxy Joint; b) Polyurethane Joint (Bouazaoui et al., 2006)
64
3.4. Shear Resistance of a Polyurethane Interface in Concrete-Steel Composite Beams, by Ramsay (2007)
A preliminary investigation that involved the testing of twenty specimens using
standard push-out tests, as recommended by the Eurocode 4 (ENV 1994-1-1), was
performed by Ramsay (2007) with the objective to develop a feasible configuration of
adhesive shear connection between concrete and steel. The resin and isocyanate were
mixed in a machine to form the two-part polyurethane and the mixture was then injected
into the cavity created between the precast concrete slab and the steel girder at a pressure
of 13.8 MPa (2000 psi) (Ramsay, 2007). Figure 3.19 shows the design of a typical push-
off specimen. After proper curing of the adhesive, the specimens were tested with the
goal to obtain the load-slip behaviour of the various connections.
The tests were not conclusive in characterizing the behaviour of the adhesive
shear connections. The polyurethane layers in the specimens were not adhering properly
to the substrates and premature brittle bond failures occurred in all of the tests conducted.
Figure 3.18 shows the debonding of the girder from the concrete slab. Generally, air
bubbles and a layer of foam were found in the polyurethane layers, and there also
appeared to be a lack of adherence of the joint to the steel surfaces. Representative from
BASF Canada Inc. (Gardin, 2007) had hypothesized the following possible causes of the
bonding failure:
1) The injection of the polyurethane under the high pressure might have caused
turbulence in the polyurethane layer, which might have been the cause for the
layer of foam and bubbles near the surface of the adhesive joint.
65
Figure 3.18: Push-Off Specimens (Ramsay, 2007)
Figure 3.19: Debonding of the Push-Off Specimens (Ramsay, 2007)
66
2) Shrinkage of the polyurethane material might be responsible for the unbonded
areas between the adhesive layer and the substrates.
3) Pressure from the chemical reaction of the two-parts polyurethane might have
lifted the concrete slab slightly and induced air bubbles near the surface of the
polyurethane layer.
The hypotheses of the possible causes of the bonding problems and the insights
obtained from the pilot testing have led to the design of the new experimental program in
this research study.
3.5. Summary
The literature review presents the research of the composite structural plates that
inspired the use of polyurethane to adhesively bond precast concrete panels and steel
girders for composite interaction. The two recent research studies discussed also
demonstrated the possibility of replacing a conventional headed shear stud connection by
an adhesive bond in concrete-steel composite beams. The research studies have also
presented the possible failure modes that should be considered when adhesively bonded
shear connections are considered. Lastly, the study by Ramsay (2007) has provided
insights into the development of the polyurethane adhesives and the adhesive joint
configuration used in the experimental program in this research study.
67
CHAPTER 4: EXPERIMENTAL PROGRAM
The goal of the experimental component of this research study was to develop a
polyurethane formulation that will meet the criteria for its use as a shear connection in
composite bridges. Although considerations of field conditions, such as the moisture and
temperature, are important, the scope of the experimental part of this study is to develop
the polyurethane adhesive under lab conditions by focusing mainly on the strength and
stiffness of the connection. The push-off tests were used to characterize the strength and
the stiffness of the polyurethane adhesive layer. Nineteen small-scale push-out specimens
were used to study the effects of the different variables on the bond strength of the
adhesive shear connection. The load-slip behaviour of each of the shear connections was
characterized. The results obtained from the experiments would then be used in the
analytical part of this research study.
This chapter begins with a description of the fabrication process of the specimens.
This is followed by a discussion of the different variables that were considered to have a
potential influence on the bond strength of the adhesive connection. Lastly, the setup and
the instrumentation of the push-off tests are presented.
4.1. Modified Push-Off Test Specimens
With the insights obtained from the pilot testing by Ramsay (2007), a new set of
push-off test specimens were designed for this study. The objectives of the experimental
component of this research study were to:
68
1) Develop a shear connection system using a polyurethane adhesive that can
adequately bond concrete slab and steel girders in composite bridge construction.
Minimum bond strength of 3MPa should be achieved.
2) Investigate the variables that can affect the bond strength between the
polyurethane and the substrates.
3) Characterize the load-slip behaviour of the adhesive bond connection.
4.1.1. Scope of the Experimental Program
An adequate adhesive shear connection system should satisfy the criteria
described in Chapter 3, namely the minimum shear and bond strength for the full
development of the plastic capacity of the concrete deck and the steel girders and
sufficient stiffness to minimize the deflection under service loads. Although the
compatibility with field conditions such as the moisture and temperature should also be
considered, the current experimental program was designed to perform under ideal lab
conditions with strictly controlled temperature and moisture level. The adequacy of the
adhesive connection is therefore defined as the following:
1) The polyurethane adhesive connection must have sufficient shear strength to resist
a minimum shear stress of 3 MPa, as verified in the analytical program
2) The polyurethane must be formulated to have sufficient stiffness that will
minimize additional deflection due the interlayer slip between the concrete slab
and steel girders in a composite bridge. Due to the lack of guideline in the current
design code to limit the deflection according to the stiffness of a bridge, this study
proposes that the adhesive connection should be stiff enough so that the ratio of
69
the deflection of a composite bridge with slip to the deflection of the same design
without slip should be less than 1 to 1.2.
3) If the bond strength is below 3 MPa, the failure mode should be ductile and
failure should occur in the adhesive and not brittle bond failure at the interfaces.
4.1.2. Design Consideration for the Specimens
The push-out specimens were designed to connect two concrete slabs and a steel
girder by a polyurethane adhesive layer. The design of the specimens is shown in Figure
4.1. Several modifications were made to standard push-off tests to suit the need for the
adhesive connection. Firstly, the specimens were designed to be one-third of the size of
the full-sized specimens used in the research study by Ramsay, which were designed
according to the Eurocode (ENV 1994-1-1). The specimens were designed to be smaller
to ease the pouring process of the polyurethane that had to be done in a chemical lab. As
will be discussed, the polyurethane needed to be hand-poured instead of being injected
from a machine and, therefore, with the quick setting time of the polyurethane, manual
pouring of the adhesive layer of a full size specimen would be difficult. The slab
measured 180mm by 180mm with a thickness of 40mm. The steel section used was the
W100 x 19 produced according to the G40.21 350W. Secondly, due to an error in the
fabrication of the specimens, the steel girders were adhered flush to the concrete slabs as
opposed to being offset. Lastly, the concrete slabs were not reinforced as failure is not
expected to be in the concrete, and the slabs would be too small to provide sufficient
development length for the reinforcement.
70
Figure 4.1: Small Scale Push-Off Specimens for the Experimental Program
The design of the specimens is shown in Figure 4.1. Three plastic tubes were
required for the pouring of the polyurethane into the cavity, which was created by
sandwiching a wooden form between the concrete slabs and the steel girder, as shown in
Figure 4.2. The 25mm plastic tubes were the pour tubes for the polyurethane and the
10mm tubes were the venting tubes from which any air in the cavity could escape as the
polyurethane adhesive filled the gap. The tubes were located as close to the edges of the
polyurethane layer as possible to allow as much air to escape from the cavity as possible.
71
Figure 4.2: Wooden Form used in the Fabrication of the Specimens
As discussed in Chapter 3, the proposed polyurethane adhesive joint would
replace the bedding layer that, conventionally, would have been filled with a grouting
material. In practice, the thickness of the bedding layer can range between 20mm to
40mm depending on the geometric tolerance required. A thickness of 25mm thickness
was for the push-out specimens in the experimental program. The edges around the
wooden frame were sealed with a silicone sealant to prevent any leakage of the
polyurethane due to its low viscosity nature in the uncured state, as shown in Figure 4.3.
72
Figure 4.3: Silicone Sealant Required to Avoid Leakage at the Joint
4.1.3. Fabrication of the Specimens
The specimens were fabricated in two phases: the first phase included the
fabrication of the concrete slabs, the steel girders, and the necessary formwork; the
second phase involved the assembly of the specimens and the pouring of the
polyurethane. Prior to the casting of the concrete, a layer of surface retarder, MBT®
DN320 (Master Builder Technical Data Sheet) was applied to the bottom face of the form
to delay the setting time of the concrete surface in order to create the roughened exposed
aggregate surface. The cementious material on the surface at which the retarder was
applied to was washed off with a pressure washer twenty-four hours after the concrete
casting. The roughness of the surface corresponds to a medium etch (5mm). (Master
Builders Technology Technical Datasheet). The concrete slabs were then moist-cured for
twenty-eight days under 70% humidity.
Once the concrete had reached its twenty-eight days strength, the slabs and steel
girders were transported to BASF for the pour of the polyurethane. The specimens could
not be assembled until the steel surfaces had been sandblasted, which must be done at
most twenty-four hours before the polyurethane pour. After the concrete slab, steel girder,
73
and the wooden frames were assembled, the composite sections were heated in an oven to
a minimum temperature of 37 oC and stored until the time of the pour.
The two components of the polyurethane, a resin and the isocyanate, were
manually mixed and poured into the cavity through the pour tubes. The pouring setup is
shown in Figure 4.4a. Once the polyurethane began to exit from both vent tubes – an
indication that the cavity was completely filled and all the air had escaped, all three tubes
were immediately tightened by C-clamps, as shown in Figure 4.4b. Since the specimens
must be laid flat on one of the concrete slab for each pour, only one cavity could be filled
at a time and the second pour must wait until the first polyurethane layer had properly set.
After the pour were completed, the specimens were allowed to cure at room temperature
for at least seven days before they were shipped to University of Toronto for the push-off
tests.
a. b.
Figure 4.4: a) Setup for polyurethane pour; b) C-clamps used to tighten tubes after pour
74
4.1.4. Materials
Concrete and Steel
All the concrete slabs were cast at the same time and stored under the same
ambient conditions. A concrete mix with a 28-days compressive strength of 55 MPa was
used for the slabs. The steel girders were 180mm in length cut from a W100 x 19 rolled
beam as specified according to the G40.21 350W with a nominal strength, f’y = 350MPa.
