ABSTRACT ROSENBOOM, OWEN ARTHUR Behavior of FRP Repair/Strengthening Systems for Prestressed Concrete (Under the direction of Dr Sami Rizkalla.) This research study examines the behavior of prestressed concrete beams retrofitted with Fiber Reinforced Polymer (FRP) materials Due to deficiencies in the built environment, engineers may be asked to retrofit or upgrade the capacity of an existing concrete structural member This could be a result of new demands on the structure, or a repair of damage from an unforeseen event Retrofits are possible using the traditional building materials of concrete and steel The cross-section of the structural element can be increased, or steel plates can be bolted or adhesively affixed to the structure to increase capacity Many of these techniques are costly, and some perform poorly under service conditions The main benefit for using FRP materials for the strengthening of existing structures is the lightweight nature of the composite material, which makes the use of extensive scaffolding (required in the installation of steel plates) obsolete The objectives of this research are twofold First, the overall structural behavior of an FRP strengthened or repaired concrete beam is studied Two different loading conditions are examined: extreme loading simulated by a monotonic load to failure, and fatigue loading designed to simulate service loads The structural behavior of the system is evaluated under these different conditions, and an analytical model is presented which predicts the flexural behavior of the system assuming certain failure modes The second objective of this research is to evaluate the bond behavior of an FRP strengthened reinforced or prestressed concrete flexural member A database of experimental failures was constructed, and an analytical model is proposed which predicts the bond failure of the FRP strengthening system BEHAVIOR OF FRP REPAIR/STRENGTHENING SYSTEMS FOR PRESTRESSED CONCRETE By Owen Arthur Rosenboom A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Civil Engineering Raleigh 2006 Approved by: _ _ Dr Sami Rizkalla Chair of Advisory Committee Civil Engineering Dr Mervyn Kowalsky Advisory Committee Civil Engineering _ _ Dr Kara Peters Advisory Committee Aerospace & Mechanical Engineering Dr Paul Zia Advisory Committee Civil Engineering UMI Number: 3233054 UMI Microform 3233054 Copyright 2007 by ProQuest Information and Learning Company All rights reserved This microform edition is protected against unauthorized copying under Title 17, United States Code ProQuest Information and Learning Company 300 North Zeeb Road P.O Box 1346 Ann Arbor, MI 48106-1346 BIOGRAPHY Owen Rosenboom completed his MSCE from North Carolina State University in 2003 Upon completion of his current work he plans to travel to Vietnam ii ACKNOWLEDGEMENTS Structural engineering research is a group effort Many different people from around the United States and around the world have contributed to the work presented here None of it, of course, would have been possible without the near continuous supervision and mentoring of my advisor, Dr Sami Rizkalla The other members of my advisory committee have also provided valuable insight, especially Dr Paul Zia Several other doctoral or post-doctoral students have made generous gifts of time and energy including Dr Tarek Hassan, Dr Ronaldson Carneiro, and Mina Dawood I had the pleasure to work with two master’s level students on the project, Anthony Miller and Catrina Walter, whose energy helped complete the extensive experimental program The North Carolina Department of Transportation funded much of this research and should be acknowledged, along with the many other contractors, FRP manufacturers and installers that generously donated time and material, especially Dr Tarek Alkhrdaji from Structural Group, and Sarah Witt and Edward Fyfe from Fyfe Corporation The construction of the database included in this dissertation followed from the momentum of Dr Kent Harries from the University of Pittsburgh within ACI Committee 440’s Bond Task Group, of which I was charitably invited to become a