Republic of Iraq Ministry of Higher Education And Scientific Research University of Technology
Behavior of R C Corbels Strengthened with CFRP under Monotonic and Repeated Loading A Thesis Submitted to the Department of Building and Construction Engineering of the University of Technology as a Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Structural Engineering
By:
Layla Ali-Ghalib Yassin BSc in Civil Engineering 1986 – University of Baghdad MSc in Structural Engineering 2006 – University of Technology
Supervised by:
Assist.Prof.
Assist.Prof.
Dr. Eyad K, Sayhood
Dr. Qais A. Hasan
Baghdad
December / 2016
بسـ ـ ـم الل الرحمن الرحيم
" و توكل على الل و كفى بالل وكيال "
صدق الل العلـ ـي العظيم سورة األحزاب آية []3
Supervisors’ Certification We certify that, this thesis titled “Behavior of R C Corbels Strengthened with CFRP under Monotonic and Repeated Loading” was prepared by Layla Ali Ghalib Yassin under our supervision at the University of Technology as a partial fulfillment of the requirements for the Degree of Doctor of Philosophy in Structural Engineering.
Assist. Prof. Dr. Eyad K. Sayhood Date: / /2016
Assist. Prof. Dr. Qais A. Hasan Date: / /2016
In view of the available recommendations, I forward this thesis for discussion by examining committee.
Assist. Prof. Dr. Eyad K. Sayhood Head of Structural Engineering Branch Building and Construction Eng. Dept. University of Technology Date: / /2016
Linguistic Certificate
I certify that this thesis entitled “Behavior of R C Corbels Strengthened with CFRP under Monotonic and Repeated Loading” was prepared under my linguistic supervision. Its language was amended to meet the style of the English language.
Signature: Name: Dr. Najem A. Al-Rubaiey Title: Assistant Professor Address: University of Technology Date: 03 / 10 / 2016
Certification of the Examining Committee We certify that we have read the thesis titled “Behavior of R C Corbels Strengthened with CFRP under Monotonic and Repeated Loading” and as an examining committee we examined the student “Layla Ali-Ghalib Yassin” in its contents and in what is concerned with it and that in our opinion it meets the standards of a thesis for the degree of Doctor of Philosophy in Structural Engineering, with the grade of Distinction.
Assist. Prof. Dr. Eyad K. Sayhood (Supervisor and Member) Date: /12/2016
Assist. Prof. Dr. Qais A. Hasan (Supervisor and Member) Date: /12/2016
Assist. Prof. Dr. Waleed A. Waryosh (Member) Date: /12/2016
Assist. Prof. Dr. Abbas A. Allawi (Member) Date: /12/2016
Assist. Prof. Dr. Iqbal N. Gorgis (Member) Date: /12/2016
Assist. Prof. Dr. Nisreen S. Mohammed (Member) Date: /12/2016
Prof. Dr. Kaiss F. Sarsam (Chairman) Date: /12/2016
Approved by the Head of the Building & Construction Engineering department of the University of Technology.
Prof. Dr. Riyad Hassan Al-Anbari (Head of Building and Construction Eng. Dept.) Date: / /2016
Dedication I Would Like To Dedicate This Work To The Souls of My Parents…… My Beloved Father, The First Person that Set My Steps on the Field of Engineering and Kept Encouraging and Supporting Me till the End of His Life. My Beloved Mother, Who Was with Me When I Started My PhD Study, but Unfortunately Passed Away before it was Ended. Without Her Prayers and Love, Which Made Everything Almost Possible, I Wouldn’t Have Reached this Stage of My Life God Bless Your Souls, Mom & Dad
Layla Yassin
Acknowledgement
IN THE NAME OF ALLAH, THE MOST COMPASSIONATE, THE MOST MERCIFUL First of all my great thanks be to ALLAH for enabling me to complete this work. Then I would like to express my sincere appreciation and deepest gratitude to Dr. Eyad K. Sayhood and Dr. Qais A. Hasan, whom I had the honor of being under their supervision. Their inspiration, rewarding discussions,
patience
and
continuous
encouragement
are
highly
acknowledged throughout this research. My thanks are due to both the Building and Construction Eng. Dept. at the University of Technology and the Civil Eng. Dept. at Al-Nahrain University for enabling me to perform the experimental part of this study at their laboratories. Thanks are also due to the staff of the concrete and structural labs at the Building and Construction Eng. Dept., their support helped me to accomplish my goal. Thanks and appreciations are due to my PhD colleagues for their help, support and criticism of my research work in general. Finally, I would like to express my thanks to my family for supporting me during the years of my PhD study without that support I would not have reached this stage. Layla Yassin
Abstract Previous studies, dealt with reinforced concrete corbels, have concentrated on the monotonic type of loading; few researches have dealt with non-strengthened or strengthened structures under the influence of reversed or non-reversed repeated loads. The progress in using composite strengthening materials, such as woven carbon fiber fabrics, to strengthen existing structures, due to changes in design, increasing in loading or a desire to repair deterioration that has taken place over the years of use, was one of the reasons that led to carry out this research work. The present study has included two parts: experimental and analytical. The aim was to investigate the effectiveness of using carbon fiber fabric materials to increase the load carrying capacity of corbels subjected to nonreversed repeated loading regimes. The experimental part has included the casting of 20 normalweight reinforced concrete corbels, having the same dimensions, flexural reinforcement and horizontal shear reinforcement; some of these corbels were externally strengthened with carbon fiber fabric strips. The corbels were divided into two groups according to the type of loading. The first group included 6 corbels tested under monotonic loading, while the second group included 14 corbels tested under non-reversed repeated loading. The studied variables were: the width and configuration of the carbon fabric strips and the load history schemes that have been used to apply the non-reversed repeated loading. While the analytical part has included using a 3D finite element methodology in the ANSYS-15 software to simulate the behavior of ten reinforced concrete corbels subjected to both monotonic and repeated loading regimes and checking whether the models chosen were adequate to model the
I
same response of the experimental tested members. The results of the experimental and analytical parts have showed that the external strengthening with carbon fiber fabric strips have enhanced the capacity of corbels. This enhancement, for the corbels strengthened with 50 mm strips and tested under monotonically applied loads, was 11%, 15% and 27% for the horizontal, inclined and mixed configurations respectively. While for the non-reversed repeated loaded corbels, the enhancement in the load carrying capacity was about 11%, 18% and 21% for the horizontal, inclined and mixed configurations respectively. For the non-reversed repeated loaded specimen, a strength gain has been recorded with increasing width of strengthening strips from 50 mm to 150 mm, this gain, ranged between of 11% to 24% for horizontal configuration, 18% to 25% for inclined configuration and 21% to 29% for mixed configuration. The ANSYS software has been used to model the failure mechanism for the reinforced concrete corbels strengthened with woven carbon fiber fabric strips; the results of simulating the behavior of these corbels under both monotonic and repeated loading regimes has agreed well with the experimental results, the differences recorded ranging between 1% and 14% for the ultimate loads and between 1% and 16% for the ultimate deflections.
II
Contents Subject ABSTRACT CONTENTS LIST OF FIGURES LIST OF PLATES LIST OF TABLES NOTATIONS, SYMBOLS AND ABBREVIATIONS 1. INTRODUCTION. 1.1. General: Reinforced Concrete Brackets or Corbels. 1.1.1. Steel Reinforcement of Reinforced Concrete Corbels. 1.1.2. Methods for Calculating the Load Carrying Capacity of Corbels. 1.1.3. Structural Behavior and Strength of Corbels. 1.1.4. Failure Mechanisms of Corbels. 1.2. Strengthening of Reinforced Concrete Structures. 1.2.1. Carbon FRP (CFRP) as a Strengthening Technique. 1.3. Reinforced Concrete Corbels under Repeated Loading. 1.4. Aim of the Present Study. 1.5. Layout of the Thesis. 2. LITERATURE REVIEW. 2.1. General. 2.2. Normalweight Reinforced Concrete Corbels under Monotonic Loading. 2.3. High Strength Reinforced Concrete Corbels, with or w/o Fibers, under Monotonic Loading. 2.4. Reinforced Concrete Corbels under Repeated Loading. 2.5. Researches on Strengthened Reinforced Concrete Corbels. 2.6. Summary and Conclusions. 3. EXPERIMENTAL WORK: 3.1. General. 3.2. Experimental Program. 3.2.1. Dimensions. 3.3. Test Variables. 3.4. Designation of Specimens. 3.5. Material Properties. III
Page I III VIII XIV XVI XIX 1 1 2 3 3 4 5 6 8 8 8 10 10 10 27 40 44 54 57 57 57 57 59 60 60
Subject 3.5.1. Cement. 3.5.2. Fine Aggregate. 3.5.3. Coarse Aggregate. 3.5.4. Water. 3.5.5. Steel Reinforcement. 3.5.6. Strengthening Materials. 3.5.7. Adhesive Materials. 3.5.8. Coating Materials. 3.6. Test Instrument Details. 3.6.1. Forms. 3.6.2. Strain Gauges. 3.7. Mix Design. 3.8. Concrete Specimens. 3.8.1. Control Specimens. 3.8.2. Installation of Strain Gauges on Steel Reinforcement. 3.9. Casting and Curing. 3.9.1. Mixing Procedure. 3.9.2. Casting and Curing of Main and Control Specimens. 3.10. Strengthening System. 3.11. Installation of Strain Gauges on Concrete and Carbon Fiber Fabric. 3.12. Data Recording. 3.13. Test Set-Up. 3.14. Loading Regimes. 3.14.1. Monotonic Loading Regime. 3.14.2. Non-Reversed Repeated Loading Regime. 4. EXPERIMENTAL RESULTS AND DISCUSSION 4.1. General. 4.2. Properties of Hardened Concrete Used in this Research. 4.2.1. The Cylinder Compressive Strength. 4.2.2. The Modulus of Elasticity. 4.2.3. The Splitting Tensile Strength. 4.2.4. The Flexural Strength. 4.3. Response of Specimens Tested under Monotonic Loading Regime. 4.3.1. Crack Pattern and Modes of Failure. IV
Page 62 63 64 65 65 67 68 69 69 69 71 72 73 73 74 75 76 76 78 80 81 82 85 85 85 88 88 88 89 89 90 90 94 94
Subject 4.3.2. Effect of Strengthening Technique on Cracking and Failure Loads. 4.3.3. Load-Displacement Response. 4.4. Response of Specimen Tested under Non-Reversed Repeated Loading Regime. 4.4.1. Crack Pattern and Modes of Failure. 4.4.2. Effect of Non-Reversed Repeated Loading Regime. 4.4.2.1. With Respect to Monotonic Tested Specimens. 4.4.2.2. With Respect to Strengthening Technique. 4.4.3. Effect of the Width of CFRP Strips. 4.4.4. Effect of the Orientation of CFRP Strips. 4.4.5. Load-Displacement Response. 4.5. Strain Records in Steel Reinforcement, Concrete and CFRP Strips. 4.5.1. Strain Records in Steel Reinforcement. 4.5.2. Surface Strain Records in Concrete. 4.5.3. Strain Records in CFRP Strips. 5. FINITE ELEMENT MODELING. 5.1. General. 5.2. Experimental Corbel used for Calibration. 5.3. Building the Model. 5.3.1. Element Types and Options. 5.3.1.1. Concrete Representation. 5.3.1.2. Reinforcement Representation. 5.3.1.3. CFRP Sheets Representation. 5.3.1.4. Using Surface-to-Surface Contact Element 5.3.1.5. Steel Plates Representation. 5.3.2. Real Constants. 5.3.3. Material Properties. 5.3.3.1. Concrete, Solid65 Element. 5.3.3.1.1. Failure Criteria for Concrete. 5.3.3.2. Steel Reinforcement Bars, Link180 Element. 5.3.3.3. Steel Plates for Loads and Supports, Solid45 Element. 5.3.3.4. CFRP Strips, Shell181 Element. 5.3.4. Modeling and Meshing. V
Page 97 98 99 102 109 110 112 113 116 119 129 129 135 144 151 151 153 154 154 155 155 157 159 160 161 163 163 164 167 170 170 171
Subject 5.3.5. Numbering Controls. 5.4. Loads and Boundary Conditions. 5.4.1. Analysis Type within the Theory of the Finite Element Method. 5.4.1.1. Static Analysis Type. 5.4.1.2. Modal Analysis Type. 5.4.1.3. Transient Analysis Type. 5.5. Building the Model. 5.6. Load-Time Histories of the Transient Analysis. 6. Results of FE Analysis for Reinforced Concrete Corbels 6.1. General. 6.2. Verification of Calibration Model, M0W. 6.3. Results of FE Analysis for Reinforced Concrete Corbels. 6.3.1. Crack Patterns and Modes of Failures. 6.3.1.1. Specimen M-50-H. 6.3.1.2. Specimens M-50-I and M-50-HI. 6.3.1.3. Transient Specimens. 6.3.2. Load versus Deflection Results. 6.3.3. Concrete and CFRP Strain and Stress Distributions. 7. CONCLUSIONS AND RECOMMENDATIONS. 7.1. General. 7.2. Conclusions. 7.2.1. Conclusions Drawn from the Experimental Phase. 7.2.2. Conclusions Drawn from the Analytical Phase. 7.3. Recommendation for Future Work. REFERENCES APPENDIX A A. Finite Element Method Concepts. A.1. The Finite Element Method Steps. A.2. Types of Analysis in FEM. A.2.1 Static Analysis. A.2.1.1 The Shape Function. A.2.1.2 The Displacement Function. A.2.1.3 Strain-Displacement Relations. A.2.1.4 Stress-Strain Relations. A.2.1.5 Stiffness Matrix [Ke]. VI
Page 177 177 178 180 183 185 187 188 191 191 191 195 195 195 196 197 197 202 205 205 205 205 207 208 209 A-1 A-1 A-1 A-4 A-4 A-4 A-6 A-6 A-7 A-8
Subject A.2.1.6 Mass Stiffness Matrix Derivation, [M] A.2.2 Nodal Analysis. A.2.2.1 Eigenvalue Problems Solution. A.2.2.2 Eigenvector Problems Solution. A.2.3 Transient Analysis. A.2.3.1 Central Difference Algorithm. A.2.3.2 The Newmark’s Method. APPENDIX B B. The Modal Analysis. B.1. Modal Analysis for case 2 – M50H. B.2. Modal Analysis for case 3 – M50I. B.3. Modal Analysis for case 4 – M50HI. B.4. Time Step, ∆t. APPENDIX C C. Properties of the strengthening materials used. C.1. SikaWrap®-300. C.2. Sikadur®-330.
VII
Page A-10 A-11 A-11 A-11 A-12 A-13 A-15 B-1 B-1 B-1 B-2 B-3 B-4 C-1 C-1 C-1 C-5
List of Figures Figure
Description
Page
CH-1 (1.1) (1.2) (1.3) CH-2
Typical Reinforced Concrete Corbel: Loads and Reinforcement Strut-and-Tie Model for Internal Forces Failure Mechanism in Corbels
1 3 5
(2.1)
Simple Truss Analogy by (Franz and Niedenhoff) for the Design of Concrete Corbels Basis for Shear-Friction Theory of Mast Refined Strut and Tie Model, (Siao, 1994) Verification in Calculated Shear Strengths Produced by Amount of Horizontal Hoops, fc’ and av/d ratio, (Hwang et al, 2000) (a) Geometry of RC Corbels and (b) Strut-and-Tie Model with Forces Acting on Corbel, (Russo et al, 2006) Strut-and-Tie Method for Concrete Corbels, (He et al, 2012) Flexural Model, (Fattuhi, 1994) Truss Model, (Fattuhi, 1994) Test Arrangement, (Bourget et al, 2001) Geometry of the Corbels, (Ahmad and Shah, 2009) Equivalent Truss Model, (Campione, 2009) Full Scale Beam-Column Joint Sub-Assemblage and Loading Regime, (Dora and Abdul Hamid, 2012) Geometry of Corbels and Details of Steel Reinforcement, (Campione et al., 2005) Equivalent Truss Model, (Campione et al., 2005) GFRP Wrapping Configurations, (Ozden, S. and Atalay, H. M., 2011) Layout of the External Composite Reinforcements, (El-Maaddawy et al, 2014) Details and Dimensions of Corbels Tested, (Ivanova et al, 2014) Design and Strengthening Configurations of Testing Specimen, (Ivanova and Assih, 2015)
11
Details of Research Specimens Schematic Test Set Up, Inverted Position Grading of Fine Aggregate Grading of Coarse Aggregate Locations of Steel Strain Gauges Non-Reversed Repeated Load History Scheme1, LH1
58 59 64 65 74 87
(2.2) (2.3) (2.4) (2.5) (2.6) (2.7) (2.8) (2.9) (2.10) (2.11) (2.12) (2.13) (2.14) (2.15) (2.16) (2.17) (2.18)
14 21 22 25 27 32 32 35 37 37 43 46 48 49 52 53 54
CH-3 (3.1) (3.2) (3.3) (3.4) (3.5) (3.6)
VIII
Figure
Description
Page
(3.7) (3.8) CH-4
Non-Reversed Repeated Load History Scheme2, LH2 Non-Reversed Repeated Load History Scheme3, LH3
87 87
(4.1)
Effect of CFRP Strips Configuration on the Cracking and Failure Loads of Group M The Load-Deflection Curves of Group M Effect of Non-Reversed Repeated Loading Regimes on the Cracking and Failure Loads of Group RH Effect of Width of CFRP strips on the Cracking and Failure Loads of Group RH Effect of Width of CFRP strips on the Cracking and Failure Loads of Group RI Effect of Width of CFRP strips on the Cracking and Failure Loads of Group RHI Effect of Configuration of CFRP strips on the Cracking and Failure Loads of R-50-H-3, R-50-I-3 and R-50-HI-3 Specimens Effect of Configuration of CFRP strips on the Cracking and Failure Loads of R-100-H-3, R-100-I-3 and R-100-HI-3 Specimens Effect of Configuration of CFRP strips on the Cracking and Failure Loads of R-150-H-3, R-150-I-3 and R-150-HI-3 Specimens The Load-Deflection Curves of R-0-W-1 The Load-Deflection Curves of R-0-W-2 The Load-Deflection Curves of R-0-W-3 The Load-Deflection Curves of R-50-H-1 The Load-Deflection Curves of R-50-H-2 The Load-Deflection Curves of R-50-H-3 The Load-Deflection Curves of R-100-H-3 The Load-Deflection Curves of R-150-H-3 The Load-Deflection Curves of R-50-I-3 The Load-Deflection Curves of R-100-I-3 The Load-Deflection Curves of R-150-I-3 The Load-Deflection Curves of R-50-HI-3 The Load-Deflection Curves of R-100-HI-3 The Load-Deflection Curves of R-150-HI-3 Load-Strain Curves for Main Steel Reinforcement in Monotonically Loaded Specimens, Group M Load-Strain Curves for Main Steel Reinforcement for Specimen R-0-W-1, Tested under LH1 Load-Strain Curves for Main Steel Reinforcement for Specimen R-0-W-2, Tested under LH2 Load-Strain Curves for Main Steel Reinforcement for Specimen R-0-W-3, Tested under LH3 Load-Strain Curves for Main Steel Reinforcement for Specimen R-50-H-1, Tested under LH1 Load-Strain Curves for Main Steel Reinforcement for Specimen IX
98
(4.2) (4.3) (4.4) (4.5) (4.6) (4.7) (4.8)
(4.9)
(4.10) (4.11) (4.12) (4.13) (4.14) (4.15) (4.16) (4.17) (4.18) (4.19) (4.20) (4.21) (4.22) (4.23) (4.24) (4.25) (4.26) (4.27) (4.28) (4.29)
99 111 115 116 116 118 118 119 121 122 122 123 123 124 124 125 125 126 126 127 127 128 130 131 131 131 132 132
Figure (4.30) (4.31) (4.32) (4.33) (4.34) (4.35) (4.36) (4.37) (4.38) (4.39) (4.40) (4.41) (4.42) (4.43) (4.44) (4.45) (4.46) (4.47) (4.48) (4.49) (4.50) (4.51) (4.52) (4.53)
Description R-50-H-2, Tested under LH2 Load-Strain Curves for Main Steel Reinforcement for R-50-H-3, Tested under LH3 Load-Strain Curves for Main Steel Reinforcement for R-100-H-3, Tested under LH3 Load-Strain Curves for Main Steel Reinforcement for R-150-H-3, Tested under LH3 Load-Strain Curves for Main Steel Reinforcement for R-50-I-3, Tested under LH3 Load-Strain Curves for Main Steel Reinforcement for R-100-I-3, Tested under LH3 Load-Strain Curves for Main Steel Reinforcement for R-150-I-3, Tested under LH3 Load-Strain Curves for Main Steel Reinforcement for R-50-HI-3, Tested under LH3 Load-Strain Curves for Main Steel Reinforcement for R-100-HI-3, Tested under LH3 Load-Strain Curves for Main Steel Reinforcement for R-150-HI-3, Tested under LH3 Locations of Strain Gauges Fixed on Concrete Load-Strain Curves in Concrete Compression Zone for M-0-W Load-Strain Curves in Concrete Compression Zone for M-50-H Load-Strain Curves in Concrete Compression Zone for M-50-I Load-Strain Curves in Concrete Compression Zone for M-50-HI Load-Strain Curves in Concrete Compression Zone for R-0-W-3 Load-Strain Curves in Concrete Compression Zone for R-0-W-1 Load-Strain Curves in Concrete Compression Zone for R-0-W-2 Load-Strain Curves in Concrete Compression Zone for R-50-H-1 Load-Strain Curves in Concrete Compression Zone for R-50-H-2 Load-Strain Curves in Concrete Compression Zone for R-50-H-3 Load-Strain Curves in Concrete Compression Zone for R-100-H-3 Load-Strain Curves in Concrete Compression Zone for R-150-H-3 Load-Strain Curves in Concrete Compression Zone for R-50-I-3 Load-Strain Curves in Concrete Compression Zone for R-100-I-3 X
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Figure
Description
Page
(4.54)
Load-Strain Curves in Concrete Compression Zone for Specimen R-150-I-3 Load-Strain Curves in Concrete Compression Zone for Specimen R-50-HI-3 Load-Strain Curves in Concrete Compression Zone for Specimen R-100-HI-3 Load-Strain Curves in Concrete Compression Zone for Specimen R-150-HI-3 Locations of Strain Gauges Fixed on CFRP Strips Load-Tensile Strain Curves in CFRP for Specimen M-50-H Load-Tensile Strain Curves in CFRP for Specimen M-50-I Load-Tensile Strain Curves in CFRP for Specimen M-50-HI Load-Tensile Strain Curves in CFRP for Specimen R-50-H-1 Load-Tensile Strain Curves in CFRP for Specimen R-50-H-2 Load-Tensile Strain Curves in CFRP for Specimen R-50-H-3 Load-Tensile Strain Curves in CFRP for Specimen R-100-H-3 Load-Tensile Strain Curves in CFRP for Specimen R-150-H-3 Load-Tensile Strain Curves in CFRP for Specimen R-50-I-3 Load-Tensile Strain Curves in CFRP for Specimen R-100-I-3 Load-Tensile Strain Curves in CFRP for Specimen R-150-I-3 Load-Tensile Strain Curves in CFRP for Specimen R-50-HI-3 Load-Tensile Strain Curves in CFRP for Specimen R-100-HI-3 Load-Tensile Strain Curves in CFRP for Specimen R-150-HI-3
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Typical Load-Displacement Response of RC Element, (Kwak and Filippou, 1990) Geometry of Analytical Model SOLID65 Geometry and Node Locations, (ANSYS Help) Models for Reinforcement in Reinforced Concrete, (Wolanski, 2004) LINK180 Geometry and Node Locations, (ANSYS Help) SHELL181 Geometry and Node Locations, (ANSYS Help) CONTA174 Geometry, (ANSYS Help) TARGE170 Geometry, (ANSYS Help) SOLID45 Geometry and Node Locations, (ANSYS Help) Compressive Uniaxial Stress-Strain Curve of Present Research 3-D Failure Surface for Concrete in Principal Stress Space Stress-Strain Relationship for Steel, (Khudhair, 2014) Schematic of CFR Fabric, (Kachlakev and Miller, 2001) The Concrete Volume for the M0W Specimen Created in ANSYS The Concrete FE Mesh for the M0W Specimen Created in ANSYS
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(4.55) (4.56) (4.57) (4.58) (4.59) (4.60) (4.61) (4.62) (4.63) (4.64) (4.65) (4.66) (4.67) (4.68) (4.69) (4.70) (4.71) (4.72) CH-5 (5.1) (5.2) (5.3) (5.4) (5.5) (5.6) (5.7) (5.8) (5.9) (5.10) (5.11) (5.12) (5.13) (5.14) (5.15)
XI
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153 155 156 157 158 159 160 161 164 165 169 170 172 172
Figure
Description
Page
(5.16) (5.17)
Mesh of the Steel Reinforcement for the Calibration Model The FE Mesh of the Concrete and Steel Reinforcement for the Calibration Model The FE Mesh for the M0W Calibration Model The Contact Properties for the CFRP Strengthened Models The Calibration Model of M50H and R50H Specimens The Calibration Model of M50I and R50I Specimens The CFRP Modeling in M50HI and R50HI Specimens The Calibration Model of M50HI and R50HI Specimens The Loading and Boundary Conditions for the Calibration Model Loading Applied on the Plate for the Calibration Model The Analysis Types Available in the ANSYS Program The First Mode Shape for Case M0W The Second Mode Shape for Case M0W The Third Mode Shape for Case M0W The Fourth Mode Shape for Case M0W The Fifth Mode Shape for Case M0W BEAM188 Geometry, (ANSYS Help) The Simulated Model for Specimen R0W1 Using BEAM188 Element Load-Time Graph of R0W1 Load-Time Graph of R0W2 Load-Time Graph of R0W3 Load-Time Graph of R50H3 Load-Time Graph of R50I3 Load-Time Graph of R50HI3
173 173
Experimental Load-Deflection Curve for the Calibration Model Load-Deflection Relationship of Specimen M-0-W Development of Crack Pattern for the Calibration Model, M0W Comparison between Numerical and Experimental Crack Pattern For Specimen M0W at Failure Deformed Shape at failure for Specimen M-0-W Nodal Solution-UY at failure for Specimen M-0-W Von Mises Stress Distribution at failure for Specimen M-0-W Von Mises Strain Distribution at failure for Specimen M-0-W Experimental and Theoretical Crack Pattern For Specimen M-50-H at Failure Development of Crack Pattern for the Calibration Model, M50H Development of Crack Pattern for Specimen M50I
192 192 193 194
(5.18) (5.19) (5.20) (5.21) (5.22) (5.23) (5.24) (5.25) (5.26) (5.27) (5.28) (5.29) (5.30) (5.31) (5.32) (5.33) (5.34) (5.35) (5.36) (5.37) (5.38) (5.39) CH-6 (6.1) (6.2) (6.3) (6.4) (6.5) (6.6) (6.7) (6.8) (6.9) (6.10) (6.11)
XII
174 175 175 175 176 176 178 178 179 184 184 184 184 184 186 188 189 189 189 190 190 190
194 194 194 194 195 196 197
Figure (6.12) (6.13) (6.14) (6.15) (6.16) (6.17) (6.18) (6.19) (6.20) (6.21) (6.22) (6.23) (6.24) (6.25) (6.26) (6.27) (6.28) (6.29) (6.30) (6.31) (6.32) (6.33) (6.34) (6.35) (6.36) (6.37) (6.38) (6.39) (6.40) (6.41) (6.42) (6.43) (6.44) (6.45) (6.46) (6.47) (6.48)
Description Development of Crack Pattern for Specimen M50HI Load-Deflection Relationship of Specimen M-50-H Nodal Solution-UY at failure for Specimen M-50-H Load-Deflection Relationship of Specimen M-50-I Nodal Solution-UY at failure for Specimen M-50-I Load-Deflection Relationship of Specimen M-50-HI Nodal Solution-UY at failure for Specimen M-50-HI Load-Deflection Relationship of Specimen R-0-W-1 Nodal Solution-UY at failure for Specimen R-0-W-1 Load-Deflection Relationship of Specimen M-50-HI Nodal Solution-UY at failure for Specimen R-0-W-2 Load-Deflection Relationship of Specimen R-0-W-3 Nodal Solution-UY at failure for Specimen R-0-W-3 Load-Deflection Relationship of Specimen R-50-H-3 Nodal Solution-UY at failure for Specimen R-50-H-3 Load-Deflection Relationship of Specimen R-50-I-3 Nodal Solution-UY at failure for Specimen R-50-I-3 Load-Deflection Relationship of Specimen R-50-HI-3 Nodal Solution-UY at failure for Specimen R-50-HI-3 Strain Distribution in Concrete for Specimen M-50-H Stress Distribution in Concrete for Specimen M-50-H Strain Distribution in Concrete for Specimen M-50-I Stress Distribution in Concrete for Specimen M-50-I Strain Distribution in Concrete for Specimen M-50-HI Stress Distribution in Concrete for Specimen M-50-HI Strain Distribution in Concrete for Specimen R-0-W-1 Stress Distribution in Concrete for Specimen R-0-W-1 Strain Distribution in Concrete for Specimen R-0-W-2 Stress Distribution in Concrete for Specimen R-0-W-2 Strain Distribution in Concrete for Specimen R-0-W-3 Stress Distribution in Concrete for Specimen R-0-W-3 Strain Distribution in Concrete for Specimen R-50-H-3 Stress Distribution in Concrete for Specimen R-50-H-3 Strain Distribution in Concrete for Specimen R-50-I-3 Stress Distribution in Concrete for Specimen R-50-I-3 Strain Distribution in Concrete for Specimen R-50-HI-3 Stress Distribution in Concrete for Specimen R-50-HI-3
XIII
Page 197 198 198 198 198 199 199 199 199 199 199 200 200 200 200 200 200 201 201 203 203 203 203 203 203 203 203 203 204 204 204 204 204 204 204 204 204
List of Plates Plate CH-3 (3-1) (3-2) (3-3) (3-4) (3-5) (3-6) (3-7) (3-8) (3-9) (3-10) (3-11) (3-12) (3-13) (3-14) (3-15) (3-16) (3-17) (3-18) (3-19) (3-20) (3-21) (3-22) (3-23) (3-24) (3-25) (3-26) (3-27) CH-4 (4-1) (4-2) (4-3) (4-4)
Description
Page
Reinforcement Caging used for Specimens Sika Wrap®-300 used for Strengthening Sikadur 330, Strengthening Material Adhesive Special Glue for Strain Gauges Special Coating Materials, SB Tape Specimen’s Form Showing its Components Specimen’s Form with Reinforcement Cage Strain Gauges used in this Study Corbels and Control Specimens Produced in One Batch Locations of Steel Strain Gauges TML CN-Y Adhesive The Installation of Strain Gauges on Steel Reinforcement Photos of the Mixer Used in this Research Main and Control Specimens after Casting Photos of Curing Tanks for the Main and Control Specimens All Specimens after Curing Photos of the Strengthening Process The White-Painted Un-Strengthened Specimen The White-Painted Horizontal 50 mm Strengthened Specimens The White-Painted Inclined 50 mm Strengthened Specimens The White-Painted Mixed 50 mm Strengthened Specimens Location of Strain Gauges on Concrete and CFRP The TDS-530 Data Logger Used in this Research Photos of the Testing Frame System Photos of the Loading System Photos of the Supporting System The Test Set-Up
66 67 68 68 69 70 70 72 73 74 75 75 76 77 77 78 79 80 80 80 80 81 82 83 83 84 84
The ADR 3000 Compression Machine with the 100 kN Flexural Testing Frame The EN Standard Testing Machine for the Modulus of Elasticity Test Values and Modes of Failure after the Compressive Strength Test The Modulus of Elasticity Test
91
XIV
91 93 93
Plate
Description
Page
(4-5) (4-6) (4-7)
Mode of Failure after the Splitting Tensile Strength Test The Modulus of Rupture Test The Crack pattern and Mode of Failure for Monotonically Loaded Specimen, M-0-W The Crack pattern and Mode of Failure for Monotonically Loaded Specimen, M-50-H The Crack pattern and Mode of Failure for Monotonically Loaded Specimen, M-50-I The Crack pattern and Mode of Failure for Monotonically Loaded Specimen, M-50-HI The Crack pattern and Mode of Failure for Specimen R-0-W-1 The Crack pattern and Mode of Failure for Specimen R-0-W-2 The Crack pattern and Mode of Failure for Specimen R-0-W-3 The Crack pattern and Mode of Failure for Specimen R-50-H-1 The Crack pattern and Mode of Failure for Specimen R-50-H-2 The Crack pattern and Mode of Failure for Specimen R-50-H-3 The Crack pattern and Mode of Failure for Specimen R-100-H-3 The Crack pattern and Mode of Failure for Specimen R-150-H-3 The Crack pattern and Mode of Failure for Specimen R-50-I-3 The Crack pattern and Mode of Failure for Specimen R-100-I-3 The Crack pattern and Mode of Failure for Specimen R-150-I-3 The Crack pattern and Mode of Failure for Specimen R-50-HI-3 The Crack pattern and Mode of Failure for Specimen R-100-HI-3 The Crack pattern and Mode of Failure for Specimen R-150-HI-3 The Crack Pattern through the Consecutive Cycles for Specimen R-0-W-3
93 93 95
(4-8) (4-9) (4-10) (4-11) (4-12) (4-13) (4-14) (4-15) (4-16) (4-17) (4-18) (4-19) (4-20) (4-21) (4-22) (4-23) (4-24) (4-25)
XV
96 96 97 105 105 105 106 106 106 106 107 107 108 108 108 108 109 110
List of Tables Table
Description
Page
Qualitative Comparison of Different Fibers used in Composite Materials.
6
Values of ( tan ) as given by Mast Average Ratios of the Tested to the Calculated Ultimate Loads Proposed by Abdul-Wahab, 1989
15 29
Details of Research Specimens Chemical Composition and Main Compounds of the Cement Physical Properties of Cement Physical Properties of Fine Aggregate Grading of Fine Aggregate Grading of Coarse Aggregate Properties of the Steel Reinforcement Characteristics of Strain Gauges used in the Present Study Trial Mixes Performed in the Present Study
61 62
Properties of Hardened Concrete at the Age of 28 Days Results of Destructive Tests Performed on Control Specimens (on the date of Test) Results of Main Corbel Specimens Tested under Monotonic Loading Regime (Group M) Effect of Strengthening Technique on the Cracking and Failure Loads for Group M The Details of the Cycles of the Repeated Loading Histories The Amplitudes of the Cycles of the Repeated Loading Histories
91 92
CH-1 (1-1) CH-2 (2-1) (2-2) CH-3 (3-1) (3-2) (3-3) (3-4) (3-5) (3-6) (3-7) (3-8) (3-9) CH-4 (4-1) (4-2) (4-3) (4-4) (4-5) (4-6)
XVI
63 63 64 65 66 71 72
94 97 100 101
Table
Description
Page
(4-7)
Results of Main Corbel Specimens Tested under NonReversed Repeated Loading Regime, (Group R W) Results of Main Corbel Specimens Tested under NonReversed Repeated Loading Regime, (All Groups) Effect of Non-Reversed Repeated loading Regimes on the Cracking Load of Group RLH Effect of Non-Reversed Repeated loading Regimes on the Failure Load of Group RLH Effect of Non-Reversed Repeated Loading Regimes on the Cracking and Failure Loads for Groups RW and RH Effect of CFRP Strips’ Width on the Cracking and Failure Loads for Group RH Effect of CFRP Strips’ Width on the Cracking and Failure Loads for Group RI Effect of CFRP Strips’ Width on the Cracking and Failure Loads for Group RHI Effect of CFRP Strips’ Width on the Cracking and Failure Loads for R-50-H-3, R-100-H-3 and R-150-H-3 Effect of CFRP Strips’ Width on the Cracking and Failure Loads for R-50-I-3, R-100-I-3 and R-150-I-3 Effect of CFRP Strips’ Width on the Cracking and Failure Loads for R-50-HI-3, R-100-HI-3 and R-150-HI-3
102
Properties for Concrete and Steel Reinforcement Element Types for Analytical Study Model Real Constants for Analytical Study Model The Compressive Uniaxial Stress-Strain Values Material Properties for Concrete, Solid65 Element Material Properties for Steel Reinforcement Material Properties for Steel Plates Material Properties for CFR Fabric Specifications and Uses of KEYOPTS Used For the Contact Pair in the Present Study
154 154 162 165 168 169 170 171 176
(4-8) (4-9) (4-10) (4-11) (4-12) (4-13) (4-14) (4-15) (4-16) (4-17)
103 110 110 113 114 114 114 117 117 117
CH-5 (5-1) (5-2) (5-3) (5-4) (5-5) (5-6) (5-7) (5-8) (5-9)
XVII
Table
Description
Page
(5-10) (5-11)
The Number of Elements used in all Strengthened Models The Cases Studied and Corresponding Types of Analysis Performed in the Theoretical Phase Commands used to Control the Basic Tab Commands used to Control the Sol'n Options Tab Commands used to Control the Nonlinear Tab The Results of Modal Analysis for the first case, M0W The Time Step, ∆t, for All Transient Tested Cases
177 180
Comparison between the Theoretical and Experimental Failure Loads for the Calibration Model, M0W Comparison between Numerical and Experimental Results Comparison between Numerical and Experimental Strain in Concrete Comparison between Numerical and Experimental Strain in Concrete
192
(5-12) (5-13) (5-14) (5-15) (5-16) CH-6 (6-1) (6-2) (6-3) (6-4)
XVIII
181 181 182 183 188
201 202 202
Notation, Symbols and Abbreviations The major notations used in the present research are listed below; other notations that are introduced throughout the research are defined as they first appear.
Notation and Symbols a , av a1
av/d Ah An As, Asc Avf b c
d E Eo Ec Ef Es F f c'
f cu
f ct
fr fy f yh
h Mn
Mu
n Nu, Nuc Pn Pu Pcr n
Shear Span, mm Depth of Rectangular Compression Block in Concrete, mm Shear Span-to-Depth Ratio Area of Secondary Reinforcement, Closed Hoop Stirrups, mm2 Area of Reinforcement Required for Resisting Horizontal Tensile Force, Nuc, mm2 Area of Main Reinforcement, Flexural Reinforcement, mm2 Area of Reinforcement Required for Resisting Shear Friction, mm2 Width of Corbel, mm Depth Of The Neutral Axis, mm Effective Depth of Flexural Reinforcement, mm Modulus of Elasticity, MPa Initial Modulus of Elasticity, MPa Modulus of Elasticity of concrete, MPa Modulus of Elasticity of CFRP, MPa Modulus of Elasticity of steel, MPa Steel Fiber Factor Cylindrical Compressive Strength of Concrete at 28 days, MPa Cubic Compressive Strength of Concrete, MPa Splitting Tensile Strength of Concrete, MPa Flexural Strength of Concrete, Modulus of Rapture, MPa Yield Strength of Main Reinforcement, MPa Yield Strength of Secondary Reinforcement, MPa Total Depth of Corbel Nominal Moment at Corbel-Column Interface, kN.m Ultimate Moment at Corbel-Column Interface, kN.m Modular Ratio of Steel and Concrete, n Es Ec Horizontal Force, kN Nominal Load Applied on Column, kN Ultimate Load Applied on Column, kN Applied Load at the appearance of first Crack, kN Shear Stress at Nominal Load, MPa
XIX
u Vn Vu α
c u
y o c cr s , sc h
x, y, z
Shear Stress at Ultimate Load, MPa Shear Force at Nominal Load, kN Shear Force at Ultimate Load, kN Angle of Internal Friction Deflection at Cracking Load, mm Deflection at Ultimate Load, mm Deflection at Yielding of Main Reinforcement, mm Shear Transfer Coefficients for an Open Crack Shear Transfer Coefficients for a Closed Crack Strain Strain at Cracking Load Stress, MPa Strength Reduction Factor Reinforcement Ratio of Main Steel Bars Reinforcement Ratio of Secondary Steel Bars Coefficient of Friction Poisson’s Ratio Global Coordinate System
Abbreviations ACI ANSYS ASTM C C.O.V. EBR FEM HSC I.Q.S LH LVDT NSC PCI RC SF SG STM
American Concrete Institute ANalysis SYStem, Finite Element Analysis Software American Society for Testing and Materials Compression Force Coefficient of Variation Externally Bonded Reinforcing Finite Element Method High Strength Concrete Iraqi Standard Specification Loading History Linear variable differential transformer Normal Strength Concrete Prestress/ Precast Concrete Institute Reinforced Concrete Shear Friction Strain Gauge Strut and Tie Method
XX
Chapter One - Introduction 1.
INTRODUCTION:
1.1. General: Reinforced Concrete Brackets or Corbels: Brackets or corbels are short structural members that cantilever out from a column or wall to support a load. Those members are generally built monolithically with the column or wall; the term “corbel” is generally used for cantilevers having shear span-to-depth ratios, av/d, less than or equal to 1 [1]. Corbels are widely used in precast construction for supporting precast beams at the column. When they project from a wall rather than from a column they are properly called corbels, although the two terms are often used interchangeably
[2]
; the term
corbel will be used throughout this study. In ACI-318M, corbels are considered as simple trusses or deep beams, rather than flexural members designed for shear
[3]
.A
typical reinforced concrete corbel is illustrated in Fig. (1.1).
Fig. (1.1) – Typical Reinforced Concrete Corbel: Loads and Reinforcement [3] The small ratio of (av/d), less than unity, changes the state of stresses of the member into a two-dimensional one. Shear deformations would affect their nonlinear stress behavior in the elastic state and beyond, and the shear strength becomes a major factor. Corbels differ from deep beams in the existence of potentially large horizontal forces transmitted from the supported beam to the corbel Introduction
[4]
. Therefore, it is widely Page 1
Chapter One - Introduction assumed that reinforced concrete corbels are principally shear transfer devices. Conventional design procedures provide horizontal stirrups throughout the corbel depth to improve their shear capacity and reduce the sudden catastrophic failure; examples of such failure are called diagonal splitting failure modes
[5,6]
.
For (av/d) exceeding unity, the diagonal tension cracks are less steeply inclined and the use of horizontal stirrups alone is not appropriate, therefore the ACI-318 suggested that such corbels, with a shear span to depth ratio (av/d) less than 2, shall be permitted to be designed following chapter 23, the Strut-and-Tie Models [3]. Steel bearing plates or angles are generally used on the top surface of the corbels to provide a uniform contact surface and to distribute the reaction. 1.1.1. Steel Reinforcement of Reinforced Concrete Corbels: The steel reinforcement used in reinforced concrete corbels, as shown in Fig. (1.1), includes the following: 1) The primary reinforcement (Asc), flexural reinforcement, which must be carefully anchored because they need to develop their full yield strength (fy) directly under the load (Vu), and for this reason they are usually welded to the underside of the bearing angle and a (90 o) hook is provided for anchorage at the column-corbel interface. 2) The secondary or horizontal reinforcement (Ah), closed hoop stirrups or ties, confine the concrete in the two compression struts, shown in Fig. (1.2), and resist a tendency for splitting in a direction parallel to the thrust. According to the ACI-318, (Ah) must be uniformly distributed within two-thirds of the effective depth adjacent to and parallel to (Asc). 3) Framing bars, of about the same diameter as the horizontal reinforcement, are usually used to improve the stirrup anchorage at the outer face of the bracket.
Introduction
Page 2
Chapter One - Introduction 1.1.2. Methods for Calculating the Load Carrying Capacity of Corbels: The load carrying capacity of reinforced concrete corbels may be calculated by several methods. They include the shear-friction approach, the truss analogy, the geometrical method of force distribution, and the theory of plasticity. The shear friction method is adopted by the ACI-318 Building Code and is generally used in the United States of America, (and will be used throughout this study), while the other methods are used in the European countries [7]. 1.1.3. Structural Behavior and Strength of Corbels: There are two ways in expressing the structural action for a corbel supported by a column, the conventional model of the ACI-318 and the strut-and-tie model. In the latter model, as shown in Fig. (1.2), the structural action consists of an inclined compression strut and a tension tie. Shears induced in the column above and below the corbel are resisted by tension in the column bars and ties and by compression forces in struts between the ties [2].
