NEARSURFACE MOUNTED, FIBERREINFORCED POLYMER STRIPS FOR
NEGATIVEMOMENT STRENGTHENING OF CONCRETE
BRIDGES?DESIGN METHODOLOGY
Except where reference is made to the work of others, the work described in this thesis is
my own or was done in collaboration with my advisory committee. This thesis does not
include proprietary or classified information.
______________________________
Jeffrey Kyle Alexy
Certificate of Approval:
______________________________ ______________________________
Anton K. Schindler Robert W. Barnes, Chair
Gottlieb Associate Professor James J. Mallett Associate Professor
Civil Engineering Civil Engineering
______________________________ ______________________________
Hassan H. Abbas George T. Flowers
Assistant Professor Dean
Civil Engineering Graduate School
NEARSURFACE MOUNTED, FIBERREINFORCED POLYMER STRIPS FOR
NEGATIVEMOMENT STRENGTHENING OF CONCRETE
BRIDGES?DESIGN METHODOLOGY
Jeffrey Kyle Alexy
A Thesis
Submitted to
the Graduate Faculty of
Auburn University
in Partial Fulfillment of the
Requirements for the
Degree of
Master of Science
Auburn, Alabama
August 10, 2009
iii
NEARSURFACE MOUNTED, FIBERREINFORCED POLYMER STRIPS FOR
NEGATIVEMOMENT STRENGTHENING OF CONCRETE
BRIDGES?DESIGN METHODOLOGY
Jeffrey Kyle Alexy
Permission is granted to Auburn University to make copies of this thesis at its discretion,
upon request of individuals or institutions and at their expense. The author reserves all
publication rights.
____________________________
Signature of Author
____________________________
Date of Graduation
iv
VITA
Jeffrey Kyle Alexy, son of Thomas and Susan Alexy, was born January 10, 1984,
in Anniston, Alabama. He graduated from Jacksonville High School as salutatorian in
2002. He attended Auburn University and graduated summa cum laude with a Bachelor
of Civil Engineering degree in 2007. He entered graduate school at Auburn University in
August, 2007, to seek the degree of Master of Science in Civil Engineering. On May 16,
2009, he will marry Brigitte Demasi of Swanton, Vermont, and then begin work as a
structural design engineer for Hodnett Hurst Engineers, Inc., in Huntsville, Alabama.
v
THESIS ABSTRACT
NEARSURFACE MOUNTED, FIBERREINFORCED POLYMER STRIPS FOR
NEGATIVEMOMENT STRENGTHENING OF CONCRETE
BRIDGES?DESIGN METHODOLOGY
Jeffrey Kyle Alexy
Master of Science, August 10, 2009
(B.C.E., Auburn University, 2007)
321 Typed Pages
Directed by Robert W. Barnes
A bridge near Letohatchee, Alabama, was found to be deficient for certain types of truck
loadings. Fiberreinforced polymer (FRP) strips were selected to use in the strengthening
scheme. Various models and code recommendations were studied and compared against
existing experimental results to determine the most effective models for FRP
strengthened members. The models were divided into three groups: plateend (PE)
debonding models for nearsurface mounted (NSM) FRP, intermediatecrack (IC)
debonding models for externallybonded (EB) FRP, and ICdebonding models for NSM
FRP.
vi
None of the three PEdebonding models correlated well with the experimental
results. Four of the six ICdebonding models for EB were relatively accurate for the test
data. All five of the ICdebonding models for NSM produced mostly conservative results,
with three models being relatively accurate. These three models?ACI 440 (2008),
Standards Australia (2008), and Seracino et al. (2007a)?were used in the proposed
strengthening scheme to determine the amount of NSM FRP the Letohatchee bridge
needed. To verify this proposed design and to further examine the behavior of NSM
strengthened concrete members, a laboratory testing program was proposed.
One of the main reasons for a laboratory testing program is that the published
experimental test configurations do not match the Letohatchee bridge very well. The
reinforcement ratios for the actual bridge are lower than the tests, and the NSM test
specimens were not cracked prior to FRP strengthening. In the proposed testing program,
the effects of the amounts of FRP and steel, the concrete compressive strength, and the
crosssectional shape were analyzed.
.
vii
ACKNOWLEDGEMENTS
First and foremost, I want to give all glory and honor to Jesus Christ, our Savior
and Lord.
I would like to thank my family?Dad, Mom, Tommy, Kristin, and Grandma?
for all of the love and support they have given me throughout the years. I would also like
to thank my fianc?e Brigitte Demasi for her love and support as well as her caring and
thoughtfulness during these last few busy semesters.
I would especially like to thank Dr. Robert Barnes for all of his wisdom and
guidance throughout my college career. I would also like to thank Dr. Anton Schindler
and Dr. Hassan Abbas, for their work as committee members, as well as all of the other
professors at Auburn University who have helped teach and mold me into the engineer I
am today.
Finally, I am grateful for the monetary support given by the Alabama Department
of Transportation through the funding of this project.
viii
Style manual used Kate L. Turabian A Manual for Writers of Term Papers, Theses, and
Dissertations. 6
th
ed._____________________________________________________
Computer software used Microsoft Word, Microsoft Excel, AutoCAD 2007_________
ix
TABLE OF CONTENTS
LIST OF TABLES........................................................................................................... xvii
LIST OF FIGURES......................................................................................................... xxii
Chapter 1: Introduction....................................................................................................... 1
1.1 Background.............................................................................................................. 1
1.2 Research Objectives and Tasks................................................................................ 3
1.3 Organization of Thesis............................................................................................. 3
Chapter 2: Behavior of Reinforced Concrete Beams Strengthened with FRP................... 5
2.1 Introduction.............................................................................................................. 5
2.2 Components and Applications of FRP..................................................................... 6
2.2.1 Different FRP Materials and Properties.......................................................... 6
2.2.2 ExternallyBonded (EB) FRP......................................................................... 8
2.2.3 NearSurface Mounted (NSM) FRP............................................................. 13
2.3 Failure Modes of FRPStrengthened Members..................................................... 15
2.3.1 PlateEnd (PE) Debonding............................................................................ 15
2.3.2 Intermediate Crack (IC) Debonding............................................................. 16
2.3.3 FRP Rupture..................................................................................................16
2.3.4 Concrete Failure............................................................................................ 17
2.3.5 Combined Failure Modes.............................................................................. 17
2.4 Available Recommended Design Provisions......................................................... 19
x
2.4.1 ACI Committee 440 Design Recommendations........................................... 20
2.4.1.1 Debonding of FRP Reinforcement....................................................... 21
2.4.1.2 Strengthened Moment Capacity........................................................... 22
2.4.1.3 Development Length............................................................................ 26
2.4.1.4 Serviceability Recommendations.........................................................26
2.4.2 fib Task Group 9.3........................................................................................ 27
2.4.3 Standards Australia....................................................................................... 29
2.4.3.1 PEDebonding Models......................................................................... 30
2.4.3.2 ICDebonding Models......................................................................... 31
2.4.3.2.1 Basic ICDebonding Models....................................................... 32
2.4.3.2.2 Beam ICDebonding Model........................................................ 32
2.5 Models for FRP Debonding Failure Modes........................................................... 33
2.5.1 PlateEnd (PE) Debonding Models............................................................... 33
2.5.1.1 Blaschko (2003)................................................................................... 33
2.5.1.2 Hassan and Rizkalla (2003)................................................................. 35
2.5.1.3 Vasquez (2008).................................................................................... 39
2.5.2 Intermediate Crack (IC) Debonding Models................................................ 43
2.5.2.1 Rosenboom (2006)............................................................................... 43
2.5.2.2 Seracino, Raizal Saifulnaz, and Oehlers (2007).................................. 48
2.5.2.3 Seracino et al. (2007a)......................................................................... 50
2.5.2.4 Said and Wu (2008)............................................................................. 52
2.6 FRP Spacing Recommendations for NSM Strips.................................................. 53
2.7 Effect of Concrete Surface Roughness.................................................................. 55
xi
2.8 Effect of Embedding NSM Strips.......................................................................... 56
2.9 Previous Testing of FRPStrengthened Members................................................. 56
2.9.1 ExternallyBonded (EB) FRP Flexural Tests............................................... 57
2.9.1.1 Reed et al. (2005)................................................................................. 57
2.9.1.2 War Memorial Bridge.......................................................................... 59
2.9.2 NearSurface Mounted (NSM) FRP Flexural Tests...................................... 60
2.9.2.1 Yost et al. (2007)..................................................................................60
2.9.2.2 Taljsten and Nordin (2007).................................................................. 61
2.9.2.3 Teng et al. (2006)................................................................................. 62
2.9.2.4 Liu, Oehlers, and Seracino (2006)....................................................... 64
2.9.3 Both EB and NSM FRP Flexural Tests........................................................ 65
2.9.3.1 ElHacha and Rizkalla (2004).............................................................. 66
2.9.3.2 Jung et al. (2005)..................................................................................67
2.9.4 NSM ModifiedBeam Pullout Tests............................................................. 70
2.9.4.1 De Lorenzis and Nanni (2002)............................................................. 70
2.9.4.2 Sena Cruz and Barros (2004)............................................................... 72
2.9.4.3 Sena Cruz et al. (2006).........................................................................73
2.10 Summary.............................................................................................................. 74
Chapter 3: Letohatchee Bridge Background..................................................................... 77
3.1 Bridge Description................................................................................................. 77
3.2 Demand on Existing Bridge................................................................................... 81
3.2.1 Dead Load..................................................................................................... 81
3.2.2 Live Load...................................................................................................... 82
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3.2.3 Factored Total Load...................................................................................... 87
3.3 Capacity of Existing Bridge................................................................................... 90
3.4 Bridge Deficiencies................................................................................................ 98
3.5 Summary.............................................................................................................. 102
Chapter 4: Evaluation of Existing Models...................................................................... 106
4.1 Introduction.......................................................................................................... 106
4.2 PEDebonding Models for NSM......................................................................... 108
4.2.1 Standards Australia (2008)......................................................................... 108
4.2.1.1 Comparison to Previous Testing........................................................ 108
4.2.1.2 Discussion of Model.......................................................................... 116
4.2.2 Blaschko (2003).......................................................................................... 116
4.2.2.1 Discussion of Model.......................................................................... 116
4.2.3 Hassan and Rizkalla (2003)........................................................................ 117
4.2.3.1 Comparison to Previous Testing........................................................ 117
4.2.3.2 Discussion of Model.......................................................................... 123
4.2.4 Vasquez (2008)........................................................................................... 124
4.2.4.1 Comparison to Previous Testing........................................................ 124
4.2.4.2 Discussion of Model.......................................................................... 129
4.3 ICDebonding Models for EB.............................................................................. 130
4.3.1 ACI 440 (2008)........................................................................................... 130
4.3.1.1 Comparison to Previous Testing........................................................ 130
4.3.1.2 Discussion of Model.......................................................................... 136
4.3.2 fib 9.3 (2001)............................................................................................... 136
xiii
4.3.2.1 Comparison to Previous Testing........................................................ 136
4.3.2.2 Discussion of Model.......................................................................... 141
4.3.3 Standards Australia (2008)......................................................................... 142
4.3.3.1 Comparison to Previous Testing........................................................ 142
4.3.3.2 Discussion of Model.......................................................................... 148
4.3.4 Rosenboom (2006)...................................................................................... 148
4.3.4.1 Comparison to Previous Testing........................................................ 149
4.3.4.2 Discussion of Model.......................................................................... 154
4.3.5 Seracino, Raizal Saifulnaz, and Oehlers (2007)......................................... 154
4.3.5.1 Comparison to Previous Testing........................................................ 154
4.3.5.2 Discussion of Model.......................................................................... 160
4.3.6 Said and Wu (2008).................................................................................... 160
4.3.6.1 Comparison to Previous Testing........................................................ 160
4.3.6.2 Discussion of Model.......................................................................... 166
4.4 ICDebonding Models for NSM.......................................................................... 166
4.4.1 ACI 440 (2008)........................................................................................... 166
4.4.1.1 Comparison to Previous Testing........................................................ 166
4.4.1.2 Discussion of Model.......................................................................... 174
4.4.2 fib 9.3 (2001)............................................................................................... 175
4.4.2.1 Comparison to Previous Testing........................................................ 175
4.4.2.2 Discussion of Model.......................................................................... 184
4.4.3 Standards Australia (2008)......................................................................... 185
4.4.3.1 Comparison to Previous Testing........................................................ 185
xiv
4.4.3.2 Discussion of Model.......................................................................... 194
4.4.4 Seracino et al. (2007a)................................................................................ 194
4.4.4.1 Comparison to Previous Testing........................................................ 194
4.4.4.2 Discussion of Model.......................................................................... 204
4.4.5 Said and Wu (2008).................................................................................... 205
4.4.5.1 Comparison to Previous Testing........................................................ 205
4.4.5.2 Discussion of Model.......................................................................... 214
4.5 Summary of Model Evaluations.......................................................................... 214
4.5.1 PEDebonding Models................................................................................ 214
4.5.2 ICDebonding Models................................................................................ 216
Chapter 5: Proposed Strengthening for the Letohatchee Bridge.................................... 222
5.1 FRP Selection.......................................................................................................222
5.2 FRP Amount Needed........................................................................................... 226
5.2.1 ACI 440 (2008)........................................................................................... 229
5.2.2 Standards Australia (2008)......................................................................... 231
5.2.3 Seracino et al. (2007a)................................................................................ 233
5.2.4 Summary of Models.................................................................................... 235
5.3 FRP Length and Termination Points....................................................................237
5.4 FRP Spacing Recommendations.......................................................................... 240
5.5 Summary of Proposed Design............................................................................. 242
5.6 Further Testing..................................................................................................... 243
Chapter 6: Proposed Laboratory Testing Program......................................................... 247
6.1 Overall Objectives and Scope of Testing Program.............................................. 247
xv
6.2 Test Procedure..................................................................................................... 251
6.3 Test Series 1......................................................................................................... 253
6.3.1 Objectives of Test Series............................................................................ 253
6.3.2 Description of Test Specimens................................................................... 253
6.3.3 Anticipated Behavior and Failure Modes................................................... 256
6.3.3.1 Unstrengthened Specimens................................................................ 257
6.3.3.2 Strengthened Specimens.................................................................... 258
6.4 Test Series 2......................................................................................................... 260
6.4.1 Objectives of Test Series............................................................................ 261
6.4.2 Description of Test Specimens................................................................... 261
6.4.3 Anticipated Behavior and Failure Modes................................................... 264
6.4.3.1 Unstrengthened Specimens................................................................ 264
6.4.3.2 Strengthened Specimens.................................................................... 265
6.5 Test Series 3......................................................................................................... 266
6.5.1 Objectives of Test Series............................................................................ 266
6.5.2 Description of Test Specimens................................................................... 266
6.5.3 Anticipated Behavior and Failure Modes................................................... 268
6.5.3.1 Unstrengthened Specimens................................................................ 268
6.5.3.2 Strengthened Specimens.................................................................... 269
6.6 Test Series 4......................................................................................................... 270
6.6.1 Objectives of Test Series............................................................................ 270
6.6.2 Description of Test Specimens................................................................... 271
6.6.3 Anticipated Behavior and Failure Modes................................................... 272
xvi
6.6.3.1 Unstrengthened Specimens................................................................ 273
6.6.3.2 Strengthened Specimens.................................................................... 273
Chapter 7: Summary and Conclusions............................................................................ 275
7.1 Summary.............................................................................................................. 275
7.2 Conclusions.......................................................................................................... 277
7.2.1 Debonding Models...................................................................................... 277
7.2.2 Letohatchee Bridge..................................................................................... 278
7.3 Recommendations................................................................................................ 279
REFERENCES................................................................................................................ 281
APPENDIX A: NOTATION........................................................................................... 286
APPENDIX B: SAMPLE CALCULATIONS.................................................................291
xvii
LIST OF TABLES
Table 21: Values of Tensile Strength and Young?s Modulus for FRP............................... 6
Table 22: Typical Density Values for FRP Materials and Steel (ACI 440 2008).............. 8
Table 23: Environment Reduction Factor Values Given by ACI 440 (2008).................. 21
Table 24: Summary of NSM Groove Spacing and Side Cover Recommendations......... 55
Table 31: Vehicle Names and Load Arrangements Used for Bridge Analysis................ 83
Table 32: AASHTO Load Combinations......................................................................... 88
Table 33: Portion of Each Bar Group?s Yield Stress Used for Positive Moment Capacity
Calculations......................................................................................................94
Table 34: Portion of Each Bar Group?s Yield Stress Used for Negative Moment
Capacity Calculations...................................................................................... 97
Table 35: PositiveMoment Deficiency for Posting Trucks at Critical Locations......... 101
Table 36: NegativeMoment Deficiencies for Posting Trucks at Critical Locations..... 102
Table 41: List of Experimental Test Series.................................................................... 106
Table 42: Comparison of the PEDebonding Model by Standards Australia (2008) to
NSM Test Results.......................................................................................... 110
Table 43: FRP Strain Predictions using the Standards Australia (2008) PEDebonding
Model and NSM Test Results........................................................................ 115
Table 44: Comparison of the PEDebonding Model by Hassan and Rizkalla (2003) to
NSM Test Results.......................................................................................... 118
xviii
Table 45: FRP Strain Predictions using the Hassan and Rizkalla (2003) PEDebonding
Model and NSM Test Results........................................................................ 123
Table 46: Comparison of the PEDebonding Model by Vasquez (2008) to NSM Test
Results............................................................................................................ 125
Table 47: FRP Strain Predictions using the Vasquez (2008) PEDebonding Model and
NSM Test Results.......................................................................................... 129
Table 48: Comparison of the ICDebonding Model by ACI 440 (2008) to EB Test
Results............................................................................................................ 131
Table 49: FRP Strain Predictions using the ACI 440 (2008) ICDebonding Model and
EB Test Results.............................................................................................. 135
Table 410: Comparison of the ICDebonding Model by fib 9.3 (2001) to EB Test
Results............................................................................................................ 137
Table 411: FRP Strain Predictions using the fib 9..3 (2001) ICDebonding Model and
EB Test Results.............................................................................................. 140
Table 412: Comparison of the ICDebonding Model by Standards Australia (2008) to
EB Test Results.............................................................................................. 143
Table 413: FRP Strain Predictions using the Standards Australia (2008) ICDebonding
Model and EB Test Results............................................................................147
Table 414: Comparison of the ICDebonding Model by Rosenboom (2006) to EB Test
Results............................................................................................................ 149
Table 415: FRP Strain Predictions using the Rosenboom (2006) ICDebonding Model
and EB Test Results....................................................................................... 153
Table 416: Comparison of the ICDebonding Model by Seracino, Raizal Saifulnaz, and
xix
Oehlers (2007) to EB Test Results.................................................................155
Table 417: FRP Strain Predictions using the Seracino, Raizal Saifulnaz, and Oehlers
(2007) ICDebonding Model and EB Test Results........................................ 159
Table 418: Comparison of the ICDebonding Model by Said and Wu (2008) to EB Test
Results............................................................................................................ 161
Table 419: FRP Strain Predictions using the Said and Wu (2008) ICDebonding Model
and EB Test Results....................................................................................... 165
Table 420: Comparison of the ICDebonding Model by ACI 440 (2008) to NSM Test
Results............................................................................................................ 168
Table 421: FRP Strain Predictions using the ACI 440 (2008) ICDebonding Model and
NSM Test Results.......................................................................................... 173
Table 422: Comparison of the ICDebonding Model by fib 9.3 (2001) to NSM Test
Results............................................................................................................ 176
Table 423: FRP Strain Predictions using the fib 9.3 (2001) ICDebonding Model and
NSM Test Results.......................................................................................... 183
Table 424: Comparison of the ICDebonding Model by Standards Australia (2008) to
NSM Test Results.......................................................................................... 186
Table 425: FRP Strain Predictions using the Standards Australia (2008) ICDebonding
Model and NSM Test Results........................................................................ 193
Table 426: Comparison of the ICDebonding Model by Seracino et al. (2007a) to NSM
Test Results.................................................................................................... 195
Table 427: FRP Strain Predictions using the Seracino et al. (2007a) ICDebonding
Model and NSM Test Results........................................................................ 203
xx
Table 428: Comparison of the ICDebonding Model by Said and Wu (2008) to NSM
Test Results.................................................................................................... 206
Table 429: FRP Strain Predictions using the Said and Wu (2008) ICDebonding Model
and NSM Test Results................................................................................... 213
Table 51: Negative Moment Deficiencies for Posting Trucks at Critical Locations...... 224
Table 52: Dimensions and Material Properties for Capacity Calculations.................... 227
Table 53: FRP Strain Values for the Letohatchee Bridge using the Model by Standards
Australia (2008)............................................................................................. 232
Table 54: FRP Strain Values for the Letohatchee Bridge using the Model by Seracino,
Jones, et al. (2007)......................................................................................... 234
Table 55: FRP Spacing Recommendations for Letohatchee Bridge.............................. 240
Table 56: Reinforcement Ratios for the Letohatchee Bridge......................................... 243
Table 57: Reinforcement Ratios for the Experimental Tests from the Literature.......... 245
Table 61: Properties and Dimensions of Steel and FRP for Proposed Testing
Program.......................................................................................................... 251
Table 62: Unstrengthened Moments for Specimens in Test Series 1............................. 257
Table 63: Predicted Strengthened Capacities, Stresses, Strains, and Failure Modes..... 259
Table 64: Unstrengthened Moments for Specimens in Test Series 2............................. 264
Table 65: Predicted Strengthened Capacities, Stresses, Strains, and Failure Modes..... 265
Table 66: Unstrengthened Moments for Specimens in Test Series 3............................. 268
Table 67: Predicted Strengthened Capacities, Stresses, Strains, and Failure Modes..... 269
Table 68: Unstrengthened Moments for Specimens in Test Series 4............................. 273
Table 69: Predicted Strengthened Capacities, Stresses, Strains, and Failure Modes..... 274
xxi
Table B1: Input for Sample Calculations for All Models.............................................. 291
Table B2: Sample Calculations using each Model......................................................... 291
xxii
LIST OF FIGURES
Figure 11: Photo of an NSM Application (Hughes Brothers 2009)................................... 2
Figure 21: StressStrain Graph of Typical FRP Systems Compared to Steel
(Vasquez 2008).................................................................................................. 7
Figure 22: Surface Preparation for a WetLayup EB System Installation......................... 9
Figure 23: Application of FRP in a WetLayup EB System.............................................. 9
Figure 24: Installation of a WetLayup System................................................................ 10
Figure 25: Completed Installation of a WetLayup EB System....................................... 10
Figure 26: Application of FRP in a Precured System (Carmichael and Barnes 2005).... 11
Figure 27: Installation of a Precured System (Carmichael and Barnes 2005).................. 12
Figure 28: Completed Installation of a Precured System (Carmichael and Barnes
2005)................................................................................................................ 12
Figure 29: Installation of an NSM System (Hughes Brothers 2009)............................... 14
Figure 210: Illustration of a PEDebonding Failure Mode (Vasquez 2008).................... 15
Figure 211: Illustration of an ICDebonding Failure Mode (Vasquez 2008)................... 16
Figure 212: Illustration of a CDC Debonding Failure Mode (Vasquez 2008)................. 18
Figure 213: Test Results of a Cover Delamination Failure (Fanning and Kelly 2001).... 19
Figure 214: Internal Strain and Stress Profiles for a Section in Flexure
(ACI 440 2008)................................................................................................ 25
Figure 215: Elevation Views of a PullOff Test (Blaschko 2003)................................... 34
xxiii
Figure 216: Elevation and Cross Section of Test Specimen and the Steel Reinforcement
Details (Hassan and Rizkalla 2003)................................................................. 36
Figure 217: MohrCoulomb Failure Criterion (Hassan and Rizkalla 2003).................... 38
Figure 218: Stress Distribution at the NSM Strip Cutoff Point (Vasquez 2008)............. 40
Figure 219: Mohr?s Circle (left) and the Resultant Stress Distribution (right)
(Vasquez 2008)................................................................................................ 42
Figure 220: Layout of CChannel Girders (Rosenboom 2006)........................................ 44
Figure 221: Both Cross Sections of the CChannel Girders (Rosenboom 2006)............. 44
Figure 222: Schematic of a PushPull Test for EB (Seracino, Raizal Saifulnaz, and
Oehlers 2007)................................................................................................... 48
Figure 223: ICDebonding Failure Plane for EB and NSM strips (Seracino, Raizal
Saifulnaz, and Oehlers 2007)........................................................................... 49
Figure 224: Diagram of a PushPull Test for NSM (Seracino et al 2007a)...................... 50
Figure 225: Cross Section of Test Specimens (Reed et al. 2005).................................... 57
Figure 226: Test Setup for Specimens (Reed et al. 2005)................................................ 58
Figure 227: Picture of War Memorial Bridge (Carmichael and Barnes 2005)................ 59
Figure 228: Test Setup with Cross Sections (Yost et al. 2007)........................................ 61
Figure 229: Test Setup for Specimens (Liu, Oehlers, and Seracino 2006)...................... 64
Figure 230: Test Setup and Cross Section (ElHacha and Rizkalla 2004)....................... 66
Figure 231: Elevation View and CrossSectional View of Test Setup
(Jung et al. 2005)..............................................................................................68
Figure 232: Plan View of the NSMStrengthening Schemes (Jung et al. 2005).............. 68
Figure 233: Plan View of the Bottom of a Specimen with Mechanical Interlocking
xxiv
Grooves (Jung et al. 2005)............................................................................... 69
Figure 234: Test Setup and Cross Section (De Lorenzis and Nanni 2002)...................... 71
Figure 235: Test Setup and Cross Section (Sena Cruz and Barros 2004)........................ 72
Figure 236: Test Setup and Cross Section (Sena Cruz et al. 2006).................................. 74
Figure 31: Location of the Letohatchee Bridge (Google Maps 2009)..............................78
Figure 32: Picture of the Letohatchee Bridge................................................................... 79
Figure 33: Plan View of Half of the Letohatchee Bridge................................................. 80
Figure 34: Sketch of the Cross Section at an Interior Support for the Letohatchee
Bridge............................................................................................................... 80
Figure 35: Moment Diagrams for Dead Load Groups for an Exterior Girder................. 82
Figure 36: Example of a loadposting sign (Carmichael and Barnes 2005)..................... 85
Figure 37: Positive Live Load Moment Envelopes across Girder 1................................. 86
Figure 38: Negative Live Load Moment Envelopes across Girder 1............................... 87
Figure 39: Factored Ultimate Moment Envelope for the H20 Loadings using the
Operating Load Combination.......................................................................... 89
Figure 310: Factored Ultimate Moment Envelope for the Posting Trucks using the
Operating Load Combination.......................................................................... 90
Figure 311: Exterior Girder Cross Section at an Interior Support Location.................... 91
Figure 312: Exterior Girder Cross Section at Midspan.................................................... 92
Figure 313: Elevation View of the Amount of Steel and the Approximate Termination
Locations in Girder 1....................................................................................... 93
Figure 314: Factored Positive Moment Capacity along Exterior Girder.......................... 96
Figure 315: Factored Negative Moment Capacity along Exterior Girder........................ 98
xxv
Figure 316: Factored Demand Versus Factored Resistance for H20 Trucks................... 99
Figure 317: Factored Demand Versus Factored Resistance for Posting Trucks............ 100
Figure 318: Elevation View of the Locations of the Letohatchee Bridge
Deficiencies.................................................................................................... 103
Figure 319: Bar Termination and Deficient Region Locations...................................... 104
Figure 41: Comparison between NSM Test Results and Standards Australia (2008)
PEDebonding Capacity Predictions..............................................................113
Figure 42: Comparison between NSM Test Results and Standards Australia (2008)
PEDebonding ChangeinCapacity Predictions............................................ 114
Figure 43: Comparison between NSM Test Results and Hassan and Rizkalla (2003)
PEDebonding Capacity Predictions..............................................................121
Figure 44: Comparison between NSM Test Results and Hassan and Rizkalla (2003)
PEDebonding ChangeinCapacity Predictions............................................ 122
Figure 45: Comparison between NSM Test Results and Vasquez (2008) PEDebonding
Capacity Predictions...................................................................................... 127
Figure 46: Comparison between NSM Test Results and Vasquez (2008) PEDebonding
ChangeinCapacity Predictions.................................................................... 128
Figure 47: Comparison between EB Test Results and ACI 440 (2008) ICDebonding
Capacity Predictions...................................................................................... 133
Figure 48: Comparison between EB Test Results and ACI 440 (2008) ICDebonding
ChangeinCapacity Predictions.................................................................... 134
Figure 49: Comparison between EB Test Results and fib 9.3 (2001) ICDebonding
Capacity Predictions...................................................................................... 138
xxvi
Figure 410: Comparison between EB Test Results and fib 9.3 (2001) ICDebonding
ChangeinCapacity Predictions.................................................................... 139
Figure 411: Comparison between EB Test Results and Standards Australia (2008) IC
Debonding Capacity Predictions....................................................................145
Figure 412: Comparison between EB Test Results and Standards Australia (2008) IC
Debonding ChangeinCapacity Predictions..................................................146
Figure 413: Comparison between EB Test Results and Rosenboom (2006) IC
Debonding Capacity Predictions....................................................................151
Figure 414: Comparison between EB Test Results and Rosenboom (2006) IC
Debonding ChangeinCapacity Predictions..................................................152
Figure 415: Comparison between EB Test Results and Seracino, Raizal Saifulnaz, and
Oehlers (2007) ICDebonding Capacity Predictions..................................... 157
Figure 416: Comparison between EB Test Results and Seracino, Raizal Saifulnaz, and
Oehlers (2007) ICDebonding ChangeinCapacity Predictions................... 158
Figure 417: Comparison between EB Test Results and Said and Wu (2008) IC
Debonding Capacity Predictions....................................................................163
Figure 418: Comparison between EB Test Results and Said and Wu (2008) IC
Debonding ChangeinCapacity Predictions..................................................164
Figure 419: Comparison between NSM Test Results and ACI 440 (2008) ICDebonding
Capacity Predictions...................................................................................... 169
Figure 420: Comparison between NSM Test Results and ACI 440 (2008) ICDebonding
ChangeinCapacity Predictions.................................................................... 170
Figure 421: Enlarged Graph of the ACI 440 (2008) NSM Capacity Comparisons....... 171
xxvii
Figure 422: Enlarged Graph of the ACI 440 (2008) NSM ChangeinCapacity
Comparisons.................................................................................................. 172
Figure 423: Comparison between NSM Test Results and fib 9.3 (2001) ICDebonding
Capacity Predictions...................................................................................... 179
Figure 424: Comparison between NSM Test Results and fib 9.3 (2001) ICDebonding
ChangeinCapacity Predictions.................................................................... 180
Figure 425: Enlarged Graph of the fib 9.3 (2001) NSM Capacity Comparisons........... 181
Figure 426: Enlarged Graph of the fib 9.3 (2001) NSM ChangeinCapacity
Comparisons.................................................................................................. 182
Figure 427: Comparison between NSM Test Results and Standards Australia (2008) IC
Debonding Capacity Predictions....................................................................189
Figure 428: Comparison between NSM Test Results and Standards Australia (2008) IC
Debonding ChangeinCapacity Predictions..................................................190
Figure 429: Enlarged Graph of the Capacity Comparisons of the Standards Australia
(2008) Model................................................................................................. 191
Figure 430: Enlarged Graph of the ChangeinCapacity Comparisons of the Standards
Australia (2008) Model.................................................................................. 192
Figure 431: Comparison between NSM Test Results and Seracino et al. (2007a) IC
Debonding Capacity Predictions....................................................................199
Figure 432: Comparison between NSM Test Results and Seracino et al. (2007a) IC
Debonding ChangeinCapacity Predictions..................................................200
Figure 433: Enlarged Graph of the Capacity Comparisons of the Seracino et al. (2007a)
Model............................................................................................................. 201
xxviii
Figure 434: Enlarged Graph of the ChangeinCapacity Comparisons of the Seracino,
Jones, et al. (2007) Model.............................................................................. 202
Figure 435: Comparison between NSM Test Results and Said and Wu (2008) IC
Debonding Capacity Predictions....................................................................209
Figure 436: Comparison between NSM Test Results and Said and Wu (2008) IC
Debonding ChangeinCapacity Predictions..................................................210
Figure 437: Enlarged Graph of the Capacity Comparisons of the Said and Wu (2008)
Model............................................................................................................. 211
Figure 438: Enlarged Graph of the ChangeinCapacity Comparisons of the Said and Wu
(2008) Model................................................................................................. 212
Figure 439: Comparison of Capacity Predictions by PEDebonding Models to NSM
Experimental Results..................................................................................... 215
Figure 440: Comparison of ChangeinCapacity Predictions by PEDebonding Models to
NSM Experimental Results............................................................................216
Figure 441: Comparison of Capacity Predictions by ICDebonding Models to EB
Experimental Results..................................................................................... 217
Figure 442: Comparison of ChangeinCapacity Predictions by ICDebonding Models to
EB Experimental Results............................................................................... 218
Figure 443: Comparison of Capacity Predictions by ICDebonding Models to NSM
Experimental Results..................................................................................... 219
Figure 444: Comparison of ChangeinCapacity Predictions by ICDebonding Models to
NSM Experimental Results............................................................................220
Figure 51: Elevation View of the Locations of the Letohatchee Bridge Deficiencies... 223
xxix
Figure 52: Recommended Groove Dimensions (ACI 440 2008)................................... 228
Figure 53: Letohatchee Bridge Capacities using the Model by ACI 440 (2008)........... 229
Figure 54: Letohatchee Bridge Capacities using the Model by Standards Australia
(2008)............................................................................................................. 231
Figure 55: Letohatchee Bridge Capacities using the Model by Seracino et al.
(2007a)........................................................................................................... 233
Figure 56: Required Amounts of Thin FRP Strips for each Model................................ 235
Figure 57: Required Amounts of Thick FRP Strips for each Model.............................. 236
Figure 58: Factored Demand Envelope and Factored Resistance.................................. 238
Figure 59: Elevation View of the Recommended FRP Lengths for the Letohatchee
Bridge (not to scale)....................................................................................... 239
Figure 510: Cross Section of a Possible Spacing Configuration for Six NSM Strips per
Girder............................................................................................................. 241
Figure 511: Cross Section of a Possible Spacing Configuration for Three NSM Strips per
Girder............................................................................................................. 241
Figure 61: Elevation View of the Proposed Test Setup for a Typical Specimen........... 249
Figure 62: Specimen Identification System.................................................................... 250
Figure 63: (a) Cross Section for Specimens with ?
s
of 0.2% (b) Cross Section for
Specimens with ?
s
of 0.6%............................................................................ 254
Figure 64: Specimen Names and Cross Sections for Test Series 1................................ 255
Figure 65: (a) Cross Section of Specimen 2LS2F00 (b) Cross Section for Deeper
Specimens...................................................................................................... 262
Figure 66: Specimen Names and Cross Sections for Test Series 2................................ 263
xxx
Figure 67: Cross Section of Specimens in Test Series 3................................................ 267
Figure 68: Specimen Names and Cross Sections for Test Series 3................................ 267
Figure 69: Cross Section of Specimens in Test Series 4................................................ 271
Figure 610: Specimen Names and Cross Sections for Test Series 4.............................. 272
1
Chapter 1: Introduction
1.1 Background
Fiberreinforced polymer (FRP) laminates are being used to effectively strengthen
reinforced concrete members. A flexural application for this material is for strengthening
of bridges. Historically, the most widely used method of strengthening bridges for
positive moment has been to bond steel plates to the underside of bridge girders. This
method is laborintensive and can become very costly due to the extensive scaffolding
required to support the steel plates during bonding to the concrete surface (Rosenboom
2006).
An alternative to this process is externallybonded (EB) FRP reinforcement. For
this application, EB strips or sheets are bonded to the concrete surface with an epoxy.
The EB reinforcement is light enough for workers to support by themselves, so extensive
scaffolding is not needed.
If the bridge girders need negativemoment strengthening, then the FRP can be
applied in a nearsurface mounted (NSM) application. For NSM FRP reinforcement, a
longitudinal groove is cut in the top of the concrete, epoxy is applied into the groove, and
the FRP strip is placed into the epoxyfilled groove. Figure 11 shows a picture of an
NSM application.
Figure 11: Photo of an NSM Application (Hughes Brothers 2009)
For this application, no traffic lanes need to be closed for the lanes underneath the
bridge, and only the bridge lanes that are being worked on need to be closed. As opposed
to the EB application, the NSM application does not need extensive surface preparation
of the concrete. It is relatively simple compared to the other methods and can be an
effective strengthening technique (ElHacha and Rizkalla 2004).
The Alabama Department of Transportation (ALDOT) has received Federal
Highway Administration (FHWA) funding to strengthen a bridge in Lowndes County,
near Letohatchee, Alabama, through the TEA21 Innovative Bridge Research and
Construction (IBRC) program. This bridge has a Bridge Inventory Number (BIN) of
8847. For this type of bridge, there are concerns about girder negativemoment capacity
2
3
in portions of each span. If the strengthening scheme proves to be effective for this
bridge, it could be used to strengthen other bridges that were constructed using the same
ALDOT standard design.
1.2 Research Objectives and Tasks
The main objectives of this research are to study the behavior of FRPstrengthened
concrete beams, quantify the amount of flexural strengthening that FRP can provide, and
develop recommendations for an NSM FRP strengthening scheme. To accomplish these
objectives, the following tasks were completed:
1. The current models in the literature were analyzed and compared to existing
experimental research to determine the most accurate models.
2. Quantify the amount of strengthening needed by determining the demand and
capacity of the Letohatchee bridge.
3. Once the extent of the current knowledge was known, a strengthening scheme
for the bridge was developed.
4. Finally, a testing program was proposed to further study ICdebonding
behavior and to result in a more efficient strengthening scheme for the bridge.
1.3 Organization of Thesis
An overview on the behavior of FRP is presented in Chapter 2. Material properties and
applications for FRP are discussed. Problems associated with FRPstrengthened members
are reviewed, as well as various models proposed by researchers to describe the behavior
of FRPstrengthened concrete beams. Existing experimental tests on FRP behavior are
then described.
4
A background on the existing bridge near Letohatchee, Alabama, is presented in
Chapter 3. A description of the bridge is given. The demand and capacity for the existing
bridge are shown along with the locations and magnitudes of the bridge?s deficiencies.
An examination of the code recommendations and some of the proposed models
that are available in the literature is presented in Chapter 4. Model predictions are
compared to published experimental results to determine the accuracy of the models. The
advantages and shortcomings of the models are also discussed.
A proposed strengthening plan for the Letohatchee bridge based on analyses of
the models discussed in the previous chapter is presented in Chapter 5. The amount,
length, and spacing of the FRP are all proposed.
A proposed laboratory testing program to further investigate FRP behavior is
presented in Chapter 6. Four different test series are suggested, and the properties and
specifications of the experimental program are given.
Chapter 7 provides a summary of the thesis and conclusions reached by the
author. Some recommendations for future testing are also given.
5
Chapter 2: Behavior of Reinforced Concrete Beams Strengthened with FRP
2.1 Introduction
Because fiberreinforced polymer (FRP) materials have been found to be stronger and
lighter than steel, there has been much research into understanding FRP behavior. For
FRP reinforcement to be used in the field, the designer must be able to quantify how
much strengthening the FRP material will add to the inplace structure. Premature
debonding has become a common observance for externallybonded FRP reinforcement,
and understanding this behavior is important for the effective implementation of FRP as a
strengthening material (Vasquez 2008).
This chapter covers basic principles associated with FRP behavior. The
composition, applications, and important properties of FRP materials are discussed. FRP
strengthened members are examined, and different failure modes are explained. The
process of determining the capacity of strengthened members is described, including
available design recommendations as well as behavioral models formulated by
researchers. Also, various factors that might affect this strengthened capacity are
discussed. Finally, an overview of some relevant experimental programs is presented.
6
2.2 Components and Applications of FRP
FRP reinforcement is manufactured through a variety of methods using various
components and is applied to existing structures in a couple of different ways. These
applications can be divided into two main categories: externallybonded (EB) FRP
systems and nearsurface mounted (NSM) FRP systems (Seracino, Raizal Saifulnaz, and
Oehlers 2007). This section discusses FRP materials and their different applications.
2.2.1 Different FRP Materials and Properties
Three fiber types are commonly used in FRP: carbon, glass, and aramid fibers. Carbon
fibers were the most commonly used fibers found in the available literature, whereas
aramid fibers were the least common.
FRP materials generally have higher tensile strengths than steel. Table 21 shows
some typical values for tensile strength and Young?s modulus of FRP materials that are
given in the document by ACI Committee 440 titled, ?Guide for the Design and
Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures
(ACI 440.2R08).?
Table 21: Values of Tensile Strength and Young?s Modulus for FRP
FRP Fiber Type Ultimate Tensile Strength Young?s Modulus
Carbon
1,020 to 2,080 MPa
(150 to 350 ksi)
100 to 140 GPa
(15,000 to 21,000 ksi)
Glass
520 to 1,400 MPa
(75 to 200 ksi)
20 to 40 GPa
(3,000 to 6,000 ksi)
Aramid
700 to 1,720 MPa
(100 to 250 ksi)
48 to 68 GPa
(7,000 to 10,000 ksi)
All of these FRP materials have a greater tensile strength than reinforcing steel?s
typical yield strength and ultimate strength of about 420 MPa (60 ksi) and 520 MPa (75
ksi), respectively. As shown in the table, the FRP materials have a smaller elastic
modulus than steel?s typical value of 200 GPa (29,000 ksi).
Unlike steel reinforcement, FRP reinforcement does not yield; it remains
practically linearelastic until failure. This property of FRP results in a brittle failure in
tension. Figure 21 shows the strength advantage of FRP reinforcement over steel
reinforcement, but it also shows the nonductile behavior of the FRP material. The FRP
ruptures at a strain of around 1 to 3%, whereas the steel ruptures at around 30%. In
Figure 21, the average values from Table 21 were used for the FRP materials.
Steel (fracture at ~30%)
Carbon
Glass
Aram id
0
200
400
600
800
1000
1200
1400
1600
1800
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Strain (%)
St
r
e
s
s
(MPa
)
Figure 21: StressStrain Behavior of Typical FRP Systems Compared to Steel
(Vasquez 2008)
7
8
Another important property of FRP is its density. According to ACI 440 (2008),
the typical density of FRP is approximately four to six times lower than that of steel.
Table 22 shows some typical density values for FRP materials and for steel.
Table 22: Typical Density Values for FRP Materials and Steel (ACI 440 2008)
Steel CFRP GFRP AFRP
7.9 g/cm
3
(490 pcf)
1.5 to 1.6 g/cm
3
(90 to 100 pcf)
1.2 to 2.1 g/cm
3
(75 to 130 pcf)
1.2 to 1.5 g/cm
3
(75 to 90 pcf)
2.2.2 ExternallyBonded (EB) FRP
The most common application of FRP for strengthening of existing reinforced concrete
structures is externallybonded (EB) systems. In this method, the FRP sheets are bonded
to the external surface of the concrete. Typical EB systems can be divided into wetlayup
systems and precured systems. Wetlayup systems involve dry unidirectional or
multidirectional fiber sheets that are saturated on site with a resin and then bonded to the
concrete surface with the resin and a compatible primer and putty. The wetlayup systems
are then cured in place, similar to castinplace concrete. Precured systems consist of
unidirectional or multidirectional precured sheets that are applied to the concrete surface
with an adhesive, primer, and putty and are cured before they arrive at the site. Both EB
systems can be used to strengthen beams in flexure or shear and to strengthen columns,
especially for seismic confinement (ACI 440 2008; fib 9.3 2001).
Figures 22 through 25 show an example of a wetlayup system installation. The
pictures were taken by fellow Auburn University researchers.
Figure 22: Surface Preparation for a WetLayup EB System Installation
Figure 23: Application of FRP in a WetLayup EB System
9
Figure 24: Installation of a WetLayup EB System
Figure 25: Completed Installation of a WetLayup EB System
10
Figures 26 through 28 show the installation and application of a precured
system.
Figure 26: Application of FRP in a Precured System (Carmichael and Barnes 2005)
11
Figure 27: Installation of a Precured System (Carmichael and Barnes 2005)
12
Figure 28: Completed Installation of a Precured System (Carmichael and Barnes 2005)
13
2.2.3 NearSurface Mounted (NSM) FRP
EB FRP systems have been found to debond at relatively low values of FRP axial strain
(Seracino et al. 2007a; Liu, Oehlers, and Seracino 2006). In response to this phenomenon,
nearsurface mounted (NSM) reinforcement has become more appealing. In NSM
systems, instead of bonding the laminate to the exterior of the concrete member, it is
bonded in grooves cut into the concrete surface. First, a groove is cut in the concrete
surface. After the groove is cleaned of dust and fine particles, epoxy is injected into the
groove, and the NSM FRP strip or bar is placed into the epoxyfilled groove. Then, the
groove is filled completely with epoxy, and the excess is scraped off so that the epoxy is
flush with the concrete surface. If more than one NSM strip or bar is needed, typically
another parallel groove is cut at a certain distance away from the first groove. Figure 29
shows the installation of an NSM system for positivemoment strengthening.