member And lastly, I thank the dedicated staff of the Constructed Facilities Laboratory (Jerry Atkinson, Bill Dunleavy, and Amy Yonai) whose help at all stages of this research has been immeasurable iii TABLE OF CONTENTS List of Figures viii List of tables xiii INTRODUCTION Research Objectives Scope of Dissertation Outline of Thesis PART 1: REPAIR AND STRENGTHENING CHAPTER 1: INTRODUCTION CHAPTER 2: BACKGROUND 10 2.1 FRP Repair / Strengthening Systems 10 Fiber Reinforced Polymer (FRP) Materials 10 Adhesives 11 2.2 Failure Mechanisms 12 2.3 History of FRP Strengthening 14 2.4 Reinforced Concrete Strengthened with FRP 14 2.5 Prestressed Concrete Strengthened with FRP 16 2.6 Near Surface Mounted Strengthening 17 2.7 Steel Reinforced Polymer Strengthening 20 2.8 Repair of Prestressed Concrete with FRP 20 2.9 Fatigue Behavior 25 Fatigue of Constitutive Materials 25 Fatigue of Prestressed Concrete 27 Fatigue of Reinforced Concrete Strengthened with FRP 28 2.10 Fatigue of Prestressed Concrete Strengthened with FRP 31 2.11 Durability of FRP Systems 33 2.12 Design Guidelines for Concrete Retrofitted with FRP 33 2.13 Conclusions 36 CHAPTER 3: EXPERIMENTAL PROGRAM: STRENGTHENING 37 3.1 Test Girders 38 The C-Channel Bridge 38 Girder Reinforcing 39 Concrete 42 Carbon Fiber Reinforced Polymer (CFRP) Materials 44 Steel Reinforced Polymer (SRP) Material 47 3.2 Design of Strengthened Girders 47 3.3 Static Tests 49 Test Setup, Procedure and Instrumentation 49 Control Girder 52 NSM Strengthened Girders 53 Externally Bonded CFRP Strengthened Type C1 Girders 54 Externally Bonded CFRP Strengthened Type C2 Girders 59 Externally Bonded SRP Strengthened Type C1 Girder 61 3.4 Fatigue Tests 62 Test Setup, Procedure and Instrumentation 62 iv Fatigue Load Determination 63 Control Girders 65 NSM CFRP Strengthened Girders 66 Externally Bonded CFRP Strengthened Type C1 Girders 67 Externally Bonded CFRP Strengthened Type C2 Girders 70 Externally Bonded SRP Strengthened Type C1 Girders 73 CHAPTER 4: EXPERIMENTAL PROGRAM: REPAIR 75 4.1 Introduction 75 4.2 Test Girders 77 4.3 Design of Repair System 82 Flexural Repair 82 Shear Repair 86 4.4 Test Setup and Procedure 88 Test Setup 88 Instrumentation 90 Loading Scheme 91 Fatigue Load Determination 92 4.5 AASHTO1 95 4.6 AASHTO2 97 4.7 AASHTO3 98 4.8 AASHTO2C 100 4.9 AASHTO2R 100 CHAPTER 5: EXPERIMENTAL RESULTS AND MODELING – STRENGTHENING AND REPAIR103 5.1 Modeling 103 Flexural Model 103 Finite Element Simulations 110 Cracked Section Analysis 112 Shear Model 112 5.2 Results and Discussion: Strengthening 115 C-Channel Static Tests 116 Type C1 Girders 117 Type C2 Girders 127 C-Channel Fatigue Tests 132 Type C1 Girders 133 Type C2 Girders 146 5.3 Results and Discussion: Repair 153 Flexural Study 153 AASHTO1 153 AASHTO2 158 AASHTO3 163 Shear Study 167 CHAPTER 6: COST EFFECTIVENESS AND VALUE ENGINEERING 174 6.1 C-Channel Strengthening 174 Cost Analysis 174 Value Engineering Analysis 178 6.2 AASHTO Repair 183 Cost Analysis 183 Value Engineering Analysis 186 v PART 2: BOND BEHAVIOR .187 CHAPTER 7: INTRODUCTION 188 CHAPTER 8: BACKGROUND 190 8.1 Plate-End (PE) Debonding 190 Interfacial Stress Models 192 Shear Strength Models 195 Concrete Tooth Models 196 Experimental Studies on Plate-End Debonding 198 Recommendations from Code Agencies 198 8.3 Intermediate Crack (IC) Debonding 200 Empirical Models 203 Mechanics Based Models 204 Width Factor 210 Fracture Based Models 211 Multiple Crack Models 219 Recommendations from Code Agencies 223 8.4 Experimental Studies .226 IC Debonding Database 226 Experimental Studies Included in Database 226 Experimental Studies not Included in Database 231 8.5 Failure Criteria 237 Mohr-Coulomb Criteria 237 Empirical Criteria 238 8.6 Mitigation of Debonding 239 Transverse CFRP U-wraps 240 Other Anchorage Details 243 8.7 Conclusions 244 CHAPTER 9: EXPERIMENTAL PROGRAM: BOND 245 9.1 Test Girders 245 9.2 Girder Strengthening, Test Setup, Procedure and Instrumentation .248 9.3 Test Descriptions: Externally Bonded Precured Strips 249 9.4 Test Descriptions: Externally Bonded Wet Lay-up Sheets 251 9.5 Results and Discussion .253 Crack