@prefix vivo: . @prefix edm: . @prefix ns0: . @prefix dcterms: . @prefix dc: . @prefix skos: . vivo:departmentOrSchool "Applied Science, Faculty of"@en, "Civil Engineering, Department of"@en ; edm:dataProvider "DSpace"@en ; ns0:degreeCampus "UBCV"@en ; dcterms:creator "Yan, Cheng"@en ; dcterms:issued "2008-09-16T21:20:42Z"@en, "1992"@en ; vivo:relatedDegree "Doctor of Philosophy - PhD"@en ; ns0:degreeGrantor "University of British Columbia"@en ; dcterms:description """The bond between reinforcing bars and concrete under impact loading was studied for plain, polypropylene fibre reinforced, and steel fibre reinforced concretes. The experimental program included setting up an impact test system, in which an impact load with considerable energy could be generated, and in which the applied loads, accelerations and the strains along the reinforcing bar could be recorded at a rate of 200 microseconds per data point. The experiments consisted of both pull-out tests and push-in tests. For both types of tests the experimental work was carried out for three different types of loading: static, dynamic and impact loading, which covered a stress (bond stress) rate ranging from 0.5 • 10' to 0.5 • 10-2 MPa/s. The other important variables considered in the experimental study were: two different types of reinforcing bars (smooth and de-formed), two different concrete compressive strengths (normal and high), two different fibres (polypropylene and steel), different fibre contents (0.1 %, 0.5% and 1.0% by volume) and surface conditions (epoxy coated and uncoated). All of the test data were processed by computer, and the output included the stress distributions in both the steel and the concrete, the bond stresses and slips, the bond stress-slip relationships, and the fracture energy in bond failure. The energy balance at different stages in the bond process was examined. The internal crack development was also investigated. It was found that for smooth rebars, there existed a linear bond stress-slip relationship under both static and high rate loading. Different loading rates, compressive strengths, types of fibres, and fibre contents were found to have no great influence on this relationship and the stresses in both the steel bar and the concrete. For deformed rebars, the shear mechanism due to the ribs bearing on the concrete was found to play a major role in the bond resistance. The bond stress-slip relationship under a dynamic (high rate) loading changes with time and is different at different points along the reinforcing bar. In terms of the average bond stress-slip relationship over the time period and the embedded length, different loading rates, compressive strengths, types of fibres, and fibre contents were found to have a great influence on this relationship. Higher loading rates, higher compressive strengths of concrete, and steel fibres at a sufficient content all significantly increased the bond resistance capacity and the fracture energy in bond failure. All of these factors had a great influence on the stress distributions in the concrete, the slips at the interface between the rebar and the concrete, and the crack development. It was also found that there is always higher bond resistance for push-in loading than for pull-out loading. The bond resistance and the fracture energy in bond failure decreased when the rebar was epoxy coated. This influence of epoxy coating on the bond strength for push-in loading was much more significant than for pull-out loading. However, high rate loading, high concrete strength, and the steel fibre additions effectively reduced the above negative effects. The addition of polypropylene fibres was found to have very little effect on the bond behaviour, in terms of the bond strength, the stress distributions both in the rebar and the concrete, the crack development, the slips, the bond stress-slip relationship, and the fracture energy in the bond failure. In the analytical study, finite element analysis with fracture mechanics was carried out to investigate the bond phenomenon under high rate loading. The analytical method took into account all of the important variables in the bond-slip process. In this approach the chemical adhesion and frictional resistance between rebar and concrete were considered only during early loading in the elastic stage. After that only the rib bearing mechanism was taken into account. The fiber concrete composite and the high strength concrete were appropriately modelled. In the finite element analysis quadratic solid isoparametric elements with 20 nodes and 60 degrees of freedom were employed for the rebar and the concrete before cracking. After cracking the concrete elements were replaced by quadratic singularity elements, which were quarter-point elements able to model curved crack fronts. A special interface element, the 'bond-link element', was adopted to model the connection between the reinforcing bar and concrete. It connected two nodes and had no physical thickness at all, and so could be thought of conceptually as consisting of two orthogonal springs, which simulated the mechanical properties in the connection, i.e. they transmitted the shear and normal forces between two nodes. A new approach was proposed in this study for the establishment of the stiffness matrix of the 'bond-link element'. Then a bond stress-slip relationship at the interface between the rebar and the concrete would be one of the output results of the finite element analysis, rather than an input parameter required before the analysis could proceed. The dynamic constitutive laws of both steel and concrete, the criteria for crack formation and propagation in concrete based on the energy release rate theorem for mixed mode fracture, and the criterion for concrete crushing were used in the finite element process. It was an iterative program with rapid convergence. Not only could the bond stress and crack distribution be found through the analysis, but also a bond stress-slip relationship under high rate loading could be established analytically. The results obtained from the finite element analysis were compared with those from the experimental method, and reasonably good correspondence was found."""@en ; edm:aggregatedCHO "https://circle.library.ubc.ca/rest/handle/2429/2097?expand=metadata"@en ; dcterms:extent "17208230 bytes"@en ; dc:format "application/pdf"@en ; skos:note "BOND BETWEEN REINFORCING BARS AND CONCRETE UNDERIMPACT LOADINGByCheng YanB. A.Sc. (Structure) Hehai University, ChinaM. A.Sc. (Structure) Public Work Research Institute, JapanA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESCIVIL ENGINEERINGWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAOctober 1992© Cheng Yan 1992(Signature)In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.Department of a/141A-The University of British ColumbiaVancouver, CanadaDate of-g—e—e- •^3 . i ,9 9 2DE-6 (2/88)AbstractThe bond between reinforcing bars and concrete under impact loading was studied forplain, polypropylene fibre reinforced, and steel fibre reinforced concretes. The experi-mental program included setting up an impact test system, in which an impact load withconsiderable energy could be generated, and in which the applied loads, accelerationsand the strains along the reinforcing bar could be recorded at a rate of 200 microsecondsper data point. The experiments consisted of both pull-out tests and push-in tests. Forboth types of tests the experimental work was carried out for three different types ofloading: static, dynamic and impact loading, which covered a stress (bond stress) rateranging from 0.5 • 10' to 0.5 • 10 -2 MPa/s. The other important variables consideredin the experimental study were: two different types of reinforcing bars (smooth and de-formed), two different concrete compressive strengths (normal and high), two differentfibres (polypropylene and steel), different fibre contents (0.1 %, 0.5% and 1.0% by vol-ume) and surface conditions (epoxy coated and uncoated). All of the test data wereprocessed by computer, and the output included the stress distributions in both the steeland the concrete, the bond stresses and slips, the bond stress-slip relationships, andthe fracture energy in bond failure. The energy balance at different stages in the bondprocess was examined. The internal crack development was also investigated.It was found that for smooth rebars, there existed a linear bond stress-slip rela-tionship under both static and high rate loading. Different loading rates, compressivestrengths, types of fibres, and fibre contents were found to have no great influence oniithis relationship and the stresses in both the steel bar and the concrete.For deformed rebars, the shear mechanism due to the ribs bearing on the concrete wasfound to play a major role in the bond resistance. The bond stress-slip relationship undera dynamic (high rate) loading changes with time and is different at different points alongthe reinforcing bar. In terms of the average bond stress-slip relationship over the timeperiod and the embedded length, different loading rates, compressive strengths, types offibres, and fibre contents were found to have a great influence on this relationship. Higherloading rates, higher compressive strengths of concrete, and steel fibres at a sufficientcontent all significantly increased the bond resistance capacity and the fracture energyin bond failure. All of these factors had a great influence on the stress distributions inthe concrete, the slips at the interface between the rebar and the concrete, and the crackdevelopment.It was also found that there is always higher bond resistance for push-in loading thanfor pull-out loading.The bond resistance and the fracture energy in bond failure decreased when the rebarwas epoxy coated. This influence of epoxy coating on the bond strength for push-inloading was much more significant than for pull-out loading. However, high rate loading,high concrete strength, and the steel fibre additions effectively reduced the above negativeeffects.The addition of polypropylene fibres was found to have very little effect on the bondbehaviour, in terms of the bond strength, the stress distributions both in the rebar andthe concrete, the crack development, the slips, the bond stress-slip relationship, and thefracture energy in the bond failure.iiiIn the analytical study, finite element analysis with fracture mechanics was carried outto investigate the bond phenomenon under high rate loading. The analytical method tookinto account all of the important variables in the bond-slip process. In this approach thechemical adhesion and frictional resistance between rebar and concrete were consideredonly during early loading in the elastic stage. After that only the rib bearing mechanismwas taken into account. The fiber concrete composite and the high strength concretewere appropriately modelled. In the finite element analysis quadratic solid isoparametricelements with 20 nodes and 60 degrees of freedom were employed for the rebar andthe concrete before cracking. After cracking the concrete elements were replaced byquadratic singularity elements, which were quarter-point elements able to model curvedcrack fronts. A special interface element, the 'bond-link element', was adopted to modelthe connection between the reinforcing bar and concrete. It connected two nodes andhad no physical thickness at all, and so could be thought of conceptually as consistingof two orthogonal springs, which simulated the mechanical properties in the connection,i.e. they transmitted the shear and normal forces between two nodes. A new approachwas proposed in this study for the establishment of the stiffness matrix of the 'bond-linkelement'. Then a bond stress-slip relationship at the interface between the rebar and theconcrete would be one of the output results of the finite element analysis, rather than aninput parameter required before the analysis could proceed.The dynamic constitutive laws of both steel and concrete, the criteria for crack for-mation and propagation in concrete based on the energy release rate theorem for mixedmode fracture, and the criterion for concrete crushing were used in the finite elementprocess. It was an iterative program with rapid convergence. Not only could the bondstress and crack distribution be found through the analysis, but also a bond stress-slipivrelationship under high rate loading could be established analytically. The results ob-tained from the finite element analysis were compared with those from the experimentalmethod, and reasonably good correspondence was found.VTO MY SISTERviTable of ContentsAbstract^ iiList of Tables^ xvList of Figures^ xviiiList of Notations^ xxixAcknowledgement^ xxxviii1^Objectives and Scope2^Literature Survey162.1 Bond Behaviour under Static Loading ^ 62.1.1 Introduction ^ 62.1.2 Flexural Bond under Static Loading ^ 92.1.2.1^Experimental Investigation 92.1.2.2^Summary ^ 222.1.3 Anchorage Bond Under Static Loading ^ 252.1.3.1^Experimental Investigation 252.1.3.2^Summary ^ 322.1.4 Bond Tests with Fiber Reinforced Concrete or Coated Rebars^. .^322.2 Bond Behaviour under Dynamic Loading ^ 352.2.1 Bond Behaviour Under Cyclic Loading 35vii2.2.2 Bond Behaviour Under Impact Loading ^ 392.2.3 Summary ^ 472.3 Analytical Investigation of Bond Behaviour ^482.3.1^Introduction ^482.3.2 Theoretical Work ^492.3.3 Fracture Mechanics and the Finite Element Method ^512.3.4 Summary ^ 602.4 Conclusions ^613 Experimental Procedures^ 643.1 Introduction ^643.2 Specimen Preparation ^653.2.1^General ^653.2.2 Reinforcing Elements ^693.2.2.1 Smooth and Deformed Bars ^ 693.2.2.2 Instrumentation of Rebars ^743.2.3 Concrete Mix ^763.2.3.1 Compressive Strength and Basic Mix Design ^763.2.3.2 Added Fibers ^763.2.4 Fabrication of Test Specimens ^773.2.5 Properties of the Fresh and Harden Concrete ^793.2.6 Summary of Test Specimens^ 813.3 Test Program ^ 893.3.1 Impact Testing ^893.3.1.1^Test Set Up ^893.3.1.2 Impact Testing Machine^ 91viii3.3.1.3^Bolt Load Cell ^963.3.1.4 Accelerometer^ 1003.3.1.5 Strain Measurement ^ 1033.3.1.6 Data Acquisition System 1083.3.1.7 High Speed Video Camera ^ 1113.3.1.8^Test Procedure^ 1133.3.2 Static and Medium Rate Testing ^ 1143.3.2.1^Test Set Up ^ 1143.3.2.2 Data Acquisition and Processing ^ 1203.3.2.3 Test Procedure^ 1203.3.3 Crack Examination 1214 Analysis of Test Data^ 1234.1 General ^ 1234.2 Data Filtration ^ 1264.2.1 Fast Fourrier Transform — FFT and Inverse FFT ^ 1264.2.2 Characteristics of External and Internal Noise 1334.2.3 Base Line Setting Method^ 1354.2.4 Digital Filtering^ 1354.2.5 Filtering of Load, Acceleration and Strain Signals^1374.3 Young's Modulus and Poisson's Ratio of Concrete^ 1384.4 Contact Load, Inertial Load and Applied Load 1394.5 Acceleration, Velocity and Displacement ^ 1414.5.1 Acceleration, Velocity and Displacement of the Rebar ^ 1414.5.2 Acceleration, Velocity and Displacement of the Hammer ^ 1424.6 Elongation of the Rebar ^ 144ix4.7 Strains and Stresses in the Rebar and the Concrete ^ 1454.8 Bond Stress and Bond Slip ^ 1484.9 Rate of Loading, Strain and Stress ^ 1494.10 Work, Energy and Energy Balance 1514.10.1 Kinetic Energy, Potential Energy, and Work done by the Hammer 1514.10.2 Strain Energies and Fracture Energies^ 1554.11 Curve Fitting ^ 1564.12 Statistical Analysis 1584.13 Computer program ^ 1595 Experimental Results^ 1625.1 Introduction 1625.2 Steel Stresses ^ 1655.2.1^General 1655.2.2 Tests with Smooth Bars ^ 1665.2.3 Tests with Deformed Bars 1705.2.3.1^Effects of Loading Rate ^ 1705.2.3.2 Effects of Concrete Strength 1765.2.3.3^Effects of Fibre Additions ^ 1785.2.3.4 Differences between Pull-out and Push-in Tests ^ 1815.3 Concrete Stresses ^ 1845.3.1^General 1845.3.2 Effects of Loading Rate^ 1845.3.3 Effects of Concrete Strength 1855.3.4 Effects of Fibre Additions ^ 1855.3.5 Differences between Pull-out and Push-in Tests ^ 1895.4 Bond Stresses ^5.4.1^General 5.4.2^Tests with Smooth Bars ^5.4.3^Tests with Deformed Bars 1901901901945.4.3.1^Effects of Loading Rate ^ 1945.4.3.2^Effects of Concrete Strength 1995.4.3.3^Effects of Fibre Additions ^ 2015.4.3.4^Differences between Pull-out and Push-in Tests ^ 2015.5 Slip and Slip Distribution ^ 2065.5.1 General ^ 2065.5.2 Tests with Smooth Bars ^ 2065.5.3 Tests with Deformed Bars 2075.5.3.1^Effects of Loading Rate ^ 2075.5.3.2^Effects of Concrete Strength 2085.5.3.3^Effects of Fibre Additions ^ 2085.5.3.4^Differences between Pull-out and Push-in Tests ^ 208r).6 Internal Cracking 2135.6.1 General ^ 2135.6.2 Effects of Loading Rate and Concrete Strength ^ 2165.6.3 Effects of Fibre Additions ^ 2165.7 Bond Stress vs. Slip Relationship 2205.7.1 General ^ 2205.7.2 Smooth Bars 2215.7.3 Deformed Bars ^ 2245.7.3.1^Effects of Loading Rate ^ 2245.7.3.2^Effects of Concrete Strength 99,5xi5.8^5.7.3.3^Effects of Fibre Additions ^5.7.3.4^Differences between Pull-out and Push-in Tests ^Results of Tests with Epoxy-Coated Rebars ^22523023:35.8.1^Effect on the Bond Stress ^ 2335.8.2^Effect on the Slip ^ 2375.8.3^Effect on the Bond Stress-slip Relationship ^ 2405.8.4^Effect on the Fracture Energy ^ 2455.8.5^Conclusions ^ 2465.9 Interpretation of Tests Results and Conclusions ^ 2486 Energy Transfer and Balance 2506.1 Introduction ^ 2506.2 Energies and Work Done by the External Force ^ 2516.3 Energy Balance in the Linear Region (t ..,-- t1) 2566.3.1^Tests with Smooth Bars ^ 2576.3.2^Tests with Deformed Bars 2596.4 Energy Balance in the Non-linear Region (t = tf) ^ 2656.4.1^Tests with Smooth Bars ^ 2666.4.2^Tests with Deformed Bars 2706.5 Energy Balance over the Entire Impact Event ^ 2716.6 Energy Absorbtion and Dissipation Capacity 2787 Analytical Study 2837.1 Introduction ^ 2837.2 Finite Element Models ^ 2857.2.1^Steel Elements 2857.2.2^Concrete Elements ^ 288xii7.2.3 Interface Elements ^ 2917.3 Constitutive Laws of the Materials ^ 2947.3.1 Constitutive Law of Steel 2947.3.2 Constitutive Law of Concrete ^ 2947.4 Criteria of Cracking, Crack Propagation and Crushing in Concrete . . . ^ 2967.5 The Algorithm for the Finite Element Analysis ^ 2977.6 The Results of the Finite Element Analysis 3017.6.1 The Mechanical Parameters of the Specimens ^ 3017.6.2 The Stress Distribution and Crack Development 3077.6.3 The Bond Stress-Slip Relationship ^ 3088 Conclusions and Recommendations^ 3158.1 Conclusions ^ 3158.2 Recommendations for Further Study ^ 319Appendices^ 321A Maximum Length of Rebar at the Struck End^ 321B The Effect of Stress Wave Propagation on Outputs of Transducers 324C Design of Electric Circuit for Strain Measurement^ 327D The Effect of Inertial Force^ 331E Tests for Determining Characteristics of Signal Noise^333E.1 Noise in Acceleration and Strain Measurement^ :333E.1.1 Test Design ^ :333E.1.2 Acceleration Waves ^ :335E.1.2.1 Analytical Solution ^ :335E.1.2.2 Experimental Approach 338E.1.2.3 Characteristics of Noise in the Acceleration Measurement 340E.1.3 Stress Waves ^ 340E.2 Noise in Load Measurement ^ 342F The Solution of Three-dimensional, Axisymmetric Problems^352G The Calculation of the Hammer Rebound^ 359H Determinations of Parameters, co , fp and fr^361H.1 The Unit Chemical Adhesion Force^ 361H.2 The Frictional Factor at the Interface 3611-1.3 The Normal Stress Factor at the Interface^ 362Bibliography^ 366xivList of Tables3.1 The Maximum Embedments for Smooth Bars (Preliminary Tests) . . . . 663.2 The Maximum Embedments for Deformed Bars (Preliminary Tests) . . .^733.3 Mechanical Properties of Steel Bars ^733.4 Basic Concrete Mix Design (per m 3 ) ^783.5 Properties and Addition of Fibers ^783.6 Test Results of Fresh Concrete ^803.7 Test Results of Hardened Concrete — Part I ^823.8 Test Results of Hardened Concrete — Part II ^823.9 Loading Rate ^8:33.10 Specimens for Push-in Tests (Deformed Bars) ^843.11 Specimens for Pull-out Tests (Deformed Bars) ^853.12 Specimens for Push-in Tests (Smooth Bars) ^863.13 Specimens for Pull-out Tests (Smooth Bars) ^873.14 Specimens with Epoxy Coated Deformed Bars ^ 884.1 The Characteristics of Noise and Their Filtering (Load cell, Accelerometersand Strain Measurement)^ 1385.1 Effects of Loading Rate on the Steel Stress ^ 1725.2 Effects of Concrete Strength on the Steel Stresses ^ 1775.3 Effects of Adding Fibres on the Steel Stresses 1795.4 Effects of Pull-out and Push-in Forces on Steel Stresses ^ 1825.5 Effects of Loading Rate on the Bond Stresses^ 196xv5.6 Effects of Concrete Strength on the Bond Stresses^ 1995.7 Effects of Fibre Additions on the Bond Stresses 20:35.8 The Effects of Pull-out and Push-in Forces on the Bond Stresses ^ 2045.9 The Local Slips at the Middle of the Embedment Length ^ 2075.10 Effects of Epoxy Coating the Rebar on the Bond Stresses (Normal StrengthConcrete)^ 2355.11 Effects of Epoxy Coating the Rebar on the Bond Stresses (High StrengthConcrete) 2365.12 Effects of Epoxy Coating the Rebar on the Slip (Normal Strength Concrete)2385.13 Effects of Epoxy Coating the Rebar on the Slip (High Strength Concrete) 2:395.14 Fracture Energy in Bond Failure (for both Epoxy Coated and UncoatedBars) ^ 2476.1 Energy Balance in the Linear Portion (Smooth Bars, Normal Strength) ^ 2606.2 Energy Balance in the Linear Portion (Smooth Bars, HighStrength) ^ 2616.3 Energy Balance in the Linear Portion (Deformed Bars, Normal Strength) 2636.4 Energy Balance in the Linear Portion (Deformed Bars, High Strength) . 2646.5 Energy Balance in the Non-linear Region (Smooth Bars, Normal Strength) 2686.6 Energy Balance in the Non-linear Region (Smooth Bars, High Strength) . 2696.7 Energy Balance in the Non-linear Region (Deformed Bars, Normal Strength)2726.8 Energy Balance in the Non-linear Region (Deformed Bars, High Strength) 27:36.9 Total Energy Balance (Smooth Bar Specimens) ^ 2756.10 Total Energy Balance (Deformed Bar Specimens) 2766.11 Energy Balance right out of the Moment of Impact ^ 2776.12 Energy Balance at Bond Failure^ 278xvi6.13 Fracture Energy in Bond Failure (Smooth Bars) ^ 2816.14 Fracture Energy in Bond Failure (Deformed Bars) 2827.1^Parameters of Mechanical Properties of Interface Elements ^ '3037.2^Dynamic Critical Stress Intensity Factors for Concrete ^ 304A.1^Geometrical and Mechanical Parameters of the Rebar ^ 322F.1^Strains in the Rebar (by the Finite Element Method) ^ 355F.2^Strains in the Concrete (By the Finite Element Method) ^ 356 6xv iiList of Figures2.1 Pull-out Test on Bond Strength ^102.2 Beam Test on Bond Strength ^ 102.3 Instrumentation to Detect Internal Cracks (after Goto [30]) ^172.4 Idealization of Interaction Between Bar & Concrete (after Goto [30]) . ^ 182.5 Nilson's Bond Stress-Slip Curves (Tanner's Tests [33]) ^202.6 Unit Bond Stress versus Unit Slip Curves (after Houde [35]) ^232.7 Some Typical Anchorage Bond Test (After Vos and Reinhardt [43]) . . ^ 262.8 Three Types of Transfer Pull-out Test Specimens (after Shah et al [47]) ^ 292.9 Testing Technique for Simulating Uniform Bond Stress (after Abrishamiand Mitchell [48]) ^ 312.10 Pull-out Specimens for Impact Test (after Hjorth [76])^ 412.11 Loading Pulse of Hjorth's Impact Test [76] ^412.12 Influence of a Connective Constant Loading of 10 771,S on the Bond Resis-tance (after Hjorth [76]) ^432.13 Influence of the Loading Rate on the Bond Resistance (after Hjorth [76])^432.14 Influence of the Loading Rate on the Bond Stress-Slip Relationship (afterHjorth [76]) ^442.15 Geometry of a Typical Disc for Bond Model (after Yankelesky [90]) . . ^ 562.16 One Dimensional Element and Local Bond Stress-slip Law (after Yanke-lesky [91]) ^ 56xvii i2.17 Two Types of Interface Elements for Bond Behaviour (after Mehlhorn ct,al [92]) ^ 582.18 A 6-Noded Bond-Slip Elements (after Rots [93]) ^582.19 Constitutive Relations for Bond-slip Elements (after Rots [93]) ^592.20 Finite Element Idealization of Tension-Pull Specimen (after Rots [94]) . ^ 593.1 A Photograph of the Pull-out and Push-in Specimens ^673.2 The Pull-out and Push-in Specimens ^683.3 The Type No.10 Test Rebar ^ 703.4 Test Rebar Instrumented with Strain Gauges ^713.5 The Stress-strain Relationship of the Straight Bar ^72:3.6 The Stress-strain Relationship of the Deformed Bar ^723.7 The Two Spirals in the Specimen ^74:3.8 Polypropylene Fibers ^773.9 Steel Fibers ^79:3.10 The Stress-strain Relationship of Concrete ^813.11 Layout of the Set Up for the Impact Test (Revised from Somaskanthan[96 ])^ 923.12 An Overall View of the Impact Machine — Push-in Test (Revised fromSomaskanthan [96])^ 93:3.1:3 An Overall View of the Impact Machine — Pull-out Test (Revised fromSomaskanthan [96]) ^ 943.14 Solid Steel Frame for Pull-out Tests ^95:3.15 The Bolt Load Cell for Impact Testing ^ 973.16 The Circuit of the Bolt Load Cell 983.17 The Calibration of the Bolt Load Cell ^ 99xixCamera 1283.18 The Quartz Accelerometer ^ 1013.19 The Calibration of the Quartz Accelerometer^ 1023.20 The Circuit of 'Opposite Arm' Wheatstone bridge 1043.21 The Dummy Strain Gauge and Connector Box ^ 1073.22 The Calibration of Strain Measurement ^ 1073.23 The Data Acquisition System ^ 109:3.24 EKTAPRO 1000 Motion Analyzer 1123.25 The Calibration of the Load Cell for Static Testing ^ 1153.26 The Calibration of the Position Measurement 1163.27 Test System for Static and Medium Rate Testing ^ 1173.28 Pull-out Test Set Up for Static and Medium Rate Loading ^ 118:3.29 Push-in Test Set Up for Static and Medium Rate Loading ^ 1193.30 The Stereoscopic Microscope ^ 1224.1 Typical Outputs from the Eight Channels of the Data Acquisition System 1244.2 Algorithm of Test Data Process 1274.3 The Motion Picture of the Rebar at T = 1 ms Taken by the High Speed4.4 The Motion Picture of the Rebar at T = 2 ms Taken by the High SpeedCamera ^ 1284.5 The Motion Picture of the Rebar at T = 3 ms Taken by the High SpeedCamera ^ 1294.6 The Motion Picture of the Rebar at T = 4 ms Taken by the High SpeedCamera ^ 1294.7 The Motion Picture of the Rebar at T = 5 ins Taken by the High SpeedCamera^ 130xx4.8 The Motion Picture of the Rebar at T = 6 ms Taken by the High SpeedCamera^ 1304.9 The Motion Picture of the Rebar at T = 7 ms Taken by the High SpeedCamera ^ 1314.10 The Displacement History of the Rebar by Two Methods^1314.11 \"Non Event\" Noise in Impact Tests^ 1344.12 Spectrum of \"Non Event\" Noise by FFT 1344.13 One of the Calculation Models for the Test Specimens ^ 1615.1 Stresses in the Smooth Rebar ^ 1675.2 Effects of Loading Rate on the Stresses in the Smooth Rebar ^ 1675.3 Effects of Concrete Strength on the Stresses in the Smooth Rebar^1685.4 Effects of Fibre Additions on the Stresses in the Smooth Rebar ^ 1685.5 The Stresses in the Smooth Rebar for Pull-out and Push-in Tests^1695.6 Effects of Loading Rate on the Stresses in the Deformed Rebar (PlainConcrete) ^ 1735.7 Effects of Loading Rate on the Stresses in the Deformed Rebar (Polypropy-lene Fibre Concrete) ^ 1735.8 Effects of Loading Rate on the Stresses in the Deformed Rebar (Steel FibreConcrete)^ 1745.9 Effects of Loading Rate on the Stresses in the Deformed Rebar (HighStrength Concrete) ^ 1745.10 Effects of Loading Rate on the Stresses in the Deformed Rebar (Pull-outTests) ^ 175^5.11 Effects of Concrete Strength on the Stresses in the Deformed Rebar 176xxi5.12 Effects of Fibre Additions on the Stresses in the Deformed Rebar (DifferentFibres) ^ 1785.13 Effects of Steel Fibre Additions on the Stresses in the Deformed Rebar(Different Fibre Content) ^ 1805.14 Stresses in the Deformed Rebar for Pull-out and Push-in Tests (Static) ^ 1815.15 Stresses in the Deformed Rebar for Pull-out and Push-in Tests (Impact) ^ 18:35.16 Effects of Loading Rate on the Stresses in the Concrete ^ 1865.17 Effect of Concrete Strength on the Stresses in the Concrete (Static) . . ^ 1865.18 Effect of Concrete Strength on the Stresses in the Concrete (Impact) . ^ 1875.19 Effects of Fibres on the Stresses in the Concrete (Static) ^ 1875.20 Effects of Fibres on the Stresses in the Concrete (Medium) ^ 1885.21 Effects of Fibres on the Stresses in the Concrete (Impact) 1885.22 The Stresses in the Concrete for Pull-out and Push-in Tests (Impact) . ^ 1895.2:3 The Bond Stresses for a Smooth Rebar^ 1915.24 Effect of Loading Rate on the Bond Stresses for a Smooth Rebar ^ 1925.25 Effect of Concrete Strength on the Bond Stresses for a Smooth Rebar . ^ 1925.26 Effect of Fibre Additions on the Bond Stresses for a Smooth Rebar . . 1935.27 The Bond Stresses for a Smooth Rebar for Pull-out and Push-in Tests . . 1935.28 Effects of Loading Rate on the Bond Stresses (Plain Concrete) 1975.29 Effects of Loading Rate on the Bond Stresses (Polypropylene Fibre Concrete)1975.30 Effects of Loading Rate on the Bond Stresses (Steel Fibre Concrete) . . 1985.:31 Effects of Loading Rate on the Bond Stresses (High Strength Concrete) . 1985.32 Effects of Loading Rate on the Bond Stresses (Pull-out Tests) 200^5.33 Effects of Concrete Strength on the Bond Stresses 2005.34 Effects of Fibre Additions on the Bond Stresses (Different Fibres) . . 2015.35 Effects of Steel Fibre Additions on the Bond Stresses (Different FibreContent) ^ 2025.36 The Bond Stresses for Pull-out and Push-in Tests (Static) ^ 2025.37 The Bond Stresses for Pull-out and Push-in Tests (Impact) ^ 2055.38 The Local Slip Distribution for Specimens with Smooth Bars ^ 2095.39 Influence of Concrete Strength on Slip Distribution (Static) 2095.40 Influence of Concrete Strength on Slip Distribution (Impact) ^ 2105.41 Influence of 0.5% by Volume Polypropylene Fibres on Slip Distribution(Impact) ^ 2105.42 Influence of 0.5% by Volume Steel Fibres on Slip Values (Static) ^ 2115.43 Influence of 0.5% by Volume Steel Fibres on Slip Distribution (Impact) ^ 2115.44 No Transverse Cracks Formed at the Interface for Specimens with SmoothBars ^ 2145.45 Internal Cracks in Pull-out Tests with Deformed Bars (Arrow Indicatesthe Crack around the Rib of the Rebar) ^ 2155.46 Internal Cracks in Push-in Tests with Deformed Bars (Arrow Indicates theCrack around the Rib of the Rebar) ^ 2155.47 Influence of Loading Rate on Internal Cracks (Normal Strength Concrete,Arrow Indicates the Crack around the Rib of the Rebar) ^ 2175.48 Influence of Loading Rate on Internal Cracks (High Strength Concrete,Arrow Indicates the Crack around the Rib of the Rebar) ^ 2185.49 Influence of 0.5% by Volume Polypropylene Fibres on Internal Cracks (Ar-row Indicates the Crack around the Rib of the Rebar) ^ 2195.50 Influence of 0.5% by Volume Steel Fibres on Internal Cracks (Arrow Indi-cates the Crack around the Rib of the Rebar) ^ 2195.51 The Bond Stress vs. Slip Relationship for a Smooth Rebar ^ 2225.52 Effects of Loading Rate on the Bond Stress vs. Slip Relationship forSmooth Rebars ^ 2225.53 Effects of Concrete Strength on the Bond Stress vs. Slip Relationship forSmooth Rebars ^ 2235.54 Effects of Fibre Additions on the Bond Stress vs. Slip Relationship forSmooth Rebars ^ 2235.55 The Bond Stress vs. Slip Relationship for a Smooth Rebar for Pull-outand Push-in Test s^ 2265.56 Effects of Loading Rate on the Bond Stress vs. Slip Relationship (PlainConcrete) ^ 2265.57 Effects of Loading Rate on the Bond Stress vs. Slip Relationship (Polypropy-lene Fibre Concrete) ^ 2275.58 Effects of Loading Rate on the Bond Stress vs. Slip Relationship (SteelFibre Concrete) ^ 2275.59 Effects of Loading Rate on the Bond Stress vs. Slip Relationship (HighStrength Concrete) ^ 2285.60 Effects of Loading Rate on the Bond Stress vs. Slip Relationship (Pull-outTests) 2285.61 Effects of Concrete Strength on the Bond Stress vs. Slip Relationship . . 2295.62 Effects of Fibre Additions on the Bond Stress vs. Slip Relationship (Dif-ferent Fibres) ^ 2295.63 Effects of Steel Fibre Additions on the Bond Stress vs. Slip Relationship(Different Fibre Content) 2315.64 The Bond Stress vs. Slip Relationship for Pull-out and Push-in Tests (Static)2315.65 The Bond Stress vs. Slip Relationship for Pull-out and Push-in Tests(Impact) ^ '232xxiv5.66 Internal Cracks at the Tips of the Ribs of an Uncoated Rebar (NormalStrength, Push-in, Impact) ^ 2415.67 Internal Cracks at the Tips of the Ribs of an Epoxy-Coated Rebar (NormalStrength, Push-in, Impact) ^ 2415.68 Internal Cracks at the Tips of the Ribs of an Uncoated Rebar (HighStrength, Push-in, Impact) ^ 2425.69 Internal Cracks at the Tips of the Ribs of an Epoxy-Coated Rebar (HighStrength, Push-in, Impact) ^ 2425.70 The Bond Stress vs. Slip Relationship for a Specimen with an EpoxyCoated Rebar (Normal Strength, Pull-out, Impact) ^ 2435.71 The Bond Stress vs. Slip Relationship for a SpecimenCoated Rebar (Normal Strength, Push-in, Impact) ^5.72 The Bond Stress vs. Slip Relationship for a SpecimenCoated Rebar (High Strength, Pull-out, Impact) ^5.73 The Bond Stress vs. Slip Relationship for a Specimenwith an Epoxy243244with an Epoxywith an EpoxyCoated Rebar (High Strength, Push-in, Impact) ^ 2446.1 Typical Tup Load History^ 2557.1 The Quadratic Solid Isoparametric Element with 20 Nodes and 60 D.O.F. 2887.2 The Shape Function of the Quadratic Solid IsoparametricElement ^ 2907.3 The Quadratic Singularity Isoparametric Element ^ 2907.4 The Interface Element (Bond-Link Element) 2917.5 Algorithm of Finite Element Analysis ^ I 2997.6 Algorithm of Finite Element Analysis — II 3007.7 The Finite Element Mesh (Fracture Mechanics, Pull-out) ^ 305xxv7.8 The Finite Element Mesh (Fracture Mechanics, Push-in) ^ 3067.9 The Bond Stress-slip Relationship by the Finite Element Method (PlainConcrete, Push-in, Impact III - 0.5 • 10 -2 11/1 P a I s) ^ :3117.10 The Bond Stress-slip Relationship by the Finite Element Method (Polypropy-lene Fibre Concrete, Push-in, Impact III -0.5 • 10 -2 MPa/s) ^ :3117.11 The Bond Stress-slip Relationship by the Finite Element Method (SteelFibre Concrete, Push-in, Impact II - 0.5 • 10' MPa/s) ^ :3127.12 The Bond Stress-slip Relationship by the Finite Element Method (SteelFibre Concrete, Push-in, Impact III - 0.5 • 10_ 2 MPals) ^ :3127.13 The Bond Stress-slip Relationship by the Finite Element Method (SteelFibre High Strength Concrete, Push-in, Impact III -0.5 • 10 -2 MPals) ^ :31:37.14 The Bond Stress-slip Relationship by the Finite Element Method (SteelFibre Concrete, Pull-out, Impact III - 0.5 • 10 -2 MPa/s) ^ :31:37.15 The Applied Load vs. Displacement Curve by the Finite Element Method(Steel Fibre Concrete, Push-in, Impact III -0.5 • 10 -2 MPa/s) ^ :314E.1 Longitudinal Impact of Bars ^ 334E.2 Absolute Velocity History at the Bottom (Analytic)^ :3:36E.:3 Acceleration History at the Bottom (Analytic) :3:36E.4 Acceleration History at Bottom (Experimental) ^ :3:39E.5 The Amplitude Spectrum of Acceleration (Analytic) :3:39E.6 The Amplitude Spectrum of Acceleration (Experimental) ^ 341E.7 Acceleration History at the Bottom (Filtered) ^ 341xx viE.8 Strain History at the Top (Analytic.) ^ 342E.9 The Amplitude Spectrum of the Strain (Analytic) ^ 343E.10 Strain History at the Top (Experimental) ^ 343E.11 The Amplitude Spectrum of The Strain (Experimental) ^ 344E.12 Strain History at the Top (Filtered)^ 344E.13 Longitudinal Impact of Bar and Block 345E.14 Load History (Analytic) ^ 349E.15 The Amplitude Spectrum of the Load (Analytic) ^ 349E.16 Load History (Experimental) ^ 350E.17 The Amplitude Spectrum of The Load (Experimental) ^ 350E.18 Load History (Filtered) ^ :351F.1 Finite Elements of a Ring 356F.2 The Finite Element Mesh (Pull-out) ^ 357F.3 The Finite Element Mesh (Push-in) 358H.1 Test Specimen for the Unit Chemical Adhesion Force^ :363H.2 Test for the Frictional Factor at the Interface 364H.3 Test for the Normal Stress Factor at the Interface^ 365List of NotationsLatin SymbolsA = the surface area of the rebarA, = the cross-sectional area of the concrete specimenA S = the cross-sectional area of the rebara = accelerationa ha = the acceleration of the hammer= the acceleration of the rebar[B] = the \"strain-displacement\" matrixCo = the unit chemical adhesion force at the interfaceC(w) = the Fourier coefficientc i = the calibration coefficient of the load cellc„ = the coefficient of variationD = the diameter of the rebard = the distancedh„ = the distance the hammer travels after impact= the distance the rebar travels after impactd„,d = the total distance the hammer travels by the end of impactE = the excitation voltage, Young's modulus, energy[E] = the matrix of elastic stiffnessE, = the Young's modulus of concreteE c,str = the strain energy stored in the concreteE f ,b = the fracture energy in bond processEh„, f r = the energy consumed by the friction and air resistanceE ha, k = the kinetic energy of the hammerEh a , /eft = the kinetic energy of the hammer leftE ha, rebound = the rebound energy of the hammerE ha , p = the potential energy of the hammerEre, str = the strain energy stored in the rebarE r ,, yield^the local yield energy of the rebar during impactEs = the Young's modulus of steelEns = the energy lost to the various machine partsere = the deformation of the rebarFb = force acting on bond areaFh = the horizontal nodal force of the interface element• = the inertial force of rebarFt = the applied load acting on the rebarFh = the vertical nodal force of the interface elementfe' = the compressive strength of concretefc,r = the tensile strength of concretefp = the normal stress factor at the interfacefT = the frictional factor at the interface= the Young's modulus of concrete in shearg = the gravitational accelerationh = the drop height of the hammerI = the minimizing function, the high rate loading (impact),^- I^the first impact loading (bond stress rate is about 0.5 • 10 -4 MPa/s)^I II^the second impact loading (bond stress rate is about 0.5 • 10 -3 MPals)I-III = the third impact loading (bond stress rate is about 0.5 • 10 -2 MPa/s)i = the imaginary[J] = the Jacobean matrixK = the standard gauge factor of strain gauge[K] = the stiffness (global) matrixK 1 , K2 = the gauge factors of a pair of strain gauges (gauge 1 and gauge 2)/(/, I(//, I(/// = the stress intensity factors for fracture mode I, II, IIIK/ KLic, Kmc = the critical stress intensity factors (dynamic) for fracturemode I, II, IIII = the length over which bond slip occurs/, = the embedment length of the rebar in concretel j = the locations of the ith and jth points along the rebar/ p = the length of the pull-out or push-in end of the rebarM = the mass of the hammer, the medium rate loadingMina = the mass of the hammerXXXM re = the mass of the rebarM— I = the first medium rate loading (bond stress rate is 0.5 • 10_ 6 ti 0.5 • 10'MPals)M— II = the second medium rate loading (bond stress rate is 0.5-10' ti 0.5.10 -4MPals)N = the number of the time interval, the total number of samples[N] = the matrix of shape functionNz = the shape functionn^the number of segments in which the slips have been calculatedP(t) [t i ,t 2] = the aperiodic signal functionPF = Polypropylene fibre concreteR 1 , R 2 = the electric resistances of a pair of strain gaugesS = the standard deviation, the static loadingS i^the concrete stress corresponding to e = 50 x 10 -6S z^the concrete stress at 40% of the ultimate loadSh„, a = the output voltage from the accelerometer attached to the hammer= the output voltage from the load cellS„, a = the output voltage from the accelerometer attached to the rebarSF = Steel fibre concrete= the location of the calculated section along the rebarT,t = the timet,„d = the duration of the impact eventt l = the time corresponding to the end of the linear region of the applied loadvs. displacement curvet f = the time corresponding to the bond failuret rebound = the time interval between the first and second blowu = the bond stressu, v, w = the displacement components in the global Cartesian coordinatesit = the bond stress rateu jj = the average bond stress between the i and j points= the horizontal displacements of node i and j (finite element method)Vout = the