Fig. (1.2) – Strut-and-Tie model for Internal Forces [2] Corbels are designed mainly to provide for the vertical reaction (Vu) at the end of the supported beam, but unless special precautions are taken to avoid horizontal forces caused by restrained Introduction
Page 3
Chapter One - Introduction shrinkage, creep or temperature change, they must also resist horizontal force (Nuc). They are usually designed for direct shear using the shear friction theory [8].
1.1.4. Failure Mechanisms of Corbels: The earliest scientists who did extensive test programs on corbels were Kris and Raths [6], from these tests the following failure mechanisms were identified: 1) Flexural tension failure that occurs due to the yielding of the flexural reinforcement which causes the crush of concrete at the sloping end of the corbel, as shown in Fig. (1.3 a). 2) Shear compression failure that occurs when diagonal splitting is developed along the diagonal compression strut after the formation of flexural cracks, as shown in Fig. (1.3 b). 3) Sliding shear failure that occurs when a series of short and steep diagonal cracks may lead to the separation of the corbel from the column face as these cracks interconnect, as shown in Fig. (1.3 c). 4) Anchorage Splitting failure that occurs when the load is applied too close to the free end of the corbel causing a splitting failure along the poorly anchored flexural reinforcement, as shown in Fig. (1.3 d). 5) Bearing failure that occurs due to two reasons, either when the bearing plates are too small or very flexible, or when the corbel is too narrow, causing a concrete crush underneath the bearing plate, as shown in Fig. (1.3 e). 6) In the presence of a horizontal force (Nu) in addition to the gravity load (Vu), several of the previous mechanisms are accentuated. This may result from dynamic effect on crane girders, or it may be induced by shrinkage, creep or temperature shortening of restrained precast concrete beams attached to the corbel. A potential failure situation can be arise when the outer face of the
Introduction
Page 4
Chapter One - Introduction corbel is too shallow and an adverse horizontal load is also introduced, as shown in Fig. (1.3 f).
(a) Flexural Tension
(b) Diagonal Splitting
(d) Anchorage Splitting
(e) Crushing due to Bearing
(c) Sliding Shear
(f) Horizontal Tension
Fig. (1.3) – Failure Mechanism in Corbels [8] The detailing requirements of corbels follow directly from the failure mechanisms listed above. It is evident that the vertical stirrups, intended for shear resistance, would be ineffective in all these situations. Comparative tests indicate that some diagonal reinforcement can be used to advantage and that an optimum combination of horizontal and diagonal steel may result in a minimum steel demand
[8]
.
1.2. Strengthening of Reinforced Concrete Structures: The progress in using composite materials in all structural elements and the research papers published in the last three decades showed that there has been a major effort to develop composite material systems. One of the major aspects of using composite material is Structural Strengthening Introduction
[9]
. The motivation to Page 5
Chapter One - Introduction strengthen an existing structure typically comes from changes in design, loading increasing and a desire to repair deterioration that has taken place over the years of use [10]. The use of fiber reinforced polymer (FRP) materials for structural repair and strengthening has continuously increased during previous years, due to several advantages associated with these composites when compared to conventional materials like steel. These benefits include low weight, easy installation, high durability and tensile strength. FRP laminates and sheets are generally applied on the faces of the elements to be strengthened, using externally bonded reinforcing (EBR) technique
[11]
. FRP materials commonly used are carbon, glass or aramid;
these materials have different properties and behavior. A qualitative comparison of the performance of these materials is presented in table (1-1) [10]. Table (1-1) - Qualitative Comparison of Different Fibers used in Materials [10] Criterion Tensile Strength Compressive Strength Young’s Modulus Long-Term Behavior Fatigue Behavior Bulk Density Alkaline Resistance Price
Composite
Type of fibers used in composite Carbon Fibers
Glass Fibers
Aramid Fibers
Very Good Very Good Very Good Very Good Excellent Good Very Good Adequate
Very Good Inadequate Good Good Good Excellent Good Adequate
Very Good Good Adequate Adequate Adequate Adequate Inadequate Very Good
1.2.1. Carbon FRP (CFRP) as a Strengthening Technique: There are many types and shapes of FRP materials which are used in the construction industry as means of external strengthening of concrete or steel elements. Two classes of FRP materials are currently available: plates and sheets. Plates consist of rigid FRP strips which are manufactured using a process called pultrusion, while the sheets are supplied as flexible fabrics of raw fibers. Both Introduction
Page 6
Chapter One - Introduction materials are usually applied onto the concrete or steel surfaces by using an epoxy resin. The FRP sheets used are usually unidirectional, where all fibers are oriented along the length of the sheet [12]. In recent years, carbon and glass FRP sheets have been used as a retrofitting technique to increase concrete confinement and bending resistance of reinforced concrete columns. This increase depends on the thickness (number of layers) and on the material properties of the FRP system as well as on the geometry of columns. EBR techniques using CFRP materials have also been used to increase the shear resistance of reinforced concrete beams [13]. The FRP materials have been considered as one of the most promising materials for the strengthening and retrofitting of existing reinforced concrete elements due to the excellent corrosion resistance, high tensile strength, high strength to weight ratio and an elastic modulus comparable to steel [14]. Extensive research focusing on the increase in the strength and mechanism of de-bonding of the plate and concrete, ripping-off of concrete beams strengthened with CFRP plates, were carried out
[15,16,17]
, some guidance has been published to assist engineers in the design
process [16,18,19]. It is understood that the failure of CFRP beams is dependent on the interaction behaviors of the plate, adhesive, concrete cover and the reinforcing bars. There are many reasons for upgrading structures such as using considerations (e.g. change in loading requirements), environmental conditions (e.g. chemical attack and reinforcement corrosion), construction and material shortcomings (e.g. incorrect placing of reinforcement, use of wrong size or grade of reinforcement, insufficient lap length at splices or insufficient transversal reinforcement such as hoops, ties, or spirals, and poor construction practices) [9].
Introduction
Page 7
Chapter One - Introduction The present research is carried out to investigate the effectiveness of using CFRP materials to increase the load carrying capacity of corbels subjected to non-reversed repeated loads. 1.3. Reinforced Concrete Corbels under Repeated Loading: Most of the recent researches performed on corbels were restricted to the case of monotonic loading. In practice there are many cases in which structural elements are subjected to repeated loading, such as corbels holding cranes in factories, or corbels supporting girders in bridges as well as structural elements with large live load to dead load ratio, or subjected to hurricanes or earthquakes. These types of loading produce higher strain, and shear distress at critical sections. Using precast concrete in seismic areas requires the development of an adequate connector between the precast members, which must exhibit high flexural strength, ductility and large energy absorbing capacities [20]. Therefore, studying the effect of repeated loading system on such structural member is of interest to researchers. 1.4. Aim of the Present Study: The main objective of the present study is to investigate the effectiveness of using CFRP as an external strengthening technique to increase the load carrying capacity of existing corbels subjected to non-reversed repeated loads. While extensive researches have been done on corbels, with or without strengthening, corbels subjected to non-reversed repeated loads have received very little attention from researchers. This thesis presents results of an experimental and analytical investigation on the behavior of reinforced concrete corbels strengthened with CFRP strips and subjected to two types of loading, monotonic and repeated 1.5. Layout of the Thesis: This thesis consists of seven chapters which can be summarized as follows: 1) Chapter one introduces an introduction to the subject. Introduction
Page 8
Chapter One - Introduction 2) Chapter two introduces a general outline of previous work performed on reinforced concrete corbels with or without strengthening. 3) Chapter three, deals with the experimental phase of the thesis describing the experimental program and test setup. Details of the tested corbels, material properties, concrete mix design, and test program are also described. 4) Chapter four discusses the results of the experimental phase. 5) Chapter five presents the analytical phase of the thesis, including the finite element formulation and nonlinear solution techniques as well as the modeling of material properties used in this part of the study. 6) Chapter six discusses the results obtained from the FE analysis for the reinforced concrete corbels and a comparison is made between experimental and analytical results. 7) Finally, chapter seven presents the conclusions drawn from the two phases of the present study with recommendations for future work.
Introduction
Page 9
Chapter Two – Literature Review 2.
LITERATURE REVIEW:
2.1. General: As mentioned before in chapter one, corbels are considered as short structural members. The nonlinear stress behavior of these short members is affected by the shear deformation in the elastic range and consequently the shear strength of the section becomes an important parameter for design consideration
[21]
.
The principal failure mode for corbels reinforced with main and secondary reinforcements (stirrups) is referred to as beam-shear failure, which is characterized by the opening of one or more diagonal cracks followed by shear failure in the compressed zone of the strut [22]. The Shear-friction concept has physical applications in reinforced concrete connections such as corbels, where Shear-friction forces must be assured at the connection interface. In recent years, repair and new design techniques for strengthening reinforced concrete structures have been developed using carbon fiber reinforced polymer (CFRP) composites [23]. This chapter presents a brief review on the experimental researches carried out on corbels in general and strengthening of corbels in particular. 2.2. Normalweight Reinforced Concrete Corbels under Monotonic Loading: Several researchers had studied the behavior and strength of reinforced concrete corbels with principal and secondary reinforcement. The effect of different variables on the behavior of corbels was investigated. One of the earliest researches in this domain was performed by (Franz and Niedenhoff, 1963)
[24]
, who presented the
simplest form of truss analogy for corbel design. They considered the corbel as a simple Strut-and-Tie system subjected to an external force V. This concept is illustrated in Fig. (2.1). The tensile force, Ft, which was slightly inclined, was assumed to be horizontal for design purposes. This force was calculated by equation (2-1). Literature Review
Page 10
Chapter Two – Literature Review
z= 0.85d
av
V
Ft Fc
d
h
Fig. (2.1) - Simple Truss Analogy by (Franz and Niedenhoff) for the Design of Concrete Corbels [25] Ft
V av z
…… (2-1)
Where Ft, the tensile force, kN, z, mm, was considered as 0.85d and the area of main steel (Ast), mm2, required for resisting force (V), kN, was calculated by equation (2-2): Ast
Ft
…… (2-2)
f s all
Where ( f s all ), is the allowable tensile stress for the reinforcement, MPa. The researchers
[24]
, showed that anchoring the main tension reinforcement at the
outside face of the corbel may be done by providing horizontal loops. Moreover, they stated that the use of heavy bars inclined to the longitudinal axis of the supporting member is generally uneconomical and unsuitable except for the rare situation where the load is applied to the underside of the corbel. Although some diagonal ties remained in Franz and Niedenhoffs’
[24]
detailing recommendations, their proposal
represented a big step forward from previous traditional methods which relied on inclined reinforcement. (Kriz and Raths, 1965)
[6]
carried out three series of tests; the first set was
exploratory tests, the second set on corbels subjected to vertical loads only and the third set on corbels subjected to combined vertical and horizontal loads. The exploratory tests involved testing procedures and reinforcing detailing. The other two Literature Review
Page 11
Chapter Two – Literature Review series involved an investigation of the effect of different variables on the strength and behavior of corbels. The ultimate strength of a corbel, (Vu), is a function of its width (b), its effective depth (d), the reinforcement ratio ( ), the concrete strength ( f c' ) and the (av/d) ratio. The exploratory tests showed that the strength of corbels is not influenced by the additional load carried by the column and the arrangement and amount of reinforcement in the column, but it is proportional to f c' . The strength decreased as the (av/d) ratio increased and increased as the main reinforcement ratio ( ) increased. Their analysis of data from testing corbels with horizontal reinforcement (stirrups) has shown that the stirrups are as effective in resisting vertical load as the main tension reinforcement. Further tests were done by Kriz and Raths to study the effect of combined horizontal and vertical loading. It was found that the stirrups did not increase the resistance of a corbel to the combined loading as was the case with a corbel subjected to vertical loads only. Therefore, it was decided that any contribution from the stirrups should be regarded as reserve strength. For that reason it was concluded that a minimum amount of stirrups should always be provided. The equation, proposed by them for calculating the ultimate strength of corbels subjected to vertical or combined loading, based on fitting curves of their extensive test data, is as follows: Vu b d f c' F1 F3
…… (2-3)
d a Where: F1 6.5 1 0.5
F3
1000 10
Literature Review
…… (2-3-a)
10.4 H V 3
0.8 H V
…… (2-3-b)
Page 12
Chapter Two – Literature Review
As Ah 0.02 , for corbels subjected to vertical loads only. …… (2-3-c) bd
As 0.013 , for corbels subjected to combined loads. bd
…… (2-3-d)
is the reinforcement ratio at column face.
ϕ is the capacity reduction factor; Corbel and bracket behavior is predominantly controlled by shear, therefore, a single value of (ϕ = 0.85) is required for all design conditions. H V is the ratio of horizontal to vertical load. 2
As is the area of tension rainforcement, mm . 2
Ah is the total area of closed stirrups, mm , Ah must not be less than As / 2 .
The design formula by Kriz and Raths has been adopted by (ACI 318-1971)
[26]
and
(PCI Deign Handbook-1972) [27] for corbels. (Mast, 1968) [28], introduced a technique to develop a simple rational approach, based on physical models (Shear-friction hypotheses), that may be used for designing different types of concrete connections. At first the auther applied the method on the design of the interface connection in composite beams, and then extended it to deal with concrete corbels using data from the tests of (Kriz and Raths, 1965) [6]. The shear-friction theory is very simple, and the behavior is easily visualized as shown in Fig. (2.2); the hypotheses developed by Mast was by considering a cracked concrete specimen, which is subjected to a normal compression across the crack and a shearing force along the crack. The shearing force may be resisted by friction along the crack. If reinforcement is applied normal to the crack, then slippage and separation of the concrete will stress the steel tension. The reinforcement will act as a tension member rather than as a dowel.
Literature Review
Page 13
Chapter Two – Literature Review
Fig. (2.2) - Basis for Shear-Friction Theory of Mast [28] The resulting tensile force set up an equal and opposite pressure between the concrete faces on the sides of the crack. As shown in the free-body diagram of Fig. (2.2 b), the maximum value of this interface pressure is (Avf fy), where (Avf) is the total steel area crossing the crack and (fy) is the yield strength. The concrete resistance to sliding may be expressed in terms of the normal force times a coefficient of friction (μ). By setting the summation of horizontal forces equal to zero: …… (2-4)
Vn Avf f y tan
Where tan , is the angle of internal friction Defining the reinforcement ratio ( Avf / Ac ), where (Ac) is the area of the cracked surface, equation (2-4) may be written as: vn f y tan
…… (2-5)
Where, vn
Vn Ac
…… (2-5-a)
vn, is the shear stress at ultimate load, MPa. Vn, is the shear force at ultimate load, kN. Avf, is the total steel area crossing the crack having yield strength of (fy). Values of ( tan ) were determined from tests.
Literature Review
Page 14
Chapter Two – Literature Review Mast gave the values shown in table (2-1) for the design purposes. These values were applied to the test data obtained by Kriz and Raths. The researcher considered the specimens having [(av/d) ≤ 0.7] and yielding steel, on the assumption that for higher (av/d) ratios, the quantity of steel required would be controlled by flexure rather than shear. When combined loading was used, the nominal shear stress was computed as: H vn f y tan bh
…… (2-6)
Where: H is the external horizontal force at ultimate load. Table (2-1) - Values of ( tan ) as given by Mast [28] tanα
Type of Surface Concrete to concrete, rough surface, (crack in monolithic concrete) Concrete to steel, composite beams Concrete to concrete, smooth surface
1.4 1 0.7
(Somerville, 1972) [29], reported reviews to the available test data and previous design methods on corbels to determine the major parameters that influence its behavior. It was stated that, Franz and Niedenhoff [24], were the first researchers who presented the simplest form of truss analogy for corbel design. An alternative method was suggested for enhancing the strength due to (av/d) ratios. This method is illustrated in the form below: Vmax 3d 6 vc av
…… (2-7)
Where, (vc) is the shear stress permitted to be carried by the concrete alone at failure; the suggested method was found to be valid for a range of (av/d) ratios between 0.6 a and 1.5, 0.6 v 1.5 . Moreover, the researcher recommended that the depth at the
d
front face of the corbel should be about one half of the total depth at the column face. Some investigators indicated that truss analogy is not applicable to corbels with low values of (av/d) ratios, but Somerville limits the use of truss analogy to values of (av/d) Literature Review
Page 15
Chapter Two – Literature Review ratios equal or greater than (0.6). Therefore, for determining the shear strength of corbels having low values of (av/d) ratios, alternative approaches have been suggested. (Hermansen and Cowan, 1974)
[30]
, proposed the modified shear-friction theory.
They assumed that when a crack forms on the shear plane the reinforcement crossing the crack is stressed to yield. The frictional resistance to concrete’s movement along the crack is given by: …… (2-8)
v c f y tan
Where (c) is an apparent cohesive stress and ( tan ) is the coefficient of friction. They proposed the value of (c) to be (4 MPa) and ( tan ) to be (0.8) for the purpose of obtaining a safe design. The major conclusion reached by Hermansen and Cowan [30] is that a specimen with single corbel (exterior corbel) showed no significant difference in behavior in comparison to those with double corbels (interior corbel). Both (Mast, 1968)
[28]
and (Hermansen and Cowan, 1974)
[30]
, proposed the
modified shear-friction theory, but their values for ( tan ) were different, therefore, for small amount of steel crossing the direct shear plane, where ( f y ) is low, and assuming (c=0), Mast’s proposal will be more conservative than equation (2-8) proposed by Hermansen and Cowan
[30]
. However for larger values of ( f y ) this
trend will be reversed. (Mattock et al, 1976)
[21]
, carried out an experimental study on the behavior of
reinforced concrete corbels subjected to vertical and horizontal loads. 28 specimens were tested, 26 of them contained horizontal stirrups; the va riables studied were shear span to effective depth ratio, (av/d), vertical to horizontal loads ratio, (V/H), the amount of main reinforcement and secondary reinforcement (stirrups) and type of aggregate. For the two specimens without stirrups, the failure was of splitting type. Literature Review
Page 16
Chapter Two – Literature Review Two of the 26 corbels had flexural failure. The remaining specimens failed as beam shear failure, in which the flexural cracks remained fine and the failure was characterized by widening of one or more diagonal tension crack leading to shearcompression failure of the concrete near the intersection of the sloping face of the corbel and the column face. The failure was quite abrupt, but less brittle with more warning than the case of the diagonal tension failure of corbels without stirrups. Based on these tests, they proposed the use of horizontal closed stirrups, (Ah), parallel to the main reinforcement, (As), such that Ah 0.5 As N u f y . These bars were to be uniformly distributed within the upper two thirds of the total depth of the corbel. This amount of horizontal reinforcement will prevent premature diagonal tension failure of the corbel and permit yield strength of the main tension reinforcement to be developed. The failure of corbel may be either a flexural failure or a beam shear failure after the yielding of the flexural reinforcement. Either of these modes of failure is considered to be acceptable by Mattock and his colleagues since the full strength of the main tensile reinforcement is attained. In the same year, (Mattock, 1976)
[31]
, proposed a simple design procedure for
corbels with (av/d) ratio of unity or less, subjected to a combination of vertical and horizontal loads, based on a simple mechanical model (flexural model), which was adopted by the ACI-318 building code. The main design procedure includes: 1) The ultimate shear stress (vu) must not exceed the values indicated in equation
(2-9). ' 0.2 f c MPa vu 5.5 MPa
…… (2-9)
2) The area of reinforcement, Avf, crossing the shear plane, need to be calculated
according to equation (2-10):
Avf Vu f y Literature Review
…… (2-10) Page 17
Chapter Two – Literature Review Where: 0.85 1.4 , for corbels cast monolithically with the column.
3) The ultimate moment needs to be calculated, the corbel-column interface must
resist the moment calculated by equation (2 -11): M u Vu av N u h d
…… (2-11)
4) The area of reinforment, Af, necessary to resist the ultimate moment calculated
in the previous item need to be calculated.
A f M u f y d a 2
…… (2-12)
5) The area of reinforment, At, necessary to resist the horizontal force, N u, needs
to be calculated.
At N u f y
…… (2-13)
6) The area of main tension reinforment, As, will be the greater value of either of
the following: A f At As 2 3 Avf At
…… (2-14)
7) Closed Stirrups with area, Ah, parallel to the main tension reinforment, As,
must be uniformly distributed within two-thirds of the effective depth, and calculated as shown in Eq. (2-15): Ah 0.5 As At
…… (2-15)
8) The steel ratio, As b d , shall not be less than 0.04 f c' f y .
(Hagberg, 1983) [32], demonstrated the application of the truss analogy by describing a mathematical model to determine the capacity, that may be applied to all types of reinforcement (main and secondary), covering the practical range of (a v/d) ratio from 0.15 to 1.5 and for any combination of horizontal and vertical loads. Hagberg proposed the following formulas:
Literature Review
Page 18
Chapter Two – Literature Review 2 f c' b d 2 f c' b a 1 tan 2 tan 1 0 Fs Fs
…… (2-16)
Where: Fs Fs 1 Fs 2 , Fs 1 As f y and Fs 2 Ah f vy As and Ah are the main and secondary reinforcement respectively, mm 2. Fy and Fvy are the yield strength of main and secondary reinforcements respectively, MPa. d
d 1 Fs 1 d 2 Fs 2 , where d1 and d2 are the distance of main reinforcement and the Fs
center of gravity of the secondary reinforcement, respectively, mm.
, is the inclination compression strut with the vertical.
f is the concrete cylinder strength, MPa. ' c
(Yong et al, 1985)
[33]
, performed a study to check the applicability of the ACI-318
code and the truss analogy theory, proposed by Hagberg
[32]
, on reinforced concrete
corbels with concrete strength greater than 41.4 MPa. A total of eight high strength concrete corbels, divided into four series with concrete strength ranging from 41.7MPa to 82.7 MPa and the shear span to depth ratio, (av/d), was equal to 0.393. The corbels were loaded monotonically to failure. The researchers in this paper concluded that the ACI-318 provisions are conservative for high streng th concrete. In addition to the above, the truss analogy model predicted values were safe and less conservative than the ACI-318, but they concluded that this conservatism of the ACI318 may not necessarily be found in corbels with larger (av/d) ratios or subjected to horizontal loads in addition to the vertical loads. (Zeller, 1991)
[34]
, concluded, from previous tests done on corbels, that for double
corbels, having depth of 690mm and width 300mm, vertical stirrups would be more sufficient when the compression strut has an angle less than 45o with the horizontal. On the other hand, horizontal stirrups would be sufficient when that angle exceeds 45o, as in the case of corbels having (av/d) ratios less than (0.7-0.9). Literature Review
Page 19
Chapter Two – Literature Review (Tan and Mansur, 1992)
[35]
, investigated the effect of partial prestressing on the
behavior and strength of concrete corbels and deep beams. The investigation was performed by testing 20 specimens to failure; the main variables were the degree of prestress and (av/d) ratios. The mode of failure was either shear-compression or flexure, changing from the former to the latter with the increasing of the degree of prestressing. Test results showed that stiffness and cracking moment of corbels and deep beams increased as the degree of prestress increased. Moreover, the ultimate shear capacity increased as the (av/d) ratios decreased, the degree of prestress increased and/or the concrete strength increased. Finally, it was concluded that the shear-friction theory and the ACI strength equations underestimated the ultimate shear capacity of corbels and deep beams while the truss analogy gave good estimates of the ultimate strength. (Prasad et al, 1993)
[36]
, analyzed reinforced concrete corbels using the nonlinear
finite element method. The analysis indicated that the method may be used to predict the response of reinforced concrete structures. Details regarding orientation and distribution of cracks as well as stresses in concrete and steel at various locations may be obtained and studied. The finite element approach is regarded as a feasible method of analysis and design especially with the increasing of experimental costs and the decreasing of computational costs. (Siao, 1994)
[37]
, described a method for analyzing the shear strength of short shear-
walls with height to length ratio of unity or less, top-loaded deep beams and corbels. A compression strut is present in all three elements, where shear force is transmitted to the support via a strut-and-tie system. By using the refined strut-and-tie system, shown in Fig. (2.3), the ultimate shear capacity may be calculated as follows: Vu 1.8 f t b d
…… (2-17)
Where: f y , is the steel yield strength. Literature Review
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Chapter Two – Literature Review
f t , is the allowable tensile strength of tension tie in refined compression strut; calculated by equation (2-17-a) prior to cracking, and by equation (2-17-b) for cracked concrete, where all stresses will be resisted by steel reinforcement.
f t 7 f c' 1 n h sin 2 v cos 2
f t h sin 2 v cos 2 f y
…… (2-17-b)
n , is the ratio of the elastic moduli of steel and concrete, n Es
h
…… (2-17-a)
Ec
and v , steel reinforcement ratio of horizontal and vertical bars, respectively.
, is the inclination of compression strut to tension tie.
Compression Tension
Fig. (2.3) - Refined Strut and Tie Model [37] (Hwang et al, 2000) [38], presented a softened strut-and-tie model for determining the shear strength in corbels. 178 test specimens from the literature were used for comparison with the proposed method. The studied corbels have various parameters, such as (av/d) ratios, different strength categories and horizontal reinforcement. The predictions of the ACI empirical equations were found to be conservative for the selected test data and more pronounced conservatism was found for corbels with low (av/d) or those made with high-strength concrete. It is thus confirmed that vertical stirrups are not useful for shear strength of a corbel with a v/d ≤ 1. In the model proposed by Hwang et al
[38]
, it was found that the web reinforcement
was efficient in two ways; the first was to form tension ties and provide shear transferring paths, the other was to control the crack widths and retard the softening Literature Review
Page 21
Chapter Two – Literature Review process of the cracked concrete. The selected corbel under study is illustrated in Fig. (2.4-a). The following parameters were taken to cover the common range in practice: (ρh fyh) between 0 and 8 MPa, (av/d) between 1/4 and 1 and ( fc′) was equal to 30 MPa for normal strength concrete and 70 MPa for high-strength concrete. Fig.s (2.4-b) and (2.4-c) illustrate the shear strengths of the corbels estimated by the softened strut-and-tie model. The concrete strength appears to set an upper limit value of (ρh fyh), this limit is increased with the increasing of the concrete strength.
Fig. (2.4) – Verification in Calculated Shear Strengths Produced by Amount of Horizontal Hoops, fc’ and av/d ratio [38] (Aziz, 2001) [39], studied the effect of crushed stone and their contribution to the shear strength of reinforced concrete corbels. The researcher found that for the same proportion, workability curing and testing conditions, the crushed stone concrete shows higher values of compressive strength, tensile strength, shear stress when compared with the natural gravel concrete. The shear stress was increased with the Literature Review
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Chapter Two – Literature Review increasing of the amount of longitudinal, shear reinforcement and compressive strength of concrete, and it was decreased with the increasing of the shear span to depth ratio (av/d). According to the results obtained from this test and other results of 168 reinforced concrete corbels failing in shear, taken from literature, an equation for shear was proposed as follows: f ' k / d w h u 2.38 c a/d
0.175
…… (2-18)
Where:
u is the ultimate shear stress of reinforced concrete corbels, MPa
f is the compressive strength of concrete, MPa k , d are properties of the section, k= 150 mm ' c
a d is the shear span to depth ratio
w
, h are the longitudinal and shear reinforcement ratios.
(Singh et al, 2005) [40], presented a complete example on the analysis and design of a double corbel using the strut-and-tie method. The purpose was to amplify the application of the practical recommendations given by the ACI-318-02 Code regarding the design of structural members using the strut-and-tie method. The strut-and-tie method of design is based on the assumption that appropriate regions in concrete structures can be analyzed and designed using hypothetical pinjointed trusses consisting of struts and ties connected at nodes. A study performed by (Russo et al, 2006) [41], aimed to resolve problems in predicting the shear strength of corbels by means of single accurate expression to avoid time consuming computing procedures. The formula for computing the shear strength of corbel was obtained based on 243 test data taken from literature; that formula is illustrated in equation (2 -20). Literature Review
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Chapter Two – Literature Review
vu 0.5 k f c' cos 0.65 h f yh cot
…… (2-20)
Where: k , is obtained from the classical bending theory of reinforced concrete beams with tensile reinforcement only. k
n 2 n n 2
f
f
…… (2-20-a)
f
n , is the ratio of the elastic moduli of steel and concrete, n Es
Ec
, is the flexural reinforcement ratio. f
f
As An bd
…… (2-20-b)
An
Nu f ys
…… (2-20-c)
f , is the yielding strength of the main reinforcement. ys
f , is the yielding strength of the stirrups. yh
h , is the stirrups ratio at column-corbel interface. f
Ah bd
…… (2-20-d)
, is the angle between the compressed concrete strut and the vertical direction, and is provided by equation (2-20-e). 1 2 arctan
2 k 2 a 0.22 1 4 d a k d 2
, is provided by equation (2-20-f) with 10 fc' 105 , 3 2 f c' f c' f c' 0.74 1 . 28 0 . 22 0 . 87 105 105 105
Literature Review
…… (2-20-e)
MPa .
…… (2-20-f)
Page 24
Chapter Two – Literature Review The authors have excluded the corbels with a flexural reinforcement amount, f , lower than the minimum provided by the ACI-318-02, f 1.4 f ys . The typical min
reinforced concrete corbel used is illustrated in Fig. (2.5).
(a)
(b)
Fig. (2.5) - (a) Geometry of RC Corbels and (b) Strut-and-Tie Model with Forces Acting on Corbel [41] The formula proposed for design was found adequately conservative and reliable. It led to an almost constant safety factor v Experimental vCalculated . (Rezaei et al, 2011) [42] investigated the effect of column-load on corbels. Single and double corbels with different levels of axial column load were modeled and analyzed by means of finite element software computer package (LUSAS version 14.1). The axial load capacity of the column was first determined, and then the load was applied on top of the column increasing gradually until reaching the predetermined level, then the load was applied on the corbels until failure was achieved. It was found that the strength of double corbels was more influenced than that of single ones due to the axial column load. The latter was found to enhance the stiffness of corbels. Extensive work has been performed on deep beams and corbels, but shear behavior of such members was difficult to clarify due to its complicated nature. To select the appropriate STM that leads to reasonable designs, a clear understanding of the sheartransfer mechanism was essential. Literature Review
Page 25
Chapter Two – Literature Review (He et al, 2012) [43], proposed theoretical models and explicit equations regarding the main shear-resisting mechanisms in deep beams and corbels to provide a better understanding of the shear behavior of concrete structures. Deep beams transfer shear through two principal mechanisms: the direct strut mechanism, in which the load is transferred directly from the load point to the support, and the truss mechanism, which is the main shear-resistance mechanism in slender beams. The fraction of the total shear resistance associated with each mechanism depends on the (av/d) ratio of the member; the truss mechanism governs in members with (av/d) ≥2 whereas the direct strut mechanism is dominant in members with ( av/d) ≤1. Members with (av/d) ratios between 1 and 2, transfer load via a combination of the two mechanisms. The fraction of load transferred by both mechanisms was derived on the basis of maximum strength criterion, and since deep beams were very similar to double corbels due to their geometry, loading arrangement and failure modes, the strength of concrete corbels has been taken as an example of the methodology. The theoretical proposal, for determining the load distribution between the direct strut mechanism and the truss mechanism in deep beams and corbels, has been derived on the basis of the maximum strength criterion. The ultimate shear capacity of concrete corbels suggested by the authors was: 1 1 1 * * Vu V1 V2 Vu V1* V * 2
…… (2-21)
k tan v f c' b d 2 1 ht sin / 2
…… (2-21-a)
tan v f c' b d 2 1 ht sin / 2
…… (2-21-b)
2 n 1 0.6 ht tan
1
Literature Review
2 ht sin / 2
2
v f b d ' 2 c
fy
…… (2-21-c) Page 26
Chapter Two – Literature Review Where: Vu , is the total ultimate shear capacity
V and V , are terms associated with the concrete and steel contributions to shear * 1
* 2
resistance. ht
z 2 1 a for 0 1 ht 3
…… (2-21-d)
The load acting on a reinforced concrete corbel and the possible load paths in view of the Strut-and-Tie Method, STM, are illustrated in Fig. (2.6).
Fig. (2.6) – Strut-and-Tie Method for Concrete Corbels [43] 2.3. High Strength Reinforced Concrete Corbels, with or w/o Fibers, under Monotonic Loading: During the last three decades of the last century, a new procedure was introduced to improve the load carrying capacity of corbels; this procedure was by replacing the conventional secondary reinforcement with steel fibers. The addition of steel fibers improves the bond between steel and concrete, and the compressive, tensile, flexural and toughness properties of the concrete, moreover, the addition of steel fibers may provide an effective reinforcement against shear failure [44, 45]. (Fattuhi, 1987)
[46]
, carried out tests on 22 (150×150×200-mm) concrete corbels
reinforced with steel fibers, under vertical loading only, to estimate the improvement in shear properties due to the addition of steel fibers. The parameter studied included Literature Review
Page 27
Chapter Two – Literature Review the fiber content and (av/d) ratio. The results obtained indicated that the shear strength was improved by the addition of fibers, and it was concluded that the use of fibers as secondary reinforcement could be an attractive alternative to stirrups. (Abdul-Wahab, 1989) [47], investigated the effect of steel fiber on reinforced concrete corbels and the applicability of the design formula of three methods to SFRC corbels, these methods are: the conventional method of the ACI-318, the truss analogy proposed by Hagberg
[32]
and the modified shear-friction equation suggested by
Fattuhi[48] which is shown in equation (2-22).
Vu Avf f fu Av f y
…… (2-22)
Where:
, is the strength reduction factor (assumed to be 0.85 for shear).
, is the overall fiber efficiency factor (with average value of 0.1).
A , is the total area of fibers at the critical section. f , is the ultimate tensile strength of the fiber. vf
fu
, is the coefficient of friction (assumed to be 1.4 for monolithic concrete). Av , is the area of reinforcement extending across the critical section.
f , is the yield strength of the reinforcement. y
Six corbels, in two groups, were tested to failure under vertical loading. In the first group, the steel fiber ratio (by volume) was varied from 0, 0.5, and 1 percent, while the (av/d) ratio was kept constant at 0.522. In the second group, the fiber content was kept constant at 1 percent while the (av/d) ratio was varied from 0.30 to 0.57; the strength reduction factor (ø) was taken as 1.0. Using equation (2-22), suggested by Fattuhi [48], the following equation was obtained:
Vu Vu1 Vuf
…… (2-23)
Where: , is the strength reduction factor (assumed to be 0.85 for shear).
, is the fiber efficiency factor (assumed to be 0.1). Literature Review
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Chapter Two – Literature Review
Vu1 , is the minimum value of the ultimate load for reinforced concrete corbels using the ACI-318 method.
V , is A
vf
uf
f fu
.
A very good correlation, compared with the three other methods, was obtained using equation (2-23). The average ratios of the tested ultimate load to the calculated load for the selected corbels with fibers are shown in table (2-2). Table (2-2) - Average Ratios of the Tested to the Calculated Ultimate Loads, (Abdul-Wahab [47]) Methods
Mean (Vu-test/Vu-cal)
Standard Deviation
1.546 1.298 1.139 1.110
0.171 0.217 0.255 0.099
ACI Code method Truss Analogy (Hagberg [32]) Eq. (2-22), (Fattuhi [48]) Proposed Eq. (2-23), (Abdul-Wahab [47])
The results obtained indicated that an increase in the ultimate shear strength of the corbels was achieved due to the addition of moderate amounts of steel fibers; an increase of 40% in the strength was obtained with the addition of 1% of fiber content. The test results showed that the method in the ACI-318 code and the truss analogy method become too conservative by neglecting the contribution of fibers to shear strength. In the same year, (Hughes and Fattuhi, 1989)
[49, 50]
, performed a series of tests on
concrete corbels reinforced with either main bars only, fibers only or main bars plus fibers, the volume fraction of steel or polypropylene fibers, or main bars, were kept constant at nearly (0.7%). Plain concrete corbels were tested as well for comparative purposes. The test results indicated that the addition of 0.7% by volume of crimped steel fibers almost doubled the ultimate load. All plain concrete and fiber reinforced concrete corbels failed in flexure. It was concluded as well that fiber reinforcement Literature Review
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Chapter Two – Literature Review was in general unlikely to be an economical alternative to the main bars for resisting flexure. Corbels with plain concrete failed in a brittle manner soon after reaching their ultimate loads, while corbels with fiber reinforced concrete failed more gradually, to provide, in some cases, an almost elastic-plastic behavior. Other tests were carried out, by the same researchers, on concrete corbels reinforced with main bars only or with steel fibers in addition to the main bars, the volume of the main bars and the (av/d) ratio were varied. The test results indicated that corbels reinforced with main bars only failed suddenly and catastrophically shortly after reaching their maximum loads, and the mode of failure was diagonal splitting or constrained shear. But with using steel fibers (as a secondary reinforcement), the strength and ductility were improved. The improvement was more obvious for corbels reinforced with low volumes of main bars and/or those tested at large (av/d) ratios. (Fattuhi, 1990) [5], carried out tests on 18 concrete corbels reinforced with main bars and steel fibers. The fibers were used as a secondary reinforcement. The volumes of main and fibrous reinforcements and shear span-to-depth ratio were varied. A concentric load was applied on the column segment of eight specimens, while, unequal loads were applied on the corbel segments of four of the double corbels. Test results indicated that loading the column segment of the specimen or the left-side corbel did not have any significant effect on the load-carrying capacity of the corbels; however, the presence of column load delayed the occurrence of the first crack. It was concluded, as well, that the addition of steel fibers improved both the strength and ductility of the corbels. Further tests were performed by (Fattuhi, 1994)
[51,52]
on normal and high-strength
concrete corbels reinforced with main bars only, with main bars and steel or monofilament polypropylene fibers, or with main bars and plastic mesh. The fibers or strips of plastic mesh were used as secondary (shear) reinforcement. These tests confirmed the findings of earlier investigations about improving both the strength and Literature Review
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Chapter Two – Literature Review ductility of reinforced concrete corbel by adding steel fibers to the concrete. It was concluded as well that steel fibers were the only form of secondary reinforcement that successfully reduced the widths of cracks in corbels. The improvement in strength due the addition of fibrous reinforcement was more significant in high-strength concrete corbels relative to low or moderate strength concrete corbels. These tests also led to the finding of semi-empirical equations to estimate the flexural strength of reinforced concrete corbels subjected to vertical loading by using two methods: flexural and truss models. Comparison between experimental and calculated shear strength of corbels using the two methods showed a good agreement. In the flexural model, as illustrated in Fig. (2.7), the corbel was assumed to behave as a short cantilever beam; by knowing the properties of the corbel, the nominal strength may be calculated as shown below: Vn
f y As a K f b a a d 1 o ct h 1 h 1 a1 a 2 2a 1 1
f A K o f ct h b Where: a1 1 c y s b 0.85 f c' b K o f ct 1
…… (2-24)
a1 , is the depth of rectangular compression block in concrete. a , is the shear span. 1 , according to the ACI 318, varies between 0.65 and 0.85. c , is the depth of the neutral axis. f ct , is the tensile splitting strength, MPa. K o , is the contribution of fibrous concrete in tension obtained from regression analysis of test results, this value was found to range between (0.185-0.675) with an overall average of 0.353 and a coefficient of variation of 30.4%; the relationship between K o and f c' from regression analysis was as follows: Literature Review
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Chapter Two – Literature Review Ko
9.519
f ' c
…… (2-25)
0.957
Fig. (2.7) - Flexural Model [51] In the truss model, as illustrated in Fig. (2.8), the semi-empirical formula derived was based on the truss analogy theory proposed by (Hagberg, 1983) [32], this formula took into consideration the tensile strength of the fibrous concrete as suggested in the flexural model.
Fig. (2.8) - Truss Model: (a) Stress Distribution, (b) Forces [51] By knowing the properties of the corbel, and using the appropriate effective depth,
d i for each layer of stirrups, the capacity of the corbel may be calculated as shown below: Literature Review
Page 32
Chapter Two – Literature Review l sin l sin f y As d f yi Asi d i 0.5 K o f ct b hh l sin 2 2 Vn a 0.5 l sin cot
…… (2-26) Where: l sin
f y As f yi Asi K o f ct b h 0.85 f c' b K o f ct b
d i , is the distance of (ith) layer of stirrups from extreme compression fiber.
l , is the width of compression strut in concrete. , is the inclination of resultant concrete compression strut with the vertical.
f , is the yield stress of (ith) layer of stirrups, MPa. yi
Asi , is the area of stirrups in (ith).
a , is the shear span. f ct , is the tensile splitting strength, MPa. (Foster et al., 1996)
[53]
, tested thirty corbels under vertical loading. The main
variables studied were concrete strength (45-105 MPa), (6500-15200 psi), shear spanto depth ratio, and the provision of secondary reinforcement. Particular attention was given to determine the concrete efficiency factor for members failing in compression. A comparison was made for the corbel behavior designed according to the ACI 31889 design method and the plastic truss model. The results showed that good load predictions can be obtained using the plastic truss. It was concluded from the results that corbels made from high-strength concrete behaved in the same manner as those made from normal-strength concrete. Moreover, the first cracks detected were flexural cracks propagating from the corbel-column intersection, and that the flexural cracking load decreased with the increase of the shear span-to-depth ratio. It was also concluded that the provision of secondary reinforcement reduces crack widths, improves ductility, and for beams failing in compression may change the failure mode from diagonal splitting to compression strut crushing. Therefore, they Literature Review
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Chapter Two – Literature Review advised the provision of a minimum quantity of horizontal stirrups, similar to that for normal-strength concrete, when fabricating high-strength concrete corbels. It was concluded as well that the ACI 318-89 design method is not recommended for use with corbels designed with high and very high-strength concretes. (Muhammad, 1998) [20], studied the strength and deformation characteristics of 48 high-strength concrete corbels with main reinforcement and with either steel fibers or stirrups as secondary reinforcement, or the latter was a combination of steel fibers and stirrups. The parameters studied were volume fraction of steel fibers, the (av/d) ratios and the horizontal stirrups ratio. 36 of the specimens were tested to failure under monotonic loading, while the remaining 12 specimens were tested under repeated loading. Test results showed that the use of high-strength fiber reinforced concrete in corbels improved their behavior and strength. Moreover, test results showed that specimens with combined shear reinforcement, stirrups and fibers, exhibited higher first cracking load than those reinforced with fibers only. Test results also showed that the addition of steel fibers had increased the ultimate shear strength and the stiffness of the corbels and reduced the deflection for a specific load. This increase was found to be dependent on the fiber volume and (av/d) ratio. On the other hand the combination of fibers and stirrups led to a higher reduction in deflection. (Bourget et al, 2001)
[54]
, carried out tests on three different concrete compositions,
established by previous researchers (De Larrard et al.)
[55]
, having mean strength of
80, 100, and 120 MPa respectively. The test specimens were divided into two series. The first one consisted of high-level reinforcement corbels, (C2-120), and the second series consisted of specimens with lower-level reinforcement quantity, (C1-80), (C2-80) and (C2-100). An anchor bar was welded to primary and secondary steel. The aim of the experimental program was to study the influence of concrete strength. The experimental corbel failure mode was first defined with the evolution of the main Literature Review
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Chapter Two – Literature Review reinforcement strain versus conventional stress: if the main reinforcement has yielded the failure mode would be considered as tension failure; if it has not then the crack pattern would indicate the failure mode by either concrete crushing or by diagonal splitting. The test arrangement is shown in Fig. (2.9).