NSM reinforcement is commonly found in two types: rods and strips. The rods
typically have a circular cross section and are usually deformed along the length, much
like deformed steel reinforcement. The crosssectional area of an NSM rod is typically
that of a SI #10 or #13 (#3 or #4 U.S. Customary size) steel reinforcing bar. The NSM
strips have a rectangular shape, with dimensions of about 2 mm (0.079 in.) thick by 16 to
20 mm (0.63 to 0.79 in.) wide (Hughes Brothers 2009).
Figure 29: Installation of an NSM System (Hughes Brothers 2009)
According to fib 9.3 (2001), pultrusion is ?an automated, continuous process for
manufacturing composite rods and structural shapes having a constant cross section.
Roving and/or tows are saturated with resin and continuously pulled through a heated die,
where the part is formed and cured. The cured part is then cut to length.? NSM rods are
formed by this pultrusion process and typically delivered to the site in the form of a
single bar. NSM strips are also formed by this pultrusion process, but are typically
delivered to the site in a 1m (3ft) diameter roll.
One of the inherent advantages of NSM systems over EB systems is the fact that
the concrete can bond to both faces of the FRP strip rather than just one face. Because EB
14
systems typically fail due to FRP debonding, the increased bond capacity of NSM strips
should, in theory, increase the FRP debonding resistance.
2.3 Failure Modes of FRPStrengthened Members
There are many different failure modes for FRPstrengthened members. The controlling
failure mode depends on many parameters, such as the location of the FRP cutoff point,
the concrete compressive strength, the bonded width of the FRP, and the FRP rupture
stress. The strengthened member can fail due to debonding of the FRP laminate, caused
by either plateend (PE) debonding or intermediate crack (IC) debonding. It can also fail
due to rupture of the FRP reinforcement, failure in the concrete, or a combination of any
of these modes.
2.3.1 PlateEnd (PE) Debonding
Plateend (PE) debonding occurs when the shear stresses in the FRP reinforcement at the
location of the cutoff point become too high and cause the strip to peel off of the
concrete. The failure can either occur in the adhesive layer or in the concrete layer (fib
9.3 2001). Figure 210 shows an illustration of this debonding mechanism.
Figure 210: Illustration of a PEDebonding Failure Mode (Vasquez 2008)
15
2.3.2 Intermediate Crack (IC) Debonding
Intermediate crack (IC) debonding occurs when a flexural crack in the concrete creates a
stress concentration in the FRP reinforcement, which typically occurs in or near the
region of maximum moment (Vasquez 2008). Figure 211 shows an illustration of this
debonding mechanism.
Figure 211: Illustration of an ICDebonding Failure Mode (Vasquez 2008)
Once the stress exceeds a limiting stress at the FRPtoconcrete interface, the FRP
reinforcement starts to separate from the concrete member. After this occurs, the
debonding propagates from the flexural crack(s) to the end of the reinforcement until the
FRP reinforcement becomes totally ineffective (Vasquez 2008).
2.3.3 FRP Rupture
Failure due to FRP rupture maximizes the use of the FRP material. By reaching the FRP
rupture stress, the full capacity of the strengthening material is attained. Up to this rupture
level, the FRP remains in the linearelastic range. Once this rupture stress is reached, the
FRP material does not yield and can no longer strengthen the concrete member. It cannot
sustain any loading beyond this point, and it results in a very brittle failure of the FRP
reinforcement. The concrete member may exhibit adequate curvature or displacement
16
17
ductility, but the FRP reinforcement will fail in a brittle manner, and no sustained loads
beyond this rupture point can be carried by the FRP material (Rosenboom 2006).
2.3.4 Concrete Failure
If the strength of the concrete is low enough or if the member is reinforced with too much
FRP reinforcement, the concrete can fail before any failure occurs in the FRP material.
Concrete failure can occur due to the crushing of the concrete in the compressive region
or due to a shear failure.
2.3.5 Combined Failure Modes
Frequently, FRPstrengthened members fail by a combination of failure modes, where the
failure modes occur almost simultaneously. Sometimes, it is difficult to distinguish which
mode caused the collapse. In a laboratory setup, if the instruments are not positioned at
the critical locations, it can be very difficult to conclude which failure mode occurs first.
Some researchers have mentioned other failure modes that are not previously
listed in this section. One of these is called critical diagonal crack (CDC) debonding.
CDC debonding is a combination of IC and PE debonding that is caused by a diagonal
shear crack (Vasquez 2008). This shear crack occurs in the shear span of the member,
and if it reaches the FRP reinforcement near the end of the plate, it could cause a peeloff
failure due to stress concentrations at the crack location and limited bonded length
beyond the crack. CDC debonding is illustrated in Figure 212.
Figure 212: Illustration of a CDC Debonding Failure Mode (Vasquez 2008)
Another failure mode that has been described by researchers is cover
delamination. Cover delamination involves a combination of PE debonding and a failure
in the concrete. Just like PE debonding, when the shear stresses at the plate cutoff
location get too high, the plate starts to peel off of the beam. However, with cover
delamination, the failure plane continues into the concrete section up to the internal
longitudinal tension steel. Instead of the FRP plate peeling off, the entire concrete cover,
starting from the location of the plate cutoff end, peels off of the beam (Fanning and
Kelly 2001). Figure 213 shows a laboratory test specimen that failed due to cover
delamination.
18
Figure 213: Test Results of a Cover Delamination Failure (Fanning and Kelly 2001)
2.4 Available Recommended Design Provisions
There are not currently any building code requirements set forth by either the American
Concrete Institute (ACI), the International Federation for Structural Concrete (fib), or
Standards Australia that specifically address FRP systems for strengthening concrete
structures. However, these organizations have published guides and recommendations for
the design and construction of externallybonded (EB) FRPstrengthened concrete
structures. In the Standards Australia document, both EB and nearsurface mounted
(NSM) systems are discussed; however, there are currently no documents published by
ACI or fib that are specifically for NSM FRP systems.
19
20
2.4.1 ACI Committee 440 Design Recommendations
The title of ACI Committee 440 is, ?Fiber Reinforced Polymer Reinforcement.? This
committee has published ACI 440.2R08, titled, ?Guide for the Design and Construction
of Externally Bonded FRP Systems for Strengthening Concrete Structures.? In this
document, the main focus is on EB FRP reinforcement, but NSM FRP reinforcement is
briefly addressed. The 2008 version of ACI 440.2R has some significant changes from
the earlier 2002 version; most of the changes occur in the debonding strain equations.
ACI 440.2R (2008) is divided into five parts: general, materials, recommended
construction requirements, design recommendations, and design examples. Design
recommendations are subdivided into six chapters: general design requirements; flexural
strengthening; shear strengthening; strengthening of members subjected to axial force or
combined axial and bending forces; FRP reinforcement details; and drawings,
specifications, and submittals.
In the general design requirements section, the ultimate FRP rupture stress and
strain are both reduced by an environmental reduction factor, C
E
, to account for any
degradation due to ?exposure to certain environments, such as alkalinity, salt water,
chemicals, ultraviolet light, high temperatures, high humidity, and freezingandthawing
cycles.? Values for this reduction factor are shown in Table 23.
Table 23: Environment Reduction Factor Values Given by ACI 440 (2008)
Exposure conditions Fiber type
Environmental
reduction factor C
E
Carbon 0.95
Glass 0.75 Interior exposure
Aramid 0.85
Carbon 0.85
Glass 0.65
Exterior exposure (bridges, piers, and
unenclosed parking garages)
Aramid 0.75
Carbon 0.85
Glass 0.50
Aggressive environment (chemical
plants and wastewater treatment plants)
Aramid 0.70
This reduction in rupture stress and strain is shown in Equations 21 and 22,
*
fuEfu
fCf =
Equation 21
*
fuEfu
C ?? =
Equation 22
where stands for the ultimate tensile strength of the FRP material as reported
by the manufacturer; stands for the design ultimate tensile strength of the FRP
material; stands for the ultimate rupture strain of the FRP reinforcement; and
*
fu
f
fu
f
*
fu
?
fu
?
stands for the design rupture strain of the FRP reinforcement.
2.4.1.1 Debonding of FRP Reinforcement
To prevent PE debonding, Section 13.1 gives three options: using anchorage near the
cutoff point, minimizing the stress in the FRP by locating the cutoff point close to or
beyond the region of zero moment, or both. To prevent IC debonding for EB systems,
Section 10.1.1 of ACI 440.2R08 limits the effective strain in the FRP reinforcement by
Equation 23,
21
fu
ff
c
fd
tnE
f
?? 9.0083.0
'
?= in in.lb units
fu
ff
c
fd
tnE
f
?? 9.041.0
'
?= in Nmm units
Equation 23
where
fd
? is the debonding strain of the FRP; is the concrete compressive
strength; n is the number of FRP plies; E
f
is the FRP elastic modulus; and t
f
is the FRP
thickness. This debonding strain equation was calibrated using a database of IC
debonding failures. By using the average measured values of strain, the coefficient of
0.083 was attained for English units (0.41 for SI units).
'
c
f
To prevent IC debonding for NSM applications, Section 10.1.1 limits the effective
strain in the NSM FRP reinforcement by Equation 24.
fufd
?? 7.0=
Equation 24
One of the biggest differences between the 2002 and 2008 versions of the ACI
440.2R document is the debonding strain equation. As shown in Equation 23, the 2008
version is in terms of the concrete compressive strength and the FRP axial stiffness per
unit width. The 2002 version, however, is only in terms of the FRP axial stiffness per unit
width. Also, the 2002 version does not have an equation for NSM, but the 2008 version
does and is shown in Equation 24.
2.4.1.2 Strengthened Moment Capacity
To accurately calculate FRP strains, the strain in the concrete before FRP strengthening
must be accurately estimated to account for any existing strain at the location of the FRP
at the time of installation. This value can be determined from an elastic crackedsection
22
analysis of the unstrengthened section. In the analysis, only the loads on the member that
will be present during strengthening need to be applied. By using this existing substrate
strain and by using strain compatibility, an effective strain level in the FRP at the ultimate
limit state can be found by using Equation 25,
fdbi
f
cufe
c
cd
???? ??
?
?
?
?
?
?
?
? ?
=
Equation 25
where
fe
? is the effective strain level in the FRP reinforcement at failure;
cu
? is
the maximum usable strain of unconfined concrete, which is generally taken as 0.003
in./in.; d
f
is the effective depth of the FRP flexural reinforcement; c is the distance from
the extreme compression fiber to the neutral axis; and
bi
? is the strain level in the
concrete substrate at the time of FRP installation. In Equation 25, if the calculated value
for
fe
? is less than
fd
? , then a concrete crushing failure will control; if it is greater, then
FRP debonding or FRP rupture will control.
The effective stress in the FRP can be calculated using the effective strain in the
FRP with the following equation:
feffe
Ef ?=
Equation 26
where
fe
f is the effective stress in the FRP.
Based on the strain in the FRP, the strain in the steel reinforcement can be
calculated as follows:
()
?
?
?
?
?
?
?
?
?
?
+=
cd
cd
f
bifes
???
Equation 27
23
where
s
? is the strain in the nonprestressed steel reinforcement; and d is the
distance from the extreme compression fiber to the centroid of the tension reinforcement.
Using the strain in the steel reinforcement, the stress in the steel reinforcement
can be calculated with the following equation:
ysss
fEf ?= ?
Equation 28
where
s
f is the stress in the nonprestressed steel reinforcement; E
s
is the modulus
of elasticity of steel; and is the yield strength of steel.
y
f
Once all of the strains and stresses for the cross section have been calculated
using Hooke?s law and strain compatibility, the neutral axis depth at failure, c, can be
calculated using Equation 29,
bf
fAfA
c
c
fefss
1
'
1
??
+
=
Equation 29
where A
s
is the area of nonprestressed steel reinforcement; A
f
is the area of FRP
reinforcement;
1
? is the multiplier on to determine the intensity of an equivalent
rectangular stress distribution for concrete;
'
c
f
1
? is the ratio of the depth of the equivalent
rectangular stress block to the depth of the neutral axis; and b is the width of the
compression face of the member. If concrete crushing is the controlling failure mode,
then the Whitney stress block can be used, and
1
? can be taken as 0.85. If FRP rupture or
debonding is the controlling failure mode, then
1
? can be calculated using the following
equation:
2
'
1
2'
1
3
3
c
ccc
??
???
?
?
=
Equation 210
24
where
c
? is the strain in the concrete; and is the maximum strain of
unconfined concrete corresponding to and is usually taken as 0.002 in./in.
'
c
?
'
c
f
Figure 214 shows an illustration of the internal strain and stress distribution for a
rectangular section under flexure at ultimate limit state.
Figure 214: Internal Strain and Stress Profiles for a Section in Flexure (ACI 440 2008)
After the neutral axis depth is known, the nominal moment capacity, M
n
, of the
section can be determined from Equation 211,
?
?
?
?
?
?
?+?
?
?
?
?
?
?=
22
11
c
hfA
c
dfAM
feffssn
?
?
?
Equation 211
where
f
? is an additional strength reduction factor for the FRP reinforcement;
and h is the overall height of the member. ACI 440 recommends that
f
? be taken as 0.85
for flexure. The two minus signs shown in Equation 211 were erroneously omitted from
the equation shown in the ACI 440 document.
25
2.4.1.3 Development Length
For EB systems, ACI 440 gives the development length of the FRP reinforcement, , by
Equation 212.
df
l
'
057.0
c
ff
df
f
tnE
l = in in.lb units
'
c
ff
df
f
tnE
l = in SI units
Equation 212
For NSM systems, ACI 440 gives the development length of the FRP
reinforcement by Equation 213,
()
fd
b
b
df
f
d
l
?4
= for circular bars
()()
fd
bbb
bb
df
f
ba
ba
l
?+
=
2
for rectangular bars
Equation 213
where d
b
is the FRP bar diameter; is the design stress of the FRP
reinforcement;
fd
f
b
? is the average bond stress for NSM FRP bars; a
b
is the smaller cross
sectional dimension for rectangular FRP bars; and b
b
is the larger crosssectional
dimension for rectangular FRP bars. ACI 440.2R08 recommends using 1000 psi (6.9
MPa) for
b
? .
2.4.1.4 Serviceability Recommendations
To avoid inelastic deformations of reinforced concrete members, ACI 440 limits the
internal steel reinforcement to 80% of its yield strength and the concrete to 45% of its
compressive strength under service loads.
26
27
2.4.2 fib Task Group 9.3
Task Group 9.3 of the International Federation for Structural Concrete (fib) prepared
Bulletin 14 in 2001. The title of Task Group 9.3 is, ?FRP (Fibre Reinforced Polymer)
reinforcement for concrete structures.? Bulletin 14 is titled, ?Externally bonded FRP
reinforcement for RC structures.? The main focus of this document is on EB FRP
reinforcement; NSM FRP reinforcement is mentioned only a few times.
Bulletin 14 provides recommendations on the design and use of EB FRP. The
design guidelines are divided into three approaches. The first approach limits the ultimate
FRP strain to a certain value and requires that the end anchorage of the EB FRP be
verified. The bulletin does not give any specific equation or value for this limiting strain,
but it does mention that previous tests show that the ultimate FRP strain can range from
0.0065 to 0.0085 mm/mm. The task group admits that a global strain limit may not be
suitable to cover the entire range of FRP applications. They predict that future models
will not just limit the FRP strain value but will be based on extensive testing and
analytical calculations. Task Group 9.3 suggests that the other two approaches will
provide a more realistic prediction of the EB FRP capacity.
The second approach involves the calculation of the change in FRP tensile stress
between two subsequent cracks. Once the stress exceeds the maximum value that can be
transferred by bond stresses, the FRP will debond. This debonding usually is initiated at
flexural cracks. This approach consists of three steps: determination of the most
unfavorable spacing of the flexural cracks; determination of the tensile force within the
EB reinforcement at two subsequent cracks; and determination of the maximum possible
increase in tensile stress in the FRP.
The third approach consists of two steps. In the first step, the end anchorage must
be verified, as in the first approach. In the second step, the shear stress at the FRP
concrete interface is calculated and compared to a limiting shear stress value. Bulletin 14
gives the shear stress by Equation 214:
xb
N
?
f
fd
b
?
?
=
Equation 214
where is the shear stress at the FRPconcrete interface; is the width of the
FRP; is the distance between the two cross sections being analyzed; and is the
change in the FRP axial force between the two cross sections. To simplify this
expression, Task Group 9.3 assumed that the steel will yield before FRP debonding
occurs. After making this assumption, they presented the following three expressions:
b
?
f
b
x? fdN?
m
d
fd
z
M
N
?
=?
Equation 215
dz
m
95.0?
Equation 216
d
d
V
x
M
?
?
?
Equation 217
where
d
is the change in moment across the two cross sections; is the
lever arm of the tensile reinforcement; d is the effective depth of the section; and is
the design shear force. Substituting these three equations into Equation 214 gives the
following equation:
M?
m
z
d
V
f
d
b
db
V
?
95.0
=
Equation 218
28
To get the limiting shear stress value, Task Group 9.3 adopts the MohrCoulomb
failure criterion where the bond strength is equal to about 1.8 times the tensile strength of
the concrete. The following equation shows this limiting stress:
c
ctk
cbd
f
f
?
8.1=
Equation 219
where is the bond shear strength of concrete, in MPa; is the
characteristic concrete tensile strength, in MPa; and
cbd
f
ctk
f
c
? is a material safety factor for the
concrete. To get the mean value for the bond shear strength, needs to be replaced
with , which is given by the 1990 CEBFIP Model Code as,
ctk
f
ctm
f
3/2
MPa10
MPa40.1
?
?
?
?
?
?
=
cm
ctm
f
f Equation 220
where is the concrete?s mean tensile strength, in MPa, and is the
concrete?s mean compressive strength, in MPa.
ctm
f
cm
f
In this derivation, it was assumed that the steel strain was approximately equal to
the FRP strain. Task Group 9.3 noted that this assumption is conservative. Another
assumption is that if this approach is used, flexural cracks will only produce micro
cracking and local debonding and will not result in bond failure (fib 9.3 2001).
2.4.3 Standards Australia
Standards Australia published a design guide titled, ?Design handbook for RC structures
retrofitted with FRP and metal plates: beams and slabs? in 2008. This design handbook
outlines the generic and fundamental behaviors of plated beams and slabs. Some design
29
rules and recommendations are also given but are shown in the commentary and not in
the guidelines.
Standards Australia?s design handbook on FRP uses the same environmental
reduction factor as ACI 440.2R08. It directly references ACI 440 and uses the same
factors. These environmental reductions factors are shown in Table 23, which is located
in ACI 440.
One of the main focuses of this handbook is plate debonding, specifically PE
debonding and IC debonding. For these types of debonding, the guidelines state that the
debonding failure will occur within the concrete because the tensile strength of the
adhesive is usually an order of magnitude stronger than that of the concrete.
2.4.3.1 PEDebonding Models
The Australian handbook?s guidelines state three locations along the beam to terminate a
plate in order to prevent PE debonding: at a point of contraflexure, where the curvature is
low, or on a compression face in a continuous beam. If any of these guidelines cannot be
met, the handbook?s commentary gives some formulas for calculating the moment at the
plate end that causes PE debonding. For EB plates on the tension face of a beam, the
following formula is given:
()[]
( )
tfpp
cbplcr
ch
tfpPE
tE
fEIK
M
474.0
.
=
Equation 221
where ()[ ]
ch
tfpPE
M is the characteristic moment at the plate end that causes PE
debonding for a tensionfaced EB plate, in Nmm; K is a constant equal to 0.53 for the
characteristic value and 1 for the mean value; ( )
plcr
EI
.
is the flexural rigidity of the
30
cracked plated cross section adjacent to the plate end, in Nmm
2
; f
cb
is the Brazilian or
splitting tensile strength of the concrete, in MPa; E
p
is the modulus of elasticity of the
plate, in MPa; and t
tfp
is the thickness of the tensionfaced EB plate, in mm.
To develop an expression to describe the PEdebonding behavior of NSM plates,
a model was first developed for EB plates that are bonded to the sides of a beam. These
EB side plates are oriented in the same direction as NSM plates, but because the NSM
plates are bonded on both sides instead of just one, the capacity for the NSM plates is
taken to be twice the EB side plate capacity. For NSM plates, the following equation is
given:
()[]
( )
()
tfpNSMtfpNSMp
cbplcr
ch
tfpNSMPE
dtE
fEIK
M
??
?
+
=
0185.0185.0
2
.
Equation 222
where ()[ ]
ch
tfpNSMPE
M
?
is the characteristic moment at the plate end that causes PE
debonding for a tensionfaced NSM plate, in Nmm; K is a constant equal to 0.81 for the
characteristic value and 1 for the mean value; t
NSMtfp
is the thickness of the tensionfaced
NSM plate, in mm; and d
NSMtfp
is the distance between the centroid of the specific NSM
plate and the neutral axis of the cracked plated section.
2.4.3.2 ICDebonding Models
The Australian handbook describes two types of ICdebonding models: a basic IC
debonding model and a more representative ICdebonding model for beams. The basic
model is based on pushpull tests and is used as a lower bound for predicting capacities
for beams. The representative model more accurately describes the behavior of a plated
beam.
31
2.4.3.2.1 Basic ICDebonding Models
There are two models given for the basic ICdebonding resistance. The first model given
is a generic model that can be used for either EB or NSM plates. This model is taken
from the paper by Seracino, Raizal Saifulnaz, and Oehlers (2007) and is further discussed
later in this chapter. The second model was taken from a paper by Teng et al. (2002) and
is shown in Equation 223,
()[]
'
cppppEB
EB
ppIC
ftEbP ??= Equation 223
where ()[ ]
EB
ppIC
P is the ICdebonding resistance for an EB plate, in N; ?
EB
is an
ICdebonding coefficient and is 0.427 for the mean value and 0.315 for the characteristic
value; b
p
is the width of the EB plate, in mm; t
p
is the thickness of the EB plate, in mm;
and ?
p
is given in Equation 224,
cp
cp
p
bb
bb
/1
/2
+
?
=? Equation 224
where ?
p
is a width factor, and b
c
is the width of the concrete, in mm.
2.4.3.2.2 Beam ICDebonding Model
There is just one model that is given to calculate the ICdebonding resistance for beams.
According to Standards Australia, this model should only be used for EB plates and
should not be used for NSM plates. No ICdebonding model for NSM plates is given by
Standards Australia as of 2008. The model to calculate the mean value of the IC
debonding resistance for EB plates is shown in the following equation:
()
'
887.0
cppppEBIC
ftEbP ?= Equation 225
32
33
To develop this equation, Equation 223 was modified by recalibrating the IC
debonding coefficient. Instead of using simple lapshear specimens to calibrate the
coefficient, FRPstrengthened beam and slab specimens were used, which resulted in a
coefficient that is twice as big.
2.5 Models for FRP Debonding Failure Modes
FRPstrengthened concrete members will often fail due to FRP debonding. Many models
have been proposed to try to predict the capacity at which this debonding occurs. FRP
debonding can be separated into plateend (PE) debonding and intermediate crack (IC)
debonding.
2.5.1 PlateEnd (PE) Debonding Models
The models in this section attempt to predict when PE debonding will occur. Most of the
models are focused on determining the bending moment at the cutoff section when the
FRP plate starts to debond. Then, this moment is used to obtain the corresponding
bending moment at midspan, which is taken as the moment capacity of the strengthened
cross section.
2.5.1.1 Blaschko (2003)
Blaschko (2003) conducted about one hundred pulloff tests to analyze the bond behavior
between NSM FRP strips and concrete. Figure 215 shows a schematic of the pulloff
tests conducted by Blaschko.
Figure 215: Elevation Views of a PullOff Test (Blaschko 2003)
In this test, an NSM strip was bonded to a concrete block and then pulled along its
longitudinal axis until it separated from the block. The concrete blocks shown in Figure
215 were 300 mm (12 in.) by 300 mm (12 in.) while all other dimensions and properties
were varied. He noted that in most of the tests, the failure occurred in the adhesive layer.
By assuming that failure will occur in the adhesive layer and by analyzing the results of
these bond tests, he proposed a design approach to calculate bond capacity at the end of
the plate. The design approach consists of two equations, given as:
for l
v
? 115mm: ( )
vvrkKLkV
llabF 0015.04.0
4
,,
?= ? Equation 226
for l
v
> 115mm:
(
?
?
?
?
?
?
?
?
??
?
?
?
?
?
+= 115
70
tanh065.02.26
4
,, v
r
rkKLkV
l
a
abF ? )
Equation 227
In Equations 226 and 227, F
V,k
stands for the characteristic bond strength, in N;
b
L
is the width of the FRP strip, in mm; ?
K,k
is the characteristic shear strength of the
adhesive, in N/mm
2
; a
r
is the distance, in mm, no greater than 150 mm (5.9 in.), between
the strip and the edge of the concrete member, in mm; and l
V
is the bond length, in mm.
34
35
Blaschko gives a typical range for ?
K,k
as 20 to 25 N/mm
2
(2900 to 3600 psi).
Blaschko limits the value of a
r
to a maximum value of 150 mm (5.9 in.) because, at this
point, the concrete edge no longer has any influence on the FRP strip.
Two equations are needed because when the slip between the FRP strip and the
concrete exceeds a certain value, the amount of bond stress that can be transferred is
limited by the amount of friction between the strip and the concrete. The FRP strip?s
bonded length is used to determine which equation to apply. The first equation is valid in
the elasticplastic range for the adhesive, and the second equation incorporates the
stresses due to friction.
2.5.1.2 Hassan and Rizkalla (2003)
In the study by Hassan and Rizkalla (2003), eight reinforced concrete beams were
strengthened with NSM FRP strips and were tested under a monotonic static loading. One
beam was left unstrengthened and used as a control beam. Different embedment lengths
were used to investigate PE debonding. Figure 216 shows an elevation and cross section
of a typical beam with its steel reinforcement details.
Figure 216: Elevation and Cross Section of Test Specimen and the Steel Reinforcement
Details (Hassan and Rizkalla 2003)
All units are in mm, and all bar sizes are SI sizes. The average concrete
compressive strength after 28 days was 48 MPa (7000 psi). A closedform analytical
solution was proposed to describe the behavior at the cutoff point of an FRP strip. The
authors assumed that PE debonding is a result of a concentration of high shear stresses at
the FRP strip?s end. Therefore, the proposed model predicts interfacial shear stresses at
this point.
In this model, different closedform solutions were derived for various loading
configurations. The first loading configuration was a simply supported beam with a
36
concentrated load at midspan. The two boundary conditions used for this case were that
the normal stress in the FRP strip was zero at its end and that the shear stress was zero at
midspan. Using these boundary conditions, the following formula was derived:
?
?
?
?
?
?
?
?
+=
?
eff
eff
?x
eff
effof
I
nPy
?e
I
ynPlt
?
222
Equation 228
where stands for the shear stress; t
f
is the thickness of the FRP strip; n is the
FRP?s modular ratio; P is the applied concentrated load; l
o
is the distance from the end of
the beam to the start of the FRP strip; y
eff
is the distance from the FRP strip to the neutral
axis of the section; I
eff
is the effective moment of inertia of the section; x is the
longitudinal coordinate starting from the cutoff point of the strip; and
?
? is defined by
Equation 229.
ffa
a
Ett
G2
2
=?
Equation 229
In Equation 229, G
a
is the shear modulus of the adhesive; t
a
is the thickness of
the adhesive; and E
f
is the elastic modulus of the FRP.
The calculated shear stress from Equation 228 is then compared to a limiting
value. The test results showed that the failure occurred in the concrete layer. Once the
compressive strength and the tensile strength of concrete are known, the MohrCoulomb
line, which is a line that is tangential to both Mohr?s circles for pure tension and pure
compression, can be found. Figure 217 shows these Mohr?s circles and the Mohr
Coulomb line.
37
Figure 217: MohrCoulomb Failure Criterion (Hassan and Rizkalla 2003)
All circles tangential to the MohrCoulomb line represent a critical stress
combination. The pure shear circle represents the critical stress combination that has its
center at the origin. The authors proposed that the limiting shear stress value is equal to
the maximum critical shear stress for the pure shear circle, given as follows:
ct
c
ct
c
ff
ff
+
=
'
'
max?
Equation 230
In Equation 230, equals the compressive strength of the concrete at 28 days,
and f
ct
equals the tensile strength of the concrete. By equating Equation 228 with
Equation 230, the PEdebonding loads can be determined for this specific support and
loading configuration. Other shear stress formulas are given in the paper for different
support and loading setups.
'
c
f
38
39
The authors compared their predicted debonding loads to the measured debonding
loads from their eight FRPstrengthened beams. They also conducted a nonlinear finite
element analysis using the ANACAP program to predict shear stresses, and they
compared these shear stresses to the predicted shear stresses from their analytical model.
They found that their model accurately predicted the PEdebonding loads and the shear
stresses when compared against the experimental results and the finite element analysis,
respectively.
2.5.1.3 Vasquez (2008)
Vasquez (2008) used finite element models and previous analytical models to derive a
new PEdebonding model for NSM FRP strips. In this model, the normal and shear
stresses were identified, some general assumptions were made regarding reinforced
concrete, and a principlestress equation was proposed. Once the normal stresses were
known, the shear stress was calculated and compared to a limiting value.
From mechanics, six different stresses can be developed at any location. These
stresses, shown in Figure 218, are specifically for a point in the concrete that is adjacent
to the cutoff point of a NSM strip.
Figure 218: Stress Distribution at the NSM Strip Cutoff Point (Vasquez 2008)
Because the concrete is assumed to be cracked, the normal stress, ?
ZZ
, was
ignored. Also shown in Figure 218 is the assumed shear stress distribution. Because this
point is located at the FRP cutoff location and because the shear stress approaches zero at
the top and bottom of the concrete, which is near the possible locations of the NSM strip,
the shear stress ?
YZ
was disregarded. Also, because the strip is located so close to the
tension face of the concrete, the normal stress ?
YY
was ignored.
After making these assumptions, the only stresses that remained were two shear
stresses, ?
XZ
, ?
XY
, and a normal stress, ?
XX
. Vasquez then derived equations for these
stresses by assuming linear elastic behavior, assuming that plane sections remain plane,
using strain compatibility, and applying Hooke?s law. Once these stresses were known, a
resultant stress was derived. The principle stresses were calculated as the roots of this
polynomial:
40
0
32
2
1
3
=?+? III ??? Equation 231
where I
1
, I
2
, and I
3
are constants.
By applying the assumptions that ?
YY
, ?
ZZ
, and ?
YZ
are negligible, Equations 232
through 234 were then derived.
XX
I ?=
1
Equation 232
22
2 XZXY
I ?? ??= Equation 233
0
3
=I
Equation 234
Substituting the constants I
1
, I
2
, and I
3
into Equation 231 yields the three
principle stresses, ?
1
, ?
2
, and ?
3
. Due to the previous assumptions made, ?
2
will always
equal zero, ?
1
will be a tensile stress, and ?
3
will be a compressive stress. For these
resultant stresses, the corresponding maximum shear stress,
max
? , is calculated by
Equation 235.
2
31
max
??
?
+
= Equation 235
The resulting Mohr?s circle and a representation of the resultant stresses are
shown in Figure 219.
41
Figure 219: Mohr?s Circle (left) and the Resultant Stress Distribution (right)
(Vasquez 2008)
Once the maximum shear stress, ?
max
, is calculated, it can be compared to the
limiting value of shear stress. Vasquez proposed that two different failure criteria be
used. The first failure criterion is the same one used by Hassan and Rizkalla (2003). It is
the maximum critical shear stress for the pure shear circle, given by Equation 230. The
other limiting value comes from a paper by Mattock and Hawkins (1972). Vasquez gives
the equation shown in Equation 236, where the only variable is f
ct
, the tensile strength of
the concrete, in MPa.
ct
f06.1
max
=?
Equation 236
The process is then iterated until the maximum shear stress calculated from
Equation 235 equilibrates the limiting shear stress value given by Equation 236.
42
43
This model was compared to existing experimental results of PEdebonding
failures to determine the accuracy of the model. Vasquez found that his model yielded
conservative yet adequately accurate results.
2.5.2 Intermediate Crack (IC) Debonding Models
The models in this section attempt to predict when failure will occur due to IC
debonding. Some models predict ICdebonding failure strains in the FRP reinforcement,
whereas others predict the bending moment that corresponds to an ICdebonding failure.
2.5.2.1 Rosenboom (2006)
In the research by Rosenboom (2006), thirty fullscale prestressed concrete bridge girders
were tested under two different loading conditions: extreme loading conditions simulated
by a monotonic load to failure and service loading conditions simulated by static and
fatigue loading. For the first phase of the research, only the repair and strengthening of
the beams was examined. For the second phase, the bond behavior of the FRP was
examined, and an analytical model was proposed to describe the behavior. Rosenboom
recommends that the analytical model should be used for EB reinforcement only.
For the repair and strengthening phase of the research, twentysix bridge girders
were tested using EB and NSM FRP. The girders were prestressed concrete Cchannel
girders with spans of 9.18 m (30.1 ft) each. All of the girders came from decommissioned
bridges in North Carolina. Figure 220 shows a diagram of the girder layout.
Figure 220: Layout of CChannel Girders (Rosenboom 2006)
Figure 221 shows the two cross sections that were used in the tests.
Figure 221: Both Cross Sections of the CChannel Girders (Rosenboom 2006)
The distances shown in Figures 220 and 221 are in mm. The specified concrete
compressive strength for these girders was 34.5 MPa (5000 psi). Rosenboom concluded
44
45
that NSM strips are the most structurally efficient strengthening technique, whereas EB
reinforcement is the most costeffective.
For the second phase of the research, four bridge girders were tested
monotonically to failure. These girders had the same cross section as the Type C1 girder
shown in Figure 221. Three beams failed by IC debonding, and the other beam failed
due to FRP rupture. Rosenboom used twentyeight existing models to predict the IC
debonding loads for these beams and for a database that was assembled of ICdebonding
failures. Two of the models included in the analysis are Bulletin 14 by fib 9.3 (2001) and
the 2002 version of the document by ACI 440. Most of the other models were derived or
based on pushpull tests. He concluded that none of the models correlated well with the
database, especially not the 2002 version of the model given by ACI Committee 440,
which he concluded is actually unconservative. He also concluded that the reason most of
the models were inaccurate is due to the fact that the models are based on pushpull tests
rather than actual beam tests. Rosenboom then proposed a new analytical model that
predicts the bond behavior at the intermediate cracks. The proposed model is based on
calculating the maximum shear stress between the point at which the internal steel first
yields and the debonding moment location, adding this shear stress component to the
component due to stress concentrations, and then setting the total shear stress equal to a
limiting value.
The proposed model is based on calculating two types of concrete shear stresses:
shear stresses directly related to the load and shear stresses related to stress
concentrations at the ?toe? of a flexural crack. In the model, a debonding strain in the
FRP is first assumed. Then, all of the strains and stresses in the cross section are
calculated using strain compatibility. Once these values are known, the moment capacity
is calculated. This moment capacity is considered the moment at which debonding
occurs. Then, the shear stress in the concrete related directly to the load is needed. To
calculate this value, the distance from the support to the location of first yielding of the
internal tensile reinforcement, , needs to be computed. For three and fourpoint
bending, Equation 237 can be used.
y
x
db
y
y
M
M
sx =
Equation 237
In this equation, s is the shear span; M
y
is the yield moment of the strengthened
section; and M
db
is the debonding moment. Using the value, the shear stress in the
concrete related directly to the load, which Rosenboom assumed was the maximum shear
stress and denoted as
y
x
maxw
? , can be calculated by using Equation 238,
y
yfdb
ffw
xs
tnE
?
?
=
@
max
??
?
Equation 238
where is the axial stiffness of FRP material per unit width;
ff
tnE
db
? is the FRP
debonding strain; and
yf @
? is the tensile strain in the FRP at first yielding of the internal
tensile steel at a moment of M
y
. All units are in N and mm.
After computing this concrete shear stress component, the other concrete shear
stress component needs to be calculated. Rosenboom assumed that the shear stress in the
concrete related to stress concentrations at the ?toe? of a flexural crack,
maxsc
? , was a
function of the concrete compressive strength and the ratio of the yield moment over the
46
debonding moment. An equation was formulated and calibrated against a database of
experimental ICdebonding failures. This expression is shown in Equation 239,
'
max
1.115.2
c
db
y
sc
f
M
M
?
?
?
?
?
?
?
?
?=?
Equation 239
where is the concrete compressive strength, in MPa.
'
c
f
For design purposes, Equation 240 was proposed to give a probability of
exceedance of 5%.
'
max
1.13
c
db
y
sc
f
M
M
?
?
?
?
?
?
?
?
?=?
Equation 240
For both Equations 239 and 240, the ratio of M
y
to M
db
should be less than one
because the model was not designed for debonding to occur before the internal steel
yields. When both concrete shear stresses are known, the total concrete shear stress,
i
? ,
can be calculated using Equation 241.
maxmax scwi
??? +=
Equation 241
The failure criterion then needs to be computed. Rosenboom derives this equation
as,
'
max
134.1
cc
f=? Equation 242
where
maxc
? is the limiting shear stress in the concrete, in MPa. Once
i
? and
maxc
? are known, the debonding strain in the FRP is iterated until these two concrete
shear stress values are equal. Once the debonding strain in the FRP is found, the
strengthened moment capacity can then be calculated using strain compatibility.
47
The proposed model was compared to the database of experimental ICdebonding
failures to determine its accuracy relative to the other models analyzed. Rosenboom
concluded that the proposed model outperformed the other models and that most of the
other models were too conservative.
2.5.2.2 Seracino, Raizal Saifulnaz, and Oehlers (2007)
In the study by Seracino, Raizal Saifulnaz, and Oehlers (2007), fourteen new pushpull
tests using NSM FRP were conducted, and an analytical model was derived that predicts
the ICdebonding resistance of FRPstrengthened reinforced concrete members. The
model was used to analyze the fourteen new tests as well as existing pushpull data from
the referenced literature for both NSM and EB. Figure 222 shows a schematic of a push
pull test for EB.
Figure 222: Schematic of a PushPull Test for EB (Seracino, Raizal Saifulnaz, and
Oehlers 2007)
The model is based on the local interface shear stressslip relationship (??) of the
debonding interface. Specifically, it uses a simplified linearsoftening interface bondslip
relationship and a unique confinement ratio that results in a generic model that can be
used for both EB and NSM FRP and for any adhesively bonded plate cross section and
48
material. This unique confinement ratio is given as the aspect ratio of the ICdebonding
failure surface. Figure 223 shows the ICdebonding failure surfaces for both EB and
NSM strips.
Figure 223: ICDebonding Failure Surfaces for EB and NSM strips (Seracino, Raizal
Saifulnaz, and Oehlers 2007)
Using these debonding planes, the confinement ratio,
f
? , can be calculated using
the following equation:
f
f
f
b
d
=?
Equation 243
where d
f
is the length of the failure plane perpendicular to the concrete surface
and b
f
is the length of the failure surface parallel to the concrete surface. The total length
of the debonding failure surface, , can be calculated using:
per
L
ffper
bdL += 2
Equation 244
49
For these debonding surfaces, the authors conducted a parametric analysis and
recommend that 1 mm (0.04 in.) be used for the values of t
b
and t
d
. Once these cross
sectional values are computed, the ICdebonding resistance is then given by:
( )
pruptppercfpIC
AfEALfP <=
33.025.0
85.0 ?? for Nmm units
( )
pruptppercfpIC
AfEALfP <=
33.025.0
393.0 ?? for lbin. units
Equation 245
where P
IC
is the ICdebonding resistance; is the concrete cylinder compressive
strength; ( is the axial rigidity of the FRP; and
c
f
)
p
EA
?
?
?
=
limit confidence 95%lower for
mean for
85.0
0.1
p
?
Equation 246
Because this model is only a function of geometric and material properties, any
plate material can be used. Once the debonding resistance is calculated, the debonding
stress and strain can be found, as can the moment capacity.
2.5.2.3 Seracino et al. (2007a)
Seracino et al. (2007a) conducted thirtysix new pushpull tests of NSM strips. Figure 2
24 shows a diagram of a pushpull test for NSM.
Figure 224: Diagram of a PushPull Test for NSM (Seracino et al. 2007a)
50
Using the new test results, the authors performed a nonlinear statistical analysis
and proposed a model for predicting the debonding failure load for an NSM FRPto
concrete joint. The authors determined from their analysis that the parameters necessary
in determining the ICdebonding failure load are the concrete compressive strength and
the FRP strip dimensions. By using these variables and conducting a nonlinear regression
analysis for optimization, the following formula was reached:
ppruptppcIC
dbfbdfP ?=
21.036.1
?? for SI units
ppruptppcIC
dbfbdfP ?=
21.036.1
3?? for U.S. Customary units
Equation 247
where is the maximum predicted ICdebonding resistance, in kN for SI units
or kips for U.S. Customary units;
IC
P
? is 0.19 or 0.16 for the mean or characteristic values,
respectively; ? is used to account for bond length; is the compressive cylinder
strength of concrete, in MPa or psi; and are the plate dimensions perpendicular
and parallel to the concrete surface, respectively, in mm or in.; and is the rupture
stress of the FRP, in GPa or ksi. The concrete compressive strength is limited to a range
of 30 to 65 MPa (4400 to 9400 psi); the FRP depth is limited to 10 mm to 20 mm (0.39 to
0.79 in.); and the FRP thickness is limited to 1.2 mm to 2.4 mm (0.047 to 0.094 in.). The
c
f
p
d
p
b
rupt
f
? factor can be found using:
?
?
?
<
?
=
mm 200for
mm 200for
200/
0.1
L
L
L
? for units of mm
?
?
?
<
?
=
in. 7.9for
in. 7.9for
9.7/
0.1
L
L
L
? for units of in.
Equation 248
where L is the bonded length of the FRP.
51
To maximize the debonding resistance, a minimum critical FRPbonded length of
200 mm (7.9 in.) is recommended. Efficiency further increases when the depth of the
FRP into the concrete increases. The improved efficiency is attributed to the increased
confinement of the interface debonding crack by the surrounding concrete cover.
2.5.2.4 Said and Wu (2008)
Said and Wu (2008) reviewed two hundred previous EB test results of beams or slabs
with ICdebonding failures in order to propose an ICdebonding model that would
accurately predict the debonding strain value of the FRP strips. They assumed that the
debonding strain,
db
? , is a function of the concrete compressive strength, the FRP elastic
modulus, and the FRP thickness. Using these parameters, they formulated the relationship
shown in Equation 249.
( )
3
2'
/)(1
C
ff
C
cdb
tEfC=? Equation 249
The values of C1, C2, and C3 are constants, and the units used are N and mm.
Using the two hundred previous tests from the literature, Said and Wu calibrated their
model to most accurately predict the debonding strain. Using values of 0.23, 0.2, and 0.35
for constants C1, C2, and C3 , respectively, they reached a closedform empirical
solution for the debonding strain, shown in Equation 250.
( )
35.0
2.0'
/)(23.0
ffcdb
tEf=? Equation 250
Said and Wu used this model to predict the debonding strains for the experimental
tests. They noted that their model predicted the ICdebonding capacity more accurately
than other models mentioned in the paper, including the approach by ACI Committee 440
in 2002 and the approach by fib 9.3 in 2001.
52
53
2.6 FRP Spacing Recommendations for NSM Strips
The distance between NSM FRP strips can affect the moment capacity of a strengthened
member. Spacing the strips at the recommended distance from each other will result in
individual failure planes. Conversely, spacing the strips too close to each other can result
in one common failure plane that will make the ultimate loadcarrying capacity prediction
less accurate (Vasquez 2008). Also, the distance of the FRP strip from the side edge of
the concrete surface is an important factor. If this distance is too small, the corner of the
concrete could split off (Blaschko 2003), or premature debonding of the FRP strip could
occur (ACI 440 2008).
For NSM systems, ACI 440 (2008) recommends that the clear spacing between
NSM grooves be no less than twice the depth of the groove to avoid any overlapping of
tensile stresses around the NSM bars. For the edge distance, their recommendation is that
this distance be a minimum of four times the depth of the groove.
fib 9.3 (2001) does not provide any spacing limits or recommendations for NSM
FRP strips.
Hassan and Rizkalla (2004) tested eight concrete beams strengthened with NSM
FRP bars and developed a finite element model to describe the NSM behavior. In the
model, they specifically looked at groove spacing and edge distance of the bars. The
groove spacing was varied from 0.25 to 2 times the bar diameter, the groove width was
varied from 1.5 to 2.5 times the bar diameter, and the edge distance was varied from 2 to
6 times the bar diameter. For the groove spacing, the authors proposed a minimum clear
spacing of twice the diameter of the FRP bars, regardless of groove width. They also
54
recommended a minimum edge distance of four times the diameter of the FRP bars to
minimize the edge effect.