Polyurethane Adhesive
As discussed in Chapter 3, polyurethane was chosen as the bonding material for
the concrete and steel because it has a fast curing time and is usually ductile. Two
different polyurethane elastomer were formulated: The first one, which will be referred as
the Type A, contains three variations – CAE 1-1, CAE 2-1, and CAE 2-3a; and the
second type, which will be referred as the Type B, also contains three variations —
CAE 1-3, CAE 1-9, and CAE 1-10. The difference between the two formulations is the
different isocyanate that was used in each one. Type A was used in series 1 to 4 of the
push-off tests and the polyurethane was brown in colour, and Type B was used in series 5
of the tests and the polyurethane was white. The detailed chemical compositions of the
polyurethane adhesive are proprietary information that cannot be disclosed, but all the
formulations developed for the experimental program is a combination of the basic resin
processed by mixing the polyol and the chain extender, and the isocyanate, as seen in
Figure 4.5. The general properties of the formulations are summarized in Table 4.2.
75
a. b.
Figure 4.5: Components of Polyurethane - a) Polyol and Chain Extender, b) Isocyanate used in Type A
The main difference between the three variations, CAE 1-1, 2-1 and 2-3a, of the
Type A polyurethane formulation is the amount of shrinkage that would occur as the
polyurethane cure and the different additives mixed into the formulation to promote
better bonding. Since one of the hypothesis for the cause of unsatisfactory bonding in the
pilot testing is the shrinkage in the polyurethane layer (Ramsay, 2007), the different
formulations were considered to address this issue. Consequently, the different
formulations also have different setting times and strength gain behaviour since the
shrinkage of the polyurethane is dictated by the curing behaviour; the faster the
polyurethane cures, the more shrinkage will occur. The CAE 2-1 and CAE 2-3a has a gel
time of 7 minutes and a shrinkage value of approximately 3-5 %, while the CAE 1-1 has
a gel time of 33 minutes and negligible shrinkage (Gardin, 2007). Variations of these
formulations with additives such as a wetting agent that could reduce the surface tension
of the polyurethane at its liquid state to promote better adhesion were also used.
76
Table 4.2: General Properties of the Formulations of Polyurethane
Formulation Gel Time (min)
Shrinkage Level
Flexural Modulus
(MPa) Comments
CAE 1-1 33 Negligible 1031 Exhibit Better Elongation
CAE 2-1 13 Medium 1370 Slight amount of foaming agent
CAE 2-3a 13 High 1370 Contains foaming and wetting agent
CAE 1-3 13 Negligible 800 Softer material with better tolerance to tearing stress;
contains wetting agent
CAE 1-9 13 Negligible 800 Softer material with better tolerance to tearing stress
CAE 1-10 13 Negligible 800 Softer material with better tolerance to tearing stress
The Type B polyurethane contains a different isocyanate that resulted in a softer
material that was designed to allow more tolerance for tearing stress. This formulation
was used in Series 5 of the push-off specimens.
4.1.5. Test Variables
In addition to the different formulations of polyurethane, other variables and
parameters that could influence the bond strength of the adhesive connection were
examined. The specimens were divided in four series and each series was fabricated after
the previous series of specimens had been tested. This allowed modifications to the test
matrix and introduction of new variables as more insights were provided from the testing
of each series. The first series, consisted of three specimens, explored the pouring method,
77
surface treatment, shrinkage in the polyurethane, and the temperature at which the
polyurethane was poured. The second series, with four specimens, examined the effect of
elevated specimen temperature when pouring the polyurethane and introduced a new type
of formwork for the cavity. The third series, consisted of three specimens, modified the
surface treatment of the steel girders. The fourth series introduced a primer and various
additives, including the polyol and the wetting agents. Lastly, the fifth series examined a
new type of polyurethane elastomer formulation. The following sections will discuss
these variables in details.
Two important surface treatments were kept common in all the specimens. Firstly,
the surfaces of all the concrete slabs that adhered to the polyurethane layer were
roughened, with exposed aggregates, because it would allow mechanical interlocking
between the adhesive and the concrete slab. Secondly, all the flanges of the steel girders
were sandblasted to ensure that the surfaces were free of rust and other surface
contaminants. This had to be done at maximum twenty-four hours before the pouring of
the polyurethane to avoid oxidation of the sandblasted surfaces.
Pouring Method
The first series consisted of three specimens that were used to explore some of the
insights obtained from the pilot investigation by Ramsay (2007). First of all, since the
turbulence, which was caused by the injection of the polyurethane through the machine at
a high pressure was hypothesized as the main cause of the foam and air bubbles in the
polyurethane layer in the pilot testing, the polyurethane adhesive was to be hand-mixed
and manually poured into the cavity of the new specimens. This eliminated all the air
bubbles and foam in the polyurethane layer in the hardened state.
78
Temperature of Substrates
The formation of the polyurethane is an exothermic reaction and substrates at a
low temperature would act as a heat sink that could greatly affect the curing of the
polyurethane near the surfaces. Initially when the first series was being fabricated, the
specimens were kept in an oven prior to the polyurethane pour so the temperature of
specimens would be at approximately 37 oC. This was the minimum temperature required
for the proper curing of the polyurethane elastomer (Gardin, 2007). However, as will be
discussed in Chapter 5, unexpected bonding problems between the polyurethane and steel
girder led to the realization that a higher temperature might be necessary for proper
bonding between the polyurethane and the steel surface. The temperature of the
specimens was then elevated to 50 oC for in the latter series with the goal to achieve
better adhesion to the steel girder.
Shrinkage The effects of shrinkage in the polyurethane on the bond strength were explored
through the different formulations. As the bond layer shrinks, the expected volume of
polyurethane in the cavity would be lower than expected. Since the wooden formwork
used to create the cavity is incompressible, the intimate contact required between the
polyurethane and the substrates might be lost. Shrinkage is addressed by using a
formulation with negligible shrinkage, and a compressible form that would allow the
polyurethane to be under constant compression.
79
Compressible Formwork and Clamping Force
One of the hypotheses for the cause of the premature bond failure in the pilot
testing by Ramsay (2007) is the pressure force generated in the chemical reaction of the
polyurethane that might have lifted the concrete slab slightly. A proposed solution to this
problem is the use of a compressible polyurethane formwork instead of wood. This
compressible formwork would allow the polyurethane layer to cure under compression
due to the self weight of the concrete slab. This not only could solve the potential
problem of the concrete slab being lifted, but it could also solve other contact problems
caused by shrinkage or occasional small leakage during the pour. The polyurethane used
as the formwork has very different properties of that used as the adhesive and the
dimensions of the forms are identical to that of the wooden forms. Figure 4.6 shows the
compressible polyurethane used in place of the wooden formwork.
Figure 4.6: Polyurethane Compressible Form
80
An alternative solution was proposed to address the problem that could have been
caused by the pressure from the curing process of the polyurethane. A clamping force
was applied to the concrete slab and the steel girder as the polyurethane layer cured to
restrain any movement in the concrete slab and prevent any potential lifting. This was
achieved by fixing each corner of the slab to the flange of the steel girder a C-Clamp.
Surface Treatment
As already discussed, all the steel girders were sandblasted twenty-four hours
before the pouring of the polyurethane to remove any existing rust and contaminants.
Given previous experience of adhering polyurethane to steel, the sandblasting was
thought to be sufficient to provide a contaminant-free surface for appropriate adhesion.
However, as will be discussed further in Chapter 5, the consistent bond failures at the
steel interfaces suggested that the polyurethane was not adhering properly to the steel
surface. Therefore, different steel surface treatments were explored in the third and fourth
series of specimens.
In addition to the sandblasting, an acetone solvent was used to clean the steel
surfaces of the specimens fabricated in the fourth series. The surfaces were either only
washed once with the acetone solvent prior to the sandblasting; or twice, before and after
the sandblasting. Furthermore, the effect of using a primer to promote better adhesion of
the polyurethane adhesive to the steel surfaces was also studied. A primer was applied to
the specimens in series four and five series with two acetone solvent wash preceding and
following the sandblasting.
81
4.1.6. List of Specimens and Variables
Table 4.2 lists the sixteen specimens and the variables associated with each one. As
shown in the table, three specimens were fabricated in series one, four in series two, three
in series three and the rest in series four.
Table 4.2: List of Specimens and Corresponding Variables
Series Specimen Polyurethane Formulation
Steel Surface Treatment
Temperature at Pour (oC) Other Variables
1-1 CAE 2-3a SB 37 1-2 CAE 2-1 SB 37 1 1-3 CAE 1-1 SB 37 2-1 CAE 1-1 SB 50 2-2 CAE 2-1 SB 50 2-3 CAE 2-3a SB 50
2
2-4 CAE 2-3a SB 50 Clamped 3-1 CAE 1-1 SB, AW1 50 3-2 CAE 1-1 SB, AW2 50 3 3-3 CAE 1-1 SB, AW2 50 PU Formwork 4-1 CAE 2-3a1 Primer 50 4-2 CAE 2-3a2 Primer 50 4-3 CAE 2-3a1 Primer 50 4-4 CAE 2-3a2 Primer 50 4-5 CAE 2-3a2 SB, AW2 50
4
4-6 CAE 2-3a2 SB, AW2, Primer
50
5-1 CAE 1-3 SB, AW2, Primer 50
5-2 CAE 1-9 SB, AW2, Primer 50 5
5-3 CAE 1-10 SB, AW2,
Primer 50 Note: SB - Sandblasting
AW1 - One acetone solvent wash prior to sandblasting AW2 - Acetone solvent wash before and after sandblasting PU - Compressible polyurethane material Primer - Prime applied to steel beams to enhance bonding
82
4.1.7. Push-Out Test Setup and Instrumentation
The test-setup is shown in Figure 4.7. Since the steel beams were adhered flush to
the concrete slabs, the specimens had to be rested on two steel blocks, measured 200 x 60
x 80 mm, to allow room for the steel girder to displace. Furthermore, in order to
minimize the resultant horizontal forces acting on the adhesive joint that would cause
undesirable peeling stresses at the interfaces, two rectangular steel blocks were placed
directly on the top of the steel flanges so the load could be applied directly to the
adhesive joint.
Figure 4.7: Experimental Test Setup
83
Figure 4.8: Riehle Machine, University of Toronto
Figure 4.9: Location of LVDT
84
The applied load was measured by a load cell and the displacements of the steel
girders were recorded by two Linear Variable Differential Transformers (LVDT). The
relative displacements between the magnetic steel plates attached to the steel beam at the
bottom right corner of each side of the web to the floor were measured, as shown in
Figures 4.7 and 4.9. Each specimen was loaded up to failure without any unloading at a
rate of approximately 0.50 kN per seconds. Due to the sensitivity of the adhesive joint to
peeling stresses, the following preparation and loading procedures were used to prevent
any uneven loading that could cause rotation in the steel girder:
Preparation
1. Ensure the top of the steel girder has a flat surface for the load cell to rest on and
any caulking should be removed.