Width 254 Ultimate Load and Displacement 255 Interface Shear Stress 256 Predicted v Experimental 260 CHAPTER 10: MODEL COMPARISON 262 10.1 Intermediate Crack Debonding Database .262 Database Requirements 262 10.2 Assessment of Existing IC Debonding Models .266 Models from National Codes 266 Other Models 274 Width Factor 286 10.3 Conclusions .292 CHAPTER 11: ANALYTICAL MODEL FOR IC DEBONDING 293 11.1 Overview 293 11.2 Interface Shear Stress .294 11.3 Design Interface Shear Stress 297 11.3 Failure Criteria 302 vi 11.4 Model Calibration 304 11.5 Rupture Check 306 11.6 Summary of Proposed Analytical Model 309 Mean Model 310 Design Model 311 11.7 Width Effect 311 11.8 Statistical Analysis 314 11.9 Scope of Analytical Model .319 CHAPTER 12: PARAMETRIC STUDY 322 12.1 Applied Loading 322 12.2 Concrete Properties 324 12.3 FRP Properties 325 12.4 Internal Steel Properties 327 12.5 Level of Prestress 329 CONCLUSIONS 331 Part 1: Repair/Strengthening 331 FRP Strengthening Experimental Program 331 FRP Repair Experimental Program 332 Flexural and Shear Modeling 333 Part 2: Bond Behavior 334 Experimental Study on Bond Behavior 334 Model Comparison and Database Construction 334 Analytical Model for IC debonding 335 Future Work 336 FRP Strengthening and Bond Behavior 336 FRP Repair 338 REFERENCES 340 RECOMMENDATIONS FOR THE INSTALLATION OF FRP SYSTEMS FOR CONCRETE STRUCTURES 352 A.1 Shipping, Storage and Handling 352 A.2 Section Restoration 353 A.3 Surface Preparation 355 A.4 Near Surface Mounted CFRP Installation 357 A.5 Externally Bonded Pre-cured CFRP Laminate Installation 357 A.6 Externally Bonded Wet Lay-up CFRP Installation 358 A.7 Use of Externally Bonded SRP 360 DESIGN EXAMPLES 364 B.1 Reinforced Concrete Beam .364 B.2 Prestressed Concrete Bridge Girder 372 IC DEBONDING DATABASE 382 vii ▐ Appendix B Bond Design Example ε db + 0.114 τ sc max nE f t f ≤ εu Step 24 – Calculate the design flexural strength of the section The flexural strength of the section at failure calculated above is multiplied by a reduction factor Because εs>> εy, a strength reduction factor of φ=0.90 is appropriate, per Equation 9-5 φ M n = ( 0.90 )( 516.4 kN-m ) = 464.8 kN-m 464.8 > 435.3 kN-m okay The strengthened section is capable of sustaining the new required moment strength φ M n = ( 0.90 ) M n B.2 Prestressed Concrete Bridge Girder Flexural Strengthening of a Prestressed Beam with FRP Laminates A number of simply supported prestressed concrete beams with φ=12.7 mm bonded tendons (Figure B.2) are located in a parking garage that is being converted to an office space All prestressing tendons are fpu=1860 MPa low-relaxation 7-wire tendons The beams require an increase in their live-load carrying capacity from 11.7 N/mm to 18.7 N/mm Analysis of the five existing beams indicates that, for the new loads, beams have adequate shear capacity but are deficient in flexure at mid-span The beam meets the deflection and crack control serviceability requirements The cast-in-place beams support a 102 mm slab For bending at midspan, the beams should be treated as a T-section Summarized in Table B.4 are the existing and new loads and associated midspan moments for the beam Figure B.2 Schematic of the idealized prestressed beam with FRP laminates 372 ▐ Appendix B Bond Design Example Table B.4 Problem Summary Length of the beam l 8.84 m Width of the beam w 610 mm dp 571 h 635 mm Effective flange width, bf 2210 mm Flange thickness, hf 102 mm f’c 41.4 MPa Tendons φ=12.7 mm fpe 1138 MPa fpy 1586 MPa fpu 1860 MPa Ep 1.96 x 105 MPa em, es φMn (w/o FRP) 64 mm2 546 kN-m Table B.5 Loadings and corresponding moments Loading / Moment Existing Loads Anticipated Loads Dead loads ωDL 20.2 N/mm 23.8 N/mm Live loads ωLL 11.7 N/mm 18.7 N/mm 31.9 N/mm 42.5 N/mm N/A 44.4 N/mm 48.1 N/mm 65.0 N/mm Dead load moment MDL 199 kN-m 232 kN-m Live Load moment MLL 115 kN-m 183 kN-m Service load moment MS 315 kN-m 414 kN-m Unstrengthened moment limit (1.2MDL+0.85MLL) N/A 432 kN-m 475 kN-m 634.5 kN-m Unfactored loads (ωDL+ ωLL) Unstrengthened load limit (1.2ωDL+ 0.85ωLL) Factored Loads (1.4ωDL+ 1.7ωLL) Factored moment Mu It is proposed