output signal voltageh„ = the velocity of the hammerha,0 = the velocity of the hammer at the moment of impactvz j vj = the vertical displacements of node i and j (finite element method)v rf, = the velocity of the rebarV rebound = the rebound velocity of the hammerW b = the work done by the bond resistanceWha = the work done by the hammerWha (t) = the work done by the hammer in the time domainWha (d) = the work done by the hammer in the displacement domainTV ha, total = the total work done by the hammer during the impactto = the bond slipto = the calculated slips for the previous segmentsw, = the bond slips at distance x from the i pointtv.t, = the bond slips at distance y from the loaded end of the rebarx = the distance between a point and the i pointx, y, z = the global Cartesian coordinatesx i = the experimental data= the mean value of sample x iy = the distance between a point and the loaded end of the rebarGreek SymbolsA = small change operatorAE = the kinetic energy lost by the hammer after impactAE Lb = the fracture energy in bond during a time period of St,AT = the time incrementSt = the time incrementAX = the length of rebar between the ith and jth point= coefficient that accounts for the nonuniform distribution of stress in theconcrete across the section= the strainE z = the strain corresponding to 82= the axial strain in concrete. = the radial strain in concrete= the tangential strain in concreteE S = the axial strain in steel (recorded)= the radial strain in steelcs,e = the tangential strain in steelEtt = the transverse concrete strain at the middle of specimen corresponding toct2 = the transverse concrete strain at the middle of specimen corresponding toS2Ex , C y , ez = the strain components in the Cartesian coordinates( 2 , E3 = the principal strains in the concrete element7i, C = the isoparametric coordinates= the Poisson's ratio,a, = 0.25 (the Poisson's ratio of concrete),a, = 0.27 (the Poisson's ratio of steel)p = the density of the rebara = the stress= the stress ratea, = the axial stress in concrete= the radial stress in concreteac,e = the tangential stress in concrete= the principal tensile stress in the concrete elementacy = the crushing strength of the concrete cylinder= the interface shear stress (finite element method)as = the axial stress in steelas ,„ = the radial stress in steelcrs,e = the tangential stress in steel= stress at the ith location in steelmss, = stress at the jth location in steel= the interface normal stress (finite element method)(Tx ay, oz = the stress components in the Cartesian coordinatesa l 7 a21 0.3 = the principal stresses in concrete elementsw = the frequency componentSubscriptsa = acceleration= concretee. = elasticend = end of impact eventf = failurefr = frictionh = horizontalha = hammeri = the ith pointj = the jth point/ = load, loadcell, linearxxxvv = the radial directionre = reinforcing bars = steelt = at time t, the tangential directionstr = strain= verticalx = distance xy = distance y= the tangential directionAcknowledgementThe author is highly indebted to Dr. Sidney Mindess for his continuous support andconstant supervision. His personal concern, encouragement and advice during author'sgraduate studies were of great help. Sincere gratitude also goes to Dr. N.D. Nathan,Dr. A. Bentur, and Dr. R.J. Gray for their help rendered during author's study in theDepartment of Civil Engineering.The author wishes to express special thanks to Dr. R.A. Spencer, Dr. A. Poursartipand Dr. P.E. Adebar for serving on the author's graduate committee and for theirinvaluable comments. Thanks are also due to M. Nazar, R. Postgate, B. Merkli, J. Wongand R. Dolling in the workshop of the Department of Civil Engineering for their helpfulparticipation in preparing and maintaining the instrumentation for the experimentalwork. The author wishes to thank Dr. N.P. Banthia for his help in the early stage ofthis research program, and thank J. Stevens in the University Computing Center for hishelp in the computer programming work.Finally, the research assistantship awarded by the Department of Civil Engineering,University of British Columbia and the research grant provided by the Natural Sciencesand Engineering Research Council of Canada, for the Network of Centers of Excellenceon High Performance Concrete are gratefully acknowledged.Chapter 1Objectives and ScopeThe initial purpose of the embedment of steel bars in concrete, in the middle of the19th century, was to produce a supporting steel network [1]. In 1886, G.I. Wayss wassuccessful. from experimental considerations, in elucidating the principles involved in theaction of reinforcement. His contributions have subsequently served as a basis for themore general utilization of reinforcement as a component in reinforced concrete whoseprimary function is to resist tensile forces.For a reinforced concrete structure, it is the bond between the steel and the concretewhich enables the two materials to act together. In the case of plain bars, the bond forcesare due to chemical adhesion and friction. In the case of deformed bars, the bond forcesare derived mainly by the bearing capacity of the ribs on the concrete. In the case ofstrands, the bond forces are due largely to a lack of fit. The behaviour of a structure isstrongly dependent upon the bond between the concrete and the reinforcing bars. Theaccurate prediction of the linear or nonlinear response of reinforced concrete structuressubjected to static or dynamic loads, using all the sophisticated methods of analysis, isbased upon our knowledge about the local bond stress vs. slip relationship governing thebehaviour at the steel-concrete interface.1Chapter 1. Objectives and Scope^ 9With the introduction of high tensile strength steel as reinforcing material, the impor-tance of bond was further increased. The development of cracks at a given working stressand the width of these cracks depend primarily on the degree of bond between the steeland the concrete. Over the past decade, high performance concretes and fibre-reinforcedconcretes have become more widely used in concrete structures. High performance con-crete is generally stronger than normal concrete, but it may be more brittle than thelatter. Concretes with fibre addition make it more difficult for cracks to propagate andmore ductile, i.e. they can absorb more fracture energy. All of these may improve thebond strength significantly. However, design engineers of reinforced concrete structuresunder different loading conditions will benefit from these developments only when thefundamental mechanisms of bond behaviour are precisely understood.Either the \"ultimate bond stress\" in the 1970 CSA A23.3-M70 [2] (and also in the 1963Building Code [3]) or the \"required development length\" in the 1973 CSA A23.3-M73and 1984 CSA A23.3-M84 [4, 5] (and also in the 1971 and 1989 ACI Building Code [6, 7]),which deal with the bond problem in engineering practice, are derived empirically basedprimarily on pull-out tests (such as the standard pull-out test recommended in ASTM C234 [8]). The assumption that the bond stress distribution along the embedment lengthis uniform, which provides the basis for the derivation of the bond formula, may notbe true in most cases. A very short embedment length in a pull-out tests may createa uniform bond stress distribution, but the result is somewhat controversial [9]. Thesevarious Code equations do not recognize the influence on the bond resistance of manyfactors, and may be conservative in most cases. Although many proposals for changehave been made, no generally accepted recommendations have yet evolved. A uniformbond stress-slip relationship based on the Code equations is convenient in applica,tions,but far from reality, and may give results with considerable variability.Chapter 1. Objectives and Scope^ 3Extensive experimental and analytical studies have been carried out and reportedon over the years, dealing with bond behaviour in reinforced concrete. Most of theseinvestigations have been associated with either pull-out loading or a combination of pull-out and push-in loading. No pure push-in tests have been reported. It was recognizedthat there are numerous factors affecting bond behaviour. Some of these factors arethe type of rebar, the compositions and properties of the materials, the layout of thereinforcement, the pattern of loading, the strain rate, and so on. It is well known thatthe size and the type of specimen used for bond tests have large effects on the results ofthe experiments. It is thus difficult for an experimental program to take into account allpossible factors affecting bond.While much experimental research has been conducted on bond behaviour under staticloading condition, only a few results are available for dynamic loading, especially forimpact loading conditions, such as explosions, earthquakes, sudden cracking of a beam,pile driving, etc. It is well known that the strength of concrete (compressive, tensileor shear) increases with increasing loading rate, and that the fracture characteristicsof concretes or cementitious composites change dramatically under dynamic loading.For this reason an influence of the loading rate on the bond resistance of reinforcingelements can be expected. Due to the difficulties in precisely modelling the mechanicalproperties under dynamic loading, however, very little analytical work has been done onthis problem.The present work deals with a study of the bond behaviour of reinforcing bars inconcrete under impact loading. It includes both experimental and analytical components.The experimental work involved the carrying out of a series of both push-in and pull-outimpact tests to investigate:Chapter 1. Objectives and Scope^ 41. the most suitable experimental models to obtain bond-slip relationships under dy-namic loading;2. the instrumentation and techniques for the measurement of bond stress and bondslip;3. the bond stress, the bond slip and the relationship between them;4. the stress distribution along the rebar and in the concrete in the vicinity of therebar;5. the crack development in concrete during the bond-slip process; and6. the transfer and balance of energy during bond-slip.The analytical work involved a study of the bond behaviour using both fracturemechanics and the finite element method approaches. It includes:1. An investigation of the mechanism of bond between the steel and the concrete fromthe viewpoint of linear or nonlinear fracture mechanics;2. The use of the finite element method to analyze the bond behaviour under impactloading; the main concerns are:• using \"cracking elements\" for concrete (concrete elements)• developing \"interface elements\" (bond-link elements) for the connection of thesteel elements and the concrete elements• setting cracking and crushing criteria. suitable for the concrete elements• setting appropriate criteria for the behaviour of the interface elementsChapter 1. Objectives and Scope^ 5• using appropriate constitutive laws for both materials• interpreting the results of the calculations reasonably3. The stress distribution and crack development in the concrete; and4. The formulation of an applied bond stress-slip model for impact loading;The following major variables were considered in both the experimental work and theanalytical work:• Strain rate in the reinforcing bar;• Strength of the concrete;• Addition of fibres; and• ( onstitutive relationship of the concrete.('SA A23.3-M84 [5] permits only deformed bars as reinforcement except for spirals,and for stirrups and ties smaller than 10 mm in size. Therefore, this study emphasizesthe bond behaviour of deformed bars.Chapter 2Literature Survey2.1 Bond Behaviour under Static Loading2.1.1 IntroductionThe bond between steel and concrete has long been under investigation. These studieshave elaborated on the influence of many variables on bond and bond strength, and canbe placed into two categories:1. The stresses produced as a result of the bonding between steel and concrete; and2. The influence of various parameters on bond strength and bond stress distribution.However, only these studies, to be described below, have been found which dealexplicitly with the bond between steel reinforcing bars and concrete under impact loading.These were all experimental studies; no analytical paper have been found. Hence, thisliterature survey will deal primarily with quasi-static investigations, which are a necessaryprelude to the study of the impact problems.6Chapter 2. Literature Survey^ 7The earliest published tests on bond between \"iron bars\" and concrete, as reportedby Abrams [10], were carried out by Thaddeus Hyatt in 1877. Abrams reported resultsfrom both pull-out tests and the reinforced concrete beam tests by 1913 [11]. Summariesof some of the major developments in the study of bond over the last century are givenby ACI Committee 408 [12, 13], ACI Committee 446 [14] and CEB Task Group VI [15].Basically, there are two types of interactions between the reinforcing bar and theconcrete which involve slip: flexural bond stress and anchorage bond stress.(1) Flexural bond stressFlexural bond stresses exist on the surface of the reinforcing bar in a flexural membersuch as a beam or a slab, due to the variation in bending moment. The change in bendingmoment between two sections of a beam of length dx, produces a change in bar forcedT. Since the bar must be in equilibrium, this change in bar force will be resisted by anequal and opposite force due to the bond at the contact surface between the steel and theconcrete. This bond stress due to the change in bending moment is called the flexuralbond stress.From the equilibrium equation,uE0 dx dT dM^(2.1)whereu = the flexural bond stressthe total perimeter of the bar at the sectionChapter 2. Literature Survey^ 8dM = the change in the bending moment= the arm of the internal resisting coupleFrom beam theory, the shear force at the section, V, is equal todV = ^Mdx(2.2)Therefore, the flexural bond stress is u = V (2.3)CEO(2) Anchorage bond stressAnchorage bond stresses develop in the anchorage zone at the ends of bars whichextend into a support, or at the ends of bars cut off within a span.If a bar is required to develop a given force dT at certain point and has an anchoragelength dl,/ , from the equilibrium consideration the anchorage bond stress, u, is determinedbydT 1u = ^dl E0Generally, the anchorage bond stress is assumed to be uniformly distributed over theanchorage length, so the average value is(2.4)Chapter 2. Literature Survey^ 9 T(2.5)whereT = the applied force/ d = the anchorage length2.1.2 Flexural Bond under Static Loading2.1.2.1 Experimental InvestigationFor the case of flexural bond stress, two major types, tension tests and beam tests, havebeen used. In these types of tests, the concrete surrounding the bar remains in tension,in an attempt to represent the actual conditions existing in a beam. In the former case,a bar is encased in a cylinder or a prism, and is subjected to tension at the protrudingends, as shown in Fig. 2.1. Thus, the conditions are similar to those in the tensionzone of a beam. For the latter case, various configurations such as ordinary rectangularbeams subjected to four point loading, hammer head beams, cantilever beams, and stubcantilever beams are tested. In all of these tests, the concrete surrounding the bar remainsin tension in order to represent the actual conditions existing in a beam. Fig. 2.2 showsone of the beam tests on bond strength.In Abrams's tests [11] nearly all of the pull-out test specimens were reinforced againstbursting by means of spiral reinforcement. All of the beams were reinforced with verticalchapter 2. Literature Survey^ 10Figure 2.1: Pull-out Test on Bond StrengthFigure 2.2: Beam Test on Bond StrengthChapter 2. Literature Survey^ 11stirrups of plain round bars. In both types of specimens, attention was given to obtain-ing accurate measurements of the slip of the bar through the concrete as the loadingprogressed.Some of the relevant conclusions of this investigation on pull-out tests are as follows:1. In order to study the load vs. slip relationship over a wide range of values it wasnecessary to guard against the splitting of the specimen;2. It was realized that the bond stress was not uniformly distributed along a rebarembedded any considerable length, and having the load applied at one end;3. Only after slip became general was there an approximately uniform bond stressthroughout the embedded length. However, in establishing a bond vs. slip curve fordifferent situations, a uniform bond distribution was assumed, and the deformationsin concrete and steel were assumed to be proportional to the stress;4. For a given amount of slip, the bond stress depended upon the stress level in thesteel;5. The tests indicated that a definite relationship existed between the amount ofmovement of the bar and the bond stress developed. After slipping began, thebond stress increased with further movement of the bar, very rapidly at the first,then more slowly until the maximum bond resistance was reached; the bond stresswas reduced with further slip;6. The load vs. slip relationships for different mixes of concrete were the same; and7. The bond resistance was greatly increased by lateral pressures.Chapter 2. Literature Survey^ 1 2Some of the relevant conclusions of this investigation on beam tests are as follows:1. To determine the bond stress at any given location in a bar in a reinforced concretemember, it was essential to determine the exact stress variation along the reinforcingbar for a given load; and2. The tests indicated that the maximum bond resistance was developed at certainpoints along the bar at loads much below that causing bond failure in the beam.Mylrea [16] concluded, based mainly on the work of Abrams 1 . that at any point alongthe bar, bond stress was a function of the slip at that point. Thus, a single relationshipcould represent the variation of bond stress with slip at all points along the length of thebar.The mechanism of bond development for plain round bars was described by Mylreaas follows. At first the load is carried by adhesion. As the load increased, more of the barbegins to slip, restricting the adhesive bond to a smaller portion of the bonded length.The maximum bond stress occurs near the loaded face at the free end. With increasingload the location of the maximum bond stress moves towards the unloaded end of thepull-out specimen while maintaining a constant value. After the slip becomes general(that is, the whole bar slips) the bond stress is nearly uniform along the full length ofthe bar. The bond stress intensity gradually diminishes with further slip.Mylrea did not discuss the mechanism of bond of deformed bars but concluded fromhis tests, that deformed bars had improved bond properties and that slip resistance wouldincrease until the deformations began to crush the concrete.1 It should be noted that the reinforcing bars which Abrams used in his tests were no longer in use in1940's.Chapter 2. Literature Survey^ 13Mylrea was the first to point out that the well-known flexural bond formula (Eq. 2.3),Vu = ^zE0yielded correct values of bond stress only when the bars were straight and extended overthe full length of the member. The tensile force in a bar varied directly with the ordinateof the moment curve. He emphasized the concept of a minimum development lengthrather than a unit bond stress. Mylrea, was also of the opinion that the bond conditionsat the bar ribs were different from those between the ribs. Therefore, it was not possiblethat a bond stress-slip curve at a particular point along the bar could represent thebehaviour at other points along the embedded length.Watstein [17, 18] reported results from pull-out specimens in which he measured thedistribution of stresses in bars with different embedment lengths. He observed that thebond stresses increased with slip most rapidly at the loaded end of the bar and, in general,least rapidly at its free end. The divergence of bond stress for a given slip, at the twoends of the bar, was more pronounced for longer embedment lengths. The bond vs. sliprelationship obtained indicated that there was a non-linear relationship and was thus inaccord with comparable data obtained by other investigators [11, 15].Mains [19] determined steel stresses and bond stresses along the rebar by a newtechnique in which electric resistance strain gauges were placed at close intervals withinthe core of a hollow bar, and the bond stresses were thus not disturbed. His methodinvolved slicing the reinforcing bar longitudinally and milling a groove in one of thehalves for the fixing of strain gauges, and then tackwelding them back into a single bar.Determinations of longitudinal stresses were made on both beam and pull-out specimens.Forces in the bars in the linear and non-linear ranges of the stress-strain diagram wereChapter 2. Literature Survey^ 14found using previously-established calibration curves.The results of Mains' investigation indicated that the locations of cracks in beamsgoverned the magnitude and distribution of both tensile and bond stresses. He alsofound that the maximum measured bar tension in the center section of the beam wasclose to the value calculated by the ordinary cracked section theory. The measured localmaximum bond stress often exceeded the value calculated from cracked section theoryby a factor of two or more for all loads after cracking was observed. Also, very highlocal bond stresses occurred near cracks in a beam. After cracking, the concrete couldnot carry any tension, so the tension in the concrete was zero at the crack and reached amaximum between cracks. This gradual increase of tension in the concrete with distancefrom the crack accounted for the decrease of tension in the steel and the development ofthe accompanying bond stress between the concrete and the steel. Since this phenomenontook place in a region of no shear, it contradicted the common assumption that bondstress was associated exclusively with shear as assumed in the classical beam theory. Themaximum local bond stress in deformed bars was observed to occur at or near the loadedend at all stages of loading while the location of the maximum local bond stress in plainbars was observed to move from the loaded end to the unloaded end with increasing load[11, 16, 20].Ferguson, Turpin and Thomson [21] investigated the influence of bar spacing, stirrups,and the depth of concrete cover on the bond strength. They conducted eccentric pull-outtests, simulating the worst beam conditions. Splitting was observed to be an importantfactor in bond strength. They concluded that the maximum bar spacing should be basedon the aggregate size. By increasing the bar spacing, a significant improvement in theultimate bond stress could be obtained.Chapter 2. Literature Survey^ 15Ferguson and Thomson [22, 23] published a two-part paper on the development lengthof high strength reinforcing bars. The test specimens consisted of simply supported beamswith overhangs. The bond failure was caused by splitting but diagonal tension was oftena complicating factor. They found that the bond strength was a function of cover over thebars, an extra inch of cover increasing the bond strength from 0.41 to 0.69 MPa. Stirrupswere found to resist bond splitting and to help in preventing sudden failure. The bondstrength was observed to vary with the square root of the concrete compressive strength,A', rather than directly with L'.In a review paper, Ferguson [24] discussed the bond stresses and the nature of bondfailure. For a deformed bar, the bearing of the ribs against the concrete and the shearstrength of the concrete between the ribs were reported to be chiefly responsible for thebond strength. Especially for a cracked beam, the local bond stress was so variable thatthe average bond stress computation over an embedment length was felt to be advisable.The bond capacity of compression bars was found to be greater than that for tensionbars because compression bars did not cross open cracks.Bresler and Bertero [25, 26] carried out tests on instrumented axially reinforced ten-sion specimens in which the reinforcing bars were subjected to repeated tensile loadingat both ends to study the mechanism of bond deterioration. They were the first to reportresults on bond stress distribution and measurements of end slip. The most significantconclusion from their work is the history-dependence of the bond deterioration. Themechanism that they proposed for bond deterioration was one of failure in a relativelythin layer of concrete (designated the \"boundary layer\") adjacent to the steel-concrete in-terface. The failure was due to cracking, local fracture, and/or inelastic deformation andcrushing of the concrete in the \"boundary layer\". The stress transfer occurred basicallyChapter 2. Literature Survey^ 16by friction and wedging action. Some slip also took place in the process.Lutz and Gergely [27, 28] studied the mechanics of the slip of deformed bars inconcrete using both experimental data and an analytical method. They used the finiteelement method to analyze the stresses and deformations in a. concrete cylinder with acentrally-placed rebar subjected to tension. This model represented two situations in a,reinforced concrete member. First, the rebar, when pulled from both sides, representedthe conditions between flexural cracks. When pulled from only one side, it represented theanchorage zone problem. Transverse cracking in concrete, slip, and separation betweenthe reinforcing bar and the concrete were considered. Radial separation was found tooccur in the vicinity of a transverse crack due to high radial stresses. They reported thatthe bond of deformed bars was mainly due to bearing of the ribs against the concrete.Slip of deformed bars could occur in two ways: the rib could push the concrete awayfrom the bar, or the ribs could crush the concrete. From their tests with a single rib andthe tests of Rehm (29], they concluded that for bars having a rib face angle of more thanabout 40° with the bar axis, the slip was mainly due to crushing of the mortar in frontof the ribs. For ribs having a face angle less than 40°, slip was mainly due to the relativemovement between the concrete and the steel along the face of the rib and due to somecrushing of the mortar.Goto [30] carried out a significant study by injecting ink into his concrete specimensduring the tests, and then cutting the specimens longitudinally. He could establish thepattern of internal cracks from which he proposed the mechanism of the interactionbetween the concrete and steel, as demonstrated in Figs. 2.3 and 2.4. The formationof internal cracks in the concrete around the rebar gave the appearance of \"comb-like\"concrete, the teeth of which were deformed in the direction of the primary crack (seered inkEcockvinyl pipereinforcing barconcreterubber pipeinjecting holebrass pipevinyl pip*cockChapter 2. Literature Survey^ 17Fig. 2.4) by compressive forces transmitted from the ribs. The inclination of the cracksbeing about 60° to the bar axis. The deformation of the teeth served to tighten theconcrete around the reinforcing bar and increased the frictional resistance. The reactionof the tightening force caused circumferential tension and was responsible for longitudinalsplitting in the concrete. It was believed that once the splitting cracks developed, thiswas an indication of the onset of bond failure.Location of notchFigure 2.3: Instrumentation to Detect Internal Cracks (after Goto [30])Nilson [31.32] arrived at a bond-slip relationship based partly on hypotheses andpartly on the experimental data reported by Bresler and Bertero [25, 26]. The steel dis-placement was calculated by integrating the strain values of the steel, and the concreteuncracked zoneforce on concreteforce components on bartightening force on bar(due to wedge action anddeformation of teeth ofcomb—like concrete)primary crackinternal crackChapter 2. Literature Survey^ 18Longitudinal section of axially loaded specimen^Cross section Figure 2.4: Idealization of Interaction Between Bar & Concrete (after Goto[30])Chapter 2. Literature Survey^ 19displacements were estimated on the basis of measured slip at the faces of the test spec-imens. A third degree polynomial was obtained by fitting the data. The relationship isgiven byu = 3.606 x 10 6 s — 5.356 x 10 9 ,5 2 + 1.986 x 10 12 s3^(2.6)whereu = local bond stress in psi= local bond slip in inchesDifferentiation of the above equation with respect to s yieldsdu = 3.606 x 10 6 — 10.712 x 10 9 s + 5.958 x 1012 s 2^(2.7)This represents the stiffness of the concrete layers transferring the forces to the steelbar.Nilson [33, 34] subsequently also devised a method for determining the bond-sliprelationship at any point along the embedment length, based on his tests in which internalembedded strain gauges were mounted to measure concrete strains at the interface of thesteel and the concrete. By integrating strains of the steel and the concrete, slip could becomputed. A series of bond stress-slip curves was obtained at different distances fromthe loaded end, as shown in Fig. 2.5 The proposed bond-slip equation was:u^3100 (1.43c + 1.5)s fe i^(2.8)01412Ett\"100ce• 8cncr 61—(n0O• 420.02 004 0 061.0 2.0 3.0c z DISTANCE FROM END OF CONCRETE BLOCKChapter 2. Literature Survey^ 20-3SLIP 10 INCHESFigure 2.5: Nilson's Bond Stress-Slip Curves (Tanner's Tests [33])Chapter 2. Literature Survey^ 21whand the maximum limiting value of bond stress wasereu < (1.43c + 1.5) L'Li^the concrete strength in p.si(2.9)c = the distance from the loaded end in inchesNilson's work definitely confirmed the original thought of Mylrea [16] that bond stressat any point is a function of slip at that point and that the bond slip curve at any partic-ular point along the bar cannot be used to represent the bond slip behaviour at any otherpoint along the embedment length. However, Nilson's equations do not consider otherimportant variables such as the bar diameter, confining pressure, and so on. Further,the computation of the slip was based on concrete deformation measured by internalembedded gauges. Due to the possibility of internal cracking in the concrete surroundingthe rebar over the gauge length, the results obtained might be doubtful.Houde [35] carried out a series of tests in which the end slips, elongations of theembedded bars, and crack formations were studied. He reported that the slip was due togradual deterioration of the concrete in front of the ribs of the reinforcing bai as a resultof high bearing and shearing stresses. Since no evidence of crushing of the concrete nearthe ribs was observed in the sliced specimens, he concluded that the slip at the interfacecould be explained entirely by the bending of the comb-like structures of the concretesurrounding the reinforcing bar. Based on the experimental results, he reported that themaximum value of bond stress at the steel-concrete interface occurred at a slip of 0.03Chapter 2. Literature Survey^ 22711,711- 1.Tp to the peak bond value, the following local bond stress-slip relationship wasproposed in the form of a polynomial:u = 1.95 x 106 s — 2.35 x 109 s 2 + 1.39 x 10 12 5 3 — 0.33 x 10 15 s4^(2.10)whereu = local bond stress in psis = local bond slip in inchesThe bond stress-slip relationship curve is shown in Fig. 2.6. The bond stress-slipbehaviour beyond the peak value was found to be dependent on the distance from theend face. The above equation also does not consider other important variables such asthe bar diameter, confining pressure, and so on.2.1.2.2 SummaryA brief summary of the notable findings regarding flexural bond stress under staticloading can be summarized as follows:1. Using classical beam theory, it was assumed that the bond stress was a function ofshear force alone. This was in contradiction to the experimental evidence.2. For most cases the bond stress-slip relationship was nonlinear.:3. The mechanism of bond failure was primarily due to cracking, inelastic deformationand failure in a relatively thin layer of the concrete adjacent to the steel-concreteChapter 2. Literature Survey^ 230^2^4^6^8^10^12^14^16^18Slip x 10-4 ( in )Figure 2.6: Unit Bond Stress versus Unit Slip Curves (after Houde [35])Chapter 2. Literature Survey^ 24interface.4. The bond stress depended upon the level of stress in steel. To evaluate the amountof bond stress being developed over the embedded length, it was essential to deter-mine the exact stress developed in the reinforcing bar at each point over this lengthfor a given load.5. The distribution of bond stress along the length of the rebar was very irregular anddepended, among other factors, upon the location of the cracks and the ratio ofcross-section area of steel and concrete; the simplifying assumptions regarding thedistribution of bond stresses were not realistic.6. The bond stress-slip relationship should be established between local values of bondstress and bond slip.7. The development of bond stress was closely related to the slip occurring at theinterface between steel and concrete. This relationship was considered to be ofvital importance and could be made a basis for comparison of the influence ofvarious factors on bond stress.8. The bond stress-slip relationship was found to be linear up to about three fourthsof the maximum bond stress.9. The bond stress-slip relationship was time dependent.Chapter 2. Literature Survey^ 252.1.3 Anchorage Bond Under Static Loading2.1.3.1 Experimental InvestigationThe anchorage of reinforcing steel in concrete is fundamental to the whole idea ofreinforced concrete. That is why a vast literature on anchorage bond can be found,dealing with pull-out tests of reinforcing bars embedded in concrete. Originally, thepurpose of such tests was to determine the required length of embedment necessary forfull development of the capacity of the reinforcing bar. Important contributions basedon pull-out test were due to Abrams [11], Richart and Jensen [36], Menzel [37], Gilkey,Chamberlin and Beal [38], Watstein and Seese [39], Clark [40], Mylrea [16], Mains [19],Konyi [41], Matyey and Watstein [42], Ferguson and Thompson [22, 23], Lutz and Gergely[27], Nilson [31, 32, 34], and many others.Fig. 2.7 shows some types of specimens that were used for anchorage bond tests.Those test specimens can be classified as:1. short embedment length (such as Type A) or long embedment length (such as TypeB^E);2. concrete stress in axial direction (such as Type A ti D), compression (such as TypeA, B and E) or tension (such as Type C and D);3. centric loading (such as Type A ti D) or eccentric loading (such as Type E);4. reinforcement loaded on one side (such as Type A ti C and E) or two sides (suchas Type In .Chapter 2. Literature Survey^ 26Figure 2.7: Some Typical Anchorage Bond Test (After Vos and Reinhardt [43])Chapter 2. Literature Survey^ 27Rehm [44] described pull-out tests which were performed on deformed bars providedwith a single rib each or plain round bars with very small lengths of embedment. Heargued that if greater lengths of embedment were used in the pullout tests, then it wasusually possible to determine only the relationship between the tensile force appliedto the test specimen and the amount of the slip at the end of the specimen. Such arelationship could not be applied to local conditions along the length of the bar. However,a relationship of this kind was considered to be useful for calculating in advance thedistribution of steel stresses and the distribution of slip resistance for any length ofembedment of the reinforcing bar.Bernander [45] investigated pull-out specimens which were long in comparison withthe expected effective anchorage length. A long specimen length was used to permit astudy of the bond stress distribution and its dependence on factors such as steel stress,type and spacing of ribs, diameter of the rebar and concrete strength. Strain gauges wereplaced along the rebar to measure the strain in steel. The distribution of steel stress alongthe rebar was found from these strain measurements. The bond stress distribution, thenecessary development length, and the total elongation of the rebar within the pull-outspecimen were then found from the steel stress distribution curves.In most of these tests bond failure appeared to take place when the steel startedyielding. After the ultimate bond stress had been reached, the bond stress decreasedwith a further increase in load. These tests revealed that both the rib pattern and theconcrete strength affected the magnitude of bond stress while the diameter of the barhad no significant effect. Bernander found that the steel stresses along ribbed bars weredistributed almost parabolically.Tassios and Koroneos [46] used an overall optical method (the differential Nloir6Chapter 2. Literature Survey^ 98method) to visualize the full field of stresses, strains and slips at the interface betweenconcrete and steel tensioned from outside. The interface was simultaneously loaded inthe transverse direction by a compressive force. From the induced mechanical interfer-ence pattern between a 20 line per mm. grating glued on the specimens, and an external(underformed) grating, the longitudinal displacement, s , was determined at grid pointson the interface. Similarly, the steel strains were determined, allowing for steel stressevaluation. Consequently, by differentiation of the stress diagrams of the steel, the localbond stress, 7, was evaluated. By compilation of coupled 7 and s values, a local-bondversus local-slip curve was determined which constituted a basic tool for the analyticaltreatment of a series of bond degradation problems..Jiang, Shah and Andonian [47] carried an experimental and analytical investigationto study the characteristics of bond transfer in reinforced concrete flexural members.They developed a new type of test specimen to facilitate the measurements of local slip,secondary cracking, and strain distribution in concrete surrounding the interface. Forthis specimen, a. reinforcing bar was split into two halves and embedded in opposite sidesof the cross section (see Fig. 2.8). A comparison of results from these types of specimenswith those from the more common tests showed that many of the important aspectsof bond transfer phenomena were identical. They performed an axisymmetrical finiteelement analysis to predict secondary cracking. Then a simple one-dimensional analysiswas developed to predict stresses in steel and concrete, local bond-slip relationships,tensile stiffening and total elongation of the reinforcing bar.Abrishami and Mitchell [48] presented a new testing technique for pull-out tests,which simulated uniform bond stress distribution along a reinforcing bar. Their methodenabled determination of the complete bond stress-slip response and investigation ofPP/2Chapter 2. Literature Survey^ 29Type CState of Stress at^State of stress atA, M' and N'^N and trFigure 2.8: Three Types of Transfer Pull-out Test Specimens (after Shah et al[47])Chapter 2. Literature Survey^ 30both pull-out and splitting failure. They cast the test specimens with a pre-tensionedreinforcing bar which was instrumented with strain gauges. By applying different loadsto each end of the rebar a linear variation in axial stresses in the bar could be achieved(see Fig. 2.9), and hence a uniformly distributed bond stress was produced. They usedthis testing technique to investigate the bond performance of reinforcing bars and theinfluence of concrete strength and the presence of an epoxy coating. The test resultsshowed that for uniform bond stress the splitting type of failure seemed more ductilethan the pull-out type.Robins and Standish [49] modified the two common bond tests, the cube pull-outand the semi-beam tests so that lateral pressure could be applied to the bond specimensto investigate their effects on the bond behaviour. The major variables studied werethe magnitude of the lateral pressure, the bar diameter, the length of embedment andthe concrete strength. The results of over 200 bond tests showed that lateral pressurecan considerably increase bond strength. However, the increased capacity, if it occurs,was achieved in different ways for smooth and deformed bars. For smooth bars theapplication of lateral pressure resulted in an increase in frictional effect at the bar-matrixinterface, and the pull-out load could increase up to 250%. For deformed bars, a lowlateral pressure could not prevent splitting or bursting failure, while a greater lateralpressure produced relatively small increases in bond strength, and a shearing-type bondfailure was observed. The corresponding increase was about 75% for deformed bars. Thedifference in bond behaviour was reflected in the theoretical work by a frictional bondstrength criterion for smooth bars and a splitting or shearing criterion for deformed bars.P, P. • AP,P,JA.Chapter 2. Literature Survey^ 31 ;VA.