Kang et al. (2005) used a finite element model to analyze the effect of FRP
spacing on the capacity of four specimens strengthened with varying configurations of
NSM strips. The specimens were 300 mm (12 in.) high and 200 mm (8 in.) wide, with a
span of 3 m (10 ft). Once the finite element model was verified against the four test
specimens, the model was used to analyze the effect of the NSM spacing. After varying
the NSM spacing from 20 to 180 mm (0.8 to 7.1 in.) and the edge distance from 90 to 10
mm (3.5 to 0.4 in.) for two separate groove depths, 15 and 25 mm (0.59 and 0.98 in.),
they concluded that the most efficient design should leave a minimum distance of 40 mm
(1.6 in.) between NSM strips and a minimum distance of 40 mm (1.6 in.) from the strip to
the concrete edge.
Rashid et al. (2008) specifically studied how the spacing of the FRP strips and the
side cover distance of the FRP affects the ICdebonding resistance of the strips. They
conducted twentytwo new pull tests, including seventeen tests on NSM strips. They
concluded that the NSM plates have a strong effect on the adjacent plates and the
concrete cover. They recommended that the lateral spacing of NSM plates be no less than
53 mm (2.1 in.), with an edge distance of no less than 3? times the depth of the NSM
plate.
In his thesis, Vasquez (2008) wrote that, as a general rule, the spacing between
adjacent grooves should be greater than 2? times the groove width, as opposed to the
depth, to ensure that there will be individual failure planes. His suggestion is based on the
recommendations of a document by Standards Australia while it was in the process of
being published; however, the final version of the document does not address any spacing
limits for NSM.
Table 24 summarizes the NSM groove spacing and side cover recommendations
found in the literature.
Table 24: Summary of NSM Groove Spacing and Side Cover Recommendations
Clear spacing of strips Side cover distance
ACI Committee 440 (2008) 2?(groove depth) 4?(groove depth)
Hassan and Rizkalla (2004) 2?(FRP bar diameter) 4?(FRP bar diameter)
Kang et al. (2005) 40 mm (1.6 in.) 40 mm (1.6 in.)
Rashid et al. (2008) 53 mm (2.1 in.) 3??(FRP depth)
Vasquez (2008) 2??(groove width) 
2.7 Effect of Concrete Surface Roughness
The roughness of the concrete surface has been investigated to examine the effects on an
FRPstrengthened member. Yalim, Kalayci, and Mirmiran (2008) conducted research on
twentysix beams that were tested in flexure with two different EB FRP systems, three
different concrete surface profiles, and six different levels of FRP anchorage. Ten
additional beams were tested in double shear to investigate the bond behavior of the FRP.
They concluded that the surface roughness of the concrete had no significant effect on the
overall performance of the FRP system, nor did it affect the bond behavior of the FRP.
However, an FRP manufacturer (Hughes Brothers 2009) and various code organizations
55
56
(ACI 440 2008; Standards Australia 2008; fib 9.3 2001) recommend that the concrete
surface be repaired and prepared before strengthening with FRP.
2.8 Effect of Embedding NSM Strips
One of the reasons that NSM strips are used instead of EB reinforcement is because of
their increased confinement and increased ICdebonding strains. Embedding NSM strips
farther into the concrete provides a larger, and better confined, bonded surface between
the two materials. In theory, this extra embedment results in higher ICdebonding strains
and, thus, greater ductility (Oehlers et al. 2008).
Oehlers et al. (2008) investigated the effects of embedding NSM strips at varying
groove depths by performing twenty new pull tests. Mathematical expressions were
developed to describe the effects of embedment on the ICdebonding resistance and the
local bond stressslip relationship. The authors stated that embedding the NSM strips at
deeper groove depths can increase the debonding resistance by up to three times over
strips embedded at shallower groove depths. Another stated benefit of embedment is that,
because of better FRP bond, larger FRP cross sections can be used. The authors also
suggest that embedment may improve the fire resistance of FRP.
2.9 Previous Testing of FRPStrengthened Members
This section discusses some of the previous tests that have been conducted on FRP
strengthened members. The test programs can be broken down into four different
categories: flexural tests on concrete members strengthened with EB FRP strips, flexural
tests on concrete members strengthened with NSM FRP strips or rods, flexural tests
including both EB and NSM types of applications, and modifiedbeam pullout tests
strengthened with NSM strips or rods.
2.9.1 ExternallyBonded (EB) FRP Flexural Tests
The tests in this section include concrete members that were strengthened with EB
reinforcement and tested in flexure. More EB tests were found in the literature, but
because the focus of this thesis is primarily on NSM behavior, only a few EB tests were
chosen to be included.
2.9.1.1 Reed et al. (2005)
In the study by Reed et al. (2005), eight concrete beams were tested in fourpoint bending
and were loaded until failure. Figure 225 shows the cross section that was used.
Figure 225: Cross Section of Test Specimens (Reed et al. 2005)
Figure 226 shows a diagram of the test setup.
57
Figure 226: Test Setup for Specimens (Reed et al. 2005)
The average concrete compressive strength was 7,100 psi (49 MPa). Seven of the
beams were strengthened with EB FRP strips; one was left unstrengthened and used as a
control beam. The researchers varied the intensity and frequency of load cycles during
the curing time of the epoxy and investigated its effect on the performance of the beams.
Other variables in this study include the epoxy layer thickness and the FRP strip
thickness. For all of the strengthened beams, failure was initiated by debonding initiating
at the maximum moment sections. The design recommendations from the 2002 version of
the ACI Committee 440 document were followed to calculate the limiting debonding
strains in the FRP. This procedure was found to be unconservative for predicting
capacities for six of the seven strengthened beams.
58
2.9.1.2 War Memorial Bridge
War Memorial Bridge is an eighteenspan reinforced concrete bridge that spans the
Uphapee Creek in Macon County, Alabama. It consists of four variabledepth girders. In
1999, the Alabama Department of Transportation (ALDOT) selected the War Memorial
Bridge for flexural strengthening because of the increased demand on the bridge. Figure
227 shows a picture of the bridge.
Figure 227: Picture of War Memorial Bridge (Carmichael and Barnes 2005)
The Auburn University Highway Research Center proposed an FRPrepair
scheme to strengthen the bridge. Auburn University researchers focused on the three
continuous spans of 161ft length and strengthened them with EB CFRP. After
strengthening, the researchers tested the girders under service loads to determine the
effectiveness of the FRPstrengthened members. They concluded that no debonding of
the FRP occurred under service loads and that the FRP should be able to provide
additional capacity to the girder (Carmichael and Barnes 2005).
59
60
2.9.2 NearSurface Mounted (NSM) FRP Flexural Tests
The tests in this section include concrete members that were strengthened with NSM
reinforcement and tested in flexure.
2.9.2.1 Yost et al. (2007)
In the study by Yost et al. (2007), twelve concrete beams were strengthened with NSM
strips and loaded in fourpoint bending until failure. Three other beams were used as
control beams and, therefore, were not strengthened. Three different steel reinforcement
ratios and two different FRP reinforcing ratios were used. The concrete compressive
strength was measured as 37.2 MPa (5400 psi). Figure 228 shows the test setup and the
different cross sections.
Figure 228: Test Setup with Cross Sections (Yost et al. 2007)
Two of the strengthened beams failed due to FRP rupture. The rest of the beams
failed due to steel yielding followed by concrete crushing. No debonding of the NSM
strips was detected.
2.9.2.2 Taljsten and Nordin (2007)
The tests conducted at Lulea University of Technology by Taljsten and Nordin (2007)
were aimed at comparing the effects of prestressed external tendons of steel and FRP,
along with prestressed and nonprestressed NSM reinforcement, on the strengthened
capacity of reinforced concrete beams. All eight strengthened Tbeams were 6 m (20 ft)
61
62
long and were tested in fourpoint bending until failure. The depth of the Tbeams was
500 mm (20 in.), and the web width was 200 mm (8 in.). The flange height was 100 mm
(4 in.), and the flange width was 400 mm (16 in.). For the two beams strengthened with
nonprestressed NSM reinforcement, rectangular CFRP rods were used, and concrete
compressive strengths of 50 and 53 MPa (7300 and 7700 psi) were used. The researchers
found that the NSM reinforcement was unable to significantly contribute to the stiffness
or strength of the beam in the elastic range. However, once the concrete cracked, the
beam had a stiffer behavior and a higher capacity when compared to the control beam.
After the NSM rods debonded from the surrounding concrete, failure in the strengthened
beams occurred.
2.9.2.3 Teng et al. (2006)
Teng et al. (2006) investigated the effect of bond length on the strengthened capacity of
NSM FRPstrengthened concrete beams. Five beams were loaded in fourpoint bending
monotonically to failure. Four of the beams were strengthened with NSM strips, each
with a different embedment length; the other beam was left unstrengthened and used as a
control beam. The different embedment lengths used were 500, 1200, 1800, and 2900
mm (20, 47, 71, and 114 in.). All of the cross sections were 300 mm (12 in.) high by 150
mm (6 in.) wide, and all of the specimens were 3 m (10 ft) long. The concrete
compressive strength was 35.2 MPa (5100 psi).
The beam with the shortest embedment length, B500, showed no improvement in
strength or stiffness over the control beam, B0. Its ineffectiveness is due to the fact that
the total length of the FRP strip, 500 mm, was not longer than the maximum moment
63
region length of 600 mm. Therefore, part of the beam was left unstrengthened in the
location where the moment was greatest, and the beam behaved similarly to the control
beam.
The beam with the second shortest embedment length, B1200, provided a 30%
increase in capacity over the control beam. Specimen B1200 also provided a greater post
cracking stiffness than the control beam. Specimen B1800 produced a 90% increase in
strength and an even greater postcracking stiffness over the control beam. Specimens
B500, B1200, and B1800 all failed due to plateend (PE) debonding, specifically concrete
cover separation starting from the cutoff section.
Specimen B2900 produced an increase in strength of 106% over the control beam.
Failure for this specimen was due to concrete crushing, followed closely by IC debonding
accompanied by debonding at the epoxyconcrete interface and localized splitting of the
epoxy.
In this research project, Teng et al. also conducted some bond characterization
tests to determine some of the bond properties of the FRP strips. These experiments
consisted of pullout tests of an FRP strip embedded in a concrete block. The concrete
block was 150 mm (6 in.) wide, 150 mm (6 in.) high, and 350 mm (14 in.) long. The
dominant failure mode was a failure at the FRPepoxy interface.
Teng et al. observed that the debonding failure found in the flexural tests differed
greatly from the debonding failure in the bond characterization tests. They noted that
debonding failure in the flexural tests was typically caused by cracking in the concrete
cover region, whereas in the bond tests, pullout failure along the FRPepoxy interface
was most prevalent. The authors attributed this discrepancy to the fact that there are many
factors present in flexural tests that are not present in bond tests. These factors include the
presence of flexural and flexuralshear cracks that change the bond stress distribution, the
internal steel forces created by the cracking of the concrete at the FRP strip?s location,
and the curvature of the beam. The authors stated that the differences between the two
types of tests prevent the direct application of any local bondslip models derived from
simple bond characterization tests to the flexural strengthening of reinforced concrete
beams.
2.9.2.4 Liu, Oehlers, and Seracino (2006)
Liu, Oehlers, and Seracino (2006) studied twospan continuous reinforced concrete
members strengthened with NSM strips. They investigated the ductility and strength of
the strengthened members, along with the amount of moment redistribution. Nine near
fullscale specimens were loaded at each midspan location with a concentrated load.
Figure 229 shows the twospan test setup.
Figure 229: Test Setup for Specimens (Liu, Oehlers, and Seracino 2006)
Six of the specimens had a slabshaped cross section, whereas the other three had
beamshaped cross sections. The slabshaped cross sections were 120 mm (4.7 in.) high
64
65
by 375 mm (15 in.) wide with a concrete compressive strength of 37 MPa (5400 psi). The
beamshaped cross sections were 240 mm (9.4 in.) high by 220 mm (8.7 in.) wide with a
concrete compressive strength of 35 MPa (5100 psi). All specimens were strengthened
with NSM strips near the top of the concrete section over the middle support. To avoid
PE debonding, the strips were terminated at a point of contraflexure. FRP strips were
used for seven of the specimens. The other two specimens were strengthened with steel
plates of approximately the same size.
Two of the NSMstrengthened beam cross sections and one of the NSM
strengthened slab cross sections failed due to IC debonding. The other specimens either
failed due to a shear failure or a concrete crushing failure in the positivemoment regions.
The researchers found that a significant amount of moment redistribution occurred in all
nine test specimens. The NSMstrengthened specimens for the slab and beam cross
sections achieved a moment redistribution of up to 35% and 39%, respectively. The
authors state that the moment redistribution for the NSMstrengthened beams is much
higher than the moment redistribution that previous researchers have noted for EB
strengthened beams. The researchers concluded that NSM plates are more applicable than
EB plates for structures where ductility is the primary concern.
2.9.3 Both EB and NSM FRP Flexural Tests
This section includes test series that consisted of EBstrengthened reinforced concrete
members and NSMstrengthened reinforced concrete members. One of the main
objectives of these test series was to examine the difference in capacity provided by each
type of FRP application.
2.9.3.1 ElHacha and Rizkalla (2004)
A total of eight reinforced concrete Tbeams were tested in the research by ElHacha and
Rizkalla (2004). The beams were simply supported and loaded monotonically until
failure. Seven of the beams were reinforced with different FRP systems; the other beam
was left unstrengthened and used as a control beam. The concrete compressive strength
was 45 MPa (6500 psi). Figure 230 shows the test setup and the typical cross section.
Figure 230: Test Setup and Cross Section (ElHacha and Rizkalla 2004)
The distances in Figure 230 are in mm, and the bar sizes are SI sizes. The
different FRP systems used were NSM strips, NSM bars, and EB strips. For the NSM
66
67
strips, two different types of FRP were used: carbon fiberreinforced polymer (CFRP)
and glass fiberreinforced polymer (GFRP). To improve the anchorage of the EB strips, a
Ushaped wrap made of CFRP was placed around the EB strips at both ends and around
the web of the Tbeams.
The researchers found that the NSM CFRP strips failed due to rupture of the strip.
For the NSM CFRP bars, the NSM GFRP strips, and the EB strips, the mode of failure
was debonding initiating from a crack either in the epoxy or in the concrete.
The NSM CFRP strips were found to have a higher capacity than the NSM CFRP
bars with the same axial stiffness. The authors explain that the higher capacity is due to
premature debonding of the NSM bars and to the smaller debonding surface of the bars
compared to the strips. They also showed that the NSM reinforcement achieved a higher
capacity than the EB reinforcement due to the increased bond area of the NSM strips.
2.9.3.2 Jung et al. (2005)
Jung et al. (2005) examined the flexural behavior of reinforced concrete beams
strengthened by EB and NSM FRP reinforcement. They tested eight 3meterlong
specimens in fourpoint bending to failure. Two beams were strengthened with EB strips,
two with NSM strips, one with an NSM rod, and two with NSM reinforcement with
mechanical interlocking grooves; the other beam was left unstrengthened. The concrete
compressive strength was measured as 31.3 MPa (4500 psi). Figure 231 shows the test
setup and the cross section.
Figure 231: Elevation View and CrossSectional View of Test Setup (Jung et al. 2005)
For Figure 231, the distances are in mm, and the bar sizes are SI sizes. Figure 2
32 shows the NSMstrengthening schemes, including the mechanical interlocking
grooves.
Figure 232: Plan View of the NSMStrengthening Schemes (Jung et al. 2005)
Figure 232 shows a plan view of the bottom of the beams; the distances shown
are in mm. Figure 233 shows a picture of the actual test specimen taken from the same
perspective.
68
Figure 233: Plan View of the Bottom of a Specimen with Mechanical Interlocking
Grooves (Jung et al. 2005)
Much like Taljsten and Nordin (2007), Jung et al. found that the FRP
reinforcement was unable to significantly contribute to the stiffness or strength of the
beam in the elastic range. However, after cracking, the EBstrengthened specimens
attained a 30 to 47% increase in capacity, and the NSMstrengthened specimens attained
a 39 to 65% increase in capacity. For one of the NSM strip applications and both of the
mechanical interlocking groove applications, failure was due to FRP rupture. For all of
the other FRPstrengthened beams, failure was due to IC debonding.
The authors concluded that beams strengthened with NSM strips had a greater
moment capacity than beams strengthened with EB strips. They also concluded that
mechanical interlocking grooves can improve the efficiency of NSM systems, prevent the
premature debonding of the FRP, and lead to higher strengths.
69
70
2.9.4 NSM ModifiedBeam Pullout Tests
The tests described in this section include atypical test setups. Instead of the typical test
setup where the objective is to try to produce a flexural failure, the objective of these tests
is to produce a pullout failure of the FRP. Because the concrete does not undergo flexure,
the concrete specimens do not have any steel reinforcement.
2.9.4.1 De Lorenzis and Nanni (2002)
De Lorenzis and Nanni (2002) tested twentytwo unreinforced concrete beams
strengthened with FRP rods to determine their effect on the bond behavior between NSM
rods and concrete. The beams were loaded under fourpoint bending until failure. They
analyzed the bonded length of the rod, the diameter and surface configuration of the rod,
the type of FRP material, and the size of the groove for the NSM rod. They used a beam
pullout test setup where a steel hinge was placed at midspan at the top of the concrete
section, and a saw cut was made at midspan at the bottom of the concrete section. Figure
234 shows the test setup and the typical cross section.
Figure 234: Test Setup and Cross Section (De Lorenzis and Nanni 2002)
The hinge and the saw cut enabled the researchers to control the internal force
distribution. An inverted Tbeam section was used to increase the tension area of the
concrete and, thus, increase the cracking moment while minimizing the overall beam
weight. Two different FRP materials and two different surface configurations for the rod
were tested: carbon fiberreinforced polymer (CFRP) and glass fiberreinforced polymer
(GFRP), and deformed rods and sandblasted rods. The average concrete compressive
strength ranged from 3880 to 4100 psi (26.7 to 28.2 MPa).
Three different failure modes were observed during the tests: splitting of the
epoxy cover, cracking of the concrete surrounding the groove, and pullout of the FRP
bar. The researchers concluded that deformed rods have a greater bond strength than
sandblasted rods. They also concluded that increasing the groove width leads to higher
71
bond strength when failure is controlled by splitting of the epoxy cover. However, if
pullout failure controls, then increasing the groove width has no effect on bond strength.
2.9.4.2 Sena Cruz and Barros (2004)
In the study by Sena Cruz and Barros (2004), they analyzed the effects that bond length
and concrete strength have on the bond between NSM strips and concrete. Nine
strengthened specimens were loaded to failure in a pulloutbending test. Figure 235
shows the setup and cross section used for this test.
Figure 235: Test Setup and Cross Section (Sena Cruz and Barros 2004)
In this type of test, two blocks of concrete are connected by a steel hinge at the
top and by an NSM strip at the bottom. The concrete blocks are then loaded near the
hinge and supported at the opposite end. For this study, the NSM strip was fully bonded
along the length of one of the concrete blocks. The strip embedded in the other block was
only bonded in the middle section of the block for a set length. To avoid rupture of the
strips, a maximum bond length of 80 mm (3.1 in.) was used. Combinations of three
72
73
different bond lengths and three different concrete strengths were analyzed. The concrete
compressive strengths ranged from 33.0 to 70.3 MPa (4800 to 10200 psi).
All beams failed due to pullout of the FRP, in accordance with the design of the
test setup. The researchers noted that the failure occurred in the concreteadhesive and the
adhesiveFRP interfaces and that no cracking was present in the concrete surface. Sena
Cruz and Barros then concluded that the concrete?s tensile and compressive strengths
have little effect on the pullout behavior and that these are not important factors for this
specific bond test. Conversely, they concluded that the FRP bond length had a significant
influence on the bond strength.
2.9.4.3 Sena Cruz et al. (2006)
In the study by Sena Cruz et al. (2006), they repeated the same type of pulloutbending
test setup that was used in the Sena Cruz and Barros (2004) paper. However, the
variables this time were bond length and the type of loading, and the dimensions were
slightly different than the previous test setup. Figure 236 shows the test setup and the
cross section used by Sena Cruz et al.
Figure 236: Test Setup and Cross Section (Sena Cruz et al. 2006)
Due to the conclusions made by Sena Cruz and Barros (2004), the concrete
strength was held constant at 30 MPa (4400 psi). Three different bond lengths were used
in a series of beams that were loaded monotonically until pullout failure. Three other
beams with three different bond lengths were loaded cyclically for ten cycles of loading
and unloading at a fixed load level. One other beam was tested with one cycle of loading
and unloading at different slip levels.
As in the previous study, all the beams that were tested monotonically failed due
to pullout of the FRP strips, and no cracks in the concrete surface were found. The
cracking was entirely in the concreteadhesive and the adhesiveFRP interface. The
authors concluded that the peak pullout force increases with increasing bond length.
2.10 Summary
The following is a summary of FRP behavior and some conclusions that were reached in
the studies discussed in this chapter:
74
75
1. FRP remains practically linearelastic until failure.
2. Carbon fibers were the most commonly used fibers found in the available
literature.
3. CFRP is approximately five times lighter and five times stronger than steel
reinforcement (ACI 440 2008).
4. The NSM technique is very effective and practical for flexural strengthening
in negativemoment regions (ElHacha and Rizkalla 2004).
5. Two of the primary failure modes for FRPstrengthened members are plate
end (PE) debonding and intermediate crack (IC) debonding.
6. As of 2008, there are no building code requirements for ACI, fib, or Standards
Australia that are specific to FRPstrengthened members. These code
organizations have only produced recommendations on this topic.
7. There have been significant changes made to the FRPdebonding model for
the ACI 440.2R document from the 2002 version to the 2008 version. One
specific change was the inclusion of the concrete compressive strength in the
2008 version of the debonding model.
8. Teng et al. (2006) stated that the debonding failure found in flexural tests
differs greatly from the debonding failure found in bond characterization tests,
such as pushpull tests. Also, there are many factors present in flexural tests
that are absent in bond characterization tests. They concluded that these
differences prevent the direct application of any local bondslip models
derived from simple bond tests to a flexural application.
76
9. Standards Australia states that models based on pushpull tests can be used as
a lower bound for flexural tests.
10. Taljsten and Nordin (2007) and Jung et al. (2005) noted that FRP
reinforcement was unable to significantly contribute to the stiffness or
strength of the beam in the elastic range.
77
Chapter 3: Letohatchee Bridge Background
3.1 Bridge Description
The focus of this chapter is the AL 97 bridge over Interstate 65 near Letohatchee,
Alabama, in Lowndes County. It has been identified by the Alabama Department of
Transportation (ALDOT) as having inadequate strength for certain truck load
configurations. ALDOT?s Bridge Inventory Number (BIN) for this bridge is 8847.
Hereafter, the bridge will be referred to as the ?Letohatchee bridge.? Figure 31 shows its
location. Figure 32 shows a picture of the Letohatchee bridge.
Figure 31: Location of the Letohatchee Bridge (Google Maps 2009)
78
Figure 32: Picture of the Letohatchee Bridge
The Letohatchee bridge is 270 feet (82.3 m) long and consists of four continuous
spans with four reinforced concrete girders at a skew angle of 12 degrees. The two
exterior spans are 60 feet (18.3 m), and the two interior spans are 75 feet (22.9 m). As
shown in Figure 32, the girders have a parabolic haunch over each interior support that
makes the girders have a greater height for increased negativemoment capacity. The
height of the girders ranges from 43 3/8 inches (1102 mm) at midspan to 77 1/8 inches
(1959 mm) over the interior supports. The girders support a 6?inch (159 mm) slab to
comprise a roadway that is 28 feet (8.5 m) wide from curb to curb. In the exterior span, 6
inch (152 mm) webwalls, or diaphragms, are located between each girder at the supports
and at midspan. In the interior span, the 6inch (152 mm) diaphragms are located between
79
each girder at the supports and at every third point of the span. ALDOT?s standard
drawing for this bridge is IC2806, and this drawing is accompanied by standard drawing
I109. Figure 33 shows a simplified plan view of the bridge (without the skew).
Figure 33: Plan View of Half of the Letohatchee Bridge
The bridge is symmetric, and only half of the bridge is shown. Figure 34 shows a
sketch of the cross section of the bridge at an interior support.
Figure 34: Sketch of the Cross Section at an Interior Support for the Letohatchee Bridge
80
81
3.2 Demand on Existing Bridge
The Letohatchee bridge was analyzed by ALDOT Bridge Rating and Load Testing
engineers using the Bridge Rating and Analysis of Structural Systems (BRASS?)
program (Wyoming DOT 2009). For this analysis and for all of the capacity calculations,
AASHTO Standard Specifications for Highway Bridges (1996) was used. Using the
results of the analysis by the ALDOT engineers, the demand on the existing bridge was
determined. The loads were divided into dead loads and live loads. Once these were
known, the loads were factored and combined to form the factored total load. All of the
figures and calculations for this chapter are specifically for an exterior girder.
Calculations were completed for an interior girder, but it was found that the exterior
girder is more critical; therefore, the exterior girder will be discussed here in detail. It was
determined from the BRASS? output that shear is not critical for the Letohatchee
bridge. Flexure will be the focus of the analysis in this chapter.
3.2.1 Dead Load
In the BRASS? program, the slab was taken to be 6 inches (152 mm), rather than 6?
inches (159 mm), due to possible degradation of the roadway surface. To account for this
missing load, an extra ? inch (6.4 mm) of slab dead load was added into the first group
of superimposed dead load (SDL), which also included the diaphragm weight. The curb
and rail system was accounted for in a second SDL group. The girder weight and the slab
weight were included in the group labeled, ?Dead Load.? By combining these three dead
load groups, the total dead load on the girder was calculated. Figure 35 shows the
moment diagrams for each dead load group and for the total dead load for an exterior
girder, which will hereafter be called ?Girder 1? or ?G1.?
800
700
600
500
400
300
200
100
0
100
200
300
0 30 60 90 120 150 180 210 240 270
Distance from CL of girder end bearing (ft)
Moment (
k
ipf
t)
Total Dead Load
Dead Load
SDL, Group 1
SDL, Group 2
Interior Support
@60 ft
Interior Support
@210 ft
Interior Support
@135 ft
Exterior
Support
@0 ft
Exterior
Support
@270 ft
Figure 35: Moment Diagrams for Dead Load Groups for an Exterior Girder
3.2.2 Live Load
Eight truck and two lane loadings were used in the BRASS? program for live load
calculations. An impact factor was included in these live loads. In the BRASS?
program, the live load distribution factors were used in accordance with AASHTO
Standard Specifications for Highway Bridges (1996). The loads and their corresponding
load arrangements are depicted in Table 31, where K stands for kips.
82
Table 31: Vehicle Names and Load Arrangements Used for Bridge Analysis
83
Vehicle ID Picture and Load Arrangement
#1: H 20S 16
Truck
#2: H 20S 16
Lane
#3: H 20 Truck
#4: H 20 Lane
#5: TwoAxle
Dump Truck
#6: ThreeAxle
Dump Truck
Table 31: Vehicle Names and Load Arrangements Used for Bridge Analysis (continued)
#7: Concrete
Truck
#8: 3S2 Alabama
#9: 3S3 Alabama
#10: School Bus
84
Trucks 1 and 3 are standard H20 trucks. Loadings 2 and 4 are the lane loads from
Trucks 1 and 3, respectively. Vehicles 5 through 10 are Alabama posting trucks, which
are trucks that appear on loadposting signs. An example of a loadposting sign is shown
in Figure 36.
Figure 36: Example of a loadposting sign (Carmichael and Barnes 2005)
For trucks heavier than those listed in Table 31, a special permit must be
obtained from ALDOT. Permit trucks are often more critical than the trucks listed in
Table 31. However, permit trucks do not have standard sizes, loads, or load
arrangements. Therefore, only the ten standard loadings shown in the table will be used in
the analysis.
The BRASS? program applied each of the ten loadings from Table 31 to an
exterior and an interior girder. By moving the trucks across each girder, the BRASS?
software developed a moment envelope for each loading. The moment was computed at
every tenth point of each span and at critical locations. Figure 37 shows the positive
moment envelopes, and Figure 38 shows the negative moment envelopes.
85
ThreeAxle Dump
AL School Bus
0
50
100
150
200
250
300
350
400
450
500
550
600
650
0 30 60 90 120 150 180 210 240 270
Location from bearing CL (ft)
Posi
tiv
e
l
i
ve
load m
o
me
n
t
(ki
p
f
t)
H20S 16 Truck
H20S 16 Lane
H20 Truck
H20 Lane
TwoAxle Dump
ThreeAxle Dump
Concrete Truck
3S2 Alabama
3S3 Alabama
AL School Bus
Interior
Support
@60 ft
Interior
Support
@210 ft
Interior
Support
@135 ft
Figure 37: Positive Live Load Moment Envelopes across Girder 1
86
ThreeAxle Dump
AL School Bus
650
600
550
500
450
400
350
300
250
200
150
100
50
0
0 30 60 90 120 150 180 210 240 270
Location from bearing CL (ft)
Negati
ve l
i
ve
l
oad
moment
(k
ipft)
H20S 16 Truck
H20S 16 Lane
H20 Truck
H20 Lane
TwoAxle Dump
ThreeAxle Dump
Concrete Truck
3S2 Alabama
3S3 Alabama
AL School Bus
Interior
Support
@60 ft
Interior
Support
@210 ft
Interior
Support
@135 ft
H20 Lane
H20S 16 Lane
Figure 38: Negative Live Load Moment Envelopes across Girder 1
As shown in Figures 37 and 38, the ThreeAxle Dump Truck is the worstcase
loading for the majority of the moment envelopes. The lane loadings control the live load
negativemoment envelope near the interior supports and near midspan of the interior
spans.
3.2.3 Factored Total Load
After the dead load and live load moment envelopes were developed, the loads were
combined and factored. The two load combinations used were operating and inventory,
given by the American Association of State Highway and Transportation Officials
(AASHTO) as follows:
87
Table 32: AASHTO Load Combinations
Load Combination Factored Moment
Operating
)(3.1 LD +
Inventory
)67.1(3.1 LD +
In Table 32, D stands for dead load, and L stands for live load (including impact).
Because the operating load combination is typically used for bridge rating and load
posting purposes, it will be the focus of this analysis, and the inventory rating will not be
discussed any further.
At this point in the analysis, the four H20 loadings, numbered 1 through 4, were
separated from the six loadposting trucks, numbered 5 through 10. The operating load
combination was then used to calculate the factored moment envelopes for each of the
loadings for positive and negative moment. Once these envelopes were found, a factored
moment envelope was developed that included all four H20 loadings and both positive
and negative moments. Figure 39 shows the factored moment envelope for positive and
negative moment using the operating load combination.
88
2000
1500
1000
500
0
500
1000
1500
0 30 60 90 120 150 180 210 240 270
Distance from CL of girder end bearing (ft)
Factor
ed
(op
e
r
a
ti
ng
) u
l
ti
mate moment (ki
p
ft)
Figure 39: Factored Ultimate Moment Envelope for the H20 Loadings using the
Operating Load Combination
The process was repeated for the loadposting trucks. Figure 310 shows the
corresponding factored ultimate moment envelope for positive and negative moment
using the operating load combination.
89
2000
1500
1000
500
0
500
1000
1500
0 30 60 90 120 150 180 210 240 270
Distance from CL of girder end bearing (ft)
F
a
cto
r
ed (
o
per
a
ting) ul
tim
a
te
mo
m
e
n
t
(ki
pft)
Figure 310: Factored Ultimate Moment Envelope for the Posting Trucks using the
Operating Load Combination
As shown in Figures 39 and 310, some sections of Girder 1 are always subjected
to positive moment and some are always subjected to negative moment. At the midspan
regions and near the discontinuous girder ends, the girder is always in positive moment
for the operating load combination. At the supports, the girder is always in negative
moment for the operating load combination.
3.3 Capacity of Existing Bridge
For capacity calculations, in accordance with the age of the bridge, the concrete
compressive strength was assumed to be 3000 psi (20 MPa), and the steel reinforcing
90
bars were assumed to have a yield strength of 40,000 psi (280 MPa). The entire 6?
inches (159 mm) was used for the slab height. For the exterior girder, 6 feet (1.8 m) was
used as the effective flange width, with 2 feet (0.6 m) as the overhang distance. The
overhang distance is a conservative approximation because of the post and rail system
that is connected to the slab. For all capacity calculations, except for the development
length, the AASHTO Standard Specification (1996) was followed. Figure 311 shows the
cross section used to model the resistance of an exterior girder.
Figure 311: Exterior Girder Cross Section at an Interior Support Location
91
The reinforcing steel shown in Figure 311 is for the cross section at an interior
support. For capacity calculations, the steel in the girder at approximately middepth and
the compression steel are ignored. Figure 312 shows the midspan cross section used to
model the resistance of the girder.
Figure 312: Exterior Girder Cross Section at Midspan
Figures 311 and 312 show the difference in steel between the support location
and the midspan location. For positive moment, the bars designated M1, N1, and P1 have
all been cut short of the support location. For negative moment, the bars designated DD1,
M2, N2, and P2 have all been cut short of midspan. The #11 bars designated DD2 are
92
spliced to #4 bars between midspan and the support. Only the DC2 bars that support the
stirrups, the E2 bars in the flange, and the R1 and R2 bars in the web are continued
through both locations. Figure 313 shows the amount of positive and negative moment
steel in the exterior girder and the approximate locations where the steel amount changes
between the interior support centerline (CL) and the midspan CL.
Figure 313: Elevation View of the Amount of Steel and the Approximate Termination
Locations in Girder 1
Figure 313 also shows where the centroid of the top and bottom steel is located
in relation to the top and the bottom surface of the concrete, respectively. This figure only
shows where the bars are physically cut off; it does not take into account the development
length of the bars.
93
94
To calculate the nominal moment capacity along Girder 1, both the amount of
steel at each cross section and the amount of stress that could be developed in each
terminated bar needed to be known. Due to overlapping bar development lengths, a
spreadsheet was created to compute the portion of steel yield stress developed in each bar
group at all of the critical locations. Table 33 shows part of the spreadsheet used for
positive moment calculations.
Table 33: Portion of Each Bar Group?s Yield Stress Used for Positive Moment Capacity
Calculations
Portion of yield stress used for calculations (expressed as a decimal)
Distance from
bearing CL (ft)
M1
2 #11
P1
2 #11
N1
2 #11
R1
2 #11
R2
2 #11
0.56
0.31 0.00 0.00
3.44 1.00 1.00
4.83 0.00 0.00 1.00 1.00
5.83 0.00 0.27 0.27 1.00 1.00
8.58 0.73 1.00 1.00 1.00 1.00
9.58 1.00 1.00 1.00 1.00 1.00
33.44 1.00 1.00 1.00 1.00 1.00
34.17 0.81 1.00 1.00 1.00 1.00
35.85 0.36 1.00 0.55 1.00 1.00
37.19 0.00 0.64 0.19 1.00 1.00
37.92 0.45 0.00 1.00 1.00
39.60 0.00 1.00 1.00
60.00 1.00 1.00
Area (in.
2
) 3.12 3.12 3.12 3.12 3.12
y (in.) 10.0 6.5 6.5 3.0 3.0
In Table 33, the distances are measured from the centerline of the bearing.
Because the girder extends 6.75 inches (171 mm), or approximately 0.56 feet, past the
support centerline, some of the distances calculated in the spreadsheet are negative.
95
In Table 33, the area shown at the bottom of the spreadsheet is the combined area
for each bar type. The parameter labeled y is the distance from the centroid of that
specific bar type to the bottom of the concrete surface. The development length for this
table was calculated according to Section 5.11 of the AASHTO LRFD Bridge Design
Specification (AASHTO 2006) because this document will provide more conservative
results than the AASHTO Standard Specification.
Another factor accounted for was the varying depth of the cross section in the
parabolic haunch region near the interior supports. The height of the girders in this
section was given by the drawings at every foot. Therefore, the moment capacity was
calculated at every foot of the haunch section.
Once the positive moment capacity along Girder 1 was calculated, the values
were factored by multiplying by the strengthreduction factor for flexure of 0.9. The
resulting factored capacity is shown in Figure 314.
In Figure 314, the supports are located at 0 feet, 60 feet, 135 feet, 210 feet, and
270 feet. The moment capacities are greatest at the midspan locations. The moment
capacity then decreases from the midspan section to the start of the haunch section. At the
start of the haunch section, the moment capacity increases to a peak directly over the
interior supports. Because the amount of bottom steel in this region remains constant, the
increased moment capacity over the supports is solely due to the increased depth of the
section.
0
200
400
600
800
1000
1200
1400
1600
1800
0 30 60 90 120 150 180 210 240 270
Distance from CL of girder end bearing (ft)
F
act
o
r
ed
M
o
m
ent
C
apaci
t
y (
ki
p

f
t
)
Figure 314: Factored Positive Moment Capacity along Exterior Girder
To calculate the negative moment capacity for Girder 1, the spreadsheet shown in
Table 34 was used.
96
97
Table 34: Portion of Each Bar Group?s Yield Stress Used for Negative Moment
Capacity Calculations
Portion of yield stress used for calculations (expressed as a decimal)
Distance from
support CL (ft)
DD1(a)
3 #11
P2
2 #11
DD1(b)
2 #11
N2
2 #11
M2
2 #11
DD2*
3? #11
E2
2 #5
DC2
3 #4
Spliced*
3? #4
0.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
10.67 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
11.25 1.00 0.89 1.00 1.00 1.00 1.00 1.00 1.00
12.08 0.78 0.73 1.00 1.00 1.00 1.00 1.00 1.00
13.25 0.47 0.51 1.00 0.78 1.00 1.00 1.00 1.00
13.33 0.44 0.49 0.98 0.76 1.00 1.00 1.00 1.00
15.00 0.00 0.17 0.53 0.44 0.68 1.00 1.00 1.00
15.92 0.00 0.29 0.27 0.51 1.00 1.00 1.00
17.00 0.00 0.06 0.30 1.00 1.00 1.00
17.33 0.00 0.24 1.00 1.00 1.00
18.58 0.00 1.00 1.00 1.00
19.00 1.00 1.00 1.00 0.00
23.00 0.00 1.00 1.00 1.00
25.00 1.00 1.00 1.00
Area (in.
2
) 4.68 3.12 3.12 3.12 3.12 5.46 0.62 0.60 0.70
y (in.) 2.875 6.375 2.875 2.875 2.875 2.875 4.3125 2.375 2.875
*These bars were located directly at the halfway point between girders, so half of the bar was included in
each girder cross section.
In Table 34, the parameter labeled y is the distance from the centroid of that
specific bar type to the top of the concrete surface. For this table, three different
development lengths were used: one for a #11 top bar, one for a typical #11 bar, and one
for a #4 bar. The development lengths were calculated according to Section 5.11 of the
AASHTO LRFD Bridge Design Specification (AASHTO 2006). Because the DD2 bars
were spliced to the #4 bars, both bars were assumed to be fully developed at opposite
ends of the splice.
Once the negative moment capacity along Girder 1 was calculated, the values
were factored by multiplying by the strengthreduction factor of 0.9. The factored
capacity is shown in Figure 315.
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0
0 30 60 90 120 150 180 210 240 270
Distance from CL of girder end bearing (ft)
F
a
c
t
o
r
e
d
M
o
m
e
n
t
C
a
p
a
c
ity
(k
ip

ft
)
Figure 315: Factored Negative Moment Capacity along Exterior Girder
3.4 Bridge Deficiencies
Once the flexural demand and capacity were known for the existing Letohatchee
bridge, a comparison could be made to discover any deficiencies. Before this comparison
was made, the demand graph was slightly modified to account for the fact that diagonal
shear cracks cause shifting of the flexural demand on the tension steel along the girder.
By assuming that such a crack would occur at an angle of fortyfive degrees, the demand
graph was shifted a distance d out from midspan for positive moments and a distance d
out from the supports for negative moments, where d is the effective depth of the
reinforced concrete cross section. The effective depth of the specific section that needed
strengthening was used as the shift distance. The shifting of the positive demand
envelope created an irregularity in the diagram resulting in an overlap region at the
98
interior supports. Figure 316 shows the comparison between the resulting factored
demand and the factored capacity of the Letohatchee bridge under H20 loadings and the
operating load combination. Figure 317 shows the same comparison for the posting
trucks.
5000
4000
3000
2000
1000
0
1000
2000
0 30 60 90 120 150 180 210 240 270
Distance from CL of girder end bearing (ft)
F
a
c
t
o
r
e
d
Mo
m
e
n
t
(k
i
p
f
t)
Factored Demand Factored Resistance
Figure 316: Factored Demand Versus Factored Resistance for H20 Trucks
99
5000
4000
3000
2000
1000
0
1000
2000
0 30 60 90 120 150 180 210 240 270
Distance from CL of girder end bearing (ft)
F
a
c
to
r
e
d
Mo
m
e
n
t
(k
ip
ft)
Factored Demand Factored Resistance
Figure 317: Factored Demand Versus Factored Resistance for Posting Trucks
Figures 316 and 317 both show deficiencies in the Letohatchee bridge. The
deficiency for the posting trucks is slightly worse than for the H20 trucks. For the posting
trucks, there is insufficient capacity for both positive and negative moment. For positive
moment, the deficiency occurs at about 40 feet (12.2 m) from the centerline of the girder
end bearing. It occurs over a length of approximately two feet (0.6 m), and the deficiency
is less than 6%. Table 35 shows the exact location and magnitude of the deficiency.
100
101
Table 35: PositiveMoment Deficiency for Posting Trucks at Critical Locations
Location from
bearing CL (ft)
M
u
(kft)
?M
n
(kft)
Strength
Deficiency
(kft)
38.7 825 825 
39.6 787 745 43
40.4 744 744 
Because the deficiency occurs over such a small region and because there is only
a 6% deficiency, positive moment strengthening for the Letohatchee bridge will not be
discussed further.
As shown in Figure 317, the negativemoment deficiencies due to the posting
trucks occur at approximately 37 feet, 83 feet, and 112 feet from each end of the girder.
These deficiencies occur over about a 7foot (2.1 m) region. Table 36 shows the exact
locations and magnitudes of the deficiencies.
102
Table 36: NegativeMoment Deficiencies for Posting Trucks at Critical Locations
Distance from
end bearing CL
(ft)
Distance from
nearest interior
support (ft)
M
u

(kft)
?M
n
(kft)
Strength
Deficiency
(kft)
Strength
increase
needed
(%)
33 27 189 226  
34 26 229 226 2 1
35 25 269 226 43 19
36 24 309 226 83 37
37 23 350 226 124 55
38 22 396 357 39 11
Region 1
39 21 443 487  
81 21 431 487  
82 22 386 357 29 8
83 23 341 226 114 50
84 24 300 226 73 32
85 25 261 226 34 15
Region 2
86 26 223 226  
108 27 198 226  
109 26 228 226 1 1
110 25 265 226 39 17
111 24 304 226 78 34
112 23 344 226 118 52
113 22 389 357 33 9
Region 3
114 21 434 487  
Because the girders are symmetric, the distances shown in Table 36 are measured
from both ends of the girder. A location on each side of the deficiency is shown to clearly
define the bounds of each deficient region.
3.5 Summary
The Letohatchee bridge was found to be deficient in six separate regions in each girder.
Figure 318 shows the approximate locations of each deficient region.
Figure 318: Elevation View of the Locations of the Letohatchee Bridge Deficiencies
In Figure 318, the hatched areas show the regions where the bridge is deficient.
The distances shown at the bottom of the figure show the locations along the girder
measured from the centerline of the girder?s end bearing.
The regions where the deficiencies are the greatest occur in the exterior spans. In
these regions, the moment capacity needs to be strengthened from a factored nominal
moment capacity of 226 kipfeet to a required factored moment capacity of 350 kipfeet,
which would be about a 55% increase in strength.
Figure 319 shows the bar termination locations and the approximate range of the
deficiency.
103
Figure 319: Bar Termination and Deficient Region Locations
The hatched region in the figure shows the deficient region. The figure is shown
from the interior support centerline to the midspan centerline of the exterior span. The
midspan centerline of the interior span is shown as a dashed line. The distances shown in
parentheses for the bar termination locations are measured from the interior support
centerline.
The cause of the negativemoment deficiencies for this bridge is not a shortage of
internal steel reinforcement at the support location. As shown in Figure 319, the
deficient region occurs at about 21 feet from interior support centerline. The cause of the
negativemoment deficiencies is the premature termination of the negativemoment steel
reinforcement. As shown in Figure 319, most of the top bars have been terminated well
before the deficient region.
One of the possible strengthening techniques is to use FRP strips. Before an FRP
strengthening scheme can be proposed or implemented, however, the amount of
104
105
strengthening that FRP strips can provide needed to be investigated and quantified. In
Chapter 2, several models were introduced that attempt to describe the debonding
behavior of FRP. Several testing programs were also introduced. In Chapter 4, the models
were compared to the experimental tests to determine the accuracy and validity of the
models.
106
Chapter 4: Evaluation of Existing Models
4.1 Introduction
In Chapter 2, several ICdebonding and PEdebonding models were introduced and
explained. Some of the models are design provisions recommended by organizations, and
some are models taken from published papers, theses, and dissertations. In this chapter,
each of the models is evaluated by comparing it to the relevant test data from the
experimental testing programs that were also introduced in Chapter 2. Table 41 shows
the experimental tests that were used in these evaluations and the type of FRP application
used in each test series.