Fig. (2.9) - Test Arrangement [54] (Campione et al, 2007)
[56]
carried out an experimental investigation on the flexural
behavior of normal and high strength fibrous reinforced concrete corbels in the presence of main and secondary reinforcement. The parameters investigated were the fiber content and geometric ratio of main and secondary steel and the concrete strength, normal- or high- strength types; the test results showed that the use of fibers instead of transverse stirrups, or coupled with them, may reduce the brittleness of the mechanism involving crushing of compressed regions. Moreover, it was found that it is possible to activate flexural failure in the case of fibrous concrete improving the ductility. A simple analytical expression, based on truss analogy, considering the presence of fibers was proposed, to determine the bearing capacity, taking into account the shear contribution due to steel reinforcement and fibers. This model was verified against experimental data of the authors and other data available in literature. The results Literature Review
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Chapter Two – Literature Review obtained showed that the proposed model fits the experimental results with a good level of approximation. (Ridha, 2008) [57], presented a nonlinear finite element investigation on the behavior of high strength fiber reinforced concrete corbels subjected to monotonic loading, in order to get a better understanding of their behavior throughout the entire loading history. The main variables were the fiber content, grade of concrete, main reinforcement and (av/d) ratio. It was found that the presence of fibers helped in enhancing the ductility and energy absorption capacity. The cracking load and post cracking stiffness were found to increase with the increasing of the compressive strength of concrete and the decreasing in the (av/d) ratios. (Ahmad and Shah, 2009)
[58]
, focused on the application of the strut-and-tie model,
STM, for the design of high strength concrete double-corbels, in an attempt to verify that the STM is an alternative design method for non-flexural disturbed regions in concrete structures. Nine double-corbels of high strength concrete (45, 52 and 59 MPa) were cast, with the minimum area of steel allowed by the ACI-318; the corbels were analyzed on the basis of STM, and then tested in the laboratory under monotonic loading to compare the theoretical and actual failure loads, which were found to be quite close and realistic. The authors recommended that further research on the application of the STM for the design of high strength concrete double corbels would be needed. The dimensions of the studied corbels are shown in Fig. (2.10). (Campione, 2009)
[59]
, proposed a softened strut-and-tie- macro model in order to
produce the load-deflection curves for corbels constructed with plain and fibrous concrete under both vertical and horizontal forces. The proposed model was based on replacing the cracked continuum structure with the strut-and-tie macro model and was able to include most of the possible modes of failure observed experimentally, such as steel yielding, concrete crushing, etc. Literature Review
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Chapter Two – Literature Review 1.5 “
6.0 “
12” × 6 “× ½” Bearing Plate 9.0 “
9.0 “ 9.0 “
9.0 “
9.0 “
1’ - 9.0 “
9.0 “
Vu = 60 kips
Vu = 60 kips 4.5 “ 2.0 “
27.11 kips
1’ - 4.0 “
60 kips
60 kips
60 kips
27.11 kips
60 kips 2.93 “
Fig. (2.10) – Geometry of the Corbels (Truss and members) [58] The scheme adopted, as shown in Fig. (2.11), was of a single or multiple truss structure. The single truss refers to corbels having the main steel reinforcement inside plain or fibrous concrete. The multiple truss structure refers to corbels having the main and secondary steel reinforcement inside plain concrete.
Fig. (2.11) - Equivalent Truss Model: a) Single Truss. b) Multiple Truss Literature Review
[59]
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Chapter Two – Literature Review A nonlinear finite element approach was implemented, in the same year, by (Yousif, 2009)
[60]
to study the behavior of high-strength reinforced concrete corbels
using a simplified softened strut-and-tie model. The analysis was based on truss analogy, following the provisions of Appendix A of the ACI-318-05. Different parameters such as (av/d) ratio, primary and secondary reinforcement ratios, and concrete compressive strength were studied. The study showed that the finite element method was a suitable tool for the analysis of high-strength concrete corbels, and that the strut-and-tie model was a simple and effective design tool that may give reasonable predictions of the failure load capacity of high-strength reinforced concrete corbels. (Al-Zahawi, 2011) [61], investigated the shear strength and the behavior of reinforced concrete corbels containing chopped carbon fibers subjected to concentrated vertical loads. His work included casting 15 reinforced concrete corbels with and without chopped carbon fibers, having the same dimensions and main reinforcement; the shear span to depth (av/d) ratios ranged from 0.3 to 0.6. The variables studied were the (av/d) ratios, the volume fraction of carbon fibers and the presence or absence of the secondary reinforcement. Test results showed that the presence of carbon fibers in the concrete has enhanced the tensile strength of the corbels and delayed the formation of inclined diagonal shear cracks. (Khalifa, 2012)
[62]
, proposed a macro-mechanical strut and tie model to analyze
fibrous high-strength concrete corbels. The fibers were applied as partial or full replacement of horizontal stirrups. The parameters studied were, the effect of fiber volume, fiber length, and fiber diameter, random distribution of fibers, fiber HSC interface, shear span to depth ratio and concrete strength. Results showed that the maximum vertical load carrying capacity applied on corbels was increased with the increasing of the fiber volume fraction, fiber aspect ratio and the increasing in concrete compressive strength. Literature Review
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Chapter Two – Literature Review (Aliewi, 2014) [63], carried out experimental and theoretical investigations to study the behavior and load carrying capacity of fibrous and non-fibrous self-compacting reinforced concrete corbels subjected to vertical loading. The experimental part studied both the material and structural properties of the self-compacting concrete used, this was performed by the cast of 29 fibrous and non-fibrous specimens; 8 non fibrous and 4 fibrous specimens were cast with normal strength self-compacting concrete, NSCC, and the same number of specimens were cast with high strength selfcompacting concrete, HSCC; finally 5 specimens were cast with non-fibrous normal conventional reinforced concrete, NC, the latter was used for comparison purposes. Results from experimental tests showed that the cracking and ultimate loads have increased with the increasing of the volume of steel fibers and the decreasing of (av/d) ratio; the percentage of increase was greater in the HSCC specimens than those in the NSCC specimens. In addition to that and for the same amount of main reinforcement and (av/d) ratio, test results showed an increase in the cracking and ultimate loads with the increasing of secondary (horizontal) reinforcement in both NSCC and HSCC types of specimens, but it was more pronounced in the latter type. Increasing the compressive strength led to an improvement in the cracking and ultimate loads; this improvement was more pronounced in fibrous specimens than that in non-fibrous ones. The theoretical part included using nonlinear regression that led to the proposing of useful expressions to predict the nominal shear strength of fibrous and non-fibrous self-compacting reinforced concrete corbels based on the experimental data obtained from 18 specimens, these formulas were: 1 1 ' 2 d 3 Vn f 665 f f 1 0.4 F b d c s y h yh 1193 a
Literature Review
…… (2-27)
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Chapter Two – Literature Review 1 ' 2 1 1 0.4 F b d Vn f c 695 s f y h f yh a 590 1 1.25 d
…… (2-28)
1 ' Vn f c 200
1.75
200 s f y h f yh 2.4
a d
1 0.4 F b d …… (2-29)
Comparisons between these three formulas and the equations provided by the ACI318M-11 and other six empirical equations available in the literature showed good agreement. The researcher recommended that using equation (2-29) in the design will lead to a safe and economic self-compacting reinforced concrete corbels. 2.4. Reinforced Concrete Corbels under Repeated Loading: Most of the researches performed in the past decades on reinforced concrete corbels were concerned with their strength and ductility under monotonically increasing loads up to failure. Corbels subjected to other types of loading, such as repeated loadings, were very rare. Such loadings become significant in specimens with large live-to-dead loads ratios, as well as in zones of seismic activity or hurricane loads. However, under repeated or reversed loads larger deflections were produced and the shear distress became more evident [61]. During the eighties of the last century, there was a gradual transition from cast-inplace construction to precast construction. The form of precast construction mostly emulates monolithic (cast-in-place) construction. The use of precast concrete in seismic areas required the development of adequate connectors between the precast members, which must exhibit high flexural strength, ductility and large energy absorbing capacities. Connections detailing and their location between precast members were one of the experimental and analytical investigation issues for researchers [1].
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Chapter Two – Literature Review Most of the researches available in the literature dealt with beam-column joints with or without corbels subjected to seismic or repeated loadings; researches on corbels under such loads were very rare. (Loo and Yao, 1995)
[64]
, conducted experimental investigations on eighteen interior
connection models to evaluate their strength and ductility properties under static and repeated loading. It was concluded that under both static and repeated loading, the precast connections attained a higher flexural strength than monolithic connections. The precast connection types under repeated loading, possessed larger energy absorbing capacities than monolithic models. (Cheok et al, 1998)
[65]
developed an enhanced and versatile hysteretic model to
represent the inelastic behavior of the hybrid precast connection region. The model parameters were calibrated using results from a separate experimental program which examined the inelastic cyclic behavior of hybrid concrete precast connections. The hybrid connection was a combination of mild steel and post-tensioning steel, where the mild steel was used to dissipate energy by yielding and the post-tensioning steel was used to provide the shear resistance through friction developed at the beamcolumn interface. Results of the inelastic dynamic analyses were used in conjunction with experimental results to develop simple design guidelines for the use of precast concrete hybrid connections in regions of high seismicity. In the same year, (Muhammad, 1998) [20] did some tests on 12 specimens of corbels cast with high-strength fiber reinforced concrete subjected to repeated loading, in addition to other specimens subjected to monotonic loading. A quasi-static type of repeated loading was applied to the 12 specimens, the test be gan by applying load via a hydraulic machine with appropriate increment (4.9 kN) until the maximum deflection was read according to the specified value of (/y) ratio, which were chosen by the researcher as 1.25 and 1.5. An unloading stage followed gradually by Literature Review
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Chapter Two – Literature Review loosening the valve of the hydraulic machine. Then the second cycle followed. The loading and unloading stages were carried out in the same manner for six cycles after which the specimens were loaded to failure. Test results showed that specimens subjected to repeated loading failed in a more ductile manner and had a larger total deflection at failure than those subjected to monotonic loading. The shape of the hysteresis loops of the load-deflection curves had shown pinching near mid cycle, which was more pronounced as the number of cycles increased, at the same ductility (/y), the pinching was a sign of decreasing in energy dissipation. (Nicholas et al, 2000)
[66]
, represented a step toward the consistent design approach
by developing a simple strut and tie method, STM, to capture the cyclic hysteretic response of a reinforced concrete cantilever beam with sectional details which are commonly found in seismic design. The suggested procedures, developed based upon the internal force distribution of the reinforced concrete structure at the elastic state, proved to adequately predict the reversed cyclic flexural response. Finally, the researchers suggested that further studies are required to clear the model deficiencies, including the kinks in unloading branches and the apparent discrepancy of the inelastic unloading stiffness between analytical results and experimental observation. (Dora and Abdul Hamid, 2012)
[67]
, conducted an experimental study to investigate
the seismic performance of full-scale precast beam-column corner joint with corbel mixed up together with steel fiber reinforced concrete (SFRC) as shown in Fig. (2.12- a and b). The sub-assemblage of beam-column joint was subjected to reversible lateral cyclic loading up to ±1.5% drift. The loading regime for the experimental work was performed using control displacement method. The loading regime is shown in Fig. (2.12-c). The visual observation and experimental results showed that the cracks start to occur from +0.75% drifts at the cast-in-place area of beam-column joints. The reinforcing Literature Review
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Chapter Two – Literature Review bar in the beam-column joint yielded at +0.75% drift with displacement of 26.39 mm in positive direction (loading).
(a) Specimen Ready for Testing.
(b) SFRC at Beam-Column Joint with Corbels Painted with Yellow and Ready for Instrumentation.
(c) Loading Regime Using Control Displacement. Fig. (2.12) - Full Scale Beam-Column Joint Sub-Assemblage [67] The force-displacement response from experimental results showed agreement with prediction using moment-rotation analysis. The displacement ductility calculated showed that ductility increased by increasing the target drift with the maximum value of 2.09. Even though SFRC was provided at the beam-column joint and corbel areas, the result showed that the precast beam-column joint presented had low ductility when subjected to bigger drift or larger displacement due to lateral loading. (Farhan, 2014)
[68]
, carried out experimental and theoretical investigations to study
the strength and deformation characteristics of reinforced concrete corbels tested under monotonic and repeated loading. For this purpose, 24 vibrated and self compacting concrete (SCC) corbels with normal and high compressive strength were cast and tested under vertical loading. Test results indicated that corbels made of SCC Literature Review
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Chapter Two – Literature Review showed an improvement in behavior and strength of the specimens from (8.2% to 14.2%). 2.5. Strengthened Reinforced Concrete Corbels: The use of fiber reinforced polymer (FRP) materials for structural repair and strengthening has continuously increased during previous years, due to several advantages associated with these composites when compared to conventional materials like steel. These benefits include low weight, easy installation, high durability and tensile strength. FRP materials are lightweight, noncorrosive, and exhibit high tensile strength. Additionally, these materials are readily available in several forms ranging from factory-made laminates to dry fiber sheets that can be wrapped to conform to the geometry of any structure [12]. (Engindeniz et al, 2005)
[69]
, presented a comprehensive literature search regarding
the performance, repair and strengthening techniques for non-seismically designed reinforced concrete beam-column joints, reported between 1975 and 2003. These techniques included: Epoxy repair, removal and replacement, concrete jacketing, concrete masonry unit jacketing, steel jacketing and addition of external steel elements and strengthening with fiber-reinforced polymeric, FRP composite applications. Test results reviewed showed that externally bonded FRP composites can eliminate some important limitations of other strengthening methods such as difficulties in construction and increases in member sizes. The shear strength of one-way exterior joints has been improved with (45 o) fibers in the joint region; however, ductile beam failures were observed in only a few specimens, while in others, composite sheets were debonded from the concrete surface before a beam plastic hinge was formed. Reliable anchorage methods need to be developed to prevent debonding and to achieve full development of fiber strength within the small area of the joint. Most of the strengthening schemes developed have a limited range of applicability, either due Literature Review
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Chapter Two – Literature Review to the unaccounted floor members (that is, transverse beams and floor slab) in real structures or to architectural restrictions. Experiments conducted to date have generally used only unidirectional load histories. Therefore, a significant amount of work is necessary to arrive at reliable, cost-effective, and applicable strengthening methods. In developing such methods, it is important that testing programs be extended to include critical joint types under bidirectional cyclic loads. The strengthening of reinforced concrete beams with CFRP sheets or strips has been of interest to many researchers. Published research work on the behavior of strengthened corbels with CFRP fabric is limited. There were a series of tests carried out by (Fattuhi alone or with others) [46, 48-52]
, (Abdul-Wahab) [47], (Mohammad) [20], (Campion et al) [56], (Ridha) [57], (Al-
Zahawi) [61] , (Khalifa)
[62]
and (Aliewi) [63], to investigate the effect of adding steel
fibers and chopped carbon fibers to reinforced concrete corbels. Tests results showed that the addition of steel fibers improved the behavior of corbels; this procedure is not a strengthening one, it may be considered as an improvement to the behavior of a structural member, which is different from the goal of using CFRP to increase the capacity of existing reinforced concrete members. (Heidayet et al, 2003)
[70]
, carried out an experimental investigation on 18 damaged
reinforced concrete corbels repaired by external steel plates subjected to vertical loads. The parameters studied were the main and secondary reinforcements, the shear span to depth (av/d) ratio and the depth of the corbels. At first the corbels were loaded close to their ultimate capacity, and then repaired using externally applied steel plates, which were fixed by bolts, finally the specimens were loaded to failure. Test results showed that the ratio between the strength of the repaired corbel to that of original ones varied from 0.71 to 1.54; it was concluded from that investigation that this repair technique may be regarded as an effective and economical technique for strengthening existing structures. Literature Review
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Chapter Two – Literature Review (Campione et al., 2005)
[71]
, performed an analytical and experimental study on the
flexural behavior of reinforced corbels made of plain and fibrous concrete with main and transverse steel bars or externally wrapped with carbon fiber reinforced polymers. Twelve corbels, having the same dimensions but differing in the amount and type of reinforcement, were cast for this purpose. Fig. (2.13), shows the geometry and steel reinforcement details.
Fig. (2.13) – Geometry of Corbels and Details of Steel Reinforcement [71] Two specimens, for each Type, were made using the following materials: 1) Plain concrete. 2) Fiber reinforced concrete with hooked steel fiber at 1% by volume percentage. 3) Plain concrete reinforced with two longitudinal bars acting as main reinforcement, having a diameter of 10 mm, placed at the bottom of the beam. 4) Plain concrete reinforced with two longitudinal bars acting as main reinforcement, having a diameter of 10 mm, placed at the bottom of the beam and four longitudinal bars acting as secondary reinforcement, having a diameter of 6 mm uniformly distributed within the depth of corbel.
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Chapter Two – Literature Review 5) Fiber reinforced concrete with hooked steel fiber at 1% by volume percentage in addition to two longitudinal bars acting as main reinforcement, having a diameter of 10 mm. 6) Plain concrete reinforced with two longitudinal bars acting as main reinforcement, having a diameter of 10 mm, placed at th e bottom of the beam and wrapped externally with one ply of flexible carbon fiber reinforced sheet (CFRP) having a thickness of 0.165 mm. For corbels reinforced with main steel the rupture was related to the brittle failure of compressed zone arising after the yielding of steel bars occurs. For corbels externally wrapped with CFRP similar mode of failure was observed but the compressive rupture was consequent to the failure of CFRP wraps in tension. A more ductile behavior was observed when using secondary reinforcement, this may be referred to the bridging action of secondary reinforcement against the principal cracks, but the flexural capacity was not completely achieved. For FRC corbels, ductile balanced flexural failure was observed, which proved the effectiveness of using fibers as shear reinforcement and in improving the confinement of the compression zone of the beam. The analytical model used in this paper was performed with an equivalent single or multiple trusses, as shown in Fig. (2.14 a and b). The single truss refers to corbels detailed in 1, 2, 3 and 5, while the multiple trusses refer to corbels detailed in 4 and 6 listed above. The bearing capacity of corbels for all cases could be determined by using this analytical model, based on the analysis at rupture of corbels by means of an equivalent multiple truss including all the possible modes of failure observed experimentally. The model showed good agreement with the experimental results and gave a physical interpretation of the behavior of corbels at rupture.
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Chapter Two – Literature Review
Fig. (2.14) – Equivalent Truss Model: a) Single Truss; b) Multiple Trusses. [71] (Elgwady et al, 2005)
[9]
, carried out an experimental investigation on six corbels
strengthened with carbon fiber reinforced plastic (CFRP) strips with different strengthening configurations subjected to monotonic loading. One specimen was left without strengthening to be considered as a control specimen; the parameters studied were the amount and orientation of CFRP strips. Test results indicated that diagonal CFRP strips can enhance the corbel capacity by about 70% relative to the control specimen. The other types of strengthening enhanced the ultimate load carrying capacity by values ranging from (8-30) %; the cracking loads of most strengthened specimens were about (70-80) % of their ultimate loads. It was observed that the specimen with mixed horizontal and diagonal strips showed an apparent delay of cracking. Most of the corbels showed a brittle mode of failure, the stiffness of all specimens was increased and they failed suddenly without adequate warning. The authors recommended that the CFRP strips should be stopped before the end of the corbel, where the distance left may be considered as the weaker portion where cracks were propagated.
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Chapter Two – Literature Review (Ozden and Atalay, 2011)
[72]
, investigated the strength and post-peak performance
of reinforced concrete corbels strengthened with GFRP overlays, which were bonded to the specimens using epoxy. Twenty four, one-third scale corbel specimens of normal strength concrete were cast for this purpose. The specimens were tested to failure under quasi-static gravity loading. The parameters studied were the strength of concrete, the main reinforcement, the shear span to depth ratio, (av/d), and the GFRP layers and orientation, the GFRP wrapping configurations are shown in Fig. (2.15).
Fig. (2.15) – GFRP Wrapping Configurations [72] Test results concluded that GFRP wrapping with 45 degrees fiber orientation (diagonal) was more effective than lateral wrapping. The level of tension steel strain on the onset of failure depended on the type and number of GFRP layers and the tension reinforcement ratio. The results also revealed that the level of strengthening with GFRP wrapping ranges from (40-200) % depending on the reinforcement ratio, (av/d) ratio and the orientation and number of GFRP layers used. (Erfan et al, 2011) [73], carried out experimental and theoretical investigations on the shear behavior, the load-carrying capacity and mode of failure of five full-scale reinforced concrete corbels strengthened with CFRP fabrics, and subjected to monotonic loading. The shear span to depth (a v/d) ratio was equal to 0.73; all specimens were designed to fail in shear. Test results indicated that this strengthening Literature Review
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Chapter Two – Literature Review technique slightly improved the shear behavior of the test specimens. The enhancement in the cracking loads of the strengthened specimens ranged from 9% to 24% and in the load-carrying capacity in shear ranged from 7% to 13%. A comparison of the experimental results and non-linear finite element analysis predictions was found to be conservative. The theoretical results for ultimate loads were compared with the ultimate loads predictions of the Egyptian Code of Practice, ECP-208-2005, and found to be conservative at different values of (a v/d) ratios. (Mohamad-Ali and Attiya, 2012)
[22]
, carried out an experimental investigation on
the shear behavior of reinforced concrete corbels externally strengthened or retrofitted with carbon fiber reinforced polymer (CFRP) sheets. The variables studied were the width, number, length, location and direction of the CFRP sheets. Test results showed that corbels strengthened with inclined strips gave best results compared with specimens strengthened with horizontal strips; the enhancement in the ultimate shear strength of the corbels was about (44.5-60) % for inclined strips and about (14.726-31.164) % for horizontal strips compared with the control specimens. It was concluded as well that the external strengthening technique had a significant effect on the first cracking load, the percentage increase in cracking load for the inclined strips was 51.43 % the percentage for the horizontal strips was 18.75 %. For the repaired specimen, an increase in the ultimate load was detected; the amount of increase was 56.68 % with respect to the control specimen. Finally, an average decrease in the width of crack was observed, this decrease was due to the presence of the CFRP strips. The percentage of decrease was 40.8% and 24.3% of the control corbels at ultimate load levels for the inclined and horizontal techniques respectively. (El-Maaddawy et al, 2014)
[74]
, carried out experimental and theoretical tests to
investigate the structural response of concrete corbels reinforced internally with steel reinforcement and externally with carbon fiber reinforced polymer (CFRP) composite sheets. Nine specimens were constructed and tested for this purpose. The specimens Literature Review
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Chapter Two – Literature Review were divided into two groups based on whether it was reinforced with main reinforcement only or a combination of main and secondary reinforcement. In each group, one specimen was considered as a control specimen left without external composite reinforcement. The remaining specimens were reinforced externally with CFRP composite sheets, as shown in Fig. (2.16). The strengthening technique included primary longitudinal CFRP reinforcement (L1), parallel to the main reinforcement, secondary longitudinal CFRP sheets (L2), and diagonal CFRP sheets (D1) and (D2) oriented at 45°. Two U-shaped CFRP sheets were wrapped around the corbel cross section outside the test region, one at each end, to provide an anchorage for the longitudinal CFRP sheets. For the theoretical analysis the FE software ATENA was used, all test specimens were represented as nine two-dimensional models, assuming a perfect bond between the CFRP and concrete. Three additional FE models were developed for the specimens with the diagonal CFRP reinforcement. In these models, an interfacial bond stress-slip model was adopted between the diagonal CFRP reinforcement and concrete. Test results concluded that the failure modes and predicted crack patterns observed demonstrated that the tested corbels resisted the applied load by two diagonal compressive struts feeding into the column segment, and the main reinforcement acted as a tie to resist the out-of balance forces at the support points. The inclined shear cracks that developed in the corbels were more curved toward the outer surface of the corbels for both types of reinforcement. It was also concluded that the load capacity of the corbels was improved by using CFRP as an external strengthening technique. This improvement was decreased with the increase in the amount of primary reinforcement. For the tested corbels reinforced with primary reinforcement only, a strength gain in the range of (21-40) % was recorded. Whereas, for other corbels with combined primary and secondary Literature Review
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Chapter Two – Literature Review reinforcement, (15-33) % strength gains were recorded. The numerical load capacity was within 10% error band.
Fig. (2.16) - Layout of the External Composite Reinforcements (Dimensions in mm) [74] Adding the primary longitudinal CFRP composite reinforcement reduced the yield and ultimate loads of the corbels. But no significant improvement was observed by the addition of the secondary CFRP composite reinforcement, which was located at the mid height of the corbels. Moreover, it was observed that the diagonal CFRP composite reinforcement resulted in a significant increase in the load capacity. (Ivanova et al, 2014)
[103, 104 and 105]
performed experimental investigations on
strengthening short reinforced concrete corbel bonded with unidirectional and bidirectional composite carbon fiber fabrics; the details and dimensions of some of the tested corbels as well as the configuration of strengthening are shown in Fig. (2.17), whereas Fig. (2.18) illustrates the test setup.
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Chapter Two – Literature Review
a) Steel reinforcement
b) Details of Corbel Geometry
c) Strengthening Configurations Fig. (2.17) - Details, Dimensions and Strengthening Configurations of Corbels Tested by Ivanova et al (Dimensions in mm) [103 and 104] The investigations included testing the corbels monotonically up to failure. Strain distributions, the load-carrying capacity and the mode of failure were recorded. The parameters studied included thickness of the carbon fiber fabric used (number of layers) and the type of strengthening, either by gluing the carbon fiber fabrics only on the front and back sides of the concrete corbels or by wrapping. Test results showed that bonding CFRP fabric on corbels had increased the failure tensile strength with about 82%; moreover it was found that the significant effect was by using two layers, more layers led to a decrease in the ultimate load. Results also showed that the wrapping strengthening technique gave the best results.
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Chapter Two – Literature Review
Fig. (2.18) – Test Set Up by Assih et al [105] 2.6. Summary and Conclusions: Reviewing the experimental researches carried out on corbels showed that there were very little researches on corbels under the effect of repeated loading; therefore, more studies are needed to investigate strengthened corbels subjected to this kind of loading, such as the present study. This investigation is important because most of th e corbels in practical life are under the effect of this kind of loading such as moving loads, of vehicles, on bridge girders supported by corbels or corbels supporting cranes in warehouses and so on. Finally, the following conclusions can be summarized from the available literature: 1)
The ultimate strength of a corbel, (Vu), is a function of its width (b), its effective depth (d), the reinforcement ratio ( ), the concrete strength ( f c' ) and the (av/d) ratio. All tests showed that the strength of corbels increased with the increasing of the amount of longitudinal, shear reinforcement and compressive strength of concrete and decreased with the increasing of the shear span to depth ratio (av/d).
2)
The horizontal reinforcement (stirrups) in corbels are as effective in resisting vertical loads as the main tension reinforcement, but they are not that effective with combined-loading, therefore, any contribution from the stirrups may be
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Chapter Two – Literature Review regarded as reserve strength. For that reason a minimum amount of stirrups should always be provided. 3)
Some investigators indicated that truss analogy is not applicable to corbels with low values of (av/d) ratios. (Somerville, 1972), as an example, limited the use of truss analogy to values of (av/d) ratios equal or greater than (0.6).
4)
Replacing the conventional secondary reinforcement with other kinds of reinforcement such as steel or polypropylene fibers, or even plastic meshes was found to be effective in improving the properties of the concrete corbels.
5)
Vertical stirrups are not useful for shear strength of a corbel with (av/d ≤ 1).
6)
Steel fibers, among many other kinds of fibers were the only form of secondary reinforcement that successfully reduced the widths of cracks in corbels. The presence of steel fibers increased the ultimate shear strength. The strength increased with the increase in the fiber volume and decreased with the increase of the (av/d) ratio.
7)
The role of fibers in combination with stirrups led to higher reduction in deflection.
8)
Fiber reinforcement is not an economical alternative to the main reinforcement for resisting flexure.
9)
The improvement in strength due the addition of fibrous reinforcement was more significant in high-strength concrete corbels relative to low or moderate strength concrete corbels.
10) Most researchers concluded that the ACI-318 code provisions for corbels were conservative for high strength concrete. 11) The provision of brackets and corbels in the ACI-318 code has only a lower limit for the volume fraction of main bars; therefore further studies should be performed to establish a more precise upper limit for the main bars that can be used efficiently in corbels. Literature Review
Page 55
Chapter Two – Literature Review 12) The finite element approach is regarded as a suitable tool for the analysis of normal and high-strength concrete corbels; the method may be used to predict the response of reinforced concrete structures in general. It is considered as a feasible method of analysis and design especially with the increasing of experimental costs and the decreasing of computational costs. 13) The strut-and-tie model is a simple and effective design tool that may give reasonable predictions of the failure load capacity of reinforced concrete corbels. 14) Using fibers as an external strengthening helped in enhancing the load carrying capacity of corbels subjected to monotonic loading; this enhancement depends on the orientation of the fibers, diagonal strips were found to be more effective than the horizontal strips. The enhancement in the corbel’s capacity for diagonal orientation was about twice the value of that for the horizontal orientation. 15) For the carbon fiber fabrics which were applied in a horizontal configuration, it was found that wrapping these fabrics around the specimens gave better results than applying them on the face and back of the corbels. For that reason the wrapping configuration was used in the present study to investigate the efficiency of this configuration with regard to the inclined configuration.
Literature Review
Page 56
Chapter Three – Experimental Work 3.
EXPERIMENTAL WORK:
3.1.
General:
The purpose of the experimental work performed in this study is to investigate the effectiveness of using unidirectional Reinforced Carbon Fiber Fabric, CFRP, as an external strengthening technique to increase the load carrying capacity of existing reinforced concrete corbels subjected to monotonic or non-reversed repeated loads. This chapter includes detailed information of construction materials used, trial mixes performed, the size and dimension of tested specimens and any information regarding the casting and curing of specimens. The experimental setup, testing procedures and instrumentation adopted throughout this investigation are presented as well. 3.2.
Experimental Program:
The experimental program consisted of casting and testing 20 normalweight reinforced concrete corbels, 15 of them were strengthened with CFRP strips and subjected to two types of loading, monotonic and non-reversed repeated loading. All specimens were cast with the same compressive strength and have the same dimensions, flexural reinforcement and horizontal shear reinforcement. The research specimens were designed following the ACI 318-M-14 [3] procedures with shear span to depth ratio of (0.461). The specimens were divided into two groups according to the nature of loading. The first group included six specimens tested under monotonic loading. The second group was divided into four subgroups which included fourteen specimens tested under non-reversed repeated loading. 3.2.1. Dimensions: The tested specimens’ scale was approximately one-third of a corbel from an actual project design. The double corbels were cast and tested as a simply supported beam where the load was applied on the column connecting the corbels, and the reactions Experimental Work
Page 57
Chapter Three – Experimental Work of the supports acted as the loads applied on the corbels. The shear span of the corbel was equal to 100 mm from the face of the column. The corbel segment had a width of 150 mm and a depth of 250 mm. All corbels were reinforced with 2 ϕ16 mm deformed longitudinal steel bars, acting as main tension reinforcement, Asc, located at an effective depth of 217 mm from the compression side of the corbel. The secondary reinforcement, A h, included 1 ϕ10 mm deformed steel bar in the form of a closed horizontal stirrup located at the mid height of the corbel. The column segment was reinforced with 4 ϕ12 mm main deformed steel bars and ϕ8 mm deformed stirrups placed at a spacing of 150 mm. The supports were located at 100 mm from the column face allowing a simply supported span of 40 mm; the concrete cover was set to 25 mm in all directions. The details of the research specimen are shown in Fig. (3.1). 150
1
2
150
4
6
Sec. (A-
5
Sec. (B-
3
100 A
250
2
B
1
A
3
B
4 5
300
6
250
200
250
Fig. (3.1) Details of Research Specimens
Experimental Work
Page 58
Chapter Three – Experimental Work The corbels were tested in an inverted position, as shown in Fig. (3.2); the vertical load, P, was applied to the top end of the column. The reactions of the supports, V, represented the loads applied to the corbel. P, Applied Load, kN P
300
mm
250
mm
100
mm
V=P/2 V=P/2 (V, kN, Reactions of Support, Load on Corbel) mm mm Load, kN mm 250 200 250 Fig. (3.2) Schematic Test Set Up, Inverted Position 3.3.
Test Variables:
The experimental program variables selected in this research included the following: Width of CFRP fabric, 50 mm (double the concrete cover), 100 mm (four times the concrete cover) and 150 mm (six times the concrete cover). Configuration of CFRP fabric, horizontal, H, Inclined, I and mixed, HI. The load history schemes used to apply the non-reversed repeated loading, LH1, LH2 and LH3). Experimental Work
Page 59
Chapter Three – Experimental Work 3.4.
Designation of Specimens:
Four categories were included in designating the specimens, the first category referred to the nature of the test, M for monotonic and R for repeated. The second category referred to the width of the strengthening strips used, 0 for specimens without strengthening, 50 for specimens with 50mm strengthening strips, 100 for specimens with 100mm strengthening strips and 150 for specimens with 150mm strengthening strips. The third category referred to the configuration of the strengthening strips used, W for specimens without strengthening, H for specimens with horizontal configuration, I for specimens with inclined configuration and HI for specimens with mixed configuration. Finally, the fourth category refers to the repeated loading history used, 1 for specimens tested under loading scheme LH1, 2 for specimens tested under loading scheme LH2 and 3 for specimens tested under loading scheme LH3. For example, the specimen (M-0-W) referred to the monotonically loaded specimen without strengthening and the specimen (R-50-H-1) referred to the non-reversed repeated loaded specimen strengthened with a 50mm horizontally-configured strip and tested under loading scheme LH1. The details of the research specimens are illustrated in Table (3-1). 3.5.
Material Properties:
In order to determine the properties of materials used throughout this investigation, standard tests were performed according to the American Society for Testing and Materials, ASTM Designation
[75-84]
and the Iraqi Standard Specification
I.Q.S NO.5-1984 [85 and 86].
Experimental Work
Page 60
Chapter Three – Experimental Work
1 2 3 4 5 6 7 8 9 10 11
M-0-W** M-0-W** Monotonic M-50-H Horizontal 50 Loading M 31.3 M-50-I Inclined 50 Regime M-50-HI** Mixed 50 M-50-HI** Mixed 50 R-0-W-1 RW R-0-W-2 30.9 R-0-W-3 R-50-H-1 Horizontal 50 30.9 RLH R-50-H-2 Horizontal 50 R-50-H-3*** Horizontal 50 12 NonR-50-H-3*** Horizontal 50 Reversed 31.3 13 R-100-H-3 Horizontal 100 RH Repeated Loading 14 R-150-H-3 Horizontal 150 Regime 15 R-50-I-3 Inclined 50 RI 16 R-100-I-3 Inclined 100 30.5 17 R-150-I-3 Inclined 150 18 R-50-HI-3 Mixed 50 RHI 19 R-100-HI-3 Mixed 100 30.5 20 R-150-HI-3 Mixed 150 * The average value of f c' 28 days for all batches = 30.9 MPa. ** Two specimens were tested for these categories. *** Specimen R-50-H-3 was studied with respect to two variables.
Experimental Work
Variables Considered
Loading History Scheme
Type of Loading Regime
fc’ (28 days) * (MPa)
Width of CFRP Strips (mm)
Configuration of CFRP Strips
Designation of Specimens
No. of Specimens
Groups
Table (3-1) – Details of Research Specimens
-
Configuration of CFRP Strips
LH1 LH2 LH3 LH1 LH2 LH3 LH3 LH3 LH3 LH3 LH3 LH3 LH3 LH3 LH3
Scheme of Loading History
Width and Configuration of CFRP Strips
Page 61
Chapter Three – Experimental Work 3.5.1. Cement: Ordinary Portland cement, type 1, was used in this investigation. The properties of the cement used conform to the Iraqi Specifications limits (I.Q.S. 5/1984)
[85]
for
ordinary Portland cement. The cement was kept in tight bags to avoid any exposure to wet conditions. The chemical composition and physical properties of the cement are listed in Tables (3-2) and (3-3) respectively.
Table (3-2) – Chemical Composition and Main Compounds of the Cement* Oxide Composition
% by weight
Iraqi Specifications Limits (I.Q.S. 5/1984)
20 61 1.6 < 5% 2 6 2.6 < 2.8% 0.28 2.04 < 4.0% 0.57 < 1.5% 0.94 0.66-1.02 Main Compounds (Bogue's Equation) C2S 70.52 C3S 2.27 C3A 6.31 C4AF 10.15 Chemical analysis was conducted at the National Center for Construction Laboratories and Researches, Baghdad.
SiO2 CaO MgO Fe2O3 Al2O3 SO3 Na2O L.O.I. I.R. L.S.F
Experimental Work
Page 62
Chapter Three – Experimental Work Table (3-3) – Physical Properties of Cement* Test Results
Physical Properties
Iraqi Specifications Limits (I.Q.S. 5/1984)
Specific Surface Area 245 > 230 (Blaine Method), (m2/kg) Autoclave Expansion % 0.34 < 0.8 Setting Time (Yicale's method) Initial Setting, hrs: min 2:10 > 45 min Final Setting, hrs: min 6:20 < 10 hrs Compressive Strength, MPa 3 days 22 > 15 7 days 35 > 23 Tests were conducted at the National Center for Construction Laboratories and Researches, Baghdad.
3.5.2. Fine Aggregate: The fine aggregate used in this investigation was brought from Al-Akhaidher region, in Karbala governorate. Before mixing the materials, the fine aggregate was sieved with a (4.75mm) sieve to separate the particle having a diameter greater than 4.75mm. The grading test results conformed to Iraqi Specification (I.Q.S. [86]
45/1984)
and (ASTM C33-13)
[76]
specifications as shown in Tables (3-4) and
(3-5) and Fig. (3.3). Table (3-4) Physical Properties of Fine Aggregate * Physical Properties
Test Results
Limits of the Iraqi Specification No.45/1984
Specific Gravity 2.58 Sulfate Content 0.231% 0.5% max. Absorption 0.75% Grading analysis was conducted by National Center for Construction Laboratories and Researches (Baghdad).
Experimental Work
Page 63
Chapter Three – Experimental Work Table (3-5) Grading of Fine Aggregate* Limits of the Iraqi ASTM, Specification C33/C33M−13 No.45/1984, (Zone 2) 9.5 100 100 100 4.75 100 90-100 95-100 2.36 88.3 75-100 80-100 1.18 60.1 55-90 50-85 0.6 37.2 35-59 25-60 0.3 9.7 8-30 5-30 0.15 1.67 0-10 0-10 Grading analysis was conducted by National Center for Construction Laboratories and Researches (Baghdad).
% Sieve Size, mm Passing
% Passing by Weight
% Passing by Weight
120 100 80 % Passing by Weight ASTM, C33M-13Lower Limit ASTM, C33M-13Upper Limit
60 40 20
120 100
0
80 % Passing by Weight
60
I. S. No.45/1984, min. (Zone 2) I. S. No.45/1984, max. (Zone 2)
40 20 0
0
1
2
3
4
5
6
7
8
9 10
0
1
2
Sieve Size, (mm)
3
4
5
6
7
8
9 10
Sieve Size, (mm)
(a) ASTM Limits (b) Iraqi Standards Limits Fig. (3.3) Grading of Fine Aggregate 3.5.3. Coarse Aggregate: The coarse aggregate used in this investigation was crushed gravel having a maximum size of 12.5 mm. The grading of the coarse aggregate tested conformed [86]
to the Iraqi Specification (I.Q.S. No. 45/1984) (ASTM C33-13) Experimental Work
[76]
and the specifications limits of
, as shown in Table (3-6) and Fig. (3.4). Page 64
Chapter Three – Experimental Work Table (3-6) Grading of Coarse Aggregate* Limits of the Iraqi ASTM, Sieve Size Specification C33/C33M−13 No. 45/1984, (5-14 mm) 19-mm 100 100 100 12.5-mm 98.6 90 - 100 90 - 100 9.5-mm 52.4 50 - 85 40 - 70 4.75-mm 4.3 0 - 10 0 – 15 Grading analysis was conducted by National Center for Construction Laboratories and Researches (Baghdad). % Passing
120
100 80 60 40 20 0 0
2
4
6
8
% Passing by Weight ASTM, C33M-13-min ASTM, C33M-13-max 10 12 14 16 18 20
Sieve Size, (mm)
% Passing by Weight
% Passing by Weight
120
100 80 60 40 20 0 0
2
4
6
% Passing by Weight I. S. No.45/1984-min I. S. No.45/1984-max 8 10 12 14 16 18 20
Sieve Size, (mm)
(a) ASTM Limits (b) Iraqi Standards Limits Fig. (3.4) Grading of Coarse Aggregate 3.5.4. Water: Ordinary tap water was used throughout this investigation for mixing and curing of all specimens. 3.5.5. Steel Reinforcement: Four sizes of deformed steel bars were used in this investigation; three specimens for each bar size were tested to determine their tensile properties according to ASTM 370-14a
[82]
; the tests were performed at three laboratories, the material
laboratory of the Material Department at the university of technology and the material laboratory of the Department of Production Engineering and Metallurgy at Experimental Work
Page 65
Chapter Three – Experimental Work the university of technology, for the small bar sizes, ϕ8, ϕ10 and ϕ12. The tests were repeated for all bar sizes at the material laboratory of the Civil Engineering Department at Al-Mustansiriya University. The results were almost the same from the three labs, for the same tested sizes, therefore the results of Al-Mustansiriya University were adopted throughout this investigation, because they included all sizes of bars. Test results for the deformed reinforcing steel bars used in this research met the ASTM A615/A615M-14 A1064/A1064M-14
[84]
[83]
for large bar sizes and
for small bar sizes. The properties of the reinforcement are
shown in Table (3-7). The caging of the reinforcement is shown in plate (3-1). The modulus of elasticity for all types of steel bars was assumed to be 200000 MPa. Table (3-7) – Properties of the Steel Reinforcement*
Purpose of Use Corbels’ Main Reinf. & Anchorage Reinf. Corbels’ Secondary Reinf. & Framing Bars Column’s Longitudinal Reinf. Ties for Column’s Reinf.
Bar Diameter (mm)
Actual Bar Diameter (mm)
Elongation (%Δ), [min. ASTM Limits]
Yield Stress fy (MPa)
Ultimate Stress fu (MPa)
16
15.9
10.7, [9]
497
760
10
9.7
10.6, [9]
756
887
12
12.7
11, [9]
655
739
8
9.03
10.7, [4.5]
667
724
Plate (3-1) - Reinforcement Caging used for Specimens Experimental Work
Page 66
Chapter Three – Experimental Work 3.5.6. Strengthening Materials: A woven carbon fiber fabric, Sika Wrap®-300 [87] , plate (3-2) and appendix C, was used for the structural strengthening of the specimens in this investigation, the CFRP strips. This material is a unidirectional woven carbon fiber fabric that consists of: 1) Mid strength carbon fibers. 2) Warp: black carbon fibers (99% of total areal weight). 3) Weft: white thermoplastic heat-set fibers (1% of total areal weight). The main characteristics of this material are: Equipped with weft fibers that keep the fabric stable (heat-set process). Multifunctional use for every kind of reinforcement. Flexibility of surface geometry (Beams, columns, chimneys, piles, walls). The manufacturer’s specifications for the laminates were as follows: Fiber Density Fabric Design Thickness Dry Fiber Properties Tensile Strength Tensile E-Modulus Elongation at Break Fabric Width:
:1.79 g/cm3 : 0.166 mm (based on fiber content) : 3’900 Mpa (nominal) : 230'000 Mpa : 1.5% (nominal) : 300 mm
Plate (3-2) - Sika Wrap®-300 used for Strengthening [87] Experimental Work
Page 67
Chapter Three – Experimental Work 3.5.7. Adhesive Materials: Two types of adhesive materials were used, one for the woven carbon fiber fabric and the other for the strain gauges. 1) Adhesive for the strengthening material: Sikadur 330
[88]
- A and B, 2-part
epoxy impregnation resin, plate (3-3) and appendix C. A B
Plate (3-3) - Sikadur 330, Strengthening Material Adhesive [88] 2) Adhesive for the strain gauges: two types of adhesive imported from TML Company
[89]
, plate (3-4), were used for gluing the strain gauges onto the
specimens during this investigation: CN-E, a single component, room-temperature-curing, for concrete. CN-Y, a single component, room-temperature-curing, Post-Yield gauge (large strain measurement), for reinforcing steel bars and carbon fiber fabrics.
Plate (3-4) - Special Glue for Strain Gauges, Imported from TML Tokyo Sokki Kenkynjo CO. Ltd, Japan [89] Experimental Work
Page 68
Chapter Three – Experimental Work 3.5.8. Coating Materials: The strain gauges used throughout this investigation were protected from natural effects by using special coating materials imported with the gauges from TML Company called SB Tape. This 3-mm thin tape-form coating, which can be considered as very convenient to use, has an operational temperature between −30 and +80 °C, and could be applied with pressure on the gauges; plate (3-5).
Plate (3-5) - Special Coating Materials, SB Tape from TML Tokyo Sokki Kenkynio CO. Ltd, Japan [89] 3.6.
Test Instrument Details:
In this section, all the devices used throughout this investigation will be introduced. 3.6.1. Forms: Four composite, steel and timber, forms were designed and manufactured for casting four corbels for each batch. The forms consist of a (650×200×150) mm column supporting two (150×250×250) mm, double corbels. A 3mm steel plate was used to manufacture the forms. Each form included four main components Experimental Work
Page 69
Chapter Three – Experimental Work working as the external edges of the specimen, and four secondary components to connect the external edges together. The main components are attached together and to a plywood base by bolts; to ensure a right angle sides, 20×20×50 mm angles were welded to support the sides of the main components. The forms were built in such a way that the specimens were cast horizontally. The details of one of the forms are shown in plate (3-6). Main Components
Secondary Components
Steel Angle
Steel Bolt Plywood Base Main Components
Plate (3-6) - Specimen’s Form Showing its Components The forms, well tightened and thoroughly cleaned, were placed, in their horizontal position, on a vibrating Table. The internal surfaces were oiled to facilitate molding. The steel reinforcement cage was placed inside the mold and the specimen was ready for casting, as shown in plate (3-7).