2. Prepare plastic for the plastering at the base of the concrete slabs on the steel
blocks. The size of the plastic should be approximately 100mm x 400mm. The
plastic should be wrapped around the base of the concrete immediately after the
plaster is poured and precautions must be made to ensure that the plaster/plastic
will not interfere with the polyurethane layer and the steel girder during the test.
Testing
1. Center the specimen to the load cell
2. Setup the LVDT at the bottom right corners on each face of the girder web. The
LVDT should rest on clamps on magnetic stands and should be in compression
for the test.
85
3. Center the rectangular steel blocks onto the flanges of the girder. This ensures that
load is applied directly to the shear connections. Shimming might be necessary to
ensure that the rectangular blocks are resting completely on the flanges.
4. Load the specimens to failure at a rate of approximately 100 lb/sec (0.445kN/ sec).
Displacements of the girder should be noted every 1000 lb (4.451 kN).
5. At failure, note the failure mode, failure surface, and any rotation that might have
occurred.
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CHAPTER 5: TEST RESULT AND DISCUSSIONS
After the polyurethane had completely cured at approximately seven days after
the day of pour, the push-off tests specimens were tested and the load-deflection
behaviour was recorded for each specimen with the exception for the first three
specimens. This chapter presents the results from the push-off tests and summarizes the
failure mode and the failure surface for each specimen. The effects of the variables in
each set of tests on the adhesive joint are then discussed in their respective sections. The
estimation of the stiffness of the polyurethane adhesive joint from the load-deflection
plots is then provided.
5.1. Ultimate Load and Deflection
The ultimate loads and the deflections at failure recorded from the push-out tests
are summarized in Table 5.1. Cohesion failure refers to material failures in either the
concrete or within the polyurethane layer and the load-slip behaviour of the connection is
usually ductile. Bond failure refers to brittle failure at the interface between the
polyurethane and the concrete or steel. The ultimate load at each adhesive bond was
taken as half of the applied load and the ultimate shear stresses were calculated from the
as-built dimensions of the polyurethane layer. The displacement at failure is the
displacement of the steel girder taken as the average between the two LVDT sensors.
Failure surface “a” denotes that it failed on the side that was poured first, and “b” denotes
the side that was poured second. This was noted to study the possible effect of the
temperature increase of the steel girders on the curing of the second polyurethane layer as
the first layer cured and released heat from the exothermic chemical reaction.
87
Table 5.1: Results from the Push-Off Tests
Series Specimen Nominal PU Area (mm2)
Peak Load (kN)
Peak Stress (MPa)
Slip at Failure (mm)
Failure Mode
Failure Surface (a or b)
1-1 14400 13.2 0.92 N/A Bond Steel (b)
1-2 14400 24.2 1.68 N/A Bond Steel (b) 1
1-3 14400 13.2 0.92 N/A Bond Steel (b)
2-1 14900 20.8 1.39 2.50 Cohesion Concrete (b)
2-2 14600 18.5 1.29 0.34 Bond Steel (b)
2-3 14900 18.0 1.21 N/A Bond Steel (b) 2
2-4 14470 18.2 1.26 1.88 Bond Steel (b)
3-1 N/A
3-2 14560 16.8 1.65 1.75 Bond Steel (b) 3
3-3 13560 27.8 2.05 1.25 Bond Steel (b)
4-1 14500 26.5 1.94 0.64 Bond Steel (b)
4-2 14600 15.0 1.11 0.54 Bond Steel (b)
4-3 14600 35.0 2.43 0.58 Bond Steel (b)
4-4 14500 26.0 1.46 0.66 Bond Steel (b)
4-5 14600 26.5 1.82 2.29 Cohesion Steel (b)
4
4-6 14400 20.5 1.92 2.94 Cohesion Steel (b)
5-1 14400 42.5 2.91 1.68 Cohesion Concrete (b)
5-2 14400 50.5 3.51 3.08 Cohesion Concrete (a) 5
5-3 14600 23.5 1.55 3.55 Cohesion Concrete (b)
88
5.2. Results and Discussion
The following sections will demonstrate the successful development of a
polyurethane formulation and the necessary surface treatment for an adequate adhesively
bonded shear connection. The results from each series will be presented and a discussion
of the effects of the variables studied in each series will also be given in their respective
section.
5.2.1. Series One Specimens 1-1, 1-2 and 1-3 were tested to explore the effects of shrinkage on the
adhesion of the polyurethane to the substrates between the three different formulations of
polyurethane CAE 1-1, 2-1 and 2-3a. For this purpose, the displacement of the steel
girder was not measured. The polyurethane layers in all the specimens were manually
mixed and poured, as opposed to being mixed in a machine and injected at a high
pressure. The resulting polyurethane layer cured properly without any visible bubbles or
foam that was present in the specimens of the pilot testing by Ramsay (2007).
a. b.
Figure 5.1: a) Visible Shrinkage in Specimen 1-1, b) Reduced Shrinkage in Specimen 1-3
89
As shown in Figures 5.1, the shrinkage of the polyurethane was visible in
specimen 1-1 and no visible shrinkage was observed in specimen 1-3. The shrinkage,
however, did not appear to be the cause of the failure. All three specimens failed in a
brittle manner and the failure load did not correlate with the shrinkage level represented
by each specimen. The surface of steel flanges after the specimen had failed, as seen in
Figure 5.1, showed that there was a lack of adhesion between the polyurethane and steel
surface in all three specimens. The steel surfaces were clean, which demonstrated that the
polyurethane was not adhering to the surface at all. All the failures happened at the
steel/polyurethane interface in all three specimens (Gardin, 2007). The reason behind the
unsatisfactory adhesion that caused the premature bond failure was not clear, but Gardin
(2007) suggested that the temperature of the specimens at the time of the polyurethane
pour could be elevated to 50 oC to promote better curing at the steel surface due to the
exothermic nature of the formation of the polyurethane. The exertion of pressure from the
polyurethane onto the concrete slab could also have lifted it slightly, allowing air to stay
in the cavity during the pour. Lastly, small leakages during the polyurethane pour, which
was thought to be negligible, might have promoted additional air voids in the cavity.
5.2.2. Series Two
Four specimens, 2-1 to 2-4, were fabricated in series two with the goal to
investigate the possibility of promoting better adhesion between the steel girders and the
polyurethane at an elevated temperature of 50oC when the polyurethane was poured. The
effect of manually clamping the specimen was also examined with Specimen 2-4.
90
Figure 5.2: Leakage Caused by Expansion of Polyurethane
Unexpected expansion in Specimen 2-1 occurred during the curing of the
polyurethane, as shown in Figure 5.2. The expansion was large enough that the concrete
slab was detached from the wooden formwork and resulted in observable leakage.
However, the leakage did not result in a significant net loss of polyurethane and the
contact between the polyurethane and the substrates were still adequate, therefore, the
testing proceeded despite of a slight distortion in the geometry of the polyurethane layer –
The layer was approximately 3mm thicker at near the bottom of the specimen than the
other end.
The load-displacement behaviour from the push-off tests of 2-1, 2-2 and 2-4 are
presented in Figure 5.3. An error occured in the LVDT setup during the test of Specimen
2-3 and the displacement of the steel beam could not be recorded, however, specimen 2-3
appeared to have a similar behaviour as Specimen 2-4.
91
Shear Stress vs. Average Girder Displacement
0
0.125
0.25
0.375
0.5
0.625
0.75
0.875
1
1.125
1.25
1.375
1.5
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25
Average Girder Displacement (mm)
Shea
r Str
ess
(MPa
)
Specimen 2-1Specimen 2-2Specimen 2-4
Figure 7 5.3: Shear Stress vs. Average Girder Displacement for Series 2.
Specimen 2-2 and 2-4 failed in a brittle manner with bond failures at the steel
surfaces similar to those in series one. The excessive initial deflection readings in
specimen 2-4 could have been caused by the initial settlement of the plaster at the base
and the shimming at the loading blocks. Furthermore, clamping of specimen 2-4 did not
appear to have improved the bonding of the polyurethane to the steel. Contrarily, despite
the expansion of the polyurethane and the leakage, specimen 2-1 exhibited ductile
behaviour and the displacement of the girder at failure was approximately 2.50 mm. The
adhesive connection sustained a peak load of 42 kN, which corresponded to a shear stress
of approximately 1.4 MPa at each joint. The failure plane of specimen 2-1 is shown in
Figure 5.4. As can be seen, the failure did not happen at the steel interface, but rather, it
was a cohesion failure in the polyurethane near the concrete roughened surface.
92
(a) (b)
Figure 5.4: Failure Surfaces of Specimen 2-1 a) Polyurethane Layer; b) Concrete Slab
Although the peak stress was lower than the expected stress of at least 5 MPa, the
ductile behaviour of specimen 2-1 suggests that satisfactory bonding between the
polyurethane and the substrates can be achieved. The unexpected expansion of the
polyurethane, which used the CAE 1-1 formulation that has a thirty minutes curing time,
might have encouraged more intimate contact between the polyurethane and the
substrates, and resulted in better adhesions.
5.2.3. Series Three
Three specimens, 3-1 to 3-3 were fabricated in the third series of the push-off
tests. However, the polyurethane did not cure properly in specimen 3-1, as seen in Figure
5.5, and the concrete slab was detached from the polyurethane layer during the
93
disassembly of the formwork. The polyurethane was still soft and had a viscosity similar
to honey. This might have been caused by either an error in the proportioning of the resin
and the isocyanate or an error in the mixing of the two components. Specimen 3-1,
therefore, could not be tested.
Figure 5.3: Improper Curing of the Polyurethane in Specimen 3-1
All of the specimens in this series were washed with an acetone solvent either
once before the sandblasting as in the case for specimen 3-1 or twice, before and after the
sandblasting, which was done for specimens 3-2 and 3-3. Unfortunately the difference
between one and two acetone wash could not be compared because of the improper
curing of the polyurethane in 3-1. The specimens, however, could be compared to the
results from series two to determine the effects of the acetone solvent wash to the bond
strength. Furthermore, the polyurethane layer in specimen 3-3 was poured in a
compressible polyurethane form that allowed the layer to be compressed under the self
weight of concrete as it cured. Similar to specimen 2-1, the slow-curing formulation of
polyurethane was used in specimen 3-3 and it expanded during the cure. The concrete
slab was partially detached from the polyurethane form and leakage occurred.