•(a) Initial stress (b) Cast concrete^(c) Initial bar stressP,P.Figure 2.9: Testing Technique for Simulating Uniform Bond Stress (after Abr-ishami and Mitchell [48])Chapter 2. Literature Survey^ 322.1.3.2 SummaryA briefly summary of these pull -out investigations is as follows:1. A reasonable measure of the anchorage length of a bar embedded in concrete couldbe obtained from the pull-out test.9. The pull-out tests emphasized the need for a particular length of bar (anchoragelength) from the point of maximum tensile stress to avoid pull-out.3. The pull-out tests provided an approximate indication of what happened adjacentto any crack in the concrete.4. The drawback of the pull-out test as a standard was that the compressive stressin the concrete complicated the stress conditions and inhibited tension cracking inthe con crete.2.1.4 Bond Tests with Fiber Reinforced Concrete or Coated RebarsThe use of short, randomly distributed fibers in concrete is relatively recent. The role ofthese fibers in improving the crack resistance and the \"ductility\" of concrete has recentlybeen reviewed (Bentur and Mindess [50]). Considerable research has been carried outin the last two decades to evaluate the response of these fiber reinforced composites,including the bond behaviour between the steel bar and fiber reinforced concrete matrix.Swamy and Al-Noori [51] were the first to report improved performance in the anchor-age bond of deformed bars embedded in steel fibre reinforced concrete. Their experimen-tal work consisted of pull-out tests on steel-fiber reinforced specimens. The steel fibersChapter 2. Literature Survey^ 33used were of the round straight type and had a length of 25 mm (or 50 mm) and a diam-eter of 0.40 mm. (or 0.50 mm). Two different fiber contents, 3.5% and 7.0% (by volume)were used. Based on the bond stress-slip relationship, they found that the anchoragebond strength of fibre reinforced concrete was 40% higher than that for plain concrete.Further, the mode of failure was found to be different in the two cases. The plain concretespecimens showed greater cracking and wider cracks than the fiber reinforced ones. Thefailure in the latter case was observed to take place more gradually.Yerex, Wenzel and Davies [52] carried out two series of tests to investigate the effectsof polypropylene fiber reinforcement on the bond between concrete and conventional mildsteel reinforcement. The first series of tests investigated the differences in the bond stress-slip relationship using the ASTM Standard Test Method (ASTM C234-71), whereas thesecond series of tests was designed to indicate changes in the transfer length of the severaldifferent concrete mixes and mild reinforcement combinations. Two polypropylene fiberlengths (60 and 90 mm), four fiber contents (0, 0.014, 0.050 and 0.086 /b/ft 3 ) 2 , and twowater-cement ratio (0.44 and 0.65) were used. The results showed that the addition ofpolypropylene fiber reinforcement does not adversely affected the bond strength and thatneither increasing the fiber content in the mix nor increasing the fiber length improvedperformance with regard to bond strength or transfer length.Recently, epoxy-coated reinforcing bars have been used in the construction of someconcrete structures which are expected to be exposed to corrosive conditions. An impor-tant consideration in the use of epoxy-coated reinforcing bars is the effect of the epoxycoating on the strength of the bond between the reinforcing bar and the concrete. Cliftonand Matey [53] carried out a series of pull-out tests with nine different epoxy coatings'They are equivalent to 0%, 0.025%, 0.09% and 0.15% (by volume), respectively.Chapter 2. Literature Survey^ :34and one polyvinyl chloride coating. In the tests, increasingly higher loads were applied toreinforcing bars embedded in concrete until the bond strength between the bar and theconcrete was exceeded. The results indicated that certain epoxy-coated reinforcing barscould have satisfactory bond strengths. More recently, Treece and .Jirsa [54] reported theresults of their study on the bond of epoxy coated reinforcing steel. The influence of barsize, concrete strength, casting position, and epoxy coating thickness on bond was con-sidered. These tests were performed on two sizes of beams, using an inverted third-pointloading. Reinforcement was spliced in the constant moment region at midspan. It wasreported that in the series in which the steel did not yield, epoxy coated reinforcementdeveloped only 66 % of the bond stress developed in uncoated steel. Cracks widths weregreater in the specimens with coated bars than in those with uncoated bars. The speci-mens with epoxy coated rebars had fewer cracks than those with uncoated rebars. Clearyand Ramirez [55] studied the bond of epoxy coated reinforcement in slab-type members.Tests were conducted on four series of specimens. All reinforcement came from the sameheat and had a spiral deformation pattern. The thickness of epoxy coating was about9.0 mil. The specimens were loaded in an inverted third-point loading with a 1.2 in,shear span and a 1.2 in constant moment region. Their study found bond ratios (theratio of the bond stress in coated steel to that in uncoated steel) to vary from 0.82 to0.95. Wider cracks were found. They concluded that if the hypothesis of increased ribbearing forces with epoxy coated reinforcement was correct, it was likely that splittingcould occur with epoxy coated bars at cover-to-bar diameter ratios greater than 3, whichhas recently been suggested in the ACI Building Code [7].(liapter 2. Literature Survey^ 352.2 Bond Behaviour under Dynamic Loading2.2.1 Bond Behaviour Under Cyclic LoadingStudies of repeated (or cyclic) bond tests are relatively more recent (after 1970).Takeda, Sozen and Nilson [56] were among the first to investigate the response of re-inforced concrete to simulated earthquakes. They observed that the stiffness and theenergy absorbing capacity of the reinforced concrete test specimens changed consider-ably throughout the duration of the simulated earthquakes. Important contributionsbased on pull-out tests under cyclic loadings were made by Hassan and Hawkins [57],Viwathanatepa, Popov and Bertero [58], Hungspreug [59], and many others.In 1973, Morita and Kaku [60] reported on the effect of the load history on thelocal bond stress-slip relationship from push-in and pull-out tests of specimens havingthe reinforcing bar bonded to the concrete over a short length. They concluded that thedeterioration of local bond depends on the magnitude of the previous maximum local slip;the larger the previous slip the greater the reduction in bond stress at lower levels. Theyalso proposed a model for a local bond stress-slip law, based on which the applied loadversus deformation characteristics of reinforced members could be predicted. However,the application of a single bond stress-slip law for every point along an anchorage lengthseemed to be a handicap to the model.Rehm and Eligehausen [61] tested the influence of repeated loading on deformed barswith a diameter of 14 nim and an embedment length of 42 mm (three times the diameter).Their conclusion was that repeated loads affected the bond in much the same way as thedeformation and failure behaviour of unreinforced concrete; they also accelerated theChapter 2. Literature Survey^ 36deformations as compared with a. sustained load.Edwards and Yannopoulus [62] also tested the influence of repeated loading. Theytested deformed bars of d = 16 mm with an embedment length of 2.4 d. They concludedthat the effectiveness of bond depended mainly upon the given stress level and the mag-nitude of the previous peak stress, and to a lesser extent upon the number of cycles. Thebond stress-slip curves under repeated loading were characterized by residual slip at zeroload and hysteresis loops formed by the loading and unloading paths. The hysteresisloops shifted by a. small amount during each cycle, but this shift tended to diminish withthe number of cycles applied.Perry and Jundi [63] tested, by repeated loading, on eccentric pull-out specimens, thedistribution of bond stresses along a deformed bar of d = 25 mm. Their conclusion wasthat the peak bond stresses tended to shift from the loaded end of the specimen to theunloaded end as the number of cycles of loading and unloading increased. This redis-tribution of stresses tended to become stabilized after several hundred cycles. This wascontrary to what Rehm [61] had calculated from his short embedment length tests; fromhis results he concluded that this redistribution of stresses would not become stabilizedbefore a. million cycles.Panda. [64], and Spencer, Panda and Mindess [65] studied the effect of reversed cyclicloading on the bond of deformed bars in plain and SFRC (steel fibre reinforced concrete),and also the cracking in the concrete surrounding the reinforcing bar. They found that:1. The mode of failure and the behaviour for plain and SFRC specimens appeared tobe different. SFRC specimens exhibited greater resistance to crack formation andpropagation than the plain concrete ones.Chapter 2. Literature Survey^ 372. No significant decrease in bond stress was observed with a small increase in thenumber of cycles under a. constant stress level, while an increase in peak stress levelproduced a significant reduction in bond stress in subsequent cycles.3. Under reversed cyclic loading with only a few loading cycles, the anchorage bondstrength of deformed bars was found to be about 20% to 30% higher in steel fibrereinforced concrete than in plain concrete.In his later research work, Panda found [66] that:1. The loading history had a significant effect on the bond deterioration.2. The specimens with steel fibers exhibited much better anchorage bond character-istics than those with no fibers. The steel fibers were found to be effective inretarding the rate of bond degradation under multiple cycles of reversed loading.3. The surface condition of the rebar had a vital influence on the bond behaviour: thepresence of grease on the reinforcing bar reduced the bond effectiveness drastically.4. An internal diagonal crack could initiate in the concrete at a very low level ofthe applied stress. This cracking caused a reduction in stiffness of the concretesurrounding the reinforcing bar.In the \"State-of-Art-Report: Bond under Cyclic Loads\" by ACI Committee 408 [67],the main factors affecting bond behaviour under cyclic loads are considered to be:1. Concrete compressive strengthChapter 2. Literature Survey^ 382. ('over and bar spacing3. Bar size4. Anchorage length5. Rib Geometry6. Steel yield strength7. Amount and position of transverse steel8. Casting position, vibration, and revibration9. Strain (or stress) range10. Type and rate of loading11. Temperature12. Surface condition (coatings)All parameters that are of importance under monotonic loading are also of importanceunder cyclic loading. In addition, however, bond stress range, type of loading (unidirec-tional or reversed, strain or load controlled), and maximum imposed bond stress are ofgreat importance under cyclic loads. The bond behaviour under the high-cycle fatigueloading is different from the low-cycle loading. Under low-cycle loading, the variousobservations can be summarized as follows:1. The higher the load amplitude, the larger the additional slip, especially after thefirst cycle. Some permanent damage seems to occur if 60% to 70% of the staticbond capacity is reached.Chapter 2. Literature Survey^ 392. When loading a bar to an arbitrary bond stress or slip value below the damagethreshold (about 60% of ultimate) and unloading to zero, the monotonic stress sliprelationship for all practical purposes can be attained again during unloading. Thisbehaviour also occurs for a large number of loadings, provided that no bond failureoccurs during cyclic loadings.3. Loading a bar to a bond stress higher than 80% of its ultimate bond strength willresult in significant permanent slip. Loading beyond the slip corresponding to theultimate bond strength results in large loss of stiffness and bond strength.4. Bond deterioration under large stress ranges (greater than 50% of ultimate bondstrength) cannot be prevented, except by the use of very long anchorage lengthsand substantial transverse reinforcement. Even in this case, bond damage near themost highly stressed area cannot be totally eliminated.2.2.2 Bond Behaviour Under Impact LoadingWhile there is an extensive literature on static bond tests, there is little experimentalwork on the bond between concrete and steel reinforcement under dynamic loading, withrather contradictory results (Mindess [14]).Concrete is a strain rate sensitive material. Generally its strength (compressive,tensile. flexural and shear strength) increases with higher loading rates, especially underimpact loading (Mindess et al [68, 69, 70]). Since the bond strength depends, to a greatextent, upon the strength of the concrete surrounding the rebar, the loading rate shouldhave a considerable effect on the bond behaviour. Also, there is some indication thatcrack velocities in concrete are proportional to the rate of loading (Mindess [71], Shahchapter 2. Literature Survey^ 40[72]). On the other hand, the presence of reinforcement, either in the form of fibersor of continuous bars tends to reduce the crack velocity (Mindess [73]), which, in turn,improves the bond strength. The effects of loading rate on the bond behaviour involvecomplex mechanisms. Test techniques for high rates of loading are far more difficult thanstatic testing (Bentur et al [74]).Hansen and Liepins [75] were the first to study the behaviour of bond under impactloading. They tested deformed bars under static and impact loading under conditionsin which splitting failures were inhibited. They used bars of d = 12.5 mm with anembedment length of 4d. The minimum raise time of the load was about 10 20 ms.The tests showed that the local static bond strengths might be as high as 0.75 L.', butthat under single pulse dynamic loading at high strain rates this strength increases toj; (cylinder strength). They concluded that for all practical lengths of embedment ofbars, steel failure might be expected under both static and dynamic loading. Bars loadeddynamically would carry a larger load than bars loaded statically. They ascertained thatthis increase in carrying capacity was due solely to the increase in steel strength underdynamic loading.In 1976 Hjorth [76] published the results of pull-out tests under impact loading. Hetested the bond resistance of plain and deformed bars of d = 16 mm, with an embedmentlength varying from 16 to 160 mm, i.e., 1 10 d. The dimensions of the test specimensare shown in Fig. 2.10 He used an electro-hydraulic loading system with load controland varied the time to failure from 500 s to 5 ms. The compressive strength of theconcrete was 24 ti 29 MPa. Because of the relatively high ratio of the wavelength of theloading pulse (about 100 m, see Fig. 2.11) to specimen size (0.1 ,-- 0.2 m) a quasi-staticapproximation of the result was justified.concrete cilinderChapter 2. Literature Survey^ 41Figure 2.10: Pull-out Specimens for Impact Test (after Hjorth [76])\\^115) / 20/ t(rris)Figure 2.11: Loading Pulse of Hjorth's Impact Test [76]Chapter 2. Literature Survey^ 42He studied the following:1. The influence of the bond stress rate -i- on the maximum bond resistance;2. The influence of increasing loading rate on the local bond stress-slip relationship:3. The maximum bond resistance if a connective constant loading (see Fig. 2.12) actsfor a time t d and4. The influence of increasing loading rate on the bond stress distribution.In the case of plain bars he found scarcely any influence of the loading rate. Thiscontrasted with deformed bars, for which he found a significant influence of the loadingrate. Some results for deformed bars are shown in Fig. 2.13.For both small and large displacements, bond resistance increased with increasingloading rate. This was in good agreement with the influence of the loading rate on theconcrete compressive strength. For this reason Hjorth explained the influence of theloading rate on bond resistance in terms of the deformation behaviour of the concreteunder the ribs.In Fig. 2.14, a typical bond stress-slip relationship is given, at different loading rates;note that the displacements are on a logarithmic scale. Hjorth remarked that the curvetended to undergo a parallel shift with increasing loading rate. A great difficulty, however.in the interpretation of his results was the rather wide scatter.An important conclusion was that the bond resistance increased by about 30% ina test with a loading time of 5 ins; this decreased to about only 10% if a connectiveconstant loading also acted for 10 ins (see Fig. 2.12).Chapter 2. Literature Survey^ 43tdyn istat2dyn stat2--failure1 1failure5^10^15t(ms)1^1^15 10^15t (ms)Figure 2.12: Influence of a Connective Constant Loading of 10 ms on the BondResistance (after Hjorth [76])max tf c■^■■5^ ■^■4 s^III^■■^a a^■1^a■3^ IN■B St 42/50 RK, d=16 mm1102 lv=112mm) io-5^10-`^10-3^10 -2^101^10 0^1Ct (1•1/m m 2 ms)0.00Figure 2.13: Influence of the Loading Rate on the Bond Resistance (afterHjorth [76])Chapter 2. Literature Survey^ 44B St^42/50 RK, c1=16I v =112mmI.--t>---t<0.550IN/mm2 msN/mm 2 msI//IP.■fR.0079...i/106(mm)Figure 2.14: Influence of the Loading Rate on the Bond Stress-Slip Relationship(after Hjorth [76])He also tested two specimens with an embedment length of 48 cm, with a rise timeof the load of 50 ms. The steel stresses were measured with 8 strain gauges which weremounted on the bar. From these tests Hjorth concluded that the displacements of thebar decreased with increasing loading rate, but a fundamentally different bond stressdistribution was not found.The results of the above investigations were in reasonable agreement with the resultsof Hansen and Liepins [75].^-Vos and Reinhardt [77] carried out a series of bond tests under impact loading. Theydeveloped a test specimen in which a central reinforcing bar was embedded over a lengthof 30 mm. Both smooth and deformed bars had a diameter of 10 mm, and the concretehad several compressive strengths (23, 45 and 55 Mpa). The impact tests were carriedout using the \"Split Hopkinson Bar\" equipment. In these tests failure was reached in0.6t/fcQ50.40.30.20 .100.01^0.1^1Chapter 2. Literature Survey^ 45less than 10' second (1 ins). To have a reference for these results, static tests were alsocarried out using electro-hydraulic testing equipment with load control. In these tests,failure was reached in about :300 ms and 60 sec, respectively.It was found that for smooth bars, the loading rate had no particular effect on themaximum bond resistance or the shape of the bond stress vs. displacement relationships.However, for deformed bars, bond resistance increased markedly with the loading rate.The following expression was obtained from a statistical analysis of the data:WhereTdyn^(TdynTstat^Tstat0.7(1-2.56)(fc )0.8 (2.11)Tdyn = bond stress under dynamic loadingTstat = bond stress under static loadingTdyn = bond stress rate under dynamic loadingTstat — bond stress rate under static loading= local relative displacement of the reinforcing element= compressive strength of concreteThey concluded that the influence of the loading rate on the bond resistance of de-formed bars must be explained in terms of the shearing mechanism causing the bondforces, i.e., for deformed bars failure was due to the local crushing of the concrete by thebar deformations. In this mechanism the concrete strength and stiffness were importantChapter 2. Literature Survey^ 46parameters. The results of the short embedment tests were translated to a long embed-ment length. The conclusion reached was that for increasing loading rates, the stiffnessof the disturbed zone increased was reached.Takeda [78] found that the strain rate sensitivity of concrete led to two different effects:on the stress-strain relationships, and on the fracture criterion. The distributed area ofstrain was much narrower under dynamic loading than under static loading. This couldcause brittle fracture of the reinforcement in reinforced concrete structures, because thedeformation was limited to only a short length of the reinforcing bars. Indeed, Bentur,Mindess and Banthia [79] and Banthia [80] showed that, under certain circumstances, thesteel reinforcement itself might fail under impact loading of reinforced concrete beams.The enhanced concrete-steel bond limited the deformations to the small area under thepoint of impact, leading to ductile fracture of the steel.According to Mindess [14, 81], the bond strength appears to be strain-rate sensitive.However, dynamic (impact) loading cannot be considered simply as an extreme case ofhigh stress rate application, in part because the complex energy transfer mechanismsassociated with impact loading appeared to be different from those under normal, staticloading. Thus, it is not possible to predict the behaviour of concrete under impact loadingon the base of quasi-static tests.No further investigations on pull-out tests on plain and deformed bars with a shortembedment length at high rates of loading have been found in the literature.Chapter 2. Literature Survey^ 472.2.3 SummarySome important conclusions could be drawn from the literature reviewed that dealingwith bond behaviour under dynamic loading:1. The bond behaviour under dynamic loading was quite different from that understatic loading. Both loading history and loading rate had significant effects on thebond behaviour. While cyclic loading might cause a much greater reduction in bondstrength than monotonic loading, impact loading might increase bond strength overthat of static loading.2. The loss in bond resistance under cyclic loading was due to a deterioration in thestress transfer mechanism, caused by inelastic deformation, cracking in the concreteetc.3. The shearing mechanism (rib bearing against the concrete) was the main mechanismfor deformed bars. The increases in the strengths of both steel and concrete with anincrease in loading rate may contribute to the higher bond resistance under impactloading.4. The strain distribution along the reinforcing bar was the most important parameterfor understanding the bond phenomenon. Dynamic loading caused much morecomplicated strain distribution than did static loading.5. The specimens with steel fibers exhibited much better anchorage bond characteris-tics than those with no fibers. This was true for all types of dynamic loading. Theenergy absorbing capacity of a specimen was more than doubled when it containedsteel fibers.Chapter 2. Literature Survey^ 486. One of the most important advantages of steel fibers was the increase of resistanceto crack formation and crack propagation. Unfortunately, adding steel fibers to theconcrete complicated the study of the bond mechanism.7. An analytical study would be helpful for a better understanding of the bond be-haviour under dynamic loading.2.3 Analytical Investigation of Bond Behaviour2.3.1 IntroductionThe extensive experimental investigations undertaken to study the bond behaviour andthe stresses produced clue to bond under different loading condition have been reviewedin the previous sections. In these investigations stresses in the bars and in the concretewere found by means of strain gauges mounted on the reinforcement and on the concretesurface, respectively. Bond stresses were obtained from the difference in adjacent strainreadings or from the slopes of the steel stress curves and, therefore, many strain gaugesand good control of variability were necessary to obtain bond stress values. Concretestresses could only be obtained at some distance from the reinforcing bar and a concretestress distribution had to be assumed in order to calculate the concrete stresses or dis-placements at the interface. The uncertain location of cracks made the experimentationdifficult. Most of the time concrete deformations were averaged over a certain gaugelength which could include many transverse cracks. The relative displacements at theinterface between steel and concrete were derived either from measurements at the endof the test specimen or by indirect means.dX2d 2 z = OA' (2.13)Chapter 2. Literature Survey^ 49In spite of much useful information obtained from these investigations, there are stillmany unanswered questions. Since there are so many variables which affect bond be-haviour, it is difficult to consider all or even a majority of them in any one experimentalprogram. The correlation of data for predicting bond behaviour from different exper-imental investigations is also questionable, because of the variable nature of concretebehaviour. Efforts have thus been directed towards finding a solution to the problem ontheoretical and analytical bases.2.3.2 Theoretical WorkRehm [82] treated the question of bond deformation theoretically by considering anon-linear bond stress-slip relationship determined from the experimental phase of hisinvestigation [44]. He concluded, on the basis of experimental work, that a bond dependedupon the rib height, the spacing and the bar size. Two of the formulae he developed were7G = FR43.A'C\"^ (2.12)andwhere T G is the bond stress,^is the slip of steel with respect to concrete on theinterface, and C' is the compressive strength of concrete; the other parameters, FR, 43',o and k were determined either by the geometrical and mechanical properties of testspecimens, or by a statistical analysis of the experimental data.The above \"fundamental law\" of bond and the differential equation of slip were usedChapter 2. Literature Survey^ 50to determine the distribution of slip, the steel stress, and the bond stress along therebar. It was concluded that the greatest value of slip resistance, in the case of deformedbars, was determined by the shear strength of the concrete. It was also demonstratedby this analysis that if the fundamental law of bond was known the distribution of thedisplacements and the stresses in a member could be predicted in advance.Odman [83] presented a theoretical interpretation of the results obtained by .Jonsson[84] from tests on concrete prisms provided with central reinforcement and subjected totension. Jonsson had indicated that bond stress was a function of slip. Odman deriveda formula expressing the crack width as a function of the steel stresses. The differentialequation of slip wasd2(x )^,E 0(1 + np) T(x)^ (2.14)dx 2^EsAswhere x is the distance from the point of zero slip, (x) is the relative slip of the sectionat x, and r(s) is the bond stress at the section considered; other parameters in the aboveequation are the geometrical and mechanical properties of the test specimens.Eq. 2.14 was derived on the assumption that the bond stress was a function of slipalone. But, as was pointed out by Kuuskoski [85], the bond stresses depended also onthe level of steel stress, the embedment length, the diameter of the rebar, the ratio ofreinforcement, the concrete strength, etc. The theoretically obtained values of slip andsteel stress at a crack were compared with the experimental values of .Jonsson. Theagreement between them was found to be closer for smooth bars than deformed ones.Chapter 2. Literature Survey^ 51Brows [86] presented a two dimensional stress analysis of reinforced concrete mem-bers by modelling the behaviour of tension and flexural members. This analysis wasbased upon the assumption that the force transmitted from the reinforcement to theconcrete could be represented as loading on the end faces of the concrete element be-tween two adjacent primary cracks. In this manner, the reinforcement was removed fromfurther considerations and the concrete was treated as a homogeneous and isotropic elas-tic medium. Results showed that high tensile stress in the concrete occurred in the area.between two adjacent tensile cracks.2.3.3 Fracture Mechanics and the Finite Element MethodIn addition to the theoretical investigations described above, some other analytical ap-proaches using Fracture Mechanics and the Finite Element Method have been developedover the past two decades. These approaches can be used to determine, more accurately,quickly and economically, the internal stress distributions in the reinforcement and theconcrete. The introduction of fracture mechanics to the analysis of bond behaviour helpsto understand the physical phenomena occurring at and around the reinforcing bar. Thishas been made possible by the development of high speed digital computers.Bresler and Bertero [87] carried out analytical investigations of a cylindrical specimen.This model was selected to simulate the tensile region of a cracked flexural member. Thefinite element analysis was carried out using two different models: a linear elastic model,and a modified \"boundary layer\" model. In the modified model the effects of inelasticdeformations and fracture of concrete adjacent to the concrete-steel interface were studiedby considering a \"homogenized boundary layer\" in which the elastic constant for thematerial was reduced. In both models, it was assumed that:Chapter 2. Literature Survey^ 521. No slip occurred at the interface; and2. Only the tensile load applied to the rebar was considered.Results obtained included the distribution of displacements, the longitudinal, trans-verse, and circumferential stresses and also the principal stresses. It was revealed thata high local stress existed at the steel-concrete interface near the end of the concreteprism. The high intensity of this stress, even at a low level of steel stress, would causelocal fracture and inelastic deformation. The boundary layer solution indicated that slipoccurs at the interface and should be considered in analysis, contrary to the assumptionabove.Lutz [27] made use of an axisymmetric finite element to study the stresses and defor-mations that occur in the vicinity of reinforcing bars after transverse cracks have formed.A short cylinder of concrete containing a concentric bar, in which both ends of the steelwere given a uniform deformation, was used to model the conditions between two flexuralcracks. The anchorage zone stress and deformation situation was modelled by a longercylinder in which one end of the bar was given a uniform displacement while the cylinderwas held along its outer cylindrical surface. The flexural zone stresses were calculatedunder many different circumstances: before or after cracking, allowing slip or separation,and so on.The stresses before cracking were quite small and of a uniform nature. The forma-tion of cracks produced large changes in these stresses. High bond stresses and tensileadhesive stresses were observed near the transverse cracks in the perfect bond base. Themagnitudes were such that separation of the concrete from the steel occurred over alength about two to three times the diameter of the bar from the face of the cracks. DueChapter 2. Literature Survey^ 53to the inclination of the ribs, this separation caused some slip to occur and producedhigh circumferential tensile stresses in the concrete near the transverse cracks. The cir-cumferential stresses were more than enough to initiate splitting cracks. For the analysisallowing slip and separation it was observed that the occurrence of slip modified thestress distributions to a significant extent. It relieved the bond stress which producedstress concentrations near the transverse cracks.The analyses were conducted on the following three models to represent differentconditions in the anchorage zone:1. There was perfect bond between the steel and the concrete;2. There was separation of the steel and concrete until the tensile adhesive stressbecame zero; and3. An experimental bond stress-slip relationship base on single rib tests by Lutz [27]was used.The first elastic solution showed that very large adhesive stresses were required toprevent separation at the interface near the loaded end. Thus, separation would occurat small loads. In the second solution separation over a distance two and half times thebar diameter was permitted. It was discovered that the bond stress and the circumfer-ential stress were exceptionally high. The third solution implied that the slip caused asignificant reduction in the stress concentration near the loaded face. The loaded endslips obtained from this solution compared well with the experimental results.Gergely, Gerstle and Ingraffea, [88] and Gergely, Ingraffea, Gerstle and Saouma [89]used linear elastic fracture mechanics principles to determine cracking behaviour at theChapter 2. Literature Survey^ 54steel-concrete interface. They found that this approach was inadequate when the analyt-ical results were compared with experimental data. They focused on radial, secondarycracking and found that this cracking did not follow the principles of linear elastic frac-ture mechanics. Subsequently, nonlinear fracture mechanics theories were used. Theymodelled the stresses acting between the sides of the crack through the use of interfaceelements. These elements were automatically inserted as the crack tip advanced in theprocess of finite element analysis. The stiffnesses of the interface elements were changedin each iteration according to a stress-COD (crack opening displacement) law which wasprogrammed. Finally, a \"tension-softening\" finite element was proposed. This elementlumped all bond-slip behaviour into a single nonlinear finite element. It provided a sig-nificant simplification in the finite element modelling of bond-slip in reinforced concrete.Yankelesky [90] presented a new model for bond action between uncracked concreteand a deformed bar. Concrete resistance was provided by a. mechanical system whichconsisted of inclined compressive disc elements normal to the bar axis, as shown inFig. 2.15 and longitudinal tensile members. The kinematics of the system was analyzed,yielding a second order differential equation with the bar tensile force as the variable. Thesolution showed an exponential decay in the stress and strain in the steel bar, approachinga constant value which depended on the relative stiffnesses of the concrete and the steel.Coefficients were then analytically calculated as a function of geometric and mechanicalproperties. Stress and strain distributions in the steel bar were calculated and the resultswere compared with the test data. He found good correspondence between measuredand calculated strain distributions along the steel bar at stresses below 160 MPa. Athigher stresses, calculations predicted a sharper decay in stress than that measured. Heconcluded that this discrepancy might result from the initiation of internal cracks andsecondary cracks which reduced system stiffness.Chapter 2. Literature Survey^ 55In another paper [91] Yankelevsky proposed a new finite element for bond-slip anal-ysis. This was a one-dimensional model which was based on equilibrium, and the localbond stress-slip law was developed (see Fig. 2.16). The relationship between the axialforce and the slip at the element node was expressed through a stiffness matrix. Theglobal stiffness matrix was then assembled, and the solution yielded the slip, strain andstress distributions along the steel bar. The nonlinear bond stress-slip relationship ledto an iterative technique which was found to converge rapidly. The predictions werecompared with experimental results of monotonic and push-pull tests, and a very goodcorrespondence was found.heuser and Mehlhorn [92] compared different approaches for bond modelling betweenconcrete and reinforcement using the finite element method. They indicated that specialinterface elements were required for solving this problem. The behaviour of the elementsand the quality of the results were influenced mainly by the displacement function of theelements, the density of the element mesh, and the bond stress-slip relationship. Theyinvestigated the influence of the displacement functions of two interface elements, theBond-Link-Element and the Contact-Element (see Fig. 2.17), not only by finite elementcalculations but also by energy considerations. They demonstrated the superiority of acontinuous bond slip function to the bond link element. It was shown that a realisticanalytical bond model required the consideration of local influences. An average bondstress-slip relationship was not suited for a detailed analysis.Rots [93] introduced a 6-noded bond-slip element including the rebar (see Fig. 2.18).The constitutional behaviour of the interface was described by a diagram which relatedthe tangential bond traction t t to the relative tangential displacement Au and a dia-gram which related the normal (radial) bond traction t„ to the relative normal (radial)Chapter 2. Literature Survey^ 56Figure 2.15: Geometry of a Typical Disc for Bond Model (after Yankelesky[90])U)cc TprnO0 rOru$l y^ Sy LSLIPFigure 2.16: One Dimensional Element and Local Bond Stress-slip Law (afterYankelesky [91])Chapter 2. Literature Survey^ 57displacement Av. When unconfined situation was considered, an adequate model wasobtained by assuming the former diagram to be bilinear and the latter diagram to belinear, as shown in fig. 2.19. In confined situation (e.g. anchorage bond) this model wastoo simple and coupling between normal and tangential components should be included.He applied this type of bond-slip element to a slender beam that contained a dominantreinforcing layer and that failed in bending and found that the inclusion of bond-slipproduced a positive effect on the crack pattern in that it was less diffuse than it was forthe case of perfect bond. Furthermore, the inclusion of bond-slip led to primary cracksthat crossed the reinforcement in a correct way. He thought that a second advantageof the use of bond-slip element was that it offered the possibility of making a directdistinction between, for example, plain rebars and deformed rebars. He concluded thatthe inclusion of bond-slip elements was essential for the fracture mechanics analysis ofconcrete structures. A perfect bond assumption may be too coarse and conflicted withthe delicate fracture mechanics of individual cracks. Rots also studied the bond-slip rela-tionship by another approach [94]. In this approach, the bond-slip elements were omittedand the steel was modelled by continuum elements which were connected to the concreteelements via an interchangeable tying scheme in order to account for the mechanical in-terlock provided by the ribs (see Fig. 2.20). It was found that in a qualitative sense thepredicted cracking behaviour agreed surprisingly well with the experimental bond-crackdetections. He thought that this would lead to a better understanding of fundamen-tal issues like bond-softening and non-uniqueness of traction-slip behaviour along therebar-axis.bond-slip interfacereinforcing bar_degrees of freedom^■^iiiiiiMt^tiv ^r_^tGs -.is=E'tractions andrelative displacementsside I•••••••am+-m.Mw-maa.1.......