Plate (3-7) - Specimen’s Form with Reinforcement Cage Experimental Work
Page 70
Chapter Three – Experimental Work 3.6.2. Strain Gauges: To detect strains on the concrete, reinforcing steel bars and the carbon fiber fabric, strain gauges were attached on each part of the specimens throughout this investigation. All the strain gauges, adhesive and all other accessories were imported from TML Tokyo Sokki Kenkynjo CO. Ltd, Japan
[89]
. The strain gauges
used were of three types: FLA-5-11-3L and FLA-10-11-3L for steel reinforcement. PFL-30-11-3L, for concrete. BFLA-5-5-3L, for carbon fiber fabrics. All gauges were pre-attached, from the factory, with a vinyl lead wire of 3m in length, to facilitate the connecting of the gauges to the data logger for the purpose of recording the readings of the strain gauges. The characteristics of the strain gauges used throughout this investigation are listed in Table (3-8). The photos of strain gauges used are shown in plate (3-8).
Table (3-8) – Characteristics of Strain Gauges used in the Present Study
Gauge Series
Applicable Specimen
Bonding Adhesive/ Coating Material
FLA-5-11-3L
Metal
CN-Y/ SB tape
5
2.13±1 119.6±0.5
－20～＋80
FLA-10-11-3L
Metal
CN-Y/ SB tape
10
2.13±1 119.6±0.5
－20～＋80
PFL-30-11-3L
Concrete
CN-E/ SB tape
30
2.13±1 119.6±0.5
－20～＋80
Composite CN-Y/ SB tape
5
2.09±1 120.4±0.5 －20～＋200
BFLA-5-5-3L
Experimental Work
Operational Gauge Gauge Gauge Temperature Length Resistance Factor Range (mm) (Ω) (oC)
Page 71
Chapter Three – Experimental Work
Plate (3-8) - Strain Gauges used in this Study [89] 3.7.
Mix Design:
Several trial mixes were performed to select the suiTable mix used in this investigation; the mixes were designed following the ACI 211.1-91
[90]
, with a
maximum size for coarse aggregate of (12.5) mm, two water/cement ratios, 0.54 and 0.47, a (216) kg water content and a slump of (75-100) mm to obtain a cylindrical compressive strength, at the age of 28 days, of approximately 30 MPa and 35 MPa respectively. Table (3-9) shows the proportions, by weight, for each trial mix. Table (3-9) – Trial Mixes Performed in the Present Study Cement Sand Gravel Water w/c Slump No. (kg/m3) (kg/m3) (kg/m3) (kg/m3) Ratio (mm) 1 2 3
460 400 400
704.3 753.4 770
901 901 884
216 216 216
0.47 0.54 0.54
80 90 100
f c' 28 days
(MPa) 37 30.9 33.7
The mix used throughout the present study, mix No. 2, has the proportion by weight of (400: 753.5: 901), (Cement: Sand: Gravel) with a water/cement ratio of 0.54. Experimental Work
Page 72
Chapter Three – Experimental Work Six 150 mm cubes and eight 150×300 mm cylinders were cast for each mix to measure the compressive strength at the age of 7 and 28 days; the selected concrete mix resulted in an average cubic compressive strength of (29.4 and 38.6) MPa and an average cylindrical compressive strength of (24.6 and 30.6) MPa at the ages of 7 and 28 days respectively. 3.8.
Concrete Specimens:
The whole project included the casting of five batches; each batch included four concrete corbels, eight 150×300 mm cylinders, six 150 mm cubes and two 100×100×400 mm prisms, as shown in Plate (3-9).
Plate (3-9) - Corbels and Control Specimens Produced in One Batch 3.8.1. Control Specimens: The total number of control specimens was as follows: 1) Forty 150×300 cylinders, for compressive strength (fc), splitting tensile (ft) and elastic modulus (Ec) tests, 10 were tested at the age of 28 days and the remaining specimens were tested on the corbel’s test date. 2) Thirty 150 mm cubes for compressive strength (fcu) test, 15 were tested at the age of 28 days and the remaining specimens were tested on the corbel’s test date. Experimental Work
Page 73
Chapter Three – Experimental Work 3) Ten 100×100×400 mm prisms for the modulus of rupture (fr) test, 2 were tested at the age of 28 days and the remaining specimens were tested on the corbel’s test date. 3.8.2. Installation of Strain Gauges on Steel Reinforcement: Before placing the reinforcement cages into the forms, strain gauges were fixed onto the main reinforcement bars to register the strain in these bars during testing. Two strain gauges, with 3 m pre-attached vinyl lead wire, were installed in each corbel mounted on the main reinforcement; one on each bar in opposite directions, the location of these gauges is shown in Fig. (3-5) and Plate (3-10). The installation of strain gauges on reinforcing bars includes three stages: 1) Surface preparation: to ensure that strains on the reinforcement surface were fully transmitted to the strain gauge. 2) Gauge bonding. 3) Protective coating: to protect the instrument from any damage during casting and from the hostile environment of the concrete itself. Steel Strain Gauges
Fig. (3-5) - Locations of Steel Strain Gauges Experimental Work
Plate (3-10) - Locations of Steel Strain Gauges Page 74
Chapter Three – Experimental Work At the beginning, the surface of the bars was smoothed using a grinder then it was further smoothed using special paper and then the surface was cleaned using acetone, then the gauges were glued onto the bars, with a special glue from TML company, CN-Y, bought for this purpose, as shown in Plate (3-11).
Plate (3-11) - TML CN-Y Adhesive Finally the gauge was covered using special coating materials, SB Tape, as shown in Plate (3-12).
(a) Surface Preparation
(b) Gauge Fixing
(c) Protective Coating
Plate (3-12) – Stages for Installing Strain Gauges on Steel Reinforcement 3.9.
Casting and Curing:
The casting and curing of all specimens were performed under laboratory conditions at the Concrete Laboratory of the Building and Construction Eng. Dept. at the University of Technology.
Experimental Work
Page 75
Chapter Three – Experimental Work The Mixer used in this project was a (0.1 m3) horizontal drum mixer; as shown in Plate (3-13). The mixer was cleaned and moistened before placing the material.
Plate (3-13) - Photos of the Mixer Used in this Research 3.9.1. Mixing Procedure: After preparing and weighing all ingredients needed for this project, the coarse and fine aggregates were loaded into the mixer then the mixer was started for 3 minutes, then the cement was added and mixed for 3 more minutes, with a gradual addition of the mixing water required. The concrete, after all ingredients in the mixer, was mixed for 3 min followed by a 3-min rest, followed by a 2-min final mixing. The open end of the mixer was covered to prevent evaporation during the mixing period. A slump test was performed at the completing of each mixing process. In order to eliminate segregation, the machine-mixed concrete was deposited in a clean, damp mixing pan and remixed by a trowel before casting the specimens. 3.9.2. Casting and Curing of Main and Control Specimens: After the mixing process was completed, the molds for main and control specimens were placed on a vibrating Table and were ready for casting; each corbel was cast Experimental Work
Page 76
Chapter Three – Experimental Work in two layers. The molds for control cylinders were filled with fresh concrete in four equal layers, while the molds for control cubes and prisms were filled in two equal layers; each layer was compacted before adding the next layer. After casting, the surface of the concrete was leveled and finished with a trowel. In order to minimize moisture loss, both the main and control specimens were covered immediately after casting with nylon cloth. The cast of specimens was performed by five batches; each batch produced four corbels as the main specimens for the project, eight (150×300) mm cylinders, six 150 mm cubes and two (100×100×400) mm prisms as control specimens, as shown in Plate (3-14). After one day, both the main and control specimens were stripped and placed into curing tanks previously designed and manufactured for that reason, as shown in Plate (3-15).
Plate (3-14) Main and Control Specimens after Casting
Plate (3-15) - Photos of Curing Tanks for the Main and Control Specimens Experimental Work
Page 77
Chapter Three – Experimental Work After 28 days all specimens were removed from the tanks and left to dry for a week, and then the strengthening materials were applied. A photo of all specimens after curing is shown in Plate (3-16).
Plate (3-16) - All Specimens after Curing 3.10. Strengthening System: The strengthening system used in this research included a unidirectional woven carbon fiber fabric, Sika Wrap®-300
[87]
and a two component adhesive resins,
Sikadur 330 [88] resin, bought from Sika Company. To ensure a correct application of the external strengthening materials, it was necessary to improve the concrete surface which should be freshly exposed and free of loose or unsound materials. This improvement was done according to the manufacturer’s instruction [87 and 88]. It included removing the cement paste, grinding the surface by using a disc sander, and removing the dust generated by surface grinding using an air blower, then cleaning the surface with cleansing material. The corners of the specimens, where the fibers were wrapped, were rounded to a minimum (13 mm) radius in order to prevent stress concentrations in the FRP system and any voids between the FRP system and the concrete [12]. Experimental Work
Page 78
Chapter Three – Experimental Work After that the relevant glue, Sikadur 330, was applied to both the carbon fiber fabric and the concrete surface. Finally the fabric strips were applied to the specimens; photos of the strengthening process are illustrated in plate (3-17).
Plate (3-17) - Photos of the Strengthening Process The specimens were left for a week and then were painted with white paint; in order to help in monitoring cracks initiation and their propagation throughout the test. Before painting, the edges of the CFRP strips were covered with protecting tape to prevent applying the paint on them. The CFRP strips were applied on the specimens in three configurations as follows: 1) Horizontal configuration performed by wrapping the fabric around the edges of the specimen; an overlap of 100mm in length was left at the end of the wrapping as means of anchorage. 2) Inclined configuration performed by applying the fabric at the center of the inclined strut path and perpendicular to it at both sides of the corbels; to achieve anchorage, small strips were applied perpendicularly at the ends of the inclined strips. 3) Mixed configuration performed by applying the horizontal configuration first and then the inclined one.
Experimental Work
Page 79
Chapter Three – Experimental Work These three configurations were performed in three widths 50 mm, 100 mm and 150 mm. Photos of the strengthening process and samples for the 50 mm strips strengthened specimens are shown in plates (3-18) through (3-21).
Plate (3-18) - The White-Painted Non-Strengthened Specimen
Plate (3-19) - The White-Painted Horizontal 50 mm Strengthened Specimens
Plate (3-20) - The White-Painted Inclined 50 mm Strengthened Specimens
Plate (3-21) - The White-Painted Mixed 50 mm Strengthened Specimens
3.11. Installation of Strain Gauges on Concrete and Carbon Fiber Fabric: Before testing the specimens, strain gauges were fixed onto the concrete and the CFRP surfaces to record the strains in these materials during testing.
Experimental Work
Page 80
Chapter Three – Experimental Work The strain gauges were installed in each corbel mounted along the inclined strut path on the front side of the corbel to measure the concrete surface strains normal to the direction of the concrete strut and on the CFRP at the middle of the strip in the direction of the fibers, as shown in plate (3-22).
(a) Non-Strengthened
(b) Horizontal Configuration
(c) Inclined Configuration
(d) Mixed Configuration
Plate (3-22) - Location of Strain Gauges on Concrete and CFRP
3.12. Data Recording Two data loggers were used to record the test data. A data logger connected to the loading frame control system, was used to control the displacement and load applied to each specimen. Data obtained from the strain gauges were collected by another data logger, TDS-530 [89], on special paper, and this device is shown in plate (3-23). The data, converted into digital readings using the data logger, were stored in the computer and then were used to graph and analyze the test results.
Experimental Work
Page 81
Chapter Three – Experimental Work
Plate (3-23) - The TDS-530 Data Logger Used in this Study 3.13. Test Set-Up All specimens were tested by a 1000 kN (100 Ton) testing frame system, one of the apparatus of the structural laboratory of the Civil Engineering Department at AlNahrain University, as shown in plate (3-24). All information regarding this apparatus is illustrated in a separate manual, called Loading Frame User Manual (2014) [91]. The test set-up was composed of two components: the loading and supporting systems. The loading system included a top hydraulic jack supported by a stiff beam attached into the testing frame that applied the load to the top of the specimen, as shown in plate (3-25).
Experimental Work
Page 82
Chapter Three – Experimental Work
Plate (3-24) - Photos of the Testing Frame System
Stiff Beam Hydraulic Jack
Plate (3-25) - Photos of the Loading System Experimental Work
Page 83
Chapter Three – Experimental Work The supporting system included a set of steel bearing plates, (100×150×25) mm, (100×150×45) mm and (100×150×20) mm, the last plate was welded to a half steel tube and placed on the support of the testing machine to support the specimen, as shown in plate (3-26).
Plate (3-26) - Photos of the Supporting System The specimens were located in an inverted position where the vertical load was applied to a bearing plate (200×150×25) mm placed on the top of the column and the corbels were seated on the supporting steel bearing plates (100×150×25) mm, as shown in plate. (3-27).
(a) Front View
(b) Side View (c) Back View Plate (3-27) - The Test Set-Up Experimental Work
Page 84
Chapter Three – Experimental Work 3.14. Loading Regimes: The specimens were subjected to two types of loading: monotonic and nonreversed repeated Loading Regimes. 3.14.1. Monotonic Loading Regime: All specimens in the first Group, the Monotonic Group, were loaded monotonically up to failure. The testing machine was programmed to apply the load with an increasing rate of 2.2 kN/sec. The load and displacement recording starts from the moment the cylinder (the hydraulic jack) touches the specimen, where the reading records of the load and displacement are equal to zero, then the loading stage starts when the load is applied through the hydraulic jack on to the top of the column and increases gradually up to failure. At each second the load and deflection were recorded; the strain gauges readings were recorded throughout the test at an increment of 5 kN. 3.14.2. Non-Reversed Repeated Loading Regime: In this study the non-reversed repeated loading regime was following the load control investigation technique; the targeted repeated loading value depended on the failure load of the control specimens which were tested under a monotonic loading regime. For each cycle of loading the applied load was gradually increased up to the targeted load, which was a percentage of the failure load of the monotonic tested control specimen, then the load was gradually decreased to zero. The cycles were repeated according to the load history selected until failure occurs. Three loading histories were applied throughout this investigation depending on the results of the monotonic tested specimens; the sequence of the cycles followed a percentage of the failure load for the monotonic tested specimen. The percentages selected were: 20%, 40%, 60%, 80%, 90% and 95%.
Experimental Work
Page 85
Chapter Three – Experimental Work 1) The first loading history, LH1, had a minimum of 10 cycles as follows: Two cycles with 20% of the failure load. Two cycles with 40% of the failure load. Two cycles with 60% of the failure load. Three cycles with 80% of the failure load. If the specimen did not fail, more cycles with 90% of the failure load were applied up to failure. 2) The second loading history, LH2, had a minimum of 15 cycles as follows: Three cycles with 20% of the failure load. Three cycles with 40% of the failure load. Three cycles with 60% of the failure load. Three cycles with 80% of the failure load. Three cycles with 90% of the failure load. If the specimen did not fail, more cycles with 95% of the failure load were applied up to failure. 3) The Third loading history, LH3, had a minimum of 16 cycles as follows: Four cycles with 40% of the failure load. Four cycles with 60% of the failure load. Four cycles with 80% of the failure load. Four cycles with 90% of the failure load. If the specimen did not fail, more cycles with 95% of the failure load were applied up to failure. For each cycle of the loading histories, the load and deflection were recorded at each second, while the strain gauges readings were recorded at an increment of 20 kN. The loading histories are illustrated in Figs. (3.6) through (3.8).
Experimental Work
Page 86
Chapter Three – Experimental Work LH1
800
Load, kN
700
90% 80%
600 500
60%
400
40%
300 200
20%
100 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Cycle No.
Fig. (3.6) – Non-Reversed Repeated Load History, LH1 LH2
800
Load, kN
700
90%
95%
80%
600
500
60%
400 40%
300 200
20%
100 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Cycle No.
Load, kN
Fig. (3.7) – Non-Reversed Repeated Load History, LH2 LH3
800 700 600 500 400 300 200 100
90%
95%
80%
60% 40%
0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Cycle No.
Fig. (3.8) – Non-Reversed Repeated Load History, LH3 Experimental Work
Page 87
Chapter Four – Experimental Results and Discussion 4. EXPERIMENTAL RESULTS AND DISCUSSION: 4.1.
General:
The results of the experimental tests carried out on twenty normalweight concrete corbels, strengthened with CFRP strips, and subjected to either monotonic loading or non-reversed repeated loading regimes, are presented in this chapter, taking into account the effect of the adopted variables in enhancing the load carrying capacity of the tested corbels. The variables studied included the width and configuration of CFRP strips and the loading history used to apply the non-reversed repeated loading regime. The variables considered throughout this study were previously illustrated in Table (3-1), page 61. Test results of main corbel specimens including cracking loads, ultimate loads, tensile strain of main steel bars and CFRP strips, and strains in concrete during testing are presented in the shape of graphs, photos and Tables. Moreover, results of destructive tests on hardened concrete are listed and discussed. 4.2.
Properties of Hardened Concrete Used in this Research:
To study the properties of hardened concrete used throughout this research, some destructive tests were performed on control specimens cast for this reason, which were 40 cylinders, 30 cubes and 10 prisms; as the casting of the specimens was performed in five batches, for the cylinders; two were selected from each batch, making the whole number of ten. For the cubes, three were selected from each batch, making the whole number of fifteen and finally for the prisms, two were selected from the five batches. These selected control specimens were tested at the age of 28 days. The remaining control specimens were left to be tested on the day of testing the main corbel specimen, after four months. The destructive tests performed on these specimens were to calculate the cylindrical compressive strength, f c' , cubic compressive strength, f cu , the
Experimental Results & Discussion
Page 88
Chapter Four – Experimental Results and Discussion splitting tensile strength,
f ct ,
the flexural strength
fr
and the modulus of
elasticity Ec . These tests were performed using the equipment and test machines available in the concrete laboratory at the Building and Construction Engineering Department. The machines used for these test were: 1) The ADR 3000 Compression Machine, with the 100 kN Flexural Testing Frame connected to the power pack, for the cylinder and cubic compressive strength, the splitting tensile strength and the flexural strength, as shown in Plate (4-1). 2) The EN Standard Testing Machine, 2000/250 kN capacity, for the modulus of elasticity test, as shown in Plate (4-2). 4.2.1. The Cylinder Compressive Strength, f c' : Testing the compressive strength of concrete was performed following the ASTM Specification C39/C39M-14a
[77]
, the compressive strength of the specimen was
calculated by dividing the maximum load carried by the specimen during the test by the average cross-sectional area; the value and the mode of failure are shown in Plate (4-3). 4.2.2. The Modulus of Elasticity, Ec : Testing the static modulus of elasticity of concrete, Ec was performed following the ASTM Specification C469/C469M-14
[78]
, the modulus of elasticity is
calculated, to the nearest 200 MPa, as in equation (4-1): Ec S2 S1 / 2 0.00005
…… (4-1)
Where: Ec = chord modulus of elasticity, MPa. S2 = stress corresponding to 40% of ultimate load, MPa. S2 = stress corresponding to a longitudinal strain, 1 , of 50 millionths, MPa. 2
longitudinal strain produced by stress S2.
Experimental Results & Discussion
Page 89
Chapter Four – Experimental Results and Discussion The photos of the test are shown in Plate (4-4). 4.2.3. The Splitting Tensile Strength, f ct : Testing the splitting tensile strength of hardened concrete, following the ASTM Specification C496/C496M-11
[79]
f ct
was performed
, the splitting tensile
strength of the specimen is calculated as in equation (4-2): f ct 2 P / l d
…… (4-2)
Where: f ct = Splitting tensile stress, MPa.
P = maximum applied load indicated by the testing machine, N. l = length, mm, d = diameter, mm. The photos of the test are shown in Plate (4.5). 4.2.4. The Flexural Strength f r : Testing the flexural strength of hardened concrete, f r , was performed following the ASTM Specification C78/C78M − 10
[80]
, the modulus of rupture is calculated
as in equation (4-3): f r PL / b d 2
…… (4-3)
Where: fr = modulus of rupture, MPa. P = Maximum applied load indicated by the testing machine, N. l = span length, mm. b = average width of specimen at fracture, mm. d = average depth of specimen at fracture, mm. The photos of the test are shown in Plate (4-6). The results of these tests, at the age of 28 days, are illustrated in Table (4-1); these values were the average of three specimens for the cubic compressive strength, the cylinder compressive strength, the splitting tensile strength and the modulus of Experimental Results & Discussion
Page 90
Chapter Four – Experimental Results and Discussion elasticity, while for the flexural strength an average of two specimens were considered. Table (4-1) – Properties of Hardened Concrete at the Age of 28 Days
-
Theoretical Values, (MPa) -
30.9
-
-
3.05
f ct 0.56 f c'
3.11
Flexural Strength f r
3.07
f r 0.62 f c'
3.45
Modulus of Elasticity Ec
25100
Ec 4700 f c'
26126.25
Type of Test, Age(28 days) Cubic Compressive Strength, f cu
Cylindrical Compressive Strength, f Splitting Tensile Strength, f ct
' c
Tested Values, (MPa) 38.5
ACI Equations
Plate (4-1) - The ADR 3000 Compression Machine with the 100 kN Flexural Testing Frame
Plate (4-2) - The EN Standard Testing Machine for the Modulus of Elasticity Test Experimental Results & Discussion
Page 91
Chapter Four – Experimental Results and Discussion The results of the destructive test at the date of testing are listed in Table (4-2). Table (4-2) – Results of Destructive Tests Performed on Control Specimens (on the date of Test) f r * * Designation Age of f c fcu f ct f ct * f r MPa Ec of Specimen MPa MPa MPa MPa MPa (ACI) GPa Specimens (days) (ACI)
M-0-W
190
M-50-H
190
M-50-I
191
M-50-HI
222
R-0-W-1
192
R-0-W-2
194
R-0-W-3
197
R-50-H-3
205
R-100-H-3
205
R-150-H-3
210
R-50-H-2
Ec * * * GPa (ACI)
38.5
49.4
3.5
3.47
5.7
3.85
28.5
29.16
37.9
47.5
3.8
3.45
5.2
3.82
27.8
28.93
37.8
47.5
3.5
3.44
5.8
3.81
27.5
28.90
210
37
46.6
3.5
3.41
4.3
3.77
27.6
28.59
R-50-H-1
213
37.8
47.5
3.8
3.44
5.2
3.81
28.1
28.90
R-50-I-3
224
R-100-I-3
225
35
44
3.5
3.31
4.7
3.67
27.1
27.81
R-150-I-3
229
R-50-HI-3
231
R-100-HI-3
233
37
46.6
3.5
3.41
4.3
3.77
27.2
28.59
R-150-HI-3
233
f f
* = * * =
ct ACI
f ct 0.56 f c'
r ACI
f r 0.62 f c'
Ec ACI * * * =
Ec 4700 f c'
Experimental Results & Discussion
Page 92
Chapter Four – Experimental Results and Discussion
Plate (4-3) – Value and Mode of Failure after the Compressive Strength Test
Plate (4-4) - The Modulus of Elasticity Test
Plate (4-5) –Mode of Failure after the Splitting Tensile Strength Test
Plate (4-6) –The Modulus of Rupture Test Experimental Results & Discussion
Page 93
Chapter Four – Experimental Results and Discussion 4.3.
Response of Specimens Tested under Monotonic Loading Regime:
The monotonic loading test was very important to decide the number and amplitude of the non-reversed repeated loading cycles used throughout this research. The M-0-W, M-50-H, M-50-I and M-50-HI were the control specimens for the rest specimens tested under non-reversed repeated loading regime. Six specimens were cast and tested under monotonic loading regime; the specimens were tested in an inverted position where the load, P, was applied at the top of the inverted column, and the reactions of the supports represented the load applied to the corbels, V, which was equal to P/2. The load was applied with an increasing increment of 2.2 kN/sec until failure occurred. The results of these tests are shown in Table (4-3). Table (4-3) – Results of Main Corbel Specimens Tested under Monotonic Loading Regime (Group M) Designation Age of Pcr Δcr Pu Δu of Specimen Mode of Failure (kN) (mm) (kN) (mm) Specimens (days) M-0-W* 190 250 3.37 652 8.00 DS*** M-50-H 190 247 3.11 725 9.31 DS*** M-50-I 191 300 3.45 750 9.41 DS*** M-50-HI** 222 390 4.02 825 9.79 DS*** * Two specimens were tested for this category and the average value was used. ** Two specimens were tested for this category, and the values of the second specimen were used. *** DS = Diagonal Splitting Failure. 4.3.1. Crack Pattern and Modes of Failure: All specimens tested under monotonic loading regime, behaved in an elastic manner at low load levels and were free from cracks at early stages of loading. As the load was increased, diagonal cracks were developed. The first crack was observed at regions close to the bottom corbel-column joint, in its inverted position, propagating along the corbel-column interface. Then other cracks were observed at Experimental Results & Discussion
Page 94
Chapter Four – Experimental Results and Discussion the inner edge of the bearing Plate. These cracks were propagated much faster than the first crack. Finally, the cracks ran between the inner edges of the bearing Plate and the top corbel-column joint and were generally responsible for the failure of the corbel. At load levels close to failure, the inclined cracks became wider and propagated towards the upper corbel-column joint. Further increase in the applied load caused the formation of other cracks until failure occurred. Almost all cracks were diagonal shear cracks and were aligned along and parallel to the load’s line of action connecting the point of load application at the bottom face of the corbel, represented by the reactions of the supports, and the point of upper corbel-column joint. The mode of failure for all the specimens tested under monotonic loading regime was diagonal splitting failure. The crack pattern and mode of failure for the monotonically loaded specimens are shown in Plates (4-7) through (4-10).
M-0-W
Plate (4-7) – The Crack pattern and Mode of Failure for Monotonically Loaded Specimen, M-0-W
Experimental Results & Discussion
Page 95
Chapter Four – Experimental Results and Discussion
M-50-H
Plate (4-8) – The Crack pattern and Mode of Failure for Monotonically Loaded Specimen, M-50-H
M-50-I
Plate (4-9) – The Crack pattern and Mode of Failure for Monotonically Loaded Specimen, M-50-I
Experimental Results & Discussion
Page 96
Chapter Four – Experimental Results and Discussion
M-50-HI
Plate (4-10) – The Crack pattern and Mode of Failure for Monotonically Loaded Specimen, M-50-HI 4.3.2. Effect of Strengthening Technique on Cracking and Failure Loads: The effect of strengthening corbels with 50mm of CFRP Strips in horizontal, inclined and mixed configurations on the cracking and failure loads are illustrated in Table (4-4) and Fig. (4.1). Table (4-4) – Effect of Strengthening Technique on the Cracking and Failure Loads for Group M Designation Pcr of (kN) Specimens M-0-W M-50-H M-50-I M-50-HI
250 247 300 396
Pcr S 100 Pcr W
98.8 120 158.4
Experimental Results & Discussion
cr S Pu Δcr 100 (mm) (kN) cr W
3.37 3.11 3.45 4.02
92.3 102 119
652 725 750 825
Pu S 100 PuW
111 115 127
u S Δu 100 (mm) uW
8.00 9.31 9.41 9.79
116 118 122
Page 97
Load, kN
Chapter Four – Experimental Results and Discussion
900 800 700 600 500 400 300 200 100 0
Monotonic Tested Specimens
Pcr Pu W/O
50mm-H
50mm-I
50mm-HI
Fig. (4.1) – Effect of CFRP Strips Configuration on the Cracking and Failure Loads of Group M It can be noted that the first crack appearance was delayed by this strengthening technique. It can also be noted that this type of strengthening helped in enhancing the load carrying capacity with about 11%, 15% and 27% for the horizontal, inclined and mixed configurations respectively, corresponding to an increase in the ultimate deflection of 16%, 18% and 22% respectively. 4.3.3. Load-Displacement Response: The load-displacement responses for the specimens M-0-W, M-50-H, M-50-I and M-50-HI are shown in Fig. (4.2). Testing was terminated when failure occurred, the failure of the specimen was recognized either by the damage occurring or when the load could no longer be increased or starts to decrease with the continued increase in deflection. The deflection represents the movements of the loading jack, which correspond to the deflection at the center of the column supporting the double corbels. For the tested specimens: M-0-W, M-50-H, M-50-I and M-50-HI, the ultimate vertical loads recorded, Pu, were 652 kN, 725 kN, 750 kN and 825 kN, corresponding to ultimate displacements, Δu, of 8 mm, 9.31 mm, 9.41 mm and 9.79 mm respectively.
Experimental Results & Discussion
Page 98
Chapter Four – Experimental Results and Discussion 900 800
Load, Pu, kN
700 600 500 400 M0W, Pu= 652 kN, Δu=8 mm
300
M50H, Pu= 725 kN, Δu= 9.31 mm
200
M50I, Pu= 750 kN, Δu= 9.41 mm
100
M50HI, Pu= 825 kN, Δu= 9.79 mm
0 0
1
2
3
4
5
6
7
8
9
10
11
12
Deflection, mm
Fig. (4.2) - The Load-Deflection Curves of Group M By observing the curves it can be noted that at early stages of loading the curves were linear with almost constant slope, which was expected because the specimens were within their elastic stage. After the initiation of first cracks the curves were taking a nonlinear form with variable slopes; the nonlinear form continued with the increasing of the load amount until failure occurred. 4.4.
Response of Specimens Tested under Non-Reversed Repeated Loading Regime:
Fourteen specimens were tested under non-reversed repeated loading regime; the specimens were divided into five groups. The first group, RW, included three nonstrengthened specimens, R-0-W, subjected to three different non-reversed repeated loading regimes, LH1, LH2 and LH3. The second group, RLH included three specimens strengthened with 50 mm width of CFRP strips in the horizontal configuration, R-50-H, subjected to the three nonreversed repeated loading regimes, LH1, LH2 and LH3, to study the effect of the different regimes on the load carrying capacity of the strengthened corbels.
Experimental Results & Discussion
Page 99
Chapter Four – Experimental Results and Discussion The third group, RH, included three specimens strengthened with three widths of CFRP strips in the horizontal configuration, R-50-H, R-100-H and R-150-H. The fourth group, RI, included three specimens strengthened with three widths of CFRP strips in the inclined configuration, R-50-I, R-100-I and R-150-I. Finally, the fifth group, RHI, included three other specimens strengthened with three widths of CFRP strips in both horizontal and inclined configurations, R-50-HI, R-100-HI and R-150-HI. The latter three groups were subjected to the third nonreversed repeated loading regime, LH3. The repeated loading histories were applied depending on the results of the monotonic tested specimens; the sequence of the cycles followed a percentage of the failure load for the monotonic tested specimen. The percentages selected were: 20%, 40%, 60%, 80%, 90% and 95%, as was explained previously in chapter 3, clause 3.14.2 and Figs. (3-6), (3-7) and (3-8). The details of the cycles, (Ci), of the three load histories are shown in Table (4-5), where (i) refers to the cycle’s number. The amplitudes of the cycles of the repeated loading histories are shown in Table (4-6). Table (4-5) – The Details of the Cycles of the Repeated Loading Histories No. of % of Load Loading Cycles History 20% 40% 60% 80% 90% 95% C3-C4 C5-C6 C7-C9 C1-C2 C1010LH1 C4-C6 C7-C9 C10-C12 C13-C15 C16C1-C3 16LH2 C5-C8 C9-C12 C13-C16 C17C1-C4 17LH3 A change in the sequence of the cycles was performed in LH3, which included 4 cycles in each percentage of the failure load. The first cycle started from 40%. This change was done after testing the first two load history schemes, where the specimens behaved in an elastic manner through the first two or three cycles with 20% of the load; therefore, it was decided to discard this percentage in LH3. Experimental Results & Discussion
Page 100
Chapter Four – Experimental Results and Discussion The failure load of the control specimen M-0-W, 652 kN, was the base for the RW group (R-0-W-1, R-0-W-2 and R-0-W-3) specimens. Table (4-6) – The Amplitudes of the Cycles of the Repeated Loading Histories Based Repeated Monotonic Group Group
Repeated Loading History Scheme
% of Load
Load kN 20%
40%
60%
80%
90%
95%
Rw
M-0-W
LH1, LH2 & LH3
652
130
260
390
520
587
620
RLH
M-50-H
LH1, LH2 & LH3
725
145
290
435
580
650
685
RH
M-50-H
LH3
725
-
290
435
580
650
685
RI
M-50-I
LH3
750
-
300
450
600
675
710
RHI
M-50-HI
LH3
825
-
320
480
650
720
750
The failure load of the control specimen M-50-H, 725 kN, was the base for both the RLH and RH groups (R-50-H-1, R-50-H-2, R-50-H-3, R-100-H-3 and R-150-H-3) specimens. The failure load of the control specimen M-50-I, 750 kN, was the base for the RI group (R-50-I-3, R-100-I-3 and R-150-I-3) specimens. Finally, the failure load of the control specimen M-50-HI, 825 kN, was the base for the RHI group (R-50-HI-3, R-100-HI-3 and R-150-HI-3) specimens. The specimens of group RW (R-0-W-1, R-0-W-2 and R-0-W-3) were tested under LH1, LH2 and LH3 respectively, where the numbers 1, 2 and 3 refer to the load history schemes used. The results for group RW regarding the effect of the repeated loading regime on the mode of failure, first crack and the reduction in the strength are described in Table (4-7).
Experimental Results & Discussion
Page 101
Chapter Four – Experimental Results and Discussion Table (4-7) – Results of Main Corbel Specimens Tested under Non-Reversed Repeated Loading Regime, (Group RW) Specimen Name
Cracking Age Load Δcr, (days) Pcr (mm) (kN)
Failure Load Pf (kN)
Δu (mm)
Max. R. L. Before Failure (kN)
Modes of Failure
% Decreasing in (Pu)
M-0-W
190
250
3.37
652
8.00
-
DS*
-
R-0-W-1
192
196-C3
2.83
577-C10
7.85
520-C9
SS**
11.5
R-0-W-2
194
230-C4
3.20
570-C13
7.19
520-C12
DS*
12.6
R-0-W-3
197
121-C1
1.86
547-C14
7.80
587-C13
DS*
16.1
* DS = Diagonal Splitting Failure ** SS = Sliding Shear Failure
From the results obtained, it can be observed that the failure loads for specimens tested under non-reversed repeated loading regimes, LH1, LH2 and LH3, were lower than those for the specimen tested under monotonic loading regime by 11.5%, 12.6% and 16.1% respectively. According to these results, it was observed that LH3 gave the worst results represented in the maximum reduction in the failure load; therefore, it was decided to use this loading history for the last three groups of the specimens tested under non-reversed repeated loading regime. Moreover, the maximum repeated load reached for the specimens tested under the first two loading schemes was 520 kN. This load is less than the maximum repeated load for the specimen tested under LH3, which reached 587 kN for one cycle before failure. 4.4.1. Crack Pattern and Modes of Failure: The results of all the specimens tested under non-reversed repeated loading regime including the first cracking load, the first cracking deflection, the ultimate load, the ultimate deflection and the modes of failure, are illustrated in Table (4-8).
Experimental Results & Discussion
Page 102
Chapter Four – Experimental Results and Discussion Table (4-8) – Results of Main Corbel Specimens Tested under Non-Reversed Repeated Loading Regime, (All Groups) Name of Specimen
Groups
RW
RLH
RH
RI
RHI
R-0-W-1 R-0-W-2 R-0-W-3 R-50-H-1 R-50-H-2 R-50-H-3 R-50-H-3 R-100-H-3 R-150-H-3 R-50-I-3 R-100-I-3 R-150-I-3 R-50-HI-3 R-100-HI-3 R-150-HI-3
Cracking Age Load Δcr (days) Pcr (mm) (kN) 192 194 197 213 210 205 205 205 210 224 225 229 231 233 233
196-C3 230-C4 121-C1 200-C3 242-C4 240-C1 240-C1 322-C5 435-C5 250-C1 410-C5 380-C5 310-C3 440-C5 400-C9
2.83 3.20 1.86 2.63 3.36 3.14 3.14 3.92 4.68 2.91 3.97 4.10 3.55 4.93 4.48
Failure Load Pf (kN)
Δu (mm)
577-C10 570-C13 547-C14 636-C11 616-C13 605-C14 605-C14 659-C17 680-C17 646-C14 683-C17 679-C15 659-C13 703-C17 687-C14
7.85 7.19 7.80 7.80 7.69 7.87 7.87 7.60 7.55 7.65 7.29 7.76 7.03 7.80 7.24
Max. No. of R. L. Modes Cycles before of before Failure Failure Failure (kN) C9-520 3 SS C12-520 3 DS C13-587 1 DS C10-650 1 DS C12-580 3 SS+LBF C13-650 1 SS C13-650 1 SS C16-650 4 SS C16-650 4 DS+STF C13-675 1 DS C16-675 4 DS C14-675 2 DS C12-650 4 DS C16-720 4 DS C13-720 1 DS+CCF
Where: DS SS STF LBF CCF
: Diagonal Splitting Failure. : Sliding Shear Failure. : Shear Tension Failure, at Extreme Fiber in Tension. : Local Bearing Failure. : Column Crushing Failure.
Test results showed that specimens, with or without strengthening, tested under LH1 and LH2, starting with 20% of the failure’s load of the monotonic tested specimens, were free from cracks through the first two or three cycles. This is because the amplitudes of these cycles were less than the cracking load of the monotonic specimens. In contrast, the first crack was observed in the first cycles of most specimens tested under LH3, starting with 40% of the failure’s load of the monotonically tested specimen, especially the specimens strengthened with 50 mm Experimental Results & Discussion
Page 103
Chapter Four – Experimental Results and Discussion of CFRP strips, as in specimens R-0-W-3, R-50-H-3 and R-50-I-3. With the increasing of the width of strengthening strips from 50 mm to 150 mm, the appearance of the first crack was delayed to the second, third, fifth and ninth cycles. After the appearance of the first cracks, more new cracks were observed in the following consecutive cycles with the same altitude. As in the monotonically tested specimens, the first crack started from regions close to the bottom corbel-column joint propagating along the corbel-column interface. No further cracks were observed during the unloading part of the cycles throughout all the tests. As the cycles progressed with 60% of the failure load, more diagonal shear cracks were observed along and parallel to the load’s line of action connecting the point of load application at the bottom face of the corbel and the point of upper corbelcolumn joint. When the load reached 80% of the failure load, new inclined cracks were progressed along the column-corbel interface and these cracks became wider and propagated towards the upper corbel-column joint, in the final cycles the cracks became wider and failure occurred in the ascending part of the cycle before reaching its peak. With successive cycles the cracks were observed to be propagated between the inner edges of the bearing Plate and the top corbel-column joint and were generally responsible for the failure of most of the corbels. Different modes of failure were observed in the groups tested under non-reversed repeated loading regimes. Diagonal splitting failure could be recognized in specimens R-0-W-2, R-0-W-3, R-50-H-1, R-50-I-3, R-100-I-3, R-150-I-3, R-50HI-3, R-100-HI-3 and R-150-HI-3; while Sliding Shear failure were observed in specimens R-0-W-1, R-50-H-3 and R-100-H-3. For specimen R-50-H-2, the mode Experimental Results & Discussion
Page 104
Chapter Four – Experimental Results and Discussion of failure was sliding shear accompanied by local bearing failure, while for specimen R-150-H-3 the mode of failure was diagonal splitting and shear-tension failure, at extreme tension fiber. The cracks and the modes of failure for all specimens tested under non-reversed repeated loading regimes are shown in Plates (4-11) through (4-24).
Plate (4-11) - The Crack pattern and Mode of Failure for Specimen R-0-W-1
Plate (4-12) - The Crack pattern and Mode of Failure for Specimen R-0-W-2
Experimental Results & Discussion
Plate (4-13) - The Crack pattern and Mode of Failure for Specimen R-0-W-3
Page 105
Chapter Four – Experimental Results and Discussion
Plate (4-14) - The Crack pattern and Mode of Failure for Specimen R-50-H-1
Plate (4-15) - The Crack pattern and Mode of Failure for Specimen R-50-H-2
Plate (4-16) - The Crack pattern and Mode of Failure for Specimen R-50-H-3
Plate (4-17) - The Crack pattern and Mode of Failure for Specimen R-100-H-3
Experimental Results & Discussion
Page 106
Chapter Four – Experimental Results and Discussion
Plate (4-18) - The Crack pattern and Mode of Failure for Specimen R-150-H-3
Plate (4-19) - The Crack pattern and Mode of Failure for Specimen R-50-I-3
Experimental Results & Discussion
Page 107
Chapter Four – Experimental Results and Discussion
Plate (4-20) - The Crack pattern and Mode of Failure for Specimen R-100-I-3
Plate (4-21) - The Crack pattern and Mode of Failure for Specimen R-150-I-3
Plate (4-22) - The Crack pattern and Mode of Failure for Specimen R-50-HI-3
Plate (4-23) - The Crack pattern and Mode of Failure for Specimen R-100-HI-3
Experimental Results & Discussion
Page 108
Chapter Four – Experimental Results and Discussion
Plate (4-24) - The Crack pattern and Mode of Failure for Specimen R-150-HI-3 4.4.2. Effect of Non-Reversed Repeated Loading Regime: Most of the previous work available in the literature has dealt with concrete corbels subjected to monotonically applied loadings regimes; few researchers studied the effect of few cycles of repeated loading regimes on corbels cast with different types of concrete such as (Muhammad, 1998) and (Farhan, 2014); others tried to strengthen the concrete corbels with different types of strengthening materials and tested their specimens under monotonically applied loadings regimes. But unfortunately, most of the structures in practice can be subjected to reversed and non-reversed repeated loading; such loadings are significant in structures subjected to moving loads, earthquakes and hurricanes. One of the objectives of this research is to investigate the effect of different schemes of non-reversed repeated loading on the behavior of normalweight concrete corbels strengthened with CFRP strips. The effect of non-reversed repeated loading on the carrying capacity of corbels would be studied through comparing similar strengthened corbels tested under both Experimental Results & Discussion
Page 109
Chapter Four – Experimental Results and Discussion monotonic and non-reversed repeated loading regimes. The comparison was performed through two fields as follows: 4.4.2.1. With Respect to Monotonic Tested Specimens: For this purpose, three specimens, strengthened with 50 mm CFRP strips, in the horizontal configuration, R-50-H-1, R-50-H-2 and R-50-H-3, were tested under the three loading histories, LH1, LH2 and LH3. The effect on the cracking and failure loads are illustrated in Tables (4-9) and (4-10) respectively, as well as in Fig. (4.3). Table (4-9) – Effect of Non-Reversed Repeated Loading Regimes on the Cracking Load of Group RLH Cracking Specimen Load Name Pcr (kN) M-50-H 247 R-50-H-1 200-C3 R-50-H-2 242-C4 R-50-H-3 240-C1
Pcr R 100 Pcr M
Δcr, (mm)
cr S 100 cr W
80.97 97.98 97.17
3.11 2.63 3.36 3.14
84.57 108.04 100.97
Table (4-10) – Effect of Non-Reversed Repeated Loading Regimes on the Failure Load of Group RLH Specimen Name M-50-H R-50-H-1 R-50-H-2 R-50-H-3
Failure Load Pf (kN) 725 636-C11 616-C13 605-C14
Experimental Results & Discussion
Pu S 100 PuW
Δu, (mm)
u S 100 uW
87.72 84.97 83.45
9.31 7.80 7.69 7.87
97.50 96.13 98.38
Page 110
Load, P, kN
Chapter Four – Experimental Results and Discussion
900 800 700 600 500 400 300 200 100 0
Repeated Loading Histories (LH1, LH2 and LH3) C11
C13
C14 Pcr Pu
C3 M50H
C4
C1
R50H1 R50H2 R50H3
Fig. (4.3) – Effect of Non-Reversed Repeated Loading Regimes on the Cracking and Failure Loads of Group RH It was observed that the load, at which the first crack of the monotonic tested specimen was appeared, has the highest value from the load at which the first crack of the other three specimens tested under LH1, LH2 and LH3; for the latter three specimens, the first crack appeared in the cycles with load amplitudes higher than or equal to the load of first crack in the monotonic tested specimen. It was also observed that there was a reduction in the cracking loads for the three specimens tested under LH1, LH2 and LH3 of about 19.03%, 2.02% and 2.83% respectively. The same reduction was observed with the failure load of about 12.28%, 15.03% and 16.55% respectively. This reduction in the load capacity, between the three histories used, showed that the sequence and magnitude of the non-reversed repeated loading regime used affect the behavior of strengthened reinforced concrete corbel. Moreover, the reduction in the load capacity could be related to the excessive cracks in the concrete specimens through the consecutive cycles of loading and was affected by the number and amplitudes of the cycles. Plate (4-25) shows the development of cracks through the consecutive cycles of LH3, for the corbel specimen R-0-W-3. Experimental Results & Discussion
Page 111
Chapter Four – Experimental Results and Discussion
(C1)
(C2-C4)
(C9-C12)
(C5-C8)
(C13-C14)
Plate (4-25) – The Crack Pattern through the Consecutive Cycles for Specimen R-0-W-3 4.4.2.2. With Respect to Strengthening Technique: Six specimens, within two groups, were cast and tested in order to study the effect of CFRP strengthening technique on normal corbels subjected to different schemes of non-reversed repeated loading. The first group included three specimens, which were kept plane without strengthening, R-0-W-1, R-0-W-2 and R-0-W-3. The other group included three specimens which were strengthened with 50 mm CFRP strips oriented horizontally, R-50-H-1, R-50-H-2 and R-50-H-3. Both groups were tested under LH1, LH2 and LH3 respectively. The results are shown in Table (4-11).