to strengthen the existing reinforced concrete beam with the FRP system described in Table B.6 Specifically, four 51 mm wide x 8534 mm long pre-cured FRP plates are to be bonded to the soffit of the beam 373 ▐ Appendix B Bond Design Example Table B.6 Manufacturer’s reported FRP system properties Thickness per ply tf 1.2 mm Ultimate tensile strength ffu* * fu Rupture strain ε 2800 MPa 0.017 mm/mm Modulus of Elasticity of FRP laminate Ef 160000 MPa By inspection, the level of strengthening is reasonable in that it does meet the strengthening limit criteria put forth in Equation 8.1 That is, the existing moment strength, (φMn)w/o FRP = 546 kN-m, is greater than the unstrengthened moment limit, (1.2MDL + 0.85MLL)new = 432 kNm The design calculations used to verify the configuration follow Procedure Calculation in SI metric units Step – Calculate the FRP system design material properties The beam is located in an interior space and a CFRP material will be used Therefore, per Table 8.1, an environmental reduction factor of 0.95 is suggested f fu = C E f fu * ε fu = CE ε fu * ( f fu = ( 0.95 ) 2800 N/mm fc β = 1.05 − 0.05 Ec = 30.2 kN/mm ' bd p Properties of the externally bonded FRP reinforcement: Af = nt f b f Ac = be h f + bw ( h − h f 2 Aps = ( 99 mm ) = 594 mm Aps Cross sectional area: 41.4 = 0.75 6.9 Ec = 4700 41.4 N/mm Properties of the existing prestressing steel: ρs = ) = 2660 N/mm ε fu = ( 0.95 )( 0.017 mm/mm ) = 0.0162 mm/mm Step – Preliminary calculations Properties of the concrete: β1 from ACI 318-05, Section 10.2.7.3 Ec = 4700 ρp = 594 mm = 0.00047 ( 2210 mm )( 572 mm ) Af = (1 layer )( strips )(1.2 mm )( 51 mm ) = 245 mm ) Distance from the top fiber to the section centroid: Ac = ( 2210 mm )(102 mm ) + ( 610 mm ) ( 612 mm − 102mm ) = 5.5 × 10 mm 374 ▐ Appendix B Bond Design Example ⎡ h 2f ⎢b f + bw ( h − h f ⎣ Ac yt = ) yt = ⎛ ( h − hf ) ⎞⎟ ⎤⎥ ⎜ hf + ⎟⎥ ⎜ ⎝ ⎠⎦ Gross moment of inertia: hf ⎞ ⎛ Ig = + b f h f ⎜ yt − ⎟ + 12 ⎠ ⎝ b f h3f bw ( h − h f ) 12 Ig = 2210 × 1023 610 × 5333 = 2210 × 102 ( 238 − 51) + 12 12 +610 × 533 ( 238 − 368 ) = 2.13 × 1010 mm + bw ( h − h f ) Radius of gyration: Ig r= 2.13 × 1010 = 197 mm 5.5 × 105 ε pe = 1138 = 0.00579 1.96 × 105 Ac Effective prestressing strain: ε pe = ) h − hf ⎞ ⎛ ⎜ yt − ⎟ ⎠ ⎝ r= ( 2210 × 102 + 610 × 533 × 368 5.5 × 10 yt = 238 mm f pe Ep Pe = 594 × 1138 = 676.0 kN Effective prestressing force: Pe = Aps f pe e = 571 − 238 = 333 mm Eccentricity of prestressing force: e = d p − yt Step – Determine the existing state of strain on the soffit The existing state of strain is calculated assuming the beam is uncracked and the only loads acting on the beam at the time of FRP installation are dead loads Distance from the top fiber to the section centroid: yb = h − yt Initial strain in the beam soffit: ε bi = − Pe ⎛ eyb ⎞ M DL yb 1+ ⎟ Ec Ac ⎜⎝ r ⎠ Ec I g yb = 635 − 238 = 397 mm ε bi = − + 676972 30200 × 5.5 × 105 ⎛ 333 × 397 ⎞ ⎜ + 197 ⎟ ⎝ ⎠ 232 × 106 × 397 = −4 × 10−5 30200 × 2.13 × 1010 375 ▐ Appendix B Bond Design Example Step – Estimate cy, the depth to the neutral axis at yielding of existing internal reinforcement A reasonable estimate of cy is 0.15d The value of cy is adjusted after checking equilibrium c y = ( 0.15 )( 571 mm ) = 85.7 mm c y = 0.15d p Step - Determine the level of strain in the existing prestressing steel at yielding The strain in the prestressing can be calculated from: ε py = ε py = f py 1586 MPa = 0.00809 mm/mm 196000 MPa Ep Step – Determine the level of strain in the FRP reinforcement, εfey, at yielding By using this equation an assumption is made that the steel will yield before FRP failure or concrete crushing ε fey = ( ε py − ε pe − ε bi ε fey = ( 0.00809 − 0.00579 + 0.00004 ) ( 635 − 85.7 ) ( 571 − 85.7 ) ε fey = 0.00265 mm/mm (h − c ) ) d −c ( ) y y Step - Calculate the stress level in the reinforcing steel and FRP at yielding For the reinforcing steel: fs = f y f s = 1860 MPa f fey = (160000 MPa )( 0.00265 mm/mm ) = 424 MPa For the FRP material: f fey = E f ε fey Step - Calculate the equivalent concrete compressive stress block parameters γ and β1 The strain in the concrete