•z.0^3^2^1liu...I—I-.Chapter 2. Literature Survey^ 58Y iXFigure 2.17: Two Types of Interface Elements for Bond Behaviour (afterMehlhorn et al [92])g.•1t^g.-1.i^....-1 4'1 1^ir.v6 side II 5^£1Figure 2.18: A 6-Noded Bond-Slip Elements (after Rots [93])Chapter 2. Literature Survey^ 59 t oa bAu^ v(a)Tangential traction versus tangential relative displacement.(b) Normal traction versus normal relative displacement.Figure 2.19: Constitutive Relations for Bond-slip Elements (after Rots [93])020kr336141^1 140 0414 14 1 14141 1410 100141414141414r041 1 14141 1410 14 1 1041 104 141 L14 041400004141 0410414100404/ 14100410414141 14 140 Frinn^04100 14 41 14141410041041 110004&r4r4r40 ■04 1414 10 1 140 104 /041 ■41404141AU1 104004141041414100 1041414141 10^r4r41410 100 1000 10410041004/004100 14 414 4^14►41 104 1414 1 14 /41 0414 / 10 14/0 100414►110/10011114 004 100 104 1414 100 /4►004►4104/0410 100000041000000414 41 14 14 OntPntial discreteprimary crackF.0 I• rigid steel-concrete connectionFigure 2.20: Finite Element Idealization of Tension-Pull Specimen (after Rots[94])Chapter 2. Literature Survey^ 602.3.4 SummaryA brief summary of analytical investigations on the bond behaviour is as follows:1. In order to derive related equations theoretically for the bond stress or the bond slipproblem, numerous assumptions were made about the stress distribution, and slipresistance distribution. Whether uniform, linear, or nonlinear, these hypothesesmight be quite different from the real conditions;2. It seemed very difficult to establish a general analytical equation which could reflectthe effects of all factors on bond and which could be applied to the general case ofthe bond problem;3. For a particular bond problem it was possible to find a theoretical solution aftermaking certain assumptions, and the results of the theoretical analysis could com-pare well with experimental values; generally speaking, there was closer agreementin the case of smooth bars rather than deformed bars;4. The finite element method of analysis combined with fracture mechanics has beensuccessfully in application to the study of bond behaviour; the development ofnumerical analysis and high speed computers enables the consideration of as manyvariables as desired;5. The accuracy of the fracture mechanics and finite element analyses depended uponhow well the characteristics of the element represent the conditions in the bond slipprocess; the behaviour of the steel-concrete interface element in transmitting stressby bond was one such important characteristic;Chapter 2. Literature Survey^ 616. There was little information available on the basis of which satisfactory bond stress-slip characteristics could be established. Previous work has either neglected thisimportant behavioral characteristic or simply used relationships which were de-veloped from experimental data (in most cases these data are insufficient) andempirical considerations;7. There was little experimental data on the bond behaviour of fiber reinforced con-crete or high strength concrete, which have great advantages in terms of mechanicalproperties and are now widely used in engineering practice; and8. There was very little study of the bond behaviour under impact loading usinganalytical approaches.2.4 ConclusionsExtensive experimental and analytical work has been carried out to study the bondbehaviour in reinforced concrete members. The experimental investigations have covered,in some detail, the factors influencing bond phenomena and have contributed considerablytowards the understanding of bond behaviour. The experimental investigations revealedthat bond stress in the desired bond stress-slip relationship was not a function of localslip alone. It was also dependent upon the values of steel stress, the embedment length,the diameter of the reinforcing bar, the reinforcement ratio, and the concrete strength,etc. It was seen, also, that the development of bond stress depended upon the regioninside the member in terms of the type of internal force.Various types of test specimens have been developed to study bond. Some of themsimulate quite closely the behaviour of reinforced concrete members for different loadingChapter 2. Literature Survey^ 62conditions and seem appropriate for further investigation.The prime advantage of adding fibers to the concrete matrix is to improve its tough-ness. Steel fibers improves the tensile strength, flexural strength, and shear strength ofthe concrete mixture, thus increasing the resistance to crack formation and crack propa-gation. Some previous investigations have shown a great improvement of bond strengthby the addition of steel fibers, especially for dynamic loading conditions. More extensiveresearch work should be carried out to study the effects of adding steel fibers on thebond behaviour. As a composite, fiber reinforced concrete is much more inhomogeneousthan plain concrete. Furthermore, it will no longer be a. continuous medium once thiscomposite has cracked. This makes it more difficult to study the bond problem of fiberreinforced concrete by conventional theories of mechanics or other analytical approaches.Recently, high strength concrete (with compressive strength over 85 M Pa) has foundmore and more applications in structural engineering. It could differ, in many aspects,from normal strength concrete. The differences in its microstructure and mechanicalproperties make many previous conclusions on bond behaviour, which were obtainedfrom specimens of normal strength concrete, inapplicable. No investigation on bondbehaviour with high strength concrete has been found in the previous literature.Both steel and concrete are strain-rate sensitive materials. Many conclusions havebeen drawn on the effects of loading rate on the mechanical behaviour of reinforcedconcrete members. Very little investigation, either by experimental methods or analyticalapproaches, has been done on the influence of loading rate on the bond phenomenon.An experimental program devised to investigate the bond behaviour, taking intoaccount the influence of all necessary variables, could be very complicated and expensive.Chapter 2. Literature Survey^ 63However, analytic approaches can provide solutions which are obtained more quickly. Thefinite element method combined with fracture mechanics has been proven to be a verypowerful tool to solve the bond problem.In this approach, many behavioral characteristics of the element, which are importantin reinforced concrete members, can be taken into account. The bond stress-slip rela-tionship between steel and concrete is an important characteristic. So far there has beennot enough information available from which the bond stress-slip characteristics couldbe derived. Experimental investigations to measure local bond stress and local slip areneeded to establish the desired characteristics.Theoretically, there will be a unique relationship between bond stress and slip at theinterface of a steel bar and concrete, of which the geometric and mechanical properties areknown. If an appropriate \"interface element\" can be developed by reasonable modellingof the constitutive laws of both materials and the criteria of cracking and crushing, itis possible to establish the bond stress-slip relationship analytically for any reinforcedconcrete member.The determination of the criteria for cracking, crack propagation and crushing in con-crete is an important aspect in any non-linear, three dimensional finite element analysis.With the application of non-linear fracture mechanics, the criteria based on the consider-ation of energy and energy release seem more reasonable than any other criteria, such asthose based on stress or strain conditions, especially for the strain rate-related problem.Also, no investigation by means of this approach has been found in literature.Chapter 3Experimental Procedures3.1 IntroductionThe two prime variables in the present study were local stress and local bond slip. Whilecracking and energy transfer were also investigated, they were not directly measured inthe experiments. The objectives of this investigation were to:1. design experimental models to obtain representative bond-slip relationships for pull-out and push-in tests under dynamic loading;2. develop instrumentation and techniques for the measurement of stress and slip;3. obtain bond-slip relationships from the experimental models;4. investigate the propagation of cracking in concrete during bond-slip process;5. investigate the transfer and balance of energy.64Chapter .3. Experimental Procedures^ 653.2 Specimen Preparation3.2.1 GeneralThe maximum weight of the hammer of the drop weight impact machine used was about:345.0 kg and the maximum drop height of the hammer was about 2.40 rat (details given inSection 3.3.1.2). In order to get as wide a range of loading rate as possible it was assumedthat a. drop height of 100.0 mm would completely push in or pull out the reinforcing barin the specimen. Some preliminary tests were carried out to determine the most suitabletype of the rebar and the corresponding embedment length. The results are given inTables 3.1 and 3.2. It can be seen from the results that in order for the reinforcing barto completely go through the specimen, the maximum embedment length was controlledby the push-in test of the steel-fiber reinforced specimen with deformed bar. It can alsobe seen that for the specimens with the deformed rebars, the diameters of which weregreater than 16.0 mm, a minimum drop height of 250.0 mm was needed to completelypush in the reinforcing bar. A CSA type No. 10 deformed bar (with nominal diameter11.3 711.711 ) was most suitable; the maximum embedment length was 63.5 mm for the steel-fiber reinforced specimen under a drop height of 100.0 mm. Therefore No. 10 deformedbar was chosen and the corresponding maximum embedment length of the reinforcing barin the concrete specimen was 63.5 mm (2.5 in). It was also found that this embedmentlength was sufficient for 5 strain gauges to be lined up along the bar (see Fig. :3.4 inSection 3.2.2.1). The purpose of this experimental investigation was to study the bond-slip relationship for pure pull-out and pure push-in failure. However, the preliminarytests showed that splitting failure would occur if there were no spirals provided in thespecimens. In order to prevent the specimens from splitting, two concentric 6.35 mmChapter 3. Experimental Procedures^ 66steel spirals. 63.5 mm and 127.0 mm in diameter were cast in the specimen.Table 3.1: The Maximum Embedments for Smooth Bars (Preliminary Tests)Diameter ofRebar(nun)Type ofConcreteMaximumEmbedment a^(mm)MinimumDrop Height(mm)Pull-out Push-in11.1^(7/16 in)Plain 114.3 101.6 50.0Polypropylene-fiber b 114.3 101.6 50.0Steel-fiber ' 101.6 88.9 60.016.0 (5/8 in)Plain 127.0 114.3 90.0Polypropylene-fiber 127.0 114.3 90.0Steel-fiber 114.3 101.6 110.019.1^(3/4 in)Plain 152.4 139.7 120.0Polypropylene-fiber 152.4 139.7 120.0Steel-fiber 139.7 127.0 150.0a For complete pulling-out or pushing-in of the reinforcing bar in the concrete specimenb Content = 0.5% (by volume)Content = 1.0% (by volume)The test specimens were chosen as concrete prisms 152.4 x 152.4 x 63.5 mm (5.0 x5.0 x 2.5 in) with either a 12.7 mm (1/2 in) diameter smooth bar or an 11.3 mm (7/16in) diameter (No. 10) deformed reinforcing bar centrally located in the specimen (Fig.3.2). The length of rebar at the push-in end was determined by two considerations:1. The possible maximum slip;2. The maximum length without buckling under impact loading.A theoretical calculation for the buckling of the rebar under the static loading gavevalues of the maximum length of 66.9 mm for a smooth bar and 49.7 mm for a deformedbar (see Appendix A). From the preliminary tests it was found that the maximum totalChapter 3. Experimental Procedures^ 67slip (the total displacement of the end of the rebar when the applied load dropped downto zero) was about 4.0 mm for a smooth bar and about 5.0 mm for a deformed bar.Considering that the striking head would go a bit further after being stopped by therebound supports (which consist of rubber pads) and the pneumatic brakes, the lengthof rebar at the push-in end was chosen as 50.8 mm (2.0 in) for all specimens, while thelength at the pull-out end was 76.2 mm (3.0 in) to suit the configuration of the pull-outtests (see Fig. 3.13 in Section 3.3.1.2). A photograph of the specimen with instrumentedrebar is shown in Fig. 3.1. The geometrical details are shown in Figs. 3.2 and 3.4.Figure 3.1: A Photograph of the Pull-out and Push-in SpecimensChapter 3. Experimental Procedures^ 68Figure 3.2: The Pull-out and Push-in SpecimensChapter 3. Experimental Procedures^ 693.2.2 Reinforcing Elements3.2.2.1 Smooth and Deformed BarsTwo different reinforcing bars, a smooth bar with diameter 12.7 mm and a deformed bar(CSA No.10, Grade 400) with nominal diameter 11.3 mm, were used. The deformationpattern and geometry, such as rib height, spacing, and so on, of the test bar are indicatedin Fig. :3.3.Standard tests were carried out to ascertain the mechanical properties of the rein-forcing bar under uniaxial tensile and compressive loads in an Instron universal testingmachine with a capacity of 150 kN. The results are given in Table 3.3.The stress-strain relationships of the smooth bar and the deformed bar under uniaxialloading are shown in Fig. :3.5 and Fig. 3.6, respectively. Compression tests revealedpractically the same relationship as tensile tests. The 6.35 mm (1/4 in) diameter steelspirals, made of hot-rolled steel, were cast concentrically in the specimen, with spiraldiameters of 63.5 mm and 127.0 mm, as shown in Fig. 3.7.1.5Chapter 3. Experimental Procedures^ 70All In mm12.5 1.3Figure 3.3: The Type No.10 Test RebarBrass coverRebarBrass cover3.0All in mm3.0A — A Strain gaugeChapter 3. Experimental Procedures^ 71Strain gaugeFigure :3.4: Test Rebar Instrumented with Strain GaugesChapter 3. Experimental Procedures^ 72Stress (Mpa)^sco^Straight Bar352320250200153100500^ ,^ 1 ^0 1,0 2,000^3,0:0^40^5,CO3Strain (micro)Figure 3.5: The Stress-strain Relationship of the Straight BarStress (Mpa)Deformed Bar •4033503C02502C0150102500 ^0 1,000^2,000^3.0Strain (micro) 4,020 LOWFigure 3.6: The Stress-strain Relationship of the Deformed BarChapter 3. Experimental Procedures^ 73Table 3.2: The Maximum Embedments for Deformed Bars (Preliminary Tests)Diameter ofRebar(min)Type ofConcreteMaximumEmbedment'^(mm)MinimumDrop Height(mm)Pull-out Push-in11.3 (No.10)Plain 88.9 76.2 90.0Polypropylene-fiber' 88.9 76.2 90.0Steel-fiber` 76.2 63.5 100.016.0 (No.15)Plain 114.3 101.6 200.0Polypropylene-fiber 114.3 101.6 200.0Steel-fiber 101.6 88.9 250.019.6 (No.20)Plain 139.7 127.0 320.0Polypropylene-fiber 139.7 127.0 320.0Steel-fiber 127.0 114.:3 380.0\"For complete pulling-out or pushing-in of the reinforcing bar in the concrete specimenb ( ontent = 0.5% (by volume)`Content = 1.0% (by volume)Table :3.3: Mechanical Properties of Steel BarsTypeof BarDiameter(Nominal)(nun)EffectiveArea(ulni2)ElasticLimit(MPa)YieldStrength(MPa)UltimateStrength(MPa)Young'sModulus(GPa)T a Smooth 12.7 126.7 200.5 286.5 :320.8 208Deformed 11.3 100.0 300.6 42:3.9 780.0 212C b S mooth 12.7 126.7 200.5 286.5 :320.8 208Deformed 11.3 100.0 300.6 423.9 780.0 212T = Tension6 C = CompressionChapter 3. Experimental Procedures^ 74Figure 3.7: The Two Spirals in the Specimen3.2.2.2 Instrumentation of RebarsExperimental measurement of strains along the reinforcing bars was necessary. Thiswas made possible by mounting strain gauges at various points along the rebar. Abouta quarter of the total number of reinforcing bars tested were instrumented with 5 pairsof strain gauges per bar to record the strain values at given points along the bar duringloading. Thus the strain distributions along the rebar and the stresses in the bar can bedetermined. In all, 200 bars (1 out of 4 or 6 in each set) were instrumented in this way.From the literature review, it was concluded that probably the best location of straingauges would be on the periphery of the test rebar [63]. The reinforcing bars for the testswere machined on diametrically opposite sides along their length to produce two groovesChapter 3. Experimental Procedures^ 75of 2.0 x 4.0 711,711. Provision was also made for placement of two thin copper strips ascovers for the grooves, by some slight additional machining on both sides of the grooves.as shown in Fig. 3.4.The strain gauges used in the test specimens were electric resistance gauges of thetype CEA-06-125UN-120 3 . Five pairs of strain gauges were mounted on diametricallyopposite sides of each test bar at a spacing of 15.9 77111i (center to center) as may be seenin Fig 3.4. This was intended to take care of the bending effect, if any, in the test barduring loading (see section 3.3.1.5 for the design details of the electric circuit for uniaxialstrain recording).To fix the strain gauges on the rebar, the grooves were sand-blasted, and then air-blasted to removed any dirt. Chlorothene NU was applied to remove grease chemically,followed by Conditioner-a and Neutralizer-5. After the surfaces were dry, the cementingmaterial, M-bond of type AE-15 adhesive, was applied in the appropriate places, thenthe strain gauges were affixed in the grooves. After that the rebar was placed in anelectric oven at 200°F for about 30 minutes. After being connected to lead wires bysoldering, the gauges were coated with M-Coat G to protect against weathering. Thena very thin layer of wax was applied to the surfaces to prevent the gauges from possibledamage during the test. Finally, the grooves were covered with strips of copper sheet.Both of the strips were held tightly by means of wires at intervals along the rebar. Eachlead wire was numbered to identify the strain gauge and its location along the length ofthe rebar.Strain gauges and other accessories were supplied by Micro-Measurement Division, MeasurementGroup Inc., Raleigh, North Carolina, U.S.A.Chapter 3. Experimental Procedures^ 763.2.3 Concrete Mix3.2.3.1 Compressive Strength and Basic Mix DesignThe design compressive strengths of the concrete were 40 MPa (normal strength) and75 MPa (high strength) at 28 days. The cement used in the concrete specimens wasCSA Type 10 Portland cement. The fine aggregate was clean sand (< 4.75mm) andthe coarse aggregate was pea gravel (4.75 ti 10.0 mm). The water-cement ratio for thenormal strength concrete was 0.50 and for the high strength concrete was 0.33. For thehigh strength concrete, silica fume' was added to increase the strength of the concreteand 0.0 — 12.0 ml of superplasticizer 5 per kg of cement was added to the mix to improvethe workability. An air-entraining admixture' was also used for all the concrete mixes toincrease the workability. The basic mix designs are given in Table 3.4.3.2.3.2 Added FibersIt was postulated that fibers added to the concrete matrix would improve the anchoragebond capacity. In the present research, two types of fibers were used. One type wasfibrillated polypropylene fibers which were 40.0 mm long with a diameter of 0.1 mm.The aspect ratio was 400 and its density was about 900 kg/n7, 3 , as shown in Fig. :3.8.The other was steel fibers 8 with crimped ends. They were 30.0 mm long with a diameterof 0.5 mm, giving an aspect ratio of 60; they had a density of about 7800 kg/rn 3 . The4 Product, of Elkem Metals Company, Canada.'Product of Conchem Company, U.S.A.'Product of Martin Marietta Company, Canada.Produced by the Fibermesh Corporation, Chattanooga, Tennessee, U.S.A.Produced by Bekaert Steel Wire Corporation, BelgiumChapter 3. Experimental Procedures^ 77Figure 3.8: Polypropylene Fiberssteel fibers were made of strain hardened mild steel wires having ultimate strengthsranging from 1180 to 1380 MPa s. They were provided in collated form with a watersoluble sizing, so the fibers would disperse adequately when mixed with the concrete.The steel fibers are shown in Fig. 3.9. There were two different contents, 0.1 % and 0.5%, respectively, by volume, for the polypropylene fibers, and 0.5 % and 1.0 % for thesteel fibers. Some details of these two types of fibers are given in Table 3.5.3.2.4 Fabrication of Test SpecimensThe procedures outlined in CSA A 23.2-2C \"Making Concrete Mixes in the Labo-ratory\" and CSA A23.2-3C \"Making and Curing Concrete Compression and FlexuralTest Specimens\" were followed. The formwork for the concrete specimens was made ofplywood. Care was taken to prevent any leakage through the joints and to keep theform square and true. A pan-type concrete mixer with a capacity of approximately 0.18711 3 was used. All concrete ingredients were added in the order: coarse aggregate, sand,Information provided by the suppliersChapter 3. Experimental Procedures^ 78Table 3.4: Basic Concrete Mix Design (per in')Ingredient Normal Strength(40 MPa)High Strength(75 MPa)Type 10 Portland Cement (kg) 343.0 513.0Silica Fume (kg) 98.0Sand (< 4.75 mm)^(kg) 686.0 958.0Aggregate (4.75 ---, 10.0 mm)^(kg) 1200.0 635.0Water (kg) 171.5 201.0Air Entraining Admixture (ml) 70.0 100.0Superplasticizer a^(ml) 0 ---, 1715 1715 ,---, 6110Fibres(Polypropylene or Steel)Variable(See Table 3.5)Variable(See Table 3.5)\" The amount varied from 0.0 - 10.0 ml per kg of cementTable 3.5: Properties and Addition of FibersPolypropyleneFibreBaekart SteelFiberTensile Strength^(MPa) 600.0 1200.0Young's Modulus (GPa) 20.0 212.0Addition(kg/ura 3 )0.1% 0.9 -0.5% 4.5 39.01.0% 78.0Chapter 3. Experimental Procedures^ 79Figure 3.9: Steel Fiberscement (and silica fume) and water followed by two admixture: air-entraining agent andsuperplasticizer. In the case of the fiber reinforced concrete specimens, polypropylenefibers or steel fibers were added by shaking them in by hand. The concrete was mixed forabout 5 minutes. 4,nd then was placed into the formwork and compacted on a small vi-brating table, combined with rodding. Finally the specimens were finished with a troweland covered with plastic sheet. The forms were removed two days after casting and thespecimens were cured for a period of 28 days in a moist room and were stored there tilltesting.3.2.5 Properties of the Fresh and Harden ConcreteOnce the mixing of the concrete was completed, a slump test was carried out inaccordance with CSA A23.2-5C \"Slump of Concrete\". Test cylinders of 100 mmChapter 3. Experimental Procedures^ 80diameter and 200 nun in length were also cast from each mix. A summary of control testresults of fresh concrete is given in Table 3.6.Table 3.6: Test Results of Fresh ConcreteCompressiveStrengthTypeofconcreteWater-cementRatioSlump(mrn)Density(kg/m 3 )AirContent(%)NormalPlain Concrete 0.500 10 2380 5.0PolypropyleneFibre Concrete0.1% 0.500 10 2378 5.20.5% 0.500 10 2378 5.3SteelFibre Concrete0.5% 0.505 10 2450 4.41.0% 0.505 10 2470 4.4HighPlain Concrete o.329 10 2420 4.8PolypropyleneFibre Concrete0.1% 0.329 10 2420 4.90.5% 0.329 10 2420 4.9SteelFibre Concrete0.5% 0.330 10 2460 4.01.0% 0.338 10 2465 4.0Tests on the compressive strength, tensile strength, Young's modulus and the stress-strain relationship was carried out in an Instron universal testing machine in accordancewith ASTM (\"39-86 \"Test Method for Compressive Strength of Cylindrical ConcreteSpecimens\", ASTM C496-86 \"Test Method for Splitting Tensile Strength of CylindricalConcrete Specimens\" and ASTM C469-87 \"Test Method for Static Modulus of Elasticityand Poisson's Ratio of Concrete in compression\". There have been very few cases inwhich the dynamic elastic modulus has been used to study bond behaviour; thus, inthis study, the Young's modulus is actually a static, elastic modulus. The stress-strainrelationship test was limited to one dimension only. Since Poisson's ratio and the modulusof elasticity in shear were also needed in the analytical study (Fracture Mechanics andFinite Element Method approaches), they were calculated according to the stress-strainrelationship curve of the concrete. The formulas used for these calculation are given inChapter 3. Experimental Procedures^ 81Stress (Mpa)Ica ^so High Strength ConcreteTOSO5040ao2010Normal Strength Concrete0503^LOCO^1,530Strain (micro)2,0382^2,530Figure 3.10: The Stress-strain Relationship of ConcreteSection 4.3 in Chapter 5.The stress-strain relationships of the concrete for normal compressive strength andhigh compressive strength are shown in Fig. 3.10, and the other results of the mechanicalproperties of the hardened concrete are given in Tables 3.7 and 3.8.3.2.6 Summary of Test SpecimensAs described in the above sections. the experiments were carried out for two differentcompressive strengths of concrete (normal and high), two different fibres (polypropyleneand steel) and different fibre contents (0.1 %, 0.5% and 1.0%). These fiber contents werechosen because they lie within the range of the contents used in practice. There were alsothree different types of loading: static. dynamic and impact loading. For the dynamicloading there were two rates (low and high) and for the impact loading there were threeChapter 3. Experimental Procedures^ 82Table 3.7: Test Results of Hardened Concrete - Part ICompressiveStrengthTypeofconcreteCompressiveStrength(MPa)TensileStrength(MPa)NormalPlain Concrete 39.8 3.72PolypropyleneFibre Concrete0.1% 38.7 3.690.5% 37.8 :3.89SteelFibre Concrete0.5% 44.3 4.321.0% 46.5 4.41HighPlain Concrete 78.2 4.87PolypropyleneFibre Concrete0.1% 77.8 4.980.5% 78.3 4.79SteelFibre Concrete0.5% 82.6 5.251.0% 83.4 5.68Table 3.8: Test Results of Hardened Concrete - Part IICompressiveStrengthTypeofconcreteYoung'sModulus(GPa)Poisson'sRatioElastic Modulusin Shear '(MPa)NormalPlain Concrete 32.1 0.252 12.8PolypropyleneFibre Concrete0.1% :32.5 0.252 1:3.00.5% :33.4 0.251 13.3SteelFibre Concrete0.5% :38.2 0.277 15.01.0% 44.6 0.286 17.3HighPlain Concrete 43.2 0.251 17.3PolypropyleneFibre Concrete0.1% 46.4 0.252 18.50.5% 48.3 0.252 19.3SteelFibre Concrete0.5% 52.6 0.278 20.61.0% 57.9 0.291 99.4CalculatedChapter^Experimental Procedures^ 8:3rates (low, medium and high). These different loading rates were designed to induce awide range of bond stress rates. The definitions and the calculations of stress rate in therebar, a s , and the bond stress rate, it, are shown in Section 4.9 in Chapter 4. Table 3.9shows the different loading types in this experimental study.As a supplementary work to this study on bond behaviour, some specimens weremade with deformed rebars which were coated with epoxy. Liquid epoxy 10 was appliedto the rebar by brush in a single run with a thickness of about 0.2 to 0.3 min (9.0 to12.0 mil). The rebars were then cured at the room temperature for 3 days before beingcasted in the specimens.Table 3.9: Loading RateLoadTypeStress Rate TestingMachineSpeed ofCrosshead(7-nin/n/in)DropHeight(mum)Steel Bond(MPa/.^) (MPa/s)S a 10-7 ''' ^10 -5 0.5 • 10 -8 ,-- 0.5 . 10 -6 Instron h 0.05 ,--, 5.0M' 10 -5 --, 10 -3 0.5 . 10 -6 — 0.5 • 10 -4 5.0 --, 500.0 -1 d 10-3 ,---, 10 -1 0.5 • 10 -4 --; 0.5 . 10_ 2 Impact ' 3.0 — 500.0a StaticInstron Universal Testing MachineMedium Rated ImpactDrop Weight Impact MachineFor the push-in tests with deformed bars each set of specimens consisted of 6 samplesand for pull-out tests each set consisted of 4 samples. Tests with smooth bars were mainlyfor comparison, and each set only included 2 samples. For tests with epoxy coated rebars,each set consisted of 2 samples. One or two bars out of each set was instrumented withDynacare epoxy resin and hardener, produced by Industrial Formulators of Canada Ltd. Burnaby,B.C., Canadailapter 3. Experimental Procedures^ 845 pairs of strain gauges, depending on the types of loading and the rebar. Tables 3.10 to3.13 show the summary of the test specimens. Table 3.14 shows the summary of the testspecimens with epoxy coated rebar.Table 3.10: Specimens for Push-in Tests (Deformed Bars)Type of ConcreteLoadingRateConcreteStrengthNo. ofSpecimensper SetTotalLow Medium High N HPlain Concrete 1 1 1 6 12PolypropyleneFibre Concrete0.1% 1 1 1 6 120.5% 1 1 1 6 12SteelFibre Concrete0.5% 1 1 1 6 121.0% 1 1 1 6 12AlPlain Concrete 1 1 1 1 6 24PolypropyleneFibre Concrete0.1% 1 - 1 1 1 6 240.5% 1 1 1 1 6 24SteelFibre Concrete0.5% 1 - 1 1 1 6 241.0% 1 - 1 1 1 6 24/Plain Concrete 1 1 1 1 1 6 36PolypropyleneFibre Concrete0.1% 1 1 1 1 1 6 360.5% 1 1 1 1 1 6 36SteelFibre Concrete0.5% 1 1 1 1 1 6 361.0% 1 1 1 1 1 6 36TOT4L 360S - Static^111 - Medium^1 - Impact^N - Normal^H - HighChapter 3. Experimental Procedures^ 85Table 3.11: Specimens for Pull-out Tests (Deformed Bars)Type of ConcreteLoadingRateConcreteStrengthNo. ofSpecimensper SetTotalLow Medium High N HPlain Concrete 1 1 1 4 8PolypropyleneFibre Concrete0.1% 1 1 1 4 80.5% 1 1 1 4 8SteelFibre Concrete0.5% 1 1 1 4 81.0% 1 1 1 4 8MPlain Concrete 1 1 1 1 4 16PolypropyleneFibre Concrete0.1% 1 1 1 1 4 160.5% 1 1 1 1 4 16SteelFibre Concrete0.5% 1 - 1 1 1 4 161.0% 1 1 1 1 4 16/Plain Concrete 1 1 1 1 1 4 24PolypropyleneFibre Concrete0.1% 1 1 1 1 1 4 240.5% 1 1 1 1 1 4 24SteelFibre Concrete0.5% 1 1 1 1 1 4 241.0% 1 1 1 1 1 4 24TO TA L 240S - Static^M - Medium^1 - Impact^N - Normal^H - HighChapter 3. Experimental Procedures^ 86Table 3.12: Specimens for Push-in Tests (Smooth Bars)Type of ConcreteLoadingRateConcreteStrengthNo. ofSpecimensper SetTotalLow Medium High N HSPlain Concrete 1 1 1 2 4PolypropyleneFibre Concrete0.1% 1 1 1 2 40.5% 1 1 1 2 4SteelFibre ( oncrete0.5% 1 1 1 2 41.0% 1 1 1 2 4MPlain Concrete 1 1 1 1 2 8PolypropyleneFibre Concrete0.1% 1 1 1 1 2 80.5% 1 1 1 1 2 8SteelFibre Concrete0.5% 1 - 1 1 1 2 81.0% 1 - 1 1 1 2 8/Plain Concrete 1 1 1 1 2 8PolypropyleneFibre Concrete0.1% 1 - 1 1 1 2 80.5% 1 1 1 1 2 8SteelFibre ( oncrete0.5% 1 1 1 1 2 81.0% 1 - 1 1 1 2 8TOTAL 100S - Static^*1 - Medium.^I - Impact^N - Normal^H - HighChapter 3. Experimental Procedures^ 87Table 3.13: Specimens for Pull-out Tests (Smooth Bars)Type of ConcreteLoadingRateConcreteStrengthNo. ofSpecimensper SetTotalLow Medium High N H,5Plain Concrete 1 1 1 2 4PolypropyleneFibre Concrete0.1% 1 1 1 2 40.5% 1 1 1 2 4SteelFibre Concrete0.5% 1 1 1 2 41.0% 1 1 1 2 411Plain Concrete 1 - 1 1 1 2 8PolypropyleneFibre Concrete0.1% 1 1 1 1 2 80.5% 1 1 1 1 2 8SteelFibre Concrete0.5% 1 - 1 1 1 2 S1.0% 1 1 1 1 2 8/Plain Concrete 1 - 1 1 1 2 8PolypropyleneFibre Con crete0.1% 1 1 1 2 80.5% 1 - 1 1 1 2 8SteelFibre Concrete0.5% 1 - 1 1 1 2 81.0% 1 - 1 1 1 2 8TOTAL 100S -- Static^Al - Medium^I - Impact^N - Normal^H - HighChapter 3. Experimental Procedures 88Table 3.14: Specimens with Epoxy Coated Deformed BarsType of ConcreteLoadingRateConcreteStrengthNo. ofSpecimensper SetTotalLow Medium High N HPush-in Tests'Plain Concrete 1 1 1 2 4PolypropyleneFibre Concrete0.1% 1 1 1 2 40.5% 1 1 1 2 4SteelFibre Concrete0.5% 1 1 1 2 41.0% 1 1 1 2 41!Plain Concrete - - 1 1 1 2 4PolypropyleneFibre Concrete0.1% - - 1 1 1 2 40.5% 1 1 1 2 4SteelFibre Concrete0.5% - 1 1 1 2 41.0% - 1 1 1 2 4/Plain Concrete - 1 1 1 2 4PolypropyleneFibre Concrete0.1% 1 1 1 2 40.5% 1 1 1 2 4SteelFibre Concrete0.5% 1 1 1 2 41.0% 1 1 1 2 4Pull-out Tests5'Plain Concrete 1 1 1 1 2PolypropyleneFibre Con crete0.1% 1 1 1 1 20.5% 1 1 1 1 2SteelFibre Concrete0.5% 1 1 1 1 21.0% 1 1 1 1 2MPlain Concrete - - 1 1 1 1 2PolypropyleneFibre Concrete0.1% 1 1 1 1 20.5% 1 1 1 1 2SteelFibre Concrete0.5% 1 1 1 1 21.0% - 1 1 1 1 2IPlain Concrete 1 1 1 1 2PolypropyleneFibre Concrete0.1% 1 1 1 1 20.5% - 1 1 1 1 2SteelFibre Concrete0.5% - 1 1 1 1 21.0% - 1 1 1 1 2TOTAL 90Static^Al - Medium^I - Impact^N -- Normal^H - HighChapter 3. Experimental Procedures^ 893.3 Test Program3.3.1 Impact Testing3.3.1.1 Test Set UpThe testing system used to carry out impact tests is an important aspect of anyexperimental program. Various techniques, such as the conventional Charpy impacttest, the split Hopkinson bar test method and the drop hammer impact machine, canbe modified to carry out bonding behaviour tests under impact loading. The followingpoints must be taken into consideration in designing or choosing an appropriate system[95]:1. The machine is able to apply load to the specimen over a very short time in themillisecond range) with a considerable amount of energy;2. The machine has as great a stiffness as possible to prevent instability and vibration;3. The kinetic energy applied to the specimen can be varied in order to induce different:strain rates in the specimens tested:4. The accelerations of the specimens and the striker in the testing machine can bemeasured, to study the effects of inertial force and energy transfer;5. The strains at different points along the reinforcing bar or in the concrete in thespecimen can be measured accurately;6. The load exerted on the specimen, the acceleration and the displacement of thereinforcing bar, and the strains can not only be measured over a very short timeChapter 3. Experimental Procedures^ 90interval (a few microseconds) but also stored completely.A drop weight type of impact testing machine\" and a bolt type of load cell werechosen to be used in the tests. A number of of reinforcing bars were instrumented withstrain gauges before being cast into the specimens, so the strains in the steel could bedetermined (see Fig. 3.4 in Section 3.2.2.2 for the placement of the strain gauges alongthe reinforcing bar).It was considered an important part of the impact test to find out the displacement his-tory of the reinforcing bar without significant error. A high speed video camera (motionanalyzer) which could capture 1000 frames per second was used to record the movementof the rebar. For an impact event that lasts 10 ins , 10 frames would be taken, but thiswasn't accurate enough to generate a displacement versus time curve by analysing thesepictures. On the other hand, a displacement transducer which was able to measure verysmall movements at high sampling rates (a period of several hundred microseconds) andrecord them was unavailable at the time this research work was carried out. However, thedisplacement history could be determined by integrating the acceleration measured bythe accelerometer from kinematics with considerate accuracy. So an accelerometer wasattached on the bottom of the reinforcing bar in the specimen to measure its accelerationduring the impact event, while the hammer of the impact machine was also instrumentedwith an accelerometer, which recorded the acceleration of the hammer for determiningthe velocity, displacement and the kinetic energy of the hammer.A high speed data acquisition system with a 16-channel A/D board, an aggregatesampling rate of up to 1 MHz and a signal conditioner was used to record all the testI I Designed, constructed and maintained by the Department of Civil Engineering. University of Britisholumbia, Vancouver, CanadaChapter 3. Experimental Procedures^ 91data from the load cell, the accelerometers and the strain gauges. All these data weretransferred to a mainframe computer for processing.The test set up is shown schematically in Fig 3.11. Each part of testing apparatus isdescribed in the following sections.3.3.1.2 Impact Testing MachineThe drop weight type of impact machine designed and constructed at the Universityof British Columbia [97], is shown in Fig. 3.12 and Fig. 3.13. It stands about 4.0 in highand is capable of dropping a 345.0 kg mass' through heights of up to about 2.40 in. Thehoist attaches itself to the hammer by means of a pin lock and can be used to raise orlower the hammer by means of a chain and a motor. When the hammer is at the desiredheight, the pneumatic brakes provided in the hammer itself, are applied. With the brakes,the hammer \"grabs on\" to the columns of the machine. Subsequently, the hoist can bedetached from the hammer. Upon releasing the pneumatic brakes the hammer falls undergravity and strikes the reinforcing bar of the concrete specimen which is supported on a,base with a hole to permit movement of the rebar. The bolt load cell attached to thehammer sends out signals to the data acquisition system during the impact. The hammercan be made to fall through different heights, and thus the specimens can be subjectedto different strain rates.For pull-out tests a solid steel frame with a stiffness of 15 times that of the reinforcingbar was used to change the push-in force to a pull-out force; as shown in Figs. 3.13 and3.14.12 1t has been modified, to provide a capacity of 505.0 kgChapter 3. Experimental Procedures^ 92Figure :3.11: Layout of the Set Up for the Impact Test (Revised from Somaskan-than [96])Chapter 3. Experimental Procedures^ 93Figure 3.12: An Overall View of the Impact Machine — Push-in Test (Revisedfrom Somaskanthan [96])Chapter 3. Experimental Procedures^ 94Figure 3.13: An Overall View of the Impact Machine — Pull-out Test (Revisedfrom Somaskanthan [96] )Chapter 3. Experimental Procedures^ 95Figure 3.14: Solid Steel Frame for Pull-out TestsChapter 3. Experimental Procedures^ 963.3.1.3 Bolt Load CellThe load cell for the impact tests and the particular specimens in this test must1. be able to send out as high electric signals (voltages) continuously as possible;2. have a linear relationship between the load exerted on it and the output;3. have a higher frequency response than that of the tests;4. have a delay, if there is any, in the output signal which is much less than the timeof the event;5. have a fully contacting surface when it hits the rebar in the specimen, and sufficienttolerance for possible eccentrical striking.A bolt type of load cell is with a capacity of 150 kN was found to meet the aboverequirements, as shown in Fig. 3.15.As the bolt tip strikes the rebar of the specimen, the strain gauges inside the boltrecord the contact load and the Wheatstone bridge circuit, as shown in Fig. :3.16, willproduce an unbalanced' signal. The signals will be collected by the data acquisitionsystem.A calibration was needed to convert these signals into a real contact load. Althoughthe bolt was to be stressed dynamically in the impact case, the mechanical propertiesunder a dynamic loading rate ranging from 0 to 0.05 M Pa/.s (N/inin 2 • s) were assumedto be the same as under static loads. A analytical study on the stress wave propagation13 Manufactured by St.rainsert Company, Bryn Mawr, Pennsylvania, U.S.A.Chapter 3. Experimental Procedures^ 97in the bolt load cell under impact loading showed that the time delay of the signals inresponse to the striking load was negligible for this test (see Appendix B). Therefore a.static calibration can reasonably be extended to the impact condition. The calibrationwas carried out in an Instron universal testing machine. Fig. 3.17 shows the calibrationcurve. It is noted that the curve was a perfectly smooth line and there was no hystereticloss.Figure 3.15: The Bolt Load Cell for Impact TestingChapter 3. Experimental Procedures^ 98-O^RedGreenBlackWhiteConnectorF;7\"; ;1 C or 3;+0+ o ^R5B or 21D or 4iR6legends:Ga: Active Gage^Gc: Complementary Gage_o Numbers correspondExcitation: +0 and^to Model EW-1 StrainSignal:^+0 and -^Indicator terminals.Figure 3.16: The Circuit of the Bolt Load CellCalibrationBolt Load CellLoadingunloading00$0403020100 '^0702 4^ 6Signal (V)a 10Chapter 3. Experimental Procedures^ 99Load (kN)Figure 3.17: The Calibration of the Bolt Load CellChapter 3. Experimental Procedures^ 1003.3.1.4 AccelerometerThe accelerometers used were piezoelectric sensors (Model 302A) 14 , a special type forshock and vibration measurement, as shown in Fig. 3.18. There is a built-in unity-gainamplifier inside the accelerometer so the output signal will directly go to the A/I) boardin the data acquisition system. Some salient features of the accelerometer are:1. resolution = 0.01 g2. resonant frequency = 45 kHz3. frequency range = 1^5000 Hz4. load recovery < 10 ftsThe calibration curves is given in Fig. 3.19.14 1\\lanufactured by PCB Piezoelectrics Inc., Buffalo, N.Y., U.S.A.484 DiaSig Pwr1 30070A09OptionalConnectorAdaptor 031 DiaGND10.32 inn468 Dia-10-32 ThoCoaxialConnector1 2 Hex10000100^ 1000Frequency In HertzFrequency Responserr.Chapter 3. Experimental Procedures^ 101See Optional Modelsbelow Specifications. EC-- Mod 08180510-32 Mtg Stud27^(supplied)t Figure 3.18: The Quartz AccelerometerCalibration-^ -Quartz AccelerometerChapter 3. Experimental Procedures^ 102Acceleration (g)503 ^4003002031000 '^0 i^2^3^4^6Signal (V)Figure 3.19: The Calibration of the Quartz AccelerometerChapter 3. Experimental Procedures^ 1033.3.1.5 Strain MeasurementThe strain gauges used in the tests were CEA-06-1251_11\\1-120, which are widely used inexperimental stress analysis. This is an electric resistance type of strain gauge, having aresistance of 120.0 + 0.3% Cl and a gauge factor of 2.050 + 0.5%.A special electric circuit was designed to measure and record the readings from the5 pairs of strain gauges mounted on the reinforcing bar. It is the circuit of the 'oppositearm Wheatstone bridge [98]. The circuit diagram is shown in Fig 3.20.A box which consisted of the five pairs of 'dummy' strain gauges and connectors wasplaced as close to the specimen tested as possible to compensate for temperature effects,as shown in Fig. 3.21.The output voltage (signal) isE (K. iRici + R1)^E • 120.010„t = (R 1 + 120.0 + K1R1(1)^(R2 + 120.0 + 1 '2R2(2)where(V)^(3.1)VQ,,t = the output signalE = the excitation voltage, K2 = the gauge factors of a pair of strain gauges (gauge 1 and gauge 2)R 1 , R2 = the electric resistances of a pair of strain gauges^(Si)( 1 . ( 2 = the strains at two opposite sidesActive Strain Gauge Dummy ResistanceDummy Resistance Active Strain GaugetExcitationData AcquisitionSystemI^Chapter 3. Experimental Procedures^ 104SignalConditionertFigure 3.20: The Circuit of 'Opposite Arm' Wheatstone bridgeChapter 3. Experimental Procedures^ 105The two dummy resistances were 120.0 1 -2 precision resistances. After rearranging andneglecting higher order terms in Eq. 3.1 (see Appendix C for details) we finally getVout = E2K (ci + 12)^(V )^(3.2)whereK = 2.050 (the standard gauge factor for model CEA-06-125UN-120)The average of two strains of the opposite gauges will represent the strain in thesection. i.e.