94
The load-displacement plots from the push-out tests of specimens 3-2 and 3-3 are
presented in Figure 5.6. The plots from specimens 2-1, 2-2 and 2-4 are also provided in
dotted lines for comparison purposes. As can be seen, both specimens 3-2 and 3-3
Shear Stress vs. Average Displacement
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25
Average Girder Displacement (mm)
Shea
r Str
ess
(MPa
)
Specimen 2-1Specimen 2-2Specimen 2-4Specimen 3-2Specimen 3-3
Figure 5.6: Shear Stress vs. Average Girder Displacement for Series 3
exhibited brittle behaviour and the failure happened in the bond between the polyurethane
and the steel. The failure surface of specimen 3-3 is shown in Figure 5.7. As the figure
shows, the leakage caused the flexible polyurethane form to distort and the contact area
between the polyurethane and the steel was reduced by approximately 10%. However,
plot shows that the specimen 3-3 has reached a peak load of 56 kN, which corresponds to
a peak stress of 2.05 MPa at each adhesive joint before failure occurred.
95
Figure 5.7: Polyurethane Layer in Specimen 3-3 with PU form
5.2.4. Series Four
Six specimens, 4-1 to 4-6 were fabricated in series four of the push-out tests. The
effects of using a primer on the steel surfaces were examined. A primer, a bonding agent
commonly used to promote better adhesion between two materials, was applied to all of
the steel surfaces in this series to promote better adhesion to the polyurethane. Different
chemical additives were also mixed into the basic formulation of CAE 2-3a in different
specimens to assist in adhesion of the polyurethane to the substrates. All of the specimens
were washed with the acetone solvent before and after the sandblasting of the steel
surfaces.
The results of the push-out tests in series four is presented in Figure 5.8. First of
all, as can been seen from the plots, specimens 4-1 to 4-4 exhibited brittle behaviour with
peak load ranging from 32 kN to 70kN; specimens 4-5 and 4-6 exhibited ductile
behaviour with a peak load of approximately 53 kN and 41 kN, respectively. Specimens
96
Shear Stress Vs. Average Displacement
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25
Average Girder Displacement (mm)
Shea
r Str
ess
(MPa
)
Specimen 4-6Specimen 4-5Specimen 4-4Specimen 4-3Specimen 4-2Specimen 4-1
Figure 5.8: Shear Stress vs. Average Displacement for Series Four.
Figure 5.9: Specimen 4-6 at Failure
97
4-5 and 4-6 experienced similar cohesion failures in the polyurethane, as shown in Figure
5.9. The failure began near the bottom of the steel girder and progressed slowly along the
flange, resulting in a slow and ductile failure. Although specimen 4-3 behaved in a brittle
manner, the connection yielded the greatest shear stiffness value and it sustained the
highest load among all specimens – 70kN, which corresponds to a shear stress of around
2.9 MPa. The low failure load – 32 kN, of specimen 4-2 could be a result of the high
moisture content of the resin and the isocyanate at the time of mixing that prevented the
proper curing of the polyurethane.
The results from the push-out tests in this series are encouraging because results
of specimens 4-5 and 4-6 further suggest that sufficient adhesion can be promoted in the
steel surface to allow a ductile behaviour in the adhesion joint. Despite of the brittle
failure, results of specimen 4-3 have demonstrated that the adhesive joint is capable of
achieving a shear stress of 2.5 MPa.
5.2.5. Series Five
Three specimens, 5-1 to 5-3 were fabricated for the last series of tests in the
experimental program. A different polyurethane formulation with three slight variations
was used in this series – namely CAE 1-3, CAE 1-9, and CAE 1-10. The basic
formulation used a different isocyanate than the one used in the previous series to form
the two-parts polyurethane. The formulation was also varied by adding different additives,
namely a wetting agent and a polyol additive, to the polyurethane with the goal to
promote better adhesion. Generally, the resulting polyurethane should have a similar
stiffness value, but it should allow a greater elongation compared to the polyurethane
98
used in the previous series (Gardin, 2007). The new softer formulation was made to
investigate the possibility of preventing brittle failure by allowing more shear
deformation in the polyurethane layer and more deformation due to tearing stress.
The load-deflection plot from series five is shown in Figure 5.10. All three
connections exhibited ductile behaviour with failures in the cohesion of the polyurethane,
shown in Figure 5.11. Peak stresses of 2.9 MPa, 3.5 MPa, and 1.7MPa were reached,
respectively in specimens 5-1 to 5-3. The post-peak deformation shown in the load-
deflection plot of specimens 5-1 and 5-3 before failure was unprecedented in the previous
series. This could be an indication that the polyurethane might have yielded and have
undergone plastic deformation before reaching failure in cohesion. Furthermore, the non-
linear characteristic shown in the plot of specimen 5-1 suggests a constant redistribution
of load in the polyurethane layer.
Shear Stress vs. Average Displacement
0
0.5
1
1.5
2
2.5
3
3.5
4
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8
Average Girder Displacement (mm)
Shea
r Str
ess
(MPa
)
Specimen 5-1Specimen 5-2Specimen 5-3
Figure 5.10: Shear Stress vs. Average Displacement for Series Five.
99
Figure 5.11: Specimen 5-1 at Failure
This last series of test has yielded agreeable results that suggest the use of a
polyurethane adhesive as the shear connection in composite bridges might be viable. First
of all, the result from specimen 5-2 indicates that the connection could sustain a
maximum shear stress of 3.5 MPa, which met the criteria as outlined in Chapter 3.
Secondly, although the connection of specimen 5-1 attained a maximum shear stress of
only 2.9 MPa that is lower than that required by the criteria, the behaviour was ductile
with plastic deformation in the polyurethane layer followed by a failure in cohesion,
which is usually desirable in the design of shear connections that do not have sufficient
bond strength. The inconsistency among the results of the three specimens could have
been caused by the different additives used in the formulations, or an imperfection in the
geometry of the test setup resulting in possible rotation during the test, which could
significantly affect the characteristic of the connection as the adhesive is very sensitive to
peeling stresses. Nevertheless, the required stress value of 3MPa as outlined by the
criteria has been met.
100
5.3. Shear Stiffness of the Adhesive Connection
As discussed in Chapter 2, the definitions of the shear stiffness from the load-slip
plot are not unified among researchers (Wang, 1998). If the behaviour of a shear
connector is linear, the shear stiffness of the connection can usually be defined as the
tangent stiffness of the load-slip plot. However, when a shear connection exhibits ductile
behaviour characterized by a nonlinear load-slip plot, the tangent stiffness would not
realistically represent the stiffness of the connection, and the secant stiffness must be
used instead. Generally, the shear connections tested in this study exhibited linear
elastically behaviour, therefore, the stiffness of the connection is taken as the tangent
stiffness, Ktangent, as determined from the load-slip plots. Table 5.2 summarizes the
stiffness of the adhesive joints tested. The area stiffness k [N/mm2] is calculated by
dividing the Ktangent by the length of the bond, which is taken as 160mm for all the
specimens. This value is important for the application of the partial interaction theory that
will be outlined in the Chapter 6.
101
Table 5.2: Stiffness of Polyurethane Adhesive Joints
Series Specimen *Ktangent (N/mm) x103 *k (N/mm2)
2-1 20 125
2-2 46 288 2
2-4 10 62.5
3-2 35 188 3
3-3 12 75.0
4-1 48 300
4-2 32 200
4-3 70 438
4-4 36 225
4-5 34 188
4
4-6 35 188
5-1 43 269
5-2 50 313 5
5-3 28 175
*intjo
KkL
= and Ktangent is the slope of the load-slip plot, as shown:
Load - Slip Plot
0
10
20
30
40
50
60
70
80
90
0 0.5 1 1.5 2 2.5 3 3.5
Slip (mm)
Load
(kN
)
Ktangent
102
CHAPTER 6: ANALYTICAL PROGRAM
The goal of the analytical component of this research project is to investigate the
feasibility of using the polyurethane adhesive developed in the experimental program as a
mean of shear connection in concrete-steel composite bridges. The analytical program is
designed to verify the proposed criteria discussed in Chapter 2 for the minimum adhesive
bond strength and stiffness required to implement the adhesive as an efficient shear
connection in composite bridges. As discussed in Chapter 2, the adhesive bond must have
sufficient strength so that the adhesive joint will not fail under loading in the ultimate
limit state and, at the same time, the adhesive must have sufficient stiffness to minimize
any additional deflection due to the slip between the concrete deck and steel girders under
loading in the serviceability limit states. Numerical analyses are used to verify that the
polyurethane adhesive developed in the experimental program has sufficient bond
strength and stiffness to meet the criteria.
The chapter begins with a brief review of the full interaction and no interaction
analysis followed by a discussion of the partial interaction theory of composite beams
proposed by Girhammar and Gopu (1993). The behaviour of ten bridges designed for
spans of 25m, 50m, and 75m under the serviceability limit state will then be investigated
and discussed based on the theories by Girhammar and Gopu (1993) and a computer
analysis by SAP2000™. The behaviour of the bridges under the ultimate limit state will
then be analyzed using a rigid plastic analysis as outlined by Oehlers and Bradford (1995).
The chapter concludes with an outline of the criteria for the minimum strength and
stiffness of the polyurethane adhesive based on the results of the numerical analyses
under both limit states.
103
6.1. Degree of Interaction in Composite Beams As already discussed in Chapter 3, composite beams can have various degrees of
interaction between the two composite components. The degree of interaction in a
conventional composite bridge with mechanical connectors is dependent on the stiffness
of the shear connection, k, which is calculated by dividing the individual connector
stiffness, Ktangent, by the spacing between the connectors, Ls. A similar analogy can be
applied to adhesively bonded shear connections, in which the shear connection stiffness
can be defined as the stiffness of the adhesive joint divided by the bond length, Ljoint, as
shown in Figure 6.1. As previously mentioned, when K approaches infinity, the shear
connection is stiff enough that a full interaction between the two materials can be
achieved. This is characterized by a linear distribution of strains along the whole cross
section at any distance, x, along the beam, as discussed in Chapter 3. When K approaches
zero, the beam is described as having no interaction between the two materials. In reality,
a composite beam can never be fully composite or completely non-composite, in another
word, the value of K is always between zero and infinity, and the subcomponents are
described as having partial interaction. Partial interaction is characterized by a slip, ∆u,
between the two composite materials, and the strain distribution along the cross-
L jointL s
a. b. Figure 6.1: Length used to determine connection stiffness, k – a) Connector Spacing, Ls; b) Length of Joint, Ljoint
104
section is characterized by individual linear distributions along each composite material
with a break at the shear connection, the difference in strain at the shear connection is
referred as the as the slip strain, ds/dx or ∆u’.