Experimental Results & Discussion
Page 112
Chapter Four – Experimental Results and Discussion Table (4-11) – Effect of Non-Reversed Repeated Loading Regimes on the Cracking and Failure Loads for Groups RW and RH Cracking Specimen Load Groups Name Pcr (kN) R-0-W-1 196-C3 RW R-0-W-2 230-C4 R-0-W-3 121-C1 R-50-H-1 200-C3 RH-50mm R-50-H-2 242-C4 R-50-H-3 240-C1
Pc S 100 Pc W
Δcr (mm)
102 109.6 198.4
2.83 3.20 1.86 2.63 3.36 3.14
Failure Load Pf (kN) 577-C10 570-C13 547-C14 636-C11 616-C13 605-C14
Pu S 100 PuW
Δu, (mm)
110.2 105 110.6
7.85 7.19 7.80 7.80 7.69 7.87
By comparing the test results of the two groups it could be noted that strengthening the corbels with 50 mm CFRP strips wrapped horizontally around the specimens helped in delaying the appearance of the first crack. The percentage of increase in the amount of cracking load was about 2%, 9.6% and 98.4% for the three schemes of non-reversed repeated loading used in this research, LH1, LH2 and LH3 respectively. It was also observed that there was an increase in the ultimate load of about 10.2%, 5% and 10.6% for the three schemes of loading used in this research respectively. 4.4.3. Effect of the Width of CFRP Strips: To study the effect of width of the CFRP strengthening strips, three sizes of strips were used in this study, twice the concrete cover, 50 mm, four times the concrete cover, 100 mm and six times the concrete cover, 150 mm, applied in different configurations, horizontally, inclined and mixed. Nine specimens were cast for that reason, R-50-H, R-100-H, R-150-H, R-50-I, R-100-I, R-150-I, R-50-HI, R-100-HI and R-150-HI. All specimens were tested under the third scheme of non-reversed repeated loading, LH3. The effect of width
Experimental Results & Discussion
Page 113
Chapter Four – Experimental Results and Discussion is shown in Tables (4-12) through (4-14) and Figs. (4.4) through (4.6) for the horizontal, inclined and mixed configurations respectively. Table (4-12) – Effect of CFRP Strips’ Width on the Cracking and Failure Loads for Group RH Name of Specimen
Cracking Load Pcr (kN)
R-50-H-3 R-100-H-3 R-150-H-3
240-C1 322-C5 435-C5
Pcr n 100 Pcr 50
134.17 181.25
Failure Load Δcr (mm) Pf (kN) 3.14 3.92 4.68
605-C14 659-C17 676-C17
Pu n 100 Pu 50
108.93 111.74
Δu (mm) 7.87 7.60 7.55
Max. R. L. before Failure (kN) 650 650 650
Table (4-13) – Effect of CFRP Strips’ Width on the Cracking and Failure Loads for Group RI Name of Specimen
Cracking Load Pcr (kN)
R-50-I-3 R-100-I-3 R-150-I-3
250-C1 410-C5 380-C5
Failure Pcr n 100 Load Δcr Pcr 50 (mm) Pf (kN) 164 152
2.91 3.97 4.10
646-C14 683-C17 679-C15
Pu n 100 Pu 50
105.73 105.11
Δu (mm) 7.65 7.29 7.76
Max. R. L. before Failure (kN) 675 675 675
Table (4-14) – Effect of CFRP Strips’ Width on the Cracking and Failure Loads for Group RHI Name of Specimen
Cracking Load Pcr (kN)
R-50-HI-3 R-100-HI-3 R-150-HI-3
310-C3 440-C5 400-C9
Pcr n 100 Pcr 50
141.94 129.03
Experimental Results & Discussion
Failure Load Δcr (mm) Pf (kN) 3.55 4.93 4.48
659-C13 703-C17 687-C14
Pu n 100 Pu 50
106.68 104.25
Δu (mm) 7.03 7.80 7.24
Max. R. L. before Failure (kN) 650 720 720 Page 114
Chapter Four – Experimental Results and Discussion From test results it can be noted that increasing the width of the strengthening CFRP strips, for the three categories of configurations, from 50 mm to 150, delayed the appearance of the first crack to the fifth and ninth cycles respectively. The increase of the strip’s width from 50 mm to 100 mm and 150 mm, led to an increase in the amount of cracking load of about 34% and 81%, for the horizontal configuration, 64% and 52%, for the inclined configuration and 42% and 29%, for the mixed configuration respectively. The same was observed in the failure load but with less percentage of increase which was about 9% and 12% for the horizontal configuration, 6% and 5%, for the inclined configuration and 7% and 4%, for the mixed configuration respectively. Moreover, it was observed that the increase in the width of the strips from 50 mm to 150 mm made the specimen stronger and was able to bear the repeated loading for more cycles before failure occurred. From these results it was obvious that the strengthening with 100mm strips, four times the concrete cover, gave the best results for the three different configurations used, therefore it may be recommended in the future to use this amount of width in strengthening reinforced concrete corbels.
Load, P, kN
Horizintal Strips 900 800 700 600 500 400 300 200 100 0
C14
C17
C17
C5 C1 50mm
C5 100mm
Pcr Pu 150nn
Fig. (4.4) – Effect of Width of CFRP strips on the Cracking and Failure Loads of Group RH Experimental Results & Discussion
Page 115
Chapter Four – Experimental Results and Discussion
Load, kN
Inclined Strips 900 800 700 600 500 400 300 200 100 0
C14
C17
C17
C5 C5 Pcr Pu
C1 50mm
100mm
150mm
Fig. (4.5) – Effect of Width of CFRP strips on the Cracking and Failure Loads for Group RI
Load, kN
Mixed-HI-Strips 900 800 700 600 500 400 300 200 100 0
C13
C17
C5
C14
C9
C3 50mm
Pcr Pu 100mm
150mm
Fig. (4.6) – Effect of Width of CFRP strips on the Cracking and Failure Loads for Group RHI 4.4.4. Effect of the Configuration of CFRP Strips: The effects of the application of the CFRP strips in different configurations are shown in Tables (4-15) through (4-17) and Figs. (4.7) through (4.9). When comparing the results of the strengthened corbels in different configurations, it was obvious that the inclined strengthening gave the best result regarding the cracking and failure loads, and as for the successive cycles of non-reversed repeated loading, this kind of strengthening technique, made the specimen stronger Experimental Results & Discussion
Page 116
Chapter Four – Experimental Results and Discussion and was able to bear more cycles from the non-reversed repeated loading regime used than the other two techniques, before failure occurred. Table (4-15) – Effect of CFRP Strips’ Configuration on the Cracking and Failure Loads for R-50-H-3, R-50-I-3 and R-50-HI-3 Name of Specimen
Cracking Load Pcr (kN)
Pc O 100 Pc H
R-50-H-3 R-50-I-3 R-50-HI-3
240-C1 250-C1 310-C3
104.17 129.17
Failure Δcr Load (mm) Pf (kN) 3.14 2.91 3.55
605-C14 646-C14 659-C13
Pu O 100 Pu H
106.78 108.93
Δu (mm) 7.87 7.65 7.65
Max. R. L. before Failure (kN) 650 675 650
Table (4-16) – Effect of CFRP Strips’ Configuration on the Cracking and Failure Loads for R-100-H-3, R-100-I-3 and R-100-HI-3 Name of Specimen
Cracking Load Pcr (kN)
Pc O 100 Pc H
R-100-H-3 R-100-I-3 R-100-HI-3
322-C5 410-C5 440-C5
127.33 136.65
Failure Δcr Load (mm) Pf (kN) 3.92 3.97 4.93
659-C17 683-C17 703-C17
Pu O 100 Pu H
103. 64 106.68
Δu (mm) 7.60 7.29 7.29
Max. R. L. before Failure (kN) 650 675 720
Table (4-17) – Effect of CFRP Strips’ Configuration on the Cracking and Failure Loads for R-150-H-3, R-150-I-3 and R-150-HI-3 Name of Specimen
Cracking Load Pcr (kN)
Pc O 100 Pc H
R-150-H-3 R-150-I-3 R-150-HI-3
435-C5 380-C5 400-C9
87.36 91.95
Experimental Results & Discussion
Failure Δcr Load (mm) Pf (kN) 4.68 4.10 4.48
680-C17 679-C15 687-C14
Pu O 100 Pu H
100.44 101.63
Δu (mm) 7.55 7.76 7.76
Max. R. L. before Failure (kN) 650 675 720 Page 117
Chapter Four – Experimental Results and Discussion Although, the horizontal strengthening gave, in some cases, higher enhancement in the load carrying capacity, but the application of this kind of strengthening technique is rather difficult on real corbels because of the inability to wrap the CFRP around the corbel and the supporting column. Moreover, using the mixed strengthening technique gave reasonable results, but it was approximate to the results of the inclined configuration; therefore, in the researcher point of view, it is economically recommended, to use the inclined strengthening technique on reinforced concrete corbels.
Load, kN
50 mm Strips in H-I-HI 900 800 700 600 500 400 300 200 100 0
C14
C14
C13
C3 C1
C1
50mm-H
50mm-I
Pcr Pu 50mm-HI
Fig. (4.7) – Effect of Configuration of CFRP strips on the Cracking and Failure Loads of R-50-H-3, R-50-I-3 and R-50-HI-3 Specimens
Load, kN
100 mm strips in H-I-HI 900 800 700 600 500 400 300 200 100 0
C17
C17
C5
C17
C5
C5
100mm-H
Pcr Pu 100mm-I
100mm-HI
Fig. (4.8) – Effect of Configuration of CFRP strips on the Cracking and Failure Loads of R-100-H-3, R-100-I-3 and R-100-HI-3 Specimens Experimental Results & Discussion
Page 118
Chapter Four – Experimental Results and Discussion
Load, kN
150 mm Strips in H-I-HI 900 800 700 600 500 400 300 200 100 0
C17
C5
C15
C14
C9 C5 Pcr Pu
150mm-H
150mm-I
150mm-HI
Fig. (4.9) – Effect of Configuration of CFRP strips on the Cracking and Failure Loads of R-150-H-3, R-150-I-3 and R-150-HI-3 Specimens 4.4.5. Load-Displacement Response: The load-displacement responses of the specimens tested under non-reversed repeated loading regimes are expressed as curves and are shown in Fig.s (4.10) through (4.23). The deflection represents the movements of the loading jack, which correspond to the deflection at the center of the column supporting the double corbels. At early stages of loading the curves were initiated in a linear form with a constant slope. Soon after cracking the behavior was changed and the load deflection response took a nonlinear form with varying slopes, gradually, the slope decreased with consecutive cycles. The shape of the load-displacement curves at post cracking stages and stages closed to failure, depend on the type of loading history applied, including number of cycles and the magnitude of each cycle. The load-displacement curve obtained under non-reversed repeated loading regime, the hysteresis curve; represent the response of reinforced concrete corbels under this kind of loading. The area under the curve for each cycle of the loadExperimental Results & Discussion
Page 119
Chapter Four – Experimental Results and Discussion displacement curve was considered a measure of the energy absorbed after several cycles of repeated loading [90,91]. The load-displacement hysteresis loops for the fourteen specimens, tested under the three non-reversed repeated loading regimes selected in this study, showed degradation in the load carrying capacity during the repeated cycles, due to the accumulation of cracks in the concrete. Reinforced concrete corbels subjected to this type of loading always showed a deflection increase through successive cycles. However, the consecutive increments of deflection decreased gradually with repeated loading. In other words, the application of the non-reversed repeated loading in the first cycle led to a residual deflection. With consecutive cycles more residual deflection was added, but with a smaller quantities compared with that occurring throughout the first cycle. Therefore, the accumulation of the residual deflection increased with the increase in the number of cycles. The presence of the residual deflection may be due to the development of cracks within the concrete. One of the important characteristic of the hysteresis curve was the area enclosed by that curve. This area was decreased with the increasing in the number of cycles. Generally, it was found that applying the non-reversed repeated loading regimes led to a decrease in the total deflection at failure when compared with specimens subjected to monotonic loading regime, as shown in Fig.s (4.10) through (4.15) and Fig.s (4.18) and (4.21). Specimen R-0-W-1, R-0-W-2 and R-0-W-3 subjected to LH1, LH2 and LH3, failed after nine, twelve and thirteen cycles, respectively, before reaching the amplitude of the last cycle, with failure load and deflection less than that of the monotonic control specimen M-0-W. The same was observed with the other specimens strengthened with 50 mm strips of CFRP, such as R-50-H-1, R-50-H -2 and R-50-H-3 subjected to LH1, LH2 and Experimental Results & Discussion
Page 120
Chapter Four – Experimental Results and Discussion LH3, which failed after ten, twelve and thirteen cycles, before reaching the amplitude of the last cycle. With failure load and deflection less than that of the monotonic control specimen M-50-H. The remaining strengthened specimens were tested under LH3, such as R-50-I-3, which failed after thirteen cycles, before reaching the amplitude of the last cycle, with failure load and deflection less than that of the monotonic control specimen M-50-I. Finally, specimen R-50-HI-3, failed after twelve cycles, before reaching the amplitude of the last cycle, with failure load and deflection less than that of the
Load, P, kN
monotonic control specimen M-50-HI.
900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
M-0-W, Pu=652 kN, Δu=8 mm R-0-W-1, Pu=577 kN, Δu=7.85 mm, C10
0
1
2
3
4
5
6
7
8
9
10
Deflection, mm
Fig. (4.10) - The Load-Deflection Curves of R-0-W-1
Experimental Results & Discussion
Page 121
Load, P, kN
Chapter Four – Experimental Results and Discussion
900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
M-0-W, Pu=652 kN, Δu=8 mm R-0-W-2, Pu=570 kN, Δu=7.19 mm, C13
0
1
2
3
4
5
6
7
8
9
10
9
10
Deflection, mm
Load, P, kN
Fig. (4.11) - The Load-Deflection Curves of R-0-W-2
900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
M-0-W, Pu=652 kN, Δu= 8 mm R-0-W-3, Pu= 547 kN, Δu= 7.8 mm, C14
0
1
2
3
4
5
6
7
8
Deflection, mm
Fig. (4.12) - The Load-Deflection Curves of R-0-W-3
Experimental Results & Discussion
Page 122
Load, P, kN
Chapter Four – Experimental Results and Discussion
900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
M-50-H, Pu= 725 kN, Δu= 9.31 mm R-50-H-1, Pu= 636 kN, Δu= 7.8 mm, C11
0
1
2
3
4
5
6
7
8
9
10
9
10
Deflection, mm
Load, P, kN
Fig. (4.13) - The Load-Deflection Curves of R-50-H-1
800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
M50H, Pu= 725 kN, Δu= 9.31 mm R-50-H-2, Pu=616 kN, Δu= 7.69 mm, C13
0
1
2
3
4
5
6
7
8
Deflection, mm
Fig. (4.14) - The Load-Deflection Curves of R-50-H-2
Experimental Results & Discussion
Page 123
Load, kN
Chapter Four – Experimental Results and Discussion
900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
M-50-H, Pu=725 kN, Δu=9.31mm R-50-H-3, Pu=605 kN, Δu=7.87 mm, C14
0
1
2
3
4
5
6
7
8
9
10
Deflection, mm
Load, P, kN
Fig. (4.15) - The Load-Deflection Curves of R-50-H-3
900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
R-100-H-3, Pu= 659 kN, Δu= 7.6 mm, C17
0
1
2
3
4
5
6
7
8
9
10
Deflection, mm
Fig. (4.16) - The Load-Deflection Curves of R-100-H-3
Experimental Results & Discussion
Page 124
Load, P, kN
Chapter Four – Experimental Results and Discussion
900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
R-150-H-3, Pu= 680 kN, Δu= 7.55 mm, C17
0
1
2
3
4
5
6
7
8
9
10
9
10
Deflection, mm
Load, P, kN
Fig. (4.17) - The Load-Deflection Curves of R-150-H-3
900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
M-50-I, Pu= 750 kN, Δu= 9.25 mm R-50-I-3, Pu= 646 kN, Δu= 7.65 mm, C14
0
1
2
3
4
5
6
7
8
Deflection, mm
Fig. (4.18) - The Load-Deflection Curves of R-50-I-3
Experimental Results & Discussion
Page 125
Load, P, kN
Chapter Four – Experimental Results and Discussion
900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
R-100-I-3, Pu= 683 kN, Δu= 7.29 mm, C17
0
1
2
3
4
5
6
7
8
9
10
Deflection, mm
Load, P, kN
Fig. (4.19) - The Load-Deflection Curves of R-100-I-3
900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
R-150-I-3, Pu= 679 kN, Δu= 7.36 mm, C15
0
1
2
3
4
5
6
7
8
9
10
Deflection, mm
Fig. (4.20) - The Load-Deflection Curves of R-150-I-3
Experimental Results & Discussion
Page 126
Load, P, kN
Chapter Four – Experimental Results and Discussion
900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
M-50-HI, Pu= 825 kN, Δu= 9.79 mm R-50-HI-3, Pu= 659 kN, Δu= 7.03 mm, C13
0
1
2
3
4
5
6
7
8
9
10
9
10
Deflection, mm
Load, P, kN
Fig. (4.21) - The Load-Deflection Curves of R-50-HI-3
900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
R-100-HI, Pu= 703 kN, Δu= 7.8 mm, C17
0
1
2
3
4
5
6
7
8
Deflection, mm
Fig. (4.22) - The Load-Deflection Curves of R-100-HI-3
Experimental Results & Discussion
Page 127
Load, P, kN
Chapter Four – Experimental Results and Discussion
900 850 800 750 700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
R-150-HI, Pu=687 kN, Δu= 7.24 mm, C14
0
1
2
3
4
5
6
7
8
9
10
Deflection, mm
Fig. (4.23) - The Load-Deflection Curves of R-150-HI-3
Finally, as a conclusion, it was noticed that a strength gain was recorded with increasing the width of strengthening strips from 50 mm to 150 mm, which ranged between of 11% to 24% for horizontal configuration, 18% to 25% for inclined configuration and 21% to 29% for mixed configuration. It was also concluded that the three strengthening configurations of the CFRP used in this research have enhanced the load carrying capacity of the corbels tested under non-reversed repeated loading regime; this enhancement is well observed by the increase in the maximum repeated load reached and the number of cycles under that load with respect to the non-strengthened specimen. The increase in the max repeated load reached was 11% for 4 cycles, 15% for 4 cycles and 23% for 4 cycles, for the 100 mm-strengthening strip of the RH, RI and RHI groups respectively.
Experimental Results & Discussion
Page 128
Chapter Four – Experimental Results and Discussion 4.5.
Strain Records in Steel Reinforcement, Concrete and CFRP Strips:
Strain gauges were installed on steel bars before the casting of the specimens; and on the concrete surface and CFRP strips, after casting and before testing, to record the strains in these materials during testing. The strain readings were recorded, using a TDS-530 data logger, on special paper, and then saved to a computer, and this device was previously shown in chapter three, Plate (3-26). The strain records were represented as Load-Strain curves between the load on the corbel, V, (which is equal to half the load applied on the column, P/2), and the strains recorded from strain gauges. 4.5.1. Strain Records in Steel Reinforcement: The strain gauges were mounted on the main steel reinforcement, in all tested specimens, at the location of maximum moment, at the column-corbel interface as previously was shown in Fig. (3.6) and Plate (3-10). One strain gauge on each bar located in opposite directions. The yielding and ultimate stresses for the steel reinforcement used in this research were discussed in chapter three, Table (3-7). According to these results, the yield strain for the main steel reinforcement (ϕ=16mm) was expected to be around 2500 10 6 mm / mm .
During the first stages of loading, the main steel reinforcement exhibited minimal strains until the initiation of the micro cracks in concrete. After the initiation of the cracks, the steel strains started to increase almost at a constant rate up to yielding of the main steel reinforcement. For the monotonically loaded specimens, the strains in the steel main bars have reached the yielding strain in either both bars as in specimen M-50-H, or in one of the bars as in specimens M-0-W and M-50-I. The Load-Strain curves for the monotonically tested specimens are shown in Fig. (4.24).
Experimental Results & Discussion
Page 129
Chapter Four – Experimental Results and Discussion For the non-reversed repeated loaded specimens, the strains of main steel reinforcing bars were recorded at each (20 or 40) kN increments of loading through the consecutive cycles of the three non-reversed repeated loading regimes.
Load, V, kN
Load, V, kN
M-0-W 400 350 300 250 200 150 100 50 0
Steel-Left Steel-Right 0
1000
2000
Strain,
3000
M-50-H
400 350 300 250 200 150 100 50 0
Steel-Left Steel-Right 0
4000
Steel-Left Steel-Right 0
1000
2000
2000
Strain,
3000
4000
M50HI Load, V, kN
Load, V, kN
M-50-I 400 350 300 250 200 150 100 50 0
1000
Strain,
3000
4000
400 350 300 250 200 150 100 50 0
Steel-Left Steel-Right 0
1000
2000
Strain,
3000
4000
Fig. (4-24) – Load-Strain Curves for Main Steel Reinforcement in Monotonically Loaded Specimens, Group M Depending on these records, it can be observed that in some specimens one or both bars had reached their yielding strains, as in R-0-W-1, R-50-H-3, R-100-H-3, R-50-I-3, R-100-I-3, R-150-I-3 and R-100-HI-3. The bars in the rest of the specimens did not reach their yielding strains. It was also observed from the curves that the application of the non-reversed repeated loading in the first cycle have led to a significant residual in the strains, while for the following consecutive cycles, the residual strains values were insignificant. The Load-Strain curves for the non-reversed tested specimens are shown in Figs. (4.25) through (4.38). Experimental Results & Discussion
Page 130
Chapter Four – Experimental Results and Discussion
R-0-W-1
Ast-Left 0
1000
2000
Strain,
R-0-W-1
350 300 250 200 150 100 50 0
Load, V, kN
Load, V, kN
350 300 250 200 150 100 50 0
3000
Ast-Right 0
1000
2000
3000
Strain,
Fig. (4.25) – Load-Strain Curves for Main Steel Reinforcement for Specimen R-0-W-1, Tested under LH1
R-0-W-2 Load, V, kN
Load, V, kN
R-0-W-2 350 300 250 200 150 100 50 0
Ast-Left 0
1000
2000
Strain,
350 300 250 200 150 100 50 0
Ast-Right
3000
0
500
1000
1500
2000
Strain,
2500
Fig. (4.26) – Load-Strain Curves for Main Steel Reinforcement for Specimen R-0-W-2, Tested under LH2
R-0-W-3 Load, V, kN
Load, V, kN
R-0-W-3 700 600 500 400 300 200 100 0
Ast-Left 0
1000
2000
3000
Strain,
4000
350 300 250 200 150 100 50 0
Ast-Right 0
500
1000
1500
2000
Strain,
2500
Fig. (4.27) – Load-Strain Curves for Main Steel Reinforcement for Specimen R-0-W-3, Tested under LH3
Experimental Results & Discussion
Page 131
R-50-H-1
350 300 250 200 150 100 50 0
Load, V, kN
Load, V, kN
Chapter Four – Experimental Results and Discussion
Ast-Left 0
1000
2000
Strain,
R-50-H-1
350 300 250 200 150 100 50 0
Ast-Right
3000
0
1000
2000
3000
Strain,
R-50-H-2
350 300 250 200 150 100 50 0
Load V, kN
Load V, kN
Fig. (4.28) – Load-Strain Curves for Main Steel Reinforcement for Specimen R-50-H-1, Tested under LH1
Ast-Left
0
500
1000
1500
2000
Strain,
R-50-H-2
350 300 250 200 150 100 50 0
2500
Ast-Right
0
500
1000
1500
Strain,
2000
2500
R-50-H-3
350 300 250 200 150 100 50 0
Load, V, kN
Load, V, kN
Fig. (4.29) – Load-Strain Curves for Main Steel Reinforcement for Specimen R-50-H-2, Tested under LH2
Ast-Left 0
1000
2000
Strain,
3000
4000
R-50-H-3
350 300 250 200 150 100 50 0
Ast-Right 0
1000
2000
Strain,
3000
4000
Fig. (4.30) – Load-Strain Curves for Main Steel Reinforcement for Specimen R-50-H-3, Tested under LH3
Experimental Results & Discussion
Page 132
R-100-H-3
350 300 250 200 150 100 50 0
Load, V, kN
Load, V, kN
Chapter Four – Experimental Results and Discussion
Ast-Left 0
500
1000
1500
2000
Strain,
R-100-H-3
350 300 250 200 150 100 50 0
2500
Ast-Right 0
1000
2000
3000
Strain,
R-150-H-3
400 350 300 250 200 150 100 50 0
Load, V, kN
Load, V, kN
Fig. (4.31) – Load-Strain Curves for Main Steel Reinforcement for Specimen R-100-H-3, Tested under LH3
Ast-Left
0
500
1000
1500
2000
Strain,
R-150-H-3
400 350 300 250 200 150 100 50 0
2500
Ast-Right
0
500
1000
1500
Strain,
2000
2500
R-50-I-3
350 300 250 200 150 100 50 0
Ast-Left 0
1000
2000
Strain,
3000
4000
Load, V, kN
Load, V, kN
Fig. (4.32) – Load-Strain Curves for Main Steel Reinforcement for Specimen R-150-H-3, Tested under LH3
R-50-I-3
350 300 250 200 150 100 50 0
Ast-Right 0
1000
2000
Strain,
3000
4000
Fig. (4.33) – Load-Strain Curves for Main Steel Reinforcement for Specimen R-50-I-3, Tested under LH3
Experimental Results & Discussion
Page 133
R-100-I-3
400 350 300 250 200 150 100 50 0
Load, V, kN
Load, V, kN
Chapter Four – Experimental Results and Discussion
Ast-Left 0
1000
2000
Strain,
R-100-I-3
400 350 300 250 200 150 100 50 0
3000
Ast-Right 0
500
1000
1500
2000
Strain,
2500
R-150-I-3
350 300 250 200 150 100 50 0
Load, V, kN
Load, V, kN
Fig. (4.34) – Load-Strain Curves for Main Steel Reinforcement for Specimen R-100-I-3, Tested under LH3
Steel-Left
0
1000
2000
Strain,
R-150-I-3
350 300 250 200 150 100 50 0
3000
Steel-Right
0
1000
2000
3000
Strain,
R-50-HI-3
350 300 250 200 150 100 50 0
Load, V, kN
Load, Vu, kN
Fig. (4.35) – Load-Strain Curves for Main Steel Reinforcement for Specimen R-150-I-3, Tested under LH3
Steel-Left 0
1000
2000
Strain,
3000
R-50-HI-3
350 300 250 200 150 100 50 0
Steel-Right 0
1000
2000
3000
Strain,
Fig. (4.36) – Load-Strain Curves for Main Steel Reinforcement for Specimen R-50-HI-3, Tested under LH3
Experimental Results & Discussion
Page 134
R-100-HI-3
400 350 300 250 200 150 100 50 0
Load, V, kN
Load, V, kN
Chapter Four – Experimental Results and Discussion
Steel-Left 0
1000
2000
3000
Strain,
R-100-HI-3
400 350 300 250 200 150 100 50 0
Steel-Right 0
1000
2000
3000
Strain,
Steel-Left
350 300 250 200 150 100 50 0
Load, V, kN
Load, V, kN
Fig. (4.37) – Load-Strain Curves for Main Steel Reinforcement for Specimen R-100-HI-3, Tested under LH3
Steel-Left
0
500
1000
1500
Strain,
2000
2500
R-150-HI-3
350 300 250 200 150 100 50 0
Steel-Right
0
1000
2000
3000
Strain,
Fig. (4.38) – Load-Strain Curves for Main Steel Reinforcement for Specimen R-150-HI-3, Tested under LH3 4.5.2. Surface Strain Records in Concrete: Strain gauges were fixed on both sides of the front face of the corbels, within the compression side, to record the surface compressive strains at the selected increments of loading. The locations of these strain gauges were selected to be perpendicular to the expected line of failure, the line connecting the point of the applied load, at the bottom face of the corbel, and the point of upper corbel-column joint, as shown in Fig. (4.39). The Concrete-SF strain gauges were chosen to detect the concrete compressive surface strain on the expected line of failure. Experimental Results & Discussion
Page 135
Chapter Four – Experimental Results and Discussion Since the application of the gauges were perpendicular to the expected line of failure, with an angle of about 60 to 70 degrees with the horizontal, therefore, their readings will be affected by the shear component, which causes tensile strains that may affect the compressive strains in that region. Moreover, in order to predict the location of the neutral axis, two extra strain gauges were fixed horizontally on the compression side of some of the non-strengthened specimens. The depth of the neutral axis was theoretically calculated within the elastic stage, and was expected to be between 7 cm to 8 cm from the extreme compression fiber. For the monotonically loaded specimens, it was observed that at early stages of loading, all specimens behaved in a linear manner and the surface strains in concrete were of minimal values. A change in the strain path was observed with the increasing in the applying load. The visible cracks in concrete were associated with the nonlinear strain path, where the strains increased at an increasing rate with respect to the applied load up to failure. Experimental compressive surface strains in concrete, for the monotonically loaded specimens, were recorded at various stages of loading, with an increment of 2.5 to 5 kN. The strain records are plotted, and illustrated in Figs. (4.40) through (4.43). Concrete-Compression Strain Gauges
Concrete-SF Strain Gauges
Fig. (4.39) - Locations of Strain Gauges Fixed on Concrete Experimental Results & Discussion
Page 136
Chapter Four – Experimental Results and Discussion
Load, V, kN -1000
M-0-W Load, V, kN
M-0-W 350 300 250 200 150 100 50 0
Concrete-SF-Left Concrete-SF-Right 0
1000
2000
3000
Strain,
4000
350 300 250 200 150 100 50 0
Concrete-C-Left Concrete-C-Right -300
-200
-100
0
Strain,
Fig. (4.40) - Load-Strain Curves in Concrete Compression Zone for Specimen M-0-W
M-50-H
M-50-I
Concrete, SF-Left Concrete, SF-Right 10000
20000
Strain,
30000
400 350 300 250 200 150 100 50 0 -1000 0
Load, Vu, kN
Load, V, kN
400 350 300 250 200 150 100 50 0 -10000 0
40000
Concrete-SF-Left Concrete-SF Right 1000 2000 3000 4000 5000
Strain,
M50HI
M50HI
400 350 300 250 200 150 100 50 0
Load, V, kN
Fig. (4.42) - Load-Strain Curves in Concrete Compression Zone for Specimen M-50-I
Load, V, kN
Fig. (4.41) - Load-Strain Curves in Concrete Compression Zone for Specimen M-50-H
Concrete-SF-Left Concrete-SF-Right 0
5000
10000
Strain,
15000
-200
Concrete-C-Left Concrete-C-Right -150
-100
-50
Strain,
400 350 300 250 200 150 100 50 0 0
50
Fig. (4.43) - Load-Strain Curves in Concrete Compression Zone for Specimen M-50-HI Experimental Results & Discussion
Page 137
Chapter Four – Experimental Results and Discussion The same was observed for the non-reversed repeated loaded specimens. During the first cycles, while the specimens within the elastic stage, the surface strains in concrete were rather small, and the cycles were close to each other; the residual strains were rather small, as shown in Fig. (4.45, a and c), for specimen R-0-W-1. Then as micro cracks were created within the concrete, a large increase was observed in the records of the strains which make it difficult to plot these strains with the small ones recorded within the elastic stage in the same graph, therefore they were plotted separately in some of the specimens, as shown in Fig.s (4.45, b and d). The same was performed for specimen R-50-H-1, as shown in Fig. (4.47, a). It can also be observed that in the latest cycles, there was an enormous increase in the residual strain readings, which may lead to a conclusion that the cracks created in concrete, during the ascending part of loading, were unable to be closed completely with the release of the applied load, in the descending part of loading. During the test of some specimens, such as, R-50-H-2, R-50-I-3 and R-150-I-3, some of the strain gauges were damaged and the readings were lost or started to give unreasonable records which were discarded. The Load-Strain curves for all the non-reversed tested specimens are shown in
R-0-W-3
400 350 300 250 200 150 100 50 0
Concrete-SF-Left
0
5000
10000
Strain,
Load, V, kN
Load, V, kN
Fig.s (4.44) through (4.57).
15000
-2000
R-0-W-3
400 350 300 250 200 150 100 50 0
Concrete-SF-Right
0
2000
4000
6000
8000
Strain,
Fig. (4.44) - Load-Strain Curves in Concrete Compression Zone for Specimen R-0-W-3 Experimental Results & Discussion
Page 138
R-0-W-1
350 300 250 200 150 100 50 0
Concrete-SF-Left
0
50
100
150
Strain,
Load, V, kN
Load, V, kN
Chapter Four – Experimental Results and Discussion
R-0-W-1
350 300 250 200 150 100 50 0
200
Concrete-SF-Left
11
2011
(a) C1-C6
Concrete-SF-Right
0
50
100
Load, V, kN
Load, V, kN -50
150
200
Strain,
2010
4010
6010
Strain,
(d) C7-C10
R-0-W-1
Concrete-C-Left 0
10011
Concrete-SF-Right 10
500
Strain,
(e) C1-C6
1000
Load, V, kN
Load, V, kN -500
8011
R-0-W-1
350 300 250 200 150 100 50 0
(c) C1-C6
350 300 250 200 150 100 50 0
6011
Strain,
(b) C7-C10
R-0-W-1
350 300 250 200 150 100 50 0
4011
-500
350 300 250 200 150 100 50 0
R-0-W-1
Concrete-C-Right 0
500
1000
Strain,
(f) C7-C10
Fig. (4.45) - Load-Strain Curves in Concrete Compression Zone for Specimen R-0-W-1
Experimental Results & Discussion
Page 139
R-0-W-2
350 300 250 200 150 100 50 0
R-0-W-2 350
Concrete-SF-Left
0
500
1000
1500
Concrete-SF-Right 300 250 200 150 100 50 0 -100 -50 0
Load, V, kN
Load, V, kN
Chapter Four – Experimental Results and Discussion
2000
Strain,
2500
-150
(a)
(b)
R-0-W-2
350 300 250 200 150 100 50 0 -40 -30 -20 -10 0
10
20
30
Strain,
40
50
R-0-W-2
350 300 250 200 150 100 50 0
Load, V, kN
Concrete-C-Left
Load, V, kN
50
Strain,
-50
Concrete-C-Right
0
50
(c)
100
150
200
Strain,
(d)
Fig. (4.46) - Load-Strain Curves in Concrete Compression Zone for Specimen R-0-W-2
R-50-H-1
-50
Concrete-SF-Left-
0
50
100
150
Strain,
(a) C1-C6
Load, V, kN
Load, V, kN
400 350 300 250 200 150 100 50 0
200
R-50-H-1
400 350 300 250 200 150 100 50 0
Concrete-SF-Left-
36
2036
4036
6036
8036
Strain,
10036
(b) C7-C11
Fig. (4.47) - Load-Strain Curves in Concrete Compression Zone for Specimen R-50-H-1 Experimental Results & Discussion
Page 140
R-50-H-2
350 300 250 200 150 100 50 0
Concrete-Left
0
100
200
Strain,
Load V, kN
Load V, kN
Chapter Four – Experimental Results and Discussion
300
400
R-50-H-2
350 300 250 200 150 100 50 0
-100
Concrete-Right 0
100
200
Strain,
300
400
R-50-H-3
400 350 300 250 200 150 100 50 0
Concrete-Left
0
5000
10000
Strain,
400 350 300 250 200 150 100 50 0
Load, V, kN
Load, V, kN
Fig. (4.48) - Load-Strain Curves in Concrete Compression Zone for Specimen R-50-H-2
-100
R-50-H-3
Concrete-Right 0
100
200
Strain,
Fig. (4.49) - Load-Strain Curves in Concrete Compression Zone for Specimen R-50-H-3
Load, V, kN -100
Load, V, kN
R-100-H-3
350 300 250 200 150 100 50 0
Concrete-Left 0
100
200
Strain,
300
400
R-100-H-3
350 300 250 200 150 100 50 0
Concrete-Right 0
2000
4000
6000
Strain,
Fig. (4.50) - Load-Strain Curves in Concrete Compression Zone for Specimen R-100-H-3 Experimental Results & Discussion
Page 141
R-150-H-3
400 350 300 250 200 150 100 50 0
Concrete-Left 0
500
1000
Strain,
1500
R-150-H-3
400 350 300 250 200 150 100 50 0 -2000 0
Load, V, kN
Load, V, kN
Chapter Four – Experimental Results and Discussion
2000
Concrete-Right 2000
4000
6000
Strain,
8000 10000
Fig. (4.51) - Load-Strain Curves in Concrete Compression Zone for Specimen R-150-H-3
Load, V, kN -2000
Concrete-Left
0
2000
4000
6000
Strain,
8000
R-50-I-3
350 300 250 200 150 100 50 0 -2000 0
Load, V, kN
R-50-I-3
350 300 250 200 150 100 50 0
Concrete-Right
2000 4000 6000 8000 1000012000
Strain,
Fig. (4.52) - Load-Strain Curves in Concrete Compression Zone for Specimen R-50-I-3
R-100-I-3
-2000
Concrete-Left
Load, V, kN
Load, V, kN
400 350 300 250 200 150 100 50 0 0
2000
4000
Strain,
6000
-2000
R-100-I-3
400 350 300 250 200 150 100 50 0
Concrete-Right
0
2000
4000
6000
8000
Strain,
Fig. (4.53) - Load-Strain Curves in Concrete Compression Zone for Specimen R-100-I-3
Experimental Results & Discussion
Page 142
R-150-I-3
350 300 250 200 150 100 50 0
Concrete-Left
Load, V, kN
Load, V kN
Chapter Four – Experimental Results and Discussion
0
2000
4000
6000
Strain,
R-150-I-3
400 350 300 250 200 150 100 50 0
8000 10000
Concrete-Right
0
5000
10000
15000
Strain,
R-50-HI-3
400 350 300 250 200 150 100 50 0
Concrete-Left
0
5000
Load, Vu, kN
Load, V, kN
Fig. (4.54) - Load-Strain Curves in Concrete Compression Zone for Specimen R-150-I-3
10000
Strain,
15000
R-50-HI-3
400 350 300 250 200 150 100 50 0
Concrete-Right
0
1000
2000
3000
Strain,
Fig. (4.55) - Load-Strain Curves in Concrete Compression Zone for Specimen R-50-HI-3
Concrete-Left 2000
4000
6000
Strain,
8000 10000
Load, V, kN
R-100-HI-3
Load, V, kN
400 350 300 250 200 150 100 50 0 -2000 0
R-100-HI-3
400 350 300 250 200 150 100 50 0
Concrete-Right 0
2000
4000
6000
Strain,
8000
10000
Fig. (4.56) - Load-Strain Curves in Concrete Compression Zone for Specimen R-100-HI-3
Experimental Results & Discussion
Page 143
R-150-HI-3
400 350 300 250 200 150 100 50 0
Concrete-Left 0
2000
4000
Strain,
6000
Load, V, kN
Load, V, kN
Chapter Four – Experimental Results and Discussion
-1000
R-150-HI-3
400 350 300 250 200 150 100 50 0
Concrete-Right 0
1000
Strain,
2000
3000
Fig. (4.57) - Load-Strain Curves in Concrete Compression Zone for Specimen R-150-HI-3 4.5.3. Strain Records in CFRP Strips: Strain gauges were mounted on the CFRP strips, on both sides of the front face of the corbels, located at the center of the strip and in the direction of the fibers’ configuration, to record the tensile strains in the CFRP during the test at the selected increments of loading. The locations of the strain gauges are shown in Fig. (4.58). Experimental Tensile strains in the CFRP strips, for all the tested specimens, were recorded and plotted at various stages of loading, as illustrated in Fig.s (4.59) through (4.72). CFRP-Inclined Strain Gauges
CFRP-Horizontal Strain Gauges
Fig. (4.58) - Locations of Strain Gauges Fixed on CFRP Strips Experimental Results & Discussion
Page 144
Chapter Four – Experimental Results and Discussion The first specimen, with strengthening, that was tested in this project was M-50-H. Load-strain curves for this specimen showed that at first stages of loading the tensile strain recorded were almost zero or of low values, which implied that the specimens were free from cracks and the strips did not suffer from any elongations. After the initiation of cracks, the CFRP strips started to work and, as shown in Fig. (4.59) the strains started to increase which means that the strips started to suffer from high elongation caused from resisting the widening and propagation of cracks. The same behavior was observed for all specimens tested under monotonically or non-reversed repeated loading regimes. The horizontal strips experienced small strains until the initiation of the cracks. Then the strains started to increase at a higher rate until failure occurred. The inclined strips exhibited a direct strain response, in the direction of fibers, until failure. This concludes to the effectiveness of the inclined strengthening in limiting the width of inclined shear cracks in comparison with the horizontal strengthening. This may allow the corbels with inclined strengthening technique to experience higher strains before failure. Almost all the CFRP strips, on all specimens, remained in full contact with the concrete until failure. The load-strain curves for all tested specimens are shown in Figs. (4.59) through (4.72).