(€1 + 2)2(3.3)wheref = the strain in the section measured^(10')It can be seen that there is a linear relationship between the output signal V and thestrain in the section 1.= C • 1/..t^ (3.4)where the coefficient C isC E K(1/V)^ (3.5)=Chapter 3. Experimental Procedures^ 106All the strain gauges used had different electric resistances R and different gaugefactors K. The manufacturer guarantees that the errors of the electric resistances ofstrain gauges for the same model are less than 0.3% of 120.0 52 and the errors of gaugefactors are less than 0.5 % of 2.050. In Eq. 3.5 the excitation voltage E remains thesame. A precise error analysis (see Appendix C) showed that taking = 120.0 C2and K = 2.050 for the calibration resulted in a less than 0.5 % error of the coefficient C.Thus the calibration curve which was a straight line could apply to all the strain gaugesused in the tests, as shown in Fig. 3.22.Chapter 3. Experimental Procedures^ 107Figure 3.21: The Dummy Strain Gauge and Connector BoxStrain (micro)3 500^Calibration,^ -Strain Gauge3,0002.50020001,5001,0006002^ ♦^ 6^ 8^10Signal (V)Figure 3.22: The Calibration of Strain MeasurementChapter 3. Experimental Procedures^ 1083.3.1.6 Data Acquisition SystemOne of the most important and perhaps the most difficult aspects of the impact testis the data collection. From the preliminary tests it was found that the time of theimpact event ranged from 5.0 to 15.0 Ins, i.e. the signals from the transducers that areof significance lasted only 5.0 to 15.0 ms. The following points must therefore be takeninto consideration in choosing and designing an appropriate data acquisition system forthis type of experimental investigation:1. The system must record the signals from the transducers correctly;2. The scanning rate of the system should be fast enough to capture all the informationwhich is needed to describe and analyze the event;3. The data that it records are sufficient but not excessive, keeping the volume of thedata as small as possible to save time and space on the computer disk;4. Specifications such as I/O voltage, frequency response, etc. must be compatiblewith the transducers used;5. The signal conditioner (filters and amplifiers) must be able to block as much noiseas possible without losing or distorting the true signals and be able to amplify thesignals to the most suitable level for A/D board.The data acquisition system used in the test consisted of an IBM PC XT computer,a 16-channel A/D conversion board and Scope Driver software'', and a. conditioner unit,as shown in Fig. 3.2:3.15 Product of R.C. Electronics Inc., Santa Barbara, California, U.S.A.Chapter 3. Experimental Procedures^ 109Figure 3.23: The Data Acquisition SystemChapter 3. Experimental Procedures^ 110Some salient features of the data acquisition system are:• 16-channel maximum I/O (input/output) port;• An aggregate sampling rate of up to 1/n MHz (n is the number of channels used);• An external instrument interface;• Internal or External trigger control;• A scope driver software;• Digital conversion with a 12 bit accuracy for a range of -10.0 V to +10.0 V;• A memory buffer size of 1 to 64 K of A/D board;• Amplifiers with gain of up to 1000 in the conditioner;Since the frequency response of the accelerometer used was 5000 Hz, (see Section3.3.1.4) which was much lower than those of the other transducers, i.e. the bolt loadcell and the strain gauges, it was decided that the sampling rate should be 200 i.t.s (0.2ni.4 For the case of collecting data through 8 channels (one for the load cell, two forthe accelerometers and 5 for the strain gauges) the maximum scanning speed of the data.acquisition system for one channel should be200 x 10 -6 x 8 = 816 (Hz)1This was much lower than the capacity of the A/D board, 1 MHz.Chapter 3. Experimental Procedures^ 111When the data acquisition system is switched to active mode, it starts collecting data.and then replacing the data with new data until triggered. The delay time, the channels,the trigger mode, the trigger control level and the buffer size of the A/D board werecarefully selected or designed so that the data collection could cover the whole periodof the impact event including a certain length of pre-impact and post-impact time. Thedata collected from the A/D board was inputted to the computer memory in compressedmode, then written to the mass storage media in an ASCII format.3.3.1.7 High Speed Video CameraA high speed video camera (ENTAPRO 1000 Motion Analyzer) 16 was used to takepictures of the specimen during the impact event (Fig. 3.24). The camera, can take1000 to 6000 frames per second. The data were stored in a special video tape and thendownloaded to a normal VCR tape.Manufactured by Eastman Kodar Company, U.S.A.Chapter 3. Experimental Procedures^ 112Figure 3.24: EKTAPRO 1000 Motion AnalyzerChapter 3. Experimental Procedures^ 1133.3.1.8 Test ProcedureAltogether 380 different types of specimens were tested under impact loading, includingnormal strength or high strength concrete, smooth or deformed rebars, plain, polypropy-lene fiber or steel fiber concrete, different fiber contents, with or without strain gaugeinstrumentation, pull-out or push-in, and different drop heights. A summary is given inTables 3.9 to 3.13 in Section 3.2.5.A typical procedure for carrying out an impact test is1. Set up the test apparatus needed, including the drop weight impact machine, thebolt load cell, the accelerometers and their power supply unit, the dummy straingauge assembly, the data acquisition system and the high speed video camera.Make the connections between them properly;2. Place the specimen on the support under the hammer of the impact machine, makealignment from both directions and adjust the height of rebound pad so that it willstop the fall of the hammer as soon as the rebar has gone through the concretespecimen;3. Check and make sure the apparatuses works properly;4. Operate the impact machine, raise the hammer to the desired height and set it toready-to-drop mode;5. Run the Scope Driver software in the data acquisition system, set the necessary pa-rameters properly including the trigger control parameters. Set the data acquisitionat active mode and set the high speed video camera at live mode;Chapter 3. Experimental Procedures^ 1146. Release the pneumatic brakes in the impact machine and trigger the high speedcamera with a delay of a certain time;7. Apply the pneumatic brakes as soon as the hammer rebounds; stop the recordingof the high speed camera;8. Check if all the data and the pictures have been recorded; save the data to thedisks in ASCII format;9. Reset the apparatus for the next specimen;10. Download the picture from the high speed type to the normal VCR type, transferthe data from the disks in the data acquisition system to a. mainframe computerfor processing.3.3.2 Static and Medium Rate Testing3.3.2.1 Test Set UpThe purpose of the static and medium rate testing was to investigate experimentallythe bond behaviour under static and medium rate loading, from both pull-out and push-in test. The results were then compared with each other and with those under impactloading. The static and medium rate tests were carried out on an Instron universaltesting machines 7 . It is a. mechanical type of testing machine, having a capacity of 150UV (33750 Ms) and stiffness of 140 LIV/77int. Its crosshead speed ranges from 0.05 to 500Mill per minute, giving a bond stress rate ranging from 0.5 10 -8 to 0.5 • 10 -4 AI Palsfor the specimens tested. All operations are controlled by a microprocessor-based central17 Model 4206. manufactured by Instron Corporation, U.S.A.CalibrationStatic Load CellloadingChapter 3. Experimental Procedures^ 115processing unit. A 150 kN load cell was used for measuring load. From the preliminarytests it was found that the maximum bond force was about 55 kN. So, for calibration, theload cell was loaded, in steps, up to 60 kN, then unloaded, down to the zero. The outputwas read. A regression analysis showed that the relationship between the load and thevoltage output was perfectly linear, and the loading and unloading curves followed thesame path. Fig. 3.25 shows the calibration curve. The crosshead position measurementunit of the testing machine was configured to represent the displacement of the rebar inthe specimen. The calibration curve of the displacement is shown in Fig. 3.26 and it isalso a perfect straight line. The test set up is shown in Fig. 3.27 and the set ups of thepull-out and push-in tests are shown in Fig. 3.28 and Fig. 3.29 respectively.70eoso403020100 ^0Load (kN)so-^2 4^6^10Signal (V)Figure 3.25: The Calibration of the Load Cell for Static Testing6 6 10CalibrationPosition Measurement4030Displacement (mm)so20104Signal (V)o ^0 2Chapter 3. Experimental Procedures^ 116Figure 3.26: The Calibration of the Position MeasurementChapter 3. Experimental Procedures^ 117Figure 3.27: Test System for Static and Medium Rate TestingChapter 3. Experimental Procedures^ 118Figure 3.28: Pull-out Test Set Up for Static and Medium Rate LoadingChapter 3. Experimental Procedures^ 119Figure 3.29: Push-in Test Set Up for Static and Medium Rate LoadingChapter :3. Experimental Procedures^ 1203.3.2.2 Data Acquisition and ProcessingThere is a built-in conditioner in the console in the Instron testing machine so theoutput from the load cell and the position measurement unit were sent directly to theA/I) board in the data. acquisition system (see Section 3.3.1.6) along with the outputsfrom the strain gauges which were conditioned first by the conditioner unit. All thedata were then stored on diskettes in a PC computer and subsequently transferred to amainframe computer for processing.3.3.2.3 Test ProcedureAltogether, 420 different types of specimens were tested under static and medium rateloading, a summary are given in Tables 3.9 to 3.13 in Section 3.2.5.A typical procedure for carrying out a static or medium rate loading test is givenbelow.1. Set up the test apparatus needed, including the Instron universal testing machine,the 150 iciV load cell, the dummy strain gauge assembly, and the data. acquisitionsystem, hook up the connections properly;2. Place the specimen on the support under the load cell in the testing machine, makealignment from both directions;3. ('heck and make sure the apparatus works properly;4. Operate the testing machine, set the crosshead speed to give with the desired stressrate;Chapter 3. Experimental Procedures^ 1215. Run the Scope Driver software in the data acquisition system, set the necessary pa-rameters properly including the trigger control parameters. Set the data acquisitionat active mode;6. Start to move the crosshead of the testing machine;7. Stop the movement of the crosshead of the testing machine;S. Check if all the data and the pictures have been recorded, save the data to thedisks in ASCII format;9. Reset the apparatus for next specimen testing;10. Transfer the data from the disks in the data acquisition system to a mainframecomputer for processing.3.3.3 Crack ExaminationIn order to investigate the crack developments in different specimens, some testedspecimens were sliced by diamond and metal saws, then the internal cracks at the interfacebetween the rebar and the concrete were examined and photographed by a stereoscopicmicroscope 18 (see Fig. :3.30).'Nikon Microscope Model SAM-10, Nippon Kogaku K.K Totyo, Japan.Chapter 3. Experimental Procedures^ 1 99\",1111. 441■7410.,^IMF MK Figure 3.30: The Stereoscopic MicroscopeChapter 4Analysis of Test Data4.1 GeneralThe usual output from the impact tests on the bond specimens consisted of the tup(the contact area between the load cell and the specimen) load, the accelerations at twolocations and the strains at five locations along the rebar. These three parameters werethe fundamental data recorded in this experimental study. These data were all obtainedas a. function of time. Fig. 4.1 shows the eight sets of data from the eight channels of thedata acquisition system connected to these transducers. The data were acquired at 200/Ls intervals; an impact event took anywhere from 5 to 30 ins, so there were hundreds tothousands data points for each test. These data were transferred as a data file in ASCIIformat to a mainframe computer via. FTP (Fast Transform Protocol) service.One important and difficult aspect of the data processing in impact tests is the noisefiltering. The true signal output from the circuits of the load cell, accelerometers orstrain gauges (Wheatstone bridges) were at a very low level, ranging from 5.0 to 30.071?. V, while the noise from several sources can reach as high as 1.0 mV. The effects of noiseon the reliability of the true signal can not be ignored. The influences of the noise on thetrue signals depend on the characteristics of the noise, such as frequency, duration and123Signal (V)10Chapter 4. Analysis of Test Data^ 12410^20^30^40Time (ms):Figure 4.1: Typical Outputs from the Eight Channels of the Data AcquisitionSystemChapter 4. Analysis of Test Data^ 125intensity, etc., as well as the characteristics of the true signals. They can be eliminatedeither by hardware filtering or by digital filtering. But either (or both) filtering methodscan be applied only when the characteristics of the noise or the true signals is known.In this experimental investigation, several preliminary impact tests were carried out todetermine the characteristics of external and internal noise. They were specially designedas there exist theoretical models for these problems and accurate analytical solutions areknown. An appropriate method for filtering, or a combination of several methods, waschosen, and the raw data from the data acquisition system were put through the digitalfiltering process by means of FFT (Fast Fourier Transform) and inverse FFT to removethe noise as much as possible; the \"true\" signals were saved for analysis.The applied pull-out and push-in forces were calculated based on the data from thechannel of the load cell. The data from the accelerometer channels were used to determinethe accelerations, velocities and displacements of the rebar and the hammer, and thekinetic energies, potential energies and fracture energies. The data from the five channelsof strain measurement were used to determine the strains and stresses in the rebar aswell as in the concrete, their distributions along the rebar and the bond stress and localbond slips. A flowchart of these processes is given in Fig. 4.2.The strains in the rebar were checked with its displacement which was evaluated byintegrating the acceleration recorded. Meanwhile, the displacement history of the rebarcan be checked by analyzing the motion pictures, which was taken at a rate of 1000 framesper second by a high speed video camera. Figs. 4.3 to 4.9 were one set of these motionpictures. which were recorded for a specimen made of steel fibre reinforced concrete witha deformed rebar under the impact of 300 mm, drop height. The vertical displacementsof the rebar at each one millisecond interval after the hammer hit the specimen can beChapter 4. Analysis of Test Data^ 126determined by comparing two consecutive pictures, using appropriate scale. Then a dis-placement history of the rebar can be drawn and compared with the displacement historycurve which was calculated from the recorded data of the acceleration. It was found theycoincided very well (Fig. 4.10). This means that the measurements of the accelerations,the method of signal processing and the calculation model of the displacement (see thefollowing sections for details) were appropriate.4.2 Data Filtration4.2.1 Fast Fourrier Transform — FFT and Inverse FFTTransient loading conditions, such as impact loading, and material and structuralresponses to them, are time-dependent variables, which should be studied using a time-domain analysis. However, these variables can be more conveniently studied using afrequency-domain analysis. Any signal output from the load cell, accelerometers or strainmeasurement channels can easily be extended from an aperiodic function defined in afinite range [t i , 1 2 ] to a periodic function defined in an infinite range (—oo, d-oo), theextended function thus satisfies the conditions for Fourier transformation. The signalfunction is considered as being comprised of many periodic wave forms and a correctevaluation of such wave form characteristics will help study the signal itself [99].Let P(t) be the aperiodic signal function defined in^12]; after being extended toa periodic function (either odd or even), P(t), which is defined in (—oo, oo), it can begiven asChapter 4. Analysis of Test Data^ 127INPUT DATA FILEI (SEARCH USEFUL PORTION OF SIGNALS iBASE LINE SETTING METHOD OF FILTERINGi APPLY FFT'i FILTER OUT UNWANTED FREQUENCIESi APPLY INVERSE FFTiFIND LOAD, PLOT LOAD HISTORY CURVESiFIND ACCELERATIONS, VELOCITIES & DISPLACEMENTSiPLOT APPLIED LOAD VS. DISPLACEMENT CURVESiFIND ELONGATIONS OF REBARiFIND STRAINS & STRESSES IN STEEL & CONCRETEiFIND BOND STRESSES & BOND SLIPSiPLOT STRESS & STRAIN DISTRIBUTION CURVESi PLOT BOND STRESS VS. SLIP CURVESiFIND LOAD, STRAIN & STRESS RATES1FIND KINETIC, POTENTIAL, STRAIN & FRACTURE ENERGIESiOUTPUT RESULTS & GRAPHSFigure 4.2: Algorithm of Test Data Process.1.21eiektaproi 210^.'19,153IiRab314. Full (1C.: FE.3)oD 6 Irl'icR)' FijlJ(1C^FF-3) 74-1ri16 Chapter 4. Analysis of Test Data^ 128Figure 4.3: The Motion Picture of the Rebar at T = 1 ins Taken by the HighSpeed Camera211 1 iT77=E--71;1C: :1 Figure 4.4: The Motion Picture of the Rebar at T = 2 is Taken by the HighSpeed Camera116^I)? .2111. C:3 21211C1. 212 I.ic,:ate31C) iH Full (1C 13 D 8Chapter 4. Analysis of Test Data^ 129Figure 4.5: The Motion Picture of the Rebar at T = 3 ms Taken by the HighSpeed CameraFigure 4.Speed C6: The Motion Picture of the Rebar at T =4 Ms Taken by the High;'arneraChapter 4. .Analysis of Test Data^ 130D:C 3.214i1CMDPrgij' Full (11: : 3 F F .3)^-!:- _, ^;1 ^;^0:3 6 rER)^.Figure 4.7: The Motion Picture of the Rebar at T 5 ins Taken by the HighSpeed CameraFigure 4.8: The Motion Picture of the Rebar at I = 6 ins Taken by the HighSpeed CameraBy Accelerometer0^ 2^ 4^ 0^ 0^10Time (ms)By High Speed Camera0ot 23 ;0Chapter 4. Analysis of Test Data^ 131116:26,`,63.2 .1.1^216 j.< Full F Figure 4.9: The Motion Picture of the Rebar at T = 7 ms Taken by the HighSpeed CameraFigure 4.10: The Displacement History of the Rebar by Two MethodsChapter 4. Analysis of Test Data^ 1321 j.+0,,P(t) :=^C(w)eiwt (4.1)where the harmonic amplitude function C(w) is+00C(w)^f^P(t)^dt^ (4.2)wheret = the time component= the frequency componentC( w) = the Fourier coefficientEqs. 4.1 and 4.2 are the pair of Fourier Transform (FFT) and Inverse Fourier Trans-form equations (inverses F FT), respectively..In this study the signal function P(1) is actually a set of discrete data, and thus anumerical integration method is required to determine C(w) from P(t) and, vice versa,P(t) from 0(w). ,A computer program in FORTRAN language was written to form theDiscrete Fourier Transform (D.FT) based on Eqs. 4.1 and 4.2, and to solve the equationsby the Fast Fourier Transform (FFT) algorithm in both conversion directions (FFT andinverse FFT).The Fourier conversion yields the necessary frequencies and their amplitudes, whichfacilitates the frequency-domain analysis. For steady-state conditions, contributing fre-quencies may be few and limited, but for transient conditions as in an impact test, aChapter 4. Analysis of Test Data^ 13:3spectrum of frequencies are obtained. The contributing frequencies and their relativeimportance for the signal function can easily be studied. Physically the spectrum offrequencies represents the distribution of energy over a certain range of frequencies. Anappropriately filtered spectrum of frequencies forms the new signal function by means ofinverse FFT.4.2.2 Characteristics of External and Internal NoiseThe noise occurring in the test can be categorized as external noise and internal noise.The former are created by external sources such as nearby motors, power lines andconnection cables, and the latter include electronic noise induced within the transducers,amplifiers, A/I) board and computer components. The frequencies of these noise covera wide range, from low to high. Their amplitudes may be up to the same order ofmagnitude as the true signals. Some of them occur throughout the test, whereas othersare only present during the actual test or actual data acquisition. This made it difficultto determine the characteristics of the noise separately from the true signals.Using the data collected from the so-called non event\" experiment, in which thedata acquisition system records the signal outputs from the transducer channels whilethe hammer drops without striking the specimens, it is possible to identify some of thenoise which is present in the system throughout the test. Fig. 4.11 shows a typical curveof this kind of noise. It oscillates around a horizontal line close to the X-axis and isperiodic in nature. The spectrum of frequencies by LET, as given in Fig. 4.12, showsthat it is comprised of some 60n (where 71 is an integer) Hz noise. This implies that thepower supply line (A( 110 V 60 Hz) may have a large contribution to the noise.Fourier Coefficient (V/Hz)05Chapter 4. Analysis of Test Data^ 134Signal 0.00030.030.040.020Om)004)(0.05)(0.03)0.1) o 10^20^30^40Time (ms)soFigure 4.11: \"Non Event\" Noise in Impact TestsFrequency (Hz)Figure 4.12: Spectrum of \"Non Event\" Noise by FFTChapter 4. Analysis of Test Data^ 135It was realized that some noise is present only during the data acquisition. To studythe characteristics of this type of noise a special test was designed and carried out.In this test the mathematical model is known and an accurate solution can be foundby analytical methods. Therefore the true signal output was determined. ApplyingFFT to both the true signal and the recorded signal will yield two different spectra offrequencies. By comparing the frequencies and amplitudes of the noise in the two spectra,their contributions to the original signals could be determined. An appropriate filter (lowpass, high pass or band filter) and the cutting limits, can then be designed. The spectrumshould be modified by the chosen filter to eliminate the frequency contributions of thenoise. Applying the inverse FFT to the new spectrum will result in a true signal.4.2.3 Base Line Setting MethodThe noise found in the \"non event\" experiment is present in the system throughoutthe test. Basically it is a low frequency noise with a constant mean value as described inthe above section. To eliminate this component of the noise all the signal outputs hadtheir mean value of the noise, as determined from the \"non event\" signal data, subtractedfrom the recorded data. The numbers were 0.03 V for the load cell and the accelerometerchannels and 0.05 V for the strain gauge channels, as shown by several preliminary tests.The subtractions were carried out by the computer program automatically.4.2.4 Digital FilteringDigital filtering is a process by which unwanted frequencies are eliminated mathemat-ically from a signal in the frequency-domain analysis. In the mathematical algorithm,Chapter 4. AnaLvsis of Test Data^ 136three type of filters are commonly employed: low pass filters, high pass filters and baudpass filters. A low pass filter cuts off all of the frequencies from the signal that are higherthan the stipulated value, whereas a high pass filter cuts off all of the frequencies lowerthan the stipulated value. A baud pass filter allows only frequencies of the signal that liewithin the set limits to pass and cuts the rest off. The filtered signal will be free of theparticular frequencies which have been cut off in the digital filtering process after it hasbeen transformed to the time-domain by means of inverse FFT. The main differencesof digital filtering from hardware filtering are that the former can eliminate unwantedfrequencies completely, are more flexible than the latter and there is no phase shift inthe filtered signal.The general procedure of digitally filtering the signal in this experimental study areas follows:Step 1 ^ Determine the Characteristics of the Noise1. Design a, similar test for which the mechanical model for the problem is known andan accurate analytical solution exists;2. (1 -iange the analytical solution from time-domain to frequency-domain by FFT,and get the spectrum of the solution;3. Carry out the test and record the signal;4. Find out the \"non event\" noise and its mean value:5. Get rid of the \"non event\" noise from the signal by the baseline setting method;6. Apply FFT to the signal to get its spectrum; andChapter 4. Analysis of Test Data^ 1377. Compare two spectra and determine the frequencies of the noise and their contri-butions to the signal.Step 2 — Determine Parameters of Digital Filtering1. Determine whether to use low pass, high pass or band pass filters, or individualelimination of certain range of frequencies; and2. Set the cut limit(s).Step 3 ^ Filter the Test Data1. Get rid of the \"non event\" noise from the signal data by the baseline setting method;2. Apply FFT to all the test data individually;3. Cut off the known frequencies of the noise in the spectrum by the chosen type offilter; and-1. Apply inverse FFT to the filtered spectrum and get the true signals.Step 4 ^ Process the True Signal Analyse the filtered signals as the true signals.4.2.5 Filtering of Load, Acceleration and Strain SignalsThree preliminary tests were designed and carried out to determine the characteristics ofthe noise which occurred in the load cell, accelerometer and strain measurement circuitsChapter 4. Analysis of Test Data.^ 138(Wheatstone bridge) during the data acquisition (see Appendix E). All the problemshave analytical solutions. The procedure is described in the above section. The resultare given in Table 4.1.Table 4.1: The Characteristics of Noise and Their Filtering(Load cell, Accelerometers and Strain Measurement)Load Cell Accelerometer Strain GaugesWheatstone BridgeSignal period^(ins) - 5.0 ,--, 30.0 6.5 ' 35.0 5.0 — 30.0Frequencies of noise^(kHz) > 9 .0 >2.4 >1 5.Filter chosen Low pass Low pass Low pass_ Cut limit^(kHz) 2.0 2.4 1.54.3 Young's Modulus and Poisson's Ratio of ConcreteBased on the stress-strain curve of concrete, Young's modulus, Ec , is given byE, = S2 - S1 (MPa)^ (4.3)(- 2 — 0.000050where= the stress corresponding to E r = 50 x 10 -6^(MPa. )the stress at 40% of the ultimate load^(MPa)fz = the strain corresponding to ,52^(10-6 )The poison's ratio p c is given byChapter 4. Analysis of Test. Data^ 139= ft2( 2 — 0.000050 (4.4)wherefly = the transverse strain at the middle of specimen corresponding to S i(10')f tz = the transverse strain at the middle of specimen corresponding to S2(1 0- '` )The Young's modulus in shear, G„, is given by E,(1h1 Pa)^ (4.5)2(1 + ti)4.4 Contact Load, Inertial Load and Applied LoadThere is a linear relationship between the output signals from the load cells (either thebolt load cell for the impact tests, or the Instron 150 kN static load cell) and the contactloads. as shown in Fig. 3.17 and Fig. 3.25. The total force acting on the rebar isFt = c 1 S 1^(N )^(4.6)whereFt = the contact load^(N)Chapter 4. Analysis of Test Data^ 140^c i = the calibration coefficient of the load cell^(N/V)= the output voltage from the load cellThe coefficient c i is different for the different load cells. It should be noted that bothF and S i are functions of time.In the impact test when the hammer strikes the rebar, the rebar suddenly gainsmomentum and accelerates in the direction of the hammer. This gives rise to d'Alambertforces, acting in a direction opposite to the direction in which the rebar accelerates. Fromthe equilibrium of force, the load that the sensor in the load cell records includes the forcedue to the inertial reaction of the rebar, which is called the inertial force. This meansthat the force between the tup and the rebar consists of the stressing load and the inertialforce. Since the acceleration of the rebar during the impact could be very high (100 200q) it is necessary to check out how important the inertial force is in the determination ofthe external force which acts on the specimen. But calculations showed that the inertialforce of the rebar is negligible when compared to the contact load (see Appendix D).Thus, the applied load, i.e. the force acting on the bonding area (either pull-out orpush-in) is the same as the contact load. That is,Fb = Ft —^= Ft^(N)^ (4.7)where= the force acting on the bonding area^(N)= the inertial force of the rebar^(N )Chapter 4. Analysis of Test Data^ 1414.5 Acceleration, Velocity and Displacement4.5.1 Acceleration, Velocity and Displacement of the RebarThe acceleration of the rebar was calculated using the data from the accelerometerwhich was attached to the bottom of the rebar. According to the product specification,the acceleration of the rebar a ,(1) is^a 7.,(t.) = 100.0 (38^(771711782)^(4.8)where^q = the gravitational acceleration^(in7n, .c 2 )= output voltage from the accelerometer^(v)Because the initial velocity is equal to zero, at any moment t the velocity of the rebarv r ,(t) and its displacement d„.(1) can be found by integrating the recorded accelerationover time:re (t) = fo a „.(t) cif^(mm/s)^ (4.9)andt it( l ,„ (t )^ 1,7.,(t)dt =^a7.,(t)(1t20^ 0 0(min)^(4.10)Chapter 4. Analysis of Test Data^ 142wheret = time elapsed from the moment of contact between the tup and the rebar(.^)Since are consisted of a series of discrete numbers recorded by the data acquisitionsystem, the above integrations were carried out numerically. As described in Section 1 ofthis chapter, the displacement of the rebar, d„, can also be calculated from the motionpictures which are recorded at a rate of 1000 frames per second (1 frame/ins) by a highspeed video camera. The results from two different methods are compared to find outthe accuracy of calculation.4.5.2 Acceleration, Velocity and Displacement of the HammerAs soon as the pneumatic brakes are released the hammer of the impact machine startsto fall as a free body under gravity. From kinematics, the time for the hammer to travelthe distance I), (the drop height) isT dr op = 9h(4.11)0.91gthe correction factor 0.91 is applied to g to account for frictional effects between thehammer and the guiding columns, and the air resistance. If we take the time when thehammer hits the rebai as a starting point, the velocity of the hammer at this momentvh„(0) isChapter 4. Analysis of Test Data^ 143ch a (0) = 2 (0.918) h (mm/.^) (4.12)At any time t after it strikes the rebar the velocity of the hammer v iia (t) isvh a (t)^2 (0.918) h^Jo. a ha (t) dt (minis)^(4.13)wherea ha (t) = the recorded accelerations^(mm, /s)After the contact between the hammer and the specimen, an impulse, given by thearea under the tup load (Ft , see Eq. 4.6) vs. Time (t) plot, acts on the hammer. From thelaws of Newtonian mechanics, this impulse must be equal to the change in the momentumof the hammer, i.e.r tFt (t)^=^ha a ha (0) — Af h„v h„(1)^(Ns)^(4.14)The above equation can be used to check the accuracy of the calculations of thevelocity of the hammer.The displacement of the hammer at any time d h a (t) is(11,,(t) =fo t [2 (0.918) h^f a 1,„(t) (mm)^(4.15)Since a h,(t) consisted of a series of discrete numbers recorded by the data acquisitionChapter 4. Analysis of Test Data^ 144system, the above Eqs. 4.13 and 4.15 can readily be solved by numerical integration.4.6 Elongation of the RebarBy comparing the displacement of the hammer d h“(t) with the displacement of therebar d„ (t). the deformation of the rebar itself during impact c„.(t) can be found.= (.11,,(1) — (.1 7.,(t)^(mm)^ (4.16)The deformation of the rebar c i.,(t) can also be determined by considering the strainin the rebar during the impact eventFtlpAsEsc„(t) = ^o (s dl(mm)^(4.17)where= the length of the pull-out or push-in end of the rebar^(mm)l c = the length of the embedded segment in concrete of the rebar^(non)In the above equation the first and second terms represent the elongation of the pull-out or push-in end and the embedded segment of the rebar, respectively. ( s is the strainin the embedded part of the rebar, evaluated by using Eq. 4.20 in the following section.The results of the two different equations, Eqs. 4.16 and 4.17, can be used to checkthe accuracy of the two calculation methods.Chapter 4. Analysis of Test Data^ 1454.7 Strains and Stresses in the Rebar and the ConcreteEither the pull-out or the push-in test for the bond specimen is a very complicatedthree-dimensional problem from the view point of the theory of elasticity, due to the inho-mogeneous material conditions (steel and concrete with greatly different elastic modules)and the complex boundary conditions. There is no analytical solution for this problem,even if the external force Fb is already known and some assumptions are made to simplifythe mechanical model, as shown in Fig. 4.13. There is, however, a fracture mechanics ap-proach combined with the finite element method for the problem which will be describedin Chapter 7.On the other hand, since the strains at some locations along the rebar were measureddirectly using strain gauges, the bond stresses can be calculated from the recorded straindata. From the theory of elasticity, the axial stress in the rebar as can be found, accordingto Hooke's law for the three-dimensional, axisymmetric problem, asEsa, ^1 + /15'is 1 —E s + es.r + cs,(9) + es](MPa)^(4.18)whereES = the Young's modulus of steel^(MPa)it s = 0.27 (Poisson's ratio of steel)E s = the axial strain in steel (recorded)^(10-6)S,7\" = the radial strain in steel^(10')Chapter 4. Analysis of Test Data^ 146( s0 = the tangential strain in steel^(10')Similarly, the axial stresses in the concrete in the vicinity of the rebar a, isa, =E, ^ ((c + c,r^ec,O) + Cc1 — 2,a,(MPa)^(4.19)1 + p cwhereE, = the Young's modulus of concrete^(MPa)p„ = 0.25 (Poisson's ratio of concrete)E, = the axial strain in concrete^(10')= the radial strain in concrete^(10')( c , 0 = the tangential strain in concrete^(10-6)In practice, it was impossible to measure the radial strain c s„ and the tangential strain6,9 , 0 in rebars with diameters of 11.3 or 12.7 mm, and the radial strain E c , r and tangentialstrain F e. a in concrete. A three-dimensional axisymmetrical analysis shows that the radialstrain c,„ and the tangential strain ( 8 ,9 do not play much of a role in the terms of thetotal strain in Eq. 4.18 (see Appendix F).The ratio^ „^s,O)I —2 ^< 5%[I -- p ,(^FSChapter 4. Analysis of Test Data^ 147Thus. Eq. 4.18 can be simplified toE, (1 — µ s )= ^(1 + 11,9)(1 — 2µs) Es (M Pa)^(4.20)Similarly, Eq. 4.19 becomesE, (1 — pc)a, , (c.^(Al Pa)^(4.21)(1 + p c ) (1 — 210Actually, the strain ( c in the concrete was always found through the stress a,. To dothis Eq. 4.21 becomes(1 + p c ) (1 — 2/t e )( c = ^ a-,^(10-6)^(4.22)E, (1 —The stresses in the concrete across the section, ac , can be calculated from the equi-librium equationt, tt- • D dl = y a,A,^(A)^(4.23)where= the locations of the ith and jth points along the rebar^(710-11)uz = average bond stress between i and j locations at the steel-concreteinterface^(AIPa)Chapter 4. Analysis of Test Data^ 148= diameter of the rebar^(rnm)= coefficient that accounts for the nonuniform distribution of stress in theconcrete across the section; y = 0.30 in this study (see Appendix F)A, = area of the concrete cross-section^(non')4.8 Bond Stress and Bond SlipThe local bond stresses between the ith and jth locations were calculated from theaxial stresses in the steel by the equilibrium condition,wheregs,^crs,j ) D4AXas , j = stress at the ith location in steel= stress at the jth location in steel(M Pa)^ (4.24)(M Pa)(M Pa)= the length of rebar between the ith and jth locations^(mm)Notice that the bond stress calculated by the above equation is the average bondst ress.The slip between the rebar and the concrete at any point between the ith and jthpoints along the rebar, w(x), can be determined by the compatibility condition betweenChapter 4. Analysis of Test Data^ 149the two materials:— F e ) dl (mm)^ (4.25)where^= the distance from the ith point^(mm)Denoting by y the distance from the starting point, the general equation for deter-mining the slip w (y) isII) (0 =^k=1 711k -Jr jo y-7 7(1 3 —1,)^— t )^(mm)^(4.26)where71^the number of segments in which the slips have been calculatedwk = the calculated slips for the previous segments^(min)All of the integrations were clone using numerical methods. The varieties of distribu-tion curves can readily be plotted, based on the results of these calculations.4.9 Rate of Loading, Strain and StressThe loading rate, strain rate or stress rate, ::(t), were calculated as=i=1Chapter 4. Analysis of Test Data^ 150;it [z(t)]^(N/s, 10 -6 /s or 114 Pais)^(4.27)where z(t) is a load, strain, direct stress or bond stress function,For the time interval between two consecutive sampling points, which is usually a veryshort time, the rate over this interval, can be evaluated by the averaging method,i.e.