at yielding can be calculated from strain compatibility as follows: ε cy = ( ε fey − ε bi ) ε cy = ( 0.00265 + 0.00004 ) β= cy 85.7 = 0.000476 635 − 85.7 ( 0.002 ) − 0.000476 ( 0.002 ) − ( 0.000476 ) = 0.68 h − cy Approximate stress block parameters may be calculated from the parabolic stress-strain γ= ( 0.000476 )( 0.002 ) − ( 0.000476 ) ( 0.70 )( 0.002 ) 2 = 0.28 376 ▐ Appendix B Bond Design Example relationship of concrete and expressed as: β1 = γ= 4ε c ' − ε c 6ε c ' − 2ε c 3ε c ε c ' − ε c 3β1ε c' Where εc’ is the strain corresponding to f’c assumed equal to 0.002 Step 10 – Calculate the internal force resultants and check equilibrium Force equilibrium is verified by checking the initial estimate of cy with the following equation: cy = Aps f py + Af f fey γβ1 f c'b cy = c y = 60.0 mm ≠ 85.7 mm N.G Revise estimate of cy and repeat Steps through until equilibrium is achieved Step 11 – Adjust cy until force equilibrium is satisfied Steps through were repeated with several different values of cy until equilibrium is satisfied cy = c y = 73.2 mm ε c = 0.00034 mm/mm β1 = 0.68 γ = 0.24 Step 12 – Calculate the sectional moment at yielding of internal reinforcement The moment at yielding of the internal steel reinforcement is calculated from: β1c y ⎞ ⎛ M y = Aps f py ⎜ d p − ⎟+ ⎠ ⎝ β1c y ⎞ ⎛ Af f fey ⎜ d f − ⎟ ⎠ ⎝ Step 13 – Estimate εdb, the applied strain level in the FRP at failure A reasonable initial estimate for εdb is ( 594 )(1586 ) + ( 245)( 430 ) ( 0.68)( 0.24 )( 41.4 )( 2210 ) c y = 73.2 mm ε fey = 0.00261 mm/mm f fey = 430 MPa ( 594 )(1586 ) + ( 245)( 424 ) ( 0.68)( 0.28)( 41.4 )( 2210 ) The value of cy selected is correct for final iteration ⎛ ( 0.68)(84.3) ⎞ + M y = ( 594 mm ) (1586 MPa ) ⎜ 571 − ⎟⎟ ⎜ ⎝ ⎠ ⎛ ( 245 mm ) ( 430 MPa ) ⎜⎜ 635 − ( 0.68)(84.3) ⎞ ⎟⎟ ⎝ ⎠ M y = 582200000 N-mm = 582.2 kN-m ε db = 0.6 ( 0.0170 mm/mm ) = 0.0102 mm/mm 377 ▐ Appendix B Bond Design Example 0.6εfu ε db = 0.6ε fu Step 14 – Estimate c, the depth to the neutral axis at failure A reasonable initial estimate of c is 0.10d The value of c is adjusted after checking equilibrium c = 0.10 ( 635 ) = 63.5 mm c = 0.10d Step 15 – Determine the effective level of strain in the FRP The effective strain level in the FRP may be found from Equation 9-3 ⎛ df −c ⎞ ⎟ − ε bi ≤ ε db ⎝ c ⎠ ε fe = 0.003 ⎜ If the right hand side of this equation controls then concrete crushing is the failure mode, else the failure is in the FRP material Step 16 – Calculate the strain level in the existing prestressing steel The strain in the prestressing steel can be calculated using the following equations: ⎛ dp − c ⎞ ⎜ d f − c ⎟⎟ ⎝ ⎠ ⎛ 635 − 63.5 ⎞ ⎟ + 0.00005 = 0.02695 mm/mm ⎝ 63.5 ⎠ ε fe = 0.003 ⎜ ε fe = 0.02695 mm/mm ≤/ 0.0102 So the failure will be in the FRP material ε fe = ε db − ε bi ε fe = 0.0102 + 0.00005 = 0.01025 mm/mm ⎛ 571 − 63.5 ⎞ ⎟ = 0.00910 mm/mm ⎝ 635 − 63.5 ⎠ ε pnet = ( 0.01025 ) ⎜ ε pnet = ( ε fe ) ⎜ ε ps = ε pe + Pe Ac Ec ⎛ e2 ⎜1 + ⎝ r ε ps = 0.00579 + ⎞ ⎟ + ε pnet ⎠ ε ps ≤ 0.035 Step 17 – Calculate the stress level in the reinforcing steel and FRP The stresses are calculated from the following equations: f ps = ⎪⎧1.96 × 10 ε ps for ε ps ≤ 0.0086 ⎨ 0.004 ⎪⎩1860 − ε −0.007 for ε ps ≤ 0.0086 ⎛ 3332 676 1+ ( 5.5 ×105 ) ( 30200 ) ⎜⎝ 1972 ⎞ ⎟ + 0.00910 ⎠ ε ps = 0.0149 mm/mm ≤ 0.035 okay f ps = 1860 − 0.276 = 1837 MPa 0.0149 − 0.007 f f = (160000 MPa )( 0.01025 mm/mm ) = 1632 MPa ps 378 ▐ Appendix B Bond Design Example f fe = E f ε fe Step 18 – Calculate the equivalent concrete compressive stress block parameters γ and β1 The strain in the concrete at FRP failure can be calculated from strain compatibility as follows: ε c = ( 0.01025 ) β= c ε c = ε fe h−c Approximate stress block parameters may be calculated from equations given in Step Step 19 – Calculate the internal force resultants and check equilibrium Force equilibrium is verified by checking the initial estimate of c with Equation 9-10 c= Aps f ps + Af f fe γβ1 f c'b γ= f ps = 1828 MPa f fe = 1632 MPa ( 0.002 ) − 0.00114 ( 0.002 ) − ( 0.00114 ) = 0.71 ( 0.00114 )( 0.002 ) − ( 0.00114 ) ( 0.76 )( 0.002 ) c= 2 = 0.66 ( 594 )(1837 ) + ( 