-2000
M-50-I
CFRP-Left CFRP-Right 0
2000
Strain,
4000
6000
Load, V, kN
Load, V, kN
M-50-H 400 350 300 250 200 150 100 50 0
-2000
400 350 300 250 200 150 100 50 0
CFRP-Left CFRP-Right 0
2000
4000
6000
Strain,
Fig. (4.59) - Load-Tensile Strain Fig. (4.60) - Load-Tensile Strain Curves in CFRP for Specimen M-50-H Curves in CFRP for Specimen M-50-I Experimental Results & Discussion
Page 145
Chapter Four – Experimental Results and Discussion
M50HI Load, V, kN
Load, V, kN
M50HI 400 350 300 250 200 150 100 50 0
CFRP-I-Left CFRP-I-Right 0
2000
4000
400 350 300 250 200 150 100 50 0
6000
Strain,
CFRP-H-Left CFRP-H-Right 0
2000
4000
6000
Strain,
R-50-H-1
400 350 300 250 200 150 100 50 0
-2000
CFRP-Left 0
2000
4000
Strain,
6000
R-50-H-1
400 350 300 250 200 150 100 50 0
Load, V, kN
Load, V, kN
Fig. (4.61) - Load-Tensile Strain Curves in CFRP for Specimen M-50-HI
-2000
CFRP-Right
0
2000
4000
6000
Strain,
Fig. (4.62) - Load-Tensile Strain Curves in CFRP for Specimen R-50-H-1
R-50-H-2
1000
2000
3000
Strain,
4000
Load V, kN
CFRP-Left
Load V, kN
400 350 300 250 200 150 100 50 0 -1000 0
5000
R-50-H-2
400 350 300 250 200 150 100 50 0
CFRP-Right 0
500
1000
Strain,
1500
2000
Fig. (4.63) - Load-Tensile Strain Curves in CFRP for Specimen R-50-H-2
Experimental Results & Discussion
Page 146
R-50-H-3
400 350 300 250 200 150 100 50 0
CFRP-Left 0
2000
4000
Strain,
6000
R-50-H-3
400 350 300 250 200 150 100 50 0
Load, V, kN
Load, V, kN
Chapter Four – Experimental Results and Discussion
-2000
CFRP-Right 0
2000
4000
Strain,
6000
R-100-H-3
400 350 300 250 200 150 100 50 0
-2000
CFRP-Left
0
2000
Strain,
4000
6000
R-100-H-3
400 350 300 250 200 150 100 50 0
Load, V, kN
Load, V, kN
Fig. (4.64) - Load-Tensile Strain Curves in CFRP for Specimen R-50-H-3
-2000
CFRP-Right
0
2000
4000
Strain,
6000
-2000
R-150-H-3
400 350 300 250 200 150 100 50 0
Load, V, kN
Load, V, kN
Fig. (4.65) - Load-Tensile Strain Curves in CFRP for Specimen R-100-H-3
CFRP-Left 0
2000
Strain,
4000
6000
R-150-H-3
400 350 300 250 200 150 100 50 0
CFRP-Right 0
2000
4000
Strain,
6000
Fig. (4.66) - Load-Tensile Strain Curves in CFRP for Specimen R-150-H-3
Experimental Results & Discussion
Page 147
R-50-I-3
400 350 300 250 200 150 100 50 0
CFRP-Left
0
2000
Load, V, kN
Load, V, kN
Chapter Four – Experimental Results and Discussion
4000
6000
Strain,
R-50-I-3
400 350 300 250 200 150 100 50 0
CFRP-Right
0
2000
4000
Strain,
6000
8000
R-100-I-3
400 350 300 250 200 150 100 50 0
Load, V, kN
Load, V, kN
Fig. (4.67) - Load-Tensile Strain Curves in CFRP for Specimen R-50-I-3
CFRP-Left
0
1000
2000
3000
4000
Strain,
R-100-I-3
400 350 300 250 200 150 100 50 0
5000
CFRP-Right
0
2000
4000
Strain,
6000
R-150-I-3
400 350 300 250 200 150 100 50 0
CFRP-Left
0
2000
Load, V, kN
Load, V, kN
Fig. (4.68) - Load-Tensile Strain Curves in CFRP for Specimen R-100-I-3
4000
Strain,
6000
R-150-I-3
400 350 300 250 200 150 100 50 0
CFRP-Right
0
2000
4000
Strain,
6000
Fig. (4.69) - Load-Tensile Strain Curves in CFRP for Specimen R-150-I-3
Experimental Results & Discussion
Page 148
Chapter Four – Experimental Results and Discussion
R-50-HI-3
R-50-HI-3
400
Load, V, kN
Load, V, kN
400 300 200 100
CFRP-H-Left
300 200 100
CFRP-H-Right
0
0 0
2000
4000
0
6000
Strain,
(a)
6000
R-50-HI-3
CFRP-I-Left
Load, V, kN
Load, V, kN
4000
Strain,
(b)
R-50-HI-3
400
2000
300 200 100 0
400 300 200 100
CFRP-I-Right
0 0
2000
4000
6000
Strain,
0
2000
4000
6000
Strain,
(c) (d) Fig. (4.70) - Load-Tensile Strain Curves in CFRP for Specimen R-50-HI-3
R-100-HI-3
300 200 100
R-100-HI-3
400
CFRP-H-Left
Load, V, kN
Load, V, kN
400
0
300 200 100
CFRP-H-Right
0 0
2000
4000
Strain,
6000
0
(a)
Load, V, kN
Load, V, kN
6000
R-100-HI-3
400
300 200 100
4000
Strain,
(b)
R-100-HI-3
400
2000
CFRP-I-Left
0
300 200 100
CFRP-I-Right
0 0
2000
4000
Strain,
6000
0
2000
4000
Strain,
6000
(c) (d) Fig. (4.71) - Load-Tensile Strain Curves in CFRP for Specimen R-100-HI-3 Experimental Results & Discussion
Page 149
Chapter Four – Experimental Results and Discussion
R-150-HI-3
R-150-HI-3 400
Load, V, kN
Load, V, kN
400 300 200 100
CFRP-H-Left
0
300 200 100
CFRP-H-Right
0 0
2000
4000
Strain,
6000
0
2000
(a)
Load, V, kN
Load, V, kN
R-150-HI-3
400
300 200 100
6000
(b)
R-150-HI-3
400
4000
Strain,
CFRP-I-Left
0
300 200 100
CFRP-I-Right
0 0
2000
4000
Strain,
6000
-2000
0
2000
Strain,
4000
6000
(c) (d) Fig. (4.72) - Load-Tensile Strain Curves in CFRP for Specimen R-150-HI-3
Experimental Results & Discussion
Page 150
Chapter Five – Finite Element Modeling 5. FINITE ELEMENT MODELING: 5.1.
General:
The finite element, FE, analysis is considered as one of the powerful computational tools to predict both the linear and nonlinear behavior of structural elements in reinforced concrete structures. Concrete and steel are the main two materials that make most of the reinforced concrete structures. Those two materials have different characteristics. Steel is considered as a homogeneous material whereas, concrete is considered as a heterogeneous material made up of cement, mortar and aggregates. Therefore, for easiest design and analysis, concrete is considered as a homogeneous material [94]. The load-deformation behavior of a simply supported reinforced concrete beam is shown in Fig. (5.1), the nonlinear response in such beams can be divided into three stages of behavior: I) The uncracked elastic stage. II) The crack propagation stage. III) The plastic stage, (yielding of steel or crushing of concrete).
Fig. (5.1) - Typical Load-Displacement Response of RC Element [94] Finite Element Modeling
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Chapter Five – Finite Element Modeling Similar relations can be obtained for other types of reinforced concrete structural elements such as the corbels in the present study. This nonlinearity in reinforced concrete structures is caused by two major effects, cracking of concrete in tension and yielding of the reinforcement or crushing of concrete in compression. Moreover, nonlinearities may also be caused from the interaction of the constituents of reinforced concrete such as bond-slip between reinforcing steel and surrounding concrete, aggregate interlock at a crack and dowel action of the reinforcing steel crossing that crack. The time-dependent effects of creep, shrinkage and temperature variation may also cause the nonlinear behavior [95]. In the present study, a nonlinear FE analysis is carried out to model and simulate the behavior of non-strengthened and strengthened reinforced concrete corbels. This chapter presents a three-dimensional nonlinear finite element modeling, performed using ANSYS-15 software, including all the necessary steps to create the FE model such as: element types, parameters for the various materials, the geometry of the model, loading and boundary conditions as well as the nonlinear analysis procedures and convergence criteria adopted to generate the analytical load-deformation response of the model under both static and dynamic loadings. The ANSYS software, ANalysis SYStem, is a computer program for the FE simulations, analysis and design. This program is a general-purpose program that can be used for almost any type of FE analysis
[96]
. The procedure for a typical
ANSYS analysis can be divided into three distinct steps: 1) Build the model, using the Preprocessor commands. 2) Choose analysis type and options, apply boundary conditions then solve, using the Solution commands. 3) Review the results, using the (General and TimeHist) Postproc commands.
Finite Element Modeling
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Chapter Five – Finite Element Modeling 5.2.
Experimental Corbel used for Calibration:
The FE analysis study included modeling a calibration model for the double-sided corbels with the short vertical column, having dimensions and properties compatible to the M-0-W corbel tested monotonically in the experimental phase of this study. After calibration, the model will be tried on other specimens to make a comparison between the theoretical and experimental analysis performed throughout this study. The geometry of the analytical calibration model is presented in chapter 3, article 3.2.1, as shown in Fig. (5.2). 200 mm 150 mm P
ϕ16 mm, Asc ϕ12 mm ϕ10 mm, Ah ϕ 8 mm
300 mm 100mm
100mm
250 mm 25mm 100 mm V=P/2
250 mm
100mm 200 mm
mm 45mm 150 25mm V=P/2 25mm
300 mm 250 mm
Fig. (5.2) – Geometry of Analytical Model The area of steel reinforcement, steel yield stress and compressive strength of concrete, at the day of test, are shown in Table (5-1). Finite Element Modeling
Page 153
Chapter Five – Finite Element Modeling Table (5-1) - Properties for Concrete and Steel Reinforcement Concrete Modulus of Elasticity, Ec (MPa) 29547
5.3.
Steel Reinforcement Diameter Area of Yield Stress of Bar Bar fy, (MPa) (mm) (mm2) ϕ16 201 497 ϕ10 79 756 ϕ12 113 655 ϕ8 50 667
Building the Model:
The Preprocessor, PREP7 commands were used to create the finite element modal as described in the following steps [97]: 5.3.1. Element Types and Options: In the field of solid mechanics, the FE analysis is usually used to find an approximate solution for structures having complicated shapes and loading arrangement
[94]
. The present FE analytical study included modeling a reinforced
concrete double corbel having the same dimensions and properties of the specimens tested throughout the experimental part of the present research. Table (5-2) presents the type of element used for each material. The Solid65 element was used to model the concrete, while the steel reinforcement was represented by Link180 element. The Solid45 element was used to represent the loading bearing plates and supports and finally the Shell81 element was adopted to represent the CFRP sheets. Table (5-2) - Element Types for Analytical Study Model Material Type
ANSYS Element
Concrete Steel Reinforcement Steel Plates (for Loads and Supports) CFRP
Solid65 Link180 Solid45 Shell181
Finite Element Modeling
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Chapter Five – Finite Element Modeling 5.3.1.1.
Concrete Representation:
The SOLID65 brick element is used for the 3-D modeling of solids with or without reinforcing bars. This element is capable of plastic deformation, cracking in tension and crushing in compression and is defined by eight nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions
[97]
. The
geometry and node locations of the SOLID65 element are shown in Fig. (5.3).
Fig. (5.3) - SOLID65 Geometry and Node Locations [97] 5.3.1.2.
Reinforcement Representation:
In analyzing reinforced concrete structures using the finite element method, the reinforcement is simulated using the three different techniques listed below as shown in Fig. (5.4): The discrete model. The embedded model. The smeared model. The bar element used in the discrete modeling is connected to the concrete nodes, making both the reinforcement and the concrete share the same nodes, (this technique was used in this study). The disadvantage of this model is that the concrete mesh is restricted by the location of the reinforcement and the volume of the steel reinforcement is not subtracted from the concrete volume; previous studies Finite Element Modeling
Page 155
Chapter Five – Finite Element Modeling showed that this modeling is the best technique to be used when modeling reinforcement. The embedded model is built by keeping the displacements of the reinforcing steel compatible with the surrounding concrete elements. This model is very useful if the reinforcement is complex. However, this representation increases the number of nodes and degrees of freedom in the model, leading to an increase in the run time and computational cost. Finally, the smeared model assumes that the reinforcement is uniformly spread throughout the concrete elements within a region of the FE mesh. This model is usually used for large-scale models where the reinforcement does not significantly affect the overall response of the structure [98].
Fig. (5.4) - Models for Reinforcement in Reinforced Concrete: (a) Discrete; (b) Embedded; and (c) Smeared [98] All steel reinforcements used in this study were represented using the LINK180 element. LINK180 is a 3-D spar that is useful in a variety of engineering Finite Element Modeling
Page 156
Chapter Five – Finite Element Modeling applications to model trusses, sagging cables, links, springs, and so on. The element is a uniaxial tension-compression element with three degrees of freedom at each node: translations in the nodal x, y, and z directions. Tension-only (cable) and compression-only (gap) options are supported. As in a pin-jointed structure, no bending of the element is considered. By default, LINK180 includes stress-stiffness terms in any analysis that includes large-deflection effects. The element is defined by two nodes, the cross-sectional area (A) input via the SECTYPE and SECDATA commands, added mass per unit length (ADDMAS) input via the SECCONTROL command, and the material properties. The element x-axis is configured along the length of the element from node I toward node J. Element loads are described in Nodal Loading. Temperatures may be input as element body loads at the nodes. LINK180 allows a change in cross-sectional area as a function of axial elongation. By default, the cross-sectional area changes such that the volume of the element is preserved, even after deformation. The default is suiTable for elastoplastic applications
[97]
. The geometry and node locations for this element type are shown
in Fig. (5.5).
Fig. (5.5) – LINK180 Geometry and Node Locations [97] 5.3.1.3.
CFRP Sheets Representation:
A SHELL181, (4-Node Finite Strain Shell), element was used to model the CFRP fabric. This element is suitable for analyzing thin to moderately-thick shell structures. It is a 4-node element with six degrees of freedom at each node: translations in the x, y, and z directions, and rotations about the x, y, and z-axes. Finite Element Modeling
Page 157
Chapter Five – Finite Element Modeling The element has translational degrees of freedom only, if the membrane option is used, as in the present study; this can be performed using certain key options. The degenerate triangular option should only be used as filler elements in mesh generation. The SHELL181 element is suited for linear, large rotation, and/or large strain nonlinear applications. Change in shell thickness is accounted for in nonlinear analyses. The SHELL181 may be used for layered applications for modeling laminated composite shells or sandwich construction. SHELL181 element is defined by shell section information and four nodes (I, J, K and L). The thicknesses, and other information, such as the orthotropic material properties are defined using either real constants or section definition. The option of using real constants is available only for single-layer shells. If the element references both real constant set data and a valid shell section type, real constant data is ignored
[97]
. The geometry, node locations, and the coordinate
system are shown in Fig. (5.6).
Fig. (5.6) – SHELL181 Geometry [97]
Finite Element Modeling
Page 158
Chapter Five – Finite Element Modeling 5.3.1.4.
Using Surface-to-Surface Contact Elements:
In problems involving contact between two boundaries, one of the boundaries is conventionally established as the "target" surface, and the other as the "contact" surface. For rigid-flexible contact, the target surface is always the rigid surface, and the contact surface is the deformable surface. For flexible-to-flexible contact, both contact and target surfaces are associated with the deformable bodies. These two surfaces together comprise the "contact pair, such as the case in the present study. The elements used to perform the contact pair are CONTA174 and TARGE170. CONTA174 is a 3-D, 8-node, Surface-to-Surface element which is used to represent contact and sliding between 3-D "target" surfaces and a deformable surface, defined by this element. The element is applicable to 3-D structural and coupled field contact analyses. This element is located on the surfaces of 3 -D solid or shell elements called under lying elements that share the same geometric characteristics. The contact surface can be either one side or both sides of the shell or beam elements [97]; the geometry of this element is presented in Fig. (5.7). This element is associated with the 3-D target segment elements, TARGE170 using a shared real constant set, because, ANSYS looks for contact only between surfaces with the same real constant set. The geometry of the TARGE170 element is presented in Fig. (5.8).
Fig. (5.7) – CONTA174 Geometry [97]
Finite Element Modeling
Page 159
Chapter Five – Finite Element Modeling Contact occurs when the element surface penetrates one of the target segment elements, TARGE170, on a specified target surface. For either rigid-flexible or flexible-flexible contact, one of the deformable surfaces must be represented by a contact surface. Translational or rotational displacement as well as forces and moments on the target segment element can be imposed. For rigid target surfaces, these elements can easily model complex shapes as a target. For flexible targets, these elements will overlay the solid, shell, or line elements which described the boundary of the deformable body [97].
Fig. (5.8) – TARGE170 Geometry [97] 5.3.1.5.
Steel Plates Representation:
The Solid45 element was used to represent the loading steel plates as well as the steel plates at the supports in all corbels models. This element is defined with eight nodes having three degrees of freedom at each node, translations in the nodal x, y, and z directions; it is defined as well with orthotropic material properties. The orthotropic material directions correspond to the element coordinate directions. The element has plasticity, creep, swelling, stress stiffening, large deflection, and large
Finite Element Modeling
Page 160
Chapter Five – Finite Element Modeling strain capabilities
[97]
. The geometry and node locations for this element type are
shown in Fig. (5.9).
Fig. (5.9) - SOLID45 Geometry and Node Locations [97] 5.3.2. Real Constants: Real constants are quantities required to be applied for each individual element. The real constants for the analytical adopted model are shown in Table (5-3). Real Constant Set 1 was used for the Solid65 element. It requires real constants for rebars assuming a smeared model. Values can be entered for Material Number, Volume Ratio, and Orientation Angles. The material number refers to the type of material for the reinforcement. The volume ratio refers to the ratio of steel to concrete in the element. The orientation angles refer to the orientation of the reinforcement in the smeared model, as shown in Fig. (5.3-c). Three rebar materials can be entered by users in the concrete. Each material corresponds to x, y, and z directions in the element, as shown in Fig. (5.2). The reinforcement has uniaxial stiffness and the directional orientation is defined by the user. In the present analytical study, the corbels were modeled using discrete reinforcement; therefore, a value of zero was entered for all real constants in order to turn off the smeared reinforcement capability of the Solid65 element.
Finite Element Modeling
Page 161
Chapter Five – Finite Element Modeling Table (5-3) - Real Constants for Analytical Study Model Real Constant Set No.
1
Solid65
2
Link180 ϕ16mm
3
Link180 ϕ12mm
4
Link180 ϕ10mm
5
Link180 ϕ 8mm
7
Real Constants
Element Type
Shell181
Material Number Volume Ratio Orientation Angle Orientation Angle Crushed Stiffness Factor (CSTIF) Cross-sectional Area (mm2) Initial Strain (mm/mm) Cross-sectional Area (mm2) Initial Strain (mm/mm) Cross-sectional Area (mm2) Initial Strain (mm/mm) Cross-sectional Area (mm2) Initial Strain (mm/mm) Shell thickness at Node I, TK(I) Shell thickness at Node I, TK(J) Shell thickness at Node I, TK(K) Shell thickness at Node I, TK(L)
Rebar 1
Rebar 2
Rebar 3
0 0 0 0
0 0 0 0
0 0 0 0
0 201 0 113 0 79 0 50 0 0.166 0.166 0.166 0.166
Real Constant Sets 2, 3, 4, and 5 were used for the Link180 element. Values for cross-sectional area were entered for each bar size; since there is no initial stress in the reinforcement, a value of zero was entered for the initial strain. Real Constant Sets 6 was used for the Solid45 element, but since no real constant set exists, therefore this set was left empty. Finite Element Modeling
Page 162
Chapter Five – Finite Element Modeling Finally, real constant Set 7 was used for the Shell181 element represented by the shell thickness. 5.3.3. Material Properties: Each element in the ANSYS program requires multiple input data for material properties as shown below: 5.3.3.1.
Concrete, Solid65 Element:
The material properties for the concrete, Solid65 element, was represented by Material Model Number 1, with linear isotropic, multilinear isotropic and nonlinear inelastic non-metal plasticity material properties
[97]
. For the linear isotropic, the
elastic modulus (Ec) and Poisson’s ratio (ν) were required, while for the multilinear isotropic, the von Mises failure criterion along with the (Willam and Warnke, 1974) [99] model were required to define the failure of the concrete. The modulus of elasticity of the concrete, Ec, was calculated using equation (5-1): Ec 4700 f c'
…… (5-1)
The ANSYS program requires the uniaxial stress-strain relationship for the concrete in compression, which was obtained using equations (5-2), (5-3) and (5-4) [100]. f
Ec 1 o
2
2 f c' o Ec Ec
f
…… (5-2)
…… (5-3) …… (5-4)
where: f , is the stress at any strain ε, MPa.
o , is the strain at the ultimate compressive strength, f c' Finite Element Modeling
Page 163
Chapter Five – Finite Element Modeling The uniaxial stress-strain relationship for the concrete used in this study is shown in Fig. (5.10), which is constructed using six points connected by straight lines, based on a value of modulus of elasticity equal to
E
c
29547 MPa
and
compressive strength of f c' 39.52 Mpa . The starting point is at zero stress and zero strain. The first point, No.1, is defined at a stress equal to 0.3 f c' , and a strain calculated using equation (5-4). The last point, No.5, is defined at the
f , ' c
ultimate compressive strength,
and the corresponding strain,
o ,
calculated using equation (5-3). The intermediate points, No. 2, No.3 and No.4 are obtained from equation (5-2) with o , calculated using equation (5-3). After point No.5, the behavior was assumed to be a perfectly plastic behavior. The
45 40 35 30 25 20 15 10 5 0
Ultimate Compressive Strength
5
4
3 2 1
Strain, , mm/mm
0.0035
0.003
0.0025
0.002
0.0015
0.001
0.0005
Strain at Ultimate Strength 0
Stress, , MPa
stress-strain values calculated are illustrated in Table (5-4).
(a) Drawn with Microsoft Excel
(b) Drawn with ANSYS
Fig. (5.10) – Compressive Uniaxial Stress-Strain Curve of Present Research 5.3.3.1.1.
Failure Criteria for Concrete:
The ANSYS model is capable of predicting failure for concrete materials, by using both cracking and crushing failure modes. In addition to cracking and crushing, the concrete may also undergo plasticity, with the Drucker-Prager
Finite Element Modeling
Page 164
Chapter Five – Finite Element Modeling failure surface being most commonly used. In this case, the plasticity is done before the cracking and crushing checks. (Willam and Warnke, 1974) [99] developed a widely used model for the triaxial failure surface of unconfined plain concrete. The failure surface in principal stress-space is shown in Fig. (5.11-a), while a 3-D failure surface for concrete, in principal stress space, as described in the ANSYS program, is shown in Fig. (5.11-b). Table (5-4) - The Compressive Uniaxial Stress-Strain Values Points Starting point Point No.1 Point No.2 Point No.3 Point No.4 Point No.5
Stress, MPa, Ec f 2 1 o 0 ' 0.3 f c 11.856 25.324737 34.15555 38.418542 f c' 39.52
a) Willam and Warnke Model [98]
Strain, mm/mm 0 0.0004013 0.0009698 0.0015382 0.0021067 o 2 f c' Ec 0.0026751
b) ANSYS Program Model [97]
Fig. (5-11) - 3-D Failure Surface for Concrete in Principal Stress Space The mathematical model considers a sextant of the principal stress-space because the stress components are ordered according to the major principal stresses, (σ1 ≥ σ2 ≥ σ3).
Finite Element Modeling
Page 165
Chapter Five – Finite Element Modeling To define the failure surface for the concrete using the Willam and Warnke model, different constants must be defined [99]. These constants are: 1. Shear transfer coefficients for an open crack, o 2. Shear transfer coefficients for a closed crack, c 3. Uniaxial tensile cracking stress, f t 4. Uniaxial crushing stress, f c 5. Biaxial crushing stress, f cb 6. Ambient hydrostatic stress state, h , to be used with constants 7 and 8. 7. Biaxial crushing stress under the ambient hydrostatic stress state, f 1 . 8. Uniaxial crushing stress under the ambient hydrostatic stress state, f 2 . 9. Stiffness multiplier for cracked tensile condition (defaults to 0.6). The first two coefficients represent the typical shear transfer, ranging from 0 to 1. The 0-value represents a smooth crack, complete loss of shear transfer, while the 1-value represents a rough crack, no loss of shear transfer. In this study, the shear transfer coefficients for open and closed cracks were set to 0.2 and 0.6, respectively. The third coefficient, uniaxial cracking stress, was based upon the modulus of rupture, f r , and is dependent on f t , which is determined using equation (5-5) [3]: f r 0.62 f c'
…… (5-5)
The fourth coefficient, uniaxial crushing stress, was based on the uniaxial unconfined compressive strength f c' and is denoted as f c . The crushing capability of the concrete element was turned off by entering a value of (-1), as suggested by (Kachlakev, et al. 2001) [101]. The fifth coefficient, biaxial crushing stress refers to the ultimate biaxial compressive strength, f cb . Finite Element Modeling
Page 166
Chapter Five – Finite Element Modeling The sixth coefficient is the ambient hydrostatic stress state, h , calculated using equation (5-6). h
1 xp yp zp 3
…… (5-
6) where xp , yp and zp are the principal stresses in the principal directions. The seventh and eighth coefficients refer to ultimate compressive strength for a state of biaxial and uniaxial compression superimposed on the hydrostatic stress state, f 1 and
f2 ,
respectively.
However, the failure surface can be specified with only two constants, f t and f c . The other constants in the concrete model, f cb , f 1 and
f2
are left for their default
values according to the model proposed by (Willam and Warnke, 1974)
[99]
, based
on equations (5-7) through (5-9). f cb 1.2 f c'
…… (5-7)
f cb 1.45 f c'
…… (5-8)
f cb 1.725 f c'
…… (5-9)
However, these default values are valid only for stress states satisfying the condition in equation (5-10). h 3 f c'
…… (5-10)
The material properties for the concrete are presented in Table (5-5). 5.3.3.2.
Steel Reinforcing Bars, Link180 Element:
The material properties for the steel reinforcement bars are represented by Material Model Number 2 through 5. The Link180 element was used for all the steel reinforcement in the specimen which was assumed to be bilinear isotropic. The bilinear isotropic material is also based on the Von Mises failure criteria. Finite Element Modeling
Page 167
Chapter Five – Finite Element Modeling The bilinear model requires the yield stress ( f y ) as well as the hardening modulus of the steel to be defined. The yield stress and the hardening modulus for all steel bar used are presented in Table (5-6). The stress-strain relationship for steel reinforcement adopted in this study is similar to the one shown in Fig. (5.12). Table (5-5) - Material Properties for Concrete, Solid65 Element Material Model Number
1
Element Type
Solid65
Material Properties
Linear Isotropic Modulus of Elasticity of the Concrete, EX 29547 Ec, MPa PRXY Poisson’s Ratio, ν 0.2 Multilinear Isotropic Points Strain, mm/mm Stress, MPa 0 0 0 ' 1, 0.3 f c 0.0004013 11.856 2 0.0009698 25.325 3 0.0015382 34.156 4 0.0021067 38.419 ' 5, f c 0.0026751 39.520 Nonlinear Inelastic Non-metal Plasticity Shear transfer coefficients for an open crack, o . 0.2 Shear transfer coefficients for a closed crack, c .
0.6
Uniaxial tensile cracking stress, f t .
4
Uniaxial crushing stress, f c .
-1
Biaxial crushing stress, f cb . Ambient hydrostatic stress state, h . Biaxial crushing stress under the hydrostatic stress state, f 1 .
ambient
Uniaxial crushing stress under the ambient hydrostatic stress state, f 2 . Stiffness multiplier for cracked tensile condition (defaults to 0.6).
Finite Element Modeling
0.6
Page 168
Chapter Five – Finite Element Modeling fs fsu fsy
Et
Es εy
εsu
εs
Fig. (5.12) – Stress-Strain Relationship for Steel Reinforcement [113] Table (5-6) - Material Properties for Steel Reinforcement Material Model Number
2
Element Type
Link180ϕ16mm
Material Properties EX PRXY Yield Stss Tang Mod
3
Link180ϕ12mm
EX PRXY Yield Stss Tang Mod
4
Link180ϕ10mm
EX PRXY Yield Stss Tang Mod
5
Link180ϕ8mm
EX PRXY Yield Stss Tang Mod
Finite Element Modeling
Linear Isotropic Modulus of Elasticity of Steel, Es, MPa Poisson’s Ratio, ν Bilinear Isotropic Yielding Stress of Bars, fy- ϕ16mm, MPa Tangent Modulus, Et=20%Es, MPa Linear Isotropic Modulus of Elasticity of Steel, Es, MPa Poisson’s Ratio, ν Bilinear Isotropic Yielding Stress of Bars, fy- ϕ12mm, MPa Tangent Modulus, Et=20%Es, MPa Linear Isotropic Modulus of Elasticity of Steel, Es, MPa Poisson’s Ratio, ν Bilinear Isotropic Yielding Stress of Bars, fy- ϕ10mm, MPa Tangent Modulus, Et=20%Es, MPa Linear Isotropic Modulus of Elasticity of Steel, Es, MPa Poisson’s Ratio, ν Bilinear Isotropic Yielding Stress of Bars, fy- ϕ8mm, MPa Tangent Modulus, Et=20%Es, MPa
200000 0.3 497 40000 200000 0.3 655 40000 200000 0.3 756 40000 200000 0.3 667 40000 Page 169
Chapter Five – Finite Element Modeling 5.3.3.3.
Steel Plates for Loads and Supports, Solid45 Element:
Steel plates were added at load and support locations in the finite element model to provide an even stress distribution over the loading and support areas. The material properties for the steel plates are represented by Material Model Number 6 and Solid45 element. The steel plates were assumed to be linear elastic isotropic materials with a modulus of elasticity for steel, Es, 210000 MPa, and poisson’s ratio, ν, 0.3, as shown in Table (5-7)
Table (5-7) - Material Properties for Steel Plates Material Model Number
Element Type
6
Solid45
5.3.3.4.
Material Properties EX PRXY
Linear Isotropic Modulus of Elasticity of Steel, Es, MPa Poisson’s Ratio, ν
210000 0.3
CFRP Strips, Shell181 Element:
The material properties for the CFRP strengthening strips are represented by Material Model Number 7. CFRP is a material that consists of two constituents. This material is an anisotropic material; meaning that their properties are not the same in all directions. A schematic drawing of the CFRP fabrics is shown in Fig. (5.13).
Fig. (5.13) – Schematic of CFRP Material[101]
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Chapter Five – Finite Element Modeling The unidirectional fabric has three orthogonal planes of material properties (xy, xz, and yz planes). The xyz coordinate axes, the principal material coordinates, where the x direction is the same as the fiber direction, and the other directions are perpendicular to it. The orthotropic material is also considered as transversely isotropic, therefore, the properties of the CFRP are assumed to be the same in any direction perpendicular to the fibers, so the properties in both the y and the z directions are the same [101]. The input data needed for the CFRP in the finite element models, as illustrated in Table (5-8), are as follows: the Number of layers, thickness of each layer, orientation of the fiber direction for each layer, the elastic modulus and the shear modulus of the CFRP in the fiber direction and the Poisson’s ratio. Table (5-8) - Material Properties for CFR Fabric Material Model Number 7
Element Type
Material Properties
Shell181
Linear Isotropic Modulus of Elasticity, GPa Poisson’s Ratio, ν Shear Modulus, GPa
EX PRXY GXY
230 0.3 88.5
5.3.4. Modeling and Meshing: The corbels along with the column were modeled as volumes by using the solidmodeling approach. The zero values for all coordinates were at the bottom left edge of the structure, the dimension of the specimen was previously mentioned in article 5.2; the specimen volume is shown in Fig. (5.14).
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Chapter Five – Finite Element Modeling
Fig. (5.14) –The Concrete Volume for the M0W Specimen Created in ANSYS
Then the concrete volume was meshed into 25 mm cubic elements by using the volume sweep command, as shown in Fig. (5-15).
Fig. (5.15) –The Concrete FE Mesh for the M0W Specimen Created in ANSYS After creating the elements for the concrete, Link180 element was used to create all the reinforcement used in this model. As mentioned earlier, the reinforcement was represented using the discrete modeling, where both the reinforcement and the Finite Element Modeling
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Chapter Five – Finite Element Modeling concrete share the same nodes. Fig. (5.16) illustrates the meshed steel reinforcement in the calibration model, and the FE mesh for the concrete and steel is shown in Fig. (5.17).
Fig. (5.16) – The Mesh of the Steel Reinforcement for the Calibration Model
Fig. (5.17) – The FE Mesh of the Concrete and Steel Reinforcement for the Calibration Model The size of the support steel plates was 25mm×100mm×150mm, while the loading steel plate has the dimensions of 25mm×200mm×150mm; the steel plates were modeled by creating nodes and elements using the direct generation approach. The Finite Element Modeling
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Chapter Five – Finite Element Modeling dimensions of the elements in the steel plates were consistent with the elements and nodes in the concrete, as shown in Fig. (5-18).
Fig. (5.18) – The FE Mesh for the M0W Calibration Model Meshing of the steel reinforcement and steel plates were performed by creating their elements through the nodes of the previously meshed concrete volume. The necessary mesh attributes were set before creating each section of both the steel reinforcement and steel plates. Elements representing the CFRP were then created for specimens strengthened with this material such as M50H, M50I, M50HI, R50H, R50I and R50HI. For the horizontally configured strengthened specimens, M50H and R50H, the elements were created in the same manner as the steel reinforcement, by using the same nodes of the concrete. Whereas for the inclined configured strengthened specimens, M50I and R50I, the elements were simulated by creating areas through specified nodes to represent the CFRP then setting the contact pair creation, using surface-to-surface contact elements. The contact properties used included the multipoint constraint algorithm, MPC algorithm, that sets the behavior of the contact surface to Bonded (always), as shown in Fig. (5.19).
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Chapter Five – Finite Element Modeling
Fig. (5.19) – The Contact Properties for the CFRP Strengthened Models The same procedure was followed for the mixed configured strengthening specimens, M50HI and R50HI, as shown in Figs. (5.20) through (5.23).
Fig. (5.20) - The Calibration Model of M50H and R50H Specimens
Finite Element Modeling
Fig. (5.21) - The Calibration Model of M50I and R50I Specimens
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Chapter Five – Finite Element Modeling
Fig. (5.22) - The CFRP Modeling in M50HI and R50HI Specimens
Fig. (5.23) - The Calibration Model of M50HI and R50HI Specimens
In order to construct and manage contact definitions, an easy-to-use interface called the Contact Manager can be used. Each contact element in the ANSYS program includes several KEYOPTS to control the contact behavior when using surface-to-surface contact elements [97]. All KEYOPTS for the contact pair used in the present study are illustrated in Table (5-9). Table (5-9) - Specifications and Uses of KEYOPTS Used For the Contact Pair in the Present Study KEYOPTS
Specifications and Uses
(2,2)
Contact algorithm, Multipoint constraint (MPC) Location of contact detection point, On nodal point- normal to target surface CNOF/ICONT Automated adjustment, No automated adjustment Element level time incrementation control, No control Asymmetric contact selection, No action Effect of initial penetration or gap, Exclude both initial geometrical penetration or gap and offset Contact stiffness update, Each iteration based on current mean stress of underlying elements (pair based) Shell thickness effect, Exclude Behavior of contact surface, Bonded (always) Contact algorithm, Multipoint constraint (MPC
(4,2) (5,0) (7,0) (8,0) (9,1) (10,2) (11,0) (12,5) (2,2)
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Chapter Five – Finite Element Modeling 5.3.5. Numbering Controls: After the creation of all elements, another command called merge items was used. This command merges separate entities, having the same location, to become single entities. A summary of the numbers of elements used in all strengthened models are summarized in Table (5-10). Table (5-10) - The Number of Elements used in all Strengthened Models Type of Element
No. of Elements
Concrete (Solid65) 2448 Steel Reinforcement (Link180) 380 Steel Plates (Solid 45) 96 Horizontal Orientation, H 136 CFRP (Shell181) Inclined Orientation, I 4656* Mixed Orientation, HI 4792* The element number increased because the inclined elements were meshed with smaller sizes, 5mm cubes. 5.4.
Loads and Boundary Conditions:
In ANSYS program the loads are applied either on the solid model, keypoints, lines, and areas, or on the finite element model, on nodes and elements. No matter how the loads are specified, the solver expects all loads to be in terms of the finite element model. Therefore, if the loads are specified on the solid model, the program automatically transfers them to the nodes and elements at the beginning of solution [97]. In the present study the load was applied on all the nodes of the loading steel plate; the full load was applied on the middle nodes while a quarter of the load was applied on the corner nodes, the rest of the nodes which were located on the circumference of the steel plate were applied with half of the load as shown in Fig. (5.25). Finite Element Modeling
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Chapter Five – Finite Element Modeling Displacement boundary conditions are needed to constrain the model and get a unique solution. To ensure that the model acts like the experimentally tested specimen, boundary conditions need to be applied at the supports and loadings locations. The support were modeled as simply supported, the nodes on one plate were given constraint in all direction, Ux, Uy, and Uz, while the nodes on the other plate were given constraint in the Uy, and Uz directions. The boundary conditions for the calibration model are shown in Fig. (5.24).
Constraint in the (x, y and z)Directions Constraint in the (y and z)Directions
Fig. (5.24) – The Loading and Boundary Conditions for the Calibration Model P/2
P/4 P/2
P/4
P/4
P
P/2
P/2 P/4
Fig. (5.25) –Loading Applied on the Steel Plate of the Calibration Model 5.4.1. Analysis Type within the Theory of the Finite Element Method There are two ways for the FEM formulation, the first is based on the Direct Variational Method, (Rayleigh-Ritz method and Energy method); the second is by Finite Element Modeling
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Chapter Five – Finite Element Modeling using the Weighted Residuals Approach (Galerkin method)
[107 and 108]
. The general
guidelines for the finite element analysis along with the methods and techniques used to solve the nonlinear equations are detailed in appendix A. The ANSYS software has a wide range capability of finite element analysis, ranging from linear analysis, static analysis to a complicate non-linear, and transient dynamic analysis
[97]
. The analysis type is based on the loading conditions
and the response wished to be calculated, as an example, a modal analysis is chosen if natural frequencies and mode shapes are to be calculated. The analysis types that are available in the ANSYS program, as shown in Fig. (5.26) are: Static (representing the monotonic loading used in the experimental phase of this research), Modal, Transient, (representing the repeated loading used in the experimental phase of this research), Harmonic, Spectrum, Eigen Buckling and Substructuring/CMS [97]. In the present study the FE analysis was performed on ten cases using three types of analysis, static, modal and transient analyses; the cases studied are listed in Table (5-11).
Fig. (5.26) – The Analysis Types Available in the ANSYS Program Finite Element Modeling
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Chapter Five – Finite Element Modeling Table (5-11) - The Cases Studied and Corresponding Types of Analysis Performed in the Theoretical Phase No. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 5.4.1.1.
Cases Studied
Analysis Type
M-0-W M-50-H M-50-I M-50-HI R-0-W-1 R-0-W-2 R-0-W-3 R-50-H-3 R-50-I-3 R-50-HI-3
Static and Modal Static and Modal Static and Modal Static and Modal Transient Transient Transient Transient Transient Transient
Static Analysis Type:
This type of analysis was performed on the first four cases. The first case, the calibration FE model for specimen M-0-W, was analyzed as a simply supported beam under vertical loading. The nonlinear problems were solved in the ANSYS program by using the Newton-Raphson and the Predictor Corrector methods. The commands used to control the Analysis type are: New Analysis, Restart and Sol’n Controls. The New Analysis command has been utilized to start the analysis after the load step was completed, followed by selecting the Static analysis type. The Restart command has been utilized to restart an analysis after the initial run has been completed [97]. The Sol’n Controls dialog box consists of five tabs; each tab contains a set of related solution controls. The tabs, listed from left to right, include: Basic, Transient, Sol'n Options, Nonlinear and Advanced NL. The commands used to control the Basic tab are: Analysis Options, Time Control and Write Items to Results File, as shown in Table (5-12).
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Chapter Five – Finite Element Modeling
Table (5-12) - Commands used to Control the Basic Tab Main Commands
Chosen Commands
Small displacement static Calculate prestress effects: no. Time at End of Loadstep: 672000 N. Automatic time stepping: on Time increment*: Time Control Time step size: 1000 Minimum time step: 1000 Maximum time step: 10000 All solution items Write Items to Results File Frequency: write every substep In static analysis the time represents a counter and the values, mentioned above, may be changed through the analysis to overcome divergence. Analysis Options
The commands used to control the Transient tab are: Full Transient Options, Damping Coefficients, Midstep Criterion and Time Integration. This tab was inactive through the Static analysis type [97]. The commands used to control the Sol'n Options tab are: Equation Solvers and Restart Control, as shown in Table (5-13).
Table (5-13) - Commands used to Control the Sol'n Options Tab Main Commands Equation Solver Restart Control
Chosen Commands Program chosen solver Frequency: Write Every Substep
The commands used to control the Nonlinear tab are: Nonlinear Options, Equilibrium Iterations, Creep Options and Cutback Control. The values of this tab are set ANSYS defaults, as shown in Table (5-14). Finite Element Modeling
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Chapter Five – Finite Element Modeling
Table (5-14) - Commands used to Control the Nonlinear Tab Main Commands
Chosen Commands
Line search: On Nonlinear Options DOF solution predictor: On VT Speedup: Off Equilibrium Iterations Maximum number of iterations: 100 Creep Options Include strain rate effect: No Limits on physical values to perform bisection: Equiv. Plastic strain: 0.15 Explicit Creep ratio: 0.1 Cutback Control Implicit Creep ratio: 0 Incremental displacement: 10000000 Points per cycle: 13 Cutback according to predicted number of iterations Set convergence criteria Sets convergence values for the analysis: 0.05 In any nonlinear FE analysis, convergence is assumed to occur when the external and internal forces differ with an acceptable small value. Thus using a convergence criterion is important in order to terminate the iterative process if the solution was considered as sufficiently accurate. Generally, in nonlinear analysis of structural members, two types of convergence criteria are available: the force and the displacement criteria. In the present study, for the first steps of loading, both convergence criteria have been adopted. As the analysis proceeds, only the displacement convergence criterion was adopted. The application of the loads up to failure was done incrementally as required by the Newton-Raphson procedure. After each load increment, if the solution was converged, the next step was started. The time used in the loading steps represents a counter that corresponds to the loading applied. Failure of the specimen occurred when convergence failed. The load deformation trace produced by the analysis confirmed the failure load. Finite Element Modeling
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Chapter Five – Finite Element Modeling 5.4.1.2.
Modal Analysis Type:
The modal analysis, (Appendix A, article 2-2), was used in this research to determine the natural frequencies of the specimens to serve as a starting point for the transient dynamic analysis to simulate the repeated loading regime applied in the experimental phase. Before performing the modal and transient analyses, the densities, of all materials used, must be input into the program because dynamic solutions depend on the properties of the materials. After performing the static analysis for the cases studied, a modal analysis, using Block Lanczos method, was performed on the first four cases to find the natural frequency for five expanded shape modes [97]. The general process for a modal analysis consists of: 1) Build the model 2) Choose analysis type and options 3) Apply boundary conditions and solve 4) Review results The results of the modal analysis for the first case, M0W, are illustrated in Table (5-15). The images of the five shape modes for that case are shown in the Figs. (5-27) through (5-31). The solutions of the other three cases are illustrated in Appendix B. Table (5-15) - The Results of Modal Analysis for the First Case, M0W 1 Case Natural Δt N ωn - max Studied Frequency 2.355 4.865 M-0-W 8.393 0.0039122 9.091 9.129 Finite Element Modeling
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Chapter Five – Finite Element Modeling
Fig. (5.27) - The First Mode Shape for Case M0W
Fig. (5.28) - The Second Mode Shape for Case M0W
Fig. (5.29) - The Third Mode Shape for Case M0W
Fig. (5.30) - The Fourth Mode Shape for Case M0W
Fig. (5.31) - The Fifth Mode Shape for Case M0W
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Chapter Five – Finite Element Modeling 5.4.1.3.
Transient Analysis Type:
Structural systems are often subjected to transient excitation. A transient excitation is a highly dynamic, time-dependent force exerted on the structure, such as earthquake, impact and shocks
[109]
. The general equation for these kinds of
structures has the following form:
M K Ft
…… (5-11)
The procedure and equations involving the solution of transient analysis are illustrated in Appendix A, article A.2.3. The cases studied in the static and modal analyses were tested to perform the transient analysis for the last six cases mentioned in Table (5-11). There are two methods in the ANSYS program that can be employed to solve equation (5-11), the forward difference time integration method, which was used for explicit transient analyses, and the Newmark time integration method, which was used for implicit transient analyses, as in the cases of this study. The Newmark method uses finite difference expansions in the time interval Δt and is described in Appendix A, article A.2.3. To perform the transient analysis in the ANSYS program, on the cases studied, the three dimensional structure for each case was treated as a one dimensional structure, which has the same dimensions and properties of the three dimensional structural system, this was done to save the computer CPU, because the former consumes time and space to be solved. The element representing this treatment in the ANSYS program is BEAM188. BEAM188, is a 3-D Finite Strain Beam that is suitable for analyzing slender to moderately stubby/thick beam structures. This element is based on Timoshenko beam theory. Shear deformation effects are included. This element is well-suited for linear, large rotation, and/or large strain nonlinear applications. Finite Element Modeling
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Chapter Five – Finite Element Modeling BEAM188 is a linear (2-node) or a quadratic beam element in 3-D that has six degrees of freedom at each node; these include translations in the x, y, and z directions and rotations about the x, y, and z directions. BEAM188 includes stress stiffness terms, by default, in any analysis. The provided stress stiffness terms enable the elements to analyze flexural, lateral, and torsional stability problems (using eigenvalue buckling or collapse studies with arc length methods) [97]. Elasticity, creep, and plasticity models are supported. A cross-section associated with this element type can be a built-up section referencing more than one material. For BEAM188, the element coordinate system is not relevant. The geometry, node locations, and coordinate system for this element are shown in Fig. (5.32) [97].