(N/s, 10 -6 /s or 111Pa/s)^(4.28)whereAz i (t) = the increment of the load, strain or stress^(N/s, 10 -6 /.s or AI Pa /s)= the time intervalThen the rate over the whole event isi( 1 )^(N/_, 10 -6 / s or Al Pals)^(4.29)whereN = the number of the time intervalChapter 4. Analysis of Test Data^ 1514.10 Work, Energy and Energy Balance4.10.1 Kinetic Energy, Potential Energy, and Work done by the HammerWhen the hammer was raised to a drop height h, its potential energy, (also the totalenergy) E h„ 13 isp^9 h^N in)^ (4.30)where= the mass of the hammerand the kinetic energy at the moment when it hits the specimen Eh a ,k isE rna, k = Mha V ha (0) 2^21 111 [2 (0.919) h]^(Nut)^(4.31)wherev h„(0) = the velocity of the hammer at the time of impact (see Eq. 4.12)(mm /.^)The energy consumed by the friction and air resistance during the first impact eventE^isChapter 4. Analysis of Test Data^ 159E h „,^P^ha , k^0.09M h a gh^(Nirt)^(4.32)From the law of conservation of energy, the kinetic energy lost by the hammer afterimpact.^E, is,1= 9 vh„ (1)]^(Nin) (4.33)where t i„(0) and z,,, a (t) are the velocity of the hammer at the beginning (t = 0) and theend (1 = t) of the contact, respectively (see Eqs. 4.12 and 4.13).Actually, the second term in the above equation represents the kinetic energy of thehammer left at any moment t during impact, Eha,/qt,1,r^2E ha, le f t = 75 11/1 (N711)^ (4.34)At the end of impact, the total loss of kinetic energy of the hammer is2 M h„ 1, 2h ( 0 )0 )^v (\"^d )^(Arm.)^(4.35)wherefeud = the duration of the impact eventIn the case of rebound, the data acquisition system generally records the second blow.The interval between the first and second blows represented the total time for the hammerChapter 4. Analysis of Test Data^ 153to rebound and fall down again. From kinetics, it is possible to determine the reboundvelocity v r ,, b,„,„d based on the recorded time data (see Appendix G). It is given byv rebound = 0.4775 t rebound (1 + 0.090^(7/i/s)^(4.36)where= the time interval recorded^(s )Thus the rebound energy of the hammer E ha ebound141^2E^2rebound =^-11. ha V re b oun d= 0.1354M h„ g2 t 2,,,bou„ d (N171, )At time I, during the impact the work done by the applied load W (I.) is, a (t) = f Ft (t) d i,„(t) (II^(N7n)^(1.37)whereFt (t) = the applied load on the rebar (see Eq. 4.6)^(N)d 10 (I) = the distance the hammer travels after impact (see Eq. 4.15)^(mm)It is more practical to change the above formula from the time-domain to the displace-meat-doinain,Chapter 4. Analysis of Test Data^ 154whered14/ h„((.1) =^Ft (d)ds0(Ntn)^(4.38)d = the distance the hammer travels^(mm)Thus the total work done by the hammer during the impact event is(tend11: 1, a (d) = 10^Ft (d)ds (Nrit)^(4.39)where(I,„ d = the total distance the hammer travels during impact^(mm)The above integration represents the area under the curve in the contact load versusdisplacement graph.From the law of conservation of energy,Etta , p I a, f r^W ha + E ha,rEdound (Nrn)^(4.40)whereW h„ = the work done by the hammer at the end of the impact event^(NIA)Chapter 4. Analysis of Test Data^ 1554.10.2 Strain Energies and Fracture EnergiesAt any moment (t = t) the fracture energy in bond can be calculated byt= 10whereu1r Dto (Ls[ft0 dt^(Nin) (4.41)/^=^the length over which bond slip occurs^12117)u.^=^the bond stress^(M Pa)=^the bond slip^(mm)D^= the diameter of the rebar^(mm)In order to study the fracture energy in bond in a time period of Si, 06176, theintegration,fol 217Dtt ,can be changed from the length-domain to the bond slip-domain, i.e.,Ati:b^[f torD (Ltd fit^(N77/)^(4.42)where^Chapter 4. Analysis of Test. Data^ 156w = the slip^(nun)The above integration represents the area under the curve in the bond stress versusslip graph.At any moment during impact the strain energy stored in the rebar, Er,,,t, is evalu-ated byE rc, sir^ft^I cr 2^JO —2E As (ill dt^(N7n)^(4.43)and the strain energy stored in the concrete, E c , str , is/ (7.2^E, sir = f^dt^(N7n)^(4.44)f o 2EAll of the above calculations are done by numerical integration in computer.4.11 Curve FittingWhen it, was necessary to fit a function through a set of experimental data valuesor calculated values, such as for establishing an explicit mathematical formula for thebond stress-slip relationship through processed data points for bond stress and bond slip,several data approximation methods were employed. To seek an approximation to thedata. a mathematical function which contains a number of coefficients was specified. Thereasons why a function might be chosen areChapter 4. Analysis of Test Data.^ 1571. the function might be known explicitly from theoretical considerations;2. it might reflect results obtained by the previous researchers;3. it has a form which can approximate the curve of the data points; and4. a combination of the above three considerations.The method of least squares was used both for possible linear and nonlinear fits.F^P2,^, p„i;Letbe the function to be fitted andbe the set of data points, where pi m) are unspecified parameters.Minimizingyd 2 (4.45)i.e. solving the equation groupapt =0 (j=1 , 2,^m)^ (4.46)will give the values of the parameters,(pi, P2^• • • , P7>, )Chapter 4. Analysis of Test Data^ 158Thus the fitting functionF (pa, p2,^p„,; x)is determined. This is also done by computer.4.12 Statistical AnalysisFor a normal distribution, the mean of a set of experimental data :r isx = (4.47)where= the total number of samplesx i = the experimental dataand its standard deviation S is,02=1 N -= (4.48)the coefficient of variation c 1, isCv = -x (4.49)Chapter 4. Analysis of Test Data^ 1594.13 Computer programA program written in FORTRAN that ran on a mainframe computer was used toprocess the data. The input is the data file which consists of the raw data from thedata acquisition system for each specimen. The program will then do the followingautomatically1. search and save the useful portion of the raw data;2. apply the base line setting method to each signal;3. apply FFT to each signal and get its spectrum;4. filter out unwanted frequencies from the spectrum;5. apply inverse FFT to the filtered spectrum to get the true signal;6. calculate the contact load, applied load, and plot the load history curve;7. calculate various accelerations, velocities and displacements of the rebar and thehammer, and plot the applied load versus displacement curve;8. calculate the elongation of the rebar;9. calculate the strains and stresses in the rebar and the concrete, find the averagevalue, and plot the distribution curves;10. calculate the bond stress and bond slip, find the average value, and plot the distri-bution curve;11. calculate the strain and stress rates; andChapter 4. Analysis of Test Data^ 16012. calculate kinetic, potential and fracture energies.Some of the above outputs were used to carry out statistical calculations and curvefitting.t t t t t t t t t t RebarPush-in Specimen ConcreteChapter 4. Analysis of Test DataPull-out Specimen161Concrete• •••f: i__,...^i- i2: ii ::i ...._i --i::•_ 4, /• ••f^ft t^t^t^tRebar1 1Figure 4.13: One of the Calculation Models for the Test SpecimensChapter 5Experimental Results5.1 IntroductionBasically the experiments described herein consisted of pull-out tests and push-in tests.For both types of tests the experimental work was carried out for two different types ofreinforcing bars (smooth and deformed), two different concrete compressive strengths(normal and high), two different fibres (polypropylene and steel), and different fibrecontents (0.1 %, 0.5% and 1.0% by volume), and three different types of loading: static,dynamic and impact loading. For the dynamic loading there were two rates (low andhigh) and for the impact loading there were three rates (low, medium and high). Table3.9 in Chapter 3 shows the different loading types in this experimental study.Altogether $00 specimens were tested, of which 600 were specimens with deformedbars and 200 were specimens with smooth bars; 640 were tested under dynamic loadingat different rates and 160 were tested under static loading. For the push-in tests withdeformed bars, each set of specimens consisted of 6 samples and for pull-out tests eachset consisted of 4 samples. Tests with smooth bars were mainly for comparison, and eachset only included 2 samples. One or two bars out of each set were instrumented with 5pairs of strain gauges, depending on the type of loading and the rebar. Tables 3.10 to162Chapter 5. Experimental Results^ 1633.13 in Chapter 3 summarize the test specimens.In order to investigate the bond phenomenon for each type of test and to comparethe results within different types of tests, it is necessary to calculate the stresses anddisplacements at different points in the steel and in the concrete. These stresses anddisplacements were time dependent under dynamic loading. That is, they varied withtime. In most cases it was appropriate to compare the corresponding \"peak\" values,which referred to the moment that the applied loads reached their peak values. In othercases, the \"mean\" values, which were computed by taking the average of all the datapoints over the time period, were compared. Then a representative value was obtainedby statistically averaging the calculated results from the same set of specimens. Theequations used in the data processing are given in the related sections in Chapter 4.Since the calculations of stresses and displacements are based on the recorded data.from the strain gauges, the spacing of these strain gauges can affect the accuracy of theresults. The bond stress computed from(as,, — as,.) I4LYX(4.24)is a local average value between two consecutive strain gauges. However, in reality, theremight be a high concentration of bond force at the interface in the concrete immediatelyahead of the ribs, because of the wedging action between the ribs of the rebar and theconcrete. Furthermore, any cracking at the interface might increase the stress level inthe bar locally to a great extent. Nevertheless, smooth curves were drawn to fit all of theexperimental or calculated data points, using the method of least squares (see SectionChapter 5. Experimental Results^ 1644.11 in Chapter 4).Note that in all of figures and tables in this chapter, the following notation is used:PF = Polypropylene fibre concreteSF = Steel fibre concreteS = The Static loadingM = The medium rate loading1 = The high rate loading (impact)Medium I = The bond stress rate is 0.5 10 -6 — 0.5 10' (111 Pa/ s)Medium II = The bond stress rate is 0.5 • 10' — 0.5 • 10' (MPa/s)Impact I = The bond stress rate is about 0.5 • 10 -4 (AlPais)Impact II = The bond stress rate is about 0.5 • 10 -3 (M Pals)Impact III = The bond stress rate is about 0.5 • 10 -2 (MPa/8)Chapter 5. Experimental Results^ 1655.2 Steel Stresses5.2.1 GeneralThe stress in the steel rebar is the direct reason for the development of bond stressat the interface between the steel and the concrete, and it is the only parameter whichcan be practically measured (strain) and calculated inside the specimen. On the otherhand, it is the difference in the strains between the steel and the concrete that producesthe slip at a given point at the interface. Therefore, the stress in the steel rebar is oneof the most important parameters in this experimental work. Stresses in the steel werecalculated directly from the recorded strain data along the rebar byEs (1 — ids) = (1 + ps) (1 — 211s) Es(4.20)Fig. 5.1 illustrates the stresses in the steel rebar at the peak load, Fe = 30 kN. Thiswas a plain concrete specimen with a smooth rebar subjected to an impact test with adrop height of 300 7n7n.It should be noted that the distribution curves of steel stresses were plotted based onthe four average data points between strain gauges and on the boundary conditions atthe loaded and free ends. However, only fitted curves are shown in all figures except inthe first one (Fig. 5.1), in which both the data points and the best fit curves are shown.Chapter 5. Experimental Results^ 1665.2.2 Tests with Smooth BarsFor the specimens with smooth rebars, the effects of concrete strength, addition of fibresor the loading rate on the stresses in the steel were not significant, in terms of either theirvalues or distributions, as shown in Figs. 5.2, 5.3 and 5.4. It can be seen from thesefigures that for static loading the stresses in the smooth rebar decrease linearly, withthe maximum stress at the loaded end and zero stress at the free end. Increasing theconcrete strength or adding steel fibres resulted in slight increases in the stress values,but the linear nature of the distribution remained unchanged. This suggested that theforce transmitted between a smooth rebar and the concrete be due to chemical adhesionand frictional resistance. A high rate of loading caused a slight stress concentration atthe loaded end, which might be due to the sudden change in the boundary conditionsof the rebar (from free surface to concrete confinement). Due to the Poisson effect therewas almost no frictional resistance at the interface between the rebar and the concreteafter the adhesion had been destroyed for the pull-out test. On the other hand, thefrictional force at the interface between the rebar and the concrete would increase to amaximum value when the push-in force increased (since the radial stress also increased),so the distribution curve of the stress in the steel exhibits greater values and slopes forthe push-in tests than for the pull-out tests, as shown in Fig. 5.5.Because the tests on specimens with smooth bars were primarily for comparisonwith the test results from the specimens with deformed bars, the following sections willemphasize the latter results. For simplicity, all of the figures given in this section, unlessspecified. are for the specimens with plain normal strength concrete and for push-in tests.SCO0^ 15.9^ VA^ 47.7Distance from the Loaded End (mm)NS0^ 151^ 911^ 47.7Distance from the Loaded End (mm)$OS0Chapter 5. Experimental Results^ 167Figure 5.1: Stresses in the Smooth RebarStatic^Medium II^Impact IIIFigure 5.2: Effects of Loading Rate on the Stresses in the Smooth Rebar0Chapter 5. Experimental Results^ 1680^ 159^ 313^ 47.7Distance from the Loaded End (mm)Normal Strength^High StrengthFigure 5.3: Effects of Concrete Strength on the Stresses in the Smooth RebarDistance from the Loaded End (mm)Plain Polypropylene Fibers (0.5%) Steel Fibers (0.5%)Figure 5.4: Effects of Fibre Additions on the Stresses in the Smooth RebarkIw 400Vte*S 2000501Chapter 5. Experimental Results^ 1690^ 15.9^ 31.8^ 47.7Distance from the Loaded End (mm)Pull-out^Push-inFigure 5.5: The Stresses in the Smooth Rebar for Pull-out and Push-in TestsChapter 5. Experimental Results^ 1705.2.3 Tests with Deformed Bars5.2.3.1 Effects of Loading RateFor all of the specimens with deformed bars, both the maximum and the averagevalues of the stresses in the steel increased considerably with the increase of loadingrate. There was more stress concentration at the loaded end than for the specimenswith smooth bars. In addition, unlike the cases of specimens with smooth rebars, thestress distribution curves are no longer straight lines. Roughly speaking, these curvestend to have larger slopes than those from tests with smooth bars. This means thathigher bond stresses were developed under higher loading rates. Fig. 5.6 shows differentdistribution curves of the stresses in the steel under different loading rates for a plainconcrete specimen.By comparing Fig. 5.7 with Fig. 5.6 it can be concluded that the addition ofpolypropylene fibres to the concrete had no significant influence on the results, in termsof the effects of the loading rate on the stresses in the steel. However, the loading rateseemed to have greater effects on specimens made of steel fibre reinforced concrete thanother types of specimens (see Fig. 5.8). This is because the shear mechanism playsa major role in the bond-slip process for deformed bars; the bond resistance is due tothe ribs bearing on the concrete. Steel fibres improved the concrete strength and thecrack resistance. This improvement was outstanding, especially under high rate loading;therefore, the force transmitted to the concrete increased dramatically with an increasein loading rate.It should be noted that Figs. 5.6 to 5.8 refer to the tests for specimens with normal'peak^ peak value under static loadingpeak value of steel stresses under a certain type of loading conditionChapter 5. Experimental Results^ 171concrete strength. Fig. 5.9 represents the specimens made with high concrete strengthreinforced with steel fibres. It was found that the influence of the loading rate was moresignificant for high strength concrete than for normal strength concrete.Similar to the case of specimens with smooth rebars, push-in tests always exhibitedhigher stresses in the steel than pull-out tests, as shown in Fig. 5.10.In order to evaluate the effects of the loading rate on the stresses in the steel withseveral different variables, two relative \"indices\", /peak and /average, were introduced.They are defined as,and /averageaverage value of steel stresses under a certain type of loading conditionaverage value under static loadingSome of the results are summarized in Table 5.1.Chapter 5. Experimental Results^ 172Table 5.1: Effects of Loading Rate on the Steel StressType ofSpecimenLoadingRate a-^Relative Index/peak /averagePlainConcreteStatic 1.00 1.00Medium I b 1.02 1.01Medium II 1.05 1.02Impact I 1.06 1.02Impact II 1.08 1.04Impact III 1.10 1.05PolypropyleneFibre Concrete(0.5%)Static 1.02 1.01Medium I 1.05 1.02Medium II 1.07 1.03Impact I 1.09 1.04Impact II 1.11 1.05Impact III 1.13 1.07SteelFibre Concrete(1.0%)Static 1.42 1.10Medium I 1.46 1.11Medium II 1.50 1.17Impact I 1.65 1.19Impact II 1.72 1.21Impact III 1.81 1.23SteelFibre Concrete(1.0%)(Pull-out)Static 0.93 0.94Medium I 0.94 0.94Medium II 0.95 0.95Impact I 0.96 0.95Impact II 0.97 0.96Impact III 0.98 0.97SteelFibre Concrete(1.0%)(High Strength)Static 1.54 1.16Medium I 1.60 1.17Medium II 1.68 1.22Impact I 1.75 1.25Impact II 1.86 1.27Impact III 1.91 1.30From push-in tests with normal strength concrete specimens, unless specified.b See Table 3.9 in Chapter :3 for details.Chapter 5. Experimental Results^ 173Distance from the Loaded End (mm)Static^Medium II^Impact IIIFigure 5.6: Effects of Loading Rate on the Stresses in the Deformed Rebar(Plain Concrete)Distance from the Loaded End (mm)Static^Medium II^Impact IIIFigure 5.7: Effects of Loading Rate on the Stresses in the Deformed Rebar(Polypropylene Fibre Concrete)15.9^ 31i^ 472Distance from the Loaded End (mm)Chapter 5. Experimental Results^ 174eco2 6004009.)20000^ 15.9^ 318^ 47.7^656Distance from the Loaded End (mm)Static^Medium II^Impact III•■■••■•••■Figure 5.8: Effects of Loading Rate on the Stresses in the Deformed Rebar(Steel Fibre Concrete)Static^Medium II^Impact IIIFigure 5.9: Effects of Loading Rate on the Stresses in the Deformed Rebar(High Strength Concrete)15$^ 318^ 47.7Distance from the Loaded End (mm)83ZChapter 5. Experimental Results^ 175Static^Medium II^Impact IIIFigure 5.10: Effects of Loading Rate on the Stresses in the Deformed Rebar(Pull-out Tests)Chapter 5. Experimental Results^ 1765.2.3.2 Effects of Concrete StrengthGeneral speaking, the stresses in the steel increased for high strength concrete spec-imens. This seems logical, since the shear mechanism is the main mechanism for thebond resistance of deformed bars. Fig. 5.11 is an example of the effects of the loadingrate. By using the relative \"index\" values, as defined in the previous section, the effectsof concrete strength on the stresses in the steel can be shown more clearly. Table 5.2gives some results.ecoai 400402C000^ 15$^ 31$^ 47.7Distance from the Loaded End (mm)Normal Strength^High StrengthFigure 5.11: Effects of Concrete Strength on the Stresses in the DeformedRebarChapter 5. Experimental Results^ 177Table 5.2: Effects of Concrete Strength on the Steel StressesLoadingType aType ofSpecimenConcreteStrengthRelative Index/ peak /averageStaticPlainConcreteNormal 1.00 1.00High 1.19 1.17PolypropyleneFibre Concrete (0.5%)Normal 1.02 1.01High 1.20 1.16SteelFibre Concrete (1.0%)Normal 1.42 1.10High 1.67 1.20Medium IIPlainConcreteNormal 1.05 1.02High 1.21 1.15PolypropyleneFibre Concrete (0.5%)Normal 1.07 1.03High 1.23 1.16SteelFibre Concrete (1.0%)Normal 1.50 1.17High 1.65 1.19Impact IIIPlainConcreteNormal 1.10 1.05High 1.28 1.18PolypropyleneFibre Concrete (0.5%)Normal 1.13 1.07High 1.32 1.22SteelFibre Concrete (1.0%)Normal 1.81 1.23High 2.02 1.34'From push-in tests.Chapter 5. Experimental Results^ 1785.2.3.3 Effects of Fibre AdditionsThe effects of adding fibres to the concrete mixture on the stresses in the deformedrebar were found to be quite different for polypropylene and steel fibres. From Fig. 5.12it can be seen that the polypropylene fibres did not have much effect on the values ofthe steel stresses and their distribution along the rebar, while the steel fibres greatlyincreased the values of the steel stresses at the loaded end of the rebar. This effect ofthe steel fibres became larger with an increase in the fibre content, as illustrated in Fig.5.13. Table 5.3 gives the relatives index numbers, which partly reflect the effects.15.9^ 819^ 47.7Distance from the Loaded End (mm)Plain Polypropylene Fibers (0.3%) Steel Fibers (0.3%)Figure 5.12: Effects of Fibre Additions on the Stresses in the Deformed Rebar(Different Fibres)63.5Chapter 5. Experimental Results^ 179Table 5.3: Effects of Adding Fibres on the Steel StressesLoadingType aType ofSpecimenFibreContentRelative Index/ peak /averageStaticPlain Concrete 0% 1.00 1.00PolypropyleneFibre Concrete0.1% 1.00 1.000.5% 1.02 1.01SteelFibre Concrete0.5% 1.10 1.031.0% 1.42 1.10Medium IIPlain Concrete 0% 1.07 1.03PolypropyleneFibre Concrete0.1% 1.10 1.050.5% 1.23 1.16SteelFibre Concrete0.5% 1.24 1.131.0% 1.65 1.19Impact IIIPlain Concrete 0% 1.10 1.05PolypropyleneFibre Concrete0.1% 1.10 1.050.5% 1.13 1.07SteelFibre Concrete0.5% 1.55 1.121.0% 1.81 1.23Impact III(pull-out)Plain Concrete 0% 0.95 0.94PolypropyleneFibre Concrete0.1% 0.95 0.940.5% 0.96 0.94SteelFibre Concrete0.5% 0.97 0.961.0% 0.98 0.97'From push-in tests.Chapter 5. Experimental Results^ 18015.9^ 31.8^ 47.7Distance from the Loaded End (mm)0.0% 0.5%^1.0% Figure 5.13: Effects of Steel Fibre Additions on the Stresses in the DeformedRebar (Different Fibre Content)Chapter 5. Experimental Results^ 1815.2.3.4 Differences between Pull-out and Push-in TestsUnder either static or impact loading, push-in tests always produced greater stressesin the steel rebar than pull-out tests. As stated earlier, this is due to the Poisson effect.Figs. 5.14 and 5.15 show some of these results. Also, Table 5.4 gives some relative indexnumbers.159^ 319^ 47.7^636Distance from the Loaded End (mm)Pull-out^Push-inFigure 5.14: Stresses in the Deformed Rebar for Pull-out and Push-in Tests(Static)Chapter 5. Experimental Results^ 182Table 5.4: Effects of Pull-out and Push-in Forces on Steel StressesLoadingRateType ofSpecimenLoadingTypeRelative Index'peak /averageStaticPlainCon cretePull-out 0.92 0.91Push-in 1.00 1.00PolypropyleneFibre Concrete (0.5%)Pull-out 0.92 0.92Push-in 1.02 1.01SteelFibre Concrete (1.0%)Pull-out 0.93 0.94Push-in 1.81 1.23Medium IIPlainConcretePull-out 0.93 0.93Push-in 1.05 1.02PolypropyleneFibre Concrete (0.5%)Pull-out 0.94 0.93Push-in 1.07 1.03SteelFibre Concrete (1.0%)Pull-out 0.95 0.95Push-in 1.50 1.17Impact IIIPlainConcretePull-out 0.95 0.94Push-in 1.10 1.05PolypropyleneFibre Concrete (0.5%)Pull-out 0.96 0.94Push-in 1.13 1.07SteelFibre Concrete (1.0%)Pull-out 0.98 0.97Push-in 1.81 1.23I140 0^15.9^815^47.7Distance from the Loaded End (mm)$35Chapter 5. Experimental Results^ 183Pull-out^Push-in1•11.111■ 0•1•MIMIO •■■•■■■••Figure 5.15: Stresses in the Deformed Rebar for Pull-out and Push-in Tests(Impact)Chapter 5. Experimental Results^ 1845.3 Concrete Stresses5.3.1 GeneralThe concrete stress refers to the axial stress inside the concrete at the interface betweensteel rebar and concrete; in some cases it also refers to the stress inside the concrete in thevicinity of the rebar. There are also radial and circumferential stresses in the concrete.However, the study of the stresses in the concrete would emphasize on the axial stress.Not only does the amount of force transmitted from the steel rebar depend on the stressstate of the concrete and its strength, but also the slip at any given point at the interfaceis determined by the difference in strain between the steel and the concrete, and by thedevelopment of cracks in the concrete. Unlike the stress in the steel, the stress in theconcrete is not easy to measure without disturbing the stress field in a small specimen. Inthis study, it was calculated from the the stress in the steel by applying static equilibriumconditions (Eqs. 4.23 and 4.24).As stated before, the distribution curves of concrete stresses were plotted based onthe four average data points between strain gauges and on the boundary conditions atthe loaded and free ends, and only fitted curves are shown in all figures except in thefirst one (Fig. 5.16), in which both the data points and the best fit curves are shown.5.3.2 Effects of Loading RateFor both plain concrete and fibre reinforced concrete specimens, the stresses in theconcrete increased with an increase in loading rate, as shown in Fig. 5.16. This isconsistent with the well-known effects of stress rate on concrete strength.Chapter 5. Experimental Results^ 1855.3.3 Effects of Concrete StrengthHigh strength concrete can carry more load without cracking or failure than normalstrength concrete under static loading. But high strength concrete containing silica fumemay allow cracking at a low level of loading under impact condition. Figs. 5.17 and5.18 show the stresses in the concrete at the interface between the steel and the concreteunder static and impact loading, respectively. Note that for normal strength concrete,the stress at the loaded end almost doubles in going from static to impact loading; forthe high strength concrete, the increase in stress is more modest, about 22%.5.3.4 Effects of Fibre AdditionsThe addition of polypropylene fibres (either 0.1% or 0.5% by volume) did not havemuch influence on the stresses in the concrete under any loading conditions, in termsof either the stresses or their distribution, as illustrated in Figs. 5.19, 5.20 and 5.21,although there were modest improvement for the dynamic loading. However, steel fibresseemed to have improved the tensile strength of the concrete mixture, and the shearstrength as well. Thus, the stresses in the concrete increased for the steel fibre concretespecimens, and the slopes of the distribution curves also increased. Furthermore, becausesteel fibres improved the crack resistance there were reduced stress concentrations in thedistribution diagram.15.9^ 31.9^ 47.7Distance from the Loaded End (mm)1033ai9V 600U0 4fiAWIEi'A o o6360^ 15.9^ 31.9^ 47.7 63.0Chapter 5. Experimental Results^ 186Static^Medium II^Impact IIIFigure 5.16: Effects of Loading Rate on the Stresses in the ConcreteDistance from the Loaded End (mm)Normal Strength^High StrengthFigure 5.17: Effect of Concrete Strength on the Stresses in the Concrete(Static)Chapter 5. Experimental Results^ 187gOOfi 4215.9^ 31.8^ 47.7Distance from the Loaded End (mm)Normal Strength^High StrengthFigure 5.18: Effect of Concrete Strength on the Stresses in the Concrete (Im-pact)15.9^ 91.8^ 47.7Distance from the Loaded End (mm)Plain Polypropylene Fibers (0.3%) Steel Fibers (0.3%)Figure 5.19: Effects of Fibres on the Stresses in the Concrete (Static)g 6O0V 420^ 15.9^ 319^ 47.7Distance from the Loaded End (mm)Chapter 5. Experimental Results^ 1880^ 159^ 318^ 47.7Distance from the Loaded End (mm)Plain Polypropylene Fibers (0.3%) Steel Fibers (0.3%)Figure 5.20: Effects of Fibres on the Stresses in the Concrete (Medium)Plain Polypropylene Fibers (0.3%) Steel Fibers (0.3%)Figure 5.21: Effects of Fibres on the Stresses in the Concrete (Impact)Chapter 5. Experimental Results^ 1895.3.5 Differences between Pull-out and Push-in TestsDue to the Poisson effect, there was no radial force acting at the contact surfaceof concrete after the chemical adhesion had been destroyed during the pull-out tests,especially for specimens with smooth rebars. The stresses in the concrete, thus, weregenerally less for pull-out tests than push-in tests. Fig. 5.22 shows the difference betweenthe pull-out and push-in tests for a specimen with steel fibre concrete under impactloading.15.9^ 819^ 47.7Distance from the Loaded End (mm)Pull-out^Push-inFigure 5.22: The Stresses in the Concrete for Pull-out and Push-in Tests (Im-pact)Chapter 5. Experimental Results^ 1905.4 Bond Stresses5.4.1 GeneralThe measurements of bond stress represent perhaps the most important results of thisexperimental study. The local bond stresses were calculated from the axial stresses inthe steel by the equilibrium condition,--^) u D=4AX(4.24)The bond stress calculated from this equation is the average bond stress over a length of15.9 mm (the spacing between two consecutive strain gauges). Fig. 5.23 illustrates thetypical bond stresses at the peak load, Fb = 30 kN, for a plain concrete specimen withsmooth rebar subjected to an impact test with a drop height of :300 mm. Note that thebond stress was constant over the entire embedded length of the rebar.As stated before, the distribution curves of bond stresses were plotted based on thefour average data points between strain gauges and on the boundary conditions at theloaded and free ends, and only fitted curves are shown in all figures except in the firstone (Fig. 5.2:3), in which both the data points and the best fit curves are shown.5.4.2 Tests with Smooth BarsFor all of the specimens with smooth rebars, the effects of loading rate, concretestrength or the addition of fibres on the bond stresses were not significant, in terms ofeither their values or distributions, as shown in Figs. 5.24, 5.25 and 5.26. It can be seenfrom these figures that for static loading the bond stresses are almost uniform along theChapter 5. Experimental Results^ 191but the nature of the distribution remained unchanged. This was because the bondstress between a smooth rebar and the concrete was due only to chemical adhesion andfrictional resistance. A high rate of loading caused a slight stress concentration at theloaded end, which might be due to the sudden change of the boundary condition of therebar (from a free surface to concrete confinement). Due to the Poisson effect there wasalmost no frictional resistance at the interface between the rebar and the concrete afterthe adhesion had been destroyed for the pull-out test. In contrast, the frictional forceat the interface between the rebar and the concrete would increase to a maximum valuewhen the push-in force increased (radial stress also increased), so the bond stress valueswere larger for push-in tests than those for pull-out tests; though the uniform nature ofthe distribution remained the same. An example of this is given in Fig. 5.27.50S 40wontcol 20I0r4 100 0^ 154^ 312^47.7Distance from the Loaded End (mm)SSAFigure 5.23: The Bond Stresses for a Smooth RebarChapter 5. Experimental Results^ 192so03 4033ehl 20A 10To o 15.9^ 31.9^ 477^ 63.6Distance from the Loaded End (mm)Static^Medium II^Impact HIFigure 5.24: Effect of Loading Rate on the Bond Stresses for a Smooth Rebar159^ siB^ 47.7Distance from the Loaded End (mm)Normal Strength^High StrengthFigure 5.25: Effect of Concrete Strength on the Bond Stresses for a SmoothRebarso15.9^ 311^ 47.7Distance from the Loaded End (mm)Chapter 5. Experimental Results^ 19315.9^ 311^ 47.7Distance from the Loaded End (mm)Plain Polypropylene Fibers (0.5%) Steel Fibers (0.5%)Figure 5.26: Effect of Fibre Additions on the Bond Stresses for a Smooth RebarPull-out^Push-inFigure 5.27: The Bond Stresses for a Smooth Rebar for Pull-out and Push-inTestsChapter 5. Experimental Results^ 1945.4.3 Tests with Deformed BarsFor simplicity, all of the figures given in this section, unless specified, are for thespecimens with normal strength concrete in push-in tests.5.4.3.1 Effects of Loading RateFor the specimens with deformed bars, the peak bond stresses increased considerablywith an increase in loading rate. There were higher stress concentrations at the loadedend than for specimens with smooth bars; Unlike the specimens with smooth rebars, thebond stress distribution curves were no longer horizontal lines. The existence of ribs onthe rebar and cracks in the concrete generally caused changes in the curvature of thesteel stress curves. In addition, the bond stress distribution curves were not as smoothas were the curves for smooth bars. Roughly speaking, these curves tended to have largerslopes than those from tests with smooth bars. This means that higher bond stresseswere developed under higher loading rates. Fig. 5.28 shows some different bond stressdistribution curves under different loading rates for a plain concrete specimen.By comparing Fig. 5.29 with Fig. 5.28 it can be concluded that the addition ofpolypropylene fibres to the concrete had no significant influence on the results, in termsof the effect of the loading rate on the bond stresses. However, the loading rate seemedto have a greater effect on specimens made of steel fibre reinforced concrete than on anyother types of specimens (see Fig. 5.30). This is because the shear mechanism plays amajor role in the bond-slip process for deformed bars; with the bond resistance due to theribs bearing on the concrete. Steel fibres definitely improved the concrete strength andthe crack resistance. This improvement is significant, especially under high rate loading./peak^ peak value under static loadingpeal: value of bond stress under a particular loading conditionChapter 5. Experimental Results^ 195Though the crack velocity in concrete may increase proportionally with the loading rate,the presence of steel fibre tends to reduce the rate of crack propagation. It was foundthat, in these tests, the effect of the addition of steel fibres dominated the behaviour.Therefore, the bond stress increased dramatically with an increase in loading rate.It should be noted that Figs. 5.28 to 5.30 are from tests of specimens with normalstrength concrete. Fig. 5.3:1 is for specimens with high strength concrete reinforced with1.0% (by volume) steel fibres. It was found that the influence of the loading rate waseven more significant for high strength concrete than for normal strength concrete.Similar to the case of specimens with smooth rebars, push-in tests always gave higherbond stresses than pull-out tests, as shown in Fig. 5.32.In order to evaluate the effects of the loading rate on the bond stresses for severalimportant variables, two relative \"indices\", / peak and /s lope were introduced. They aredefined asandslope under a particular loading condition/slope^slope value under static loadingthe slope are calculated based on the bond stress vs. distance from the loaded end.Some of the results are summarized in Table 5.5.Chapter 5. Experimental Results^ 196Table 5.5: Effects of Loading Rate on the Bond StressesType ofSpecimenLoadingRate aRelative Indexpeak_pea slopePlainConcreteStatic 1.00 1.00Medium I b 1.02 1.01Medium II 1.05 1.02Impact I 1.06 1.02Impact II 1.08 1.04Impact III 1.10 1.05PolypropyleneFibre Concrete(0.5%)Static 1.02 1.01Medium I 1.05 1.02Medium II 1.07 1.03Impact I 1.09 1.04Impact II 1.11 1.05Impact III 1.13 1.07SteelFibre Concrete(1.0%)Static 1.42 1.10Medium I 1.46 1.11Medium II 1.50 1.17Impact I 1.65 1.19Impact II 1.72 1.21Impact III 1.81 1.23SteelFibre Concrete(1.0%)(Pull-out)Static 0.93 0.94Medium I 0.94 0.94Medium II 0.95 0.95Impact I 0.96 0.95Impact II 0.97 0.96Impact III 0.98 0.97SteelFibre Concrete(1.0%)(High Strength)Static 1.54 1.16Medium I 1.60 1.17Medium II 1.68 1.22Impact I 1.75 1.25Impact II 1.86 1.27Impact III 1.91 1.30'From push-in tests with normal strength concrete specimen, unless specified.b See Table 3.9 in (liapter 3 for details.Ss 40II1 0)^15$^ 311^ 472Distance from the Loaded End (mm)Static^Medium II^Impact III .(;^ i.e.... ...re.... warm, angrier. Chapter 5. Experimental Results^ 197Figure 5.28: Effects of Loading Rate on the Bond Stresses (Plain Concrete)15$^ 311^ 472^116Distance from the Loaded End (mm)Static^Medium II^Impact IIIFigure 5.29: Effects of Loading Rate on the Bond Stresses (Polypropylene FibreConcrete).