In practice, when headed shear connectors are used, the connectors would be
spaced close enough to allow a full interaction between the two composite elements.
Designers would usually provide sufficient shear connectors to avoid the complexity of a
partial interaction analysis. However, in the case of an adhesively bonded connection,
the strength and stiffness of the bond depends on the properties of the adhesive and the
width and thickness of the adhesive joint.
In the case where the strength of the composite beam is dictated by the strength of
the shear connection, the beam is referred to as having partial shear connection, and a
partial interaction analysis must be used to study the exact behaviour of the beam. As will
be discussed further, the simple rigid plastic analysis outlined by Oehlers and Bradford
(1995) can be used to determine the ultimate flexural strength of the composite section
under the ultimate limit state. The analysis by Oehlers and Bradford (1995) is simple
because the concrete deck and the steel girder are assumed to have reached their plastic
capacity, therefore, the distribution of forces within the composite section is known.
However, when the beam is subjected to service loads and the elements in the section
remain elastic, the distribution of strains and forces within the cross-section will not be
obvious. The use of partial interaction analysis to determine the maximum deflection of a
partially composite beam under serviceability limit state requires more a complicated
analysis that often involves complex closed-form solutions. Guidelines, such as the
Eurocode (1994), usually recommend a simpler approach by using an empirical formula
105
to determine the deflection of a concrete-steel composite beam with partial shear
connection. An example of such formula as outlined by the Eurocode (1994) is shown in
Equation 6.1,
wp = wf + α ( wo - wf) (1- η) Eq. 6.1
where wp, wo and wf represent the deflection of the beam with partial interaction, no
interaction, and full interaction respectively. η is referred to as the degree of shear
connection, and is determined by the ratio of the shear connection strength to the required
shear connection strength for full composite interaction between the materials. α is a
value less than unity that is empirically determined by experimental data, and values of
around 0.4 are recommended by the Eurocode for the use of shear studs.
Although Equation 6.1 can be used to estimate the increase in deflection due the
slip between the concrete section and the steel section, the equation does not demonstrate
the actual behaviour of the beam under service loads. The study of the partial interaction
behaviour in composite beams is well documented, in fact, one of the first theories of
incomplete interaction in composite beams dates back to as early as 1951, by Newmark et
al. The theory developed was derived based on several assumptions: 1) the shear
connection is continuous; 2) the amount of slip of the connector is proportional to the
shear force transmitted; 3) the behaviour of all the individual components of the
composite beam is linear elastic; and 4) the curvature and vertical deflection of both
components of the composite beam are the same. In addition to the research study by
Newmark et al. (1951), Granholm (1949) also conducted a study on beams with partial
106
composite action, which was based on similar assumptions and resulted in similar
second-order differential equations, of which the solutions showed that the total
deflection of a beam with incomplete interaction is the sum of the deflection of the
corresponding beam with full interaction plus an additional deflection due to slip.
Numerous studies on partial interaction behaviour have been conducted since (Example:
Girhammar & Gopu, 1993; Wang, 1998; Seracino et al. 2000), and a recent study based
on similar assumptions conducted by Girhammar and Gopu (1993) have provided closed-
form solutions to the second-order differential equations. The following sections will
outline the theory proposed by Girhammar and Gopu (1993) and its application in the
analytical program to determine the behaviour of composite bridges connected with the
polyurethane adhesive developed in the experimental program.
Prior to understanding the analysis outlined by Girhammar and Gopu (1993), the
analyses used to predict the behaviour of the composite beams with full interaction and
no interaction should be understood, since they are the upper and lower bounds of the
solutions to beams with partial interaction. The discussion in the following sections is
based on a composite section, shown schematically in Figures 6.3, that the analysis by
Girhammar and Gopu (1993) was developed for. The cg,f represents the neutral axis of
the composite section with full interaction. Each subcomponent i, where i = 1 or 2 in the
case shown in Figure 6.2, has a corresponding Young’s modulus Ei, Moment of Inertia, Ii.
and cross-sectional area Ai. bi and hi represents the width and height of each component.
ri represents the distance between the centroid of each component to the shear connection,
and r is the distance between the centroid of the two elements.
107
1
2
b1
h1
h2
b2
cg, 1
cg, 2
r1
r2r
zcg,
r - zcg,
cg, f
f
f
Figure 6.2: Schematic Composite Section in Partial Interaction Analysis (Picture taken from Girhammar & Gopu, 1993)
cg,∞
z, w
x, u
q
L
Figure 6.3: Uniformly Distributed Load Acting on the Composite Beam (Picture taken from Girhammar & Gopu, 1993)
In the case where conventional mechanical shear connectors are used, r is simply:
Eq. 6.2
If the two components are connected by an adhesive layer with thickness, t, r should
be taken as:
trrr ++= 21 Eq. 6.3
21 rrr +=
108
6.1.1. Full Interaction Analysis in Composite Beams To analyze the behaviour of the beam when the shear connectors are strong
enough to allow full interaction, one of the components needs to be transformed into an
equivalent section of the material of the other component. This can be achieved by
dividing the width of its section by the modular ratio n, where n is ratio of the Young’s
Modulus, Ei, of the two components. For example, in the cross section shown in Figure
6.2, Section 1 can be transformed into an equivalent section of the material in Section 2
by dividing b1 by n, where n is the ratio of E2 to E1, shown in Equation 6.4:
1
2
EEn = Eq. 6.4
Based on the equivalent section, the section properties can be re-evaluated and the
deflection of a simply supported beam, under uniformly distributed load as shown in
Figure 6.3, can be predicted by Equation 6.5:
45
384ff
qLwEI
= Eq. 6.5
where q is the magnitude of the distributed load, L is the span, and (EI)f is the stiffness of
the transformed section with full interaction. As already discussed, this prediction serves
as the upper bound of the deflection of composite beams with only partial interaction.
The distributions of strains under service loads can be assumed to be linear along the
whole cross-section and the stresses in each subcomponent can be evaluated accordingly
based on the equilibrium of forces.
109
6.1.2. No Interaction Analysis in Composite Beams In the case when there is no interaction between the two composite elements, the
applied load is simply distributed to each section according to their corresponding
stiffness. Therefore, an applied load, q, can be proportioned to section 1 and 2 according
to Equation 6.6 and 6.7:
( )
1 11
0
E Iq qEI
= Eq. 6.6
( )
2 22
0
E Iq qEI
= Eq. 6.7
where,
( ) 1 1 2 20EI E I E I= + Eq. 6.8
The deflection of the beam with no interaction can then be estimated by:
4
20
2 2
5384
q LwE I
= Eq. 6.9
Often when Section 1 is a concrete slab and Section 2 is a steel beam, as in the
case in this study, all the loads are assumed to be taken by the steel section since most of
the concrete section will be cracked under bending, as demonstrated by Oehlers &
Bradford (1995). Contrary to the case with full interaction, the deflection of the beam
with no interaction serves as the lower bound to the deflection with only partial
interaction.
110
6.1.3. Partial Interaction Analysis of Composite Beam by Girhammar and Gopu (1993)
The study conducted by Girhammar and Gopu (1993) provides closed-form
solutions to the displacement functions and the internal forces of simply supported
composite beams with interlayer slip under a distributed load. Similar to the analyses by
Newmark et al. (1951) and Granholm (1949), the equations are designed for conventional
mechanical shear connectors, but the stiffness of discrete connectors are assumed to be
distributed uniformly along the length of the member. This assumption allows the
application of the analysis to be extended to adhesive bonds that provide a continuous
shear connection. Furthermore, Girhammar and Gopu (1993) also assumed that:
1) The relative slip is small and it occurs at the interface of the two
components
2) Any friction and uplift between the subcomponents are ignored. As a
result, the curvature of the subcomponents is assumed to be equal;
3) The load-slip behaviour of the shear connectors is assumed to be linear
elastic, therefore, the slip modulus k (N/m2) is assumed to be constant;
4) The behaviours of the constituent materials are linearly elastic and the
assumption that plane sections remain plane still applies to the individual
components of the beam.
The analysis by Girhammar and Gopu (1993) also extends to include the effect of
an applied axial load on the beam, and outlines a second-order analysis that takes into
111
account the P-Delta effect of the axial load on the beam. This, however, is beyond the
scope of the current study, so only the first-order analysis of their study will be adopted.
Consider a differential element, shown in Figure 6.4, of a composite beam
subjected to a uniformly distributed load q. The internal forces, including bending
moment, the vertical shear, axial force, and the slip force per unit length, which is often
referred as the shear flow, are denoted by Mi, Vi, Ni and Vs, respectively, where i = 1 or 2
denotes the subcomponent. The applied force, F, is taken as zero for all the analyses in
this study. The first and second derivative of the deflection, w, of the beam at any
distance x along the beam is often referred as the rotation and the curvature, respectively.
1d1 VV +
2d2 VV +
1d1 NN +1d1 MM +
2d2 MM +
2d2 NN +
sV
1V
2V
1N
1M
2N
2M
xd
q(x)
'w
' ' 'w w dx+
,cg
, 2cg
, 1cg
,cgz
x
MV
M dM+
V dV+
N F
N F
f
f
Figure 6.4: Differential Element in a Composite Beam Subjected to an Axial Load, F, and a Uniformly Distributed Load, q(x) (Girhammar & Gopu, 1993)
Since Girhammar and Copu (1993) assumed that all the materials in the analysis
behave linear elastically, the theory is based on a constant shear connection area stiffness,
k [N/mm2], which should not be confused with the individual shear connector stiffness, K
112
[N/mm]. K is usually obtained from push-off tests, as described in Chapter 3, and usually
taken as the tangent stiffness.
Based on this stiffness, Girhammar and Gopu (1993) analyzed the behaviour of
the beam with partial interaction based on the following equations from equilibrium of
internal and external forces:
21 NN −= Eq. 6.10
21 VVV += Eq. 6.11
rNMMM 121 −+= Eq. 6.12
rwuuu ′+−=∆ 21 Eq. 6.13
rwu ′′+−=′∆ 21 εε Eq. 6.14
where u is the individual horizontal displacement of each component and ∆u is the
relative slip between the two components. u′∆ represents the difference in strain at the
shear interface, which more commonly referred as the slip strain. The first and second
derivative of the vertical deflection, w, denoted by w′and w ′′ , represent the rotation and
curvature of the beams, respectively.