Table 41: List of Experimental Test Series
Test Series
Number
Name EB Tests NSM Tests
1 ElHacha and Rizkalla (2004) YES YES
2 Jung et al. (2005) YES YES
3 Reed et al. (2005) YES NO
4 Carmichael and Barnes (2005) YES NO
5 Taljsten and Nordin (2007) NO YES
6 Yost et al. (2007) NO YES
7 Liu, Oehlers, and Seracino (2006) NO YES
8 Teng et al. (2006) NO YES
9 De Lorenzis and Nanni (2002) NO YES
10 Sena Cruz and Barros (2004) NO YES
11 Sena Cruz et al. (2006) NO YES
12 Hassan and Rizkalla (2003) NO YES
107
In this chapter, each test series is identified by the corresponding number shown
in Table 41. The test series with only EB specimens, test series 3 and 4, were
specifically chosen because these studies were conducted by previous Auburn University
researchers and all test data were already known. The other test series were chosen
because they also included specimens strengthened with NSM. Most of the tests that were
chosen are flexural tests. A few of the tests, however, include modifiedbeam tests, with
specimens that were not loaded in flexure.
As documented in this chapter, the moment capacities and the FRP strain values
at flexural failure were predicted using recommended models and compared to
experimental values. The experimental FRP strain values taken from the twelve test
series were measured at various locations along the length of the girders. In all of the test
series, the FRP strain values were measured at least at midspan and underneath the load
points, which are the most likely locations for a crack. The Reed et al. (2005) study was
the only test series that explicitly stated that the strain gauges were placed at crack
locations. Also, the Reed et al. study and the Carmichael and Barnes (2005) study were
the only test series where the specimens were cracked before strengthening.
This rest of this chapter is divided into four parts:
1. PEdebonding models for NSM,
2. ICdebonding models for EB,
3. ICdebonding models for NSM, and
4. Summary of model evaluation results.
In the section about the PEdebonding models for NSM, only one organization ?
Standards Australia ? gives quantitative design provisions. The American Concrete
108
Institute (ACI) and the International Federation of Structural Concrete (fib) only give
qualitative design provisions for both NSM and EB, which were introduced in Chapter 2.
For the ICdebonding models for EB and for the ICdebonding models for NSM, three
organizations give design provisions: ACI, fib, and Standards Australia.
4.2 PEDebonding Models for NSM
Four different PEdebonding models for NSM FRP were analyzed in this section. Each of
the four models was used to predict strengthened moment capacities for different
experimental specimens. The predictions of these models were compared to experimental
results to determine the accuracy and level of safety of each model. The four models
discussed in this section are Standards Australia (2008), Blaschko (2003), Hassan and
Rizkalla (2003), and Vasquez (2008). The experimental tests used in this section are test
series 8 through 12.
4.2.1 Standards Australia
The PEdebonding model for NSM FRP given by Standards Australia was compared to
the existing experimental NSM tests that were introduced in Chapter 2 to determine the
accuracy and level of safety of the model.
4.2.1.1 Comparison to Previous Testing
The model discussed in this section was used to predict the moment at the plate end when
debonding occurs. This moment was used to calculate the predicted maximum moment
for the beam and then was compared to the experimental moment. The experimental tests
used for this analysis were ones that involved varying embedment lengths of EB, which
109
included test series 8 through 12. These test series were presented in Chapter 2. Table 42
shows a comparison of capacities using the PEdebonding model from Standards
Australia.
For test series 8, one of the four specimens was predicted to debond at a load that
was less than the predicted failure load of the control beam, which is the reason the
change in capacity is negative. The value shown in Table 42 for specimen B500 is the
capacity at which PE debonding occurs. Failure for this beam would not occur until the
concrete crushed, which would happen at a capacity close to the predicted capacity for
the control beam of 21.5 kipft. The premature PE debonding of the FRP is the reason
that the experimental capacity was 25% larger than the predicted capacity for this
specimen.
For specimens B500 and B1200, the changes in capacity shown in Table 42 are
misleading. For specimen B500, the experimental change in capacity was very small
compared to the prediction; therefore, the ratio of changes in capacity was very small. For
specimen B1200, the predicted change in capacity was very small compared to the
experimental change in capacity; therefore, therefore, the ratio of changes in capacity was
very large.
110
Table 42: Comparison of the PEDebonding Model by Standards Australia (2008) to
NSM Test Results
Predicted Experimental Test
Series
#
Specimen
ID
M
n
(kft)
?M
n
(kft)
Failure
Mode
M
exp
(kft)
?M
exp
(kft)
Failure
Mode
M
exp
/
M
n,pred
?M
exp
/
?M
n,pred
8 B500 16.8 4.7 PE 21.1 0.4 PE 1.25 0.08
8 B1200 22.5 0.9 PE 28.0 6.5 PE 1.25 7.02
8 B1800 33.7 12.2 PE 40.6 19.1 PE 1.20 1.57
8 B2900 34.3 12.8 R 44.1 22.6 CC 1.28 1.77
9 G4D6a 9.9 N/A PE 4.4 N/A P 0.44 N/A
9 G4D12a 11.9 N/A PE 6.2 N/A P 0.52 N/A
9 G4D12b 11.9 N/A PE 6.6 N/A P 0.55 N/A
9 G4D12c 11.9 N/A PE 7.6 N/A P 0.64 N/A
9 G4D18a 14.9 N/A PE 7.6 N/A P 0.51 N/A
9 G4D24c 17.9 N/A R 11.0 N/A P 0.62 N/A
9 C3D6a 5.7 N/A PE 2.8 N/A P 0.49 N/A
9 C3D12a 6.5 N/A PE 4.8 N/A P 0.73 N/A
9 C3D12b 6.5 N/A PE 5.4 N/A P 0.84 N/A
9 C3D12c 6.5 N/A PE 5.1 N/A P 0.79 N/A
9 C3D18a 7.5 N/A PE 7.5 N/A P 1.00 N/A
9 C3D24b 8.9 N/A PE 7.8 N/A P 0.88 N/A
9 C3S6a 5.6 N/A PE 2.3 N/A P 0.42 N/A
9 C3S12a 6.4 N/A PE 3.1 N/A P 0.49 N/A
9 C3S12b 6.4 N/A PE 2.7 N/A P 0.43 N/A
9 C3S12c 6.4 N/A PE 3.1 N/A P 0.49 N/A
9 C3S18a 7.4 N/A PE 4.4 N/A P 0.60 N/A
9 C3S24a 8.7 N/A PE 4.0 N/A P 0.45 N/A
10 fcm35_Lb40 1.6 N/A PE 1.4 N/A P 0.88 N/A
10 fcm35_Lb60 1.7 N/A PE 2.1 N/A P 1.23 N/A
10 fcm35_Lb80 2.1 N/A PE 2.1 N/A P 0.97 N/A
10 fcm45_Lb40 1.9 N/A PE 1.4 N/A P 0.74 N/A
10 fcm45_Lb60 2.0 N/A PE 1.8 N/A P 0.91 N/A
10 fcm45_Lb80 2.5 N/A PE 2.4 N/A P 0.97 N/A
10 fcm70_Lb40 2.6 N/A PE 1.4 N/A P 0.56 N/A
10 fcm70_Lb60 2.9 N/A PE 1.7 N/A P 0.60 N/A
10 fcm70_Lb80 3.3 N/A PE 2.4 N/A P 0.72 N/A
11 Lb60_M 2.3 N/A PE 1.0 N/A P 0.44 N/A
11 Lb90_M 2.3 N/A PE 1.3 N/A P 0.57 N/A
11 Lb120_M 2.3 N/A PE 1.5 N/A P 0.66 N/A
12 B1 15.2 4.7 PE 24.4 0.5 PE 1.61 0.10
12 B2 16.7 6.2 PE 24.9 0.9 PE 1.49 0.15
12 B3 22.3 11.8 PE 27.7 3.7 PE 1.24 0.31
12 B4 22.7 12.2 R 34.1 10.1 PE 1.50 0.83
12 B5 22.7 12.2 R 36.4 12.4 R 1.60 1.02
12 B6 22.7 12.2 R 34.6 10.6 R 1.52 0.87
12 B7 22.7 12.2 R 36.9 12.9 R 1.62 1.06
12 B8 22.7 12.2 R 36.9 12.9 R 1.62 1.06
Notes: CC crushing of the concrete (preceded by steel yielding); P pullout of the FRP
PE plateend debonding; R rupture of the FRP
111
For specimen B1800, the failure mode was correctly predicted as PE debonding,
but the experimental capacity was 20% greater than the predicted capacity. For this
specimen, the experimental change in capacity was 57% larger than the predicted change
in capacity. For specimen B2900, the failure mode was predicted to be FRP rupture, but
the beam actually failed due to crushing of the concrete. Because of this incorrect failure
mode, the experimental capacity was consequently 28% greater than the predicted
capacity, and the experimental change in capacity was 77% greater than the predicted
change in capacity.
For the G4 and C3S series in test series 9, the model did not predict the capacity
very accurately. For these series, the experimental capacity ranged from 42 to 64% of the
predicted capacity. For the C3D series, the model did not predict the capacity very
accurately for the shorter bonded lengths, but as the bonded length increased, from six
bar diameters to 24 bar diameters, the accuracy of the model improved. For the
specimens with a bonded length of six or twelve bar diameters, C3D6 or C3D12, the
experimental capacity ranged from 49 to 84% of the predicted capacity. For the
specimens with a bonded length of eighteen or twentyfour bar diameters, C3D18 or
C3D24, the experimental capacity was 100 and 88% of the predicted capacity,
respectively.
For test series 10 and 11, the model predicted PEdebonding failures for all of the
specimens, and all of the specimens failed due to pullout of the FRP. The comparison that
was used for the other specimens, the ratio of the experimental capacity to the predicted
capacity, is not a good measure of accuracy due to the small magnitudes of the capacities.
The experimental capacities range from 1.0 to 2.4 kipft, and the predicted capacities
112
range from 1.6 to 3.3 kipft. The most that the capacity was overestimated is 1.3 kipft,
and the most that it was underestimated is 0.4 kipfoot.
For specimens B1, B2, and B3 in test series 12, the failure mode was correctly
predicted as PE debonding. For these specimens, the experimental strengthened moment
capacities are 61, 49, and 24% higher, respectively, than the predicted strengthened
moment capacities, and the experimental changes in capacity are just 10, 15, and 31% of
the predicted changes in capacity. For specimens B4 through B8, the experimental
capacities were well above the predicted capacities, but the experimental changes in
capacity were relatively close to the predicted changes in capacity.
Figure 41 shows a graph of the experimental capacity versus the predicted
capacity. Figure 42 shows a graph of the experimental change in capacity versus the
predicted change in capacity.
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45
Predicted Moment (kft)
Exper
i
mental Moment (kft)
TS #8: Teng et al. (2006)
TS #9: De Lorenzis and Nanni (2002)
TS #10: Sena Cruz and Barros (2004)
TS #11: Sena Cruz et al. (2006)
TS #12: Hassan and Rizkalla (2003)
Figure 41: Comparison between NSM Test Results and Standards Australia (2008) PE
Debonding Capacity Predictions
113
0
5
10
15
20
25
0 5 10 15 20 25
Change in Predicted Moment (kft)
Change
in Experime
ntal Moment
(kft)
TS #8: Teng et al. (2006)
TS #12: Hassan and Rizkalla (2003)
Figure 42: Comparison between NSM Test Results and Standards Australia (2008) PE
Debonding ChangeinCapacity Predictions
As shown in Figures 41 and 42, there was a wide dispersion of data points with
some on the conservative side and some on the unconservative side. The series that did
not involve pullout failure, test series 8 and 12, all produced conservative predictions for
capacity but produced mixed results for the change in capacity. Test series 9, 10, and 11
mostly produced unconservative predictions of capacity. Only test series 10 and 11 were
relatively close to the line of accuracy shown in Figure 41. The change in capacity for
specimen B500 is not shown in Figure 42 because it was predicted to be negative.
Table 43 shows the measured and predicted strain values for the FRP.
114
115
Table 43: FRP Strain Predictions using the Standards Australia (2008) PEDebonding
Model and NSM Test Results
Predicted Experimental Test
Series #
Specimen
ID ?
f,pred
?
f,pred
/?
f,rupt
?
f,exp
?
f,exp
/?
f,rupt
?
f,exp
/
?
f,pred
8 B500 0.21% 0.14 0.23% 0.15 1.07
8 B1200 0.29% 0.18 0.37% 0.23 1.27
8 B1800 1.30% 0.82 0.73% 0.46 0.56
8 B2900 *1.37% *0.87 *0.97% *0.61 0.71
12 B1 0.19% 0.56% 0.05% 0.04 0.09
12 B2 0.21% 0.72% 0.17% 0.13 0.24
12 B3 0.29% 1.32% 0.71% 0.53 0.54
12 B4 *1.33% *1.00 1.18% 0.89 0.89
12 B5 *1.33% *1.00 *1.27% *0.95 0.95
12 B6 *1.33% *1.00 *1.28% *0.96 0.96
12 B7 *1.33% *1.00 *1.29% *0.97 0.97
12 B8 *1.33% *1.00 *1.31% *0.98 0.98
*denotes a failure mode other than PE debonding
The FRP strain predictions for test series 8 were not very accurate. For specimens
B500 and B1200, the experimental FRP strains were 107 and 127%, respectively, of the
predicted FRP strains. For specimens B1800 and B2900, the experimental FRP strains
were 56 and 71%, respectively, of the predicted FRP strains.
The model did not accurately predict the strain in the FRP for specimens B1, B2,
and B3 in test series 12. These test specimens debonded at a relatively low strain value,
and the predicted strain values were much higher. The experimental strains were 9, 24,
and 54% of the predicted strains, respectively. For specimen B4, the predicted strain
matched the experimental strain relatively well. The experimental strain 89% of the
predicted strain. For specimens B5 through B8, the failure mode was correctly predicted
as FRP rupture. Consequently, the strain in the FRP was very accurately predicted. The
experimental strain ranged from 95 to 98% of the predicted strain.
116
4.2.1.2 Discussion of Model
The NSM PEdebonding model given by Standards Australia was not very accurate at
predicting strengthened moment capacities. The commentary of the design handbook
HB3052008 states that there is not enough research at the present time to sufficiently
quantify PE debonding in NSM plates. The model proposed by Standards Australia is
simply the model used for EB side plates multiplied by two. It is doubled because NSM
plates are bonded to the concrete on both sides as opposed to just one side. Because the
model is not analytically or empirically derived and because Standards Australia even
recommends that it still needs to be validated with tests, this model should be used with
caution.
4.2.2 Blaschko (2003)
The model by Blaschko (2003) was one of the first models focused on NSM FRP. Most
of the previous models and research had been on EB FRP only. In his NSM model,
Blaschko assumed that the failure occurs in the adhesive layer. He then developed an
equation to calculate the bond strength of the FRP.
4.2.2.1 Discussion of Model
The model by Blaschko is based on knowing the shear strength of the epoxy. Most epoxy
manufacturers only report tensile and compressive strengths, and most researchers either
do not run tests for this property of the epoxy or do not report it. Therefore, this model
cannot be used for any of the experiments unless a reasonable guess is made for this
value. Because the adhesive layer is the layer that is being investigated and because the
shear strength of the epoxy is the only variable for the adhesive, assuming a value for the
117
shear strength of the epoxy would make the Blaschko equation trivial. Any assumption
made, even if it is conservative, would put the equation only in terms of the FRP bonded
length, the FRP width, and the FRP distance from the concrete edge. Therefore, because
this value was not reported by the experimental tests in the referenced literature, it cannot
be evaluated.
For IC debonding to occur, the concrete must be cracked. However, for the
Blaschko model, the failure is assumed to occur in the adhesive layer, and the concrete
compressive strength is not even a variable in the model. Because many of the
experimental tests resulted in an ICdebonding failure and many failed in the concrete
layer, the Blaschko model is not compared with these tests.
4.2.3 Hassan and Rizkalla (2003)
The model by Hassan and Rizkalla (2003) that was introduced in Chapter 2 was used to
evaluate the PEdebonding resistance of the NSM experimental tests that were also
introduced in Chapter 2.
4.2.3.1 Comparison to Previous Testing
Table 44 shows a comparison between the predicted strengthened moment capacity and
the experimental strengthened moment capacity.
118
Table 44: Comparison of the PEDebonding Model by Hassan and Rizkalla (2003) to
NSM Test Results
Predicted Experimental Test
Series
#
Specimen
ID
M
n
(kft)
?M
n
(kft)
Failure
Mode
M
exp
(kft)
?M
exp
(kft)
Failure
Mode
M
exp
/
M
n,pred
?M
exp
/
?M
n,pred
8 B500 8.1 13.5 PE 21.1 0.4 PE 2.61 0.03
8 B1200 11.1 10.4 PE 28.0 6.5 PE 2.51 0.63
8 B1800 16.5 5.0 PE 40.6 19.1 PE 2.46 3.80
8 B2900 34.3 12.8 R 44.1 22.6 CC 1.28 1.77
9 G4D6a 6.0 N/A PE 4.4 N/A P 0.73 N/A
9 G4D12a 7.0 N/A PE 6.2 N/A P 0.88 N/A
9 G4D12b 7.1 N/A PE 6.6 N/A P 0.92 N/A
9 G4D12c 7.2 N/A PE 7.6 N/A P 1.05 N/A
9 G4D18a 8.4 N/A PE 7.6 N/A P 0.90 N/A
9 G4D24c 10.5 N/A PE 11.0 N/A P 1.05 N/A
9 C3D6a 5.2 N/A PE 2.8 N/A P 0.54 N/A
9 C3D12a 5.8 N/A PE 4.8 N/A P 0.82 N/A
9 C3D12b 5.8 N/A PE 5.4 N/A P 0.93 N/A
9 C3D12c 5.8 N/A PE 5.1 N/A P 0.88 N/A
9 C3D18a 6.5 N/A PE 7.5 N/A P 1.15 N/A
9 C3D24b 7.4 N/A PE 7.8 N/A P 1.06 N/A
9 C3S6a 4.8 N/A PE 2.3 N/A P 0.49 N/A
9 C3S12a 5.3 N/A PE 3.1 N/A P 0.58 N/A
9 C3S12b 5.3 N/A PE 2.7 N/A P 0.52 N/A
9 C3S12c 5.3 N/A PE 3.1 N/A P 0.59 N/A
9 C3S18a 6.0 N/A PE 4.4 N/A P 0.74 N/A
9 C3S24a 6.4 N/A PE 4.0 N/A P 0.62 N/A
10 fcm35_Lb40 3.9 N/A PE 1.4 N/A P 0.36 N/A
10 fcm35_Lb60 4.2 N/A PE 2.1 N/A P 0.50 N/A
10 fcm35_Lb80 4.4 N/A R 2.1 N/A P 0.47 N/A
10 fcm45_Lb40 4.5 N/A R 1.4 N/A P 0.32 N/A
10 fcm45_Lb60 4.5 N/A R 1.8 N/A P 0.41 N/A
10 fcm45_Lb80 4.5 N/A R 2.4 N/A P 0.54 N/A
10 fcm70_Lb40 4.5 N/A R 1.4 N/A P 0.32 N/A
10 fcm70_Lb60 4.5 N/A R 1.7 N/A P 0.39 N/A
10 fcm70_Lb80 4.5 N/A R 2.4 N/A P 0.53 N/A
11 Lb60_M 3.3 N/A PE 1.0 N/A P 0.31 N/A
11 Lb90_M 4.1 N/A R 1.3 N/A P 0.33 N/A
11 Lb120_M 4.1 N/A R 1.5 N/A P 0.37 N/A
12 B1 12.8 2.3 PE 24.4 0.5 PE 1.91 0.20
12 B2 14.1 3.6 PE 24.9 0.9 PE 1.77 0.26
12 B3 18.7 8.2 PE 27.7 3.7 PE 1.48 0.45
12 B4 22.7 12.2 R 34.1 10.1 PE 1.50 0.83
12 B5 22.7 12.2 R 36.4 12.4 R 1.60 1.02
12 B6 22.7 12.2 R 34.6 10.6 R 1.52 0.87
12 B7 22.7 12.2 R 36.9 12.9 R 1.62 1.06
12 B8 22.7 12.2 R 36.9 12.9 R 1.62 1.06
Notes: CC crushing of the concrete (preceded by steel yielding); P pullout of the FRP
PE plateend debonding; R rupture of the FRP
119
For test series 8, three of the four specimens were predicted to debond at a load
that was less than the predicted failure load for the control beam. The values shown in
Table 44 are the capacities at which PE debonding occurs. Failure for these beams
would not occur until the concrete crushed, which would happen at a capacity close to the
predicted capacity for the control beam of 21.5 kipft. The premature PE debonding of
the FRP is the reason that the experimental capacity was about one and a half times larger
than the predicted capacity. The premature debonding is also the reason that the changes
in moment for these specimens are negative.
For specimen B500, the experimental capacity was actually less than the capacity
of the control beam. This premature failure was due to the fact that the FRP strip was
only bonded for 500 mm, and the constant moment region was 600 mm long. Therefore,
part of the beam in the maximum moment region was left unstrengthened, and the FRP
was rendered useless. For specimen B2900, the experimental capacity was 28% larger
than the predicted capacity.
In test series 9, the specimen names that end with ?a? have the smallest groove
size at 5/8 inch; the specimen names that end with ?b? have a groove size of 3/4 inch; and
the specimen names that end with ?c? have the largest groove size at 1 inch. As shown in
Table 44, as the groove size increases, the predictions of the model become more
accurate.
All of the specimens in test series 9 failed due to pullout of the FRP. For the No. 4
deformed rods, denoted G4D, the predicted capacities matched the experimental results
relatively well except for the shortest bonded length, denoted G4D6a. For the other five
120
specimens in the G4D series, the experimental strengthened moment capacities were in
the range of 88 to 105% of the predicted capacities.
For the No. 3 deformed rods, denoted C3D in test series 9, the experimental
capacity was in the range of 82 to 115% of the predicted capacity, except for the shortest
bonded length and the smallest groove width, denoted C3D6a.
The model did not predict the strengthened moment capacity very well for the No.
3 sandblasted rods, denoted C3S. The experimental capacities for the C3S series ranged
from 49 to 74% of the predicted capacities.
In tests series 10 and 11, the ratio of experimental capacity to predicted capacity
was very poor and ranged from 0.31 to 0.54. The fact that these moment capacities were
very small might be the reason that these ratios were very low. For example, in specimen
fcm35_Lb60, the difference between the predicted and the experimental capacity was
only 2.1 kipft, but because the experimental capacity was only 2.1 kipft, this resulted in
an experimental to predicted capacity ratio of 0.50. Another possible reason for the big
discrepancy in moment ratios is the fact that all of the tests in test series 9, 10, and 11
failed due to a pullout failure; however, the model by Hassan and Rizkalla does not
anticipate a pullout failure. The failure mode was never predicted correctly, which most
likely resulted in an erroneous prediction of capacity.
In test series 12, the failure mode was correctly predicted in seven out of the eight
specimens; however, the experimental capacity ranged from 48 to 91% larger than the
predicted capacity. For the specimens where PE debonding was predicted, the ratios of
experimental change in capacity to predicted change in capacity showed a poor
relationship, ranging from 0.20 to 0.45. This poor relationship could be due to the small
magnitude of the changes in moment. For the specimens where FRP rupture was
predicted, the changeinmoment ratios ranged from 0.83 to 1.06.
Figure 43 shows a graph of the experimental capacity versus the predicted
capacity. Figure 44 shows a comparison between the experimental change in capacity
and the predicted change in capacity.
121
0
5
0 5 10 15 20 25 30 35 40 45
Predicted Moment (kft)
10
15
20
25
30
35
40
45
E
x
peri
menta
l
M
o
ment
(k
ft)
TS #8: Teng et al. (2006)
TS #9: De Lorenzis and Nanni (2002)
TS #10: Sena Cruz and Barros (2004)
TS #11: Sena Cruz et al. (2006)
TS #12: Hassan and Rizkalla (2003)
Figure 43: Comparison between NSM Test Results and Hassan and Rizkalla (2003) PE
Debonding Capacity Predictions
0
5
10
15
20
0 5 10 15 20 25
Change in Predicted Moment (kft)
Change in Ex
peri
menta
l
M
o
ment
(k
ft)
25
TS #8: Teng et al. (2006)
TS #12: Hassan and Rizkalla (2003)
Figure 44: Comparison between NSM Test Results and Hassan and Rizkalla (2003) PE
Debonding ChangeinCapacity Predictions
As seen in Figure 43, most of the data points are not very close to the line that
separates the conservative from the unconservative. In Figure 44, very few of the data
points are close to the line shown. The changes in capacity for three of the specimens in
test series 8 are not shown in Figure 44 because the predicted capacities for the FRP
strengthened specimens were less than the predicted capacities for the control beams,
which resulted in negative changes in capacity.
Table 45 shows the measured and predicted strain values for the FRP.
122
123
Table 45: FRP Strain Predictions using the Hassan and Rizkalla (2003) PEDebonding
Model and NSM Test Results
Predicted Experimental Test
Series #
Specimen
ID ?
f,pred
?
f,pred
/?
f,rupt
?
f,exp
?
f,exp
/?
f,rupt
?
f,exp
/
?
f,pred
8 B500 0.10% 0.06 0.23% 0.15 2.24
8 B1200 0.14% 0.09 0.37% 0.23 2.59
8 B1800 0.21% 0.13 0.73% 0.46 3.48
8 B2900 *1.37% *0.87 *0.97% *0.61 0.71
12 B1 0.31% 0.23 0.05% 0.04 0.16
12 B2 0.44% 0.33 0.17% 0.13 0.39
12 B3 0.93% 0.70 0.71% 0.53 0.76
12 B4 *1.33% *1.00 1.18% 0.89 0.89
12 B5 *1.33% *1.00 *1.27% *0.95 0.95
12 B6 *1.33% *1.00 *1.28% *0.96 0.96
12 B7 *1.33% *1.00 *1.29% *0.97 0.97
12 B8 *1.33% *1.00 *1.31% *0.98 0.98
*denotes a failure mode other than PE debonding
For test series 8, the FRP strain predictions were not very accurate. For specimens
B500, B1200, and B1800, the predicted FRP strains were 6, 9, and 13%, respectively, of
the rupture strain; the experimental strains were 15, 23, and 46%, respectively. For
specimen B2900, the experimental strain was 71% of the predicted strain.
For the specimens where PE debonding was predicted in test series 12, the
experimental strains were much lower than the predicted strains, with the ratios of the
experimental to the predicted strain ranging from 0.16 to 0.76. For the five specimens
where FRP rupture was predicted, the experimental strains matched the predicted strains
much better, with the experimental FRP strains being 89 to 98% of the predicted strains.
4.2.3.2 Discussion of Model
The model by Hassan and Rizkalla did not correlate well with the three test series that
failed due to pullout of the FRP. Pullout failure was not anticipated by the model and
occurred before PE debonding was predicted to occur. Due to the relatively small
124
moment capacities, the ratios of experimental capacity to predicted capacity are not close
to 1.0. Therefore, a comparison between the test results and the predictions is difficult to
make.
The Hassan and Rizkalla model predicted the failure mode fairly well for test
series 8 and 12; the model correctly predicted the failure mode in ten out of the twelve
specimens. The capacities predictions were not very accurate for these test series, but the
changes in moment capacity for test series 12 were relatively accurate.
The model used for this analysis was specifically derived for a simplysupported
beam with a concentrated load at midspan. A different form of the model must be derived
for test setups that include other loading conditions or support configurations.
4.2.4 Vasquez (2008)
The model by Vasquez (2008) that was introduced in Chapter 2 was used to evaluate the
PEdebonding resistance of experimental tests using NSM FRP.
4.2.4.1 Comparison to Previous Testing
Table 46 shows a comparison between the predicted strengthened moment capacity and
the experimental strengthened moment capacity.
125
Table 46: Comparison of the PEDebonding Model by Vasquez (2008) to NSM Test
Results
Predicted Experimental Test
Series
#
Specimen
ID
M
n
(kft)
?M
n
(kft)
Failure
Mode
M
exp
(kft)
?M
exp
(kft)
Failure
Mode
M
exp
/
M
n,pred
?M
exp
/
?M
n,pred
8 B500 15.0 6.6 PE 21.1 0.4 PE 1.41 0.06
8 B1200 19.9 1.6 PE 28.0 6.5 PE 1.40 4.11
8 B1800 29.9 8.4 PE 40.6 19.1 PE 1.36 2.28
8 B2900 34.3 12.8 R 44.1 22.6 CC 1.28 1.77
9 G4D6a 17.9 N/A R 4.4 N/A P 0.25 N/A
9 G4D12a 17.9 N/A R 6.2 N/A P 0.34 N/A
9 G4D12b 17.9 N/A R 6.6 N/A P 0.37 N/A
9 G4D12c 17.9 N/A R 7.6 N/A P 0.43 N/A
9 G4D18a 17.9 N/A R 7.6 N/A P 0.42 N/A
9 G4D24c 17.9 N/A R 11.0 N/A P 0.62 N/A
9 C3D6a 17.4 N/A PE 2.8 N/A P 0.16 N/A
9 C3D12a 19.8 N/A PE 4.8 N/A P 0.24 N/A
9 C3D12b 19.8 N/A PE 5.4 N/A P 0.27 N/A
9 C3D12c 19.8 N/A PE 5.1 N/A P 0.26 N/A
9 C3D18a 21.0 N/A R 7.5 N/A P 0.36 N/A
9 C3D24b 21.0 N/A R 7.8 N/A P 0.37 N/A
9 C3S6a 16.0 N/A PE 2.3 N/A P 0.15 N/A
9 C3S12a 18.2 N/A PE 3.1 N/A P 0.17 N/A
9 C3S12b 18.2 N/A PE 2.7 N/A P 0.15 N/A
9 C3S12c 18.2 N/A PE 3.1 N/A P 0.17 N/A
9 C3S18a 19.1 N/A R 4.4 N/A P 0.23 N/A
9 C3S24a 19.1 N/A R 4.0 N/A P 0.21 N/A
10 fcm35_Lb40 4.4 N/A R 1.4 N/A P 0.31 N/A
10 fcm35_Lb60 4.4 N/A R 2.1 N/A P 0.47 N/A
10 fcm35_Lb80 4.4 N/A R 2.1 N/A P 0.47 N/A
10 fcm45_Lb40 4.5 N/A R 1.4 N/A P 0.32 N/A
10 fcm45_Lb60 4.5 N/A R 1.8 N/A P 0.41 N/A
10 fcm45_Lb80 4.5 N/A R 2.4 N/A P 0.54 N/A
10 fcm70_Lb40 4.5 N/A R 1.4 N/A P 0.32 N/A
10 fcm70_Lb60 4.5 N/A R 1.7 N/A P 0.39 N/A
10 fcm70_Lb80 4.5 N/A R 2.4 N/A P 0.53 N/A
11 Lb60_M 4.1 N/A R 1.0 N/A P 0.25 N/A
11 Lb90_M 4.1 N/A R 1.3 N/A P 0.33 N/A
11 Lb120_M 4.1 N/A R 1.5 N/A P 0.37 N/A
12 B1 20.3 9.8 PE 24.4 0.5 PE 1.20 0.05
12 B2 22.3 11.8 PE 24.9 0.9 PE 1.11 0.08
12 B3 22.7 12.2 R 27.7 3.7 PE 1.22 0.30
12 B4 22.7 12.2 R 34.1 10.1 PE 1.50 0.83
12 B5 22.7 12.2 R 36.4 12.4 R 1.60 1.02
12 B6 22.7 12.2 R 34.6 10.6 R 1.52 0.87
12 B7 22.7 12.2 R 36.9 12.9 R 1.62 1.06
12 B8 22.7 12.2 R 36.9 12.9 R 1.62 1.06
Notes: CC crushing of the concrete (preceded by steel yielding); P pullout of the FRP
PE plateend debonding; R rupture of the FRP
126
As in the results of the Hassan and Rizkalla model, the Vasquez model predicted
PE debonding would occur in two of the specimens at a capacity less than the predicted
capacity of the control beam. The values shown in Table 46 are the capacities at which
PE debonding was predicted to occur. Because these capacities are less than the predicted
capacities of the control beam, the test specimens, once the FRP debonds, were expected
to achieve a capacity about equal to the capacity of the control beam. The Vasquez model
predicted higher PEdebonding capacities for test series 8 than the Hassan and Rizkalla
model, which resulted in a more accurate prediction. The experimental capacities for
specimens B500 and B1200 were 41 and 40% higher, respectively, than the predicted
capacities using the Vasquez model.
For test series 9, 10, and 11, pullout failure controls for all of the specimens. The
Vasquez model does not, however, anticipate this failure mode and, therefore, does not
accurately predict the strengthened moment capacities. For these three test series, the
experimental capacities ranged from 15 to 62% of the predicted capacities, with an
average of 33%.
For specimens B1, B2, and B3 in test series 12, the experimental strengthened
moment capacities were only 20, 11, and 22% higher, respectively, than the predicted
strengthened moment capacities; however, the experimental changes in capacity were 5,
8, and 30% of the predicted changes in capacity. For specimens B4 through B8, the
experimental capacities were well above the predicted capacities, but the experimental
changes in capacity were very close to the predicted changes in capacity. The model by
Hassan and Rizkalla produced similar results.
Figure 45 shows a graph of the experimental capacity versus the predicted
capacity. Figure 46 shows a comparison between the experimental change in capacity
and the predicted change in capacity.
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45
Ex
pe
rimental
M
o
ment (k
ft)
Predicted Moment (kft)
TS #8: Teng et al. (2006)
TS #9: De Lorenzis and Nanni (2002)
TS #10: Sena Cruz and Barros (2004)
TS #11: Sena Cruz et al. (2006)
TS #12: Hassan and Rizkalla (2003)
Figure 45: Comparison between NSM Test Results and Vasquez (2008) PEDebonding
Capacity Predictions
127
0
5
10
15
20
0 5 10 15 20 25
Change in Predicted Moment (kft)
Change
in Ex
p
e
rimenta
l
Mo
ment (kft)
25
TS #8: Teng et al. (2006)
TS #12: Hassan and Rizkalla (2003)
Figure 46: Comparison between NSM Test Results and Vasquez (2008) PEDebonding
ChangeinCapacity Predictions
As shown in Figures 45 and 46, there was a wide dispersion of data points with
some on the conservative side and some on the unconservative side. The series that did
not involve pullout failure, test series 8 and 12, all produced conservative predictions of
capacity. Test series 9, 10, and 11 all produced unconservative predictions. Few of the
predictions of capacity were very close to the line of equality shown in Figure 45, and
very few of the predictions of the change in capacity were close to the line of equality
shown in Figure 46. The changes in capacity for two of the specimens in test series 8 are
not shown in Figure 46 because they were predicted to be negative.
Table 47 shows the measured and predicted strain values for the FRP.
128
129
Table 47: FRP Strain Predictions using the Vasquez (2008) PEDebonding Model and
NSM Test Results
Predicted Experimental Test
Series #
Specimen
ID ?
f,pred
?
f,pred
/?
f,rupt
?
f,exp
?
f,exp
/?
f,rupt
?
f,exp
/
?
f,pred
8 B500 0.19% 0.12 0.23% 0.15 1.20
8 B1200 0.25% 0.16 0.37% 0.23 1.44
8 B1800 0.90% 0.57 0.73% 0.46 0.81
8 B2900 *1.37% *0.87 *0.97% *0.61 0.71
12 B1 1.10% 0.83 0.05% 0.04 0.04
12 B2 1.32% 0.99 0.17% 0.13 0.13
12 B3 *1.33% *1.00 0.71% 0.53 0.53
12 B4 *1.33% *1.00 1.18% 0.89 0.89
12 B5 *1.33% *1.00 *1.27% *0.95 0.95
12 B6 *1.33% *1.00 *1.28% *0.96 0.96
12 B7 *1.33% *1.00 *1.29% *0.97 0.97
12 B8 *1.33% *1.00 *1.31% *0.98 0.98
*denotes a failure mode other than PE debonding
The FRP strain predictions for test series 8 were not very accurate. For specimens
B500 and B1200, the experimental FRP strains were 120 and 144%, respectively, of the
predicted FRP strains. For specimens B1800 and B2900, the experimental FRP strains
were 81 and 71%, respectively, of the predicted FRP strains.
The Vasquez model did accurately predict the strain in the FRP for specimens B1,
B2, and B3 in test series 12. These test specimens debonded at a relatively low strain
value. The experimental strains were 4, 13, and 53% of the predicted strains, respectively.
For the other five specimens in test series 12, the predicted strains matched the
experimental strain very well.
4.2.4.2 Discussion of Model
As in the Hassan and Rizkalla model, the Vasquez model did not anticipate a pullout
failure for the FRP and, consequently, did not predict the capacities very well for test
series 9, 10, and 11.
130
For test series 8 and 12, the predictions by the Vasquez model were conservative
but not very accurate. However, the capacity predictions from the Vasquez model were
more accurate than the predictions by the Hassan and Rizkalla model.
4.3 ICDebonding Models for EB
Six different ICdebonding models for EB are analyzed in this section. Each model was
used to predict strengthened moment capacities for different experimental specimens.
The predictions of the models were compared to experimental results of EB tests to
determine the accuracy and level of safety of each model. The six models discussed in
this section are ACI 440 (2008), fib 9.3 (2001), Standards Australia (2008), Rosenboom
(2006), Seracino, Raizal Saifulnaz, and Oehlers (2007), and Said and Wu (2008). The
experimental tests used in this section are test series 1 through 4.
4.3.1 ACI 440 (2008)
The EB ICdebonding model given by ACI 440 (2008) was compared to the existing
experimental EB tests that were introduced in Chapter 2. These tests include test series 1?
4: ElHacha and Rizkalla (2004), Jung et al. (2005), Reed et al. (2005), and the tests
conducted on War Memorial Bridge by Carmichael and Barnes (2005).
4.3.1.1 Comparison to Previous Testing
Using the ACI 440 model, nominal moment capacities were predicted for each
strengthened test specimen and compared to previous testing. The objective of this
capacity calculation was to predict the actual capacity at which failure occurs, rather than
conservatively predicting a capacity to use in design. Therefore, the strength reduction
131
factor, ?, was not applied to the total moment capacity; the reduction factor, ?
f
, was not
applied to the FRP contribution to the moment capacity; and the environmental reduction
factor, C
E
, was not applied to the ultimate FRP stress or strain. Table 48 shows the
predicted capacities, the experimental results, and comparisons between the two.
Table 48: Comparison of the ICDebonding Model by ACI 440 (2008) to EB Test
Results
Predicted Experimental Test
Series
#
Specimen
ID
M
n
(kft)
?M
n
(kft)
Failure
Mode
M
exp
(kft)
?M
exp
(kft)
Failure
Mode
M
exp
/
M
n,pred
?M
exp
/
?M
n,pred
1 B2a 29.7 4.1 IC 1.19 0.61
1 B2b
24.9 6.7 IC
29.7 4.1 IC 1.19 0.61
1 B4a 25.7 7.5 IC 32.6 7.0 IC 1.27 0.93
2
CPL50
BOND
26.6 10.0 IC 28.4 6.7 IC 1.07 0.67
2 SHBOND 26.7 10.2 IC 31.9 10.2 IC 1.19 1.00
3 B1 82.4 13.3 IC 1.02 0.81
3 B2 85.2 16.1 IC 1.05 0.98
3 B3 82.7 13.6 IC 1.02 0.82
3 B4 85.4 16.3 IC 1.06 0.99
3 B5 82.7 13.6 IC 1.02 0.82
3 B6
80.9 16.5 IC
84.2 15.1 IC 1.04 0.92
3 B7 83.7 19.2 IC 88.3 19.3 IC 1.06 1.00
4 G3S9 787 N/A IC 320 N/A
no
failure
0.41 N/A
4 G3S10 787 N/A IC 280 N/A
no
failure
0.36 N/A
4 G4S9 776 N/A IC 300 N/A
no
failure
0.39 N/A
4 G4S10 924 N/A IC 300 N/A
no
failure
0.32 N/A
Notes: IC intermediate crack debonding
In the study conducted by Carmichael and Barnes (2005), test series 4, the War
Memorial Bridge was only loaded in the service level range. Because no failure occurred
in the tests, the high capacity predictions relative to the experimental applied moments
132
were expected. Also, because there was no control beam, no changeinmoment
calculations could be made.
The specimen ID used in this table and in the following tables is the specimen
label that was used by the original researchers. The change in the moment predicted by
ACI 440 was calculated by subtracting the predicted capacity of the control beam from
the predicted capacity of the strengthened beam. The experimental change in moment
was calculated by subtracting the measured capacity at failure for the control beam from
the measured capacity at failure for the strengthened beam. By incorporating the
predicted capacity of the control beam and the measured capacity of the control beam, the
actual contribution of the FRP was more accurately assessed. The capacity of
unstrengthened reinforced concrete is typically underestimated due to a couple of
reasons, such as ignoring strain hardening of the internal steel and assuming a
conservative concrete compressive stress distribution at failure (i.e. the Whitney stress
block). By including the predicted and measured capacities of the control beam in the
changeinmoment calculations, the FRP contribution can be measured more directly.
To create a normalized comparison, the experimental moment capacity was
divided by the predicted moment capacity. A ratio of 1.0 is ideal, a ratio greater than 1.0
indicates a conservative prediction, and a ratio less than 1.0 indicates an unconservative
prediction. The same rules apply to the changeinmoment comparisons. Figure 47
shows the relationship between the experimental and the predicted strengthened moment
capacities. Figure 48 shows a comparison between the experimental change in capacity
and the predicted change in capacity.
0
10
0 10203040506070809010
Predicted Moment (kft)
20
30
40
50
60
70
80
90
100
Experimental Mome
n
t
(kft)
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #3: Reed et al. (2005)
Figure 47: Comparison between EB Test Results and ACI 440 (2008) ICDebonding
Capacity Predictions
133
0
2
0 2 4 6 8 101214161820
Change in Predicted Moment (kft)
4
6
8
10
12
14
16
18
20
Change in Experimental Mome
n
t
(kft)
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #3: Reed et al. (2005)
Figure 48: Comparison between EB Test Results and ACI 440 (2008) ICDebonding
ChangeinCapacity Predictions
In test series 1, specimens B2a and B2b were identical to each other. Likewise, in
test series 3, specimens B1 through B6 had identical cross sections, except for varying
thicknesses of epoxy, which is not a variable in the ACI 440 model. For these reasons,
multiple experimental results are shown for these specimens, but only one prediction
corresponds to each type of specimen.
For test series 1, 2, and 3, the predictions made by the ACI 440 model were all
conservative for the strengthened moment capacity but unconservative for the change in
moment capacity. As shown in Table 48, the ratio of the experimental moment capacity
to the predicted moment capacity ranges from 1.02 to 1.27, but the ratio of the
134
135
experimental change in moment to the predicted change in moment ranges from 0.61 to
1.00. The model correctly predicted an ICdebonding failure for all of the test specimens
that were loaded to failure.
The ultimate strain in the FRP was measured at failure for each of the specimens
in the first three test series. Table 49 shows these FRP strain values.
Table 49: FRP Strain Predictions using the ACI 440 (2008) ICDebonding Model and
EB Test Results
Predicted Experimental Test
Series #
Specimen
ID
?
f,pred
?
f,pred
/?
f,rupt
?
f,exp
?
f,exp
/?
f,rupt
?
f,exp
/
?
f,pred
1 B2a 0.48% 0.44 1.28
1 B2b
0.37% 0.35
0.44% 0.41 1.18
1 B4a 0.42% 0.19 0.62% 0.28 1.49
2 CPL50BOND 0.49% 0.33 0.44% 0.30 0.91
2 SHBOND 1.04% 0.69 0.85% 0.56 0.81
3 B1 0.44% 0.22 0.66
3 B2 0.51% 0.25 0.77
3 B3 0.49% 0.24 0.74
3 B4 0.53% 0.26 0.80
3 B5 0.51% 0.25 0.77
3 B6
0.67% 0.33
0.56% 0.28 0.84
3 B7 0.57% 0.28 0.47% 0.23 0.82
Note: All predicted and experimental failure modes were IC debonding.
In Table 49, ?
f,pred
is the predicted failure strain in the FRP; ?
f,exp
is the
experimental failure strain in the FRP; and ?
f,rupt
is the rupture strain in the FRP. The ratio
of the experimental FRP strain to the predicted FRP strain at failure is shown in the far
right column. For this ratio, a value greater than 1.0 would be conservative, and a value
less than 1.0 would be unconservative.
136
For the tests conducted by ElHacha and Rizkalla (2004), test series 1, the ACI
440 model underestimates the ICdebonding strain. For the other two test series, the
model overestimates the ICdebonding strain for all specimens.
4.3.1.2 Discussion of Model
The ACI 440 (2008) model does not predict very accurately the amount of strengthening
the FRP provides. As shown in Table 48, it frequently overestimates the change in
moment. However, the amount that the ACI 440 model overestimates the FRP
contribution is balanced by the amount that is underestimated in the actual strength of the
unstrengthened reinforced concrete member, which results in a fairly accurate and
slightly conservative prediction of the strengthened moment capacity. Even though the
FRP overestimation was balanced by the underestimation of strength of the
unstrengthened specimens in these laboratory specimens, the beneficial excess strength
could be smaller in fullscale bridge girders with older steel reinforcing bar types.