•■■■■•■•a40a,Iso10aro0so159^ 31.8^ 47.70 ^0Chapter 5. Experimental Results^ 19815.9^ 31.8^ 47.7Distance from the Loaded End (mm)Static^Medium II^Impact IIIFigure 5.30: Effects of Loading Rate on the Bond Stresses (Steel Fibre Con-crete)Distance from the Loaded End (mm)Static^Medium II^Impact IIIFigure 5.31: Effects of Loading Rate on the Bond Stresses (High StrengthConcrete)Chapter 5. Experimental Results^ 1995.4.3.2 Effects of Concrete StrengthGenerally speaking, the bond stresses increased for high strength concrete specimens.This seems logical, since the shear mechanism is the main mechanism for the bondresistance of deformed bars. Fig. 5.33 gives an example to show the different effectsof loading rate. By using the relative \"index\" number, which is defined in the previoussection, the effects of concrete strength on the bond stresses can be shown more clearly.Table 5.6 gives some of these results.Table 5.6: Effects of Concrete Strength on the Bond StressesLoadingType aType ofSpecimenConcreteStrengthRelative Index/peak /slopeStaticPlainConcreteNormal 1.00 1.00High 1.19 1.17PolypropyleneFibre Concrete (0.5%)Normal 1.02 1.01High 1.20 1.16SteelFibre Concrete (1.0%)Normal 1.42 1.10High 1.67 1.20Medium IIPlainConcreteNormal 1.05 1.02High 1.21 1.15PolypropyleneFibre Concrete (0.5%)Normal 1.07 1.03High 1.23 1.16SteelFibre Concrete (1.0%)Normal 1.50 1.17High 1.65 1.19Impact IIIPlainConcreteNormal 1.10 1.05High 1.28 1.18PolypropyleneFibre Concrete (0.5%)Normal 1.13 1.07High 1.32 1.22SteelFibre Concrete (1.0%)Normal 1.81 1.23High 2.02 1.34'From push-in tests.0^ 15.9^ 31.0^ 47.7Distance from the Loaded End (mm)Chapter 5. Experimental Results^ 200159^ 312^ 477Distance from the Loaded End (mm)Static^Medium II^Impact IIIFigure 5.32: Effects of Loading Rate on the Bond Stresses (Pull-out Tests)Normal Strength^High StrengthFigure 5.33: Effects of Concrete Strength on the Bond Stresses40zotoChapter 5. Experimental Results^ 2015.4.3.3 Effects of Fibre AdditionsThe effects on the bond stress of adding fibres to the concrete mixture were found tobe quite different for polypropylene and steel fibres. Figs. 5.34 and 5.35 illustrate twoexamples. Table 5.7 gives the relatives index numbers, which partly reflect these effects.154^ 919^ 477^63.6Distance from the Loaded End (mm)Plain Polypropylene Fibers (0.5%) Steel Fibers (0.5%)Figure 5.34: Effects of Fibre Additions on the Bond Stresses (Different Fibres)5.4.3.4 Differences between Pull-out and Push-in Tests• •^•Under either static or impact loading, push-in tests always produced greater bondstresses in the rebar than pull-out tests. Figs. 5.36 and 5.37 shows some of these results,while Table 5.8 gives some relative index numbers.Chapter 5. Experimental Results^ 202SOa 4030I14 20002 100 015.9^ 3I9^ 47.7Distance from the Loaded End (mm)0.0% 0.5% 1.0%Figure 5.35: Effects of Steel Fibre Additions on the Bond Stresses (DifferentFibre Content)15.9^ 313^ 47.7Distance from the Loaded End (mm)Pull-out^Push-inSIBFigure 5.36: The Bond Stresses for Pull-out and Push-in Tests (Static)Chapter 5. Experimental Results^ 203Table 5.7: Effects of Fibre Additions on the Bond StressesLoadingType aType ofSpecimenFibreContentRelative Index/ peak / slopeStaticPlain Concrete 0% 1.00 1.00PolypropyleneFibre Concrete0.1% 1.00 1.000.5% 1.02 1.01SteelFibre Concrete0.5% 1.10 1.031.0% 1.42 1.10Medium IIPlain Concrete 0% 1.07 1.03PolypropyleneFibre Concrete0.1% 1.10 1.050.5% 1.23 1.16SteelFibre Concrete0.5% 1.24 1.131.0% 1.65 1.19Impact IIIPlain Concrete 0% 1.10 1.05PolypropyleneFibre Concrete0.1% 1.10 1.050.5% 1.13 1.07SteelFibre Concrete0.5% 1.55 1.121.0% 1.81 1.23Impact III(pull-out)Plain Concrete 0% 0.95 0.94PolypropyleneFibre Concrete0.1% 0.95 0.940.5% 0.96 0.94SteelFibre Concrete0.5% 0.97 0.961.0% 0.98 0.97From push-in tests.Chapter 5. Experimental Results^ 204Table 5.8: The Effects of Pull-out and Push-in Forces on the Bond StressesLoadingRateType ofSpecimenLoadingTypeRelative Index/- kpea / slope StaticPlainConcretePull-out 0.92 0.91Push-in 1.00 1.00PolypropyleneFibre Concrete (0.5%)Pull-out 0.92 0.92Push-in 1.02 1.01SteelFibre Concrete (o.5%)Pull-out 0.93 0.94Push-in 1.81 1.23Medium IIPlainConcretePull-out 0.93 0.93Push-in 1.05 1.02PolypropyleneFibre Concrete (0.5%)Pull-out 0.94 0.93Push-in 1.07 1.03SteelFibre Concrete (0.5%)Pull-out 0.95 0.95Push-in 1.50 1.17Impact IIIPlainConcretePull-out 0.95 0.94Push-in 1.10 1.05PolypropyleneFibre Concrete (0.5%)Pull-out 0.96 0.94Push-in 1.13 1.07SteelFibre Concrete (0.5%)Pull-out 0.98 0.97Push-in 1.81 1.23Chapter 5. Experimental Results^ 205Distance from the Loaded End (mm)Pull-out^Push-inFigure 5.37: The Bond Stresses for Pull-out and Push-in Tests (Impact)Chapter 5. Experimental Results^ 2065.5 Slip and Slip Distribution5.5.1 GeneralThe local slip between the rebar and the concrete at any point along the rebar wascomputed from the compatibility condition between the two materials,w (x) = o (E S — c, )^(4.25)since the strain values in both steel and concrete, c s and c„, were average numbersbetween any two consecutive measurement points, the local slips calculated were averagenumbers also.As stated before, the distribution curves of slips were plotted based on the four averagedata points between strain gauges and on the boundary conditions at the loaded and freeends, and only fitted curves are shown in all figures except in the first one (Fig. 5.38),in which both the data points and the best fit curves are shown.5.5.2 Tests with Smooth BarsFor specimens with smooth bars, the slips uniformly distributed along the rebars (seeFig. 5.38). This was true for all loading conditions, since the bond between the steel andthe concrete was due only to the chemical adhesion and frictional resistance between thesteel and the concrete. In many pull-out or push-in tests the local slips were found bydividing the measured end slips by the embedment lengths. This method is appropriatefor smooth bars.Chapter 5. Experimental Results^ 2075.5.3 Tests with Deformed BarsThe results for specimens with deformed bars were quite different from those for smoothbars. They will be discussed in the following sections.5.5.3.1 Effects of Loading RateAt the same load level, the slip values were generally lower for higher loading ratesthan for lower loading rates. Table 5.9 gives one example of this, in terms of the localslip values at the middle of the embedment length.Table 5.9: The Local Slips at the Middle of the Embedment LengthConcreteStrengthType ofSpecimenLoadingTypeLocal Slip (0.001 7n7n)Static Medium ImpactNormalPlainConcretePull-out :34 :35 :38Push-in :31 32 :35PolypropyleneFibre Concrete (0.5%)Pull-out 33 :33 36Push-in 30 :31 :34SteelFibre Concrete (1.0%)Pull-out 28 30 31Push-in 27 30 :39HighPlainConcretePull-out :33 :35 :37Push-in :39 :33 35PolypropyleneFibre Concrete (0.5%)Pull-out :34 :34 35Push-in :3:3 34 :36SteelFibre Concrete (1.0%)Pull-out 26 27 :30Push-in 24 26 31Chapter 5. Experimental Results^ 2085.5.3.2 Effects of Concrete StrengthThe influence of concrete strength on the slip and slip distribution was found to beslight, under either static or dynamic loading conditions, as illustrated in Figs. 5.39 and5.40.5.5.3.3 Effects of Fibre AdditionsAdding polypropylene fibres to the concrete mixture does not change either its strengthor Young's modulus significantly, and thus has little effect on the slip distribution forany loading conditions, as shown in Fig. 5.41.Adding steel fibres to the concrete mixture at 1.0% by volume increased not only thestrength, but also the Young's modulus. This resulted in a. relatively small slip at thesame loading level compared to plain concrete, as can be seen from Fig. 5.42. For thepurpose of comparison the slip distribution curves in Fig. 5.42 were referred to the sameexternal load , and not the peak load. It is known that the presence of steel fibres makescrack propagation slower and inhibits crack opening, especially for dynamic loading. Thisimproved the \"slip concentration\" at the interface between steel and concrete. One ofthe representative curves is shown in Fig. 5.43.5.5.3.4 Differences between Pull-out and Push-in TestsDifferences in the local slips between pull-out and push-in tests can also be found fromTable 5.9. Slips in push-in tests were less than in pull-out tests. This was mainly due toChapter 5. Experimental Results^ 2095•0 ^0 153 31.3^ 47.7 OnDistance from the Loaded End (mm)Figure 5.38: The Local Slip Distribution for Specimens with Smooth Barss i!0 ^0 15.9^ 31.8^ 47.7^03.5Distance from the Loaded End (mm)Normal Strength^High StrengthFigure 5.39: Influence of Concrete Strength on Slip Distribution (Static)Chapter 5. Experimental Results^ 2101.11••■■15.9^ 31.5^ 47.7Distance from the Loaded End (mm)Normal Strength^High StrengthFigure 5.40: Influence of Concrete Strength on Slip Distribution (Impact)a4d 3TM 215.9^ 315^ 47.7Distance from the Loaded End (mm)Plain Polypropylene Fibers (0.5%)Figure 5.41: Influence of 0.5% by Volume Polypropylene Fibres on Slip Distri-bution (Impact)^••■•■••••....,TAM. ....maChapter 5. Experimental Results^ 211159^ 318^ 47.7Distance from the Loaded End (mm)Plain^Steel Fibers (0.3%)■••••■• ••■•■ •■■■•Figure 5.42: Influence of 0.5% by Volume Steel Fibres on Slip Values (Static)15.9^ 318^ 472Distance from the Loaded End (mm)Plain^Steel Fibers (0.5%)aemmow •••••••■• ..•=1•11016Figure 5.43: Influence of 0.5% by Volume Steel Fibres on Slip Distribution(Impact)Chapter 5. Experimental Results^ 212the fact that there were higher radial force in push-in tests than in pull-out tests.Chapter 5. Experimental Results^ 2135.6 Internal Cracking5.6.1 GeneralFor specimens with smooth bars, the basic mechanism of the bond-slip process is afailure of the chemical adhesion and frictional forces at the interface between steel andconcrete. Failure occurs when the high local stresses reach critical values, after whichthere is no further mechanical interlocking taking place at the interface for smooth bars.The force due to adhesion and friction is always less than that needed to initial transversecracks. Several specimens with smooth rebars were examined by cutting through alongtheir central plane, and no transverse cracks due to the bond action were found (see Fig.5.44).For specimens with deformed bars, the cracking mechanism of the pull-out tests wasdifferent from that of the push-in tests. In the case of pull-out tests, when the bondstress reached the critical value, a longitudinal tensile stress and a radial tensile stress(tending to cause separation), combined to produce the first internal cracks from the topsof ribs because of the stress concentrations at these locations. With a further increasein external loading, the Poisson effect in the steel would result in a decrease in the bardiameter, and the contact area between the concrete and the ribs of the deformed barwould be reduced. This would increase the bearing stress between the concrete and theribs, and enhance crack development around the tip of each rib, as shown in Fig. 5.45.For the push-in tests, the stress transfer mechanism involved was quite different, as thepush-in force in the rebar deformed the concrete inwards (in the direction of the force).This served to tighten the concrete around the bar and increased the frictional resistanceChapter 5. Experimental Results^ 214between the concrete and the rebar. The slight increase in the diameter of the rebar dueto the Poisson effect also improved the frictional resistance. A small zone of concrete wassubjected to compression-tension-tension in the radial, longitudinal and circumferentialdirections, respectively. However, few cracks were found after slicing the specimens. Theinward deformation of the concrete provided some lateral compression in the concretesurrounding the bar, and thus reduced the radial component of the wedging force. Therewere fewer and smaller cracks found for push-in loading cases. One photograph of theinternal cracks for push-in tests is shown in Fig. 5.46.The test results showed that there was not much difference between the normalstrength concrete specimens and the high strength concrete specimens under static load-ing, in terms of the internal cracking.Figure 5.44: No Transverse Cracks Formed at the Interface for Specimens withSmooth Bars10 min.44011Figure 5.45: Internal Cracks in Pull-out Tests with DeformedIndicates the Crack around the Rib of the Rebar)Bars (ArrowChapter 5. Experimental Results^ 215Figure 5.46: Internal Cracks in Push-in Tests with Deformed Bars (ArrowIndicates the Crack around the Rib of the Rebar)Chapter 5. Experimental Results^ 2165.6.2 Effects of Loading Rate and Concrete StrengthThe test results showed that the influence of loading rate on crack development wasquite different for normal and high strength concrete. There were fewer cracks for normalstrength concrete specimens with an increase in loading rate, as illustrated in Fig. 5.47.This may be explained by the fact that the crack velocity in the normal strength concretemixture was relatively slow, so there was not sufficient time for a crack to develop undera high rate loading (impact loading). The interesting thing was that an opposite resultwas obtained for high strength concrete specimens. That is, there seemed to be morecracks when the loading rate increased (see Fig. 5.48). This may be due to the highercrack velocity in the high strength concrete, in which a considerable amount of silicafume was used. As for the bond behaviour normal strength concrete is inherently lessbrittle than high strength concrete containing silica fume.5.6.3 Effects of Fibre AdditionsBoth polypropylene fibres and steel fibres improved the crack resistance. The pres-ence of fibres made crack propagation slower and inhibited crack opening. The fibresenabled stress to be transferred across cracked sections, allowing the affected parts of thecomposites to retain some post-cracking strength and to withstand greater deformation.Photographs in Figs. 5.49 and 5.50 show the effects of fibres. There were more and widercrack in the plain concrete specimens than in the fibre reinforced concrete specimens.Chapter 5. Experimental Results^ 217Figure 5.47: Influence of Loading Rate on Internal Cracks (Normal StrengthConcrete, Arrow Indicates the Crack around the Rib of the Rebar)Chapter 5. Experimental Results^ 218Figure 5.48: Influence of Loading Rate on Internal Cracks (High StrengthConcrete, Arrow Indicates the Crack around the Rib of the Rebar)Chapter 5. Experimental Results^ 219Figure 5.49: Influence of 0.5% by Volume Polypropylene Fibres on InternalCracks (Arrow Indicates the Crack around the Rib of the Rebar)Figure 5.50: Influence of 0.5% by Volume Steel Fibres on Internal Cracks (Ar-row Indicates the Crack around the Rib of the Rebar)Chapter 5. Experimental Results^ 2205.7 Bond Stress vs. Slip Relationship5.7.1 GeneralThe bond stress-slip relationship represent the most important result of this experi-mental work. For a particular specimen, the type of rebar, the concrete strength, thefibre type and content, and the type of loading and loading rate were given. The resultingbond stress-slip relationship contained four variables: the bond stress, u, the slip, w, thetime, t, and the location, x. From the results and discussions in the previous sections, itis obvious that the bond stress-slip relationships kept changing with time under dynamicloading; in other words, there were different relationships between the bond stress andthe slip at different stages of loading. For deformed bars the bond stress-slip relationshipwere not uniformly distributed, and thus, strictly speaking, a bond stress-slip relation-ship is meaningless unless specified for a particular moment and a particular point. Thatis, the bond stress-slip relationship should be expressed as,u = u (w,t,x)^ (5.1)this made it almost impossible to establish and analyze the bond stress-slip relationshipsfor all of the specimens tested.In practice and for simplicity, all of the bond stress-slip relationships were referredto an average value over the embedment length, unless specified. Also, since the slips ofsome specimens might still develop up to greater values after the 'peak bond stresses', allof the bond stress vs. slip relationship curves were plotted a bit beyond the peak bondstresses; this makes the comparisons between different specimens easier.After the bond stress-slip relationship and the slips were determined, the relationshipsChapter 5. Experimental Results^ 221between them were established through the variable time. The related equations arederived and listed in Chapter 4.5.7.2 Smooth BarsFig. 5.51 illustrates the bond stress-slip relationship at the peak load, Fb = 30 kN.This was a plain concrete specimen with a smooth rebar subjected to an impact test witha drop height of :300 mm.For the specimens with smooth rebars, the effects of loading rate, concrete strengthand fibre additions on the bond stress-slip relationship were not significant, as shown inFigs. 5.52, 5.53 and 5.54. It can be seen from these curves that for static loading thebond stress-slip relationships were linear up to a very high loading level. Increasing theconcrete strength or adding steel fibres resulted in a slight increase in the slopes of thecurves, but the linearity remained unchanged.A high rate of loading caused a slight stress concentration at the loaded end, whichmight be due to the sudden change of the boundary condition of the rebar (from a freesurface to concrete confinement). Due to the Poisson effect there was almost no frictionalresistance existing at the interface between the rebar and the concrete after the adhesionhad been destroyed for the pull-out test. In contrast, the frictional force at the interfacebetween the rebar and the concrete would increase to a maximum value when the push-inforce increased (radial stress also increased), so the bond stress values were much largerfor push-in tests than for pull-out tests, though the uniform nature of the distributionremained the same. One of the example is given in Fig. 5.55.Chapter 5. Experimental Results^ 222es 40a2xxEix 20ae000:1 102^3^4^6Local Slip (0.01 mm)Figure 5.51: The Bond Stress vs. Slip Relationship for a Smooth Rebar1^2^8^4^5Local Slip (0.01 mm)Static^Medium II^Impact IIIFigure 5.52: Effects of Loading Rate on the Bond Stress vs. Slip Relationshipfor Smooth RebarsChapter 5. Experimental Results^ 2232^4Local Slip (0.01 mm)Normal Strength^High StrengthFigure 5.53: Effects of Concrete Strength on the Bond Stress vs. Slip Rela-tionship for Smooth Rebarsso3020160O1000^ 1^ 2^ 3^ 4^ 6Local Slip (0.01 mm)Plain Polypropylene Fibers (0.5%) Steel Fibers (0.5%)Figure 5.54: Effects of Fibre Additions on the Bond Stress vs. Slip Relationshipfor Smooth RebarsChapter 5. Experimental Results^ 2245.7.3 Deformed BarsFor simplicity, all of the results including figures given in this section, unless specified,are for the specimens with normal strength concrete in push-in tests.5.7.3.1 Effects of Loading RateFor all the specimens with deformed bars, the peak bond stress increased considerablywith an increase in loading rate. There were higher stress concentrations at the loadedends than for the specimens with smooth bars. Unlike the specimens with smooth rebars,the bond stress-slip relationship curves were no longer straight lines. The existence ofribs and cracks generally caused changes in curvature of the steel stress curves, and thebond stress-slip relationship curves were not as smooth as the curves for smooth bars.Higher bond stresses were developed under higher loading rates. Fig. 5.56 shows twodifferent bond stress-slip relationships under different loading rates for a plain concretespecimen.By comparing Fig. 5.57 with Fig. 5.56 it can be concluded that the addition ofpolypropylene fibres to the concrete had no significant influence on the results, in termsof the effects of the loading rate on the bond stress values and the shape of the curves.However, the loading rate seemed to have greater effects on specimens made of steelfibre reinforced concrete (see Fig. 5.58). The reason for this phenomenon is again thatthe shear mechanism plays a major role in the bond-slip process for deformed bars (seeSections 5.3 and 5.6).It should be noted that Figs. 5.56 to 5.58 are from the tests for specimens with normalChapter 5. Experimental Results^ 225concrete strength. Fig. 5.59 is for specimens with high concrete strength reinforced bysteel fibres. It was found that the influence of the loading rate was more significant forhigh strength concrete than for normal strength concrete.Similar to specimens with smooth rebars, the bond stress-slip relationships from push-in tests were quite different from those from pull-out tests. There were higher bondstresses at the loaded end and larger slopes in the bond stress-slip relationship curves inpush-in tests than in pull-out tests, as shown in Fig. 5.60.5.7.3.2 Effects of Concrete StrengthGeneral speaking, the peak bond stress value increased for high strength concretespecimens. This seems logical because the shear mechanism is the main mechanism inthe bond resistance for deformed bars. Fig. 5.61 give an example to show the effect ofdifferent loading rates.5.7.3.3 Effects of Fibre AdditionsThe effects of adding fibres to the concrete mixture on the bond stress vs. slip werefound to be different for polypropylene and steel fibres. Figs. 5.62 and 5.63 illustratetwo examples of this. Polypropylene fibre additions had very little influence; while steelfibre additions greatly changed the peak values and the shapes of the curves. higher fibrecontent seemed to increase this effect.Chapter 5. Experimental Results^ 226i^2^ 3^4^ sLocal Slip (0.01 mm)Pull-out^Push-in,...,..^........ .....,,Figure 5.55: The Bond Stress vs. Slip Relationship for a Smooth Rebar forPull-out and Push-in Testsso......0 4010oX30CAE11 206000 10• 0 0^ 1^ 2^ 3^ 4Local Slip (0.01 mm)^Static^Medium II^Impact IIIsFigure 5.56: Effects of Loading Rate on the Bond Stress vs. Slip Relationship(Plain Concrete)^Aommmliwwwwww■IChapter 5. Experimental Results^ 227Local Slip (0.01 mm)Static^Medium II^Impact IIIFigure 5.57: Effects of Loading Rate on the Bond Stress vs. Slip Relationship(Polypropylene Fibre Concrete)•1^2^3^4^5^6^7Local Slip (0.01 mm)Static^Medium II^Impact III•5055 402ag 1 0Figure 5.58: Effects of Loading Rate on the Bond Stress vs. Slip Relationship(Steel Fibre Concrete)5050Chapter 5. Experimental Results^ 2283^4^5^6^7Local Slip (0.01 mm)Static^Medium II^Impact IIIFigure 5.59: Effects of Loading Rate on the Bond Stress vs. Slip Relationship(High Strength Concrete)2^3^4^5^6^7^5Local Slip (0.01 mm)Static^Medium II^Impact IIIFigure 5.60: Effects of Loading Rate on the Bond Stress vs. Slip Relationship(Pull-out Tests)Chapter 5. Experimental Results^ 2292^3^4^5^6^7^6Local Slip (0.01 mm)Normal Strength^High StrengthFigure 5.61: Effects of Concrete Strength on the Bond Stress vs. Slip Rela-tionship1^2^3^4^5^6^7Local Slip (0.01 mm)Plain Polypropylene Fibers (0.5%) Steel Fibers (0.5%)am.11••■Figure 5.62: Effects of Fibre Additions on the Bond Stress vs. Slip Relationship(Different Fibres)Chapter 5. Experimental Results^ 2305.7.3.4 Differences between Pull-out and Push-in TestsUnder either static or impact loading, push-in tests always produced greater bondstresses than pull-out tests. Figs. 5.64 and 5.65 show some of these results.Chapter 5. Experimental Results^ 2313^4^5^6^7^eLocal Slip (0.01 mm)0.0% 0.3%^1.0% Figure 5.63: Effects of Steel Fibre Additions on the Bond Stress vs. SlipRelationship (Different Fibre Content)Local Slip (0.01 mm)Pull-out^Push-in•••■•■■■ .1■1••• ■■■■■•Figure 5.64: The Bond Stress vs. Slip Relationship for Pull-out and Push-inTests (Static)am,64 401 0Chapter 5. Experimental Results^ 2323^4^5^6^7^8Local Slip (0.01 mm)Pull-out^Push-in■••Figure 5.65: The Bond Stress vs. Slip Relationship for Pull-out and Push-inTests (Impact)Chapter 5. Experimental Results^ 2335.8 Results of Tests with Epoxy-Coated RebarsAs a. supplementary work to this study on bond behaviour, some tests with speci-mens made of epoxy coated deformed rebars were carried out under static, medium IIand impact III loading. These specimens were made of both normal strength and highstrength concrete, and about two third of them were tested for push-in loading and therests for pull-out loading. Details of the specimen preparation are given in Section 3.2.6in Chapter 3.5.8.1 Effect on the Bond StressResults of the bond stresses are given in Table 5.10 (for normal strength concrete) andTable 5.11 (for high strength concrete). Similar to the discussion in the previous sections,two relative \"indices\" , /peak and /average were introduced to represent the differencesbetween specimens with uncoated rebars and those with coated rebars. They are definedaspeak value of bond stress for specimens with coated rebarspeak^peak value of bond stress for specimens with uncoated rebarsand/average = average value of bond stress for specimens with uncoated rebarsIt can be seen from these results that there were some decreases in both the peakand the average value of the bond stress for push-in tests, this was true for both nor-mal strength and high strength concrete. For epoxy coated reinforcements the chemicalaverage value of bond stress for specimens with coated rebarsChapter 5. Experimental Results^ 234adhesion and friction mechanisms were much reduced in this effect, and thus the bondresistance decreased. However, even in the push-in case, in which the frictional resistanceincreased due to a higher radial force acting at the interface between the rebar and theconcrete, the shearing mechanism, i.e. the rib bearing action, still played a vital rolein the bond resistance, and therefore the decrease in the bond stress due to the coatingwas relatively small. Under a high rate loading the chemical adhesion is more easily de-stroyed than under static or low rate loading. Also, the frictional factor at the interfacemay be reduced under a high rate of loadings. These factors reduced the difference inthe bond stresses between specimens with coated rebars and those with uncoated rebarsunder impact loading, as shown by the indices of the peak and the average values of thebond stress in Tables 5.10 and 5.11. Polypropylene fibre additions did not have mucheffect on this. For specimens with steel fibre reinforced concrete, the shearing mechanismdominates in the bond behaviour, while changes in the chemical adhesion and frictionalresistance always have little effect on the total bond resistance. This can also be seenfrom the Tables 5.10 and 5.11. These results also showed that epoxy coating the rebarhad less effect on bond in specimens made of higher concrete strength than low concretestrength, in terms of bond resistance. The least reductions in both the peak and theaverage bond stress were found for the specimens made of steel fibre reinforced concrete(1.09 content by volume), as can be seen in Table 5.11. For pull-out tests, the decreasein the rebar diameter reduced the frictional effects at the interface no matter what thecontact condition between the rebar and the concrete is, this resulted in very little differ-ence in the bond stress between the tests with coated bars and uncoated bars, as shownby the data in Table 5.10 and 5.11.Chapter 5. Experimental Results^ 235Table 5.10: Effects of Epoxy Coating the Rebar on the Bond Stresses (NormalStrength Concrete)LoadingTypeType ofSpecimenCoatingConditionRelative Index/peak /averageStatic(Push-in)PlainConcreteUncoated 1.00 1.00Coated 0.83 0.80PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 0.84 0.80SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 0.92 0.90Medium II(Push-in)PlainConcreteUncoated 1.00 1.00Coated 0.85 0.82PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 0.85 0.83SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 0.94 0.92Impact III(Push-in)PlainConcreteUn coated 1.00 1.00Coated 0.89 0.84PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 0.89 0.84SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 0.96 0.94Medium II(Pull-out)PlainConcreteUncoated 1.00 1.00Coated 0.92 0.92PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 0.92 0.92SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 0.95 0.96Impact III(Pull-out)PlainConcreteUncoated 1.00 1.00Coated 0.95 0.95PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 0.95 0.94SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 0.97 0.96Chapter 5. Experimental Results^ 236Table 5.11: Effects of Epoxy Coating the Rebar on the Bond Stresses (HighStrength Concrete)LoadingTypeType ofSpecimenCoatingConditionRelative Index'peak /averageStatic(Push-in)PlainConcreteUncoated 1.00 1.00Coated 0.85 0.82PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 0.85 0.83SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 0.93 0.93Medium II(Push-in)PlainConcreteUncoated 1.00 1.00Coated 0.86 0.83PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 0.87 0.83SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 0.95 0.93Impact III(Push-in)PlainConcreteUncoated 1.00 1.00Coated 0.90 0.85PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 0.90 0.85SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 0.97 0.95Medium II(Pull-out)PlainConcreteUncoated 1.00 1.00Coated 0.92 0.92PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 0.9:3 0.92SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 0.96 0.95Impact III(Pull-out)PlainConcreteUncoated 1.00 1.00Coated 0.96 0.95PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 0.96 0.95SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 0.97 0.96Chapter 5. Experimental Results^ 2375.8.2 Effect on the SlipResults of the slips are given in Tables 5.12 and 5.13. Two relative \"indices\", /peakand /average are defined as /peakpeak value of slip for specimens with coated rebarsandpeak value of slip for specimens with uncoated rebars/ average =average value of slip for specimens with coated rebarsaverage value of slip for specimens with uncoated rebarsFrom Tables 5.12 and 5.13it can be seen that the peak values of slips for specimenwith coated rebars are larger than those for specimens with uncoated rebars. This may bedue to the fact that most of the bond stresses developed at the tips of the uncoated rebarribs from the very beginning during the bond process; the stress concentrations at thesepoints caused wider cracks in the concrete, as shown by the four photographs in Figs. 5.66to 5.69. The first two photographs are for specimens with uncoated rebar, and the lasttwo for specimens with epoxy coated rebars. For specimens made of steel fibre reinforcedconcrete, especially made of high strength concrete, this effect was relatively small, whichmight be due to the improved resistance of the fibre matrix to crack development. Similarto the bond stress, and for the same reasons, the effects of coated rebars on the slips werealso found to be small for pull-out tests and for high rate loading, as shown in Tables5.12 and 5.1:3.Chapter 5. Experimental Results^ 238Table 5.12: Effects of Epoxy Coating the Rebar on the Slip (Normal StrengthConcrete)LoadingTypeType ofSpecimenCoatingConditionRelative Index/ peak / averageStatic(Push-in)PlainConcreteUncoated 1.00 1.00Coated 1.19 1.17PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 1.20 1.16SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 1.10 1.08Medium II(Push-in)PlainConcreteUncoated 1.00 1.00Coated 1.16 1.10PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 1.15 1.11SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 1.08 1.07Impact III(Push-in)PlainConcreteUncoated 1.00 1.00Coated 1.14 1.08PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 1.15 1.08SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 1.06 1.04Medium II(Pull-out)PlainConcreteUncoated 1.00 1.00Coated 1.03 1.02PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 1.03 1.03SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 1.02 1.02Impact III(Pull-out)PlainConcreteUncoated 1.00 1.00Coated 1.04 1.02PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 1.04 1.02SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 1.02 1.01Chapter 5. Experimental Results^ 239Table 5.13: Effects of Epoxy Coating the Rebar on the Slip (High StrengthConcrete)LoadingTypeType ofSpecimenCoatingConditionRelative Index'peak 'averageaverStatic(Push-in)PlainConcreteUncoated 1.00 1.00Coated 1.17 1.15PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 1.18 1.15SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 1.09 1.08Medium II(Push-in)PlainConcreteUncoated 1.00 1.00Coated 1.15 1.09PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 1.15 1.10SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 1.07 1.06Impact III(Push-in)PlainConcreteUncoated 1.00 1.00Coated 1.12 1.08PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 1.13 1.08SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 1.05 1.04Medium II(Pull-out)PlainConcreteUncoated 1.00 1.00Coated 1.03 1.02PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00Coated 1.03 1.02SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 1.02 1.02Impact III(Pull-out)PlainConcreteUncoated 1.00 1.00Coated 1.03 1.02PolypropyleneFibre Concrete (0.5%)Uncoated 1.00 1.00( oated 1.03 1.02SteelFibre Concrete (1.0%)Uncoated 1.00 1.00Coated 1.02 1.01Chapter 5. Experimental Results^ 2405.8.3 Effect on the Bond Stress-slip RelationshipFigs 5.70 to 5.73 show four samples in comparisons of the bond stress-slip relationships forspecimens with coated rebars and uncoated rebars, two for pull-out tests (normal strengthconcrete) and the other for push-in tests (high strength concrete). The specimens testedwere steel fibre reinforced (1.0% by volume) and subjected to impact loading III. For thepull-out tests, the difference between the curve for the epoxy coated rebar specimen andthe curve for the uncoated rebar specimen is quite small, in terms of the shape. For thepush-in tests, the peak bond stress and the slip in the curve of the coated rebar specimenare a bit smaller than those for the uncoated rebar specimen. The difference betweenthe coated rebar specimens and the uncoated rebar specimens reduced when the concretestrength increased.Chapter 5. Experimental Results^ 241Figure 5.66: Internal Cracks at the Tips of the Ribs of an Uncoated Rebar(Normal Strength, Push-in, Impact)AMIFigure 5.67: Internal Cracks at the Tips of the Ribs of an Epoxy-Coated Rebar(Normal Strength, Push-in, Impact)Chapter 5. Experimental Results^ 242401117,49~'1 m d int '.ri^ifok -4104^....*\".Ar^•Figure 5.68: Internal Cracks at the Tips of the Ribs of an Uncoated Rebar(High Strength, Push-in, Impact)Figure 5.69: Internal Cracks at the Tips of the Ribs of an Epoxy-Coated Rebar(High Strength, Push-in, Impact)50TT 402 30\"6- 20Oo^1^2^3^4^5^6Local Slip (0.01 mm)7Chapter .5. Experimental Results^ 2432^3^4^5^6^7^8Local Slip (0.01 mm)Figure 5.70: The Bond Stress vs. Slip Relationship for a Specimen with anEpoxy Coated Rebar (Normal Strength, Pull-out, Impact)Figure 5.71: The Bond Stress vs. Slip Relationship for a Specimen with anEpoxy Coated Rebar (Normal Strength, Push-in, Impact)5030(.75 20§ 10^0 '^^0 1^2^3^4^5^6Local Slip (0,01 mm)7Chapter 5. Experimental Results^ 24450401 3065 20QS 101^2^3^4^5^6^7^8Local Slip (0.01 mm)Figure 5.72: The Bond Stress vs. Slip Relationship for a Specimen with anEpoxy Coated Rebar (High Strength, Pull-out, Impact)Figure 5.73: The Bond Stress vs. Slip Relationship for a Specimen with anEpoxy Coated Rebar (High Strength, Push-in, Impact)Chapter 5. Experimental Results^ 2455.8.4 Effect on the Fracture EnergyThe energy transfer, energy dissipation and energy balance during the bond process forspecimens with uncoated rebars will be discussed in detail in Chapter 7. Some results ofthe fracture energy calculation for specimens with epoxy coated bars are presented here inTable 5.14. The definition of the fracture energy in bond failure and the related formulasfor calculation are given in Section 4.10 in Chapter 4 and Section 6.2 in Chapter 6. Forcomparison, the results for specimens with uncoated rebars are also given in the sametable. It can be found that for push-in tests with specimens made of normal strengthconcrete, the fracture energy decreased by about 8.8% (static) to 5.8% (impact) forspecimens with plain or polypropylene fibre concrete, and by about 5.1% (static) to 3.0%(impact) for specimens with steel fibre concrete; while for push-in tests with specimensmade of high strength concrete, the fracture energy decreased by about 6.7% (static) to4.7% (impact) for specimens with plain or polypropylene fibre concrete, and by about3.5% (static) to 1.8% (impact) for specimens with steel fibre concrete. This suggeststhat the influence of epoxy coating is reduced with an increase in the loading rate or inthe concrete strength. For pull-out tests there were also no significant decreases in thefracture energy when the epoxy coated rebars were used, for specimens made of normalstrength concrete the decrease ranges from 4.1% for plain concrete (static) to 1.6% forsteel fibre concrete (impact); while for specimens made of normal strength concrete thedecrease ranges from 3.1% for plain concrete (static) to 1.2% for steel fibre concrete(impact).Chapter 5. Experimental Results^ 2465.8.5 ConclusionsBased on the data from these limited tests, which were carried out for a particular barsize, coating material and thickness, and embedded length, some preliminary conclusionsmay be drawn:1. Bond resistance decreases slightly for epoxy coated rebars, in terms of the maximumlocal bond stress and the average bond stress.2. Wider cracks develop during the bond process at the tips of the ribs of the deformedrebars when they are coated with epoxy.3. The fracture energy during the bond failure decreases for epoxy coated rebars, i.e.a. reinforced concrete member may become more brittle when this type of rebar isused.4. Under high rate loading, the above effects, i.e. the weakening of bond strength,wider crack development and brittleness, are reduced.5. Steel fibre additions at a sufficient content also effectively reduce the above effectson the bond strength, crack development and brittleness of epoxy coated rebars.Polypropylene fibres were much less effective in this regard.6. Higher concrete strength also reduces the above effects. The bond strength andcrack opening do not have as much change in comparison to as when lower strengthconcrete is used.7. The influence of epoxy coated rebars on the bond behaviour is more pronouncedfor push-in loading than for pull-out loading.Chapter 5. Experimental Results^ 247Table 5.14: Fracture Energy in Bond Failure (for both Epoxy Coated andUncoated Bars)Type ofConcretePull-out Tests^(Nin) Push-in Tests^(N7n)Uncoated Coated Uncoated CoatedNormal Strength ConcreteSPlain Concrete 40.2 38.5 44.0 40.1PolypropyleneFibre Concrete0.1% 40.6 38.8 44.3 40.20.5% 40.7 39.8 44.5 40.0SteelFibre Concrete0.5% 54.6 53.2 62.3 59.21.0% 71.5 69.4 80.2 76.1MIIPlain Concrete 42.8 41.2 47.3 43.5PolypropyleneFibre Concrete0.1% 42.9 41.2 47.5 43.60.5% 43.2 42.5 47.6 43.8SteelFibre Concrete0.5% 60.3 59.2 68.2 65.41.0% 75.9 74.7 88.6 85.7IIIIPlain Concrete 50.2 49.2 53.8 50.7PolypropyleneFibre Concrete0.1% 50.3 49.2 54.2 51.00.5% 50.5 49.3 60.1 57.6SteelFibre Concrete0.5% 70.9 70.0 74.3 72.21.0% 94.6 93.1 103.4 100.3High ,Strength ConcreteSPlain Concrete 42.1 40.8 45.1 42.1PolypropyleneFibre Concrete0.1% 42.4 41.1 45.2 42.10.5% 44.2 43.3 46.0 42.9SteelFibre Concrete0.5% 58.4 57.4 65.6 62.21.0% 75.3 73.4 86.1 83.1AlIIPlain Concrete 45.2 43.5 49.8 46.5PolypropyleneFibre Concrete0.1% 45.3 43.4 50.3 46.80.5% 45.5 43.5 50.5 46.9SteelFibre Concrete0.5% 64.2 63.4 77.4 75.41.0% 80.7 79.2 94.7 92.7/IIIPlain Concrete 52.3 50.9 58.7 55.9PolypropyleneFibre Concrete0.1% 52.5 50.8 61.3 58.70.5% 52.6 51.0 64.6 62.6SteelFibre Concrete0.5% 76.5 75.9 85.2 83.41.0% 100.5 99.3 110.3 108.3S - Static^M - Medium,^I - ImpactChapter 5. Experimental Results^ 2485.9 Interpretation of Tests Results and ConclusionsFor smooth bars, the bond resistance is due to the chemical adhesion and the frictionalforce at the interface between the rebar and the concrete. There existed a linear bondstress-slip relationship under both static. and high rate loading. Different compressivestrengths, types of fibres, fibre contents, and loading rates were found to have no greatinfluence on this relationship and the stresses in both the steel bar and the concrete.For deformed rebars, the chemical adhesion and the frictional force at the interfacebetween the rebar and the concrete are less important in the bond resistance. The shearmechanism due to the ribs bearing on the concrete plays a major role in the bond process.The bond stress-slip relationship under a dynamic (high rate) loading changed with timeand was different at different points along the reinforcing bar.Higher loading rate, higher concrete strengths, steel fibres, and higher fibre contentsignificantly increased the bond resistance capacity, and changed the bond stress-slip rela-tionship (an average bond stress-slip relationship over the time period and the embeddedlength).Under high rate loading, the stress distribution along the rebar was not uniform, andeven not a straight lines; there was more stress concentration along the rebar than understatic loading. Higher stresses both in the rebar and in the concrete, greater slips, andhigher bond stresses were developed with an increase in the loading rate. These effectswere especially noticeable when steel fibres were added to the concrete mixture.The steel fibre additions greatly increased the bond strength. Steel fibres caused lessstress concentrations along the rebar, higher stresses in the concrete, and greater crackChapter 5. Experimental Results^ 249resistance. The bond stress-slip relationship of steel fibre concrete was quite differentfrom that of the plain concrete and polypropylene fibre concrete, in terms of the peakvalue, the average value and the slope of the curve. These effects were more significantwhen subjected to high rate loading. Higher steel fibre content increased this effect.The addition of polypropylene fibres to the concrete had no significant effect on thebond behaviour, in terms of the bond strength, the stress distributions both in the rebarand the concrete, the crack development, the slips, and the bond stress-slip relationship.Higher compressive strength increased the bond strength, especially steel fibres wereadded to the concrete.