Fig. (5.32) - BEAM188 Geometry [97] This element is defined by nodes I and J in the global coordinate system. Node K is a preferred way to define the orientation of the element. BEAM188 is a one-dimensional line element in space. The cross-section details are provided separately using the SECTYPE and SECDATA commands; it allows change in cross-sectional inertia properties as a function of axial elongation. By default, the cross-sectional area changes such that the volume of the element is Finite Element Modeling
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Chapter Five – Finite Element Modeling preserved
after
deformation.
The
default
is
suitable
for
elastoplastic
applications [97]. 5.5.
Building the Model:
The model was built in the ANSYS program using the same data used in the static and modal analyses previously performed on the cases studied, the M0W case was the reference model for cases R0W1, R0W2 and R0W3 and the M50H was the reference model for case R50H3, M50I was the reference model for case R50I3 and finally M50HI was the reference model for case R50HI3. The data used included the modulus of elasticity of the system, the mass density of each material and the time step used in the analysis. The simulated model for specimen R0W1 is shown in Fig. (5-33). The geometry of this model will be the same for the other five specimens studied under transient analysis except for the properties and time steps which depend on the reference model for each case. The time step was calculated through the maximum natural frequency to obtain the least time step to include all cases, as follows [97]:
t
1 N n max
…… (5-12)
Where: ∆t is the time step in seconds. N is the maximum number of divisions per structure. ωn-max is the maximum natural frequency. In the present study, the values of the time step, ∆t, for each case are illustrated in Table (5-16).
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Chapter Five – Finite Element Modeling
Fig. (5.33) - The Simulated Model for Specimen R0W1 Using BEAM188 Element Table (5-16) - The Time Step, ∆t, for All Transient Tested Cases No. 1 2 3 4 5 6 5.6.
Case Studied R-0-W-1 R-0-W-2 R-0-W-3 R-50-H-3 R-50-I-3 R-50-HI-3
Reference Model
Δt
1 N ωn - max
M-0-W
0.0039122
M-50-H M-50-I M-50-HI
0.0039109 0.0039096 0.0039083
Load-Time Histories of the Transient Analysis:
The load histories implemented in the experimental phase of this study was simulated in the ANSYS program. Three schemes of loading were used to investigate the effect of this kind of loading on the strengthened reinforced concrete corbels. For the first three cases, R0W1, R0W2 and R0W3, the effect of changing the repeated loading scheme was investigated, while for the remaining three cases, R50H3, R50I3 and R50HI3, the effect of strengthening under load history schemeFinite Element Modeling
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Chapter Five – Finite Element Modeling LH3 was investigated. The Load-Time Tables used were adopted from the experimental phase of the present study; the time represented the accumulated time for each cycle in the experimental phase. These Tables were entered as an array into the program. Dimensions for these arrays were saved for each cycle and for the applied load in the program. The load was applied on one node on the top of the column in the simulated model. The graphs of the load histories of the cases studied are shown in Figs. (5-34)
800 600 400 200 0
R0W1-FEM
R0W1
Exp F L
520 130
390 260
520
587 577
520
390
260
0 60 120 180 240 300 360 420 480 540 600 660 720 780 840 900 960 1020 1080 1140 1200 1260 1320 1380 1440 1500 1560 1620 1680 1740 1800 1860 1920 1980 2040 2100 2160 2220 2280 2340 2400 2460 2520 2580 2640 2700 2760 2820 2880 2940 3000 3060 3120 3180 3240 3300 3360 3420 3480
Load. kN
through (5-39).
Time, sec
800 600 400 200 0
R0W2-FEM 260 260 260
EXP FL 390 390
R0W2 390
520
520
587
520
570
130 0 60 120 180 240 300 360 420 480 540 600 660 720 780 840 900 960 1020 1080 1140 1200 1260 1320 1380 1440 1500 1560 1620 1680 1740 1800 1860 1920 1980 2040 2100 2160 2220 2280 2340 2400 2460 2520 2580 2640 2700 2760 2820 2880 2940 3000 3060 3120 3180 3240 3300 3360 3420 3480 3540 3600 3660 3720 3780 3840 3900 3960 4020 4080 4140 4200
Load, kN
Fig. (5.34) – Load-Time Graph of R0W1
Time, sec
800 600 400 200 0
R0W3-FEM 390 260
EXP FL 390
390
R0W3 390
520
520
520
520
587
587 547
260 260
0 120 240 360 480 600 720 840 960 1080 1200 1320 1440 1560 1680 1800 1920 2040 2160 2280 2400 2520 2640 2760 2880 3000 3120 3240 3360 3480 3600 3720 3840 3960 4080 4200 4320 4440 4560 4680 4800 4920 5040 5160 5280 5400 5520
Load, kN
Fig. (5.35) – Load-Time Graph of R0W2
Time, sec
Fig. (5.36) – Load-Time Graph of R0W3 Finite Element Modeling
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0 138 276 414 552 690 828 966 1104 1242 1380 1518 1656 1794 1932 2070 2208 2346 2484 2622 2760 2898 3036 3174 3312 3450 3588 3726 3864 4002 4140 4278 4416 4554 4692 4830 4968 5106 5244 5382 5520 5658 5796 5934 6072 6210 6348
Load, kN 0 134 268 402 536 670 804 938 1072 1206 1340 1474 1608 1742 1876 2010 2144 2278 2412 2546 2680 2814 2948 3082 3216 3350 3484 3618 3752 3886 4020 4154 4288 4422 4556 4690 4824 4958 5092 5226 5360 5494 5628 5762 5896 6030 6164
Load, kN 800 600 400 200 0
800 600 400 200 0
800 700 600 500 400 300 200 100 0 0 148 296 444 592 740 888 1036 1184 1332 1480 1628 1776 1924 2072 2220 2368 2516 2664 2812 2960 3108 3256 3404 3552 3700 3848 3996 4144 4292 4440 4588 4736 4884 5032 5180 5328 5476 5624 5772 5920 6068
Load, kN
Chapter Five – Finite Element Modeling
290
320
R50H3-FEM 435 290 290
R50I3-FEM 450
300 300
R50HI3-FEM
Finite Element Modeling
R50H3 EXP FL 580 435 435 435
EXP FL 450 450 450
EXP FL 480 480 480 480
580
600
580
600
640
580
600
640
650
R50I3 675
640 640
650 605
Time, sec
Fig. (5.37) – Load-Time Graph of R50H3
675
600 646
300
Time, sec
Fig. (5.38) – Load-Time Graph of R50I3
R50HI3
720 659
320 320
Time, sec
Fig. (5.39) – Load-Time Graph of R50HI3
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Chapter Six –Results of FE Analysis for Reinforced Concrete Corbels 6. Results of FE Analysis for Reinforced Concrete Corbels: 6.1.
General:
In this chapter the accuracy and validity of the ANSYS program to predict the load carrying capacity of reinforced concrete corbels strengthened with CFRP strips is checked. At first, the check will be performed by comparing the results obtained from the calibration model, M0W, with the results obtained from the experimental phase of this research for the same specimen. The main purpose of the calibration FE model is to ensure that the elements, material properties, real constants and convergence criterions chosen were adequate to model the same response of the experimental tested member. After this verification, nine more specimens will be analyzed using the ANSYS-15, the results of the analysis will be discussed and a comparison will be made with the experimental results. 6.2.
Verification of Calibration Model, M0W:
In this article, the analytical results of the calibration model are compared with the experimental results as means of verification for the use of the ANSYS programs in predicting the load carrying capacity of reinforced concrete corbels strengthened with CFRP strips. The theoretical ultimate load for the studied corbel was calculated following the ACI 318M-14, and was found to be, 554 kN, while the experimental ultimate load reached was 652 kN. A plot of the load versus the deflection for specimen M-0-W is shown in figure (6.1). This figure shows as well the different components analyzed for the sake of comparison which were: the linear region, initial cracking, the nonlinear region, and failure. The values obtained from the calibration FE model along with the experimental results are illustrated in table (6-1), while the load-deflection curve obtained using the FEM and experimental analysis for this model are shown in figure (6.2). Results of FE Analysis for Reinforced Concrete Corbels
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Chapter Six –Results of FE Analysis for Reinforced Concrete Corbels
M0W(ACI) - Theoretical Ultimate Load, 554 kN
700 650 600 550 500 450 400 350 300 250 200 150 100 50 0
NonLinear Region Pc = 250 kN Linear Region
Δc = 3.37 mm
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0
Load, kN
M0W, Pu= 652 kN, Δu=8 mm
Deflection, mm
Fig. (6.1) – Experimental Load-Deflection Curve for the Calibration Model, M0W Table (6-1) - Comparison between the Theoretical and Experimental Failure Loads for the Calibration Model, M0W Pu-ACI (kN)
Pu-EXP (kN)
Pu-FEM (kN)
Pu ACI Pu EXP
Pu FEM Pu EXP
M-0-W
554
652
605
0.85
0.93
Load, kN
Specimen
M-0-W
800 700 600 500 400 300 200 100 0
652 kN 605 kN
M0W-FEM M0W-EXP 0
1
2
3
4
5
6
7
8
9
10
Deflection, mm
Fig. (6.2) – Load-Deflection Relationship of Specimen M-0-W The crack pattern, after each load step, is recorded by the ANSYS program. The development of crack patterns for the calibration model is shown in figure (6.3), while a comparison with the experimental crack patterns, at failure load, is illustrated in figure (6.4). Results of FE Analysis for Reinforced Concrete Corbels
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Chapter Six –Results of FE Analysis for Reinforced Concrete Corbels
At Load 134 kN
At Load 202 kN
At Load 269 kN
At Load 336 kN
At Load 470 kN
At Load 538 kN
At Load 578 kN
At Load 605 kN
Fig. (6.3) –Development of Crack Pattern for the Calibration Model, M0W Results of FE Analysis for Reinforced Concrete Corbels
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Chapter Six –Results of FE Analysis for Reinforced Concrete Corbels
Fig. (6.4) – Comparison between Numerical and Experimental Crack Pattern For Specimen M0W at Failure For the calibration FE model, the deformation shape, the Y-component of deflection and the Von Mises stress and strain distributions are shown in figures (6.5) through (6.8), respectively.
Fig. (6.5) – Deformed Shape at failure for Specimen M-0-W
Fig. (6.6) – Nodal Solution-∆y at failure for Specimen M-0-W
Fig. (6.7) –Stress Distribution at failure for Specimen M-0-W
Fig. (6.8) –Strain Distribution at failure for Specimen M-0-W
Results of FE Analysis for Reinforced Concrete Corbels
Page 194
Chapter Six –Results of FE Analysis for Reinforced Concrete Corbels The results of this model showed that the numerical approach adopted agrees well with the experimental results of specimen M0W, therefore this approach was adopted again to simulate nine other models to compare their results with the experimental results obtained from the experimental phase of this study. 6.3.
Results of FE Analysis for Reinforced Concrete Corbels
The other nine cases were analyzed using the ANSYS program, as mentioned in table (5-11). Analysis for these cases was similar to the calibration model, for the static analysis cases, monotonic loading, and differs for the transient analysis cases, repeated loading. In the latter cases, different load steps were used, according to the load history schemes used during the experimental phase of this research. The analysis led to the following results: 6.3.1. Crack Patterns and Modes of Failures: 6.3.1.1.
Specimen M-50-H:
The experimental and numerical crack pattern at failure for this specimen is shown in figure (6.9).
Fig. (6.9) – Experimental and Theoretical Crack Pattern for Specimen M-50-H at Failure The crack pattern from ANSYS and the experimental tested specimen agreed very well. The first cracks, obtained from ANSYS, appeared at time 2000, corresponding to a load of 145 kN. These cracks started at the bottom corbelcolumn joint, propagating along the corbel-column interface, as shown in figure Results of FE Analysis for Reinforced Concrete Corbels
Page 195
Chapter Six –Results of FE Analysis for Reinforced Concrete Corbels (6.10). Then the cracks started to propagate inside the column and towards the upper corbel-column joint. Almost all cracks were diagonal shear cracks and were aligned along and parallel to the load’s line of action connecting the point of load application at the bottom face of the corbel and the point of upper corbel-column joint. The crack pattern shown reveals that the mode of failure for specimen M50H was diagonal splitting failure. The development of crack pattern for specimen M50H is shown in figure (6.10)
At Load 145 kN
At Load 218 kN
At Load 290 kN
At Load 363 kN
At Load 435 kN
At Load 508 kN
At Load 580 kN
At Load 652 kN
At Load 689 kN
Fig. (6.10) –Development of Crack Pattern for the Simulated Model, M-50-H 6.3.1.2.
Specimens M-50-I and M-50-HI:
Almost the same behavior was obtained for the other two specimens analyzed statically (monotonic loading), M50I and M50HI. The results obtained are in good agreement with the experimental results, as shown in figure (6.11) and (6.12) respectively. Results of FE Analysis for Reinforced Concrete Corbels
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Chapter Six –Results of FE Analysis for Reinforced Concrete Corbels
Fig. (6.11) – Experimental and Theoretical Crack Pattern for Specimen M-50-I at Failure
Fig. (6.12) – Experimental and Theoretical Crack Pattern for Specimen M-50-HI at Failure 6.3.1.3.
Transient Specimens:
For the remaining specimens analyzed with transient analysis, R-0-W-1, R-0-W-2, R-0-W-3, R-50-H-3, R-50-I-3 and R-50-HI-3, no crack pattern was available because the element type used for the analysis, BEAM188, is not supported with cracking or crushing nonlinearities, as in SOLID65, which uses different expressions to resemble crack patterns such as: Crushed, Open, Closed and Neither. 6.3.2. Load versus Deflection Results: The load-deflection curves obtained from the ANSYS program reveal that the finite element analysis gives solutions that are in acceptable agreement with the results obtained from the experimental phase of this study. It was observed that both the experimental and numerical load-deflection curves shared the same behavior, Results of FE Analysis for Reinforced Concrete Corbels
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Chapter Six –Results of FE Analysis for Reinforced Concrete Corbels except that the numerical curves were a little bit stiffer at the first stages of loading; but the behavior was changed with the increasing of loads up to failure, where the final failure loads recorded were lower than those obtained in the experimental phase of the study. Nevertheless, the ANSYS solution, regarding both types of analysis used, is considered within reasonable agreement with the experimental results, for all analyzed specimens, and throughout the entire range of loading. Both the numerical and experimental load-deflection curves, for the monotonically analyzed specimens, along with the numerical nodal solution for the displacement in the y-direction, are illustrated in figures (6.13) through (6.18), while figures (6.19) through (6.30) show these results for the transient analyzed specimens. The failure load for FE analysis was the load recorded at the last load step after which
Load, kN
the solution starts to diverge and produce unacceptable results. 800 700 600 500 400 300 200 100 0
M-50-H
725 kN
689 kN
M50H-EXP M50H-FEM 0 1 2 3 4 5 6 7 8 9 10
Deflection, mm
Load, kN
Fig. (6.13) – Load-Deflection Relationship of Specimen M-50-H 800 700 600 500 400 300 200 100 0
M50I
Fig. (6.14) – Nodal Solution, ∆y, at failure for Specimen M-50-H
750 kN 712 kN
M50I-EXP M50I-FEM 0 1 2 3 4 5 6 7 8 9 101112
Deflection, mm
Fig. (6.15) – Load-Deflection Relationship of Specimen M-50-I Results of FE Analysis for Reinforced Concrete Corbels
Fig. (6.16) – Nodal Solution, ∆y, at failure for Specimen M-50-I Page 198
Chapter Six –Results of FE Analysis for Reinforced Concrete Corbels
1000
M50HI 825 kN
Load, kN
800 600
816 kN
400 200
EXP FEM
0 0 1 2 3 4 5 6 7 8 9 10 11
Deflection, mm
Load, kN
Fig. (6.17) – Load-Deflection Relationship of Specimen M-50-HI
800 700 600 500 400 300 200 100 0
Fig. (6.18) – Nodal Solution, ∆y, at failure for Specimen M-50-HI
R0W1-FEM 570 kN C10
0 1 2 3 4 5 6 7 8 9 10
Deflection, mm
Load, kN
Fig. (6.19) – Load-Deflection Relationship of Specimen R-0-W-1
800 700 600 500 400 300 200 100 0
Fig. (6.20) – Nodal Solution, ∆y, at failure for Specimen R-0-W-1
R0W2-FEM 528 kN C13
0 1 2 3 4 5 6 7 8 9 10
Deflection, mm
Fig. (6.21) – Load-Deflection Relationship of Specimen R-0-W-2
Results of FE Analysis for Reinforced Concrete Corbels
Fig. (6.22) – Nodal Solution, ∆y, at failure for Specimen R-0-W-2
Page 199
Load, kN
Chapter Six –Results of FE Analysis for Reinforced Concrete Corbels
800 700 600 500 400 300 200 100 0
R0W3-FEM
469.6 kN C14
0 1 2 3 4 5 6 7 8 9 10 11 12
Deflection, mm
Load, kN
Fig. (6.23) – Load-Deflection Relationship of Specimen R-0-W-3
800 700 600 500 400 300 200 100 0
Fig. (6.24) – Nodal Solution, ∆y, at failure for Specimen R-0-W-3
R50H3-FEM 619.8 kN C14
0 1 2 3 4 5 6 7 8 9 10
Deflection, mm
Load, kN
Fig. (6.25) – Load-Deflection Relationship of Specimen R-50-H-3
800 700 600 500 400 300 200 100 0
Fig. (6.26) – Nodal Solution, ∆y, at failure for Specimen R-50-H-3
R50I3-FEM 622.7 kN C14
0 1 2 3 4 5 6 7 8 9 10
Deflection, mm
Fig. (6.27) – Load-Deflection Relationship of Specimen R-50-I-3
Results of FE Analysis for Reinforced Concrete Corbels
Fig. (6.28) – Nodal Solution, ∆y, at failure for Specimen R-50-I-3
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Chapter Six –Results of FE Analysis for Reinforced Concrete Corbels
R50HI3-FEM 800 700 600 500 400 300 200 100 0
Load, kN
631.4 kN C13
0 1 2 3 4 5 6 7 8 9 10
Deflection, mm
Fig. (6.30) – Nodal Solution, ∆y, at failure for Specimen R-50-HI-3
Fig. (6.29) – Load-Deflection Relationship of Specimen R-50-HI-3
All data regarding ultimate loads and deflections for both numerical and experimental analysis are listed in table (6-2). The difference between the finite element analysis and experimental results ranged between 1% and 14% for the ultimate loads and between 1% and 16% for the ultimate deflections. These ranges are considered within acceptable agreement. Table (6-2) - Comparison between Numerical and Experimental Results No. Specimen
Pu-EXP (kN)
Cn
∆u-EXP (mm)
Pu-FEM (kN)
Cn
∆u-FEM (mm)
Pu FEM Pu EXP
u FEM u EXP
1
M-0-W
652
-
8.00
605
-
7.83
0.93
0.98
2
M-50-H
725
-
9.31
689
-
8.90
0.95
0.96
3
M-50-I
750
-
9.41
712
-
7.90
0.95
0.84
4
M-50-HI
825
-
9.79
816
-
9.28
0.99
0.95
5
R-0-W-1
577
10
7.85
570
10
6.83
0.99
0.87
6
R-0-W-2
570
13
7.19
528
13
7.17
0.93
1.00
7
R-0-W-3
547
14
7.80
470
14
10.78
0.86
1.38
8
R-50-H-3
605
14
7.87
620
14
7.76
1.02
0.99
9
R-50-I-3
646
14
7.65
623
14
7.18
0.96
0.94
10
R-50-HI-3
659
13
7.03
631
13
6.90
0.96
0.98
Results of FE Analysis for Reinforced Concrete Corbels
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Chapter Six –Results of FE Analysis for Reinforced Concrete Corbels 6.3.3. Concrete and CFRP Strain and Stress Distributions: During the experimental phase of this study strain gauges were installed on the concrete and CFRP strips to record their strains. When analyzing with ANSYS program, one of the results obtained was the values of strains. The results of the recorded strains for both numerical and experimental tests are illustrated in table (6-3) for the concrete strains and table (6-4) for CFRP strains, the results show that the values obtained from the ANSYS program agree well with the results recorded from the experimental test. The distribution of the Von Mises stress and total mechanical strain in concrete are shown in figures (6.31) through (6.48). Table (6-3) - Comparison between Numerical and Experimental Strain in Concrete No. 1 2 3 4 5 6 7 8 9 10
Specimen M-0-W M-50-H M-50-I M-50-HI R-0-W-1 R-0-W-2 R-0-W-3 R-50-H-3 R-50-I-3 R-50-HI-3
εConcrete-EXP Shear Friction 3.563×10-3 0.0100915 0.001745 0.010448 3.528×10-3 2.375×10-3 8.494×10-3 2.9×10-3 5.0685×10-3 7.692×10-3
Compression -2.18×10-4 -1.42×10-4 -7.5×10-5 -1.2×10-5 -
εConcrete-FEM Range 0.948×10-5-0.2324 0.583×10-5-0.230625 0.104×10-4-0.05996 0.921×10-5-0.02289 0.317×10-18-16.0197 0-0.00490 0-0.00736 0-0.00354 0.00165-0.00327 0.00165-0.00496
Table (6-4) - Comparison between Numerical and Experimental Strain in CFRP No. 1 2 3 4 5 6
Specimen M-50-H M-50-I M-50-HI R-50-H-3 R-50-I-3 R-50-HI-3
εCFRP-EXP Horizontal 4.697×10-3 5.731×10-3 3.186×10-3 2.47×10-3
Inclined 4.188×10-3 4.589×10-3 4.893×10-3 4.51×10-3
Results of FE Analysis for Reinforced Concrete Corbels
εCFRP-FEM Range 0.583×10-5-0.076845 0.104×10-4-0.11991 0.921×10-5-0.02289 0-0.00354 0-0.001634 0-0.003306 Page 202
Chapter Six –Results of FE Analysis for Reinforced Concrete Corbels
Fig. (6.31) – Strain Fig. (6.32) – Stress Fig. (6.33) – Strain Distribution in Concrete for Distribution in Concrete for Distribution in Concrete for Specimen M-50-H Specimen M-50-H Specimen M-50-I
Fig. (6.34) – Stress Fig. (6.35) – Strain Fig. (6.36) – Stress Distribution in Concrete for Distribution in Concrete for Distribution in Concrete for Specimen M-50-I Specimen M-50-HI Specimen M-50-HI
Fig. (6.37) – Strain Fig. (6.38) – Stress Fig. (6.39) – Strain Distribution in Concrete for Distribution in Concrete for Distribution in Concrete for Specimen R-0-W-1 Specimen R-0-W-1 Specimen R-0-W-2
Results of FE Analysis for Reinforced Concrete Corbels
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Chapter Six –Results of FE Analysis for Reinforced Concrete Corbels
Fig. (6.40) – Stress Fig. (6.41) – Strain Distribution in Concrete for Distribution in Concrete for Specimen R-0-W-2 Specimen R-0-W-3
Fig. (6.42) – Stress Distribution in Concrete for Specimen R-0-W-3
Fig. (6.43) – Strain Fig. (6.44) – Stress Distribution in Concrete for Distribution in Concrete for Specimen R-50-H-3 Specimen R-50-H-3
Fig. (6.45) – Strain Distribution in Concrete for Specimen R-50-I-3
Fig. (6.46) – Stress Fig. (6.47) – Strain Distribution in Concrete for Distribution in Concrete for Specimen R-50-I-3 Specimen R-50-HI-3
Fig. (6.48) – Stress Distribution in Concrete for Specimen R-50-HI-3
Results of FE Analysis for Reinforced Concrete Corbels
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Chapter Seven – Conclusions and Recommendations 7. CONCLUSIONS AND RECOMMENDATIONS: 7.1.
General:
Based on the experimental and analytical results within the scope of the present investigation, the following conclusions and recommendations for future work are drawn. 7.2.
Conclusions:
The investigation in the present research included two phases; the experimental phase and the analytical phase. The conclusions drawn from each phase are presented. 7.2.1. Conclusions Drawn from the Experimental Phase: From the experimental results the following conclusions can be drawn: 1) Test results of CFRP strengthened reinforced corbels showed an improvement in the ultimate load carrying capacity of these corbels. For the monotonically loaded corbels, strengthening corbels with 50 mm of CFRP strips helped in enhancing the load carrying capacity with about 11%, 15% and 27% for the horizontal, inclined and mixed configurations respectively. While for the non-reversed repeated loaded corbels, the enhancement was about 11%, 18% and 21% for the horizontal, inclined and mixed configurations respectively. 2) The inclined configuration strengthening technique was found to be better than the horizontal wrapping one and is recommended for future work. 3) The most suitable width for the strengthening technique is 4 times the concrete cover, 100 mm in the present study, and is recommended for future work. 4) The first crack appearance was delayed by using a 50 mm of CFRP strengthening strips in the three selected configurations. For the monotonically tested specimens, the increase in the first visual observed Conclusions and Recommendations
Page 205
Chapter Seven – Conclusions and Recommendations crack reached 158%, while for the non-reversed repeated loaded specimen the appearance of first crack was delayed to the third, fifth and ninth cycles. 5) For the non-reversed repeated loaded specimen, a strength gain was recorded with increasing the width of strengthening strips from 50 mm to 150 mm, this gain, ranged between of 11% to 24% for horizontal configuration, 18% to 25% for inclined configuration and 21% to 29% for mixed configuration. 6) The three strengthening configurations of the CFRP used in this research enhanced the load carrying capacity of the corbels tested under non-reversed repeated loading regime; this enhancement is well observed by the increase in the maximum repeated load reached and the number of cycles under that load with respect to the non-strengthened specimen. The increase in the max repeated load reached was 11% for 4 cycles, 15% for 4 cycles and 23% for 4 cycles, for the 100 mm-strengthening strip of the RH, RI and RHI groups respectively. 7) The three strengthening configurations of the CFRP used in this research reduced the main steel reinforcement strains at the section of maximum moment, and hence, increased their yield load leading to an increase in the failure loads of the corbels. For the monotonically loaded specimens, the yielding load was increased with about 8%, 13% and 30% for the horizontal, inclined and mixed configurations. For the non-reversed repeated loaded specimens, this increase was about 27%, 25% and 30% for the horizontal, Inclined and mixed configurations respectively. Moreover, the diagonal CFRP strengthening controlled the widening and growth of shear cracks, leading to an obvious increase in the load capacity.
Conclusions and Recommendations
Page 206
Chapter Seven – Conclusions and Recommendations 8) Records of strain gauges fixed on CFRP indicated that there was little or no measured strain prior to cracking. Therefore, it was obvious that the CFRP started its work in resisting loads soon after the initiation of cracks. 9) The shape of the load-deflection curves at post cracking stages and stages closed to failure, depended on the type of loading history applied, which included the number of cycles and the altitude of each cycle. 7.2.2. Conclusions Drawn from the Analytical Phase: From the analytical results the following conclusions can be drawn: 1) The failure mechanism for the reinforced concrete corbels was well modeled using the ANSYS program; the FE models predicted reached failure loads that were almost the same as the loads measured during experimental phase of the study. Therefore it can be concluded that the ANSYS program is able to simulate the behavior of reinforced concrete corbels strengthened with CFRP and subjected to both monotonic and repeated loading regimes. 2) The predicted behavior, simulated by the finite element analysis, was in good agreement with the experimental results for both monotonic and repeated loading regimes. 3) The difference between the finite element analysis and experimental results ranged between 1% and 14% for the ultimate loads and between 1% and 16% for the ultimate deflections. 4) The mechanical strains in concrete obtained by the finite element analysis were well agreed with the results recorded experimentally. 5) The same agreement was obtained for the strain in the CFRP strips.
Conclusions and Recommendations
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Chapter Seven – Conclusions and Recommendations 7.3.
Recommendation for Future Work:
To complete the work in the present research and previous researches performed on reinforced concrete corbels, the following future work is recommended for farther investigations: 1) Most of the previous investigations performed included strengthened reinforced concrete corbels under the influence of vertical loads only; therefore, further investigations are needed to study the behavior of such corbels under the influence of both vertical and horizontal loads. 2) Researches are needed to investigate the effectiveness of using near surface mounted CFRP strips in reinforced concrete corbels. 3) Researches are needed to investigate the effectiveness of strengthening reinforced concrete corbels
with cementitious composites, such as
cementitious carbon fiber reinforced composite. 4) Investigating the effect of using fiber reinforced polymer, FRP sheets to retrofit damaged reinforced concrete corbels subjected to repeated loading regimes. 5) Investigating the behavior of SCC corbels subjected to a combination of vertical and horizontal load. 6) Investigating the effect of using prestressed reinforcement on the behavior of corbels cast with different types of concrete and subjected to monotonic or repeated loading regimes.
Conclusions and Recommendations
Page 208
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Futtuhi I. N., “Reinforced Corbels Made with High-Strength Concrete and Various Secondary Reinforcements", ACI Structural Journal, V. 91, No. 4, July-August, 1994, pp. (376-383). Foster, S. J., Powell, R. E. and Selim, H. S. “Performance of High-Strength Concrete Corbels", ACI Structural Journal, V. 93, No. 5, September-October 1996, pp. (555-563). Bourget, M., Delmas, Y. and Toutlemonde, F., “Experimental study of the behaviour of reinforced concrete short corbels”, Materials and Structures Journal, V. 34, No. 5, April, 2001, pp. (155-162). De Larrard, F. et Baroghel-Bouny, V., “Aging in wild concrete: An experiment for the twenty-first century. I: General and mechanical characteristics of concrete”, Laboratories Bulletin of Bridges and Pavement, 225 (2000), [Cited by Ref. (54)]. Campione, G., La Mendola, L. and Mangiavillano, M. L., “Steel Fiber-Reinforced Concrete Corbels: Experimental Behavior and Shear Strength Prediction”, ACI Structural Journal, V. 104, No. 5, Sep.-Oct., 2007, pp. (570-579). Ridha, M. M. S., “Nonlinear Finite Element Analysis of High Strength Fiber Reinforced Corbels”, Engineering & Technology Journal, V. 26, No. 1, 2008, pp. (1-15). Ahmad, S. and Shah A., “Evaluation of Shear Strength of High Strength Concrete Corbels Using Strut and Tie Model (STM)”, the Arabian Journal of Science and Engineering, V. 34, No. 1B, April, 2009, pp. (27-35). Campione, G., “Performance of Steel Fibrous Reinforced Concrete Corbels Subjected to Vertical and Horizontal Loads”, the Journal of Structural Engineering, Vol. 135, No. 5, May 1, 2009, pp. (519-529). Yousif, A. R., “Prediction of Ultimate Load Capacity of High-Strength Reinforced Concrete Corbels”, Al-Rafidain Engineering Journal, V. 17, No. 4, August, 2009, PP. (12-27). Al-Zahawi, S. Kh. R., “Experimental and Analytical Behavior of CFRP Reinforced Concrete Corbels”, Ph.D. thesis, University of Sulaimani, Iraq, 2011, pp. 175. Khalifa, E. S., “Macro-mechanical Strut and Tie Model for Analysis of Fibrous HighStrength Concrete Corbels”, Ain Shams Engineering Journal, V. 3, Issue 4, December 2012, Pages 359–365. Aliewi, J. M. A., “Behavior and Strength of Self-Compacting Fiber Reinforced Concrete Corbels”, PhD thesis, Civil Engineering Department, Al-Mustansiriya University, Baghdad, Feb., 2014, 206 pp. Loo, Y.C. and Yao, B.Z, “Static and Repeated Load Tests on Precast Concrete Beam-toColumn Connections”, PCI Journal, 40 (2), 1995, pp. (106-115). Cheok,G. S., Stone, W. C. and Kunnath, S. K., “Seismic Response of Precast Concrete Frames with Hybrid Connections”, ACI Structural Journal, V. 95, No. 5, September, 1, 1998, pp. (527-539). Nicholas, H. T. T., Jason, M. I. and Sritharan, S., “Cyclic Strut & Tie Modelling of Simple Reinforced Concrete Structures”, the World Conference on Earthquake Engineering, 12WCEE, January-February, 2000, No. 1249, 8 pp. Dora, A.G. and Abdul Hamid, N.H., “Seismic Performance of SFRC Beam-Column Joint with Corbel under Reversible Lateral Cyclic Loading”, IACSIT, International Journal of Engineering and Technology, Vol. 4, No. 1, February 2012. Farhan, R. Sh., “Behavior of Reinforced Concrete Corbels under Repeated Loading”, PhD thesis, Civil Engineering Department, Al-Nahrain University, Baghdad, Aug., 2014, 206 pp. Page | 212
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Engindeniz, M., Kahn, L. F., and Zureick, A. H., “Repair and Strengthening of Reinforced Concrete Beam-Column Joints: State of the Art”, ACI Structural Journal, V. 102, No. 2, March-April 2005, pp. (1-14). Heidayet, A., Ramadhan, A. and Qarani, O., “Repairing of Damaged Reinforced Concrete Corbels Strengthened by Externally Bonded Steel Plates”, Zanco Journal for Pure and Applied Science, Salahaddin University, V. 16, No. 1, 2004, Hawler-Iraqi Kurdistan Region. Campione, G., La Mendola L. and Papia, M., “Flexural Behaviour of Concrete Corbels Containing Steel Fibers or Wrapped with FRP Sheets”, Materials and Structures, V. 38, July 2005, pp. (617-625). Ozden, S. and Atalay H., M. Mangiavillano, “Strengthening of Reinforced Concrete Corbels with GFRP Overlays”, Science and Engineering of Composite Materials, V. 18, No. 1, 2011, PP. (69-77). Erfan, A. M., Abdel-Rahman G.T., Nassif, M. K. and Hammad, Y.H., “Behaviour of Reinforced Concrete Corbels Strengthened With CFRP Fabrics”, Scientific and Research Journal (ESRJ), V. 13, No. 4, March, 2011, Benha University, Egypt. El-Maaddawy, T. A. and El-Sayed, I. Sh., “Response of Concrete Corbels Reinforced with Internal Steel Rebars and External Composite Sheets: Experimental Testing and Finite Element Modeling”, Journal of Composites for Construction, 18, 2014. DOI: 10.1061/ (ASCE) CC.1943-5614.0000403, American Society of Civil Engineers. ASTM Designation: C192/C192M–14, “Standard Practice for Making and Curing Concrete Test Specimens in the Laboratory”, 2014, ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States. ASTM Designation: C33/C33M−13, “Standard Specification for Concrete Aggregates”, 2013, ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States. ASTM Designation: C39/C39M−14a, “Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens”, 2014, ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States. ASTM Designation: C469/C469M–14, “Standard Test Method for Static Modulus of Elasticity and Poisson’s Ratio of Concrete in Compression”, 2014, ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States. ASTM Designation: C496/C496M–11, “Standard Test Method for Splitting Tensile Strength of Cylindrical Concrete Specimens”, 2011, ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States. ASTM Designation: C78/C78M−10´1, “Flexural Strength of Concrete (Using Simple Beam with Third-Point Loading)”, 2010, ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States. ASTM Designation: C617/C617M−14, “Standard Practice for Capping Cylindrical Concrete Specimens”. ASTM Designation: A370-14- “Standard Test Methods and Definitions for Mechanical Testing of Steel Products”. ASTM Designation: A615/A615M−14, “Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement”.
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ASTM Designation: A1064/A1064M−14, “Standard Specification for Deformed and Plain Carbon-Steel Bars for Concrete Reinforcement”, Replacement of ASTM Designation: A496, which was withdrawn in 2013. 85) Iraqi Standard Specification, I.Q.S, No.5, “Iraqi Cement”, 1984. 86) Iraqi Standard Specification, I.Q.S, No.45, “Natural Aggregate used in Concrete and Building”, 1984. 87) Sika Corporation, Product Data Sheet for “SikaWrap®-300”, 34957 Tuzla, İstanbul, Türkiye, (www.sika.com). 88) Sika Corporation, Product Data Sheet for “Sikadur 330”, 34957 Tuzla, İstanbul, Türkiye, (www.sika.com). 89) TML Product Guide, 2014, Tokyo Sokki Kenkynjo CO. Ltd, Japan – TML Pam E8501B. 90) ACI 211.1-91, Reapproved 1997, “Standard Practice for Selecting Proportions for Normal Heavyweight, and Mass Concrete, Reported by ACI Committee 211. 91) Static Monotonic and Cyclic Loading, 100 tons Capacity, Loading Frame User Manual (2014), Al Sarmad Al-Abadi Company for Electrical and Mechanical Heavy Industries. 92) Ruiz, W. M., and Winter, G., “Reinforced Concrete Beams under Repeated Loads”, Journal of Structural Division, ASCE, V. 95, No. ST7, June, 1969. 93) Hwang, T. H., and Scribner, C. F., “RC Member Cyclic Response During Various Loading”, Journal of Structural Engineering, ASCE, V. 110, No. 3, March, 1984, pp. 477- 489. 94) Kwak , H. G. and Filippou, F. C., “Finite Element Analysis of Reinforced Concrete Structures under Monotonic Loads”, Report No. UCB/SEMM-90/14, Structural Engineering, Mechanics and Materials, Department of Civil Engineering, University of California, Berkeley, November 1990, p.120. 95) Phillips, D. V., and Zienkiewics, O. C., "Finite Element Nonlinear Analysis of Concrete Structures", Journal of Structural Division, ASCE Proceedings, Part 2, Vol. 61, 1976, pp. 59-88. 96) Barkanov, E., “Introduction to the Finite Element Method”, Institute of Materials and Structures, Faculty of Civil Engineering, Riga Technical University, 2001, p.70. 97) ANSYS Structural Analysis Guide, "ANSYS Help", “A Finite Element Computer Software and User Manual for Nonlinear Structural Analysis,” ANSYS Release 15.0, © SAS IP, Inc., Canonsburg, PA, 2014. 98) Wolanski A. J.,“Flexural Behavior of Reinforced and Prestressed Concrete Beams Using Finite Element Analysis”, MSc thesis, the Faculty of the Graduate School, Marquette University, Milwaukee, Wisconsin, May, 2004, p.76. 99) Willam, K.J. and Warnke, E.P., “Constitutive Model for Triaxial Behaviour of Concrete”, Seminar on Concrete Structures Subjected to Triaxial Stresses, International Association of Bridge and Structural Engineering Conference, Bergamo, Italy, 1974, p.174, [Cited by Ref. (98)]. 100) MacGregor, J.G. (1992), Reinforced Concrete Mechanics and Design, Prentice-Hall, Inc., Englewood Cliffs, NJ. 101) Kachlakev, D. and Miller, T. “Finite element modeling of reinforced concrete structures strengthened with FRP laminates”, Final Report, SPR 316, Oregon Department of Transportation Research Group 200 Hawthorne SE, Suite B-240, Salem, OR 973015192 and Federal Highway Administration 400 Seventh Street SW Washington, DC 20590, May 2001, p.99. Page | 214
References 102) Wang, Z. H., “Study on the Combined Bending and Shear Behavior of RC Beam Strengthened with FRP Composites”, the 28th Conference on Our World in Concrete and Structures, 27-28 August, 2001, Singapore, pp. 671-676. 103) Ivanova, I., Assih, J., LI, A. and Delmas, Y., “Influence Of Fabrics Layers On Strengthened Reinforced Concrete Short Corbels” International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online), Vol. 5, No. 11, November, 2014, pp. 33-43. 104) Ivanova, I. and Assih, J., “Experimental Study of Local Behavior of Strengthened Reinforced Concrete Short Corbel by Bonding Carbon Fiber Fabrics”, International Journal of Structural & Civil Engineering Research, Vol. 4, No. 1, February, 2015, pp. 148-158, www.iaeme.com/Ijciet.asp. 105) Assih, J., Ivanova, I., Dontchev, D. and Li, A., “Concrete damaged analysis in strengthened corbel by external bonded carbon fiber fabrics”, Applied Adhesion Science, a Springer Open Journal, Vol. 3, No. 21, 2015, www.appliedadhesionscience.com. 106) Huebner, H.H., Dewhirst, D.L., Smith, D. E., and Byrom, T. G., “The Finite Element Method for Engineers”, 4th ed., New York: J. Wiley, 2001. 107) Rao, S. S. , “The finite Element Method in Engineering”, 2nd edition, 1989, [Cited by Ref. (109)]. 108) Moaveni, S.,”Finite Element Analysis Theory and Application With ANSYS”, 2nd edition , 2003, Prentice Hall, USA. 109) Said, M. W., “The Effect of Dynamic Loading on Stresses Induced in Hip Joint Prothesis”, MSc. Thesis, College of Engineering, University of Baghdad, Iraq, 2013, pp. 100. 110) Nakasone, Y., Yoshimoto, S. and Stolarski, T. A., “Engineering Analysis with ANSYS Software”, 1st Edition, 2006, [Cited by Ref. (109)]. 111) Dawe, D. J., "Matrix and Finite Element Displacement Analysis of Structures", Clarendon Press, Oxford, U. K., 1984, 565 pp. 112) Bhavikatti, S.S., “Finite Element Analysis), Book, 4835/24, Ansari Road, Daryaganj, New Delhi – 110002, ISBN (13): 978-81-224-2524-6, 2005, [Cited by Ref. (109)]. 113) Khudhair, H. M. A., “Behavior of High Strength Reinforced Concrete Deep Beams under Repeated Loading”, PhD. Thesis, the College of Engineering, Al-Nahrain University, Iraq, 2014, pp. 181. 114) Nyssen, C., “An Efficient and Accurate Iterative Method, Allowing Large Increment Steps, to Solve Elasto-Plastic Problems”, Computers and Structures, Vol.13, pp.63 – 71, 1981, [Cited by Ref. (109)].
Page | 215
Appendix A – Finite Element Method Concepts A.
Finite Element Method Concepts:
A.1.
The Finite Element Method Steps:
The general guideline of the finite element analysis follows the steps described below: Step 1- Discrimination of the Real Structure: Create and discretize the solution domain into finite elements, by subdividing the problem into nodes and elements, the typical and commonly used elements are shown in Fig. (A.1) [109]. 1) Bar Element. 2) Triangular Element.
3) Quadrilateral Element.
4) Axisymmetric Element.
5) Tetrahedron Element.
6) Hexahedron Element.
Fig. (A.1) – Geometry of Commonly Used Elements [109]
Finite Element Method Concepts
Page A-1
Appendix A – Finite Element Method Concepts Step 2- Identification of the Primary Unknown Quantities and the Appropriate Interpolation Shape Function: Depending on the nature of the problem, the primary unknown quantity varies from case to case. In vibration analysis problem, the displacement component is chosen as the primary unknown quantity, which is represented by a vector quantity in the analysis, . A proper form of the interpolation shape function must be then chosen. This function relates the primary unknown quantity in the elements to that of the associated nodes. The general equations for the 3-Dimensional element with six degree of freedom are illustrated in equations (A-1) through (A-7) [112].
u
v w x y z
u u1 N1 u2 N 2 u3 N3 .......... ui Ni v v1 N1 v2 N 2 v3 N3 .......... vi Ni
…… (A-1) …… (A-2) …… (A-3)
w w1 N1 w2 N 2 w3 N3 .......... wi Ni
…… (A-4)
x x1 N1 x 2 N 2 x 3 N3 .......... x i Ni
…… (A-5)
y y1 N1 y 2 N 2 y 3 N3 .......... y i Ni
…… (A-6)
z z1 N1 z 2 N 2 z 3 N3 .......... z i Ni
…… (A-7)
Where:
, is the vector of nodal displacement. Ni, is the shape function of the node Step 3- Define Relationship between Action and Reaction: The physical law that relates the actions, loads F , and reactions, displacements
, in a structural analysis case is the minimization of potential energy [97]. Step 4- Derive Element Equation: The element equation connects the reactions, in terms of the primary unknown, to the actions. There are generally two distinct methods used in the finite element Finite Element Method Concepts
Page A-2
Appendix A – Finite Element Method Concepts method for the derivation of such equations, the Rayleigh-Ritz method and the weighted residual method (Galerkin method) [108]. For almost all structural problems, solved using the finite element method, the equations of the element can be expressed in the following general form [108].