Therefore, a more conservative estimate of the true amount of strengthening due to FRP
is desirable.
4.3.2 fib 9.3 (2001)
The EB ICdebonding model given by fib 9.3 (2001) was compared to the existing
experimental EB tests that were introduced in Chapter 2 to determine the accuracy and
level of safety of the model.
4.3.2.1 Comparison to Previous Testing
Table 410 shows a comparison of capacities for EB FRP using Bulletin 14 of the fib.
137
Table 410: Comparison of the ICDebonding Model by fib 9.3 (2001) to EB Test
Results
Predicted Experimental Test
Series
#
Specimen
ID
M
n
(kft)
?M
n
(kft)
Failure
Mode
M
exp
(kft)
?M
exp
(kft)
Failure
Mode
M
exp
/
M
n,pred
?M
exp
/
?M
n,pred
1 B2a 29.7 4.1 IC 1.25 0.73
1 B2b
23.8 5.6 IC
29.7 4.1 IC 1.25 0.73
1 B4a 29.8 11.6 IC 32.6 7.0 IC 1.10 0.60
2
CPL50
BOND
43.9 27.4 CC 28.4 6.7 IC 0.65 0.25
2 SHBOND 31.2 14.7 R 31.9 10.2 IC 1.02 0.69
3 B1 82.4 13.3 IC 0.70 0.25
3 B2 85.2 16.1 IC 0.72 0.30
3 B3 82.7 13.6 IC 0.70 0.25
3 B4 85.4 16.3 IC 0.72 0.30
3 B5 82.7 13.6 IC 0.70 0.25
3 B6
118.1 53.7 R
84.2 15.1 IC 0.71 0.28
3 B7 137.7 73.2 R 88.3 19.3 IC 0.64 0.26
4 G3S9 1122 N/A R 320 N/A
no
failure
0.29 N/A
4 G3S10 1122 N/A R 280 N/A
no
failure
0.25 N/A
4 G4S9 1173 N/A R 300 N/A
no
failure
0.26 N/A
4 G4S10 1322 N/A R 300 N/A
no
failure
0.23 N/A
Notes: CC crushing of the concrete (preceded by steel yielding)
IC intermediate crack debonding
R rupture of the FRP
As in the results of the ACI 440 model, Bulletin 14 of Task Group 9.3 predicted
very high strengthened moment capacities for test series 4 relative to the experimental
loads. Because these specimens were only tested under service loads and the predicted
capacities were calculated using ultimate loads, the relatively high ratios of predicted
capacity to applied bending moment were expected. Once again, these specimens will be
excluded from further discussion.
Figure 49 shows a comparison between the experimental capacity and the
predicted capacity. Figure 410 shows a comparison between the experimental change in
capacity and the predicted change in capacity.
0
20
40
60
80
100
120
204060801012014
Predicted Moment (kft)
Ex
pe
rimental
M
o
ment (k
ft)
140
0
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #3: Reed et al. (2005)
Figure 49: Comparison between EB Test Results and fib 9.3 (2001) ICDebonding
Capacity Predictions
138
0
10
20
30
40
1020304050607080
Change in Predicted Moment (kft)
Change
in Ex
p
e
rimenta
l
50
60
70
80
Mo
ment (kft)
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #3: Reed et al. (2005)
Figure 410: Comparison between EB Test Results and fib 9.3 (2001) ICDebonding
ChangeinCapacity Predictions
For test series 1, the failure mode was predicted correctly, and the predicted
strengthened moment capacity was slightly underestimated when compared to the
experimental results. Conversely, the changes in moment were overestimated.
For test series 2 and 3, the failure mode (actually ICdebonding for all) was not
predicted correctly for any of the specimens. Consequently, the strengthened moment
capacities were overestimated for all but one specimen, and the changes in moment
capacity were extremely inaccurate, with the experimental change in moment capacity
ranging from 25 to 69% of the predicted change in moment capacity.
139
140
The predicted FRP strains and the comparisons to the experimental strains are
shown in Table 411.
Table 411: FRP Strain Predictions using the fib 9.3 (2001) ICDebonding Model and EB
Test Results
Predicted Experimental Test
Series #
Specimen
ID
?
f,pred
?
f,pred
/?
f,rupt
?
f,exp
?
f,exp
/?
f,rupt
?
f,exp
/
?
f,pred
1 B2a 0.48% 0.44 1.79
1 B2b
0.27% 0.25
0.44% 0.41 1.64
1 B4a 0.58% 0.26 0.62% 0.28 1.07
2 CPL50BOND *1.30% *0.88 0.44% 0.30 0.34
2 SHBOND *1.51% *1.00 0.85% 0.56 0.56
3 B1 0.44% 0.22 0.22
3 B2 0.51% 0.25 0.25
3 B3 0.49% 0.24 0.24
3 B4 0.53% 0.26 0.26
3 B5 0.51% 0.25 0.25
3 B6
*2.03% *1.00
0.56% 0.28 0.28
3 B7 *2.03% *1.00 0.47% 0.23 0.23
*denotes a failure mode other than IC debonding
Like Table 410, Table 411 shows an underestimation of the predicted FRP strain
for test series 1 and an overestimation of the predicted FRP strain for test series 2 and 3.
For specimens B2a and B2b of test series 1, the fib model predicted an FRP strain of
0.0027, but the experimental FRP strains were 0.0048 and 0.0044, respectively. For
specimen B4a, the predicted FRP strain matched the experimental value much better. The
predicted strain was 0.0058, and the experimental strain was 0.0062, which resulted in an
experimental strain only 7% higher than the predicted strain.
Because the model does not predict ICdebonding failure modes for any of the
specimens in test series 2 or 3, the corresponding predicted FRP strain values at failure
were very high compared to the experimental strain values. As shown in Table 411, the
141
ratios of the predicted strain to the rupture strain for test series 2 were predicted to be 88
and 100% of the rupture strain, which is much greater than the experimental FRP strains
of 30 and 56% of the rupture strain, respectively. For the ratio of 0.88, the predicted
failure mode was crushing of the concrete; for the ratio of 1.00, the predicted failure
mode was FRP rupture. Test series 3 has experimental FRP strains ranging from 22 to
28% of the rupture strain when IC debonding occurred, which is much less than the
predicted FRP rupture failure of 100% of the rupture strain.
4.3.2.2 Discussion of Model
When compared to the EB tests, the model by Task Group 9.3 of fib did not correlate
well with the experimental results. Out of the twelve laboratory specimens, the model
only correctly predicted the failure mode three times. For most of the specimens, the
model overestimated the strengthened moment capacities and was not very accurate.
Task Group 9.3 also reported two other approaches for calculating the IC
debonding resistance of reinforced concrete members. Approach 1 is a simplified method
that provides a global strain limit on the FRP, which ranges from 0.0065 to 0.0085
mm/mm. This approach is very similar to the approach by ACI 440 where the strain is
limited to 70% of the ultimate strain. Both limit the maximum strain value that can be
used, but the strain limit of ACI 440 depends on the ultimate strain of the FRP whereas
the strain limit of Task Group 9.3 is fixed at a constant value. Task Group 9.3 does not
recommend Approach 1 and even states that the other two approaches will provide a
more realistic prediction of ICdebonding resistance. Approach 2 is more detailed and is
based on computation of the maximum possible increase in tensile stress within the FRP
142
that can be transferred by means of bond stresses between two adjacent flexural cracks.
Said and Wu (2008) examined this approach and concluded that it has wide ranges of
prediction ratios and high levels of dispersion; however, future work should involve a
more detailed investigation of Approach 2. Approach 3, the approach used in this chapter,
did not prove to be very accurate or precise. One cause of its inadequacy could be that
Bulletin 14 was last published in 2001. Since then, new research has been conducted and
newer models have been proposed that more accurately predict FRPstrengthened
capacity. Another possible reason for its inaccuracies could be because the model is
based on the assumption that ICdebonding can only occur in the presence of sectional
shear force (i.e. moment changing along member). Thus, the local ?in and out? bond
stresses that transmit forces from the FRP to concrete adjacent to cracked sections are not
considered.
4.3.3 Standards Australia (2008)
The ICdebonding model for EB FRP given by Standards Australia was compared to the
existing experimental EB tests introduced in Chapter 2 to determine the accuracy and
level of safety of the model.
4.3.3.1 Comparison to Previous Testing
Table 412 shows a comparison of capacities using the ICdebonding model from
Standards Australia.
143
Table 412: Comparison of the ICDebonding Model by Standards Australia (2008) to
EB Test Results
Predicted Experimental Test
Series
#
Specimen
ID
M
n
(kft)
?M
n
(kft)
Failure
Mode
M
exp
(kft)
?M
exp
(kft)
Failure
Mode
M
exp
/
M
n,pred
?M
exp
/
?M
n,pred
1 B2a 29.7 4.1 IC 1.04 0.39
1 B2b
28.6 10.4 IC
29.7 4.1 IC 1.04 0.39
1 B4a 36.3 18.1 IC 32.6 7.0 IC 0.90 0.38
2
CPL50
BOND
27.2 10.7 IC 28.4 6.7 IC 1.04 0.63
2 SHBOND 25.0 8.5 IC 31.9 10.2 IC 1.27 1.20
3 B1 82.4 13.3 IC 1.03 0.87
3 B2 85.2 16.1 IC 1.07 1.05
3 B3 82.7 13.6 IC 1.04 0.88
3 B4 85.4 16.3 IC 1.07 1.06
3 B5 82.7 13.6 IC 1.04 0.88
3 B6
79.9 15.4 IC
84.2 15.1 IC 1.05 0.98
3 B7 82.4 17.9 IC 88.3 19.3 IC 1.07 1.07
4 G3S9 757 N/A IC 320 N/A
no
failure
0.42 N/A
4 G3S10 757 N/A IC 280 N/A
no
failure
0.37 N/A
4 G4S9 726 N/A IC 300 N/A
no
failure
0.42 N/A
4 G4S10 874 N/A IC 300 N/A
no
failure
0.34 N/A
Notes: IC intermediate crack debonding
As shown in Table 412, the failure mode was correctly predicted as IC
debonding for test series 1, 2, and 3. For the B2 specimens in test series 1, the
experimental moment capacities were both 4% greater than the predicted moment
capacities. For the B4a specimen, the experimental capacity was 80% of the predicted
capacity. The changes in capacity for all three specimens were overestimated. The
predicted changes in moment capacity were about 2.5 times the experimental changes in
moment capacity.
For test series 2, the experimental capacities were 4 and 27% greater than the
predicted capacities. The changes in capacity predictions were both underestimated and
144
overestimated. The experimental changes in capacity were 63 and 120% of the predicted
changes in capacity.
For test series 3, the capacity predictions were very accurate, with the
experimental capacities ranging from 103 to 107% of the predicted capacities. The
changes in capacity were relatively accurate, with the experimental changes in moment
ranging from 87 to 107% of predicted changes in capacity.
Once again, the high capacity predictions for test series 4 relative to the applied
moments were expected as the War Memorial Bridge was only loaded in the service level
range.
Figure 411 shows a comparison between the experimental moment capacity and
the predicted moment capacity. Figure 412 shows a comparison between the
experimental change in capacity and the predicted change in capacity.
0
10
20
30
40
50
60
70
80
90
0 102030405060708090
Predicted Moment (kft)
Ex
per
i
me
nta
l
Mome
nt
(k
ft
)
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #3: Reed et al. (2005)
Figure 411: Comparison between EB Test Results and Standards Australia (2008) IC
Debonding Capacity Predictions
145
0
2
4
6
8
10
12
14
16
18
20
0 2 4 6 8 101214161820
Change in Predicted Moment (kft)
Ch
ang
e
in Experimental Moment (kft)
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #3: Reed et al. (2005)
Figure 412: Comparison between EB Test Results and Standards Australia (2008) IC
Debonding ChangeinCapacity Predictions
As shown in Figure 411, the data points are fairly close to the line shown, which
means that the model is fairly accurate. Most of the points are above and to the left of the
line, which means that the model is typically conservative in its predictions of capacity.
In Figure 412, most of the data points are relatively close the line shown, but three of the
points are very inaccurate and unconservative.
Table 413 shows the FRP strain predictions and experimental results.
146
147
Table 413: FRP Strain Predictions using the Standards Australia (2008) ICDebonding
Model and EB Test Results
Predicted Experimental Test
Series #
Specimen
ID
?
f,pred
?
f,pred
/?
f,rupt
?
f,exp
?
f,exp
/?
f,rupt
?
f,exp
/
?
f,pred
1 B2a 0.48% 0.44 0.85
1 B2b
0.57% 0.52
0.44% 0.41 0.78
1 B4a 0.98% 0.44 0.62% 0.28 0.63
2 CPL50BOND 0.52% 0.35 0.44% 0.30 0.86
2 SHBOND 0.87% 0.58 0.85% 0.56 0.97
3 B1 0.44% 0.22 0.66
3 B2 0.51% 0.25 0.76
3 B3 0.49% 0.24 0.73
3 B4 0.53% 0.26 0.80
3 B5 0.51% 0.25 0.77
3 B6
0.67% 0.33
0.56% 0.28 0.84
3 B7 0.57% 0.28 0.47% 0.23 0.82
Note: All predicted and experimental failure modes were IC debonding.
In test series 1, the predicted strain values were 44 and 52% of the rupture strain,
while the experimental strains ranged from 28 to 44% of the rupture strain. The ratio of
experimental FRP strain to predicted FRP strain ranged from 0.63 to 0.85 for the
specimens in this test series.
In test series 2, the predicted strains were slightly greater than the experimental
strains. For specimens CPL50BOND and SHBOND, the predicted FRP strains were
0.0052 and 0.0087, respectively, and the experimental failure strains in the FRP were
0.0044 and 0.0085, respectively. The ratios of experimental strain to predicted strain were
0.86 and 0.97.
In test series 3, the predicted strains were greater than the experimental strains.
For specimens B1 through B6, the model predicted an FRP strain of 33% of the rupture
strain. The experimental FRP strains at failure for these specimens ranged from 22 to
28% of the rupture strain, which resulted in ratios of experimental strain to predicted
148
strain of 0.66 to 0.84. For specimen B7, the ratio of experimental strain to predicted strain
was 0.82.
4.3.3.2 Discussion of Model
When compared to the experimental tests of EB FRP, the ICdebonding model given by
Standards Australia was very accurate for predicting strengthened moment capacities. All
but two of the specimens had experimental capacities that were in the range of 3 to 7%
greater than the predicted capacities. The two specimens that were outside of this range
had experimental capacities that were 90 and 127% of the predicted capacities.
The changes in capacity predictions for test series 1 and 2 were not very accurate,
but the changes in capacity predictions for test series 3 were relatively accurate. For test
series 3, the difference in the changes in capacity for each specimen was about 2 kipft or
less.
When compared to the results of the other EB ICdebonding models, the model
given by Standards Australia was very accurate at predicting FRP strain values. The
strains were overestimated but not as severely as the other models.
4.3.4 Rosenboom (2006)
The model by Rosenboom (2006) was used to evaluate the ICdebonding resistance of
experimental tests using EB FRP.
149
4.3.4.1 Comparison to Previous Testing
Using the Rosenboom model, nominal moment capacities were predicted for each
strengthened test specimen and compared to previous testing. Table 414 shows the
predicted capacities, the experimental results, and comparisons between the two.
Table 414: Comparison of the ICDebonding Model by Rosenboom (2006) to EB Test
Results
Predicted Experimental Test
Series
#
Specimen
ID
M
n
(kft)
?M
n
(kft)
Failure
Mode
M
exp
(kft)
?M
exp
(kft)
Failure
Mode
M
exp
/
M
n,pred
?M
exp
/
?M
n,pred
1 B2a 29.7 4.1 IC 0.75 0.19
1 B2b
39.6 21.4 R
29.7 4.1 IC 0.75 0.19
1 B4a 24.1 5.9 IC 32.6 7.0 IC 1.35 1.18
2
CPL50
BOND
25.6 9.1 IC 28.4 6.7 IC 1.11 0.74
2 SHBOND 24.6 8.0 IC 31.9 10.2 IC 1.30 1.26
3 B1 82.4 13.3 IC 0.97 0.64
3 B2 85.2 16.1 IC 1.00 0.77
3 B3 82.7 13.6 IC 0.97 0.65
3 B4 85.4 16.3 IC 1.00 0.78
3 B5 82.7 13.6 IC 0.97 0.65
3 B6
85.4 20.9 IC
84.2 15.1 IC 0.99 0.72
3 B7 87.5 23.0 IC 88.3 19.3 IC 1.01 0.84
4 G3S9 866 N/A IC 320 N/A
no
failure
0.37 N/A
4 G3S10 880 N/A IC 280 N/A
no
failure
0.32 N/A
4 G4S9 830 N/A IC 300 N/A
no
failure
0.37 N/A
4 G4S10 1008 N/A IC 300 N/A
no
failure
0.30 N/A
Notes: IC intermediate crack debonding
R rupture of the FRP
For the B2 specimens in test series 1, the model incorrectly predicted an FRP
rupture failure model. For all other specimens in test series 1, 2, and 3, the model
correctly predicted the failure mode as IC debonding. For test series 1, the model was not
150
very precise; it both underestimated and overestimated the capacity and the change in
capacity.
The model more accurately predicted the capacities in test series 2 than in test
series 1. Both predictions for the specimens in test series 2 were conservatively
underestimated. The experimental capacities were 11 and 30% of the predicted
capacities. For the changes in capacity, however, the model overestimated it for one
specimen and underestimated it for the other.
The model was extremely accurate when compared to test series 3. The
experimental capacities ranged from 97 to 101% of the predicted capacities. The changes
in moment capacities, however, were not very accurate. The experimental changes in
capacity ranged from 64 to 84% of the predicted changes in capacity.
In test series 4, the War Memorial Bridge was only loaded in the service level
range; therefore, the high capacity predictions relative to the experimental moments were
expected.
Figure 413 shows a comparison between the experimental capacity and the
predicted capacity. Figure 414 shows a comparison between the experimental change in
capacity and the predicted change in capacity.
0
10
20
30
40
50
60
70
20406080
Predicted Moment (kft)
Expe
rimental Mom
e
nt (k
ft)
80
90
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #3: Reed et al. (2005)
Figure 413: Comparison between EB Test Results and Rosenboom (2006) IC
Debonding Capacity Predictions
151
0
5
10
15
20
0 5 10 15 20 25
Change in Predicted Moment (kft)
Cha
nge in E
x
perim
e
nta
l
Mom
e
nt (k
25
ft)
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #3: Reed et al. (2005)
Figure 414: Comparison between EB Test Results and Rosenboom (2006) IC
Debonding ChangeinCapacity Predictions
As shown in Figure 413, most of the data points lie fairly close to the line that
separates a conservative and an unconservative prediction. In Figure 414, however, very
few of the data points lie close to the line.
Table 415 shows the FRP strain values that were measured for each test
specimen and that were predicted by the Rosenboom model.
152
153
Table 415: FRP Strain Predictions using the Rosenboom (2006) ICDebonding Model
and EB Test Results
Predicted Experimental Test
Series #
Specimen
ID
?
f,pred
?
f,pred
/?
f,rupt
?
f,exp
?
f,exp
/?
f,rupt
?
f,exp
/
?
f,pred
1 B2a 0.48% 0.44 0.44
1 B2b
*1.08% *1.00
0.44% 0.41 0.41
1 B4a 0.33% 0.15 0.62% 0.28 1.88
2 CPL50BOND 0.41% 0.28 0.44% 0.30 1.09
2 SHBOND 0.67% 0.44 0.85% 0.56 1.27
3 B1 0.44% 0.22 0.53
3 B2 0.51% 0.25 0.62
3 B3 0.49% 0.24 0.60
3 B4 0.53% 0.26 0.65
3 B5 0.51% 0.25 0.62
3 B6
0.83% 0.41
0.56% 0.28 0.68
3 B7 0.67% 0.33 0.47% 0.23 0.70
*denotes a failure mode other than IC debonding
The predicted FRP strains shown in Table 415 do not correlate well with the
experimental strains. Except for specimen CPL50BOND, which has a ratio of
experimental strain to predicted strain of 1.09, none of the specimens have a ratio of
experimental to predicted FRP strain between 0.75 and 1.25.
For the B2 specimens in test series 1, the model predicts a rupture failure, but the
experimental strains only reach 44 and 41% of the rupture strain. For specimen B4a, the
model underestimates the FRP strain by nearly two times.
For test series 2, the model had the most accurate predictions. The experimental
strains were 9 and 27% higher than the predicted FRP strains.
For test series 3, the model overestimated the FRP strains. The ratio of
experimental to predicted strains ranged from 0.53 to 0.70.
154
4.3.4.2 Discussion of Model
The Rosenboom model was fairly accurate at predicting strengthened moment capacities.
As shown in Figure 413, most of the data points were close to the line that corresponds
to an experimental to predicted capacity ratio of 1.0. However, the model did not predict
the changes in capacity or the FRP strains very well. Most of the FRP strains were
overestimated, which resulted in overestimations for most of the changes in capacity.
Because the strengthened moment capacities were fairly accurate and the FRP
contribution was overestimated, other factors must have affected the strengthened
capacity. One possible explanation is that the reinforced concrete was stronger and had a
greater contribution to the strengthened capacity than was predicted, which may have
been due to inaccuracies in the concrete compressive strength, assuming the Whitney
stress block, or possible overstrength or strain hardening of the reinforcing steel.
4.3.5 Seracino, Raizal Saifulnaz, and Oehlers (2007)
The model by Seracino, Raizal Saifulnaz, and Oehlers (2007) is a generic ICdebonding
model that was designed to be used for both EB and NSM. Standards Australia has
accepted the model in their design provisions but has recommended a different model for
EB that is specific to beams, which was evaluated in Section 4.3.3.
In this section, the Seracino, Raizal Saifulnaz, and Oehlers model is compared to
EB tests to determine the accuracy of the model.
4.3.5.1 Comparison to Previous Testing
Using the generic ICdebonding model, nominal moment capacities were predicted for
each EBstrengthened test specimen and compared to previous testing. Table 416 shows
155
the predicted capacities, the experimental results, and comparisons between the two for
specimens with EB FRP.
Table 416: Comparison of the ICDebonding Model by Seracino, Raizal Saifulnaz, and
Oehlers (2007) to EB Test Results
Predicted Experimental Test
Series
#
Specimen
ID
M
n
(kft)
?M
n
(kft)
Failure
Mode
M
exp
(kft)
?M
exp
(kft)
Failure
Mode
M
exp
/
M
n,pred
?M
exp
/
?M
n,pred
1 B2a 29.7 4.1 IC 0.75 0.19
1 B2b
39.6 21.4 R
29.7 4.1 IC 0.75 0.19
1 B4a 62.0 43.8 R 32.6 7.0 IC 0.53 0.16
2
CPL50
BOND
22.1 5.6 IC 28.4 6.7 IC 1.28 1.20
2 SHBOND 20.7 4.1 IC 31.9 10.2 IC 1.54 2.45
3 B1 82.4 13.3 IC 0.70 0.25
3 B2 85.2 16.1 IC 0.72 0.30
3 B3 82.7 13.6 IC 0.70 0.26
3 B4 85.4 16.3 IC 0.73 0.31
3 B5 82.7 13.6 IC 0.70 0.26
3 B6
117.6 53.2 IC
84.2 15.1 IC 0.72 0.28
3 B7 124.4 59.9 IC 88.3 19.3 IC 0.71 0.32
4 G3S9 1122 N/A R 320 N/A
no
failure
0.29 N/A
4 G3S10 1122 N/A R 280 N/A
no
failure
0.25 N/A
4 G4S9 1173 N/A R 300 N/A
no
failure
0.26 N/A
4 G4S10 1322 N/A R 300 N/A
no
failure
0.23 N/A
Notes: IC intermediate crack debonding
R rupture of the FRP
As shown in Table 416, the failure mode was correctly predicted as IC
debonding for test series 2 and 3, but the failure mode was incorrectly predicted as FRP
rupture for test series 1. Because the model predicted that the FRP would reach higher
FRP strains in test series 1, the capacities were overestimated. For the three specimens in
test series 1, the experimental moment capacities ranged from 53 to 75% of the predicted
moment capacities. The changes in capacity, however, were extremely overestimated.
156
The experimental changes in moment capacity ranged from 16 to 19% of the predicted
changes in moment capacity.
For test series 2, the predicted capacities and the predicted changes in capacity
were actually underestimated. The experimental capacities were 28 and 54% greater than
the predicted capacities, and the experimental changes in capacity were 20 and 145%
greater than the predicted changes in capacity.
For test series 3, the capacity predictions were very inaccurate, with the
experimental capacities ranging from 70 to 73% of the predicted capacities. The changes
in capacity were even more inaccurate, with the predicted changes in moment ranging
from three to four times as large as the experimental changes in capacity.
Once again, the high capacity predictions for test series 4 relative to the
experimental moments were expected as the War Memorial Bridge was only loaded in
the service level range.
Figure 415 shows a comparison between the experimental moment capacity and
the predicted moment capacity. Figure 416 shows a comparison between the
experimental change in capacity and the predicted change in capacity.
0
20
40
60
80
100
120
204060801012014
Predicted Moment (kft)
Exp
e
r
i
mental
Mo
men
t
(kf
t)
140
0
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #3: Reed et al. (2005)
Figure 415: Comparison between EB Test Results and Seracino, Raizal Saifulnaz, and
Oehlers (2007) ICDebonding Capacity Predictions
157
0
10
20
30
40
50
10203040506
Change in Predicted Moment (kft)
Ch
ang
e
i
n
Exper
imen
tal Mo
men
t (kft)
60
0
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #3: Reed et al. (2005)
Figure 416: Comparison between EB Test Results and Seracino, Raizal Saifulnaz, and
Oehlers (2007) ICDebonding ChangeinCapacity Predictions
As shown in Figures 415 and 416, the data points are not very close to the lines
shown, which means that the model is not very accurate. Most of the points are below
and to the right of the lines, which means that the model was unconservative in its
predictions.
Table 417 shows the FRP strain predictions and experimental results.
158
159
Table 417: FRP Strain Predictions using the Seracino, Raizal Saifulnaz, and Oehlers
(2007) ICDebonding Model and EB Test Results
Predicted Experimental Test
Series #
Specimen
ID
?
f,pred
?
f,pred
/?
f,rupt
?
f,exp
?
f,exp
/?
f,rupt
?
f,exp
/
?
f,pred
1 B2a 0.48% 0.44 0.44
1 B2b
*1.08% *1.00
0.44% 0.41 0.41
1 B4a *2.22% *1.00 0.62% 0.28 0.28
2 CPL50BOND 0.27% 0.18 0.44% 0.30 1.64
2 SHBOND 0.38% 0.25 0.85% 0.56 2.24
3 B1 0.44% 0.22 0.22
3 B2 0.51% 0.25 0.25
3 B3 0.49% 0.24 0.25
3 B4 0.53% 0.26 0.27
3 B5 0.51% 0.25 0.26
3 B6
2.01% 0.99
0.56% 0.28 0.28
3 B7 1.66% 0.82 0.47% 0.23 0.28
*denotes a failure mode other than IC debonding
As shown in Table 417, the predicted FRP strains do not match the experimental
FRP strains very well. In test series 1 and 3, the predicted strains were very high, with
predicted strain values ranging from 82 to 100% of the rupture strain. The experimental
strains for test series 1 and 3, however, only ranged from 22 to 44% of the rupture strain,
which is about one quarter to one half of the predicted strain for most cases. For the two
specimens in test series 2, the predicted strains were 18 and 25% of the rupture strain,
while the experimental strains were 30 and 56% of the rupture strain.
Even though the model correctly predicted IC debonding as the failure mode for
the specimens in test series 3, the predicted FRP strains were very close to the rupture
strain value. For specimens B1 through B6, the predicted strain was 99% of the rupture
strain, which almost resulted in a predicted failure mode of FRP rupture. However, the
strains in the actual test specimens never approached this level prior to IC debonding.
160
4.3.5.2 Discussion of Model
The model given by Seracino, Raizal Saifulnaz, and Oehlers (2007) did not accurately
predict the strengthened moment capacities for EB tests. Most of the specimens had
experimental capacities that were 75% or less of the predicted capacities, which resulted
in a very unconservative model.
Because it was based on pushpull tests, this model should give a lower bound for
the moment capacity (Standards Australia 2008). For the EB tests, this model produced
unconservative results; therefore, this model should not be used as a lower bound for any
predictions for EB FRP
4.3.6 Said and Wu (2008)
The model by Said and Wu (2008) was used to evaluate the ICdebonding resistance of
experimental tests using EB FRP.
4.3.6.1 Comparison to Previous Testing
Using the ICdebonding model by Said and Wu (2008), nominal moment capacities were
predicted for each strengthened test specimen and compared to previous testing. Table 4
18 shows the predicted capacities, the experimental results, and comparisons between the
two for specimens with EB FRP.
161
Table 418: Comparison of the ICDebonding Model by Said and Wu (2008) to EB Test
Results
Predicted Experimental Test
Series
#
Specimen
ID
M
n
(kft)
?M
n
(kft)
Failure
Mode
M
exp
(kft)
?M
exp
(kft)
Failure
Mode
M
exp
/
M
n,pred
?M
exp
/
?M
n,pred
1 B2a 29.7 4.1 IC 1.27 0.78
1 B2b
23.5 5.3 IC
29.7 4.1 IC 1.27 0.78
1 B4a 25.7 7.5 IC 32.6 7.0 IC 1.27 0.93
2
CPL50
BOND
22.8 6.3 IC 28.4 6.7 IC 1.25 1.07
2 SHBOND 29.9 13.3 IC 31.9 10.2 IC 1.07 0.76
3 B1 82.4 13.3 IC 1.00 0.76
3 B2 85.2 16.1 IC 1.04 0.91
3 B3 82.7 13.6 IC 1.01 0.77
3 B4 85.4 16.3 IC 1.04 0.93
3 B5 82.7 13.6 IC 1.01 0.77
3 B6
82.1 17.6 IC
84.2 15.1 IC 1.03 0.86
3 B7 86.1 21.7 IC 88.3 19.3 IC 1.03 0.89
4 G3S9 816 N/A IC 320 N/A
no
failure
0.39 N/A
4 G3S10 816 N/A IC 280 N/A
no
failure
0.34 N/A
4 G4S9 810 N/A IC 300 N/A
no
failure
0.38 N/A
4 G4S10 959 N/A IC 300 N/A
no
failure
0.31 N/A
Notes: IC intermediate crack debonding
R rupture of the FRP
As shown in Table 418, the failure mode was correctly predicted as IC
debonding for test series 1, 2, and 3. For the three specimens in test series 1, the
experimental moment capacities were all 27% greater than the predicted moment
capacities. The changes in capacity, however, were slightly overestimated. The predicted
changes in moment capacity ranged from 0.5 to 1.2 kipft greater than the experimental
changes in moment capacity.
For test series 2, the predicted capacities and the predicted changes in capacity
were underestimated. The experimental capacities were 7 and 25% greater than the
162
predicted capacities, respectively, and the experimental changes in capacity were 76 and
107% of the predicted changes in capacity, respectively.
For test series 3, the capacity predictions were very accurate, with the
experimental capacities ranging from 100 to 104% of the predicted capacities. The
changes in capacity were less accurate, with the experimental changes in moment ranging
from 76 to 93% of predicted changes in capacity.
Once again, the high capacity predictions for test series 4 relative to the
experimental moments were expected as the War Memorial Bridge was only loaded in
the service level range.
Figure 417 shows a comparison between the experimental moment capacity and
the predicted moment capacity. Figure 418 shows a comparison between the
experimental change in capacity and the predicted change in capacity.
0
10
20
30
40
50
60
70
0 102030405060708090
Predicted Moment (kft)
E
x
periment
al Moment (k
ft)
80
90
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #3: Reed et al. (2005)
Figure 417: Comparison between EB Test Results and Said and Wu (2008) IC
Debonding Capacity Predictions
163
0
5
10
15
20
0 5 10 15 20 25
Change in Predicted Moment (kft)
Chang
e
in
Experi
men
tal Moment
(kft
)
25
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #3: Reed et al. (2005)
Figure 418: Comparison between EB Test Results and Said and Wu (2008) IC
Debonding ChangeinCapacity Predictions
As shown in Figure 417, the data points are fairly close to the line shown, which
means that the model is fairly accurate for predicting the strengthened moment capacity.
All of the points are above and to the left of the line, which means that the model was
conservative in its predictions. In Figure 418, the data points are relatively close to the
line of equality, which means that the model is relatively accurate at predicting the
change in capacity.
Table 419 shows the FRP strain predictions and experimental results.
164
165
Table 419: FRP Strain Predictions using the Said and Wu (2008) ICDebonding Model
and EB Test Results
Predicted Experimental Test
Series #
Specimen
ID
?
f,pred
?
f,pred
/?
f,rupt
?
f,exp
?
f,exp
/?
f,rupt
?
f,exp
/
?
f,pred
1 B2a 0.48% 0.44 1.63
1 B2b
0.29% 0.27
0.44% 0.41 1.49
1 B4a 0.41% 0.18 0.62% 0.28 1.52
2 CPL50BOND 0.61% 0.41 0.44% 0.30 0.73
2 SHBOND 1.03% 0.68 0.85% 0.56 0.82
3 B1 0.44% 0.22 6.84
3 B2 0.51% 0.25 7.96
3 B3 0.49% 0.24 7.67
3 B4 0.53% 0.26 8.31
3 B5 0.51% 0.25 8.02
3 B6
0.06% 0.03
0.56% 0.28 8.77
3 B7 0.06% 0.03 0.47% 0.23 7.53
Note: All predicted and experimental failure modes were IC debonding.
As shown in Table 419, the predicted FRP strains do not match the experimental
FRP strains very well. In test series 1, the predicted strain values were 18 and 27% of the
rupture strain, while the experimental strains ranged from 28 to 44% of the rupture strain.
The ratio of experimental FRP strain to predicted FRP strain was around 1.5 for the
specimens in this test series.
In test series 2, the predicted strains were greater than the experimental strains.
The ratios of experimental strain to predicted strain were 0.73 and 0.82.
In test series 3, the predicted strains were extremely low compared to the
experimental strains. For all of the specimens, the model predicted an FRP strain of 3%
of the rupture strain. The experimental strains at failure were 22 to 28% of the rupture
strain, which resulted in ratios of experimental strain to predicted strain of 6.84 to 8.77.
166
4.3.6.2 Discussion of Model
When compared to EB tests from the referenced literature, the Said and Wu model was
very accurate. For test series 1 and 2, the model was slightly conservative. For test series
3, the model was extremely accurate. For the changes in capacity predictions, the model
was relatively accurate. The predicted FRP strains, however, were not accurate at all,
with some of the experimental strains being more than seven times greater than the
predicted strains.
4.4 ICDebonding Models for NSM
Five different ICdebonding models for NSM are analyzed in this section. Each model
was used to predict strengthened moment capacities for different experimental
specimens. The predictions of the models were compared to experimental results of NSM
tests to determine the accuracy and level of safety of each model. The five models
discussed in this section are ACI 440 (2008), fib 9.3 (2001), Standards Australia (2008),
Seracino et al. (2007a), and Said and Wu (2008). The experimental tests used in this
section are test series 1, 2, and 5 through 11.
4.4.1 ACI 440 (2008)
The NSM ICdebonding model given by ACI Committee 440 was compared to existing
experimental tests to determine the accuracy of the model.
4.4.1.1 Comparison to Previous Testing
Using the NSM model given by ACI 440, nominal moment capacities were predicted for
each test specimen and compared to experimental results. Like the predictions by the ACI
167
440 EB model, the NSM model predictions do not include any reduction factors. Table 4
20 shows the capacity predictions and comparisons to the test results.
For test series 9, 10, and 11, the embedment length of the FRP was the main
variable in each test, and the only failure mode that occurred was pullout of the FRP. For
each test series, only the specimens with the longest embedment lengths were included in
the database of ICdebonding tests used in the analysis of the ICdebonding models.
Because these tests incorporated an unusual test setup and because the ACI 440 model is
based on an assumed long bonded length (i.e. no pullout failure), these tests will be
ignored in the determination of the accuracy of the model.
168
Table 420: Comparison of the ICDebonding Model by ACI 440 (2008) to NSM Test
Results
Predicted Experimental Test
Series
#
Specimen
ID
M
n
(kft)
?M
n
(kft)
Failure
Mode
M
exp
(kft)
?M
exp
(kft)
Failure
Mode
M
exp
/
M
n,pred
?M
exp
/
?M
n,pred
1 B1 32.9 14.7 IC 43.1 17.4 IC 1.31 1.19
1 B2 32.4 14.2 IC 45.7 20.1 R 1.41 1.42
1 B3 35.5 17.3 IC 50.6 25.0 R 1.43 1.45
1 B4 46.9 28.7 IC 47.4 21.7 IC 1.01 0.76
2 NSMPL15 23.5 7.0 IC 30.3 8.6 R 1.29 1.23
2 NSMPL25 28.2 11.7 IC 33.4 11.7 IC 1.18 1.00
2 CRDNSM 32.8 16.2 IC 35.8 14.1 IC 1.09 0.87
5 NSMR 1 284.2 186.6 IC 278.4 180.9 IC 0.98 0.97
5 NSMR 2 283.6 186.0 IC 274.7 177.2 IC 0.97 0.95
6 61Fa 22.3 5.3 CC 1.04 1.53
6 61Fb
21.4 3.5 CC
20.9 3.9 CC 0.98 1.13
6 62Fa 22.5 5.5 CC 0.95 0.94
6 62Fb
23.7 5.8 CC
24.2 7.2 CC 1.02 1.25
6 91Fa 25.4 6.8 CC 1.07 1.56
6 91Fb
23.7 4.4 IC
25.1 6.6 CC 1.06 1.51
6 92Fa 33.3 14.8 CC 1.20 1.74
6 92Fb
27.8 8.5 IC
32.2 13.7 CC 1.16 1.61
6 121Fa 26.6 7.6 R 1.10 1.72
6 121Fb
24.2 4.4 IC
27.9 8.9 R 1.15 2.01
6 122Fa 30.4 11.4 CC 1.06 1.29
6 122Fb
28.6 8.8 IC
37.6 18.5 CC 1.31 2.11
7 NS_F1 19.6 N/A CC 18.7 N/A S 0.96 N/A
7 NS_F2 12.9 N/A IC 14.6 N/A CC 1.13 N/A
7 NS_F3 10.1 N/A IC 14.0 N/A CC 1.38 N/A
7 NS_F4 12.7 N/A IC 12.8 N/A IC 1.00 N/A
7 NB_F2 29.5 N/A IC 49.6 N/A IC 1.68 N/A
7 NB_F3 38.6 N/A IC 54.0 N/A IC 1.40 N/A
8 B2900 30.5 8.9 IC 44.1 22.6 CC 1.45 2.53
9 G4D24c 12.7 N/A IC 11.0 N/A P 0.87 N/A
9 C3D24b 16.3 N/A IC 7.8 N/A P 0.48 N/A
9 C3S24a 13.4 N/A IC 4.0 N/A P 0.30 N/A
10 fcm35_Lb80 3.1 N/A IC 2.1 N/A P 0.66 N/A
10 fcm45_Lb80 3.1 N/A IC 2.4 N/A P 0.78 N/A
10 fcm70_Lb80 3.1 N/A IC 2.4 N/A P 0.75 N/A
11 Lb120_M 2.9 N/A IC 1.5 N/A P 0.53 N/A
Notes: CC crushing of the concrete (preceded by steel yielding)
IC intermediate crack debonding
P pullout of the FRP
R rupture of the FRP
S shear failure in the concrete
Figure 419 shows a comparison between the experimental strengthened moment
capacity and the predicted strengthened moment capacity. Figure 420 shows a
comparison between the experimental change in capacity and the predicted change in
capacity.
0
50
100
150
200
0 50 100 150 200 250 300
Predicted Moment (kft)
Experimental Moment
(kft)
250
300
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #5: Taljsten and Nordin (2007)
TS #6: Yost et al. (2007)
TS #7: Liu, Oehlers, and Seracino (2006)
TS #8: Teng et al. (2006)
Figure 419: Comparison between NSM Test Results and ACI 440 (2008) ICDebonding
Capacity Predictions
169
0
20
40
0 20 40 60 80 100 120 140 160 180 200
Change in Predicted Moment (kft)
Cha
n
ge
60
80
100
120
140
160
180
200
in Experimental Moment
(kft)
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #5: Taljsten and Nordin (2007)
TS #6: Yost et al. (2007)
TS #8: Teng et al. (2006)
Figure 420: Comparison between NSM Test Results and ACI 440 (2008) ICDebonding
ChangeinCapacity Predictions
To more closely examine the dispersion of the data points, test series 5 will be
excluded; the relatively large moments greatly change the scale of the graph. Figures 4
21 and 422 show these enlarged regions of the graphs.
170
0
10
10203040506
Predicted Moment (kft)
20
30
40
50
60
0
Experimental Moment
(kft)
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #6: Yost et al. (2007)
TS #7: Liu, Oehlers, and Seracino (2006)
TS #8: Teng et al. (2006)
Figure 421: Enlarged Graph of the ACI 440 (2008) NSM Capacity Comparisons
For test series 1 and 2, the ACI 440 NSM model was mostly conservative, with
the experimental strengthened capacities up to 43% greater than the predicted
strengthened capacities. For three of the specimens, the failure mode was incorrectly
predicted as IC debonding, while the actual failure mode was FRP rupture. The change
inmoment comparisons for these test series were conservative for four of the specimens,
but two of the comparisons were actually unconservative. The two unconservative
predictions corresponded to the two specimens that had the largest area of FRP
reinforcement. Specimen B4 had five NSM strips; the other NSM specimens in test series
1 had one or two strips. Specimen CRDNSM had an FRP area of 63.6 mm
2
; the other
two NSM specimens in test series 2 had much smaller FRP areas of 21 and 35 mm
2
.
171
0
5
0 5 10 15 20 25 30
Change in Predicted Moment (kft)
Cha
n
ge
10
15
20
25
30
in Experimental Moment
(kft)
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #6: Yost et al. (2007)
TS #8: Teng et al. (2006)
Figure 422: Enlarged Graph of the ACI 440 (2008) NSM ChangeinCapacity
Comparisons
For the tests conducted by Taljsten and Nordin (2007) and Yost et al. (2007), test
series 5 and 6, respectively, the ACI model was relatively accurate. However, for eight of
the twelve specimens in the Yost et al. test series, the failure mode was incorrectly
predicted, which resulted in very conservative estimates of the change in moment in all
but three specimens.
The tests conducted by Liu, Oehlers, and Seracino (2006), test series 7, had mixed
results when compared to the ACI 440 model. The predicted failure mode only matched
the experimental failure mode in half of the specimens. Three of the specimens had an
experimental strengthened capacity of 38% or greater than the predicted strengthened
172
173
capacity. This test series did not have a control beam so no changeinmoment
comparisons could be made.
Table 421 shows the experimental and predicted FRP strains using the ACI 440
NSM model.
Table 421: FRP Strain Predictions using the ACI 440 (2008) ICDebonding Model and
NSM Test Results
Predicted Experimental Test
Series #
Specimen
ID
?
f,pred
?
f,pred
/?
f,rupt
?
f,exp
?
f,exp
/?
f,rupt
?
f,exp
/
?
f,pred
1 B1 0.80% 0.70 0.88% 0.77 1.10
1 B2 0.76% 0.70 *1.34% *1.24 1.76
1 B3 0.93% 0.70 *1.38% *1.04 1.48
1 B4 1.55% 0.70 1.35% 0.61 0.87
2 NSMPL15 1.04% 0.70 *1.54% *1.04 1.49
2 NSMPL25 1.04% 0.70 1.24% 0.83 1.19
2 CRDNSM 1.08% 0.70 1.31% 0.84 1.21
5 NSMR 1 1.21% 0.70 0.92% 0.53 0.76
5 NSMR 2 1.21% 0.70 0.92% 0.53 0.76
7 NS_F1 *0.82% *0.51 *0.72% *0.45 0.88
7 NS_F2 1.13% 0.70 *1.30% *0.81 1.15
7 NS_F3 1.13% 0.70 *1.50% *0.93 1.33
7 NS_F4 1.17% 0.70 0.84% 0.50 0.72
7 NB_F2 1.13% 0.70 1.02% 0.63 0.91
7 NB_F3 1.17% 0.70 0.83% 0.50 0.71
8 B2900 0.96% 0.70 *0.97% *0.71 1.01
*denotes a failure mode other than IC debonding
Only test series 1, 2, 5, 7, and 8 are shown in Table 421 because these are the
only series that provided experimental strain values for the FRP.