245 )(1632 ) ( 0.71)( 0.66 )( 41.4 )( 2210 ) c = 34.8 ≠ 63.5 N.G Revise estimate of c and repeat Steps 14 through 18 until equilibrium is achieved Step 20 – Adjust c until force equilibrium is satisfied Steps 14 through 19 were repeated with several different values of c until equilibrium is satisfied c = 46.1 mm ε fe = 0.01025 mm/mm 63.5 = 0.00114 635 − 63.5 c= ( 594 )(1828) + ( 245)(1632 ) ( 0.69 )( 0.51)( 41.4 )( 2210 ) c = 46.1 mm The value of c selected is correct for final iteration ε c = 0.00081 mm/mm β1 = 0.69 γ = 0.51 Step 21 – Calculate flexural strength of section, Mn The flexural strength can be calculated using Equation 9-11 The reduction factor φ will be applied later ⎛ ( 0.69 )( 46.1) ⎞ + M n = ( 594 mm ) (1828 MPa ) ⎜ 571 − ⎟⎟ ⎜ ⎝ ⎠ ⎛ ( 0.69 )( 46.1) ⎞ ⎟⎟ ( 245 mm2 ) (1632 MPa ) ⎜⎜ 635 − ⎝ ⎠ M n = 850300000 N-mm = 850.3 kN-m 379 ▐ Appendix B Bond Design Example Step 22 – Determine the interface shear stress The interface shear stress due to the applied loading (τwmax) is related to the tensile strains in the CFRP at yielding and at failure τ w max = nE f t f ε db − ε fey xy = − 8.842 ⎛ ( 850.3) + ⎜− × 850.3 ⎝ 8.84 ⎞ ⎛ ( 850.3) ⎞ ⎛ 850.3 ⎞ 533.3 ⎟ ⎜ ⎟ − 16 ⎜ ⎟ ⎟ 8.84 8.84 ⎝ ⎠ ⎝ ⎠ ⎠ x y = 1908 mm s − xy where xy is the distance from the support to the section in which the internal steel first yields and is equal to: L2 ⎛ M n xy = − + ⎜− 8M n ⎝ L ⎛ 4M n ⎞ ⎛ Mn ⎜ ⎟ − 16 ⎜ ⎝ L ⎠ ⎝ L ⎞ ⎟My ⎠ ⎞ ⎟ ⎟ ⎠ The interface shear stress due to stress concentration (τscmax) can be found by: ⎛ τ sc max = ⎜1.1 − ⎝ The total interface shear stress is then equal to: τ i = τ w max + τ sc max ≤ 1.134 f ' c Step 23 – Revise the estimate of debonding strain εdb in Step 13, and Repeat Steps 14 through 22 Steps 14 through 22 were repeated with several different values of εdb until equilibrium was satisfied ε db = 0.00717 mm/mm f fe = 1181 MPa τ w max ⎛ 533.3 kN-m ⎞ ⎝ ⎠ = 9.12 MPa τ sc max = ⎜1.1 − 41.4 MPa 850.3 kN-m ⎟ τ sc max My ⎞ ' ⎟ fc Mn ⎠ 0.01025 − 0.00262 8840 − 1908 = 0.583 MPa τ w max = (1 ply )(160000 )(1.2 ) τ i = 0.583 + 9.12 = 9.70 MPa 5.29 < 1.134 41.4 = 7.30 MPa N.G Revise estimate of εdb and repeat Steps 14 through 21 the specified value of interface shear stress is achieved τ i = 0.407 + 6.86 = 7.30 MPa 7.30 = 7.30 okay The value of εdb for the final iteration is correct M n = 770.4 kN-m τ wmax = 0.407 MPa τ scmax = 6.86 MPa 380 ▐ Appendix B Bond Design Example Step 24 – Check for rupture of FRP FRP failure will occur Whether the failure is due to rupture or debonding can be determined from: ε db + 0.114 τ sc max nE f t f ≤ εu Step 25 – Calculate the design flexural strength of the section The flexural strength of the section at failure calculated above is multiplied by a reduction factor Because εs>> εy, a strength reduction factor of φ=0.90 is appropriate, per Equation 9-5 0.00717 + 0.114 6.86 (1 ply )(160000 MPa )(1.2 mm ) = 0.0090 mm/mm 634.5 kN-m okay The strengthened section is capable of sustaining the new required moment strength φ M n = ( 0.90 ) M n 381 ▐ Appendix C: IC Debonding Database APPENDIX C: IC DEBONDING DATABASE A database was constructed of the intermediate crack (IC) debonding failures from the literature, as described in Chapter 10 The database is included here 382 ▐ Appendix C: IC Debonding Database Reference specimen No 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Aidoo et al 2006 Brena et al 2003 Brena et al 2003 Brena et al 2003 Brena et al 2003 Dias et al 2004 Dias et al 2004 Fang 2002 Fang 2002 Fang 2002 Grace et al 2002 Grace et al 2002 Kaminska and Kotynia 2000 Kaminska and Kotynia 2000 Kaminska and Kotynia 2000 Kaminska and Kotynia 2000 Khomwan et al 2004 Kotynia and Kaminska 2003 Kotynia and Kaminska 2003 Kotynia and Kaminska 2003 Matthys 2000 Matthys 2000 Matthys 2000 Matthys 2000 Matthys 2000 CS B1 C1 C2 D2 V2 V4 B1 B2 B3 C-3 C-1 BF-04/0.5S BF-06/S B-08/S BO-08/S B3 B-083m B-08S B-08M BF2 BF3 BF4 BF5 BF8 height width ds ds mm test span L mm shear span a mm h mm b mm 825 356 406 406 406 180 180 200 200 200 254 254 300 300 300 300 700 300 300 300 450 450 450 450 450 343 203 203 203 203 120 120 150 150 150 152 