The analysis by Girhammar and Gopu (1993) has yielded the following governing
differential equation in terms of the displacement function, w:
0
22
EIM
EIMww
f
IV ′′−=′′− αα Eq. 6.15
where α is a shear connection stiffness parameter defined as:
( )( ) ( )
22 0
0p
EA rKEA EI
α⎛ ⎞⎜ ⎟= +⎜ ⎟⎝ ⎠
Eq. 6.16
113
and,
( ) 1 1 2 20EA E A E A= + Eq. 6.17
( ) 1 1 2 2pEA E A E A= ∗ Eq. 6.18
Girhammer and Gopu (1993) have solved the differential equation and provided the
general equation for the deflection, at any distance x along the beam, for a simply
supported beam with partial composite action, subjected to a uniformly distributed load, q,
shown in Equation 6.19:
( )
( )( )
( )
4 3 30 04
0
2 2 2 2
( 2 ) 124
1 1tanh sinh( ) cosh 12 2 2
f
f
EIq qw x x xLEI EI EI
L x x x x L
α
α α α α α
⎛ ⎞= − + + −⎜ ⎟⎜ ⎟∞ ⎝ ⎠
⎡ ⎤⎛ ⎞− + − + −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦
Eq. 6.19
slipfp www += Eq. 6.20
where the first term is the deflection of a section with full interaction and the second term
is the additional deflection due to interlayer slip of a partial composite section.
Girhammer and Gopu (1993) have also deduced the equations for the maximum
deflection and the maximum internal forces, and they are given as:
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−+⎟⎠⎞
⎜⎝⎛⎟⎟
⎠
⎞⎜⎜⎝
⎛−+= 1
81
2cosh
113845 22
04
04
0max, L
LEIEI
EIq
EILqw f
ffp α
αα Eq. 6.21
114
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⎟⎠⎞
⎜⎝⎛
−⎟⎟⎠
⎞⎜⎜⎝
⎛−+=
2cosh
1118 0
2011
2011
max,1 LEIEIq
EIIELq
EIIE
M f
ff αα Eq 6.22
max,111
22max,2 M
IEIEM = Eq 6.23
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛−+
−++=
2tanh1211
2 01
101112
0max,1
LEIEI
LrEIrEIrIE
rrLq
V f
f
αα
Eq 6.24
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛−+
−++=
2tanh1211
2 02
202222
0max,2
LEIEI
LrEIrEIrIE
rrLq
V f
f
αα
Eq 6.25
the slip can also be estimated by considering that:
uKVs ∆⋅−=− eq. 6.26
Equations 6.21 to 6.26 can be used to predict the behaviour of the beam and determine
the strain distribution along the cross-section under service loads. This will allow
designers to decide if the shear connection is stiff enough that the additional deflection
due to interlayer slip is acceptable within deflection limits. Equation 6.21 can be re-
arranged to a simpler form, shown by Wang (1998) as the following:
⎟⎟⎠
⎞⎜⎜⎝
⎛−+= 11
0EIEI
ww f
f
p β Eq. 6.27
where
115
( )( )4
2
53841
81
2cosh
1L
LL α
αα
β⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
−+⎟⎠⎞
⎜⎝⎛
= Eq. 6.28
As can be seen, β is a function of the shear connection stiffness parameter αL.
Figure 6.5 shows the plot of β against αL, where β = 1 and β = 0 represent the beam with
non-composite and fully composite behaviour, respectively. As shown from the plot, the
relationship is non-linear and the range of interest for partial interaction analysis is
usually when 1 < αL <10. When αL < 1, the beam essentially behaves with no interaction
between the composite materials, on the other hand, when αL > 10, the value of β
becomes really small and the increase in deflection due to the interlayer slip is minimal
compared to the overall deflection, as shown in Figure 6.6.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
αL
β
Figure 6.5: Graphical Presentation of Equation 6.28 (after Wang, 1998)
116
β versus dβ/d(αL)
-0.25
-0.2
-0.15
-0.1
-0.05
00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
αL
β
Figure 6.6: β versus dβ /d(αL)
The study conducted by Wang (1998) that investigated the deflection of steel-
concrete composite beams with partial shear interaction has verified the analysis of
Girhammer and Gopu (1993) with a finite element analysis. Generally, Wang found that
the predicted deflections of the finite element analysis are within 4% of those predicted
by Equation 6.21.
6.2. Computer Analysis using Frame and Spring Elements
In additional to the numerical analyses mentioned in the previous section, a
computer model designed using the program SAP2000™ is used as part of the analytical
program. The computer model is used to:
1) Determine the increase in deflection of a composite beam that is connected by the
polyurethane adhesive developed in the experimental program;
117
2) Conduct a parametric study to analyze the effect of varying the thickness of the
polyurethane layer and the stiffness of the shear connection on the deflection and
interlayer slip of composite beams;
3) Validate the results predicted by the equations outlined by Girhammar and Gopu
(1993).
6.2.1. Material Properties and Element Representation
The 2-D frame model designed for a typical composite bridge section shown in
Figure 6.3 is presented in Figure 6.7. Frame elements are used to represent the concrete
deck, the steel beam, and the discrete rigid links that are used to transfer the forces
between the subcomponents. The adhesive bond layer is represented by discrete spring
elements, which are rigid and fixed in the vertical direction, but only partially fixed in the
horizontal direction. The stiffness of the springs in the horizontal direction is based on
the shear connector stiffness, K, from the experimental program. Since the stiffness of the
adhesive bond is also dictated by the thickness, the width and the length of the joint, the
value K from the push-off tests has to be magnified based on the respective ratios of the
geometry of the joint in the push-off tests to the geometry of the model. For example, if
the stiffness of the joint obtained from the push-off test is Ktangent, the K of the studied
beam can be calculated by:
model modeltangent
joint joint
L wKL w
⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
Eq. 6.31
where Lmodel is the spacing of the frame elements in the model, wmodel is the width of the
adhesive joint of the studied beam, and Ljoint and wjoint are the length and the width of the
118
joint of the push-off specimens, respectively. All the materials, namely the concrete, steel
and the polyurethane are assumed to be linear, elastic, and isotropic. To ensure that the
links are rigid, the frame elements that are used to represent them are assigned a Young’s
Modulus that is one hundred times that of steel, therefore, an E value of around 20 x 106
MPa. Lastly, the beam was simply supported and a uniformly distributed load was
applied to the concrete frame element.
Figure 6.8: 2D SAP2000™ Model – a) A Complete Span b) Detail of the Elements
119
6.3. Problem Definition To determine if the polyurethane adhesive developed in the experimental program
is a suitable material to bond the concrete deck to the steel beams in composite bridges,
the computer model and the equations discussed in the previous sections will be used to
predict the behaviour of the composite bridges that use a polyurethane adhesive as the
shear connection. The typical section analyzed is depicted in Figure 6.9 and Figure 6.10.
The concrete deck is designed to have a width of 13m and supported by four steel I-
beams, therefore, the composite sections to be studied will have a constant concrete deck
width of 3.25m. The parameters considered include the span of the bridge, the thickness
of the polyurethane layer, the shear stiffness of the polyurethane adhesive joint, and the
width of the polyurethane layer. The concrete is assumed to have a strength of f’c = 45
MPa, and the steel is assumed to have a yield strength of f’y = 350 MPa. The geometry of
the concrete slab and the steel beams depend on the span of the bridge, but the overall
depth to span ratio is kept at a typical value of approximately 1 to 25. Table 6.1
summarizes the design of the composite bridges studied in the analytical program. Since
the range of the typical shear connection stiffness values, K, of the polyurethane joint
obtained from the experimental program are within 35 kN/mm to 55 kN/mm, therefore,
the stiffness values considered in the analytical program will be based on the adhesive
joint with K= 35 kN/mm and 55 kN/mm.
The bridges are analyzed under the serviceability limit state, where the loading
considered is the nominal, unfactored live load. Dead load is not included in the analysis
because during the construction of composite bridges, all the dead load, namely the self
weight of the steel girders and the wet concrete, are assumed to be taken by the steel
120
girders alone. Designers usually provide sufficient camber so that the net deflection is
zero when the concrete decks (cast in-situ or precast) are placed on the girders. Since this
chapter focuses on developing and verifying the criteria proposed in Chapter 2, namely,
the additional deflection due to slip shall not exceed 20% of that of the design that is fully
composite, therefore, a constant live load of 100kN/m will be applied to all the bridges
and the percentage increase in deflection due to slip will be noted.