The ACI model limits the FRP strain to 70% of the rupture strain for all test
specimens except one in Table 421. For this one specimen, the predicted failure mode
was not IC debonding but rather crushing of the concrete prior to IC debonding. As
shown in Table 421, the predicted FRP debonding strains did not match the experimental
failure strains very well. Most of the strain values were either less than 65% of the FRP
174
rupture strain or greater than 75% of the FRP rupture strain. Only one specimen?s
experimental failure strain was within this range. A possible source of error could be due
to the fact that it is not clear whether these strains were measured at crack sections. If
they were not, tension stiffening would reduce the strains relative to the crackedsection
values.
Specimens B2, B3, and NSMPL15 all failed due to FRP rupture at a measured
strain higher than the reported rupture strain of the FRP. Specimen B3 attained a strain
that was 24% higher than the reported rupture strain, while the other two specimens
failed at a strain that was 4% higher than the reported rupture strain. A possible
explanation for the incorrect rupture strain value that was reported could be due to some
level of safety and conservatism built into the rupture strain value given by the
manufacturer. Another explanation could be due to material irregularities that increased
the strength of the FRP.
The ratios of experimental FRP strains to predicted FRP strains are also shown in
Table 421. These ratios show a poor correlation between the predicted versus the
experimental results; only three of the specimens resulted in an experimental FRP strain
that was within the range of 90 to 110% of the predicted strain. The other thirteen
specimens fell outside of this range.
4.4.1.2 Discussion of Model
By taking the FRP strain as 70% of the rupture strain, the ACI 440 (2008) NSM model
makes a rough approximation of the ICdebonding failure strain in the FRP. This method
only works if the failure strain is close to this value. For the tests analyzed, only one
175
specimen fell within the range of 65 to 75% of the rupture strain. By using this simplistic
method, the strengthened moment capacities were accurate for some of the test series and
overly conservative for other test series. The precision of the model was poor for the
changeinmoment comparisons; for some of the specimens, it greatly underestimated the
capacity, while for others it overestimated it. These inaccuracies might be related to the
amount of FRP reinforcement that was provided.
For three of the specimens, the measured FRP strain at failure was higher than the
reported rupture strain. This overestimation of the rupture strain is partly why the model
was conservative for some of the specimens.
4.4.2 fib 9.3 (2001)
In Bulletin 14, Task Group 9.3 does not report the procedure for an NSM application of
FRP. NSM is briefly mentioned in the bulletin, but no NSMspecific model was given;
however, because the ICdebonding model for EB is generic in nature, it was compared
to NSM test results to determine the accuracy and level of safety of the model for NSM.
4.4.2.1 Comparison to Previous Testing
Table 422 shows the comparison between the fib 9.3 (2001) model and NSM test results.
176
Table 422: Comparison of the ICDebonding Model by fib 9.3 (2001) to NSM Test
Results
Predicted Experimental Test
Series
#
Specimen
ID
M
n
(kft)
?M
n
(kft)
Failure
Mode
M
exp
(kft)
?M
exp
(kft)
Failure
Mode
M
exp
/
M
n,pred
?M
exp
/
?M
n,pred
1 B1 39.2 21.0 R 43.1 17.4 IC 1.10 0.83
1 B2 24.0 5.8 IC 45.7 20.1 R 1.91 3.46
1 B3 38.1 19.9 IC 50.6 25.0 R 1.33 1.26
1 B4 29.8 11.6 IC 47.4 21.7 IC 1.59 1.88
2 NSMPL15 26.9 10.3 R 30.3 8.6 R 1.13 0.83
2 NSMPL25 25.4 8.8 IC 33.4 11.7 IC 1.32 1.33
2 CRDNSM 40.4 23.8 R 35.8 14.1 IC 0.89 0.59
5 NSMR 1 362.2 264.6 R 278.4 180.9 IC 0.77 0.68
5 NSMR 2 360.5 262.9 R 274.7 177.2 IC 0.76 0.67
6 61Fa 22.3 5.3 CC 1.04 1.53
6 61Fb
21.4 3.5 CC
20.9 3.9 CC 0.98 1.13
6 62Fa 22.5 5.5 CC 0.95 0.94
6 62Fb
23.7 5.8 CC
24.2 7.2 CC 1.02 1.25
6 91Fa 25.4 6.8 CC 1.02 1.21
6 91Fb
24.9 5.7 CC
25.1 6.6 CC 1.01 1.17
6 92Fa 33.3 14.8 CC 1.16 1.58
6 92Fb
28.6 9.4 CC
32.2 13.7 CC 1.12 1.46
6 121Fa 26.6 7.6 R 1.02 1.18
6 121Fb
26.2 6.4 R
27.9 8.9 R 1.06 1.38
6 122Fa 30.4 11.4 CC 0.94 0.91
6 122Fb
32.2 12.4 R
37.6 18.5 CC 1.17 1.49
7 NS_F1 17.5 N/A IC 18.7 N/A S 1.07 N/A
7 NS_F2 13.2 N/A IC 14.6 N/A CC 1.11 N/A
7 NS_F3 22.5 N/A R 14.0 N/A CC 0.62 N/A
7 NS_F4 12.9 N/A IC 12.8 N/A IC 0.99 N/A
7 NB_F2 30.3 N/A IC 49.6 N/A IC 1.64 N/A
7 NB_F3 29.9 N/A IC 54.0 N/A IC 1.81 N/A
8 B2900 34.3 12.8 R 44.1 22.6 CC 1.28 1.77
9 G4D24c 3.9 N/A IC 11.0 N/A P 2.85 N/A
9 C3D24b 2.9 N/A IC 7.8 N/A P 2.73 N/A
9 C3S24a 2.9 N/A IC 4.0 N/A P 1.39 N/A
10 fcm35_Lb80 1.0 N/A IC 2.1 N/A P 2.06 N/A
10 fcm45_Lb80 1.2 N/A IC 2.4 N/A P 2.07 N/A
10 fcm70_Lb80 1.5 N/A IC 2.4 N/A P 1.55 N/A
11 Lb120_M 0.6 N/A IC 1.5 N/A P 2.73 N/A
Notes: CC crushing of the concrete (preceded by steel yielding)
IC intermediate crack debonding
P pullout of the FRP
R rupture of the FRP
S shear failure in the concrete
177
For test series 1, the failure mode was only predicted correctly for one of the four
test specimens. For specimen B1, fib 9.3 predicted that the FRP would rupture before
debonding. In the experiment, however, the FRP debonded before it ruptured. Even
though the failure mode was incorrectly predicted, the strengthened moment capacity
prediction was relatively accurate. For specimens B2 and B3, the model predicted an IC
debonding failure, but the actual failure was rupture of the FRP, which resulted in very
low estimations of capacity. The failure mode was correctly predicted for specimen B4,
but the strengthened capacity prediction was well below the experimental capacity.
For test series 2 and 5, the failure mode was predicted correctly for two of the five
specimens. For these two specimens, the strengthened capacity was conservatively
predicted as lower than the experimental capacity. For the other three specimens,
however, the capacity was unconservatively predicted as higher than the experimental
capacity.
For test series 6, the failure mode was correctly predicted for five of the six types
of specimens, which resulted in relatively accurate predictions of capacity. All of the
experimental capacities in test series 6 fell within the range of 94 to 117% of the
predicted capacity, with seven of the twelve specimens within 5% of the predicted
capacity. No ICdebonding failures were reported or predicted for this test series.
For three of the four slab specimens in test series 7, denoted ?NS,? the predicted
capacity matched the experimental capacity relatively well. These three experimental
capacities were within 11% of the predicted capacities. For the other slab specimen and
the two beam specimens, the predictions were not very accurate. The experimental
178
moments were not within 35% of the predicted moments. Only three of the six specimens
had a correctly predicted failure mode.
In test series 8, the experimental moment was 28% larger than the predicted
moment, and the failure mode was incorrectly predicted.
The changes in moment for all of the specimens showed a wide dispersion of
results. Some experimental changes in moment were as low as 59% of the predicted
change in moment, and some were as high as 346% of the predicted change in moment.
Figure 423 shows a comparison between the experimental strengthened moment
capacity and the predicted strengthened moment capacity. Figure 424 shows a
comparison between the experimental change in capacity and the predicted change in
capacity.
0
50
100
150
200
250
300
0 50 100 150 200 250 300 350 400
Predicted Moment (kft)
E
x
peri
menta
l
M
o
ment
(k
ft)
350
400
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #5: Taljsten and Nordin (2007)
TS #6: Yost et al. (2007)
TS #7: Liu, Oehlers, and Seracino (2006)
TS #8: Teng et al. (2006)
Figure 423: Comparison between NSM Test Results and fib 9.3 (2001) ICDebonding
Capacity Predictions
179
0
50
100
150
200
250
0 50 100 150 200 250 300
Change in Predicted Moment (kft)
Change in Ex
peri
menta
l
M
o
ment
(k
ft)
300
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #5: Taljsten and Nordin (2007)
TS #6: Yost et al. (2007)
TS #8: Teng et al. (2006)
Figure 424: Comparison between NSM Test Results and fib 9.3 (2001) ICDebonding
ChangeinCapacity Predictions
Because the Taljsten and Nordin (2007) test series includes specimens with
relatively high moments, they were excluded from the enlarged graphs shown in Figures
425 and 426.
180
0
5
10
15
20
25
30
35
40
0 5 10 15 20 25 30 35 40 45 50
Predicted Moment (kft)
Ex
peri
menta
l
M
o
ment
(k
ft)
45
50
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #6: Yost et al. (2007)
TS #7: Liu, Oehlers, and Seracino (2006)
TS #8: Teng et al. (2006)
Figure 425: Enlarged Graph of the fib 9.3 (2001) NSM Capacity Comparisons
181
0
5
10
15
20
25
0 5 10 15 20 25 30
Change in Predicted Moment (kft)
C
h
ange in Ex
peri
menta
l
M
o
ment (k
30
ft)
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #6: Yost et al. (2007)
TS #8: Teng et al. (2006)
Figure 426: Enlarged Graph of the fib 9.3 (2001) NSM ChangeinCapacity
Comparisons
A data point to the left and above the line is a conservative prediction. A data
point below and to the right of the line is an unconservative prediction. An ideal
prediction would result in a data point that falls directly on the line.
Table 423 shows the experimental failure strains in the FRP, the predicted failure
strains in the FRP, and comparisons between the two.
182
183
Table 423: FRP Strain Predictions using the fib 9.3 (2001) ICDebonding Model and
NSM Test Results
Predicted Experimental Test
Series #
Specimen
ID ?
f,pred
?
f,pred
/?
f,rupt
?
f,exp
?
f,exp
/?
f,rupt
?
f,exp
/
?
f,pred
1 B1 *1.14% *1.00 0.88% 0.77 0.77
1 B2 0.28% 0.26 *1.34% *1.24 4.71
1 B3 1.06% 0.80 *1.38% *1.04 1.30
1 B4 0.60% 0.27 1.35% 0.61 2.24
2 NSMPL15 *1.48% *1.00 *1.54% *1.04 1.04
2 NSMPL25 0.78% 0.53 1.24% 0.83 1.59
2 CRDNSM *1.55% *1.00 1.31% 0.85 0.85
5 NSMR 1 *1.73% *1.00 0.92% 0.53 0.53
5 NSMR 2 *1.73% *1.00 0.92% 0.53 0.53
7 NS_F1 0.68% 0.42 *0.72% *0.45 1.06
7 NS_F2 1.22% 0.76 *1.30% *0.81 1.07
7 NS_F3 *1.61% *1.00 *1.50% *0.93 0.93
7 NS_F4 1.23% 0.74 0.84% 0.50 0.68
7 NB_F2 1.22% 0.76 1.02% 0.63 0.84
7 NB_F3 0.66% 0.40 0.83% 0.50 1.25
8 B2900 *1.37% *1.00 *0.97% *0.71 0.71
*denotes a failure mode other than IC debonding
For two of the specimens in test series 1, the FRP strain was only predicted to be
about a quarter of the rupture strain. The corresponding experimental strains were more
than two and four times these predicted values. For the other two specimens in test series
1, the experimental FRP strains were 77 and 130% of the predicted strains.
For specimen NSMPL15, fib 9.3 correctly predicted the failure mode as FRP
rupture and also made a very accurate prediction of the debonding strain. For specimen
NSMPL25, however, the failure mode was correctly predicted as IC debonding, but the
experimental FRP strain was 59% higher than the predicted strain.
For test series 5, FRP rupture was predicted for both specimens, but failure
occurred due to IC debonding instead, resulting in an experimental strain that was about
half of the predicted strain.
184
In test series 7, the failure mode was correctly predicted for specimen NS_F4 and
for both beam specimens, denoted ?NB.? The failure mode was incorrectly predicted for
the other three slab specimens, denoted NS_F1, NS_F2, and NS_F3. However, the
predicted strains for the three slab specimens had a better correlation with the
experimental strains than the three specimens where the failure mode was correctly
predicted.
In test series 8, the failure mode was incorrectly predicted, and the experimental
FRP strain was 71% of the predicted strain.
4.4.2.2 Discussion of Model
The fib model did not correlate well with the NSM tests. Out of the twentyeight
specimens, not including the pullout failures, the model correctly predicted the failure
mode sixteen times. If the Yost et al. series is removed because of a lack of ICdebonding
failures in this test series, then only six of the sixteen specimens had a correctly predicted
failure mode. Also, only five of the nine ICdebonding failures were correctly predicted.
These incorrect failure modes led to incorrect FRP strain predictions and, consequently,
incorrect strengthened moment capacities. As shown in Figures 425 and 426, the data
were widely dispersed.
In Bulletin 14, Task Group 9.3 does not report the procedure for an NSM
application of FRP. NSM is briefly mentioned in the bulletin, but no NSMspecific model
was given, which is most likely the reason that the NSM test results did not match the
predicted values very well.
185
4.4.3 Standards Australia (2008)
The ICdebonding model for NSM given by Standards Australia (2008) is the same
model given by Seracino, Raizal Saifulnaz, and Oehlers (2007). This model is a generic
ICdebonding model designed to be used for both EB and NSM. In this section, the
model by Standards Australia is compared to NSM tests to determine the accuracy of the
model.
4.4.3.1 Comparison to Previous Testing
The model given by Standards Australia (2008) was used to predict capacities for NSM
test specimens. Table 424 shows the predicted capacities, the experimental results, and
comparisons between the two.
In test series 1, the failure mode was correctly predicted in three of the four
specimens. In these three specimens, the capacity was underestimated. For specimen B1,
which failed due to IC debonding, the experimental capacity was 55% greater than the
predicted capacity. For specimens B2 and B3, which failed due to FRP rupture, the
experimental capacity was just 19% greater than the predicted capacity. Specimen B4
failed due to IC debonding but was predicted to fail due to FRP rupture. The
experimental capacity was 80% of the predicted capacity.
For test series 1, the changes in moment capacity were underestimated by about
two times for specimen B1 and overestimated by about two times for specimen B4. For
specimens B2 and B3, the changes in moment capacity were extremely accurate.
186
Table 424: Comparison of the ICDebonding Model by Standards Australia (2008) to
NSM Test Results
Predicted Experimental Test
Series
#
Specimen
ID
M
n
(kft)
?M
n
(kft)
Failure
Mode
M
exp
(kft)
?M
exp
(kft)
Failure
Mode
M
exp
/
M
n,pred
?M
exp
/
?M
n,pred
1 B1 27.8 9.6 IC 43.1 17.4 IC 1.55 1.81
1 B2 38.4 20.2 R 45.7 20.1 R 1.19 0.99
1 B3 42.7 24.5 R 50.6 25.0 R 1.19 1.02
1 B4 59.1 40.9 R 47.4 21.7 IC 0.80 0.53
2 NSMPL15 25.2 8.6 IC 30.3 8.6 R 1.20 1.00
2 NSMPL25 32.0 15.4 IC 33.4 11.7 IC 1.04 0.76
2 CRDNSM 23.7 7.2 IC 35.8 14.1 IC 1.51 1.96
5 NSMR 1 166.6 69.0 IC 278.4 180.9 IC 1.67 2.62
5 NSMR 2 164.9 67.3 IC 274.7 177.2 IC 1.67 2.63
6 61Fa 22.3 5.3 CC 1.04 1.53
6 61Fb
21.4 3.5 CC
20.9 3.9 CC 0.98 1.13
6 62Fa 22.5 5.5 CC 0.95 0.94
6 62Fb
23.7 5.8 CC
24.2 7.2 CC 1.02 1.25
6 91Fa 25.4 6.8 CC 1.02 1.21
6 91Fb
24.9 5.7 CC
25.1 6.6 CC 1.01 1.17
6 92Fa 33.3 14.8 CC 1.16 1.58
6 92Fb
28.6 9.4 CC
32.2 13.7 CC 1.12 1.46
6 121Fa 26.6 7.6 R 1.02 1.20
6 121Fb
26.1 6.3 IC
27.9 8.9 R 1.07 1.41
6 122Fa 30.4 11.4 CC 0.95 0.93
6 122Fb
32.0 12.2 IC
37.6 18.5 CC 1.17 1.51
7 NS_F1 19.6 N/A CC 18.7 N/A S 0.96 N/A
7 NS_F2 13.8 N/A CC 14.6 N/A CC 1.06 N/A
7 NS_F3 10.8 N/A IC 14.0 N/A CC 1.30 N/A
7 NS_F4 11.6 N/A IC 12.8 N/A IC 1.11 N/A
7 NB_F2 31.8 N/A IC 49.6 N/A IC 1.56 N/A
7 NB_F3 34.7 N/A IC 54.0 N/A IC 1.55 N/A
8 B2900 31.9 10.4 IC 44.1 22.6 CC 1.38 2.18
9 G4D24c 6.3 N/A IC 11.0 N/A P 1.76 N/A
9 C3D24b 6.5 N/A IC 7.8 N/A P 1.21 N/A
9 C3S24a 8.0 N/A IC 4.0 N/A P 0.50 N/A
10 fcm35_Lb80 3.3 N/A IC 2.1 N/A P 0.63 N/A
10 fcm45_Lb80 3.5 N/A IC 2.4 N/A P 0.69 N/A
10 fcm70_Lb80 4.0 N/A IC 2.4 N/A P 0.58 N/A
11 Lb120_M 2.8 N/A IC 1.5 N/A P 0.54 N/A
Notes: CC crushing of the concrete (preceded by steel yielding)
IC intermediate crack debonding
P pullout of the FRP
R rupture of the FRP
S shear failure in the concrete
187
The failure mode was correctly predicted in two of the three specimens in test
series 2. For specimen NSMPL15, the model predicted a capacity of 25.2 kipft and a
failure mode of IC debonding. The experimental specimen failed due to FRP rupture at a
capacity of 30.3 kipft, which was 20% higher than the predicted capacity. The change in
moment for this specimen was perfectly predicted to be 8.6 kipft. For specimen NSM
PL25, the predicted capacity was 32.0 kipft, and the experimental capacity was 33.4
kipft, which is only 4% higher than the prediction. The experimental change in moment
capacity, however, was 76% of the predicted change in moment capacity. For specimen
CRDNSM, the predicted capacity was 51% greater than the experimental capacity, and
the predicted change in capacity was nearly half as large as the experimental change in
capacity.
For test series 5, the model was very conservative in its estimation of capacity.
The experimental capacity was 67% of the predicted capacity for both specimens. The
experimental changes in capacity were more than 1.5 times larger than the predicted
changes in capacity.
In test series 6, the failure mode was correctly predicted as crushing of the
concrete for the 6inch and the 9inch wide specimens. For the 12inch wide specimens,
the failure mode was predicted as IC debonding, but the specimens failed due to FRP
rupture and due to crushing of the concrete. The model was relatively accurate for all of
the specimens. The experimental capacities ranged from 95 to 117% of the predicted
capacities. The changes in capacity, however, were not as accurate. The experimental
changes in capacity ranged from 93 to 158% of the predicted changes in capacity, with
most of the experimental values being greater than the predictions.
188
For the slab specimens in test series 7, the model was relatively accurate at
predicting strengthened moment capacities. The capacity for slab specimen NS_F1 was
slightly overestimated. The capacities for the other three slab specimens were
underestimated. The experimental capacities for these three specimens were 6, 30, and
11% higher, respectively, than the corresponding predicted capacities. The failure mode
was only correctly predicted for two of the four slab specimens.
For the beam specimens in test series 7, the failure mode was correctly predicted
as IC debonding; however, the experimental capacities were 56 and 55% greater,
respectively, than the predicted capacities.
The capacity and failure mode for specimen B2900 in test series 8 were not
accurately predicted. The experimental capacity was 38% greater than the predicted
capacity, and the experimental change in capacity was more than two times the predicted
change in capacity. The predicted failure mode was IC debonding, but the beam failed
due to crushing of the concrete.
In test series 9, 10, and 11, the failure mode was pullout of the FRP. The predicted
failure mode for all of these specimens was IC debonding. Consequently, the capacity
predictions were not very accurate. These specimens are not shown in the following
comparison graphs.
Figure 427 shows a comparison between the experimental moment capacity and
the predicted moment capacity. Figure 428 shows a comparison between the
experimental change in capacity and the predicted change in capacity.
0
50
100
150
200
250
300
0 50 100 150 200 250 300
Predicted Moment (kft)
Ex
pe
rimental
M
o
ment (k
ft)
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #5: Taljsten and Nordin (2007)
TS #6: Yost et al. (2007)
TS #7: Liu, Oehlers, and Seracino (2006)
TS #8: Teng et al. (2006)
Figure 427: Comparison between NSM Test Results and Standards Australia (2008) IC
Debonding Capacity Predictions
189
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 100 120 140 160 180 200
Change in Predicted Moment (kft)
Ch
a
n
ge i
n
Exper
i
menta
l
Moment
(
k

f
t
)
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #5: Taljsten and Nordin (2007)
TS #6: Yost et al. (2007)
TS #8: Teng et al. (2006)
Figure 428: Comparison between NSM Test Results and Standards Australia (2008) IC
Debonding ChangeinCapacity Predictions
Because the Taljsten and Nordin (2007) test series includes specimens with
relatively high moments, they were excluded from the enlarged graphs shown in Figures
429 and 430.
190
0
10
20
30
40
50
60
1020304050
Predicted Moment (kft)
Experimental Mome
n
t
(kft)
60
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #6: Yost et al. (2007)
TS #7: Liu, Oehlers, and Seracino (2006)
TS #8: Teng et al. (2006)
Figure 429: Enlarged Graph of the Capacity Comparisons of the Standards Australia
(2008) Model
191
0
5
10
15
20
25
30
35
40
45
50
0 5 10 15 20 25 30 35 40 45 50
Change in Predicted Moment (kft)
Ch
a
n
ge i
n
Exper
i
menta
l
Moment
(
k

f
t
)
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #6: Yost et al. (2007)
TS #8: Teng et al. (2006)
Figure 430: Enlarged Graph of the ChangeinCapacity Comparisons of the Standards
Australia (2008) Model
Figures 429 and 430 show that the model was relatively accurate for most of the
specimens in test series 6 and 7; however, for test series 1, 2, and 8, the model was not as
accurate or as precise.
Table 425 shows the measured and predicted strain values for the FRP.
192
193
Table 425: FRP Strain Predictions using the Standards Australia (2008) ICDebonding
Model and NSM Test Results
Predicted Experimental Test
Series #
Specimen
ID ?
f,pred
?
f,pred
/?
f,rupt
?
f,exp
?
f,exp
/?
f,rupt
?
f,exp
/
?
f,pred
1 B1 0.53% 0.47 0.88% 0.77 1.65
1 B2 *1.08% *1.00 *1.34% *1.24 1.24
1 B3 *1.33% *1.00 *1.38% *1.04 1.04
1 B4 *2.22% *1.00 1.35% 0.61 0.61
2 NSMPL15 1.24% 0.84 *1.54% *1.04 1.24
2 NSMPL25 1.36% 0.92 1.24% 0.83 0.91
2 CRDNSM 0.49% 0.32 1.31% 0.84 2.66
5 NSMR 1 0.46% 0.27 0.92% 0.53 1.98
5 NSMR 2 0.46% 0.26 0.92% 0.53 2.02
7 NS_F1 *0.82% *0.51 *0.72% *0.45 0.88
7 NS_F2 *1.33% *0.83 *1.30% *0.81 0.98
7 NS_F3 1.38% 0.86 *1.50% *0.93 1.09
7 NS_F4 0.92% 0.55 0.84% 0.50 0.91
7 NB_F2 1.35% 0.84 1.02% 0.63 0.75
7 NB_F3 0.93% 0.56 0.83% 0.50 0.89
8 B2900 1.11% 0.81 *0.97% *0.71 0.88
*denotes a failure mode other than IC debonding
As shown in Table 425, the FRP strain for specimen B1 was underestimated, the
strain for specimen B4 was overestimated, and the strains for specimens B2 and B3 were
relatively accurate. These strain values correspond to the pattern already shown in Table
424, where the capacity for specimen B1 was underestimated, the capacity for specimen
B4 was overestimated, and the capacities for specimens B2 and B3 were relatively
accurate.
For specimen NSMPL15, the FRP strain was predicted to be 84% of the rupture
strain. In the experimental specimen, the failure mode was FRP rupture, but the FRP
strain was 4% greater than the rupture strain. For specimen NSMPL25, the FRP strain
was slightly overestimated, with the ratio of experimental to predicted strain being 0.91.
For specimen CRDNSM, the experimental FRP strain was 166% greater than the
predicted strain.
194
In test series 7 and 8, the predicted FRP strains were relatively accurate for most
of the specimens. Most of the experimental strains ranged from 88 to 109% of the
predicted strains, except for specimen NB_F2, which had an experimental strain that was
75% of the predicted strain.
4.4.3.2 Discussion of Model
The majority of the capacity predictions for the NSM specimens were on the conservative
side. Most of the specimens were relatively accurate, but there were some specimens that
had very inaccurate predictions, especially in test series 1, 2, 5, and 8.
Because it was based on pushpull tests, this model should give a lower bound for
the moment capacity (Standards Australia 2008). For the NSM tests, the model was
conservative for most of the tests, but unconservative for some of the tests, which would
not be possible if this model were accurate and a true lower bound to the capacity.
4.4.4 Seracino et al. (2007a)
The model by Seracino et al. (2007a) is an ICdebonding model that was used to evaluate
the moment capacities for experimental tests using NSM FRP.
4.4.4.1 Comparison to Previous Testing
The ICdebonding model by Seracino et al. (2007a) was used to predict strengthened
moment capacities for NSM test specimens. Table 426 shows the predicted capacities,
the experimental results, and comparisons between the two.
195
Table 426: Comparison of the ICDebonding Model by Seracino et al. (2007a) to NSM
Test Results
Predicted Experimental Test
Series
#
Specimen
ID
M
n
(kft)
?M
n
(kft)
Failure
Mode
M
exp
(kft)
?M
exp
(kft)
Failure
Mode
M
exp
/
M
n,pred
?M
exp
/
?M
n,pred
1 B1 25.6 7.4 IC 43.1 17.4 IC 1.68 2.36
1 B2 38.4 20.2 R 45.7 20.1 R 1.19 0.99
1 B3 42.7 24.5 R 50.6 25.0 R 1.19 1.02
1 B4 59.1 40.9 R 47.4 21.7 IC 0.80 0.53
2 NSMPL15 25.6 9.1 IC 30.3 8.6 R 1.18 0.95
2 NSMPL25 33.3 16.8 R 33.4 11.7 IC 1.00 0.70
2 CRDNSM 21.5 5.0 IC 35.8 14.1 IC 1.66 2.84
5 NSMR 1 147.0 49.5 IC 278.4 180.9 IC 1.89 3.66
5 NSMR 2 145.2 47.6 IC 274.7 177.2 IC 1.89 3.72
6 61Fa 22.3 5.3 CC 1.04 1.53
6 61Fb
21.4 3.5 CC
20.9 3.9 CC 0.98 1.13
6 62Fa 22.5 5.5 CC 0.95 0.94
6 62Fb
23.7 5.8 CC
24.2 7.2 CC 1.02 1.25
6 91Fa 25.4 6.8 CC 1.02 1.21
6 91Fb
24.9 5.7 CC
25.1 6.6 CC 1.01 1.17
6 92Fa 33.3 14.8 CC 1.16 1.58
6 92Fb
28.6 9.4 CC
32.2 13.7 CC 1.12 1.46
6 121Fa 26.6 7.6 R 1.02 1.18
6 121Fb
26.2 6.4 R
27.9 8.9 R 1.06 1.38
6 122Fa 30.4 11.4 CC 0.94 0.91
6 122Fb
32.2 12.4 R
37.6 18.5 CC 1.17 1.49
7 NS_F1 19.6 N/A CC 18.7 N/A S 0.96 N/A
7 NS_F2 13.8 N/A CC 14.6 N/A CC 1.06 N/A
7 NS_F3 11.1 N/A IC 14.0 N/A CC 1.27 N/A
7 NS_F4 11.7 N/A IC 12.8 N/A IC 1.10 N/A
7 NB_F2 32.7 N/A IC 49.6 N/A IC 1.52 N/A
7 NB_F3 35.0 N/A IC 54.0 N/A IC 1.54 N/A
8 B2900 32.5 10.4 IC 44.1 22.6 CC 1.36 2.06
9 G4D24c 8.0 N/A IC 11.0 N/A P 1.38 N/A
9 C3D24b 5.0 N/A IC 7.8 N/A P 1.56 N/A
9 C3S24a 5.0 N/A IC 4.0 N/A P 0.80 N/A
10 fcm35_Lb80 3.3 N/A IC 2.1 N/A P 0.64 N/A
10 fcm45_Lb80 3.7 N/A IC 2.4 N/A P 0.66 N/A
10 fcm70_Lb80 4.5 N/A IC 2.4 N/A P 0.53 N/A
11 Lb120_M 2.6 N/A IC 1.5 N/A P 0.58 N/A
Notes: CC crushing of the concrete (preceded by steel yielding)
IC intermediate crack debonding
P pullout of the FRP
R rupture of the FRP
S shear failure in the concrete
196
In test series 1, the failure mode was correctly predicted in three of the four
specimens. In these three specimens, the capacity was underestimated. For specimen B1,
which failed due to IC debonding, the experimental capacity was 68% greater than the
predicted capacity. For specimens B2 and B3, which failed due to FRP rupture, the
experimental capacities were just 19% greater than the predicted capacities. Specimen B4
failed due to IC debonding but was predicted to fail due to FRP rupture. The
experimental capacity was 80% of the predicted capacity.
For specimen B1, the changes in moment capacity were underestimated by more
than two times. For specimen B4, it was overestimated by about two times. For
specimens B2 and B3, the changes in moment capacity were extremely accurate.
The failure mode was correctly predicted in one of the three specimens in test
series 2. For specimen NSMPL15, the model predicted a capacity of 25.6 kipft and a
failure mode of IC debonding. The experimental specimen failed due to FRP rupture at a
capacity of 30.3 kipft, which was 18% higher than the predicted capacity. The change in
moment for this specimen was slightly overestimated as 9.1 kipft. The experimental
change in moment was actually 8.6 kipft. For specimen NSMPL25, the model?s
prediction was extremely accurate. The predicted capacity was 33.3 kipft, and the
experimental capacity was 33.4 kipft. The experimental change in moment capacity,
however, was 70% of the predicted change in moment capacity. For specimen CRD
NSM, the predicted capacity was 66% greater than the experimental capacity, and the
predicted change in capacity was nearly one third as large as the experimental change in
capacity.
197
For test series 5, the model was very conservative in its estimation of capacity.
The experimental capacity was 89% of the predicted capacity for both specimens. The
experimental changes in capacity were over 2.5 times larger than the predicted changes in
capacity.
In test series 6, the failure mode was correctly predicted as crushing of the
concrete for the 6inch and the 9inch wide specimens. For specimens 121Fa and 12
1Fb, the failure was correctly predicted as FRP rupture. For specimens 122Fa and 12
2Fb, the failure mode was predicted as FRP rupture, but the specimens failed due to
crushing of the concrete. The model was relatively accurate for all of the specimens in
test series 6. The experimental capacities ranged from 94 to 117% of the predicted
capacities. The changes in capacity, however, were not as accurate. The experimental
changes in capacity ranged from 91 to 158% of the predicted changes in capacity, with
most of the experimental values being greater than the predictions.
For the slab specimens in test series 7, the model was relatively accurate at
predicting strengthened moment capacities. The capacity for slab specimen NS_F1 was
slightly overestimated. The capacities for the other three slab specimens were
underestimated. The experimental capacities for these three specimens were 6, 27, and
10% higher, respectively, than the corresponding predicted capacities. The failure mode
was only correctly predicted for two of the four slab specimens.
For the beam specimens in test series 7, the failure mode was correctly predicted
as IC debonding; however, the experimental capacities were 52 and 54% greater than the
predicted capacities, respectively.
198
The capacity and failure mode for specimen B2900 in test series 8 were not
accurately predicted. The experimental capacity was 36% greater than the predicted
capacity, and the experimental change in capacity was more than two times the predicted
change in capacity. The predicted failure mode was IC debonding, but the beam failed
due to crushing of the concrete.
In test series 9, 10, and 11, the failure mode was pullout of the FRP. The predicted
failure mode for all of these specimens was IC debonding. Consequently, the capacity
predictions were not very accurate and are not shown in the following comparison
graphs.
Figure 431 shows a comparison between the experimental moment capacity and
the predicted moment capacity. Figure 432 shows a comparison between the
experimental change in capacity and the predicted change in capacity.
0
50
100
150
200
250
0 50 100 150 200 250 300
Predicted Moment (kft)
Experimental Mome
n
t
(kft)
300
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #5: Taljsten and Nordin (2007)
TS #6: Yost et al. (2007)
TS #7: Liu, Oehlers, and Seracino (2006)
TS #8: Teng et al. (2006)
Figure 431: Comparison between NSM Test Results and Seracino et al. (2007a) IC
Debonding Capacity Predictions
199
0
20
40
60
80
100
120
140
160
0 20 40 60 80 100 120 140 160 180 200
Change in Predicted Moment (kft)
Cha
n
ge
in Experimental Moment
(kft)
180
200
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #5: Taljsten and Nordin (2007)
TS #6: Yost et al. (2007)
TS #8: Teng et al. (2006)
Figure 432: Comparison between NSM Test Results and Seracino et al. (2007a) IC
Debonding ChangeinCapacity Predictions
Because the Taljsten and Nordin (2007) test series includes specimens with
relatively high moments, they were excluded from the enlarged graphs shown in Figures
433 and 434.
200
0
10
20
30
40
50
1020304050
Predicted Moment (kft)
E
x
peri
menta
l
M
o
ment
(k
ft)
60
60
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #6: Yost et al. (2007)
TS #7: Liu, Oehlers, and Seracino (2006)
TS #8: Teng et al. (2006)
Figure 433: Enlarged Graph of the Capacity Comparisons of the Seracino et al. (2007a)
Model
201
0
5
10
15
20
25
30
35
40
0 5 10 15 20 25 30 35 40 45 50
Change in Predicted Moment (kft)
Cha
n
ge
in Experimental Moment
(kft)
45
50
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #6: Yost et al. (2007)
TS #8: Teng et al. (2006)
Figure 434: Enlarged Graph of the ChangeinCapacity Comparisons of the Seracino et
al. (2007a) Model
Figures 433 and 434 show that the model was relatively accurate for most of the
specimens in test series 6 and 7; however, for test series 1, 2, and 8, the model was not as
accurate or as precise.
Table 427 shows the measured and predicted strain values for the FRP.
202
203
Table 427: FRP Strain Predictions using the Seracino et al. (2007a) ICDebonding
Model and NSM Test Results
Predicted Experimental Test
Series #
Specimen
ID ?
f,pred
?
f,pred
/?
f,rupt
?
f,exp
?
f,exp
/?
f,rupt
?
f,exp
/
?
f,pred
1 B1 0.42% 0.36 0.88% 0.77 2.12
1 B2 *1.08% *1.00 *1.34% *1.24 1.24
1 B3 *1.33% *1.00 *1.38% *1.04 1.04
1 B4 *2.22% *1.00 1.35% 0.61 0.61
2 NSMPL15 1.31% 0.88 *1.54% *1.04 1.18
2 NSMPL25 *1.48% *1.00 1.24% 0.83 0.83
2 CRDNSM 0.36% 0.23 1.31% 0.84 3.64
5 NSMR 1 0.34% 0.20 0.92% 0.53 2.68
5 NSMR 2 0.33% 0.19 0.92% 0.53 2.76
7 NS_F1 *0.82% *0.51 *0.72% *0.45 0.88
7 NS_F2 *1.33% *0.83 *1.30% *0.81 0.98
7 NS_F3 1.49% 0.93 *1.50% *0.93 1.01
7 NS_F4 0.94% 0.56 0.84% 0.50 0.90
7 NB_F2 1.45% 0.90 1.02% 0.63 0.70
7 NB_F3 0.95% 0.57 0.83% 0.50 0.87
8 B2900 1.17% 0.86 *0.97% *0.71 0.83
*denotes a failure mode other than IC debonding
As shown in Table 427, the FRP strain for specimen B1 was underestimated, the
strain for specimen B4 was overestimated, and the strains for specimens B2 and B3 were
relatively accurate. These strain values correspond to the pattern already shown in Table
426, where the capacity for specimen B1 was underestimated, the capacity for specimen
B4 was overestimated, and the capacities for specimens B2 and B3 were relatively
accurate.
For specimen NSMPL15, the FRP strain was predicted to be 88% of the rupture
strain. In the experimental specimen, the failure mode was FRP rupture, but the FRP
strain was 4% greater than the rupture strain. For specimen NSMPL25, the FRP strain
was slightly overestimated, with the ratio of experimental to predicted strain being 0.83.
For specimen CRDNSM, the experimental FRP strain was more than 2.5 times larger
than the predicted strain.
204
In test series 7 and 8, the predicted FRP strains were relatively accurate for most
of the specimens. Most of the experimental strains ranged from 83 to 101% of the
predicted strains, except for specimen NB_F2, which had an experimental strain that was
70% of the predicted strain.
4.4.4.2 Discussion of Model
The model given by Seracino et al. was compared to experimental tests of NSM FRP.
The majority of the capacity predictions for the specimens were on the conservative side,
but some of the data points were on the unconservative side. Because this model was
based on pushpull tests, the model should theoretically give a lower bound to the
capacity (Standards Australia 2008); however, the model should not be used as a lower
bound because of the unconservative predictions. Most of the specimens were relatively
accurate, but there were some specimens that had very inaccurate predictions, especially
in test series 1, 2, 5, and 8.
The Seracino et al. model and the Standards Australia model produced very
similar results for many reasons. First, the Standards Australia model was based on the
model by Seracino, Raizal Saifulnaz, and Oehlers (2007), and both of the referenced
papers were coauthored by two of the same people? Seracino and Oehlers. Secondly,
both models are based on pushpull tests. Finally, both models are statistical models that
are based solely on the dimensions of the FRP and the compressive strength of the
concrete.
205
4.4.5 Said and Wu (2008)
The model by Said and Wu (2008) is an ICdebonding model that was calibrated using a
database of ICdebonding failures of EB FRP. Because the model is empirical, however,
and is not derived for an EB type of application, the model was also used to evaluate
capacities for experimental tests using NSM FRP. In this section, the model was
compared to NSM test results to determine the accuracy of the model.
4.4.5.1 Comparison to Previous Testing
The ICdebonding model by Said and Wu was used to predict strengthened moment
capacities for NSM test specimens. Table 428 shows the predicted capacities, the
experimental results, and comparisons between the two.
In test series 1, the failure mode was correctly predicted for two of the four
specimens; however, the strengthened moment capacity was underestimated for all four
specimens. The experimental capacities ranged from 36 to 72% greater than the predicted
capacities. The predictions for the changes in capacity were even more conservative. The
experimental changes in capacity ranged from 30 to 155% greater than the predicted
changes in capacity.
206
Table 428: Comparison of the ICDebonding Model by Said and Wu (2008) to NSM
Test Results
Predicted Experimental Test
Series
#
Specimen
ID
M
n
(kft)
?M
n
(kft)
Failure
Mode
M
exp
(kft)
?M
exp
(kft)
Failure
Mode
M
exp
/
M
n,pred
?M
exp
/
?M
n,pred
1 B1 25.0 6.8 IC 43.1 17.4 IC 1.72 2.55
1 B2 29.5 11.3 IC 45.7 20.1 R 1.55 1.78
1 B3 31.4 13.2 IC 50.6 25.0 R 1.61 1.90
1 B4 34.9 16.7 IC 47.4 21.7 IC 1.36 1.30
2 NSMPL15 23.1 6.6 IC 30.3 8.6 R 1.31 1.31
2 NSMPL25 23.1 6.6 IC 33.4 11.7 IC 1.45 1.78
2 CRDNSM 19.1 2.5 IC 35.8 14.1 IC 1.88 5.59
5 NSMR 1 148.3 50.8 IC 278.4 180.9 IC 1.88 3.56
5 NSMR 2 147.4 49.8 IC 274.7 177.2 IC 1.86 3.56
6 61Fa 22.3 5.3 CC 1.07 1.78
6 61Fb
20.9 3.0 IC
20.9 3.9 CC 1.00 1.31
6 62Fa 22.5 5.5 CC 0.96 0.98
6 62Fb
23.5 5.6 IC
24.2 7.2 CC 1.03 1.29
6 91Fa 25.4 6.8 CC 1.14 2.34
6 91Fb
22.2 2.9 IC
25.1 6.6 CC 1.13 2.25
6 92Fa 33.3 14.8 CC 1.32 2.51
6 92Fb
25.2 5.9 IC
32.2 13.7 CC 1.28 2.32
6 121Fa 26.6 7.6 R 1.17 2.65
6 121Fb
22.6 2.9 IC
27.9 8.9 R 1.23 3.10
6 122Fa 30.4 11.4 CC 1.18 1.92
6 122Fb
25.7 5.9 IC
37.6 18.5 CC 1.46 3.12
7 NS_F1 17.1 N/A IC 18.7 N/A S 1.09 N/A
7 NS_F2 10.4 N/A IC 14.6 N/A CC 1.40 N/A
7 NS_F3 8.8 N/A IC 14.0 N/A CC 1.59 N/A
7 NS_F4 9.5 N/A IC 12.8 N/A IC 1.34 N/A
7 NB_F2 24.3 N/A IC 49.6 N/A IC 2.04 N/A
7 NB_F3 27.0 N/A IC 54.0 N/A IC 2.00 N/A
8 B2900 26.5 10.4 IC 44.1 22.6 CC 1.67 4.57
9 G4D24c 4.4 N/A IC 11.0 N/A P 2.53 N/A
9 C3D24b 4.9 N/A IC 7.8 N/A P 1.60 N/A
9 C3S24a 6.5 N/A IC 4.0 N/A P 0.61 N/A
10 fcm35_Lb80 1.7 N/A IC 2.1 N/A P 1.25 N/A
10 fcm45_Lb80 1.7 N/A IC 2.4 N/A P 1.40 N/A
10 fcm70_Lb80 1.9 N/A IC 2.4 N/A P 1.25 N/A
11 Lb120_M 1.5 N/A IC 1.5 N/A P 1.03 N/A
Notes: CC crushing of the concrete (preceded by steel yielding)
IC intermediate crack debonding
P pullout of the FRP
R rupture of the FRP
S shear failure in the concrete
207
The Said and Wu model was very conservative in its predictions of capacity in
test series 2. Despite correctly predicting the failure mode in two of the three specimens,
the experimental capacities ranged from 31 to 88% greater than the predicted capacities.
For the changes in capacity predictions for specimens NSMPL15 and NSMPL25, the
model was conservative. The experimental changes in capacity were 31 and 78% greater
than the predicted changes in capacity. For specimen CRDNSM, the model was
extremely conservative; it predicted a change in capacity of 2.5 kipft, and the
experimental change in capacity was 14.1 kipft, which is more than 5.5 times the
prediction.
For the two specimens in test series 5, the model was very conservative in its
estimations of capacity. The experimental capacities were 88 and 86% of the predicted
capacities, respectively. The experimental changes in capacity were over 2.5 times larger
than the predicted changes in capacity.
In test series 6, the model predicted an ICdebonding failure for all of the
specimens, but none of the specimens failed due to an anchorage failure. Consequently,
the model underestimated the capacity and the change in capacity for most of the
specimens. For the 6inch specimens, the model was relatively accurate. The
experimental capacities ranged from 96 to 107% of the predicted capacities, and the
experimental changes in capacity ranged from 98 to 178% of the predicted changes in
capacity.
The predictions for the 9inch and 12inch specimens were more conservative
than the predictions for the 6inch specimens. The experimental capacities ranged from
13 to 46% greater than the predicted capacities. The changes in capacity were much more
208
conservative, with the experimental changes in capacity ranging from 92 to 212% greater
than the predicted changes in capacity.
For the slab specimens in test series 7, denoted NS, the model was conservative at
predicting strengthened moment capacities. The experimental capacities for these four
specimens were 9, 40, 59, and 34% higher, respectively, than the corresponding predicted
capacities. The failure mode was only correctly predicted for one of the four slab
specimens.
For the two beam specimens in test series 7, denoted NB, the failure mode was
correctly predicted as IC debonding; however, the experimental capacities were about
twice as large as the predicted capacities.