M e Ke e Fe t
…… (A-8)
Ke BT D BdVol
…… (A-9)
And Vol
Where: [Ke] is the element property matrix (stiffness matrix) [B] is the strain-displacement matrix [B]T is the transposed strain-displacement matrix [D] is the stress-strain matrix {δe} is the vector of primary unknown quantities at the nodes, (Displacements) {Fe} is the vector of nodal forces Step 5- Derive the Overall Structure Stiffness Equation: In this step of the analysis, an assemblage of all individual element equations is performed to provide stiffness equations for the entire structure. The mathematical expression for this step is as follows [109]: [ M ]{} [ K ]{ } {F (t )}
…… (A-10)
Where: [M ] , is the overall mass matrix m
M M e
…… (A-11)
i 1
[K ] , is the overall stiffness matrix m
K K e
…… (A-12)
i 1
Finite Element Method Concepts
Page A-3
Appendix A – Finite Element Method Concepts [F (t )] , is the vector of nodal forces
Step 6: Solve Most of the structural problems are linear elastic problems with significant inertia effects. To find a solution for these problems, the Solving step is divided into three basic types [109]: 1) The Steady State Response, Static Analysis: [ K ]{ } {F } 2) Natural Frequency Analysis, Modal Analysis: [ M ]{} [ K ]{ } 0 3) Transient Response, Transient Analysis: [ M ]{} [ K ]{ } {F (t )} A.2.
Types of Analysis in FEM:
A.2.1. Static Analysis: Static analysis involves the solving of equation (A-10) without the term with the global mass matrix, [M]. Hence as discussed, the static system of equations takes the form [109]. [ K ]{ } {F}
…… (A-13)
The methods often used to solve the above matrix equation are Gauss elimination and LU decompositions, for small systems, and iterative methods for large systems. A.2.1.1.
The Shape Function:
Shape functions are interpolation functions that define their variation in the displacements and their derivatives, through an element in terms of their values at the nodes. Therefore, the shape functions are closely related to the number of nodes depending on the type of elements. It is convenient to express the shape functions in terms of non-dimensional element coordinates ξ, ε and δ which ranges between (–1) and (+1) over the element in local coordinates and between (0) and (+1) over the element in intrinsic coordinates [112]. In the finite element method the region of interest is sub divided into a number of sub regions known as elements, which are defined by the location of their nodal points. In general, suppose an element with n-nodes is considered and a set of Finite Element Method Concepts
Page A-4
Appendix A – Finite Element Method Concepts polynomial interpolation functions, N1, N2, N3, …., Ni, is introduced in association with each node in the element subdivision or mesh. A typical shape function, Ni, associated with node i has a value of unity at node i and a zero value over the other nodes within the elements, by following simple rules in the construction of Ni, the unknown variable can be represented by the following expression [112]: N11 N 22 N33 ...... Nii
…… (A-14)
N , , 1
…… (A-15)
n
i 1
e i
Where the notation (e) means element and 1 , 2 , 3 , ......, i have a physical meaning at either the local coordinate level or the global coordinate level. The geometry of an 8-node element can be defined in terms of the shape functions and can be expressed by: x , , y , , z , ,
N , , x 8
i 1 8
i
i
N , , y i 1 8
i
N , , z i 1
i
i
i
…… (A-16)
Where: Ni , , is the shape function at the ith node.
xi, yi and zi are the global coordinates of the node i. The shape function for the 8-node brick elements has the form:
Ni (ξ,η,ζ)=
1 1+ξξ i 1+ηηi 1+ζζ i 8
…… (A-17)
Where: ξi 1 , ηi 1, ζi 1
Finite Element Method Concepts
Page A-5
Appendix A – Finite Element Method Concepts A.2.1.2.
The Displacement Function:
The displacement functions for an 8-node isoparametric element are u, v and w, representing the displacements in the global directions x, y and z, respectively. The same shape functions are used to express the displacements through the element in terms of the nodal displacements. These functions are given by: u , , v , , w , ,
N , , u n
i 1 n
i
i
N , , v i 1 n
i
i
N , , w i 1
i
i
…… (A-18)
Where: ui, vi and wi are the nodal displacements of node i. A.2.1.3.
Strain-Displacement Relations:
The relationship between linear strains and displacements can be expressed as follows:
x
u x
, xy
u v y x
y
v y
, yz
v w z y
z
w z
, zx
w u x z
It can be written in a general matrix form as follows:
[B]{}
…… (A-19)
Where:
Finite Element Method Concepts
Page A-6
Appendix A – Finite Element Method Concepts x y { } z xy yz zx
…… (A-20)
[B] is strain-nodal displacement matrix based on the element shape functions in global coordinate system. N i x 0 0 [ B ] N i y 0 N i z
0 N i y 0 N i x N i z 0
0 0 N i z 0 N i y N i x
…… (A-21)
is the nodal displacement vector . A.2.1.4.
Stress-Strain Relations:
The general form of the stress-strain relationship for an elastic material may be written as follows [109]: {} [D]{}
…… (A-22)
Where: [ζ] is the stress vector: [D] is the constitutive matrix defined [ε] is the strain vector: The general stress-strain form can be expressed as follows: [D] is the constitutive matrix defined as follows:
Finite Element Method Concepts
Page A-7
Appendix A – Finite Element Method Concepts (1 ) x y z E 0 xy (1 )(1 2 ) yz 0 zx 0
1
1
0
0
0
0
0
0
0 0 0 x 0 0 0 y 1 2 0 0 z 2 xy 1 2 0 0 yz 2 1 2 zx 0 0 2 0
0
0
…… (A-23) A.2.1.5.
Stiffness Matrix [Ke]:
The element stiffness matrix for a homogeneous isotropic material is expressed as follows:
K [ B]T [ D][ B] dVol
…… (A-24)
Vol
Where: dVol=dx.dy.dz, representing the element volume in global coordinate system, to transform the element volume into local coordinate would be as follows: dVol dx dy dz J d d d
…… (A-25)
Where: J is the determinate of the Jacobian matrix, the latter is shown below: N i xi N i [J ] xi N i xi
N i yi N i yi N i yi
N i zi N i zi N i zi
…… (A-26)
By setting the limits of integration in the local coordinate to be from –1 to +1, then the element stiffness matrix becomes: 1 1 1
K [ B]T [ D][ B]
J d d d
…… (A-27)
1 1 1
Finite Element Method Concepts
Page A-8
Appendix A – Finite Element Method Concepts These integrals can be solved using numerical integration technique, such as “Gauss-Legendre Quadrature Scheme”, 8-point Gauss quadrature, which was found to be accurate and efficient. The stiffness matrix for a flexural element is as follows:
K e Flexural Element
AE L 0 0 AE L 0 0
0
0
12 EI L3 6 EI L2
6 EI L2 4 EI L
0
0
12 EI L3 6 EI L2
6 EI L2 2 EI L
AE L 0 0
AE L
0 0
0 12 EI L3 6 EI 2 L
0 12 EI L3 6 EI 2 L
6 EI L2 2 EI L 0 6 EI 2 L 4 EI L 0
…… (A-28)
The stiffness matrix for an axial element is as follows:
K e Axial Element
AE L 0 0 AE L 0 0
0 0
AE L 0 0 AE L 0
0 0
0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
…… (A-29) Where: L is the length of the element A is the cross–sectional area of the element I is the moment of inertia of the element E is the Young’s modulus of the element Finite Element Method Concepts
Page A-9
Appendix A – Finite Element Method Concepts A.2.1.6.
Mass Stiffness Matrix Derivation, [M]:
The mass matrix of a 3-dimensional, n-node solid element structure is derived as follows: 1) Define Nodal Velocities: The nodal displacement vector is defined:
u1
v1 w1 u2
v2
w2 . . . u1 v1 w1
…… (A-30)
Then the nodal velocity vector can be defined as the derivative of the displacement vector:
u
v1 w1 u2 v2 w 2 . . . u1 v1 w1
1
…… (A-31)
2) Express the velocity vector at any point in terms of nodal velocities and shape function: M
u u i N i
…… (A-32)
i 1 M
v vi N i
…… (A-33)
i 1
M
w w i N i
…… (A-34)
i 1
Defining the velocity vector, at the given point:
q u
v w
…… (A-35)
Then the velocity vector can be expressed as follows:
q N
…… (A-36)
Where: N1 N 0 0
0 N1
0 0
N2 0
0 N2
0 0
. . . Ni . . . 0
0 Ni
0
N1
0
0
N2 . . .
0
0
0 0 N i
…… (A-37)
3) Express the kinetic energy of the element in terms of nodal velocities: K E
1 qT q dV 2V
Finite Element Method Concepts
…… (A-38) Page A-10
Appendix A – Finite Element Method Concepts 1 T N T N dV 2 V
K E
…… (A-39)
4) Deduce the element mass matrix [M] from the definition of kinetic energy:
…… (A-40)
M S N T N dV
…… (A-41)
1 T M S 2
K E
V
A.2.2. Nodal Analysis: Also referred to as natural frequency analysis, where the general equation, (A-10) is solved without applying any load as follows:
M K 0 A.2.2.1.
…… (A-42)
Eigenvalue Problems Solution
To solve eigenvalue problems, using the finite element method, the matrices [K] and [M] will be symmetric of (n) order [109]. Multiplying by [M]–1 the following is obtained: [ I ] 2{ } [ H ]{ } 0
…… (A-43)
[ H ] M K
…… (A-44)
2
…… (A-45)
H I { } 0
…… (A-46)
Where: 1
For non-trivial:
H I 0 A.2.2.2.
…… (A-47)
Eigenvector Problems Solution [109]:
When the FEM is applied to find the mode shape for a system, it can be expressed in the following equation: Finite Element Method Concepts
Page A-11
Appendix A – Finite Element Method Concepts
G H I G 1 Adj G G
…… (A-48) …… (A-49)
By Multiplying equation (A-49) by G [G] the following is obtained: G [G] Adj[G]
…… (A-50)
By substituting equation (A-48) into equation (A-50) the following is obtained:
H I [H I ] Adj[H I ]
…… (A-51)
If λ is one of the eigenvalues then:
H i I [H i I ] Adj[H i I ]
…… (A-52)
The left side of the equation (A-52) becomes zero, then: 0 H i [ I ]Adj H i[ I ]
i Adj[ H ] i [ I ]
…… (A-53)
0 [ H ] i [ I ] i
…… (A-54)
Where: { }i is the eigenvector at i
A.2.3. Transient Analysis: A transient analysis is performed to describe a highly dynamic, time-dependent force exerted on a structure, such as moving loads, earthquake and impact [109]. The general equation, (A-10) is solved using a different solver from the one used in eigenvalue analysis. One of the widely used methods to do so is the direct integration method that basically uses the finite difference method for time stepping to solve equation (A-10). The direct integration method has two main types: implicit and explicit. The Implicit type is generally more efficient for relatively slow phenomena, whereas the explicit type is more efficient for a very fast phenomenon, such as impacts and explosions. In the following item the idea of Finite Element Method Concepts
Page A-12
Appendix A – Finite Element Method Concepts time stepping used in finite difference methods is introduced in order to solve transient problems [109]. A.2.3.1.
Central Difference Algorithm:
At first the system equation should be written in the following forms
[108]
:
M F K F Fint F residual
…… (A-55)
F int K
…… (A-56)
M F
…… (A-57)
1
residual
In practice, the above equation does not usually require solving of the matrix equation, since lumped masses are usually used which form a diagonal mass matrix. Therefore, the solution of equation (A-56) would be trivial, and the matrix equation would be a set of independent equations for each (i) degree of freedom as follows [109]:
i
fi
residual
…… (A-58)
mi
By using the following central finite difference equations:
t t 2 t t t t
…… (A-59)
2 t t t t
…… (A-60)
1 2 t t t t 2 t t
…… (A-61)
t t
t
By eliminating
t t
from equations (A-59) and (A-61) the following is
obtained:
t t t t t t
2
2
Finite Element Method Concepts
t
…… (A-62)
Page A-13
Appendix A – Finite Element Method Concepts To explain the time stepping procedure, the time stepping/marching procedure in the central difference method starts at t=0, and computes the acceleration 0 using equation (A-56).
M F …… (A-63) And as and are known from the initial conditions given; then by substituting , and into equation (A-62), is obtained. 1
residual
0
0
0
0
0
0
t t
0
By considering half the time step, t / 2 and using the central difference equations (A-59) and (A-60) the following is obtained:
t t / 2 t t t t / 2
…… (A-64)
…… (A-65)
t t / 2
t t
The velocity,
t / 2
t t / 2
, can be obtained from equation (A-64) by substituting
t t / 2 leading to the following:
t / 2
0 t
…… (A-66)
t
Then by using equation (A-65) at t 0 ,
as shown below: t
and
t / 2
can be obtained with respect to 0
t / 2
t / 2
0
t / 2
…… (A-67)
Then, by using equation (A-64) once more at t t / 2 , t can be obtained:
t t t / 2 0
…… (A-68)
Once t is determined, equation (A-65) at t t / 2 can be used to obtain t
is
by assuming the acceleration to be constant over the step t and t / 2 0 , and using 0 resembling the initial velocity. On the next time step,
Finite Element Method Concepts
t
Page A-14
Appendix A – Finite Element Method Concepts calculated using equation (A-57); then the above process is repeated and the loading continues until the desired final time is reached. It can be noted that in the previous process, the solution, regarding displacement, velocity and acceleration, was obtained without solving any matrix form of the system equation, it only involve using equations (A-57), (A-64), and (A-65) repeatedly. Therefore, the central difference method can be considered an explicit method. In such method, the loading time will be extremely fast. This kind of method is particularly suited for simulating highly nonlinear, large deformation structures. The central difference method, like most explicit methods, is conditionally stable, which means that if the time step, t , becomes too large to exceed a critical time step, t cr , then the solution obtained will become unstable and might grow without limit. The critical time step, t cr , should be the time taken for the fastest stress wave in the structure to cross the smallest element in the mesh. Therefore, the time steps used in the explicit methods are typically 100-1000 times smaller than those used with implicit methods. The need to use small time steps, makes the explicit methods lose out to implicit methods especially for problems of slow time variation. One of the most widely used implicit methods is the Newmark’s Method, which the ANSYS program uses to solve such problems. A.2.3.2.
The Newmark’s Method
The standard Newmark’s method will be introduced in this item. It is first assumed that [108]:
t t t t t t 2 1 t t t 2
t t
t t 1 t t t
Finite Element Method Concepts
…… (A-69) …… (A-70) Page A-15
Appendix A – Finite Element Method Concepts Where, β and γ are constants to be chosen by the analyst. By substituting equations (A-69) and (A-70) into the system equation (A-10) the following is obtained:
2
K t t t t 2 1 t t t M t t F t t
…… (A-71) Then by grouping all the terms involving t t , on the left side of the equation, and shifting the remaining terms to the right, equation (A-71) can be written in the following form:
residual K cm t t F t t
Where:
…… (A-72)
K cm K t M 2
…… (A-73)
And:
2 F tresidual F t t K t t t t t
1 t 2
…… (A-74) The acceleration, t t , can then be obtained by solving the matrix system equation (A-55), as follows:
t t
K cm
1
F tresidual t
…… (A-75)
The above equation involves matrix inversion, which is the same as solving a matrix equation, making this solver as an implicit method. The algorithm normally starts with a prescribed initial displacement and velocity,
0
and 0 . The initial acceleration, 0 , can then be obtained by substituting
0
and 0 into equation (A-10).
Finite Element Method Concepts
Page A-16
Appendix A – Finite Element Method Concepts If 0 is not prescribed initially, then equation (A-72) can be used to obtain the acceleration at the next time step, t . The displacements t and velocities t can then be calculated using equations (A-67) and (A-68), respectively. The procedure then is repeated forwardly in time until reaching the final desired time. At each time step, the matrix system equation (A-71) has to be solved; this procedure is a time consuming one, and leads to a slow process in time stepping. Newmark’s method is an unconditionally stable method, when 0.5 and
2 12 / 16 . Unconditionally stable methods are those where the size of the time step, t , have no effect on the stability of the solution, but it is rather governed by accuracy considerations. The unconditionally stable property allows the implicit algorithms to use significantly larger time steps when the external excitation is of a slow time variation. Fig. (A.3) represent a schematic graph for calculating the uploading and downloading time step, t .
Finite Element Method Concepts
Page A-17
Appendix A – Finite Element Method Concepts
and
are prescribed and
can be obtained from Eq. (A-57) Use Eq. (A-65) to obtain assuming
Obtain
then obtain
using Eq. (A-62)
using Eq. (A-57)
Loading time is half the time step, so by replacing ∆t with ∆t/2 into Eqs. (A-59) and (A-60)
Find
Find
at time (t = - ∆t/2) using Eq. (A-64)
using the average acceleration at time (t = 0) using Eq. (A-65)
Find
using the average velocity at time (t = ∆t/2) using Eq. (A-64)
Fig. (A.3) – Schematic Graph for Calculating the Uploading and Downloading Time Step, t
Finite Element Method Concepts
Page A-18
Appendix B – Modal Analysis B. The Modal Analysis: B.1. Modal Analysis for Case 2 – M50H:
Fig. (B.1) - The First Mode Shape for Case M50H
Fig. (B.2) - The Second Mode Shape for Case M50H
Fig. (B.3) - The Third Mode Shape for Case M50H
Fig. (B.4) - The Fourth Mode Shape for Case M50H
Fig. (B.5) - The Fifth Mode Shape for Case M50H
Modal Analysis
Page B-1
Appendix B – Modal Analysis B.2.
Modal Analysis for Case 3 – M50I:
Fig. (B.6) - The First Mode Shape for Case M50I
Fig. (B.7) - The Second Mode Shape for Case M50I
Fig. (B.8) - The Third Mode Shape for Case M50I
Fig. (B.9) - The Fourth Mode Shape for Case M50I
Fig. (B.10) - The Fifth Mode Shape for Case M50I
Modal Analysis
Page B-2
Appendix B – Modal Analysis B.3.
Modal Analysis for Case 4 – M50HI:
Fig. (B.11) - The First Mode Shape for Case M50HI
Fig. (B.12) - The Second Mode Shape for Case M50HI
Fig. (B.13) - The Third Mode Shape for Case M50HI
Fig. (B.14) - The Fourth Mode Shape for Case M50HI
Fig. (B15) - The Fifth Mode Shape for Case M50HI Modal Analysis
Page B-3
Appendix B – Modal Analysis B.4.
Time Step, ∆t:
The time step used for Transient analysis was calculated through the natural frequency as follows [97]: t
1
…… (B-1)
N n max
Where: ∆t is the time step, in seconds. N is the maximum number of divisions per structure. ωn-max is the maximum natural frequency. Table (A-1) - The Results of Modal Analysis No.
Modal Analysis
Case Studied
1.
M-0-W
2.
M-50-H
3.
M-50-I
4.
M-50-HI
Natural Frequency 2.355 4.865 8.393 9.091 9.129 2.355 4.867 8.408 9.092 9.132 2.359 4.867 8.393 9.091 9.135 2.359 4.869 8.408 9.092 9.138
Δt
1 N ωn - max
(Sec) 0.0039122
0.0039109
0.0039096
0.0039083
Page B-4
Appendix C
Product Data Sheet Edition 24/08/2009 Revision no: 1 Identification no: 01 04 01 02 001 0 000011 ® SikaWrap -300 C/60
C. Properties of the Strengthening Materials Used
C.1 SikaWrap ®-300 C/60
Construction
Woven carbon fiber fabric for structural strengthening ®
Product Description
SikaWrap -300 C/60 is a unidirectional woven carbon fiber fabric for the dry or wet application process.
Uses
Strengthening of reinforced concrete structures, brickwork and timber in case of flexural and shear load due to: n Increase of loading capacity n Changes of building utilisation n Repair of defects n Prevention of defects caused by earthquakes n Meeting of changed standards or specifications
Characteristics / Advantages
n Equipped with weft fibers that keep the fabric stable (heat-set process) n Multifunctional use for every kind of reinforcement n Flexibility of surface geometry (Beams, columns, chimneys, piles, walls)
Product Data Form Fiber Type
Mid strength carbon fibers.
Fabric Construction
Fiber orientation: 0° (unidirectional). Warp: black carbon fibers (99% of total areal weight). Weft:
white thermoplastic heat-set fibers (1% of total areal weight).
Packaging
1 roll in cardboard box
Fabric length / roll
Fabric width
≥ 50 m
300 / 600 mm
Storage Storage Conditions / Shelf Life
24 months from date of production if stored properly in undamaged original sealed packaging in dry conditions at temperatures between +5°C and +35°C. Protect from direct sunlight.
C-1
®
SikaWrap -300 C/60
Technical Data 2
2
Areal Weight
300 g/m + 15 g/m
Fabric Design Thickness
0.166 mm (based on fiber content).
Fiber Density
1.79 g/cm
3
Mechanical / Physical Properties Dry Fiber Properties
Tensile strength: 2 3’900 N/mm (nominal). Tensile E-modulus: 2 230'000 N/mm Elongation at break: 1.5% (nominal).
Laminate Properties
®
With Sikadur -330 Laminate thickness: 1.0 mm per layer.
Silinmiş: 3
Ultimate load: 420 kN/m width per layer
Silinmiş: 480
Tensile E-modulus: 2 33.0 kN/mm (based on typical laminate thickness of 1.0 mm).
Silinmiş: (at typical laminate thickness of 1.3 mm). Silinmiş: 30
Note: The above values are typical and indicative only. The achievable laminate properties obtained from tensile test are dependant on the impregnating/laminating resin used and the type of tensile testing procedure. Apply material reduction factors according to the relevant design standard. Design
Design strain: Max. 0.6% (this value is dependent on the type of loading and must be adapted according to the relevant local design standards)
Silinmiş: 3
Silinmiş: 75
Tensile strength: (theoretical tensile strength for the design): -
at elongation 0.4%: 132 kN/m width (= 40 kN / 30 cm) (= 80 kN / 60cm)
-
at elongation 0.6%: 200 kN/m width (= 60 kN / 30 cm) (= 120 kN / 60 cm)
Silinmiş: 135
System Information System Structure
The system configuration as described must be fully complied with and may not be changed. ®
®
®
Concrete primer - Sikadur -330 or Sikadur -300 with Sikadur -513 ®
®
Impregnating / laminating resin - Sikadur -330 or Sikadur -300. ®
Structural strengthening fabric - SikaWrap -300 C/60. For detailed resin properties, fabric application details and general information, refer ® ® to Sikadur -330 or Sikadur -300 Product Data Sheet.
C-2
®
SikaWrap -300 C/60
Application Details Consumption
Dry Application: -
2
®
Impregnating of the first layer incl. primer: ~ 1.0 - 1.5 kg/m (Sikadur -330). 2
®
Impregnating of the following layers: ~ 0.8 kg/m (Sikadur -330).
Wet Application: Primer on prepared substrate (depending on the roughness): -
2
®
®
Smooth surface: ~ 0.5 kg/m (Sikadur -300 or Sikadur -330). 2
®
®
Rough surface: ~ 0.5 - 1.0 kg/m (Sikadur -330 or Sikadur -300 mixed with ® max. 5% thixotropic agent Sikadur -513).
Impregnation resin for every layer (manually or with saturator): -
2
®
~ 0.7 kg/m (Sikadur -300).
Substrate Quality
Specific requirements: 2 Minimal substrate tensile strength: 1.0 N/mm
Substrate Preparation
Concrete and masonry: Substrates must be sound, dry, clean and free from laitance, ice, standing water, grease, oils, old surface treatments or coatings and any loosely adhering particles. Concrete must be cleaned and prepared to achieve a laitance and contaminant free, open textured surface. Repairs and levelling: If carbonised or weak concrete cover has to be removed or levelling of uneven surfaces is needed, the following systems can be applied: (Details on application and limitation see the relevant Product Data Sheets) Biçimlendirilmiş: Madde İşaretleri ve Numaralandırma
•
Protection of corroded rebars: SikaTop® Armatec® 110 EpoCem®
•
Structural repair materials: Sikadur -41 epoxy repair mortar, Sikadur -30 ® ® adhesive or cementitious Sika MonoTop -412 (horizontal, vertical, ® ® overhead) or Sika MonoTop -438 (horizontal, top-side) range.
®
®
Application Instructions Application Method / Tools
The fabric can be cut with special scissors or razor knife. Never fold the fabric!
Notes on Application / Limitations
This product may only be used by experienced professionals.
®
®
Refer to Sikadur -330 or Sikadur -300 Product Data Sheet for impregnating / laminating procedure.
Minimum radius required for application around corners: > 10 mm. ® Grinding edges or building up with Sikadur mortars may be necessary. In fiber direction, overlapping of the fabric must be at least 100 mm depending on ® SikaWrap type or as specified in the strengthening design. For side-by-side application, no overlapping length in the weft direction is required. Overlaps of additional layers must be distributed over the column circumference. The strengthening application is inherently structural and great care must be taken when choosing suitably experienced contractors. ®
The SikaWrap -300 C/60 fabric is coated to ensure maximum bond and durability ® with the Sikadur impregnating/laminating resins. To maintain system compatibility do not interchange system parts. ®
The SikaWrap -300 C/60 may be / must be coated with a cementitious overlay or coatings for aesthetic and / or protective purposes. Selection will be dependent on ® exposure requirements. For basic UV protection use Sikagard -550 W Elastic, ® ® Sikagard ElastoColor-675 W or Sikagard -680 S.
Value Base
All technical data stated in this Product Data Sheet are based on laboratory tests. Actual measured data may vary due to circumstances beyond our control.
C-3
®
SikaWrap -300 C/60
Construction
Local Restrictions
Please note that as a result of specific local regulations the performance of this product may vary from country to country. Please consult the local Product Data Sheet for the exact description of the application fields.
Health and Safety Information
For information and advice on the safe handling, storage and disposal of chemical products, users shall refer to the most recent Material Safety Data Sheet containing physical, ecological, toxicological and other safety-related data.
Legal Notes
The information, and, in particular, the recommendations relating to the application and end-use of Sika products, are given in good faith based on Sika's current knowledge and experience of the products when properly stored, handled and applied under normal conditions in accordance with Sika’s recommendations. In practice, the differences in materials, substrates and actual site conditions are such that no warranty in respect of merchantability or of fitness for a particular purpose, nor any liability arising out of any legal relationship whatsoever, can be inferred either from this information, or from any written recommendations, or from any other advice offered. The user of the product must test the product’s suitability for the intended application and purpose. Sika reserves the right to change the properties of its products. The proprietary rights of third parties must be observed. All orders are accepted subject to our current terms of sale and delivery. Users must always refer to the most recent issue of the local Product Data Sheet for the product concerned, copies of which will be supplied on request.
Sika Yapı Kimyasalları A.Ş. Deri Org. San. Böl. 2. Yol J–7 Parsel, Aydınlı, Orhanlı Mevkii, 34957 Tuzla, İstanbul, Türkiye
Çağrı Merkezi Telefon Faks
[email protected]
+90 216 444 74 52 +90 216 581 06 00 +90 216 581 06 99 www.sika.com.tr
C-4
®
SikaWrap -300 C/60
Product Data Sheet Edition 31/12/2008 Identification no: 01 04 01 04 001 0 000004 Sikadur®-330
C.2 Sikadur®-330
Construction
2-part epoxy impregnation resin Product Description
Sikadur®-330 is a two part, solvent free, thixotropic epoxy based impregnating resin / adhesive.
Uses
n
Characteristics / Advantages
n n
Impregnation resin for SikaWrap® fabric reinforcement for the dry application method Primer resin for the wet application system Structural adhesive for bonding Sika® CarboDur® plates to even surfaces
n n n n n n n
Easy mix and application by trowel and impregnation roller Manufactured for manual saturation methods Excellent application behaviour to vertical and overhead surfaces Good adhesion to many substrates High mechanical properties No separate primer required Solvent free
Tests Approval / Standards
Conforms to the requirements of: -
SOCOTEC (France): Cahier des charges Sika® CarboDur, SikaWrap®.
-
Road and Bridges Research Institute (Poland): IBDiM No AT/2003-04-336.
Product Data Form Appearance / Colours
Packaging
Resin part. A: Hardener part B:
paste paste
Colour: Part A: Part B: Part A+B mixed:
white grey light grey
Standard: 5 kg (A+B) pre-dosed units Industrial: Part A: 24 kg pails Part B: 6 kg pails
Storage Storage Conditions / Shelf life
24 months from date of production if stored properly in original unopened, sealed and undamaged packaging in dry conditions at temperatures between +5°C and +25°C. Protect from direct sunlight.
C-5
Sikadur®-330
Technical Data Chemical Base
Epoxy resin.
Density
1.30 kg/l + 0.1 kg/l (parts A+B mixed) (at +23°C)
Viscosity
Shear rate: 50 /s Temperature
Viscosity
+10°C
~ 10'000 mPas
+23°C
~ 6'000 mPas
+35°C
~ 5'000 mPas
Thermal Expansion Coefficient
4.5 x 10-5 per °C (-10°C to +40°C)
Thermal Stability
Heat Distortion Temperature (HDT) Curing
Temperature
HDT
7 days
+10°C
+36°C
7 days
+23°C
+47°C
7 days
+35°C
+53°C
-
+43°C
7 days, +10°C plus 7 days, +23°C
Service Temperature
(ASTM D648)
-40°C to +45°C
Mechanical / Physical Properties Tensile Strength
30 N/mm2 (7 days at +23°C)
(DIN 53455) 2
Bond Strength
Concrete fracture (> 4 N/mm ) on sandblasted substrate: > 1 day
(EN 24624)
E-Modulus
Flexural: 3800 N/mm2 (7 days at +23°C)
(DIN 53452)
Tensile: 4500 N/mm2 (7 days at +23°C)
(DIN 53455)
Elongation at Break
0.9% (7 days at +23°C)
(DIN 53455)
Resistance Chemical Resistance
The product is not suitable for chemical exposure.
Thermal Resistance
Continuous exposure +45°C.
System Information System Structure
Substrate primer - Sikadur®-330. Impregnating / laminating resin - Sikadur®-330. Structural strengthening fabric - SikaWrap® type to suit requirements.
Application Details Consumption
This will be dependant on the roughness of the substrate and the type of SikaWrap® fabric to be impregnated. See respective SikaWrap® fabric Product Data Sheet. Guide: 0.7 - 1.5 kg/m2
C-6
Sikadur®-330
Substrate Quality
The substrate must be sound and of sufficient tensile strength to provide a minimum pull off strength of 1.0 N/mm2 or as per the requirements of the design specification. The surface must be dry and free of all contaminants such as oil, grease, coatings and surface treatments etc. The surface to be bonded must be level (max. deviation 2 mm per 0.3 m length), with steps and formwork marks not greater than 0.5 mm. High spots can be removed by abrasive blasting or grinding. Wrapped corners must be rounded to a minimum radius of 20 mm (depending on the SikaWrap® fabric type) or as per the design specification. This can be achieved by grinding edges or by building up with Sikadur® mortars.
Substrate Preparation
Concrete and masonry substrates must be prepared mechanically using abrasive blast cleaning or grinding equipment, to remove cement laitance, loose and friable material to achieve a profiled open textured surface. Timber substrates must be planed or sanded. All dust, loose and friable material must be completely removed from all surfaces before application of the Sikadur®-330 preferably by brush and industrial vacuum cleaner. Weak concrete/masonry must be removed and surface defects such as honeycombed areas, blowholes and voids must be fully exposed. Repairs to substrate, filling of blowholes/voids and surface levelling must be carried out using Sikadur®-41 or a mixture of Sikadur®-30 and Sikadur®-501 quartz sand (mix ratio 1 : 1 max parts by weight). Bond tests must be carried out to ensure substrate preparation is adequate. Inject cracks wider than 0.25 mm with Sikadur®-52 or other suitable Sikadur® injection resin.
Application Conditions / Limitations Substrate Temperature
+10°C min. / +35°C max.
Ambient Temperature
+10°C min. / +35°C max.
Substrate Moisture Content
< 4% pbw. Test method: Sika-Tramex meter.
Dew Point
Beware of condensation! Substrate temperature during application must be at least 3°C above dew point.
Application Instructions Mixing
Part A : part B = 4 : 1 by weight When using bulk material the exact mixing ratio must be safeguarded by accurately weighing and dosing each component.
Mixing Time
Pre-batched units: Mix parts A+B together for at least 3 minutes with a mixing spindle attached to a slow speed electric drill (max. 600 rpm) until the material becomes smooth in consistency and a uniform grey colour. Avoid aeration while mixing. Then, pour the whole mix into a clean container and stir again for approx. 1 more minute at low speed to keep air entrapment at a minimum. Mix only that quantity which can be used within its potlife. Bulk packing, not pre-batched: First, stir each part thoroughly. Add the parts in the correct proportions into a suitable mixing pail and stir correctly using an electric low speed mixer as above for pre-batched units.
C-7
Sikadur®-330
Application Method / Tools
Preparation: Prior to application confirm substrate moisture content, relative humidity and dew point. Cut the specified SikaWrap® fabric to the desired dimensions.
Resin Application: Apply the Sikadur®-330 to the prepared substrate using a trowel, roller or brush.
Fabric Placement and Laminating: Place the SikaWrap® fabric in the required direction onto the Sikadur®-330. Carefully work the fabric into the resin with the Sika plastic impregnation roller parallel to the fiber direction until the resin is squeezed out between and through the fiber strands and distributed evenly over the whole fabric surface. Avoid excessive force when laminating to prevent folding or creasing of the SikaWrap® fabric.
Additional Fabric Layers: For additional layers of SikaWrap® fabric, apply Sikadur®-330 to previous applied layer wet on wet within 60 minutes (at +23°C) after application of the previous layer and repeat laminating procedure. If it is not possible to apply within 60 minutes, a waiting time of at least 12 hours must be observed before application of next layer.
Overlays: If a cementitious overlay is to be applied over SikaWrap® fabric an additional Sikadur-330 resin layer must be applied over final layer at a max. 0.5 kg/m2. Broadcast with quartz sand while wet which will serve as a key for the overlay. If a coloured coating is to be applied the wet Sikadur®-330 surface can be smoothed with a brush. Overlaps Fiber Direction: Overlapping of the SikaWrap® fabric must be at least 100 mm (depending on the SikaWrap® fabric type) or as specified in the strengthening design. Side by Side:
Cleaning of Tools
-
Unidirectional fabrics: when placing several unidirectional SikaWrap® fabrics side by side no overlapping is required unless specified in the strengthening design.
-
Multi-directional fabrics: overlapping in the weft direction must be at least 100 mm (depending on the SikaWrap fabric type) or as specified in the strengthening design.
Clean all equipment immediately with Sika® Colma Cleaner. Cured material can only be mechanically removed.
C-8
Sikadur®-330
Potlife
Potlife: Temperature
Time
+10°C
90 minutes (5 kg)
+35°C
30 minutes (5 kg)
Potlife starts with the mixing of both parts (resin and hardener). At low ambient temperature pot life will be extended, at elevated temperatures this will be reduced. The higher the quantity of material mixed, the shorter the potlife. To achieve a longer potlife at high temperatures the mixed material may be divided into smaller units or both parts may be cooled before mixing. Open time:
Waiting Time / Overcoating
Temperature
Time
+10°C
60 minutes
+35°C
30 minutes
To (pre-) cured resin: Products
Substrate temperature
Minimum
Maximum
+10°C
24 hours
+23°C
12 hours
+35°C
6 hours
Cured resin older than 7 days has to be ® degreased with Sika Colma Cleaner and gently grinded with a sandpaper before coating.
Substrate temperature
Minimum
+10°C
5 days
+23°C
3 days
+35°C
1 day
®
Sikadur -330 ®
Sikadur -330
Products ®
Sikadur -330 ®
Sikagard -coloured coatings
Maximum Cured resin older than 7 days has to be ® degreased with Sika Colma Cleaner and gently grinded with a sandpaper before coating.
Times are approximate and will be affected by changing ambient conditions.
C-9
Sikadur®-330
Construction
Notes on Application / Limitations
This product may only be used by experienced professionals. The Sikadur®-330 must be protected from rain for at least 24 hours after application. Ensure placement of fabric and laminating with roller takes place within open time. The SikaWrap® fabric must be coated with a cementitious overlay or coating for aesthetic and/or protective purposes. Selection will be dependent on exposure requirements. For basic UV protection use Sikagard®-550W Elastic, Sikagard® ElastoColor-675W or Sikagard®-680S. At low temperatures and / or high relative humidity, a tacky residue (blush) may form on the surface of the cured Sikadur-330 epoxy. If an additional layer of fabric, or a coating is to be applied onto the cured epoxy, this residue must first be removed to ensure adequate bond. The residue can be removed with water. In both cases, the surface must be wiped dry prior to application of the next layer or coating. For application in cold or hot conditions, pre-condition material for 24 hours in temperature controlled storage facilities to improve mixing, application and pot life limits. The number of additional fabric layers applied wet on wet must be closely controlled to avoid creeping, creasing or slippage of the fabric during curing of the Sikadur®-330. The number of layers will be dependent on the type of SikaWrap® fabric used and the ambient climate conditions.
Curing Details Applied Product ready for use
Temperature
Full cure
+10°C
7 days
+23°C
5 days
+35°C
2 days
All cure times are approximate and will be affected by changing ambient conditions.
C-10
Sikadur®-330
Value Base
All technical data stated in this Product Data Sheet are based on laboratory tests. Actual measured data may vary due to circumstances beyond our control.
Local Restrictions
Please note that as a result of specific local regulations the performance of this product may vary from country to country. Please consult the local Product Data Sheet for the exact description of the application fields.
Health and Safety Information
For information and advice on the safe handling, storage and disposal of chemical products, users shall refer to the most recent Material Safety Data Sheet containing physical, ecological, toxicological and other safety-related data.
Legal Notes
The information, and, in particular, the recommendations relating to the application and end-use of Sika products, are given in good faith based on Sika's current knowledge and experience of the products when properly stored, handled and applied under normal conditions in accordance with Sika’s recommendations. In practice, the differences in materials, substrates and actual site conditions are such that no warranty in respect of merchantability or of fitness for a particular purpose, nor any liability arising out of any legal relationship whatsoever, can be inferred either from this information, or from any written recommendations, or from any other advice offered. The user of the product must test the product’s suitability for the intended application and purpose. Sika reserves the right to change the properties of its products. The proprietary rights of third parties must be observed. All orders are accepted subject to our current terms of sale and delivery. Users must always refer to the most recent issue of the local Product Data Sheet for the product concerned, copies of which will be supplied on request.
Sika Yapı Kimyasalları A.Ş. Deri Org. San. Böl. 2. Yol J–7 Parsel, Aydınlı, Orhanlı Mevkii, 34957 Tuzla, İstanbul, Türkiye
Çağrı Merkezi Telefon Faks
[email protected]
layla2016 +90 216 581 06 00 +90 216 581 06 99 www.sika.com.tr
C-11
Sikadur®-330
الخالصة انذساساخ انساتقح انرٍ ذُاوند يىضىع انكرائف انخشساَُح انًسهسح سكضخ ػهً اَىاع انرسًُم انسراذُكٍ ،انقهُم يُها ذُاول انًُشآخ انًؼشضح الزًال يركشسج والَىخذ اٌ تسىز زىل انكرائف انخشساَُح انًسهسح وانًقىاج تاٌ َىع يٍ يىاد انرقىَح يثم انُاف انكاستىٌ انًسهسح . انرقذو فٍ اسرخذاو يىاد انرقىَح انًشكثح يثم انُاف انكاستىٌ انًسهسح ،نرقىَح انًُشآخ انقائًح ايا تسثة ذغُُش فٍ انرصايُى ،صَادج فٍ انرسًُم او تسثة انشغثح فٍ ذشيُى انرذهىس انزٌ زذز ػهً يذي سُىاخ يٍ االسرخذاو ،كاٌ ازذ االسثاب انرٍ ادخ انً هزا انؼًم انثسثٍ .انثسس انسانٍ شًم يشزهرٍُ ػًهُح وذسهُهُح .انهذف يٍ انثسس كاٌ نهرسقق يٍ فؼانُح اسرخذاو انُاف انكاستىٌ انًسهسح نضَادج قاتهُح ذسًم انكرائف انخشساَُح انًؼشضح انً االزًال انًركشسج . انًشزهح انؼًهُح يٍ انثسس شًهد صة ًَ 02ىرج يٍ انكرائف انًصُىػح يٍ انخشساَح انًسهسح االػرُادَح وانرٍ نها َفس االتؼاد وَفس ذسهُر االَثُاء وَفس ذسهُر انقص وانرٍ ذى ذقىَح تؼضها خاسخُا تششائط انُاف انكاستىٌ .ذى ذقسُى انكرائف انً يدًىػرٍُ اػرًادا ػهً َىع انرسًُم انًسهط .انًدًىػح االونً شًهد 6يٍ انكرائف انخشساَُح انًؼشضح نالزًال انسراذُكُح وانًدًىػح انثاَُح شًهد 41يٍ انكرائف انخشساَُح انًؼشضح نالزًال انًركشسج .انًرغُشاخ انرٍ ذًد دساسرها شًهد ػشض واذداِ ششائط انُاف انكاستىٌ وانًخطط انضيٍُ نُظاو انرسًُم انًركشس انًسرخذو . تًُُا شًهد انًشزهح انرسهُهُح اسرخذاو تشَايح اَسُس 41-نًساكاج سهىك 42يٍ انكرائف انخشساَُح وانًؼشضح نُىػٍُ يٍ اَظًح انرسًُم انسراذُكٍ وانًركشس وانرسقق يٍ اٌ انًُارج انًخراسج كاَد كافُح نهسصىل ػهً َفس ذصشف انًُارج انًفسىصح ػًهُا. اظهشخ َرائح انًشزهرٍُ انؼًهُح وانرسهُهُح اٌ انرقىَح انخاسخُح تانُاف انكاستىٌ انًسهسح قذ زسُد قاتهُح ذسًم انكرائف انخشساَُح ،واٌ هزا انرسسٍُ تانُسثح نهكرائف انًقىاج تششائط تؼشض 12يهى وانًؼشضح نالزًال انسراذُكُح كاٌ %41 ، %44و %02نهرقىَح االفقُح ،انًائهح وانًخرهطح ػهً انرىانٍ .تًُُا نهكرائف انًؼشضح نالزًال انًركشسج فاٌ انرسسٍ تقاتهُح انرسًم كاٌ %44نثالز دوساخ %41 ،نثالز دوساخ و %04نثالز دوساخ نكم يٍ اَىاع انرقىَح االفقُح ،انًائهح وانًخرهطح ػهً انرىانٍ. تانُسثح نهًُارج انًؼشضح نالزًال انًركشسج فقذ ذى ذسدُم صَادج فٍ انقىج يغ اصدَاد ػشض ششائط انرقىَح يٍ 12يهى انً 412يهى ،واٌ هزِ انضَادج ذشاوزد تٍُ %44انً %01نهرقىَح تاالذداِ االفقٍ %41 ،انً %01نهرقىَح تاالذداِ انًائم و %04انً %02نهرقىَح تاالذداِ انًخرهط. ذى اسرخذاو تشَايح اَسُس 41-نرًثُم آنُح انفشم نهكرائف انخشساَُح انًسهسح وانًقىاج تششائط انُاف انكاستىٌ انًسهسح ،اٌ َرائ ح يساكاج انرصشف نهزِ انكرائف وذسد اَظًح االزًال انسراذُكُح وانًركشسج كاَد يرىافقح يغ انُرائح انؼًهُح واٌ َسثح االخرالف ذرشاوذ تٍُ %4انً %41نالزًال انقصىي وتٍُ %4انً %46نههطىل االقصً .
جمهورية العراق
وزارة التعليم العالي والبحث العلمي
الجامعة التكنولوجية
قسم هندسة البناء واالنشاءات
تصرف الكتائف الخرسانية االعتيادية المسلحة والمقواة بشرائط الياف الكاربون تحت لالحمال الستاتيكية و المتكررة اطروحة مقدمة الى قسم هندسة البناء واالنشاءات في الجامعة التكنولوجية كجزء من متطلبات نيل شهادة دكتوراه ف لسفة في الهندسة اإلنشائية من قبل
ليلى علي غالب ياسين بكلوريوس هندسة مدنية-1891-جامعة بغداد ماجستير هندسة إنشائية-2001-الجامعة التكنولوجية باشراف
أ.م .د .اياد كاظم صيهود بغداد
و
أ.م.د .قيس عبد المجيد حسن كانون أول 2011 /م