152 150 150 150 150 350 150 150 150 200 200 200 200 200 683.6 320.4 365.4 365.4 365.4 162 162 180 180 180 216 216 260 260 260 260 615 260 260 260 405 405 405 405 405 8840 2690 3000 3000 3000 1800 1800 1500 1500 1500 2440 2440 3000 3000 3000 3000 6000 4200 4200 4200 3800 3800 3800 3800 3800 4420 1065 1220 1220 1220 750 750 550 550 550 839 839 1500 1500 800 800 2500 1400 1400 1400 1250 1250 1250 1250 1250 a/h 5.36 2.99 3.00 3.00 3.00 4.17 4.17 2.75 2.75 2.75 3.30 3.30 5.00 5.00 2.67 2.67 3.57 4.67 4.67 4.67 2.78 2.78 2.78 2.78 2.78 concrete strength fc' MPa 45 37.2 35.1 35.1 37.2 41 41 24.96 24.96 24.96 55.2 55.2 33 32.5 33.8 36.5 37 34.4 32.3 37.3 36.5 34.9 30.8 37.4 39.4 bar size mm varies 16 16 16 16 8 8 16 16 10 12 12 12 20 12 12 12 16 16 16 16 16 Tension Steel number reinforcing yield ratio strength p fy MPa varies 2 2 2 3 2 2 3 2 4 4 0.0262 0.0056 0.0049 0.0049 0.0049 0.0047 0.0047 0.0050 0.0050 0.0050 0.0104 0.0104 0.0035 0.0050 0.0075 0.0075 0.0050 0.0050 0.0050 0.0089 0.0089 0.0089 0.0089 0.0045 364 440 440 440 440 533 533 288 288 288 415 415 449 490 CFRP CFRP 557 436 493 493 590 590 590 590 590 383 ▐ Appendix C: IC Debonding Database Longitudinal FRP FRP type Reference Ef MPa No 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Aidoo et al 2006 Brena et al 2003 Brena et al 2003 Brena et al 2003 Brena et al 2003 Dias et al 2004 Dias et al 2004 Fang 2002 Fang 2002 Fang 2002 Grace et al 2002 Grace et al 2002 Kaminska and Kotynia 2000 Kaminska and Kotynia 2000 Kaminska and Kotynia 2000 Kaminska and Kotynia 2000 Khomwan et al 2004 Kotynia and Kaminska 2003 Kotynia and Kaminska 2003 Kotynia and Kaminska 2003 Matthys 2000 Matthys 2000 Matthys 2000 Matthys 2000 Matthys 2000 modulus CFRP CFRP CFRP CFRP CFRP CFRP sheets CFRP HM Strips CFRP CFRP CFRP CFRP sheets CFRP sheets CFRP CFRP 165000 165000 CFRP strips CFRP CFRP CFRP CFRP strips CFRP strips CFRP strips CFRP strips CFRP strips 155000 230000 62000 62000 155000 240000 200000 235000 235000 235000 49250 28333 165000 165000 1.20 1.20 160000 65400 172000 220000 159000 159000 159000 159000 159000 ply number thickness of plies tf n mm # 1.40 0.17 1.04 1.04 1.19 0.111 1.4 0.11 0.11 0.11 1.90 0.13 1.20 1.20 1 1.40 0.38 1.20 1.40 1.20 1.20 1.20 1.20 1.20 2 2 1 1 1 1 80 80 1 1 1 width bf mm rupture strain efu ue span of FRP L mm 200 75 50 50 50 70 20 150 150 150 152 152 40 80 17000 17000 240 150 50 120 100 100 100 100 100 18000 15000 12000 12000 14000 15000 11000 14894 14894 14894 14000 12000 17000 17000 198000 198000 14000 15000 17000 12400 18500 18500 18500 18500 18500 8540 2338 2744 2744 2744 1740 1740 940 940 940 1474 1474 2700 2700 2700 2700 5500 4100 4100 4100 3700 3700 3700 3700 3700 Adhesive type Fyfe MBrace Resin Sikadur30 Sikadur30 Sikadur30 Sikadur30 MBrace Resin Sikadur30 Sikadur30 Sikadur30 shear modulus Ga MPa failure type FRP strain at debond ue 750 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1624 1624 FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP Rupture FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding 9400 7200 7600 7000 4800 8070 6870 7834 7100 5868 6700 11000 5800 5400 5000 5500 9800 6810 6170 5060 6700 7200 6800 5700 5800 1000 1624 1624 1624 1000 1000 1000 1000 1000 384 ▐ Appendix C: IC Debonding Database Reference No 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 Pan and Leung 2005 Pan and Leung 2005 Quattlebaum et al 2005 Rahimi & Hutchinson 2001 Rahimi & Hutchinson 2001 Rahimi & Hutchinson 2001 Reeve 2005 Reeve 2005 Reeve 2005 Reeve 2005 Saadatmanesh 1991 Spadea et al 1997 Yao et al 2005 Yao et al 2005 Yao et al 2005 Zhang et al 2003 Zhang et al 2003 Zhang et al 2003 Zhang et al 2003 Zhang et al 2003 Zhang et al 2003 Zhang et al 2003 Current Study Current Study Current Study Current Study specimen B5 B6 CS A5 B3 B6 L1 L2 L2x1 L4 B A3.1 III-1 III-2 III-4 A-C1 A-AT A-AK B-C1 B-C2 B-AT B-AK EB1SB EB1SB2 EB8SB EB9SB max height width ds h mm 200 200 254 150 150 150 250 250 250 250 455 300 155 156.5 153.5 250 250 250 400 400 400 400 432 432 432 432 825 150 b mm 150 150 152 200 200 200 150 150 150 150 205 140 203 199 150.1 150 150 150 150 150 150 150 127 