The capacity and failure mode for specimen B2900 in test series 8 were not
accurately predicted. The experimental capacity was 67% greater than the predicted
capacity, and the experimental change in capacity was more than three times greater than
the predicted change in capacity. The predicted failure mode was IC debonding, but the
beam failed due to crushing of the concrete.
In test series 9, 10, and 11, the failure mode was pullout of the FRP. The predicted
failure mode for all of these specimens was IC debonding. Consequently, the capacity
predictions were not very accurate and are not shown in the following comparison
graphs.
Figure 435 shows a comparison between the experimental moment capacity and
the predicted moment capacity. Figure 436 shows a comparison between the
experimental change in capacity and the predicted change in capacity.
0
50
100
150
200
250
0 50 100 150 200 250 300
Predicted Moment (kft)
E
x
p
e
rimen
t
al M
o
m
e
n
t
(kft)
300
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #5: Taljsten and Nordin (2007)
TS #6: Yost et al. (2007)
TS #7: Liu, Oehlers, and Seracino (2006)
TS #8: Teng et al. (2006)
Figure 435: Comparison between NSM Test Results and Said and Wu (2008) IC
Debonding Capacity Predictions
209
0
20
40
60
80
100
120
140
160
180
0 20 40 60 80 100 120 140 160 180 200
Change in Predicted Moment (kft)
C
h
ange in Expe
r
i
ment
al
Moment
(k
f
t
)
200
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #5: Taljsten and Nordin (2007)
TS #6: Yost et al. (2007)
TS #8: Teng et al. (2006)
Figure 436: Comparison between NSM Test Results and Said and Wu (2008) IC
Debonding ChangeinCapacity Predictions
Because the Taljsten and Nordin (2007) test series includes specimens with
relatively high moments, they were excluded from the enlarged graphs shown in Figures
437 and 438.
210
0
10
20
30
40
50
10203040506
Predicted Moment (kft)
Exp
e
rime
nta
l
Mo
men
t
(kft)
60
0
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #6: Yost et al. (2007)
TS #7: Liu, Oehlers, and Seracino (2006)
TS #8: Teng et al. (2006)
Figure 437: Enlarged Graph of the Capacity Comparisons of the Said and Wu (2008)
Model
211
0
5
10
15
20
25
0 5 10 15 20 25 30
Change in Predicted Moment (kft)
C
h
an
ge in Exp
e
r
i
ment
al
Mo
ment
(k
ft
)
30
TS #1: ElHacha and Rizkalla (2004)
TS #2: Jung et al. (2005)
TS #6: Yost et al. (2007)
TS #8: Teng et al. (2006)
Figure 438: Enlarged Graph of the ChangeinCapacity Comparisons of the Said and
Wu (2008) Model
Figure 437 shows that the model was conservative for capacity predictions for
test series 6 and 7 and extremely conservative for test series 1, 2, and 8. Most of the data
points in Figure 438 are well above and to the left of the line shown; therefore, the
model is conservative for most of the test specimens for changeincapacity predictions.
Table 429 shows the measured and predicted strain values for the FRP.
212
213
Table 429: FRP Strain Predictions using the Said and Wu (2008) ICDebonding Model
and NSM Test Results
Predicted Experimental Test
Series #
Specimen
ID ?
f,pred
?
f,pred
/?
f,rupt
?
f,exp
?
f,exp
/?
f,rupt
?
f,exp
/
?
f,pred
1 B1 0.39% 0.34 0.88% 0.77 2.28
1 B2 0.61% 0.56 *1.34% *1.24 2.20
1 B3 0.71% 0.54 *1.38% *1.04 1.93
1 B4 0.91% 0.41 1.35% 0.61 1.49
2 NSMPL15 0.61% 0.41 *1.54% *1.04 2.54
2 NSMPL25 0.61% 0.41 1.24% 0.83 2.03
2 CRDNSM 0.37% 0.24 1.31% 0.84 3.55
5 NSMR 1 0.35% 0.20 0.92% 0.53 2.62
5 NSMR 2 0.35% 0.20 0.92% 0.53 2.65
7 NS_F1 0.65% 0.40 *0.72% *0.45 1.11
7 NS_F2 0.64% 0.40 *1.30% *0.81 2.02
7 NS_F3 0.64% 0.40 *1.50% *0.93 2.34
7 NS_F4 0.51% 0.31 0.84% 0.50 1.64
7 NB_F2 0.64% 0.40 1.02% 0.63 1.60
7 NB_F3 0.52% 0.31 0.83% 0.50 1.60
8 B2900 0.57% 0.41 *0.97% *0.71 1.71
*denotes a failure mode other than IC debonding
As shown in Table 429, the FRP strains for test series 1 were all underestimated.
The ratios of experimental strain to predicted strain range from 1.49 to 2.28.
For specimen NSMPL15, the FRP strain was predicted to be 41% of the rupture
strain. In the experimental specimen, the failure mode was FRP rupture, but the FRP
strain was 4% greater than the rupture strain. For specimen NSMPL25, the FRP strain
was predicted to be about half of the experimental strain. For specimen CRDNSM, the
experimental FRP strain was 255% greater than the predicted strain.
The predicted FRP strains for test series 7 and 8 were also very conservative. For
specimen NS_F1, the ratio of experimental FRP strain to predicted FRP strain was 1.11.
For the other specimens in test series 7 and 8, the ratios ranged from 1.60 to 2.34.
214
4.4.5.2 Discussion of Model
The Said and Wu model was very conservative in its predictions of capacity, change in
capacity, and FRP strain for practically all of the NSM specimens. The inaccuracy of the
model for NSM FRP was expected. The model by Said and Wu was not intended to be
used for NSM, and the results in this chapter verify that.
4.5 Summary of Model Evaluations
In this section, a summary of all of the models analyzed in this chapter is presented. For
this discussion, the models are divided into PEdebonding models and ICdebonding
models. The ICdebonding models are subdivided into models for EB FRP and models
for NSM FRP.
4.5.1 PEDebonding Models
There are three PEdebonding models that were analyzed: those recommended by
Standards Australia (2008), Hassan and Rizkalla (2003), and Vasquez (2008) Figure 439
shows a graph that compares the accuracy and level of safety of the capacity predictions
of each model against the experimental tests from the referenced literature. Figure 440
shows the same comparison for the experimental change in capacity versus the predicted
change in capacity.
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45
Predicted Capacity (kft)
E
xpe
rime
ntal Cap
acity
(kf
t)
Hassan and Rizkalla (2003)
Vasquez (2008)
Standards Australia (2008)
Figure 439: Comparison of Capacity Predictions by PEDebonding Models to NSM
Experimental Results
215
0
5
10
15
20
25
0 5 10 15 20 25
Change in Predicted Capacity (kft)
C
h
ange i
n
E
x
p
e
r
i
m
e
nt
al
C
a
paci
t
y
(
k

f
t
)
Hassan and Rizkalla (2003)
Vasquez (2008)
Standards Australia (2008)
Figure 440: Comparison of ChangeinCapacity Predictions by PEDebonding Models
to NSM Experimental Results
As shown in Figures 439 and 440, none of the models accurately predicts the
strengthened moment capacity for all of the experimental tests. There is a wide dispersion
of data points on the graphs, with some points on the conservative side of the line and
some on the unconservative side.
4.5.2 ICDebonding Models
There are six ICdebonding models for EB FRP that were analyzed: ACI 440 (2008), fib
9.3 (2001), Standards Australia (2008), Rosenboom (2006), Seracino, Raizal Saifulnaz,
and Oehlers (2007), and Said and Wu (2008). Figure 441 shows a graph that compares
the accuracy and level of safety of the capacity predictions of each model against the
216
experimental tests from the referenced literature. Figure 442 shows the same comparison
for the experimental change in capacity versus the predicted change in capacity.
0
20
40
60
80
100
120
140
2040608010120140
Predicted Capacity (kft)
E
x
p
e
r
i
m
e
n
t
a
l
C
a
p
a
c
i
ty
(k
f
t)
ACI 440 (2008)
fib 9.3 (2001)
Rosenboom (2006)
Seracino, Raizal Saifulnaz, and Oehlers (2007)
Said and Wu (2008)
Standards Australia (2008)
Figure 441: Comparison of Capacity Predictions by ICDebonding Models to EB
Experimental Results
217
0
10
20
30
40
50
60
102030405060
Change in Predicted Capacity (kft)
C
h
ange i
n
E
x
per
i
m
e
nt
al
C
a
paci
t
y
(
k

f
t
ACI 440 (2008)
fib 9.3 (2001)
)
Rosenboom (2006)
Seracino, Raizal Saifulnaz, and Oehlers (2007)
Said and Wu (2008)
Standards Australia (2008)
Figure 442: Comparison of ChangeinCapacity Predictions by ICDebonding Models
to EB Experimental Results
From Figures 441 and 442, the fib 9.3 (2001) model is shown to be mainly
unconservative and not very accurate. The fib model did not include variables for the
concrete compressive strength, the FRP modulus of elasticity, or the thickness of the
FRP. A possible reason why this model was not very accurate could be due to the
absence of these variables in the model. The model by Seracino, Raizal Saifulnaz, and
Oehlers (2007) also had mostly unconservative results, but it included the previously
mentioned variables; no conclusions could be made why this model did not perform well.
The other four models were relatively accurate at predicting the strengthened moment
218
capacities for the experimental tests but slightly unconservative at predicting changes in
capacity.
For the models related to NSM FRP, there are five ICdebonding models that
were examined: ACI 440 (2008), fib 9.3 (2001), Standards Australia (2008), Seracino et
al. (2007a), and Said and Wu (2008). Figure 443 shows a graph that compares the
accuracy and level of safety of the capacity predictions of each model against the
experimental tests from the referenced literature. Figure 444 shows the same comparison
for the experimental change in capacity versus the predicted change in capacity.
0
10
20
30
40
50
60
102030405060
Predicted Capacity (kft)
Ex
p
e
r
i
m
e
n
t
a
l
C
a
pa
c
i
ty
(k
ft
)
ACI 440 (2008)
fib 9.3 (2001)
Standards Australia (2008)
Seracino et al. (2007a)
Said and Wu (2008)
Figure 443: Comparison of Capacity Predictions by ICDebonding Models to NSM
Experimental Results
219
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30 35 40 45
Change in Predicted Capacity (kft)
C
h
a
n
g
e
in
E
x
p
e
r
i
me
n
t
a
l
C
a
p
a
c
i
ty
(k
ft
)
ACI 440 (2008)
fib 9.3 (2001)
Standards Australia (2008)
Seracino et al. (2007a)
Said and Wu (2008)
Figure 444: Comparison of ChangeinCapacity Predictions by ICDebonding Models
to NSM Experimental Results
As shown in Figure 443, the model by Said and Wu (2008) was very
conservative for most of its predictions of capacity. The main cause of this conservatism
is most likely due to the fact that this model was not calibrated using NSM tests. The
model by fib 9.3 (2001) was also conservative for most of its capacity predictions but was
unconservative for a few of the test specimens. The main cause of the inaccuracy of the
model is probably due to the fact that the model was only intended for EB and not NSM.
Also, this model did not include variables for the concrete compressive strength, the FRP
modulus of elasticity, or the thickness of the FRP. The models by Seracino et al. (2007a)
220
221
and Standards Australia (2008) are very similar to each other; these two models were
relatively accurate and usually on the conservative side of the line. These two models
both included variables for the concrete compressive strength, the depth of the FRP, and
the thickness of the FRP. The model by Seracino et al. did not include the FRP modulus
of elasticity directly, but it used this variable for strain compatibility to determine the
moment capacity. The model given by ACI 440 (2008) was also relatively accurate and
typically on the conservative side. This model was only based on the FRP rupture strain;
no conclusions could be made regarding why this model outperformed some of the other
models. None of the models shown in Figure 444 was determined to be more accurate
than the others, and no conclusions could be drawn from the figure. Standards Australia
does not give an ICdebonding model for NSMstrengthened beam specimens; it only
gives an NSM model for pushpull specimens, which Standards Australia says is a lower
bound for beam tests. This NSM model for pushpull specimens is the exact same model
given by Seracino, Raizal Saifulnaz, and Oehlers (2007).
The data points that were the most unconservative in Figures 443 and 444
correspond to specimens B4 and CRDNSM from the studies by ElHacha and Rizkalla
(2004) and Jung et al. (2005), respectively. The FRP reinforcement ratios for these
specimens were 0.27 and 0.12%, respectively, which are higher than all of the other FRP
reinforcement ratios in these test series.
Because the models by Seracino et al. (2007a), Standards Australia (2008), and
ACI 440 (2008) were relatively accurate compared to the other models, they were used to
propose an NSM FRP strengthening scheme for the Letohatchee bridge in Chapter 5 and
to propose a laboratory testing scheme in Chapter 6.
222
Chapter 5: Proposed Strengthening for the Letohatchee Bridge
5.1 FRP Selection
To develop a strengthening scheme for the Letohatchee bridge, the FRP type and
application first needed to be chosen. Out of the three most common types of fibers used
in the literature ? carbon, glass, and aramid ? carbon fibers were found to be the most
common and the most readily available. Also, carbon fibers are typically stronger, as
shown in Table 51, than glass or aramid fibers. For these reasons, carbon fibers were
chosen for the FRP used in the Letohatchee bridge.
The two choices for the type of FRP application were externallybonded (EB) and
nearsurface mounted (NSM). The focus of the strengthening of the Letohatchee bridge is
negativemoment strengthening over the interior supports of the continuous structure. For
an EB type of application, the EB strips would need to be located near the top of the
concrete cross section. If the strips were bonded to the top of the concrete slab, the FRP
would be exposed to vehicular traffic, and continual traffic loads could cause degradation
or debonding. An alternative to bonding the strips to the top of the slab is to bond them to
the bottom of the slab. The main disadvantage of this type of application is the
discontinuity that would be caused by the diaphragms. The diaphragms, or webwalls, are
located at every support and at midspan of both 60foot exterior spans and at every third
point of both 75foot interior spans. As shown in Figure 51, which is a reproduction of
Figure 318, the biggest deficiencies occur at the approximate locations of the
diaphragms.
Figure 51: Elevation View of the Locations of the Letohatchee Bridge Deficiencies
Table 51, which is a reproduction of Table 36, shows the exact locations and
magnitudes of the deficiencies and the strength increase needed.
223
224
Table 51: Negative Moment Deficiencies for Posting Trucks at Critical Locations
Distance from
end bearing CL
(ft)
Distance from
nearest interior
support (ft)
M
u
(kft)
?M
n
(kft)
Difference
in moment
(kft)
Strength
increase
needed
(%)
33 27 189 226 38 
34 26 229 226 2 1
35 25 269 226 43 19
36 24 309 226 83 37
37 23 350 226 124 55
38 22 396 357 39 11
Region 1
39 21 443 487 43 
81 21 431 487 55 
82 22 386 357 29 8
83 23 341 226 114 50
84 24 300 226 73 32
85 25 261 226 34 15
Region 2
86 26 223 226 4 
108 27 198 226 28 
109 26 228 226 1 1
110 25 265 226 39 17
111 24 304 226 78 34
112 23 344 226 118 52
113 22 389 357 33 9
Region 3
114 21 434 487 53 
Figure 51 and Table 51 are specifically for an exterior girder. The exterior girder
was found to be more critical than the interior girder. For the interior girder, the critical
location still occurred at 37 ft from the bearing centerline, but the magnitude of the
deficiency was slightly smaller, and the range over which it occurred was also smaller.
Because the exterior girder and the interior girder were so similar, the amount and length
of FRP recommended for the exterior girder was also used for the interior girder.
For the 60foot exterior span, the deficiency ranges from about 33 to 39 ft from
the centerline of the girder?s end bearing. The diaphragm for this span is located at 30 ft.
Even though the diaphragm is not located in the range of the deficiency, the FRP would
225
need to be extended past this location for adequate anchorage, and the diaphragm would
obstruct its path. Holes could be drilled through the diaphragm to allow passage of the
FRP, but this would add considerable construction time and therefore greatly increase
labor and trafficcontrol costs.
For the 75ft interior spans, the deficiencies occur from about 81 to 86 ft and 108
to 114 ft from the centerline of the girder?s end bearing. The diaphragms for this span
occur at 85 and 110 ft from the reference point, which results in both diaphragms actually
being in the range of the deficiencies.
Because the diaphragms are found at the locations of where the FRP is needed,
applying the EB FRP to the underside of the slab is not a feasible option. The FRP should
not be terminated in regions of high moment demand due to possible debonding at the
plate end. Because the diaphragms would force the FRP plates to be terminated in these
regions, the EB type of application is not the most attractive option for the Letohatchee
bridge.
NSM was also investigated to determine if it would be a viable FRP strengthening
technique for this specific bridge. As stated by several researchers, the NSM type of
application is very effective and practical for flexural strengthening of continuous
concrete members in negativemoment regions (ElHacha and Rizkalla 2004; De
Lorenzis and Nanni 2002; Hassan and Rizkalla 2003). The NSM strip can be placed
inside the concrete, and the concrete surface can remain flush with the surrounding
concrete, which mitigates any adverse effects due to the environment or due to vehicular
traffic. Therefore, the NSM FRP can be installed from above, which greatly decreases the
costs and complexities associated with controlling traffic on the interstate highway that
226
passes beneath the bridge. Because the Letohatchee bridge is a continuous structure that
needs negativemoment strengthening, the NSM type of application was chosen for this
bridge.
5.2 FRP Amount Needed
Based on the analysis of the FRPdebonding models presented in Chapter 4, the models
by ACI 440 (2008), Standards Australia (2008), and Seracino et al. (2007a) were selected
to determine the amount of FRP needed for the Letohatchee bridge. As shown in Table 5
1, the critical location for the exterior girder occurs in Region 1 at approximately 37 ft.
The factored moment at this location is 350 kipft. By dividing the factored moment by
the reduction factor ?, which was assumed to be 0.9, the required nominal moment
strength was calculated. For this critical location, the required nominal moment capacity
is 389 kipft, which was used to determine the amount of FRP needed for the Letohatchee
bridge.
To calculate the available nominal moment capacity for the Letohatchee bridge,
the crosssectional dimensions, the amount and location of the flexural steel, and the
concrete, steel, and FRP material properties need to be known. These values are shown in
Table 52.
Table 52: Dimensions and Material Properties for Capacity Calculations
b
w
16.75 in.
Concrete
h 43.375 in.
A
s
1.92 in.
2
d 40.19 in.
E
s
29000 ksi
Steel
f
y
40 ksi
FRP thickness (#2 thin) 0.079 in.
FRP thickness (#3 thick) 0.177 in.
FRP width 0.63 in.
d
f
43.06 in.
E
f
18000 ksi
*
fu
f (thin strip)
300 ksi
FRP
*
fu
f (thick strip)
285 ksi
The FRP values shown in Table 52 are specifically for a product manufactured
by Hughes Brothers called Aslan 500 CFRP Tape (Hughes Brothers 2009). This product
consists of a precured strip with unidirectional carbon fibers formed through the
pultrusion process and shaped into rectangular plates. For this product, there are two sizes
of NSM FRP available. Hereafter, these sizes will be referred to as the ?thin? strip and
the ?thick? strip. The thin strip is 2mm (0.079in.) thick and 16mm (0.63in.) wide and
has a tensile strength of 2068 MPa (300 ksi). The thick strip is 4.5mm (0.177in.) thick
and 16mm (0.63in.) wide and has a tensile strength of 1965 MPa (285 ksi). The
concrete and steel values in Table 52 are for an exterior girder at the critical cross
section, which is located at 37 ft from the centerline of the girder?s end bearing. The
concrete compressive strength was assumed to be 3000 psi for the Letohatchee bridge;
however, for the capacity calculations, the concrete strength was varied from 3000 to
8000 psi.
ACI 440 recommends a groove size as shown in Figure 52.
227
Figure 52: Recommended Groove Dimensions (ACI 440 2008)
For rectangular plates, the groove width should be at least 3.0 times the plate
thickness, a
b
, and the groove depth should be at least 1.5 times the plate depth, b
b
(ACI
440 2008). Hughes Brothers (2009) recommends that the ACI 440 guidelines be followed
for the groove dimensions. For the thin plates, a groove dimension of 0.24 in. wide by
0.95 in. deep is recommended. For the thick plates, a groove dimension of 0.53 in. wide
by 0.95 in. deep is recommended.
To determine the amount of FRP needed, each of the three models was employed
using different numbers of thin and thick strips and different concrete compressive
strength values. From these analyses, it was determined that the bridge needed anywhere
from four to six thin strips or three to five thick strips; therefore, the graphs shown in this
section are limited to these amounts of FRP. To try to accurately match the concrete
properties in the Letohatchee bridge, the concrete compressive strength values were
limited to the range of 3000 to 8000 psi.
In this chapter, each model?s design (characteristic) values were used instead of
the mean values; therefore, the prescribed reduction factors and safety factors were
applied to the strength calculations.
228
5.2.1 ACI 440 (2008)
Using the ACI 440 model, the strengthened nominal moment capacities for the
Letohatchee bridge were predicted for different amounts of FRP and different concrete
compressive strengths. Figure 53 indicates these capacities.
389 kft required
0
100
200
300
400
500
600
3000 4000 5000 6000 7000 8000
Concrete Compressive Strength (psi)
M
o
m
e
n
t c
ap
a
ci
t
y
(ki
p
f
t)
4 thin strips 5 thin strips 6 thin strips
3 thick strips 4 thick strips 5 thick strips
Unstrengthened bridge capacity
Figure 53: Letohatchee Bridge Capacities using the Model by ACI 440 (2008)
As shown in the figure, the ACI 440 model is not sensitive to the concrete
compressive strength. The lines have a very small slope, which is similar to the slope for
the unstrengthened bridge, and the moment capacity does not increase very much from
3000 to 8000 psi. In fact, the concrete compressive strength does not affect the FRP
contribution to the capacity directly; it only affects the reinforced concrete contribution,
which causes the lines in the graph to be almost horizontal.
229
230
Because the ACI 440 model limits the FRP strain to a fixed percentage of the
rupture strain, all of the FRP strain values for each strip size are the same. The FRP strain
value for the thin strips is 0.0099 in./in., which is 60% of the rupture strain of the thin
strip. The FRP strain value for the thick strips is 0.0094 in./in., which is 60% of the FRP
rupture strain of the thick strip. The concrete strain values using the ACI 440 model
ranged from 0.0007 to 0.0014 in./in. Because these values were so low, a concrete
crushing failure was not imminent. The ACI 440 model predicted an ICdebonding
failure for all of the combinations of FRP strips and concrete compressive strengths.
Appendix B shows some sample calculations with all of the intermediate values used in
the calculations.
In Figure 53, the nominal flexural strength required by the Letohatchee bridge is
shown as a line at 389 kipft. None of the data points for the four thin strips or the five
thin strips lies above the line, and all of the data points for the six thin strips lie above this
line. For the thick strips, all of the data points for all amounts of FRP and all concrete
strengths are above the line.
According to the ACI 440 model, the most efficient selection of strips would be
either six thin FRP strips or three thick FRP strips. As long as the concrete strength is
between 3000 and 8000 psi, it has no effect on the number of strips chosen for this
bridge.
According to Hughes Brothers, for the Aslan 500 CFRP Tape, the thick strips cost
about 1.5 times more than the thin strips. Therefore, using three thick strips instead of six
thin strips is more costeffective, not only in material costs but also in labor costs.
5.2.2 Standards Australia (2008)
Using the model by Standards Australia, the strengthened nominal moment capacities for
the Letohatchee bridge were predicted for different amounts of FRP and different
concrete compressive strengths. Figure 54 indicates these capacities.
389 kft required
0
100
200
300
400
500
600
3000 4000 5000 6000 7000 8000
Concrete Compressive Strength (psi)
M
o
m
e
n
t
c
a
p
a
c
i
ty
(k
i
p
f
t)
4 thin strips 5 thin strips 6 thin strips
3 thick strips 4 thick strips 5 thick strips
Unstrengthened bridge capacity
Figure 54: Letohatchee Bridge Capacities using the Model by Standards Australia
(2008)
As shown in Figure 54, this model is somewhat sensitive to the concrete
compressive strength. Some of the lines shown have a slope that actually crosses the line
at 389 kipft, which is the required capacity for the Letohatchee bridge. For 3000psi
concrete, six thin strips are needed; for 4000 to 6000psi concrete, five thin strips are
needed; and for 7000 to 8000psi concrete, four thin strips are needed. For the thick
231
strips, four are needed if the concrete strength is between 3000 and 5000 psi, and three
are needed if the concrete strength is between 6000 and 8000 psi.
Table 53 shows the FRP strain values for thin and thick strips using the
Standards Australia model.
Table 53: FRP Strain Values for the Letohatchee Bridge using the Model by Standards
Australia (2008)
Thin FRP Strip Thick FRP Strip
'
c
f
(psi) f
?
(in./in.)
f
? /
ruptf ,
?
f
?
(in./in.)
f
? /
ruptf ,
?
3000 0.0087 52% 0.0053 34%
4000 0.0096 57% 0.0058 37%
5000 0.0103 62% 0.0063 40%
6000 0.0109 66% 0.0067 42%
7000 0.0115 69% 0.0070 44%
8000 0.0120 72% 0.0074 46%
Table 53 shows how the FRP strain values varied for different concrete
compressive strengths. The FRP strain values were not dependent upon the number of
FRP strips. As shown in the table, the FRP strain values for the thin strips ranged from 52
to 72% of the rupture strain of the thin strips. For the thick strips, the FRP strain values
ranged from 34 to 46% of the rupture strain of the thick strips. The concrete strain values
were not very high and did not change much; they varied from 0.0006 to 0.0012 in./in.
This model predicted an ICdebonding failure for all of the combinations of FRP strips
and concrete compressive strengths
232
5.2.3 Seracino et al. (2007a)
Using the model by Seracino et al., the strengthened nominal moment capacities for the
Letohatchee bridge were predicted for different amounts of FRP and different concrete
compressive strengths. Figure 55 indicates these capacities.
389 kft required
0
100
200
300
400
500
600
3000 4000 5000 6000 7000 8000
Concrete Compressive Strength (psi)
M
o
m
e
n
t c
a
p
a
c
i
t
y
(k
i
p
f
t)
4 thin strips 5 thin strips 6 thin strips
3 thick strips 4 thick strips 5 thick strips
Unstrengthened bridge capacity
Figure 55: Letohatchee Bridge Capacities using the Model by Seracino et al. (2007a)
As shown in Figure 55, this model is also sensitive to the concrete compressive
strength. The lines shown have a slope that actually crosses the line at 389 kipft, which
is the required capacity for the Letohatchee bridge. For 3000psi concrete, six thin strips
are needed; for 4000psi concrete, five thin strips are needed; and for 5000 to 8000psi
concrete, four thin strips are needed. For the thick strips, five are needed if the concrete
233
strength is 3000 psi, four are needed if the concrete strength is between 4000 and 5000
psi, and three are needed if the concrete strength is between 6000 and 8000 psi.
Table 54 shows the FRP strain values for thin and thick strips using the Seracino
et al. model.
Table 54: FRP Strain Values for the Letohatchee Bridge using the Model by
Seracino et al. (2007a)
Thin FRP Strip Thick FRP Strip
'
c
f
(psi) f
?
(in./in.)
f
? /
ruptf ,
?
f
?
(in./in.)
f
? /
ruptf ,
?
3000 0.0092 55% 0.0049 31%
4000 0.0106 64% 0.0056 35%
5000 0.0118 71% 0.0063 40%
6000 0.0130 78% 0.0069 43%
7000 0.0140 84% 0.0074 47%
8000 0.0142 85% 0.0079 50%
Table 54 shows how the FRP strain values varied for different concrete
compressive strengths. The FRP strain values were not dependent upon the number of
FRP strips. As shown in the table, the FRP strain values for the thin strips ranged from 55
to 85% of the rupture strain of the thin strips. For the thick strips, the FRP strain values
ranged from 31 to 50% of the rupture strain of the thick strips. The concrete strain values
were not very high and did not change much; they varied from 0.0007 to 0.0013 in./in.
This model predicted an ICdebonding failure for all of the combinations of FRP strips
and concrete compressive strengths
234
5.2.4 Summary of Models
The results of the three design models were combined into one graph to determine the
amount of FRP needed to attain a strengthened nominal moment capacity of 389 kipft
for the Letohatchee bridge. This graph, which is dependent upon the concrete
compressive strength, is shown in Figure 56 for thin FRP strips.
0
1
2
3
4
5
6
7
3000 4000 5000 6000 7000 8000
Concrete compressive strength (psi)
N
u
m
b
e
r
o
f
t
h
in
st
r
i
p
s
ACI 440 (2008)
Standards Australia (2008)
Seracino et al. (2007a)
Figure 56: Required Amounts of Thin FRP Strips for each Model
Figure 57 shows the graph of the required amount of thick FRP strips needed to
attain a strengthened nominal moment capacity of 389 kipft.
235
0
1
2
3
4
5
6
7
3000 4000 5000 6000 7000 8000
Concrete compressive strength (psi)
N
u
m
b
er
o
f
t
h
i
ck st
r
i
p
s
ACI 440 (2008)
Standards Australia (2008)
Seracino et al. (2007a)
Figure 57: Required Amounts of Thick FRP Strips for each Model
As shown in Figures 56 and 57, the amount of FRP required decreases as the
concrete compressive strength increases for two of the models. The results of the ACI
440 model, however, are not very sensitive to the concrete compressive strength. Because
the ACI 440 model is the most conservative model for the thin FRP, as shown in Figure
56, six strips would be the most conservative number of strips to use for any concrete
compressive strength from 3000 to 8000 psi; however, for the thick FRP, it would be
very advantageous to know the concrete strength. Without any knowledge of the strength
of the concrete, it would be conservative to use five thick strips, but by taking
representative concrete core samples from the Letohatchee bridge, a reduction in the
number of strips may be possible. Because the deck and the girders are assumed to have
been cast monolithically and because the bond between the FRP and the concrete is
important, the core samples should be taken from the bridge deck. To ensure that the core
236
237
samples are representative of the proposed FRP locations, the samples should be taken at
different locations across the roadway surface and along the length of the girder. If the
concrete strength is between 4000 and 6000 psi, then four thick strips can be used. If the
concrete strength is between 6000 and 8000 psi, then only three thick strips need to be
used.
For borderline cases, such as for concrete strengths between 3000 and 4000 psi
and between 5000 and 6000 psi, calculations could be made to determine the number of
thick strips that are needed.
5.3 FRP Length and Termination Points
The models mentioned in the previous section are based on prevention of IC debonding.
To prevent PE debonding, however, the issue is not the number of strips that are needed
but the distance the strips need to be extended. Some code recommendations state that the
FRP should be extended to a point of contraflexure (ACI 440 2008, Standards Australia
2008). In a continuous bridge girder that is subjected to a moving set of loads, there is no
fixed point of contraflexure. Rather, the location of contraflexure moves within a range
bounded by the positive moment envelope and the negative moment envelope, as
discussed in Chapter 3. Because it is recommended that the strips be terminated at a point
of contraflexure and no fixed point of contraflexure exists in a continuous bridge girder,
this recommendation cannot be satisfied.
A similar approach to prevent PE debonding is to terminate the FRP strip on the
compression face of a continuous beam, which means that the strip needs to be extended
past the last possible point of contraflexure as opposed to terminating it directly at the
point (Standards Australia 2008). This second approach is slightly different than the first
approach. A possible reason for this difference could be that the first approach tries to
limit both the negative moment and the curvature at the termination point, and the second
approach only tries to limit the negative moment at the termination point. To find the
locations where the deck surface is in compression, the negativemoment envelope was
examined to find the locations where no negative moment is possible under the design
loads. The negativemoment envelope is shown in the factored demand and factored
resistance graph, which was shown in Chapter 3 and is shown again in Figure 58.
5000
4000
3000
2000
1000
0
1000
2000
0 30 60 90 120 150 180 210 240 270
Distance from CL of girder end bearing (ft)
F
a
c
to
r
e
d
Mo
m
e
n
t
(k
ip
ft)
Factored Demand Factored Resistance
Figure 58: Factored Demand Envelope and Factored Resistance
As shown in Figure 58, the factored negativemoment demand envelope is not
always negative. At four different locations, it crosses over into the positive side. In these
regions, the top of the beam is always in compression and the bottom is always in
238
tension; therefore, these four regions are where the FRP strips could be terminated. The
following locations are the specific distances from the centerline of the girder?s end
bearing where the negativemoment envelope is zero: 27.1, 93.6, 100.9, 169.1, 176.4, and
242.9 ft. For easier installation, the start distances will be rounded down to the nearest
halffoot, and the end distances will be rounded up to the nearest halffoot.
To prevent PE debonding, it is recommended that the FRP strips extend over the
deficient regions shown in Table 51 and then be terminated in one of the four regions
where the negativemoment envelope is positive. Figure 59 shows the recommended
lengths of the FRP for the Letohatchee bridge relative to the centerline of the girder?s
end.
Figure 59: Elevation View of the Recommended FRP Lengths for the Letohatchee
Bridge (not to scale)
An alternative to the recommended lengths shown in Figure 59 is to have one
216ft continuous strip from the 27ft mark to the 243ft mark. A possible drawback for
this approach might be constructability issues associated with the installation of 216ft
long strips of FRP.
239
240
5.4 FRP Spacing Recommendations
The spacing of the FRP was determined by using the various models shown in the ?FRP
Spacing Recommendations for NSM Strips? section of Chapter 2. By assuming a groove
side of 1/4 inch by 7/8 inch, which was recommended by Hughes Brothers for their Aslan
500 CFRP Tape, the following table was created:
Table 55: FRP Spacing Recommendations for Letohatchee Bridge
Minimum
clear spacing
of strips (in.)
Minimum
side cover
distance (in.)
ACI Committee 440 (2008) 1.8 3.5
Hassan and Rizkalla (2004) 1.3 2.5
Kang et al. (2005) 1.6 1.6
Rashid, Oehlers, and Seracino (2008) 2.1 2.2
Vasquez (2008) 0.6 
For the model by Hassan and Rizkalla, the FRP bar diameter was conservatively
taken to be equal to the FRP depth. As shown in Table 55, the greatest of the clear
spacing limits is 2.1 in., and the greatest of the side cover limits is 3.5 in. Because the
Letohatchee bridge needs negativemoment strengthening, the entire slab width can be
used for FRP placement, so there should be no spacing problems. Figure 510 shows a
cross section with a possible spacing configuration for six strips per girder. Figure 511
shows a cross section with a possible spacing configuration for three strips per girder.
Figure 510: Cross Section of a Possible Spacing Configuration for Six NSM Strips per
Girder
Figure 511: Cross Section of a Possible Spacing Configuration for Three NSM Strips
per Girder
As shown in Figures 510 and 511, the smallest spacing for these configurations
is 10 in., and the largest value from Table 55 is 3.5 in.; therefore, spacing should not be a
problem for the Letohatchee bridge. As shown in Figures 510 and 511, the FRP is
241
242
spaced more closely directly over the girder to control flexural cracking, which tends to
have increased crack widths over the girder (ACI 318 2008). In Section 10.6.6 of ACI
318 (2008), it is recommended to add additional flexural reinforcement to the outer
portions of the flange when the effective flange width is greater than onetenth of the
span. Because the Letohatchee bridge already has flexural reinforcement at these
locations, no additional FRP reinforcement is needed in these outer regions of the flange.
5.5 Summary of Proposed Design
It is recommended that NSM carbon fiberreinforced polymer (CFRP) strips be used for
negativemoment strengthening of the Letohatchee bridge. Concrete core samples need to
be taken from the bridge to determine the concrete compressive strength. If these core
samples are not taken, then twentyfour thin NSM FRP strips, six strips per girder, should
be spaced out across the roadway surface, as shown in Figure 510. An alternative would
be to use five thick NSM FRP strips per girder, totaling twenty thick strips.
If the concrete strength is known, then fewer thick strips could be used. If the
strength is between 4000 and 6000 psi, then four thick strips per girder can be used. If the
strength is between 6000 and 8000 psi, then three thick strips per girder can be used.
The FRP strips should extend over the following distance ranges, measured
relative to the centerline of the girder end bearing: from 27 to 94 ft; from 100.5 to 169.5
ft; and from 176 to 243 ft. The corresponding strip lengths are 67, 69, and 67 ft,
respectively.
It is also recommended that a survey be done on the bridge deck to verify the
locations and depths of the flexural steel reinforcement. If the steel bars are located too
close to the surface, then there may be some interaction between the steel and the FRP.
5.6 Further Testing
More testing should be performed to verify the accuracy and level of safety of the
models. The testing program should include specimens that fail due to IC debonding to
determine if the models can predict when and if an ICdebonding failure will occur. The
steel and FRP reinforcement ratios of the test specimens should attempt to match the pre
existing steel and added FRP reinforcement ratios of the Letohatchee bridge to try to
accurately replicate the flexural response expected in the bridge, which would result in a
more efficient bridge strengthening scheme. Table 56 shows the flexural reinforcement
ratios for the critical regions of the Letohatchee bridge.
Table 56: Reinforcement Ratios for the Letohatchee Bridge
s
?
f
? *
f
?
sf
?? /*
0.29% 0.030% 0.018% 0.064
In Table 56,
s
? is the steel reinforcement ratio;
f
? is the FRP reinforcement
ratio; *
f
? is the normalized FRP reinforcement ratio; and
sf
?? /* is the relative
strengthening ratio. The steel reinforcement ratio, the FRP reinforcement ratio, and the
normalized FRP reinforcement ratio can be calculated using the following equations:
243
bd
A
s
s
=? Equation 51
bd
A
f
f
=? Equation 52
?
?
?
?
?
?
?
?
=
s
f
ff
E
E
?? *
Equation 53
where A
s
is the area of steel reinforcement; b is the width of the compression face
of the member; d is the distance from the extreme compression fiber to the centroid of the
tension reinforcement; A
f
is the area of FRP reinforcement; E
f
is the FRP modulus of
elasticity; and E
s
is the steel modulus of elasticity.
The reinforcement ratios for some of the experimental tests from the literature,
which were introduced in Chapter 2 and then compared to the models in Chapter 4, are
shown in Table 57.
244
Table 57: Reinforcement Ratios for the Experimental Tests from the Literature
Test Series Specimen ID
s
?
f
? *
f
?
sf
?? /*
B1 0.34% 0.10% 0.058% 0.17
B2 0.34% 0.085% 0.060% 0.17
B3 0.34% 0.080% 0.060% 0.17
ElHacha and
Rizkalla (2004)
B4 0.34% 0.27% 0.060% 0.17
NSMPL15 0.39% 0.039% 0.032% 0.082
NSMPL25 0.39% 0.065% 0.054% 0.14 Jung et al. (2005)
CRDNSM 0.39% 0.12% 0.072% 0.18
NSMR 1 0.33% 0.17% 0.12% 0.36 Taljsten and
Nordin (2007) NSMR 2 0.33% 0.17% 0.12% 0.36
61Fa 1.72% 0.16% 0.11% 0.064
61Fb 1.72% 0.16% 0.11% 0.064
62Fa 1.72% 0.32% 0.22% 0.13
62Fb 1.72% 0.32% 0.22% 0.13
91Fa 1.11% 0.11% 0.073% 0.066
91Fb 1.11% 0.11% 0.073% 0.066
92Fa 1.11% 0.22% 0.15% 0.13
92Fb 1.11% 0.22% 0.15% 0.13
121Fa 0.83% 0.081% 0.055% 0.066
121Fb 0.83% 0.081% 0.055% 0.066
122Fa 0.83% 0.16% 0.11% 0.13
Yost et al. (2007)
122Fb 0.83% 0.16% 0.11% 0.13
NS_F1 0.72% 0.40% 0.35% 0.48
NS_F2 0.72% 0.12% 0.11% 0.15
NS_F3 0.72% 0.061% 0.053% 0.074
NS_F4 0.72% 0.14% 0.10% 0.14
NB_F2 1.09% 0.18% 0.16% 0.15
Liu, Oehlers, and
Seracino (2006)
NB_F3 1.09% 0.40% 0.28% 0.26
Teng et al. (2006) B2900 0.56% 0.079% 0.057% 0.10
In Table 57, the specimen ID is the label that was given for the specimens by the
original researchers. The test series shown were chosen because all of them included
NSM tests. As shown in the table, the steel reinforcement ratio ranges from 0.33 to
1.72%, and the FRP reinforcement ratio ranges from 0.039 to 0.40%; the Letohatchee
bridge values for the steel and FRP reinforcement ratios are 0.29% and 0.030%,
respectively.
The normalized FRP reinforcement ratio was used to compare the relative amount
of FRP force in beams strengthened with different FRP stiffnessses. This value for the
245
246
experimental tests ranges from 0.032 to 0.35%; the value for the Letohatchee bridge is
0.018%.
The relative strengthening ratio was used to compare the amount of strengthening
relative to the original strength of the beam. This value for the experimental tests ranges
from 0.064 to 0.48; the value for the Letohatchee bridge is 0.064.
When compared to the steel reinforcement ratio, the FRP reinforcement ratio, the
normalized FRP reinforcement ratio, and the relative strengthening ratio, the Letohatchee
bridge falls at or beyond the boundary of the FRPstrengthened specimens tested in the
past.
For the proposed testing program, a range of reinforcing amounts of both steel
and FRP should be investigated that encompasses the reinforcement ratios of the
Letohatchee bridge. A range of concrete strengths should also be investigated so as to
generate results that will be applicable to a range of potential bridge strengthening
projects. A proposed testing program was developed and is shown in Chapter 6.
247
Chapter 6: Proposed Laboratory Testing Program
6.1 Overall Objectives and Scope of Testing Program
In Chapter 5, the steel and FRP reinforcement ratios for past published experimental
tests, which were introduced in Chapter 2, were compared to the ratios for the
Letohatchee bridge. The reinforcement ratios for the tests were found to be larger than
the ratios for the bridge; therefore, the results from the tests are not directly applicable to
the Letohatchee bridge. Also, none of the NSM test specimens were cracked prior to FRP
strengthening. To be able to use laboratory test results that can be directly applied to the
bridge, a laboratory testing program was proposed. Because the proposed strengthening
scheme that was presented in Chapter 5 employed NSM strips, only NSM will be
evaluated in the testing program. The proposed testing program has four main objectives:
1. Develop a relationship between the test specimens and the Letohatchee bridge
to more effectively and more efficiently propose an NSM FRPstrengthening
scheme for the bridge.
2. Study the ICdebonding behavior to better quantify when and if it will occur
and to verify the existing ICdebonding models.
3. Study the effects of the concrete compressive strength, amount of steel
reinforcement, amount of NSM reinforcement, and crosssectional shape on
the strengthened moment capacity.
248
4. Evaluate the effectiveness of the NSM in a strengthening type of situation by
cracking the unstrengthened specimens before applying the FRP.
To achieve the first objective, specimens were designed to match the Letohatchee
bridge girders in a couple of different ways. The mechanical reinforcement ratio, the
concrete cover distance, and the flange thickness will all be about the same. Also, the
concrete compressive strength will be varied from 3000 to 7000 psi.
To achieve the second objective, each of the three NSM ICdebonding models
from the previous chapter ? ACI 440 (2008), Standards Australia (2008), and Seracino et
al. (2007a) ? were used to predict the strengthened moment capacities of the specimens.
These predictions will then be evaluated using the experimental results in order to
determine the most accurate model for the test specimens, to suggest modifications to the
models, or to generate a more effective model.
To achieve the third objective, each of the four test series will be used to assess
one or more of the key variables listed. In Test Series 1, the amount of steel will be
studied. In Test Series 2, the crosssectional shape will be studied. In Test Series 3 and 4,
the concrete compressive strength will be studied. In each of the test series, the amount of
FRP will be varied as well.
To achieve the fourth objective, the unstrengthened specimens will be loaded until
the concrete cracks. After cracking, the specimens will be strengthened with NSM and
loaded again until failure. Very few of the previously reported beam tests included
specimens that were cracked prior to strengthening with FRP. More testing is needed to
evaluate the effectiveness of FRP in strengthening situations, particularly because
reinforced concrete bridge girders in need of strengthening are usually cracked under
existing service loads.
Four different test series are proposed in this laboratory testing program. In all of
the test series, thin NSM FRP strips are used. Thin strips are used instead of thick strips
to try to match the FRP reinforcement ratio of the proposed strengthening scheme of the
Letohatchee bridge. Because the volume of concrete is so small for the proposed test
specimens relative to the Letohatchee bridge girders, a smaller amount of FRP is needed;
therefore, thin strips were chosen over thick strips.
For all of the test series, the specimens are designed to be loaded in a simply
supported configuration in symmetric fourpoint bending, with the two concentrated
loads located 3 ft apart. The flanges for the specimens will be at the bottom of the cross
section as the beams are subjected to positive moment. This setup is opposite to the
Letohatchee bridge. The flange for the bridge is at the top of the cross section as the
critical section is subjected to negative moment. Figure 61 shows the proposed test setup
for the typical specimen.
Figure 61: Elevation View of the Proposed Test Setup for a Typical Specimen
249
The specimen identification system used throughout this chapter is summarized in
Figure 62.
1LS2F03d
[blank] (h=18 in.)