Figure 6.9: Figure 6.9: Overall Cross-Section of the Composite Bridge with 13m with Deck Supported on four Steel beams
Figure 6.10: Parameters of the Beam Studied – Thickness of Slab dc, Depth of Steel Beam ds, Width of Flanges, wf, Thickness of web tw, and Thickness of Flanges tf
121
Table 6.1: Dimensions of the Studied Composite Bridges
Design L (m) tpu (mm) ds (mm) wf (mm) tw (mm) tf (mm)
1 25 1500 600 20 30
2 35 1500 600 20 30
3 45 1500 600 20 30
4
50
50 1500 600 20 30
5 25 1000 400 20 25
6 35 1000 400 20 25
7 45 1000 400 20 25
8
25
50 1000 400 20 25
9 25 2100 700 25 50
10 75
50 2100 700 25 50 *the effective width with L = 25m is 0.125L = 3.13m (Eurocode 4, 1994)
6.4. Results and Discussion – Serviceability Limit State The properties of the sections for each design are calculated based on the
dimensions summarized in Table 6.1. The maximum deflections at the midspan, the
maximum slips and the maximum longitudinal shear stresses at serviceability limit states
are summarized in Table 6.2. The stiffness connector values, K, shown are based on the
35 N/mm or 50 N/mm obtained from the push-out tests and modified by taking the ratios
of thickness of the layer in the designs to the 25mm thickness of the joint in the push-off
tests. A comparison between the deflections of the designs with connection stiffness of 35
N/mm calculated from Equation 6.21 and the computer model is shown in Table 6.3. wf,
wslip and wtotal are the deflection of the bridge with full interaction, the additional
deflection due to slip, and the total overall deflection, respectively. The percentage
increase represents the percentage increase in deflection due to slip compared to the
122
Table 6.2: Results of the Partial Interaction Analysis
Design *K
(N/mm) x 103
k (MPa)
wf (mm)
wslip (mm)
wp (mm)
% increase
∆u
(mm)
τs (MPa)
35.0 1310 168 1.82 169 1.08 0.230 0.546 1
50.0 1870 168 1.27 169 0.76 0.162 0.551 25.0 934 166 2.53 168 1.53 0.318 0.539
2 35.7 1330 166 1.78 167 1.07 0.225 0.546 19.4 725 164 3.24 167 1.98 0.405 0.533
3 27.7 1030 164 2.45 166 1.50 0.309 0.539 17.5 653 163 3.21 166 1.98 0.402 0.533
4 25.0 931 163 2.51 165 1.54 0.317 0.538 35 594 41.0 2.06 43.1 5.01 0.297 0.705
5 50 849 41.0 1.45 42.5 3.54 0.212 0.719
25.0 424 40.2 2.83 43.0 7.03 0.405 0.687 6
35.7 606 40.2 2.00 42.2 4.98 0.290 0.704 19.4 329 39.4 3.58 43.0 9.08 0.510 0.672
7 27.7 490 39.4 2.80 42.2 7.11 0.403 0.685 17.5 297 39.0 3.93 42.9 10.1 0.559 0.665
8 25 424 39.0 2.79 41.8 7.15 0.403 0.684
35.0 1660 337 2.00 339 0.59 0.234 0.556 9
50.0 2380 337 1.40 338 0.42 0.165 0.561 17.5 832 337 3.98 341 1.18 0.458 0.545
10 25.0 1190 337 2.80 339 0.83 0.325 0.551
*K values need to be proportioned according the thickness. i.e. K of a 50mm thick joint is calculated by: K*(25/50)
deflection of the same design with full interaction. ∆u is the maximum slip between the
concrete deck and the steel girder. Generally, the results of the computer model and the
prediction by Equation 6.21 are agreeable and the discrepancies are usually within 5%.
The SAP2000™ model tends to overestimate the deflection and underestimate the slip.
123
Table 6.3: Comparison of Results from SAP2000™ and Equation 6.21.
Design wp from Eq. 6.8 (mm)
wp from SAP2000™
(mm)
% Difference*
∆u from Eq. 6.8 (mm)
∆u from SAP2000™
(mm)
% Difference*
1 171 168 2.1 0.223 0.230 -3.0 2 169 166 1.8 0.307 0.318 -3.3 3 168 164 2.1 0.397 0.405 -1.8 4 166 163 1.8 0.393 0.402 -2.3 5 42.7 41 4.0 0.285 0.297 -4.0 6 42.3 40.2 5.0 0.385 0.405 -5.0 7 41.0 39.4 4.0 0.501 0.510 -1.7 8 39.9 39.0 2.3 0.547 0.559 -2.1 9 345 337 2.4 0.227 0.234 -2.8 10 341 337 1.3 0.452 0.458 -1.4
*% Difference calculated by: -(value of Eq. 6.8 - value of SAP2000™ ) / (value of Eq. 6.8)
The distributions of strains along the composite sections of the 50m and the 25m
span are shown in Figures 6.11 and 6.12, respectively. As can be seen, the slip strains in
the 50m-span section are small (a maximum value of approximately 0.03 µε) and the
strain distributions are similar to that of a composite section with perfect bond. However,
the distributions of the strains in the 25m-span section start to deviate from that of a
perfect bond, with a noticeable slip strain of approximately 0.096 µε.
Generally, the increase in deflection at midspan due to the interlayer slip between
the concrete and steel sections of the 50m and 75m-span designs is less than 5% of the
maximum deflection of a fully composite section. However, the increase in deflection of
the 25m-span design ranges from approximately 7% to as high as 10%. Figure 6.13
shows the relationship between the percentage increase in the maximum deflection due to
slip and the decrease in stiffness. As can be seen, the decrease in K has a much greater
effect on the 25m-span design than it does on the 50m-span design. The reason why the
124
Strain Distribution at Midspan with Different PU Thickness (50m Span)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-0.750 -0.250 0.250 0.750 1.250 1.750
Strain (x 10E-3)
Dist
ance
from
the
Botto
m o
f the
Cr
oss-
Sec
tion
(mm
)25mm35mm45mm50mmPerfect Bond
Figure 6.11: Strain Distributions of the Cross-Section at Midspan for Polyurethane Layer Thickness of 25mm, 35mm, 45mm and 50mm – 50m-Span Design
Strain Distribution at Midspan with Different PU Thickness (25m Span)
0100200300400500600700800900
100011001200
-0.500 -0.250 0.000 0.250 0.500 0.750 1.000 1.250 1.500 1.750
Strain (x10E-3)
Dis
tanc
e fro
m th
e Bo
ttom
of t
he
Cros
s-S
ectio
n (m
m)
25mm35mm45mm50mmPerfect Bond
Figure 6.12: Strain Distributions of the Cross-Section at Midspan for Polyurethane Layer Thickness of 25mm, 35mm, 45mm and 50mm – 25m-Span Design
125
% Increase in Max. Deflection vs. Connection Stiffness
0
2
4
6
8
10
12
14
16
0 10 20 30 40 50 60
Shear Connector Stiffness, K (N/mm) x10E3
% In
crea
se in
Max
imum
Def
lect
ion
25m50m
Figure 6.13: Relationship between the percentage increase in maximum deflection versus shear connection stiffness, K, for 25m and 50m-span designs according to Equation 6.21.
shorter spans tend to be more sensitive to a decrease in the shear connection stiffness than
the longer spans are is because of the non-linear relationship between the stiffness
parameter αL and the deflection function of beams with partial shear connection, as
already shown in Figure 6.5. The rate at which the deflection increases at lower αL values
is much greater than it is at higher values of αL. As the connection stiffness and the span
length decreases, the parameter αL also decreases since α is directly proportional the
connection stiffness. For example, the αL values for the designs of the 50m-span range
approximately from 19 to 26, where the αL values for the designs of the 25m-span range
from 11 to 15.
Results from the analysis shows that, in general, the additional deflection due to
slip in adhesively bonded composite bridges is insignificant compared to its overall
deflection. Therefore, it is reasonable to conclude that adhesively bonded connections can
be designed and the adhesive can be formulated to provide sufficient stiffness that
126
additional deflection due to slip can be limited to be under 20% of the deflection of the
same design with full interaction, as was proposed in Chapter 2.
Although the cross-sections discussed above are designed according to the typical
span to depth ratio of 25 to 28 (Brozzetti, 2003), parameter such as the width of the top
steel flange can greatly affect the behaviour of the composite sections since the stiffness
of the adhesive bond connection is proportional to the width of the joint, which cannot be
greater than the width of the top flange of the steel beam.
6.5. Flexural Strength at Ultimate Limit State In addition to having sufficient stiffness to satisfy the deflection limit of the
composite beams in the serviceability limit state, the adhesive layer must also have
sufficient strength to allow the development of the full capacity of the concrete and steel
sections under the ultimate limit state. The ultimate flexural capacity of a composite
section can be determined using a rigid plastic analysis outlined by Oehlers and Bradford
(1995). The analysis is based on equilibrium of forces at the cross-section assuming that
the concrete and steel have developed their full plastic strength. The following sections
will discuss and outline the rigid plastic analysis and its application to determine if the
polyurethane adhesive joint developed has sufficient bond strength under loadings in the
ultimate limit states.
6.5.1. Rigid Plastic Analysis by Oehlers and Bradford (1995) Consider the three possible stress distributions of a concrete-steel composite
section at its maximum strength, as shown in Figure 6.14. Cases 1 and 2 represent the
states of stress when the neutral axis is in the concrete and steel, respectively, and that the
127
shear connection has sufficient strength to fully transfer the forces between the two
sections, hence a full shear connection. Case 3 represents the state of stress where the
shear connection has lower strength than that of the concrete and steel sections, and the
forces in each section are dictated by the ultimate strength of the shear connection. The
composite beam in this case is referred to as having a partial shear connection. In the
current study, only Cases 2 and 3 will be considered because Case 1 involves possible
cracking of the concrete at the shear connection, which should be avoided in adhesive
bond connection to avoid detachment of the polyurethane layer from the concrete surface.
The strength of the adhesive bond required for full shear connection and the
ultimate flexural strength of a composite section can be estimated by the following
procedure:
1) Fix the stresses on the concrete and steel sections at their plastic strengths, namely
cfPconcrete ′= 85.0 for concrete in compression (Oehlers & Bradford, 1995) and
ysteel fP = , the yield strength for steel in both tension and compression, as shown
in Figure 6.15.
2) Determine the position of the neutral axis that will allow equilibrium of forces at
the cross-section. In other words, the sum of the compression forces above the
neutral axis must equal to the sum of the tension forces below the neutral axis.
3) The minimum shear connection strength, shearP , required is the force that needs to
be transferred between the concrete and steel sections. In the case where the
neutral axis is in the steel section, concreteshear PP = .
128
Figure 6.14: Three Possible Strain and Stress Distributions (Figures taken from Oehlers & Bradford, 1995)
129
4) If the shear connection has sufficient strength to transfer the forces between the
two sections, the flexural strength can be determined by taking moment of all the
forces at the cross section.
5) If the shear connection does not have sufficient strength to transfer the forces, the
resultant forces in the concrete and steel sections must be set to shearP , since
neither the concrete nor the steel section can develop its full strength. As shown in
Figure 6.16, the positions of the neutral axes that will result in a force of Pshear in
each section must be determined.
The outlined procedure is used to analyze the composite beams summarized in
Table 6.1 and the strengths of the polyurethane adhesive bond required for full shear
connections are determined. The predicted strengths will be compared to the shear
strengths of the polyurethane adhesive joints tested in the experimental program to
investigate the feasibility of using the developed formulation as the shear connection of
composite bridges. Since the polyurethane joints of the push-out specimens in the
experimental program are all 25mm thick and the effect of the thickness on the bond
strength is unknown, only the designs with an adhesive layer of 25mm are analyzed. The
analysis is also used to verify the suggestion by Si Larbi et al. (2006) that the longitudinal
shear stress at the shear connection in typical composite bridges do not exceed 3MPa.