127 127 127 350 120 ds mm 180 180 228.6 120 120 120 225 225 225 225 400 275 121 122.5 122 210 210 210 360 360 360 360 683.6 120 test span L mm 2000 2000 4600 2100 2100 2100 4537 4537 4537 4537 4880 4800 2000 2000 2000 2600 2600 2600 2600 2600 2600 2600 8928 8928 8928 8928 8840 1500 shear span a mm 750 750 2300 750 750 750 2269 2269 2269 2269 1982 1800 1000 1000 1000 1050 1050 1050 1050 1050 1050 1050 4337 4337 4337 4337 4420 550 a/h 3.75 3.75 9.06 5.00 5.00 5.00 9.07 9.07 9.07 9.07 4.36 6.00 6.45 6.39 6.51 4.20 4.20 4.20 2.63 2.63 2.63 2.63 10.04 10.04 10.04 10.04 9.074 2.625 concrete strength fc' MPa 42.9 42.9 29.9 54 54 54 23.3 23.3 23.3 23.3 35 24.9 22.1 20.9 22.1 31.5 31.5 31.5 31.5 31.5 31.5 31.5 61.4 61.4 61.4 61.4 55.2 20.9 bar size mm 10 10 12.7 10 10 10 12.7 12.7 12.7 12.7 25 16 10 10 10 16 16 16 16 16 16 16 varies varies varies varies 25 Tension Steel number reinforcing yield ratio strength p fy MPa 0.0052 531 0.0052 531 0.0098 446 0.0052 575 0.0052 575 0.0052 575 0.0101 429 0.0101 429 0.0101 429 0.0101 429 0.0105 456 0.0096 435 0.0050 346 0.0050 373 0.0068 351 0.0107 407 0.0107 407 0.0107 407 0.0067 407 0.0067 407 0.0067 407 0.0067 407 varies 0.00418 1241 varies 0.00418 1241 varies 0.00418 1241 varies 0.00418 1241 0.02619 590 0.00349 288 385 ▐ Appendix C: IC Debonding Database Longitudinal FRP FRP type Reference No 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 Pan and Leung 2005 Pan and Leung 2005 Quattlebaum et al 2005 Rahimi & Hutchinson 2001 Rahimi & Hutchinson 2001 Rahimi & Hutchinson 2001 Reeve 2005 Reeve 2005 Reeve 2005 Reeve 2005 Saadatmanesh 1991 Spadea et al 1997 Yao et al 2005 Yao et al 2005 Yao et al 2005 Zhang et al 2003 Zhang et al 2003 Zhang et al 2003 Zhang et al 2003 Zhang et al 2003 Zhang et al 2003 Zhang et al 2003 Current Study Current Study Current Study Current Study max CFRP sheets CFRP sheets CFRP CFRP CFRP CFRP CFRP CFRP CFRP CFRP GFRP CFRP strips CFRP CFRP CFRP CFRP sheets AFRP sheets AFRP sheets CFRP sheets CFRP sheets AFRP sheets AFRP sheets CFRP CFRP CFRP CFRP CFRP GFRP, AFRP modulus Ef MPa 235000 235000 155000 127000 127000 127000 155000 155000 155000 155000 37200 152000 257000 257000 257000 230000 78500 118000 230000 440000 78500 118000 164785 164785 95834 95834 440000 1.2 ply number thickness of plies tf n mm # 0.22 0.22 1.40 0.80 0.40 1.20 1.40 1.40 1.40 1.40 6.00 1.20 0.165 0.165 0.165 0.17 0.38 0.29 0.17 0.19 0.38 0.29 1.194 1.194 2.032 2.032 80 0.11 width bf mm 150 150 50 150 150 150 25 50 50 100 152 80 50 100 50 130 130 130 130 130 130 130 102 102 102 102 17000 20 rupture strain efu ue 17872 17872 18000 12100 12100 12100 18000 18000 18000 18000 10753 15789 17600 17600 17600 14800 29900 17500 14800 5500 29900 17500 17000 17000 10000 10000 198000 5500 span of FRP L mm 1700 1700 4400 1330 1330 1330 4337 4337 4337 4337 4260 4700 1800 1800 1800 2400 2400 2400 2400 2400 2400 2400 8230 8230 8230 8230 8540 940 Adhesive type Fyfe Sikadur23 Sikadur23 Sikadur23 Sikadur23 Sikadur 30 Sikadur 30 Fyfe Fyfe shear modulus Ga MPa 1000 1000 750 1000 1000 1000 807 807 807 807 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 failure type FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP debonding FRP Rupture FRP debonding FRP debonding FRP debonding FRP Rupture FRP debonding FRP debonding FRP debonding FRP debonding FRP Rupture FRP debonding FRP strain at debond ue 10489 9399 6400 7200 9700 5500 5300 6688 7878 6595 5200 7000 5508 7692 11291 14800 17342 13825 8880 5500 10465 10675 10600 10000 9500 8680 17342 4800 386 ... reinforcement, 5) FRP repair of prestressed concrete, 6) Fatigue behavior of reinforced /prestressed concrete, 7) Fatigue behavior of reinforced /prestressed concrete strengthened with FRP materials,... FRP systems and failure mechanisms, 2) History of FRP strengthening, 3) FRP strengthening of reinforced and prestressed concrete structures, 4) The use of near surface mounted (NSM) FRP reinforcement,... the behavior of retrofitted prestressed concrete, with most of the studies focusing on retrofitted reinforced concrete There exist several differences between reinforced and prestressed concrete