S2 (?
s
=0.2%) d (h=33 in.)
S6 (?
s
=0.6%)
F00 (no FRP)
F03 (?
f
=0.03%)
F08 (?
f
=0.08%)
F16 (?
f
=0.16%)
Reinforcement
Test Series Number
}
Height of beam
Amount of FRP
Concrete
Strength
L (Low 3000 psi)
M (Medium 5000 psi)
Amount
of Steel
Tension
H (High 7000 psi)
{
{
{
Figure 62: Specimen Identification System
The main goal in choosing the steel and FRP properties is to match the properties
and appropriately scale the flexural behavior of the critical region of the Letohatchee
bridge. For the test specimens, a yield stress of 50 ksi is selected for the steel. The
Letohatchee bridge is assumed to have 40 ksi steel, but achieving an actual yield stress
that low is not likely in modern reinforcement. Previous work at Auburn University
(Reed 2003), has indicated that a yield strength of 50 ksi is likely for commercially
available ASTM A 615 Grade 40 reinforcing steel. The FRP properties used in the test
specimens are the same as the FRP properties used in the proposed strengthening scheme
in Chapter 5. Table 61 shows a summary of some of the assumed steel and FRP
properties.
250
251
Table 61: Properties and Dimensions of Steel and FRP for Proposed Testing Program
f
y
50 ksi
Steel
E
s
29000 ksi
f
fu
300 ksi
E
f
18000 ksi
FRP width 0.63 in
FRP*
FRP thickness 0.079 in
*Aslan 500 CFRP Tape (Hughes Brothers 2009)
The intended failure mode for all but one of the specimens in the four test series is
IC debonding; the other specimen is predicted to fail due to crushing of the concrete. The
FRP is extended to the end of the specimen to prevent PE debonding.
6.2 Test Procedure
The proposed testing procedure is the same for all of the specimens except the
unstrengthened comparison specimens (referred to as ?control? specimens) for each
series. The first step is to place the concrete in the forms so that the flange is on top. After
the concrete has cured and reached the desired compressive strength, the beam needs to
be inverted so that the flange is on the bottom. Once the beam is correctly oriented, it can
be loaded until the concrete cracks.
For the specimens that will be left unstrengthened, the load can be applied again
until the beam fails, but this testing should not occur until the companion beams have
been strengthened and are ready for testing. For the FRPstrengthened specimens, the
load should be removed once sufficient cracking has occurred, and the beam should be
inverted again so that the flange is on top. The specimen should then be fully supported
along its length, thereby ensuring that there are minimal flexural deformations due to
252
selfweight along the length during strengthening. By minimizing the flexural
deformations at the time of strengthening, the specimen closely reflects the conditions in
the actual bridge, and it also simplifies the analysis. The groove for the FRP can then be
cut using a diamondblade concrete saw. The groove size, as recommended by Hughes
Brothers, should be 1/4in. wide by 7/8in. deep. Once the groove is cut, it needs to be
thoroughly cleaned using a vacuum, compressed air, or both. Next, a structural adhesive
recommended by Hughes Brothers, such as the Hilti HITRE 500, can be injected into the
groove while ensuring that there are no entrapped air voids. The FRP strip is then placed
in the groove, and the excess epoxy is removed.
According to Hilti?s product information (Hilti 2009), it takes a minimum of
twelve hours for the epoxy to fully cure for a base material temperature of 68 degrees
Fahrenheit. To ensure that the epoxy curing duration is not a factor in the test, however, it
is recommended that the epoxy be allowed to cure for at least seven days. After this time
has elapsed, the beam can be flipped over onto its flange, and the specimen can be loaded
until failure.
During loading, the vertical beam deflections, as well as the concrete, steel, and
FRP strains, should be measured and recorded at critical locations. The steel strain
gauges should be placed at several locations along the length of the specimens, especially
at midspan, at the load points, and at the stirrup locations inside the maximum moment
region. These are the probable locations for flexural cracks. The FRP strain gauges
should be placed at the cracked sections. The specimens will be cracked prior to
installation of FRP, so placing the FRP strain gauges at cracked locations can be done
with certainty. The strains at the flexural cracks are desired because the behavior at
253
cracked sections is being investigated. The strains at cracked sections are larger than the
strains between two cracks, and knowing the strains at the cracked sections will produce
more accurate results. The applied load should also be recorded for the duration of the
test.
6.3 Test Series 1
Eight different specimens are proposed for Test Series 1. Four of the specimens have a
mechanical reinforcement ratio (?
s
) similar to the Letohatchee bridge; the other four
specimens have a mechanical reinforcement ratio that is three times as large. The amount
of steel was tripled to observe the effects of the amount of steel on the strengthened
moment capacity. For each set of four specimens, one beam is left unstrengthened and
used as a control beam; the other three beams in each set are strengthened with one, three,
and six thin FRP strips, respectively.
6.3.1 Objectives of Test Series
The main objectives of Test Series 1 are to study the effects of the amount of steel and
the amount of FRP on the strengthened moment capacity and to determine the most
accurate ICdebonding model for the test results. By analyzing the effects of the amounts
of flexural steel and FRP together, the effects on the strengthened moment capacity of the
amount of FRP relative to the amount of flexural steel can also be analyzed.
6.3.2 Description of Test Specimens
For the specimens in this test series, a concrete compressive strength of 3000 psi is used
because it matches the assumed value of the Letohatchee bridge?s concrete. The
specimens in this test series were sized so that all of the concrete for the specimens could
come from the same batch, thereby maintaining concrete properties throughout the test
series. The amount of steel was also chosen to try to match the Letohatchee bridge. For
the Letohatchee bridge, the mechanical reinforcement ratio, ?
s
, is 3.80%. This ratio was
the target value for four of the specimens in this test series. Two #4 bars are used in the
first four specimens, giving them a mechanical reinforcement ratio of 3.56%. The
flexural steel reinforcement ratio for the Letohatchee bridge is 0.29%, and the flexural
steel reinforcement ratio for these specimens is about 0.2%. For the second set of four
specimens, the amount of steel was tripled. Six #4 bars are used in the second set, giving
them a mechanical reinforcement ratio of 10.7% and a flexural steel reinforcement ratio
of about 0.6%. Figure 63 shows both of the cross sections used in Test Series 1.
Figure 63: (a) Cross Section for Specimens with ?
s
of 0.2% (b) Cross Section for
Specimens with ?
s
of 0.6%
254
Figure 63 shows the specimens before the FRP is applied. For each cross section,
there are one, three, and six thin FRP strips applied, respectively. Also, one beam per
cross section is left unstrengthened and is used as a control beam. The specimen names
and cross sections for Test Series 1 are shown in Figure 64.
Figure 64: Specimen Names and Cross Sections for Test Series 1
As shown in Figure 64, the lateral spacing of the NSM strips is 2 1/2 in. The
spacing was held constant to prevent any possible effects from the FRP spacing being
included in the tests; however, if noticeable distress is observed in the concrete
surrounding the NSM strips in specimen 1LS6F16, then the spacing of the FRP relative
to the flexural steel could be a concern. To determine the length of the beams, the shear
255
256
spantodepth ratio was studied. Because the Letohatchee bridge is subjected to moving
loads and has variabledepth girders, its shear spantodepth ratio is not clear; however,
the shear spantodepth ratio was estimated to be about 1 to 2. To minimize the influence
of shear on the flexural behavior, the test specimens were designed to have a shear span
todepth ratio of approximately 4. Because the effective depth of the specimens is 15 5/8
in., the required shear span was calculated to be about 5 ft. By doubling the shear span,
adding 3 ft for the spreader beam, and adding 6 in. on both ends of the girder for extra
bearing, the total length of each specimen is 14 ft.
6.3.3 Anticipated Behavior and Failure Modes
The cracking moments, yield moments, and nominal moment capacities were all
calculated for the unstrengthened beams. The cracking moment calculations were based
on Section 9.5.2.3 of ACI 31808, except that a transformed section was used for the
reinforced concrete instead of a gross section. The yield moment and nominal moment
capacity calculations were based on a crackedsection analysis. To calculate the nominal
moment capacity, the equivalent rectangular concrete stress distribution as stated in
Section 10.2.7 of ACI 31808 was assumed. The FRPstrengthened moment capacities
and the stresses and strains for the steel, FRP, and concrete were calculated using three
different models that address IC debonding: ACI 440 (2008), Seracino et al. (2007a), and
Standards Australia (2008).
257
6.3.3.1 Unstrengthened Specimens
Table 62 shows the computed cracking moments, yield moments, and nominal moment
strengths for the unstrengthened specimens 1LS2F00 and 1LS6F00. These values are
also valid for the other specimens in Test Series 1 before the FRP is applied.
Table 62: Unstrengthened Moments for Specimens in Test Series 1
Specimen M
cr
(kipft) M
y
(kipft) M
n
(kipft)
1LS2 series 30.4 24.5 25.5
1LS6 series 31.8 70.6 73.2
As shown in Table 62, the cracking moment, M
cr
, is greater than both the yield
moment, M
y
, and the nominal moment, M
n
, for specimens in the 1LS2 series. This
unusual behavior is most likely because the required minimum amount of flexural steel is
greater than the actual amount of steel. For these specimens, the minimum amount of
flexural steel required by ACI and AASHTO is 0.75 and 0.89 in.
2
, respectively; for these
specimens, 0.40 in.
2
is provided. For specimens in the 1LS6 series, the amount required
is 0.75 and 0.98 in.
2
, respectively; for these specimens, 1.20 in.
2
are provided. For the
Letohatchee bridge, only 1.92 in.
2
of flexural steel are provided, and ACI and AASHTO
require 3.37 and 6.25 in.
2
, respectively. A possible reason for the large discrepancy
between the two organizations might be because the AASHTO requirement is dependent
upon the cracking moment, and the Letohatchee bridge has a very large cracking moment
relative to the nominal moment capacity because of its wide flange.
258
6.3.3.2 Strengthened Specimens
Using the three models previously mentioned, the strengthened moment capacities at
which IC debonding occurs were predicted for the FRPstrengthened specimens. For
these models, the mean values were used to try to accurately predict the FRP
strengthened beam behavior; therefore, no reduction factors were used. The capacities
were also calculated for nonanchorage failures, such as rupture of the FRP or crushing of
the concrete, to show the relative size of the ICdebonding capacities compared to the
capacities for the nonanchorage failures. Table 63 shows the predicted nominal moment
capacities, stresses and strains for the steel and FRP, concrete strains, and failure modes.
259
Table 63: Predicted Strengthened Capacities, Stresses, Strains, and Failure Modes
Specimen
ID
Model used for
predictions
M
n
(kft)
?
s
f
s
(ksi)
?
frp
f
frp
(ksi)
?
c
Failure
mode
M1 (ACI) 39.9 0.0102 50 0.0117 210 0.0012 IC
M2 (Seracino) 38.9 0.0095 50 0.0109 196 0.0012 IC
M3 (SA) 38.0 0.0089 50 0.0102 184 0.0011 IC
1LS2F03
nonanch. failure 46.3 0.0145 50 0.0167 300 0.0017 R
M1 (ACI) 68.6 0.0101 50 0.0117 210 0.0017 IC
M2 (Seracino) 65.8 0.0094 50 0.0109 196 0.0016 IC
M3 (SA) 63.3 0.0089 50 0.0102 184 0.0015 IC
1LS2F08
nonanch. failure 86.8 0.0144 50 0.0167 300 0.0027 R
M1 (ACI) 109.9 0.0100 50 0.0117 210 0.0025 IC
M2 (Seracino) 104.6 0.0094 50 0.0109 196 0.0023 IC
M3 (SA) 99.9 0.0088 50 0.0102 184 0.0021 IC
1LS2F16
nonanch. failure 118.4 0.0111 50 0.0130 233 0.003 CC
M1 (ACI) 87.2 0.0101 50 0.0117 210 0.0022 IC
M2 (Seracino) 86.3 0.0094 50 0.0109 196 0.0021 IC
M3 (SA) 85.4 0.0088 50 0.0102 184 0.0020 IC
1LS6F03
nonanch. failure 92.4 0.0140 50 0.0162 292 0.003 CC
M1 (ACI) 113.8 0.0100 50 0.0117 210 0.0028 IC
M2 (Seracino) 111.3 0.0093 50 0.0109 196 0.0026 IC
M3 (SA) 109.1 0.0088 50 0.0102 184 0.0024 IC
1LS6F08
nonanch. failure 115.9 0.0106 50 0.0124 223 0.003 CC
M1 (ACI)       CC
M2 (Seracino)       CC
M3 (SA)       CC
1LS6F16
nonanch. failure 139.1 0.0083 50 0.0097 175 0.003 CC
Notes: M1 ACI 440 (2008)
M2 Seracino et al. (2007a)
M3 Standards Australia (2008)
CC crushing of the concrete
IC intermediatecrack debonding
R rupture of the FRP
In Table 63, M
n
is the nominal moment; ?
s
is the steel strain; f
s
is the steel stress;
?
frp
is the FRP strain; f
frp
is the FRP stress; and ?
c
is the concrete strain. For all of the
specimens, the steel reaches its yield stress of 50 ksi, and the strengthened capacity is
greater than the unstrengthened capacity, which is shown in Table 62.
For five of the six strengthened specimens, the models predict an ICdebonding
failure; however, for specimen 1LS6F16, all three models predict a concrete crushing
260
failure. Because the stresses and strains are already shown for the nonanchorage failure,
the values are not repeated for the models.
As shown in Table 63, the concrete strains become higher as more FRP strips are
added. Similarly, as the amount of steel increases, the concrete strains increase.
Consequently, the specimen with the most FRP and the most internal steel resulted in a
concrete crushing failure prediction.
According to the ICdebonding models, the FRP stress and strain appear to be
independent of both the amount of steel and the amount of FRP on the beams. As more
steel and more FRP strips are added, the ICdebonding strain in the FRP remains constant
for all three ICdebonding models. One of the main objectives of this test series is to
investigate whether the ICdebonding behavior is actually independent of the amount of
flexural reinforcement (steel or FRP).
6.4 Test Series 2
Three different specimens are proposed for Test Series 2: 2LS2F00, 2LS2F00d, and 2
LS2F03d. Specimen 2LS2F00 is identical to specimen 1LS2F00, the control beam
from Test Series 1 that had a mechanical reinforcement ratio similar to the Letohatchee
bridge. Specimen 2LS2F00d has an effective depth of about twice that of the first
specimen. It also has twice the amount of steel so that the mechanical reinforcement ratio
remains about the same. Specimen 2LS2F03d has the deeper cross section and is
strengthened with two thin NSM strips.
Specimen 2LS2F00 was included to provide a reference point to the specimens in
Test Series 1. By duplicating the control beam from Test Series 1, the capacities can be
261
adjusted for any changes in the concrete compressive strength between the two test series,
and a more accurate comparison can be made between the beams in Test Series 1 and the
deeper beams in Test Series 2. All of the specimens in Test Series 2 should be cast from
the same batch of concrete.
6.4.1 Objectives of Test Series
The main objectives of Test Series 2 are to study the effects of the crosssectional shape,
specifically the depth of the section, and the amount of FRP on the strengthened moment
capacity and to determine the most accurate ICdebonding model for the test results.
6.4.2 Description of Specimens
As in Test Series 1, the specimens in Test Series 2 have a concrete compressive strength
of 3000 psi. The steel reinforcement ratio for the deeper beams was held constant at about
0.2% by doubling the amount of steel from two to four #4 bars. Figure 65 shows both of
the cross sections used in Test Series 2.
Figure 65: (a) Cross Section of Specimen 2LS2F00 (b) Cross Section for Deeper
Specimens
For the two specimens represented by the cross section in Figure 65b, one beam
is left unstrengthened and is used as a control beam, and the other is strengthened with
two thin NSM strips. The specimen names and cross sections for Test Series 2 are shown
in Figure 66.
262
Figure 66: Specimen Names and Cross Sections for Test Series 2
As in Test Series 1, the shear spantodepth ratio was studied to determine the
lengths of the beams for Test Series 2. For specimen 2LS2F00, which is exactly like
specimen 1LS2F00, 5 ft will be used for its shear span, and 14 ft will be used for its
length. The other two specimens have an effective depth of 30 5/8 in. By using a shear
spantodepth ratio of approximately 4 again, the shear span was calculated to be about
10 ft, which makes the total length of the specimens 24 ft.
Only three specimens were proposed for Test Series 2 because of practical
considerations. The volume of concrete that a concrete truck can transport is about 9 yd
3
.
The volume of concrete for the three specimens in this test series is about 6.5 yd
3
. Adding
another deep beam to the test series would have exceeded the limit of the concrete truck.
263
264
Because it was a priority to have all of the concrete be from the same batch for this test
series, only three specimens are proposed.
6.4.3 Anticipated Behavior and Failure Modes
The cracking moments, yield moments, and nominal moment capacities were all
calculated for the unstrengthened beams as described above for Test Series 1. Likewise,
the FRPstrengthened moment capacities and the stresses and strains for the steel, FRP,
and concrete were calculated using three different models: ACI 440 (2008), Seracino et
al. (2007a), and Standards Australia (2008).
6.4.3.1 Unstrengthened Specimens
Table 64 shows the cracking moments, yield moments, and nominal moment capacities
for the unstrengthened specimens 2LS2F00 and 2LS2F00d. The values for specimen 2
LS2F00d are also valid for specimen 2LS2F03d before the FRP is applied.
Table 64: Unstrengthened Moments for Specimens in Test Series 2
Specimen M
cr
(kipft) M
y
(kipft) M
n
(kipft)
2LS2F00 30.4 24.5 25.5
2LS2F00d
2LS2F03d
97.3 95.9 99.9
The values for specimen 2LS2F00 are the same as the values from Table 62 for
the 1LS2 series because they are exactly the same. Once again, the cracking moment is
shown to be greater than both the yield moment and the nominal moment. For specimens
2LS2F00d and 2LS2F03d, the cracking moment is greater than the yield moment but
less than the nominal moment. For these two specimens, the required minimum amount
265
of steel is 1.47 and 1.46 in.
2
using the ACI and AASHTO methods, respectively. For
these specimens, only 0.80 in.
2
is provided, which results in large cracking moments in
relation to nominal moment capacities.
6.4.3.2 Strengthened Specimens
Using the three models previously mentioned, the strengthened moment capacity at
which IC debonding occurs was predicted for the FRPstrengthened specimen. For these
models, the mean values were used to try to accurately predict the FRPstrengthened
beam behavior; therefore, no reduction factors were used. The capacity was also
calculated for nonanchorage failures, such as rupture of the FRP or crushing of the
concrete, to show the relative size of the ICdebonding capacities compared to the
capacity for the nonanchorage failures. Table 65 shows the predicted nominal moment
capacities, stresses and strains for the steel and FRP, concrete strains, and failure modes.
Table 65: Predicted Strengthened Capacities, Stresses, Strains, and Failure Modes
Specimen ID
Model used for
predictions
M
n
(kft)
?
s
f
s
(ksi)
?
frp
f
frp
(ksi)
?
c
Failure
mode
M1 (ACI) 153.0 0.0108 50 0.0117 210 0.0013 IC
M2 (Seracino) 149.4 0.0101 50 0.0109 196 0.0012 IC
M3 (SA) 146.2 0.0095 50 0.0102 184 0.0012 IC
2LS2F03d
nonanch. failure 176.7 0.0155 50 0.0167 300 0.0018 R
Notes: M1 ACI 440 (2008)
M2 Seracino et al. (2007a)
M3 Standards Australia (2008)
IC intermediatecrack debonding
R rupture of the FRP
For the strengthened specimen shown in Table 65, the steel reaches its yield
stress of 50 ksi. Also, the strengthened capacity is greater than the unstrengthened
capacity from Table 64 by about 50 kipft, which results in a strengthened capacity
266
about 50% greater than the unstrengthened capacity. For this specimen, all of the models
predict an ICdebonding failure will occur before a nonanchorage failure.
6.5 Test Series 3
Four different specimens are proposed for Test Series 3: 3MS2F00, 3MS2F03, 3
MS2F08, and 3MS2F16. These specimens all have the same cross section initially, but
three of the specimens are strengthened with one, three, and six thin FRP strips,
respectively. These four specimens are very similar to the first set of specimens in Test
Series 1, except the specimens in Test Series 3 have a proposed concrete compressive
strength of 5000 psi.
6.5.1 Objectives of Test Series
The main objectives of Test Series 3 are to study the effects of the concrete compressive
strength and the amount of FRP on the strengthened moment capacity and to determine
the most accurate ICdebonding model for the test results.
6.5.2 Description of Specimens
The specimens in Test Series 3 all have the same cross section initially. This cross section
is shown in Figure 67.
Figure 67: Cross Section of Specimens in Test Series 3
Three of the specimens will be strengthened with one, three, and six thin FRP
strips, respectively. The specimen names and cross sections for Test Series 3 are shown
in Figure 68.
Figure 68: Specimen Names and Cross Sections for Test Series 3
267
268
Because the specimens in this test series have the same crosssectional
dimensions as the specimens in Test Series 1, the same shear span of 5 ft and the same
beam length of 14 ft will be used. Once again, the number and size of the specimens was
dependent upon the volume of concrete that could be transported in one batch.
6.5.3 Anticipated Behavior and Failure Modes
The cracking moments, yield moments, and nominal moment capacities were all
calculated for the unstrengthened beams as described above for Test Series 1. Likewise,
the FRPstrengthened moment capacities and the stresses and strains for the steel, FRP,
and concrete were calculated using three different models: ACI 440 (2008), Seracino et
al. (2007a), and Standards Australia (2008).
6.5.3.1 Unstrengthened Specimens
Table 66 shows the cracking moment, yield moment, and nominal moment capacities for
the unstrengthened specimen. The values shown are also valid for the strengthened
specimens before the FRP is applied.
Table 66: Unstrengthened Moments for Specimens in Test Series 3
Specimen M
cr
(kipft) M
y
(kipft) M
n
(kipft)
all specimens 39.0 24.6 25.7
For these specimens, the required minimum amount of steel is 0.80 and 1.14 in.
2
using the ACI and AASHTO methods, respectively, and only 0.40 in.
2
is provided. As in
Test Series 1, the lack of steel causes the cracking moment to be greater than the
unstrengthened nominal moment capacity.
269
6.5.3.2 Strengthened Specimens
Using the three models previously mentioned, the strengthened moment capacities at
which IC debonding occurs were predicted for the FRPstrengthened specimens. For
these models, the mean values were used to try to accurately predict the FRP
strengthened beam behavior; therefore, no reduction factors were used. The capacities
were also calculated for nonanchorage failures, such as rupture of the FRP or crushing of
the concrete, to show the relative size of the ICdebonding capacities compared to the
capacities for the nonanchorage failures. Table 67 shows the predicted nominal moment
capacities, stresses and strains for the steel and FRP, concrete strains, and failure modes.
Table 67: Predicted Strengthened Capacities, Stresses, Strains, and Failure Modes
Specimen
ID
Model used for
predictions
M
n
(kft)
?
s
f
s
(ksi)
?
frp
f
frp
(ksi)
?
c
Failure
mode
M1 (ACI) 40.3 0.0102 50 0.0117 210 0.0009 IC
M2 (Seracino) 43.4 0.0123 50 0.0141 253 0.0011 IC
M3 (SA) 40.9 0.0106 50 0.0121 218 0.0010 IC
3MS2F03
nonanch. failure 46.8 0.0146 50 0.0167 300 0.0012 R
M1 (ACI) 69.6 0.0102 50 0.0117 210 0.0013 IC
M2 (Seracino) 78.8 0.0123 50 0.0141 253 0.0015 IC
M3 (SA) 71.4 0.0106 50 0.0121 218 0.0013 IC
3MS2F08
nonanch. failure 88.6 0.0145 50 0.0167 300 0.0018 R
M1 (ACI) 112.8 0.0101 50 0.0117 210 0.0017 IC
M2 (Seracino) 130.5 0.0122 50 0.0141 253 0.0021 IC
M3 (SA) 116.1 0.0105 50 0.0121 218 0.0018 IC
3MS2F16
nonanch. failure 149.1 0.0144 50 0.0167 300 0.0027 R
Notes: M1 ACI 440 (2008)
M2 Seracino et al. (2007a)
M3 Standards Australia (2008)
IC intermediatecrack debonding
R rupture of the FRP
For all of the strengthened specimens shown in Table 67, the steel reaches its
yield stress of 50 ksi, and the strengthened capacity is greater than the unstrengthened
270
capacity from Table 66. For this specimen, all of the models predict an ICdebonding
failure will occur before an FRP rupture failure.
For Test Series 1 and 2, all of the models produced very similar results, with the
ACI 440 (2008) model producing the largest strengthened capacity; however, in Test
Series 3, the Seracino et al. (2007a) model produced the largest strengthened capacity,
which is most likely a result of the increased concrete compressive strength of Test Series
3. The ACI 440 model is not highly sensitive to the concrete compressive strength, and
the Seracino et al. model is the most sensitive to it.
6.6 Test Series 4
Four different specimens are proposed for Test Series 4: 4HS2F00, 4HS2F03, 4
HS2F08, and 4HS2F16. These specimens all have the same cross section initially, but
three of the specimens are strengthened with one, three, and six thin FRP strips,
respectively. These four specimens are very similar to the first set of specimens in Test
Series 1 and all of the specimens in Test Series 3, except the specimens in Test Series 4
have a proposed concrete compressive strength of 7000 psi.
6.6.1 Objectives of Test Series
The main objectives of Test Series 4 are to study the effects of the concrete compressive
strength and the amount of FRP on the strengthened moment capacity and to determine
the most accurate ICdebonding model for the test results.
6.6.2 Description of Specimens
The specimens in Test Series 4 all have the same cross section initially. This cross section
is shown in Figure 69.
Figure 69: Cross Section of Specimens in Test Series 4
Three of the specimens will be strengthened with one, three, and six thin FRP
strips, respectively. The specimen names and cross sections for Test Series 4 are shown
in Figure 610.
271
Figure 610: Specimen Names and Cross Sections for Test Series 4
Because the specimens in this test series have the same crosssectional
dimensions as the specimens in Test Series 1 and Test Series 3, the same shear span of 5
ft and the same beam length of 14 ft will be used. Like the other test series, the number
and size of the specimens was dependent upon the volume of concrete that could be
transported in one batch.
6.6.3 Anticipated Behavior and Failure Modes
The cracking moments, yield moments, and nominal moment capacities were all
calculated for the unstrengthened beams as described above for Test Series 1. Likewise,
the FRPstrengthened moment capacities and the stresses and strains for the steel, FRP,
and concrete were calculated using three different models: ACI 440 (2008), Seracino et
al. (2007a), and Standards Australia (2008).
272
273
6.6.3.1 Unstrengthened Specimens
Table 68 shows the cracking moment, yield moment, and nominal moment capacities for
the unstrengthened specimen. The values shown are also valid for the strengthened
specimens before the FRP is applied.
Table 68: Unstrengthened Moments for Specimens in Test Series 4
Specimen M
cr
(kipft) M
y
(kipft) M
n
(kipft)
all specimens 46.0 24.8 25.8
For these specimens, the required minimum amount of steel is 0.94 and 1.34 in.
2
using the ACI and AASHTO methods, respectively, and only 0.40 in.
2
is provided. As in
Test Series 1 and Test Series 3, the lack of steel causes the cracking moment to be greater
than the unstrengthened nominal moment.
6.6.3.2 Strengthened Specimens
Using the three models previously mentioned, the strengthened moment capacities at
which IC debonding occurs were predicted for the FRPstrengthened specimens. For
these models, the mean values were used to try to accurately predict the FRP
strengthened beam behavior; therefore, no reduction factors were used. The capacities
were also calculated for nonanchorage failures, such as rupture of the FRP or crushing of
the concrete, to show the relative size of the ICdebonding capacities compared to the
capacities for the nonanchorage failures. Table 69 shows the predicted nominal moment
capacities, stresses and strains for the steel and FRP, concrete strains, and failure modes.
274
Table 69: Predicted Strengthened Capacities, Stresses, Strains, and Failure Modes
Specimen
ID
Model used for
predictions
M
n
(kft)
?
s
f
s
(ksi)
?
frp
f
frp
(ksi)
?
c
Failure
mode
M1 (ACI) 40.5 0.0102 50 0.0117 210 0.0008 IC
M2 (Seracino) 47.0 0.0146 50 0.0166 300 0.0010 IC
M3 (SA) 42.9 0.0119 50 0.0135 244 0.0009 IC
4HS2F03
nonanch. failure 47.0 0.0146 50 0.0167 300 0.0010 R
M1 (ACI) 70.1 0.0102 50 0.0117 210 0.0010 IC
M2 (Seracino) 89.2 0.0145 50 0.0166 300 0.0014 IC
M3 (SA) 77.3 0.0118 50 0.0135 244 0.0012 IC
4HS2F08
nonanch. failure 89.3 0.0146 50 0.0167 300 0.0014 R
M1 (ACI) 113.9 0.0101 50 0.0117 210 0.0014 IC
M2 (Seracino) 151.3 0.0145 50 0.0166 300 0.0020 IC
M3 (SA) 128.0 0.0118 50 0.0135 244 0.0016 IC
4HS2F16
nonanch. failure 151.4 0.0145 50 0.0167 300 0.0020 R
Notes: M1 ACI 440 (2008)
M2 Seracino et al. (2007a)
M3 Standards Australia (2008)
IC intermediatecrack debonding
R rupture of the FRP
For all of the strengthened specimens shown in Table 69, the steel reaches its
yield stress of 50 ksi, and the strengthened capacity is greater than the unstrengthened
capacity from Table 68. For this specimen, all of the models predict an ICdebonding
failure will occur before an FRP rupture failure. As in Test Series 3, the Seracino et al.
(2007a) model produced the largest strengthened capacities, which were significantly
greater than the strengthened capacities predicted by the ACI 440 (2008) model. Once
again, the Seracino et al. model is the most sensitive to the concrete compressive
strength, while the ACI 440 model is the least sensitive to it.
275
Chapter 7: Summary and Conclusions
7.1 Summary
The Letohatchee bridge has been identified as being deficient under certain types of truck
loadings. For this bridge, there are currently load restrictions on some vehicles due to
deficiencies in the negativemoment regions of the girders. To remove the load
restrictions, different FRPstrengthening techniques were investigated. Because the
deficiencies occurred in the negativemoment regions of the continuous bridge girders,
nearsurface mounted (NSM) FRP strips, as opposed to externallybonded (EB) FRP
strips, are proposed for the strengthening of the Letohatchee bridge.
As reported in this thesis, the Letohatchee bridge was specifically investigated to
determine the amount of strengthening that is needed. NSM behavior was then examined
to determine the amount of strengthening that it can provide.
The Bridge Rating and Analysis of Structural Systems (BRASS?) program was
used to determine the flexural demands on the Letohatchee bridge. These moments were
then factored using the operating load combination. Once the demand was known, the
bridge?s capacity was calculated. The capacity was reduced by a reduction factor and
compared to the demand to determine the exact locations and magnitudes of the
deficiencies. The locations of the deficiencies for the exterior and interior girders were
the same. Because the deficiencies in the exterior girder were found to be more critical
276
than the deficiencies in the interior girder, the exterior girder was used for the design of
the strengthening scheme.
Various models and code recommendations that are used to predict FRP
strengthened moment capacities were investigated. Two types of debonding models were
analyzed: plateend (PE) debonding and intermediatecrack (IC) debonding. The IC
debonding models consisted of models for EB and models for NSM. For the PE
debonding models, the focus was solely on NSM. Using previous experimental results,
the various models were compared to each other to determine the most accurate models
for the given tests.
Once the more accurate models were determined, a strengthening scheme was
designed for the Letohatchee bridge using these models. In the proposed strengthening
scheme, the amount and spacing of the NSM were chosen for different concrete
compressive strengths.
The steel and FRP reinforcement ratios for the Letohatchee bridge were compared
to the ratios for previous experimental tests. The reinforcement ratios for the bridge were
found to be lower than the ratios for the experimental tests. Also, none of the NSM test
specimens were cracked prior to FRP strengthening. To be able to use laboratory test
results that can be directly applied to the bridge, a laboratory testing program was
developed. Because the proposed strengthening scheme employed NSM strips, only NSM
was studied in the testing program. The proposed testing program has four main
objectives. The first objective is to develop a relationship between the proposed test
specimens and the Letohatchee bridge to more effectively and more efficiently propose
an NSM FRPstrengthening scheme for the bridge. The second objective is to study the
277
ICdebonding behavior to better quantify when and if it will occur and to verify the
existing ICdebonding models. The third objective is to study the effects of the concrete
compressive strength, amount of steel reinforcement, amount of FRP reinforcement, and
crosssectional shape on the strengthened moment capacity. The fourth objective is to
evaluate the effectiveness of the FRP in a strengthening type of situation by cracking the
unstrengthened specimens before applying the FRP.
Four different test series are proposed to achieve these objectives. In the first test
series, the amount of tension steel and the amount of FRP are varied to determine the
corresponding effects on the strengthened moment capacity. In the second test series, the
overall height of the specimens is increased while holding the reinforcement ratio
constant to evaluate whether a size effect is present. In the third and fourth test series, the
concrete compressive strength is increased to 5000 and 7000 psi, respectively, to
establish whether the concrete strength has a significant effect on the ICdebonding
behavior.
7.2 Conclusions
Several conclusions are reported in this section for the various FRPdebonding models
and the Letohatchee bridge and its strengthening scheme.
7.2.1 Debonding Models
After using the existing experimental tests to determine the accuracy of the debonding
models, several conclusions were reached:
1. None of the PEdebonding models correlated with the existing NSM tests.
278
2. For the ICdebonding models for EB FRP, the fib 9.3 (2001) model and the
Seracino, Raizal Saifulnaz, and Oehlers (2007) model were not very accurate.
The other four models ? ACI 440 (2008), Standards Australia (2008),
Rosenboom (2006), and Said and Wu (2008) ? were all relatively accurate.
3. For the ICdebonding models for NSM FRP, the fib 9.3 (2001) model and the
Said and Wu (2008) model were overly conservative and not very accurate.
The other three models ? Seracino et al. (2007a), Standards Australia (2008),
and ACI 440 (2008) ? were all relatively accurate.
7.2.2 Letohatchee Bridge
Because three of the ICdebonding models were relatively accurate for the existing NSM
tests, they were all used to determine the amount of NSM needed for the Letohatchee
bridge. The following conclusions were reached for the Letohatchee bridge and its
strengthening scheme:
1. The Letohatchee bridge?s deficiencies occur in three main regions of the
bridge. The FRP strips should extend over the following distance ranges,
measured relative to the centerline of the girder end bearing: from 27 to 94
feet; from 100.5 to 169.5 feet; and from 176 to 243 feet. The lengths of the
strips are 67, 69, and 67 feet, respectively.
2. If no concrete cores are taken from the bridge, then either twentyfour total
thin NSM strips, six strips per girder, or twenty total thick NSM strips, five
strips per girder, should be used.
279
3. If the concrete strength is determined to be between 4000 and 6000 psi, then
sixteen total thick strips, four strips per girder, can be used.
4. If the concrete strength is determined to be between 6000 and 8000 psi, then
twelve total thick strips, three strips per girder, can be used.
5. If thin strips are chosen, then twentyfour total strips, six strips per girder,
should be used for any concrete strengths of 3000 psi or greater.
6. Spacing the strips fairly evenly across the cross section should effectively
control servicelevel cracking while minimizing debonding interaction
between the strips.
7.3 Recommendations
For the Letohatchee bridge, concrete core samples should be extracted and tested to
determine the compressive strength of the concrete. Once the concrete strength is known,
a more efficient FRPstrengthening scheme can be implemented if thick strips are used.
In this study, debonding models were compared to previous test results to
determine the accuracy of the models. Based on the results of this study, however, more
testing on NSM is needed to verify the validity of the models and code recommendations.
Flexural tests, as opposed to pushpull tests, are specifically needed to better simulate the
actual conditions of the unstrengthened members. Another way to simulate the actual
conditions is to crack the test specimens before the FRP is applied. The most direct
approach, however, would be to have testing of fullscale strengthened bridge girders.
Fullscale testing would be ideal for determining the effectiveness of the FRP systems.
Inplace testing of the strengthened Letohatchee bridge will provide valuable data about
280
the servicelevel performance of fullsize members, but failure testing of an inservice
bridge is not feasible.
281
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APPENDIX A: NOTATION
A
s
= area of nonprestressed steel reinforcement
A
f
= area of FRP reinforcement
a
b
= smaller crosssectional dimension for rectangular FRP bars
a
r
= distance between the strip and the edge of the concrete member
b = width of the compression face of the member
b
286
b
= larger crosssectional dimension for rectangular FRP bars
b
c
= width of the concrete
f
b
= width of the FRP (fib 9.3 2001)
f
b
= length of the failure surface parallel to the concrete surface
(Seracino, Raizal Saifulnaz, and Oehlers 2007)
b
L
= width of the FRP strip
p
b
= width of the EB plate (Standards Australia)
p
b
= plate dimension parallel to the concrete surface (Seracino et al.
2007a)
w
b
= web width of the concrete member
c = distance from the extreme compression fiber to the neutral axis
C1 = constant
C2 = constant
C3 = constant
C
E
= environmental reduction factor
CLR. = clear
d = distance from the extreme compression fiber to the centroid of the
tension reinforcement
d
b
= FRP bar diameter
d
f
= effective depth of the FRP flexural reinforcement
d
f
= length of the failure surface perpendicular to the concrete surface
(Seracino, Raizal Saifulnaz, and Oehlers 2007)
d
NSMtfp
= distance between the centroid of the specific NSM plate and the
neutral axis of the cracked plated section
p
d
= plate dimension perpendicular to the concrete surface
()
p
EA
= axial rigidity of the FRP
E
f
= modulus of elasticity of the FRP
()
plcr
EI
.
= flexural rigidity of the cracked plated cross section adjacent to the
plate end
E
p
= modulus of elasticity of the plate
E
s
= modulus of elasticity of steel
c
f
= concrete cylinder compressive strength
'
c
f
= concrete compressive strength
cb
f
= Brazilian or splitting tensile strength of the concrete
cbd
f
= bond shear strength of concrete
cm
f
= concrete?s mean compressive strength
F
conc
= force in the concrete
ct
f
= tensile strength of the concrete
ctk
f
= characteristic concrete tensile strength
ctm
f
= concrete?s mean tensile strength
fd
f
= design stress of the FRP reinforcement
fe
f
= effective stress in the FRP
frp
f
= stress in the FRP
F
frp
= force in the FRP
fu
f
= design ultimate tensile strength of the FRP material
*
fu
f
= ultimate tensile strength of the FRP as reported by the manufacturer
rupt
f
= rupture stress of the FRP
f
s
= stress in the nonprestressed steel reinforcement
F
steel
= force in the steel
F
V,k
= characteristic bond strength
f
y
= yield strength of the nonprestressed steel reinforcement
G
a
= shear modulus of the adhesive
h = overall height of the member
I
1
= constant
I
2
= constant
I
3
= constant
I
eff
= effective moment of inertia of the section
K = constant
L = bonded length of the FRP
df
l
= development length of the FRP reinforcement
l
o
= distance from the end of the beam to the start of the FRP strip
per
L
= total length of the debonding failure surface
l
v
= bond length
M
cr
= cracking moment
M
db
= debonding moment
M
exp
= experimental moment
M
n
= nominal moment
()[ ]
ch
tfpNSMPE
M
?
= characteristic moment at the plate end that causes PE debonding for
a tensionfaced NSM plate
()[ ]
ch
tfpPE
M
= characteristic moment at the plate end that causes PE debonding for
a tensionfaced EB plate
287
M
u
= ultimate moment
M
y
= yield moment
n = FRP?s modular ratio (Hassan and Rizkalla 2003)
n = number of FRP plies (ACI 440)
ff
tnE
= axial stiffness of FRP material per unit width
O.C. = on center
P = applied concentrated load
P
IC
= IC debonding resistance
()
EBIC
P
= mean value of the ICdebonding resistance for EB plates
()[ ]
EB
ppIC
P
= ICdebonding resistance for an EB plate
s = shear span
t
a
= thickness of the adhesive
t
f
= FRP thickness
t
NSMtfp
= thickness of the tensionfaced NSM plate
t
p
= thickness of the EB plate
t
tfp
= thickness of the tensionfaced EB plate
TYP. = typical
d
V
= design shear force
x = longitudinal coordinate starting from the cutoff point of the strip
y
x
= distance from the support to the location of first yielding of the
internal tensile reinforcement
y
eff
= distance from the FRP strip to the neutral axis of the section
m
z
= lever arm of the tensile reinforcement
? = ICdebonding coefficient
1
?
=
multiplier on to determine the intensity of an equivalent
rectangular stress distribution for concrete
'
c
f
?
EB
= ICdebonding coefficient
?
p
= ICdebonding coefficient
? = factor used to account for bond length
1
?
= ratio of the depth of the equivalent rectangular stress block to the
depth of the neutral axis
?
p
= width factor
c
?
= material safety factor for the concrete
d
M?
= change in moment across the two cross sections
exp
M?
= change in experimental moment
n
M?
= change in nominal moment
fdN? = change in the FRP axial force between the two cross sections
x? = distance between the two cross sections
bi
?
= strain level in the concrete substrate at the time of FRP installation
c
?
= strain in the concrete
frpc,
?
= strain in the concrete at the location of the FRP
288
cu
?
= maximum usable strain of unconfined concrete, which is generally
taken as 0.003
db
?
= FRP debonding strain
yf @
?
= tensile strain in the FRP at first yielding of the internal tensile steel
at a moment of M
y
fd
?
= debonding strain of the FRP
fe
?
= effective strain level in the FRP reinforcement at failure
exp,f
?
= experimental failure strain in the FRP
predf ,
?
= predicted failure strain in the FRP
frp
?
= strain in the FRP
ruptf ,
?
= rupture strain in the FRP
fu
?
= design rupture strain of the FRP reinforcement
*
fu
?
= ultimate rupture strain of the FRP reinforcement
s
?
= strain in the steel reinforcement
?
= strength reduction factor
f
?
= FRP reinforcement ratio
*
f
?
= normalized FRP reinforcement ratio
sf
?? /*
= relative strengthening ratio
s
?
= steel reinforcement ratio
?
= normal stress
?
1
= one of the principal normal stresses
?
2
= one of the principal normal stresses
?
3
= one of the principal normal stresses
?F
= summation of forces
? = shear stress
b
?
= average bond stress for NSM FRP bars (ACI 440)
b
?
= shear stress at the FRPconcrete interface (fib 9.3 2001)
maxc
?
= limiting shear stress in the concrete
i
?
= total concrete shear stress
max
?
= maximum shear stress
kK ,
?
= characteristic shear strength of the adhesive
maxsc
?
= shear stress in the concrete due to stress concentrations at the toes
of the flexural cracks
maxw
?
= shear stress in the concrete due to the load
f
?
= confinement ratio
?
f
= FRP strength reduction factor
289
? = defined in Equation 229 (Hassan and Rizkalla 2003)
s
?
= mechanical reinforcement ratio
290
APPENDIX B: SAMPLE CALCULATIONS
Table B1: Input for Sample Calculations for All Models
Concrete Properties
Steel Reinforcement
Properties
FRP Properties
Reduction
Factors
b
w
= 16.75 in. A
s
= 1.92 in.
2
# grooves = 6
?
= 0.7
h = 43.375 in. d = 40.19 in. t
f
= 0.079 in. C
E
= 0.85
f?
c
= 3000 psi E
s
= 29000 ksi d
f
= 0.63 in.
?
f
= 0.85
?
bi
= 0.0481% f
y
= 40 ksi E
f
= 18000 ksi
f
f,rupt
= 300 ksi
291
Table B2: Sample Calculations using each Model
Model
P
IC
(kips)
f
fu
(ksi)
?
frp
(%)
?
c,frp
(%)
c*
(in.)
?
s
(%)
?
c
(%)
f
s
(ksi)
?
1
?
1
F
frp
(kips)
F
steel
(kips)
F
conc
(kips)
?F
(kips)
a
(in.)
M
n
(kft)
1 N/A 179 0.99 1.04 4.95 0.96 0.14 40 0.72 0.73 53.3 76.8 130.1 0.0 3.54 402
2 7.8 157 0.87 0.92 5.06 0.85 0.12 40 0.71 0.69 46.8 76.8 123.6 0.0 3.59 407
3 8.2 165 0.92 0.97 5.01 0.89 0.13 40 0.71 0.70 49.3 76.8 126.1 0.0 3.56 415
Notes: Model 1 ACI 440 (2008)
Model 2 Seracino, Raizal Saifulnaz, and Oehlers (2007)
Model 3 Seracino et al. (2007a)
?
c,frp
is the strain in the concrete at the location of the FRP.
F
frp
is the force in the FRP; F
steel
is the force in the steel; and F
conc
is the force in the concrete.
?F is the summation of the forces.
Model 1 uses all three reduction factors, ?, C
E
, and ?
f
. Models 2 and 3 only use the environmental reduction factor, C
E
.
*The value for c was guessed, calculated, and then iterated until the sum of the forces (?F) was equal to 0.