130
Figure 6.15: Stresses of the Composite Section with Full Interaction at the Ultimate Limit State Neutral Axis in the Steel Beam. (Figures taken from Oehlers & Bradford, 1995)
Figure 6.16: Stresses of the Composite Section with Partial Shear Connection at the Ultimate Limit State (Figures taken from Oehlers & Bradford, 1995)
131
6.5.2. Results and Discussion – Ultimate Limit State Table 6.4 summarizes the flexural strengths, the maximum load at the connection
at the midspan, and the required strength of the shear connection of the 25m, 50m, and
75m-span designs with a 25mm thick polyurethane adhesive layer under the ultimate
limit state based on the rigid plastic analysis. Different concrete strengths are also
considered since that will greatly influence the plastic strength of the concrete slabs.
Table 6.4: Results from the Rigid Plastic Analysis
Span Concrete Strength
Maximum Load at the Connection at Midspan
(kN)
Required Shear Connection Strength
(MPa)
25 25 13700 2.73 35 13700 2.73 45 13700 2.73 55 13700 2.73
50 25 15500 0.89 35 21800 1.24 45 28000 1.60 55 34200 1.95
75 25 15500 0.59 35 21800 0.83 45 28000 1.06 55 34200 1.23
As can be seen, the required strength of the shear connection in all the cases does
not exceed 3 MPa. This conforms to the results from the study of Si Larbi et al. (2006),
which suggested that the longitudinal shear stress in typical composite sections usually do
not exceed 3 MPa. Results of Specimens 5-1 and 5-3 from the push-off tests, summarized
132
in Chapter 4, demonstrate that the polyurethane elastomer can be formulated to withstand
a maximum shear stress of approximately 2.9 MPa and 3.5 MPa, respectively. The results
suggest that the polyurethane adhesive joint developed in the experimental program has
sufficient strength to allow the full development of the plastic flexural strength in
composite bridges spanning from 25m to 75m. Although the results shown in Table 6.4
are specific to the proposed designs, which can change depending on numerous
parameters such as the number of steel girders, the thickness of the concrete slab, the
widths of the top flanges of the steel beams, and the concrete strength. However, the
results demonstrate, at a preliminary level, that the composite sections can be designed to
adopt the adhesive bond and satisfy the requirements under the ultimate limit state.
6.6. Criteria Having demonstrated the feasibility of using the polyurethane adhesive developed
in the experimental program as the shear connection in composite bridges, general
criteria for the use of the adhesive bond can be established. In general, the adhesive layer
should be stiff enough to minimize the interlayer slip between the two composite
components under the serviceability limit state, and also, the adhesive bond must have
sufficient strength to transfer the forces between the subcomponents to allow the full
development of the plastic capacity of the composite section. Based on the results from
the analytical program, the criteria for the two limit states are:
Under the serviceability limit state:
1) The additional deflection due to slip should not exceed 20% of the overall
deflection of the design with full interaction.
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2) The stiffness parameter of the connection, αL, should be at least 10. As shown in
Figures 6.6 and 6.7, the additional deflection due to slip increases at a quick rate
when αL < 10. The typical span range of composite bridges, from 25m to 75m,
can be designed to have a αL value from 11 to 25.
3) The materials of the composite sections should remain elastic and the stiffness of
the connection required must be within the linearly elastic range due to the
assumptions made in the analysis proposed by Girhammar and Gopu (1993).
4) For the prediction of the deflection, full composite assumption can be assumed for
αL values greater than 10, since the increase of deflection due to slip is usually
less than 10%.
5) Since shorter spans are more sensitive to changes in the shear connection stiffness,
increasing the thickness of the adhesive layer from 25mm should be avoided in
shorter spans of 20m to 30m as it will significantly decrease the stiffness of the
connection.
6) The stiffness, K, can be increased easily by increasing the width of the adhesive
layer, which is dictated mainly by the width of the top flange of the steel beams.
Under the ultimate limit state:
1) Generally, the adhesive layer should be able to resist a minimum longitudinal
shear stress of 3 MPa, as suggested by Si Larbi (2003) and verified by the
analytical program.
2) The maximum shear stress in the adhesive layer can easily be decreased by
increasing the width of the adhesive layer to increase the shear area at the
interfaces.
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CHAPTER 7: SUMMARY, CONCLUSION AND RECOMMENDATIONS
7.1. Summary The primary motivation behind this research study was to develop a system that
can facilitate bridge deck rehabilitation projects of composite bridges, and this can
usually be achieved by using full-depth precast concrete decks. However, conventional
headed stud connectors require shear pockets in the precast decks, which can become
vulnerable areas for durability problems. The objective of this research is to investigate
the feasibility of adhesively bonding the concrete deck to the steel girders in composite
bridges with a polyurethane elastomer adhesive, which not only has a quick curing and
setting time, but it can also provide sufficient strength and stiffness to be used in civil
engineering application.
The feasibility of the adhesively bonded connection is determined based on the
deflection requirement according to the serviceability limit state and the strength
requirement of the ultimate limit state. The adhesive joint should:
1. Have sufficient strength to allow the full development of the plastic
capacity of the concrete and steel sections. The minimum shear stress that
the adhesive joint should be able to resist was determined to be 3MPa.
2. Have sufficient stiffness that additional deflection due to the interlayer slip
between the concrete and steel is minimum and full composite behaviour
can be attained.
This research study included an experimental program that tested 19 small-scale
push-off tests to develop a polyurethane elastomer adhesive that could satisfy the
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abovementioned criteria. The strength and stiffness of adhesive joints were also
characterized in the push-off tests. These values were then used in the analytical program
of this research study.
The analytic program was designed to establish a list of criteria used to determine
the feasibility of using the polyurethane adhesive as a shear connection in composite
bridges. The partial interaction theory proposed by Girhammar and Gopu (1993) was
used to determine the maximum deflection of the composite bridges with spans of 25m,
50m, and 75m, which were designed to have a bonded shear connection using the
polyurethane adhesive developed in the experimental program. A SAP2000™ computer
model was also designed to verify the results obtained from the partial interaction theory.
The analytical program also studied the behaviour of the bridges under ultimate limit
state using a rigid plastic analysis proposed by Oehlers and Bradford (1996). The analysis
was used to determine if the polyurethane adhesive bond tested in the experimental
program had sufficient strength to allow the composite sections to develop their full
plastic flexural strength.
7.2. Conclusion The following conclusions can be made for this research study:
1) According to the criteria established in this study, the use of polyurethane
adhesive as the shear connection in composite bridges is feasible.
2) The maximum shear stress that a shear connection must resist in typical
composite bridges is lower than 3MPa.
136
3) The polyurethane adhesive joint developed in the experimental program
could provide sufficient strength for the development of the plastic capacity
of composite bridges with spans of 25m, 50m and 75m.
4) The adhesive joint developed had sufficient stiffness that the behaviour of
the bridges study was close to that of a fully composite bridge.
5) The additional deflection due to interlayer slip when an adhesive bond is
used is insignificant compared to the overall deflection. The maximum
additional deflection due to slip of a composite bridge when the adhesively
bonded connection is used shall not exceed 20% of overall deflection of the
corresponding design with full interaction.
6) The strength and stiffness of the polyurethane layer used as the shear
connection greatly depends on the width of adhesive joint, which cannot be
greater than the width of the top flange of the steel girders.
7) The partial interaction theory proposed by Girhammar and Gopu (1993) can
be used to analysis composite beams with only partial shear connection.
8) Bridges with shorter spans are more sensitive to a decrease in the stiffness of
the shear connection due to the non-linear relationship between the increase
in deflection with the stiffness parameter, αL, used in the partial interaction
theory. To ensure a full interaction, αL should be kept at above 10.
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7.3. Recommendations and Future Work
Since a formulation of the polyurethane that can provide sufficient strength and
stiffness was developed in the experimental program, full-scale standard push-off tests
should be conducted to obtain more consistent load-slip plots for the adhesive joint. An
experimental program should be designed to test composite beams that use the adhesive
bond as the shear connection, where the degree of interaction can be studied. Production
of the polyurethane outside of ideal lab conditions will be necessary to ensure that the
adhesive can be used under field conditions. Factors that greatly influence the properties
of the curing of polyurethane such as the temperature, moisture content, and different
surface conditions should be examined. Lastly, the behaviour of the adhesively bonded
composite bridges under long-term loading, and the behaviour in the fatigue limit state
should be examined.
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Appendix A:
Data Input for Finite Element Analysis
Program used: SAP2000™
Frame Elements:
Concrete Slab
Material Properties:
Material Type: Reinforced Concrete
Concrete Strength: 45MPa
Reinforcement Yield Strength: 413MPa
Modulus of Elasticity: 36900MPa
Poisson Ratio: 0.2
Assumed Linearly Elastic, Isotropic
Sectional Properties
Section Type: Rectangular Section
Width: 3250mm
Depth: 225mm
Steel Girder
Material Properties
Material Type: Steel
Strength: Fy = 350MPa
Fu = 450 MPa
Modulus of Elasticity: 200000MPa
Poison Ratio: 0.3
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Assumed Linearly Elastic, Isotropic
Sectional Properties
Section Type: I-Beam
Geometry Varies
Rigid Frame Elements
Material Properties:
Material Type: None
Modulus of Elasticity: 2x107MPa
Poisson Ratio: 0.3
Assumed Rigid, Isotropic
Sectional Properties
Section Type: Rectangular Section
Width: 100mm
Depth: 100mm
*Rigid Frame Elements are spaced 100mm apart over the span of the studied bridges.
Spring Elements
Constraints:
U1 – Fixed
U2 – Partially Fixed, with stiffness K
Free in other directions
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Adhesive joint stiffness 35kN/m or 50kN/m is used. The K input can be calculated as
follows:
Since the stiffness if for a 25mm thick joint with a bond length of 160mm and width of
92mm, the experimental stiffness value must be proportioned according to the geometry
of the model of the studied bridges. For example, if the adhesive layer of the bridge in
consideration has a joint width of 400mm, thickness of 50mm, and the experimental
stiffness of 35kN/m is used, K can be calculated by:
100 400 2535160 92 50input
kN mm mm mmKm mm mm mm
⎛ ⎞ ⎛ ⎞ ⎛ ⎞= ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠i i i
The first term is the experimental stiffness, second term is the ratio of the frame element
spacing to the joint length, third term is the ratio of the joint width in the studied bridge to
the experimental joint width, and the last term is the ratio of the joint thicknesses. This
Kinput is that entered as the spring stiffness of the spring element in the U2 direction.