(ienerally there were higher bond resistance and more stress concentrations along therebar for push-in loading than for pull-out loading. The stress distribution both in therebar and the concrete was different for these two loading cases. The patterns of crackingand the bond failure, the bond stress-slip relationship for the pull-out loading and forthe push-in loading were also different.For epoxy-coated rebar the bond resistance decreases, and there was wider cracksdeveloped. This influence of epoxy-coated rebars on the bond strength for push-in loadingwas much more significant than for pull-out loading. However, high rate loading, highconcrete strength and steel fibre additions at a sufficient content effectively reduced theeffects of coating epoxy on the bond behaviour. Polypropylene fibre had little effect inaltering the response as effective by epoxy coating.Chapter 6Energy Transfer and Balance6.1 IntroductionBoth steel and concrete are known to be strain rate sensitive materials, Thus, the bondbehaviour between a reinforcing bar and the concrete under dynamic loading shouldbe studied by a method which can take into account this strain rate sensitivity of thematerials, rather than the conventional testing method for static loading. Unfortunately,there has been no standard testing technique developed to investigate this problem.At present, conclusions derived from different investigations are not really comparable,because of different testing arrangements, different methods of analysis, and differentinterpretations of tests results. The consideration of energy transfer and balance, basedon the principle of the conservation of energy, may provide an effective method for boththe verification of a particular testing technique and the comparison of results fromdifferent investigations. Indeed, a method based on the consideration of energy has beenfound very useful in the study of crack propagation in linear and nonlinear fracturemechanics. Generally speaking, many types of energy, such as kinetic energy, potentialenergy, strain energy and fracture energy, are easy to calculate and have explicit physicalmeanings. The study of the energy transfer, energy dissipation and energy balance canhelp us to achieve a physical understanding of the bond mechanism.250Chapter 6. Energy Transfer and Balance^ 251Recently, measures such as adding fibers to the concrete matrix, or increasing theconcrete strength, have been under taken to improve the bond strength between rein-forcing bars and concrete under dynamic loading. Because of the complexity of the bondphenomena, the introduction of the concept of fracture energy could be an effective andconvenient way of evaluating the effectiveness of these measures.6.2 Energies and Work Done by the External ForceIf the hammer is raised to a height of h, it possesses a potential energy (also the totalenergy), E ha , p , Which isE h.a,p^M liagh^(4.30)When it strikes the specimen the kinetic energy of the hammer, E ha, k, is given byE h a' k —^ha [2 (0.91g) h]^(4.31)(as stated earlier, due to friction in the guides, the hammer falls with an acceleration of0.91g).On striking the specimen, the hammer suffers a loss of kinetic energy, L\\Ehri , whichmay be evaluated by(lapter 6. Energy Transfer and Balance^ 2521ta^h.AEha = —Mi rv 2 a (0) — vL,(t)2 (4.3:3)Of course, not all of this energy lost by the hammer may be transferred to the speci-men. Some of the energy is lost to the testing machine itself (Banthia [80]).From the law of conservation of energy, at any moment during the impact there mustbe an energy balance, expressed asEha ,p^E ha, fr^E ha, lef t^ (6.1)where the energy lost due to the frictional force and air resistance, Eha ,f r , and thekinetic energy remaining, Eha,t,:ft, can be found by Eqs. 4.32 and 4.34, respectively.Since the loss of the kinetic energy of the hammer, Ew a , is evaluated from the recordedacceleration data (Eqs. 4.12, 4.13 and 4.33), the above equation (Eq. 6.1) was mainlyused for checking the balance of the total energy, rather than for evaluating any individualterm.At any moment during the impact event the work done by the applied load, W ha (d),isWw a (d) =^Ft (d)dsThe total work done by the hammer during the impact, 14.^ha, total, i 8(4.38)Chapter 6. Energy Transfer and Balance^ 253d,nd1/17 ha , total =^Ft(d) ds^ (4.39)On the other hand, the work done by the bond stress at any moment during theimpact event can be evaluated byI/Vb^[11 u7rDw d.s] dto^o(4.41)From the law of conservation of energy, there must be the following energy balance,A E ha = E sys W ha^(AT In)^ (6.2)whereE 8y, = the energy lost to the various machine parts^(Nm-)^(Nm)W h„ = the work done by the applied load^(Nnt)^(Nm)147 /,„ is obtained from the area under the applied load vs. the total displacement of therebar plot (Eq. 4.39), and comprises both the elastic strain energy in the rebar and theconcrete and the work done by the bond stress. The equation for this energy balance is=^c, str^E re , yi( Id + 1/17^(N7n)^(6.3)Chapter 6. Energy Transfer and Balance^ 254where E rr ,^and .E c, sir are the elastic strain energies in the rebar and in the concrete,respectively, which are evaluated by Eqs. 4.43 and 4.44. The term E r ,, y i eid is the localyield energy of the rebar.The transfer of energy can be studied by subdividing it into two regions (Fig. 6.1):1. Energy balance at the end of the linear portion of the applied load vs. displacementcurve (at t = ti); and2. Energy balance just after complete bond failure (at t = tTherefore, all of the terms in Eq. 6.3 can be divided into two parts,^W = 1/1 7 h a (t.^ha(t f )^= E rr,51,(t1)^E str(tE c,str =^str (t^E c , str (t f)E rr , y i eld^E re, yield(t1)^E re , yield(t i)W b = W b(t1) W b(t f)After the bond failure all of the strain energies in the rebar and the concrete will bereleased, and eventually transferred to the fracture energy, i.e.Ere, str = 0so914201.1aof 10Chapter 6. Energy Transfer and Balance^ 255andE c, str = 0Thus, the energy balance equation (Eq. 6.3) becomesW ha = Ere, yield + W b (Nm)^ (6.4)For most specimens, the values of the applied load at the point t = t 1 were found tobe about 80% to 90 % of the peak load, at this point, in general, the applied load vs.displacement curves became significantly non-linear.Linear Region Nonlinear Regionrso0 0^ 3^ 6^t = t I Time (ms)12t = t f15Figure 6.1: Typical Tup Load HistoryChapter 6. Energy Transfer and Balance^ 2566.3 Energy Balance in the Linear Region (t = t1)The material behaviour in the region from the starting point to the end of the linearpart of the applied load vs. displacement (see Fig. 6.1) curve can be considered to belinear elastic.At the beginning of this region the applied load is quite low and so is the stress inthe rebar. A more or less \"perfect bond\" exists between the rebar and the concrete alongthe entire length of the rebar, and the slip between the reinforcing bar and the concreteis zero all along the rebar. All of the work done by the applied load is transferred intothe strain energies in the steel and the concrete. No work is done by the bond stress.Calculations based on the recorded data showed that the work done (and also the strainenergies in the rebar and the concrete) was relatively small, depending on the 'criticaladhesive bond strength'. It ranged from 10% (for specimens with smooth bars) to 20%(for specimens with deformed bars) of the total work done by the applied load.As the load in the rebar is further increased, the bond stress reaches the 'criticaladhesive bond strength', and the bond due to adhesion disappears. At this point someslip occurs, but it is of a very small magnitude. Further loading mobilizes the mechanicalinterlocking by the mortar or the aggregate on the microscopic irregularities on the barsurface. For specimens with deformed bars, the interlocking of the concrete with the ribsof the rebar is also induced. However, up to a particular stage of loading, the appliedload vs. displacement relationship remains linear, and no cracking is developed in theconcrete surrounding the rebar.At this stage, the energy balance equation can be written asChapter 6. Energy Transfer and Balance^ 257E r , str(t1)^E c, str(t1)^E re, yzeld(t1)^E(t!)^(N7n)^(6.5)where Wha (t1) is the work done by the hammer at time t1, E,,, ir (t1) and E c , sir (t i ) arethe elastic strain energies stored in the rebar and the concrete, respectively, E r , yiel (01)is the energy of local yielding in the rebar and Wb(t i ) is the work done by the bond stress.6.3.1 Tests with Smooth BarsThe experimental results for smooth rebars are summarized in Tables 6.1 (for normalstrength concrete) and 6.2 (for high strength concrete). Data are presented for differ-ent concrete compressive strengths, different fibres and fibre contents, different types ofloading and different loading rates. Similar to Chapter 5, in these tables and the onesthat follow in this chapter, the following notation is used:PF = Polypropylene fibre concreteSF = Steel fibre concreteM = The medium rate loadingI = The high rate loading (impact)M I = The bond stress rate is 0.5 10 -6 0.5 • 10' (MPa/s)M II = The bond stress rate is 0.5 • 10 -5 ti 0.5 10 -4 (M Pais)II = The bond stress rate is about 0.5 • 10' (MPa/s)Chapter 6. Energy Transfer and Balance^ 258/11 = The bond stress rate is about 0.5 • 10' (MPa/s)I III = The bond stress rate is about 0.5 • 10_ 2 (MPa/s)It was found that although the four terms in Eq. 6.5, W h a (t1) Er,,er(ti), E',,str(ti)and Wb(t/), were calculated independently, they generally satisfied the energy balanceequation. This means that the energy consumed by the local yielding of the steel at thecontact surface between the hammer and the rebar, E r ,, y ieid (ti), was very small and canbe neglected, and that the errors in deriving the relevant formulae for each componentof the energy and work were fairly small. The following conclusions can also be drawnfrom the results:1. At this stage (the end of the linear portion of the applied load vs. displacementcurve) most of the work done by the hammer (Wha (1, 1 )) was transferred to thestrain energies in the rebar and in the concrete (E„, str (t i ) and E c , str (i i )); the workdone by the bond stress (147A)) was relatively small compared to the two strainenergies. 1/17b(ti) constituted about 15% of the work done by the applied load forplain and polypropylene fibre concrete specimens, and 35% for steel fibre concretespecimens. This was because the bond mechanism between the smooth bar andconcrete was only due to chemical adhesion and frictional resistance, and so only a.relatively small bond force could be transmitted.2. All of the components of energy and work for push-in tests were larger than thosefor pull-out tests. This was because there was larger radial force acting at theinterface, which caused a larger frictional resistance in the push-in case than in thepull-out case.3. The effect of fiber additions (either polypropylene fibers or steel fibers) on theChapter 6. Energy Transfer and Balance^ 259components of the work and the strain energies seemed very small.4. There was a slight decrease in the work and the strain energies with an increase inloading rate. This might be due to the fact that both the chemical adhesion andthe frictional resistance decreased under a higher loading rate.5. Higher concrete strengths increased the work done by the bond stress and the strainenergy in the rebar. Better adhesion between the rebar and the high strengthconcrete may have contributed to this effect.6.3.2 Tests with Deformed BarsThe experimental results for specimens with deformed bars in the linear region aresummarized in Tables 6.3 (for normal strength) and 6.4 (for high strength). Similar tothe specimens with smooth bars, the data are presented for different concrete compres-sive strengths, different fibres and fibre contents, different types of loading and differentloading rates. A very good balance in the energy equation was also found for virtuallyall of the specimens. The following conclusions may be drawn:1. Unlike the tests with smooth bars, the proportion of the work done by the bondstress increased considerably, ranging from about 80% to 90% of the work doneby the applied load (i.e. the hammer). For deformed bars, the bond mechanismat this stage can be considered to be a combination of the chemical adhesion, thefrictional resistance and the shear resistance. In the elastic state, the bond forcecaused by the ribs bearing on the concrete can develop to the same order as thatcaused by the chemical adhesion and frictional resistance.Chapter 6. Energy Transfer and Balance^ 260Table 6.1: Energy Balance in the Linear Portion (Smooth Bars, NormalStrength)Type ofConcretePull-out Tests^(Nrn) Push-in Tests^(N7n)Wha Ere, str Ec, str 1471) Wha Ere, str Ec, str '47bSPlain 2.10 0.81 0.75 0.44 2.48 1.01 0.93 0.44PFConcrete0.1% 2.10 0.81 0.75 0.44 2.47 1.01 0.9:3 0.440.5% 2.10 0.81 0.75 0.44 2.50 1.02 0.9:3 0.44SFConcrete0.5% 3.60 0.99 0.91 1.61 4.35 1.25 1.15 1.851.0% 4.30 1.18 1.08 1.94 5.06 1.46 1.34 2.16MIPlain 1.90 0.78 0.72 0.31 2.32 1.00 0.92 0.30PFCon crete0.1% 1.90 0.78 0.72 0.31 2.32 1.00 0.92 0.300.5% 1.90 0.78 0.72 0.31 2.31 0.99 0.91 0.30SFConcrete0.5% 3.20 0.96 0.89 1.25 3.98 1.26 1.16 1.471.0% 4.10 1.09 1.01 1.90 4.87 1.36 1.25 2.15AlIIPlain 1.90 0.74 0.68 0.37 2.52 1.03 0.95 0.4:3PFConcrete0.1% 1.80 0.74 0.68 0.27 2.:37 1.03 0.94 0.300.5% 1.80 0.74 0.68 0.27 2.37 1.0:3 0.94 0.30SFConcrete0.5% 3.10 0.90 0.83 1.26 4.14 1.27 1.17 1.611.0% 4.10 1.07 0.99 1.94 4.97 1.36 1.25 2.25IIPlain 1.80 0.74 0.68 0.28 2.52 1.08 1.00 0.:34PFConcrete0.1% 1.80 0.73 0.67 0.29 2.59 1.11 1.02 0.360.5% 1.80 0.74 0.68 0.27 2.57 1.11 1.02 0.33SFConcrete0.5% 3.10 0.89 0.82 1.29 4.21 1.27 1.17 1.671.0% :3.80 1.08 0.99 1.64 4.77 1.42 1.31 1.95/IIPlain 1.80 0.70 0.65 0.35 2.71 1.11 1.02 0.48PFConcrete0.1% 1.80 0.70 0.65 0.35 2.72 1.12 1.0:3 0.480.5% 1.80 0.70 0.65 0.35 2.72 1.12 1.03 0.48SFConcrete0.5% 2.90 0.85 0.78 1.17 4.26 1.31 1.21 1.641.0% :3.80 1.01 0.9:3 1.76 5.05 1.41 1.30 2.24IIIIPlain 1.70 0.67 0.61 0.32 2.96 1.22 1.12 0.52PFConcrete0.1% 1.70 0.67 0.61 0.32 2.96 1.22 1.12 0.520.5% 1.70 0.67 0.61 0.32 2.95 1.21 1.11 0.52SFConcrete0.5% 2.90 0.81 0.74 1.25 4.:3:3 1.26 1.16 1.801.0% :3.80 0.96 0.88 1.86 5.17 1.:37 1.26 2.44Chapter 6. Energy Transfer and Balance^ 261Table 6.2: Energy Balance in the Linear Portion (Smooth Bars, HighStrength)Type ofConcretePull-out Tests^(Nm) Push-in Tests^(Nm)Wha Ere, str Ec, str Wb Wha Ere, str Ec, str WbSPlain 2.21 0.90 0.83 0.38 2.59 1.05 0.97 0.46PFConcrete0.1% 2.21 0.90 0.83 0.38 2.60 1.06 0.97 0.470.5% 2.22 0.91 0.83 0.39 2.59 1.05 0.97 0.46SFConcrete0.5% 3.75 1.08 0.99 1.58 4.64 1.33 1.23 1.981.0% 4.66 1.34 1.24 1.99 5.34 1.54 1.42 2.29MIPlain 2.05 0.88 0.81 0.26 2.43 1.05 0.96 0.32PFConcrete0.1% 2.05 0.88 0.81 0.26 2.43 1.05 0.96 0.320.5% 2.04 0.88 0.81 0.25 2.42 1.04 0.96 0.32SFConcrete0.5% 3.27 1.03 0.95 1.18 4.09 1.29 1.19 1.511.0% 4.45 1.25 1.15 1.96 5.17 1.45 1.33 2.29MIIPlain 2.07 0.85 0.78 0.:34 2.67 1.09 1.01 0.47PFConcrete0.1% 1.95 0.85 0.78 0.23 2.52 1.09 1.01 0.3:30.5% 1.96 0.85 0.78 0.23 2.50 1.08 1.00 0.32SFConcrete0.5% 3.22 0.99 0.91 1.23 4.10 1.26 1.16 1.591.0% 4.38 1.20 1.11 1.97 5.32 1.46 1.34 2.42IIPlain 1.98 0.85 0.79 0.24 2.7:3 1.17 1.08 0.37PFConcrete0.1% 1.98 0.85 0.78 0.25 2.72 1.16 1.07 0.390.5% 1.98 0.86 0.79 0.23 2.70 1.17 1.08 0.36SFConcrete0.5% :3.24 0.98 0.90 1.26 4.00 1.21 1.11 1.581.0% 4.02 1.20 1.10 1.63 5.09 1.51 1.39 2.091IIPlain 2.03 0.8:3 0.76 0.33 2.88 1.18 1.09 0.52PFConcrete0.1% 2.02 0.8:3 0.76 0.33 2.89 1.19 1.09 0.520.5% 2.02 0.83 0.76 0.33 2.89 1.19 1.09 0.52SFConcrete0.5% 3.01 0.93 0.85 1.13 3.81 1.17 1.08 1.461.0% 4.11 1.15 1.06 1.80 5.28 1.48 1.36 2.34IIIIPlain 1.99 0.82 0.75 0.32 :3.16 1.30 1.20 0.56PFConcrete0.1% 1.99 0.82 0.75 0.32 :3.24 1.33 1.2:3 0.580.5% 1.99 0.82 0.75 0.:32 :3.24 1.33 1.23 0.58SFConcrete0.5% 3.01 0.88 0.81 1.22 :3.83 1.12 1.0:3 1.591.0% 4.14 1.10 1.01 1.9:3 5.43 1.44 1.:32 2.57Chapter 6. Energy Transfer and Balance^ 2622. Similar to the tests with smooth bars, all of the components of energy and workfor push-in tests were 10 ti 15% larger than those for pull-out tests. Again, thiswas due to the larger radial force acting at the interface for push-in tests than forpull-out tests.3. Because the addition of steel fibers improved the shear strength and the crackingresistance of the concrete, the four components in the right hand side of the energybalance equation (Eq. 6.5) increased by 2 to 4 times for specimens with steel fiberscompared to those with plain concrete and polypropylene fibre concrete. A higherfiber content resulted in more strain energy and more work done. However, theeffects of the polypropylene fiber additions seemed quite small, the same as for thetests with smooth bars.4. t7nlike the tests with smooth bars, there was some increase in the work and thestrain energies with an increase in loading rate. This was because the shearingmechanism plays a vital role in the bond strength for deformed bars. In thismechanism the bond stress increased with loading rate, and compensated for theloss in bond strength due to the chemical adhesion and the frictional resistanceunder higher loading rates.5. A higher concrete strength increased the work done by the bond stress and thestrain energy in the rebar. Both the better adhesion between the rebar and thehigh strength concrete, and the higher shear strength of the concrete contributedto this effect.Chapter 6. Energy Transfer and Balance^ 263Table 6.3: Energy Balance in the Linear Portion (Deformed Bars, NormalStrength)Type ofConcretePull-out Tests^(Nni) Push-in Tests^(N7n)Wha Ere, str Ec, str 144 Wha Ere, str E c, str 14/1,SPlain 10.05 0.98 0.90 8.06 11.00 1.07 0.99 8.84PFConcrete0.1% 10.15 0.98 0.90 8.17 11.08 1.07 0.98 8.930.5% 10.18 0.99 0.91 8.19 11.13 1.08 0.99 8.96SFConcrete0.5% 16.34 1.21 1.12 13.91 18.64 1.38 1.27 15.891.0% 2:3.10 1.41 1.30 20.28 25.91 1.59 1.46 22.76MIPlain 10.53 0.97 0.89 8.57 11.61 1.07 0.98 9.45PFConcrete0.1% 10.55 0.97 0.89 8.59 11.63 1.07 0.98 9.470.5% 10.58 0.96 0.88 8.64 11.71 1.06 0.98 9.57SFConcrete0.5% 16.74 1.22 1.12 14.29 18.95 1.38 1.27 16.201.0% 26.:37 1.32 1.22 2:3.73 30.26 1.52 1.40 27.24MIIPlain 10.70 1.00 0.92 8.68 11.83 1.10 1.02 9.60PFConcrete0.1% 10.73 1.00 0.92 8.72 11.88 1.10 1.01 9.660.5% 10.80 1.00 0.92 8.79 11.90 1.10 1.01 9.69SFConcrete0.5% 19.01 1.2:3 1.13 16.55 21.50 1.39 1.28 18.731.0% 27.34 1.32 1.22 24.70 31.91 1.54 1.42 28.85IIPlain 11.30 1.05 0.97 9.18 12.35 1.15 1.06 10.04PFConcrete0.1% 11.35 1.08 0.99 9.18 12.38 1.18 1.08 10.020.5% 11.38 1.08 0.99 9.21 12.41 1.18 1.08 10.05SFConcrete0.5% 20.09 1.24 1.14 17.62 22.26 1.37 1.26 19.531.0% 29.87 1.37 1.26 27.1:3 35.13 1.62 1.49 31.9:3IIIPlain 11.8:3 1.08 0.99 9.66 12.98 1.18 1.09 10.61PFConcrete0.1% 11.98 1.08 1.00 9.80 13.03 1.18 1.08 10.670.5% 12.00 1.08 1.00 9.82 13.05 1.18 1.08 10.69SFConcrete0.5% 22.63 1.27 1.17 20.09 25.18 1.41 1.30 22.361.0% 33.23 1.37 1.26 30.50 37.01 1.53 1.40 :33.98IIIIPlain 12.55 1.18 1.08 10.19 13.45 1.26 1.16 10.92PF( oncrete0.1% 12.58 1.18 1.08 10.22 1:3.56 1.27 1.17 11.020.5% 12.63 1.17 1.08 10.28 15.03 1.40 1.29 12.25SF(,oncrete0.5% 23.56 1.22 1.12 21.11 24.69 1.28 1.18 22.131.0% :36.79 1.3:3 1.22 34.1:3 40.21 1.46 1.34 :37.32Chapter 6. Energy Transfer and Balance^ 264Table 6.4: Energy Balance in the Linear Portion (Deformed Bars, HighStrength)Type ofConcretePull-out Tests^(Nnz) Push-in Tests^(Arm)Wha Err, str Ec, str Wb Wha Ere, str Ec, str WbSPlain 10.53 1.03 0.95 8.45 11.28 1.10 1.01 9.06PFConcrete0.1% 10.60 1.02 0.94 8.54 11.30 1.09 1.00 9.110.5% 11.06 1.07 0.99 8.90 11.51 1.11 1.03 9.26SFCon crete0.5% 17.48 1.30 1.19 14.89 19.63 1.46 1.34 16.731.0% 24.33 1.49 1.37 21.37 27.82 1.70 1.57 24.45M1Plain 10.83 1.00 0.92 8.82 12.03 1.11 1.02 9.81PFConcrete0.1% 10.88 1.00 0.92 8.86 12.05 1.11 1.02 9.820.5% 11.03 1.00 0.92 9.01 12.33 1.12 1.03 10.08SFConcrete0.5% 18.26 1.33 1.23 15.60 20.19 1.47 1.36 17.261.0% 28.28 1.42 1.30 25.45 32.70 1.64 1.51 29.45MIIPlain 11.30 1.06 0.97 9.17 12.45 1.16 1.07 10.12PFConcrete0.1% 11.3:3 1.05 0.97 9.21 12.58 1.17 1.07 10.240.5% 11.38 1.05 0.96 9.26 12.63 1.16 1.07 10.29SFConcrete0.5% 20.24 1.31 1.21 17.62 24.40 1.58 1.45 21.271.0% 29.07 1.41 1.29 26.27 34.11 1.65 1.52 :30.84IIPlain 11.85 1.10 1.01 9.63 13.30 1.24 1.14 10.82PFConcrete0.1% 11.9:3 1.13 1.04 9.65 1:3.55 1.29 1.18 10.980.5% 11.96 1.13 1.04 9.68 13.66 1.29 1.19 11.07SFConcrete0.5% 21.54 1.32 1.22 18.89 24.74 1.52 1.40 21.721.0% 32.09 1.48 1.36 29.15 37.69 1.7:3 1.60 34.25IIIPlain 12.5:3 1.14 1.05 10.24 14.18 1.29 1.19 11.60PFConcrete0.1% 12.56 1.13 1.04 10.28 14.23 1.29 1.18 11.660.5% 12.6:3 1.14 1.05 10.34 14.55 1.31 1.21 11.9:3SFConcrete0.5% 24.56 1.:38 1.27 21.81 27.58 1.55 1.42 24.511.0% 35.31 1.46 1.:34 :32.41 40.56 1.67 1.54 :37.25/IIIPlain 1:3.08 1.2:3 1.13 10.62 14.68 1.38 1.27 11.9:3PFConcrete0.1% 13.13 1.23 1.13 10.67 15.:33 1.44 1.32 12.470.5% 1:3.16 1.22 1.13 10.71 16.16 1.50 1.38 1:3.17SFConcrete0.5% 25.42 1.32 1.21 22.79 28.31 1.47 1.35 25.391.0% 39.08 1.41 1.30 36.27 42.90 1.55 1.43 :39.82Chapter 6. Energy Transfer and Balance^ 2656.4 Energy Balance in the Non-linear Region (t = tf)This stage begins at the end of the linear portion and goes on to complete bond failure(at t = t f ), as shown in Fig. 6.1.At this stage the equation of energy balance can be written as11: h a (t f) = E re, sir(t f^E c, str(t f)^E re,yielcl(t f) W^6( t f)^(Nm)^(6.6)where W ha ( t f) is the work done by the hammer at time t f , E„, sir (tf) and E c , str (i f ) arethe elastic strain energy stored in the rebar and the concrete, respectively, Er,,yi,td(tf) isthe energy in local yielding in the rebar and W b (t f ) is the work done by the bond stress.For the pull-out specimens, as the applied load was further increased, a large longitu-dinal tensile stress and a radial tensile stress were developed. They combined to producelarge diagonal tensile stresses, and caused diagonal cracks to emanate from the tip of theribs because of the stress concentration. With a further increase in load, more diago-nal cracks initiated and propagated outwards in the concrete. The 'teeth' of comb-likeconcrete (see Fig. 2.4) were subjected to bending in the direction of the load, and thereaction of the wedging force caused circumferential tension in the concrete and formedradial cracks.For the push-in specimens, the push-in force served to tighten the concrete aroundthe rebar and increased the frictional resistance between the rebar and the concrete. Theslight increase in the diameter of the rebar due to Poisson's effect also improved theChapter 6. Energy Transfer and Balance^ 266frictional resistance. The inward deformation of the concrete provided some lateral com-pression in the concrete surrounding the rebar, and thus reduced the radial componentof the wedging force, so no splitting cracks developed.6.4.1 Tests with Smooth BarsFor the specimens with smooth bars the experimental results are summarized in Tables6.5 (for normal strength) and 6.6 (for high strength). Similar to the results for the linearregion, the equation of energy balance was well satisfied without considering the energyloss due to local yielding in the rebar. The following conclusions can be drawn from theresults:1. Different from the linear region, in this non-linear region of the applied load vs.displacement curve, most (about 80% to 85%) of the work done by the hammer(1/1/, a (tf )) was transferred to the work done by the bond stress (Wb (tf )). In thisregion, as the applied load increased, at a particular load the chemical adhesion wasdestroyed and the frictional resistance at the interface between the steel and theconcrete became the only mechanism for bond resistance. The frictional resistancecould continue to increase, especially for the push-in tests, up to a certain value butthen declined because of the decrease in the frictional factor with displacement.2. Beyond the point t = t 1 , the strain energies in the rebar and in the concrete(E,,,str(tf) and E c , str (t f )) kept increasing until the applied load (and also thebond stress) reached its peak value, then remained the same for a while beforedecreasing to zero after complete bond failure (at t = tf). After the peak point ofthe bond stress, the stresses in the rebar and the concrete stopped increasing, andChapter 6. Energy Transfer and Balance^ 267so the strain energies in both materials remained the same. With the decrease inthe bond resistance with further movement of the rebar, both the steel stress andthe concrete stress released. Thus the strain energies stored in both materials inthe previous stage were transferred to the work done by the bond stress.3. All of the components of energy and work for push-in tests were larger than thosefor pull-out tests. This was same as that in the linear stage.4. For the pull-out tests fiber additions (either polypropylene fibers or steel fibers)did not have much effect on the work or the strain energies. For the push-in tests,some cracks developed at this stage. The addition of steel fibers increased the crackresistance; thus the work done by the bond stress increased.5. For all pull-out tests and push-in tests with specimens made of plain concrete or ofpolypropylene fiber reinforced concrete, there was some decrease in the work andthe strain energies with an increase in loading rate, which was same as in the linearregion. But for the push-in tests with specimens made of steel fiber reinforcedconcrete, there was an opposite results; both the work and the strain energiesincreased with the loading rate. This occurred even though both the chemicaladhesion and the frictional resistance apparently decreased under a higher loadingrate and the crack velocities in concrete are proportional to the rate of loading(Mindess [71], Shah [72]). However, these decreases were compensated for by theeffect of the steel fibers in reducing the crack velocities and the bond strengths.This resulted in the increases in the work done and in the strain energies.6. Higher concrete strength increased both the work done by the bond stress and thestrain energy in the rebar.Chapter G. Energy Transfer and Balance^ 268Table 6.5: Energy Balance in the Non-linear Region (Smooth Bars, NormalStrength)Type ofConcretePull-out Tests^(Nm) Push-in Tests^(Nnt)Wha Ere, str Ec, str Wb Wha Ere, str Ec, str 'WI)SPlain 18.10 1.81 1.68 14.61 21.42 2.25 2.09 16.98PFConcrete0.1% 18.10 1.81 1.68 14.61 21.33 2.24 2.08 16.900.5% 18.10 1.81 1.68 14.61 21.50 2.26 2.10 17.05SFConcrete0.5% 25.70 2.19 2.04 21.47 :31.05 2.78 2.58 25.591.0% :32.40 2.62 2.44 27.34 38.14 3.24 3.01 31.79MIPlain 17.70 1.73 1.61 14.36 21.58 2.22 2.06 17.21PFConcrete0.1% 17.70 1.73 1.61 14.36 21.58 2.22 2.06 17.210.5% 17.80 1.73 1.61 14.46 21.59 2.20 2.05 17.24SFConcrete0.5% 25.50 2.14 1.99 21.37 :31.72 2.80 2.60 26.231.0% :32.:30 2.43 2.26 27.61 38.33 3.03 2.82 32.39MIIPlain 16.90 1.65 1.53 13.72 22.38 2.29 2.1:3 17.85PFConcrete0.1% 17.10 1.65 1.53 13.92 22.5:3 2.28 2.12 18.020.5% 17.10 1.65 1.5:3 13.92 22.53 2.28 2.12 18.02SFConcrete0.5% 24.20 2.01 1.87 20.32 32.36 2.82 2.62 26.811.0% :32.30 2.:38 2.21 27.71 39.13 3.03 2.82 33.19IIPlain 16.80 1.64 1.5:3 13.6:3 2:3.48 2.41 2.24 18.74PFConcrete0.1% 16.80 1.63 1.52 13.65 24.21 2.47 2.29 19.350.5% 16.90 1.65 1.53 13.72 24.1:3 2.47 2.:30 19.26SFConcrete0.5% 24.20 1.98 1.84 20.38 32.89 2.83 2.6:3 27.331.0% 32.10 2.39 2.22 27.49 40.:33 3.15 2.93 34.14IIIPlain 16.30 1.56 1.45 1:3.29 24.59 2.47 2.30 19.72PFConcrete0.1% 16.30 1.56 1.45 13.29 24.68 2.48 2.31 19.790.5% 16.30 1.56 1.45 13.29 24.68 2.48 2.31 19.79SFConcrete0.5% 23.60 1.89 1.76 19.95 34.64 2.91 2.71 28.921.0% 31.40 2.25 2.09 27.06 41.75 3.14 2.92 :35.59IIIIPlain 15.50 1.48 1.38 12.64 26.94 2.70 2.51 21.63PFConcrete0.1% 15.50 1.48 1.38 12.64 26.94 2.70 2.51 21.6:30.5% 15.50 1.48 1.38 12.64 26.85 2.69 2.50 21.56SFConcrete0.5% 23.30 1.79 1.66 19.85 34.77 2.80 2.61 29.261.0% :31.:30 2.1:3 1.98 27.19 42.63 3.05 2.8:3 36.65Chapter 6. Energy Transfer and Balance^ 269Table 6.6: Energy Balance in the Non-linear Region (Smooth Bars, HighStrength)Type ofConcretePull-out Tests^(Nm) Push-in Tests^(Nm)Wha Ere, str Ec, str Wb Wha Ere, str Ec, str WbSPlain 19.09 2.00 1.86 15.12 22.31 2.34 2.18 17.69PFConcrete0.1% 19.09 2.00 1.86 15.12 22.40 2.35 2.19 17.760.5% 19.18 2.01 1.87 15.19 22.31 2.34 2.18 17.69SFConcrete0.5% 26.75 2.39 2.23 22.03 33.16 2.97 2.76 27.331.0% 35.14 2.98 2.77 29.28 40.26 3.42 3.18 :33.56MIPlain 19.05 1.96 1.82 15.18 22.67 2.3:3 2.16 18.08PFConcrete0.1% 19.05 1.96 1.82 15.18 22.67 2.33 2.16 18.080.5% 19.06 1.95 1.81 15.21 22.68 2.31 2.15 18.11SFConcrete0.5% 26.03 2.29 2.13 21.51 32.61 2.87 2.67 26.961.0% 35.05 2.77 2.57 29.61 40.7:3 :3.22 2.99 34.42MIIPlain 18.4:3 1.89 1.76 14.68 23.73 2.43 2.26 18.94PFConcrete0.1% 18.55 1.88 1.75 14.82 23.98 2.4:3 2.26 19.190.5% 18.64 1.89 1.76 14.89 23.80 2.41 2.24 19.04SFConcrete0.5% 25.18 2.20 2.04 20.84 32.00 2.79 2.60 26.511.0% 34.52 2.67 2.48 29.26 41.88 3.24 3.01 35.53IIPlain 18.52 1.90 1.77 14.75 25.47 2.61 2.43 20.:33PFConcrete0.1% 18.52 1.89 1.75 14.78 25.:38 2.59 2.40 20.290.5% 18.62 1.91 1.77 14.83 25.40 2.60 2.42 20.27SFConcrete0.5% 25.26 2.17 2.02 20.97 :31.20 2.68 2.49 25.9:31.0% :33.98 2.66 2.47 28.75 4:3.01 :3.36 3.13 :36.42IIIPlain 18.37 1.85 1.72 14.71 26.12 2.62 2.44 20.95PFConcrete0.1% 18.28 1.84 1.71 14.64 26.21 2.6:3 2.45 21.020.5% 18.28 1.84 1.71 14.64 26.21 2.6:3 2.45 21.02SFConcrete0.5% 24.49 2.06 1.92 20.42 30.99 2.61 2.42 25.861.0% :3:3.99 2.56 2.38 28.95 43.62 :3.28 3.05 :37.19/IIIPlain 18.11 1.82 1.69 14.51 28.84 2.89 2.69 2:3.16PFConcrete0.1% 18.11 1.82 1.69 14.51 29.56 2.96 2.76 2:3.740.5% 18.11 1.82 1.69 14.51 29.56 2.96 2.76 23.74SFConcrete0.5% 24.19 1.95 1.81 20.32 30.77 2.48 2.:31 25.881.0% :34.06 2.43 2.26 29.27 44.77 :3.20 2.97 :38.49Chapter 6. Energy Transfer and Balance^ 2706.4.2 Tests with Deformed BarsThe experimental results of specimens with deformed bars in the non-linear region aresummarized in Tables 6.7 (for normal strength) and 6.8 (for high strength). A very goodbalance in the energy equation was again found for almost all of the specimens. Thefollowing conclusions may be made:I. In this non-linear region of the applied load vs. displacement curve, most of thework done by the hammer (Wh a (t f )) was transferred to the work done by thebond stress (W b (tf )). For deformed bars, the shearing mechanism became the onlymechanism for bond resistance at this stage. Diagonal cracks at the tips of the ribsprobably developed at a relatively low level of bond stress and propagated in theconcrete. The work done by the applied load was mainly consumed in the initiationand development of these internal cracks.2. Similar to the specimens with smooth bars, beyond the point t = t 1 the strainenergies in the rebar and in the concrete (E str (t f) and E c , str (t f)) kept increasinguntil the applied load (and also the bond stress) reached the peak value, and thenremained the same for a while. Because the wedging action of the ribs of thedeformed bars could produce much larger and longer bond resistances, these strainenergies were found to be much greater than those for the specimens with smoothbars. However, they released gradually with a decrease of the bond resistance dueto further crack propagation in the concrete. At the moment of bond failure (t = t f )all of these strain energies were converted to the fracture energy, which dissipated!in the development of internal cracks in the concrete.Chapter 6. Energy Transfer and Balance^ 271:3. All of the components of energy and work for push-in tests were about 10% largerthan those for pull-out tests. This was similar to the results in the linear region.4. The addition of polypropylene fibers did not have much effect on the work or thestrain energies. However, steel fibers were found to greatly increase both the strainenergies (by 150% ) and the work done by the bond stress (by 200%).5. There were significant increases in the work and the strain energies with an in-crease in loading rate, especially for the specimens made with steel fiber reinforcedconcrete.6. A higher concrete strength increased the work done by the bond stress and thestrain energy in the rebar.6.5 Energy Balance over the Entire Impact EventThe experimental results for the total energy balance based on Eq. 6.1 are presentedin Tables 6.9 and 6.10. For simplicity of presentation, data are given only for specimensmade of normal compressive strength concrete with one fiber content (0.5% by volumefor both polypropylene fibres and steel fibres) and three loading rates (Impact I, II andIII). It can be found that the total energy was well balanced for all of the specimens.The errors were less than 3.0% of the total energy.The experimental results for the energy balance right out the moment of impact basedon Eq. 6.2 are presented in Table 6.11. The balance condition was also satisfied here.Because a solid steel frame with several mechanical connections was used in the pull-outChapter 6. Energy Transfer and Balance^ 272Table 6.7: Energy Balance in the Non-linear Region (Deformed Bars, NormalStrength)Type ofConcretePull-out Tests^(N7n) Push-in Tests^(Nin)W ha Ere, str E c, str Wb W ha Ere, str E e, str WbSPlain 30.15 2.18 2.03 25.84 33.00 2.39 2.22 28.29PFConcrete0.1% :30.45 2.17 2.02 26.16 33.23 2.37 2.20 28.550.5% 30.52 2.19 2.04 26.19 33.37 2.40 2.23 28.64SFConcrete0.5% 38.26 2.70 2.51 32.96 43.66 3.08 2.86 37.621.0% 48.40 3.14 2.92 42.23 54.29 3.53 3.28 47.39MIPlain 31.57 2.15 2.00 27.31 34.79 2.37 2.21 30.11PFConcrete0.1% :31.65 2.15 2.00 27.39 34.88 2.37 2.21 30.200.5% :31.72 2.1:3 1.98 27.50 :35.09 2.36 2.20 30.44SFCon crete0.5% 41.46 2.72 2.53 36.12 46.95 3.08 2.86 40.911.0% 46.9:3 2.94 2.73 41.16 53.84 3.37 3.14 47.24MIIPlain :32.10 2.22 2.07 27.71 35.48 2.45 2.28 :30.64PFConcrete0.1% 32.17 2.21 2.06 27.80 :35.62 2.45 2.28 :30.790.5% 32.40 2.21 2.06 28.03 35.70 2.44 2.27 :30.90SFConcrete0.5% 41.29 2.74 2.54 35.91 46.70 3.09 2.88 40.6:31.0% 48.56 2.94 2.73 42.79 56.69 :3.4:3 :3.19 49.96IIPlain :3:3.90 2.:34 2.17 29.29 :37.05 2.55 2.:38 :32.02PFConcrete0.1% 34.05 2.40 2.2:3 29.33 :37.1:3 2.61 2.4:3 :31.980.5% 34.12 2.40 2.23 29.40 37.19 2.61 2.43 :32.05SFConcrete0.5% 43.81 2.75 2.55 38.41 48.54 3.04 2.8:3 42.571.0% 49.63 3.06 2.84 43.6:3 58.37 3.59 :3.:34 51.3:31IIPlain 35.47 2.40 2.23 30.75 38.92 2.63 2.44 :3:3.75PFConcrete0.1% 35.92 2.41 2.24 31.18 39.07 2.62 2.43 :33.920.5% 36.00 2.41 2.24 31.26 39.15 2.62 2.43 :34.00SFConcrete0.5% 43.17 2.82 2.63 37.62 48.02 3.14 2.92 41.861.0% 54.67 3.05 2.83 48.69 60.89 3.39 :3.15 54.24IIIIPlain :37.6,5 2.62 2.44 32.50 40.:35 2.81 2.61 34.8:3PFConcrete0.1% :37.72 2.62 2.44 :32.57 40.64 2.82 2.62 35.100.5% 37.87 2.61 2.43 :32.73 45.07 3.11 2.89 :38.98SFConcrete0.5% 47.:34 2.72 2.53 42.00 49.61 2.85 2.65 44.021.0% 57.81 2.96 2.75 52.00 63.19 :3.2:3 3.01 56.85Chapter 6. Energy Transfer and Balance^ 273Table 6.8: Energy Balance in the Non-linear Region (Deformed Bars, HighStrength)Type ofConcretePull-out Tests^(Nm) Push-in Tests^(Nin)Wha Ere, str Ec, str 144 Wha Ere, str Ec, str WbSPlain 31.58 2.29 2.13 27.06 33.83 2.45 2.28 29.00PFConcrete0.1% 31.80 2.27 2.11 27.32 33.90 2.42 2.25 29.1:30.5% 33.14 2.38 2.21 28.45 34.49 2.48 2.30 29.61SFConcrete0.5% 40.92 2.88 2.68 35.26 45.97 3.24 3.01 39.621.0% 50.97 3.31 :3.08 44.48 58.28 3.78 3.52 50.88AlIPlain 32.47 2.21 2.06 28.10 36.07 2.46 2.29 :31.22PFConcrete0.1% 32.63 2.22 2.06 28.24 36.15 2.46 2.29 :31.:300.5% 33.07 2.22 2.07 28.68 :36.97 2.49 2.31 :32.07SFConcrete0.5% 45.24 2.96 2.76 39.42 50.01 3.28 3.05 4:3.591.0% 50.32 3.15 2.93 44.14 58.20 3.64 3.:39 51.06/11IIPlain 3:3.90 2.35 2.18 29.27 37.35 2.58 2.40 32.26PFConcrete0.1% 33.97 2.:34 2.17 29.36 :37.72 2.59 2.41 :32.610.5% 34.13 2.33 2.17 29.53 37.88 2.59 2.40 :32.79SFConcrete0.5% 43.96 2.91 2.71 38.24 53.00 3.51 3.27 46.121.0% 51.6:3 3.12 2.91 45.50 60.59 3.67 :3.41 5:3.41/IPlain :35.55 2.45 2.28 30.72 39.90 2.75 2.56 34.49PFConcrete0.1% 35.78 2.52 2.34 30.82 40.65 2.86 2.66 35.030.5% 35.84 2.52 2.34 30.89 40.94 2.88 2.67 35.30SFConcrete0.5% 46.96 2.94 2.74 41.18 53.96 3.38 3.14 47.3:31.0% 5:3.:31 :3.28 3.05 46.88 62.61 :3.85 3.59 55.07IIIPlain 37.57 2.54 2.:36 :32.57 42.52 2.87 2.67 36.88PFConcrete0.1% 37.64 2.52 2.34 32.68 42.67 2.86 2.66 :37.050.5% 37.88 2.53 2.35 32.89 43.65 2.92 2.71 :37.92SFConcrete0.5% 46.84 3.06 2.85 40.83 52.62 3.44 :3.20 45.881.0% 58.09 :3.24 :3.01 51.74 66.74 3.72 3.46 59.46IIIIPlain 39.2:3 2.73 2.54 :3:3.86 44.0:3 :3.06 2.85 :38.01PFConcrete0.1% 39.37 2.73 2.54 :3:3.99 45.97 3.19 2.97 :39.710.5% :39.44 2.72 2.53 34.10 48.44 3.34 3.10 41.90SFConcrete0.5% 51.08 2.93 2.73 45.32 56.89 3.26 3.04 50.491.0% 61.42 3.14 2.92 55.25 67.40 3.45 :3.21 60.65Chapter 6. Energy Transfer and Balance^ 274tests (see Chapter 3), there was a bit more energy lost at the moment of impact for thepull-out specimens than for the push-in specimens.The data for the final energy balance after impact (based on Eq. 6.4) are presentedin Table 6.12. Since the test specimens were so designed as to avoid possible yieldingof the steel, the energy lost in local yielding at the contact surface between the hammerand the rebar was found to be very little.Therefore the experimental arrangements, the measurements of the important pa-rameters, and the mathematical models for data analysis in the tests are believed to bereasonable and accurate from the viewpoint of energy conservation.Chapter 6. Energy Transfer and Balance^ 275Table 6.9: Total Energy Balance (Smooth Bar Specimens)Type ofSpecimenEnergy^(Nil')Eha,p E ha, f r A Eha E ha, le f t ErrorIIPlainConcretePull-out 70.8 4.6 19.5 45.5 1.2Push-in 70.8 4.6 26.6 :38.6 1.0PFConcretePull-out 170.0 15.3 19.9 131.4 3.4Push-in 170.0 15.3 27.6 123.9 3.2SFConcretePull-out :305.0 27.5 28.7 244.8 4.1Push-in :305.0 27.5 38.6 2:35.1 3.9IIIPlainConcretePull-out 70.8 4.6 19.1 45.8 1.3Push-in 70.8 4.6 28.5 35.4 2.3PFConcretePull-out 170.0 15.3 19.2 133.5 2.0Push-in 170.0 15.3 28.4 122.9 3.4SFConcretePull-out 305.0 27.5 28.1 245.8 :3.7Push-in 305.0 27.5 40.3 234.2 3.1/IIIPlainConcretePull-out 70.8 4.6 18.4 45.7 2.1Push-in 70.8 4.6 31.0 33.3 1.9PFConcretePull-out 170.0 15.3 18.5 133.0 :3.2Push-in 170.0 15.3 31.3 120.1 :3.:3SFConcretePull-out :305.0 27.5 27.9 245.4 4.:3Push-in :305.0 27.5 41.0 232.4 4.2/ I = 0.5 - 10'^I II = 0.5 • 10 -3^/III = 0.5 - 10 -2^(MPa/s)PF - Polypropylene Fibre^SF - Steel FibreChapter 6. Energy Transfer and Balance^ 276Table 6.10: Total Energy Balance (Deformed Bar Specimens)Type ofSpecimenEnergy^(Nm)Eha,p E ha, f r A Eha E lia,lef t ErrorIIPlainConcretePull-out 70.8 4.6 45.5 18.8 1.9Push-in 70.8 4.6 49.8 15.0 1.4PFConcretePull-out 170.0 15.3 46.0 106.3 2.4Push-in 170.0 15.3 50.2 102.6 1.9SFConcretePull-out 305.0 27.5 64.6 210.0 2.9Push-in 305.0 27.5 71.5 202.9 3.1IIIPlainConcretePull-out 70.8 4.6 47.8 16.2 2.2Push-in 70.8 4.6 52.6 11.0 2.6PFConcretePull-out 170.0 15.3 48.6 10:3.7 2.4Push-in 170.0 15.3 53.0 99.8 1.9SFConcretePull-out 305.0 27.5 66.7 207.7 3.1Push-in 305.0 27.5 74.0 200.6 2.9IIIIPlainConcretePull-out 70.8 4.6 50.9 12.4 2.9Push-in 70.8 4.6 54.5 9.3 2.4PFConcretePull-out 170.0 15.3 51.1 101.0 2.6Push-in 170.0 15.3 60.8 90.5 :3.4SFConcretePull-out 305.0 27.5 71.7 202.4 3.4Push-in 305.0 27.5 75.3 198.6 :3.6/ I = 0.5 • 10'^/ II = 0.5 • 10'^/ III = 0.5 - 10'^(MPa/s)PF - Polypropylene Fibre^SF - Steel FibreChapter 6. Energy Transfer and Balance^ 277Table 6.11: Energy Balance right out of the Moment of ImpactType ofSpecimenEnergies^(Nm)Smooth Bars Deformed BarsA E ha W ha E sys A E ha W ha E sysIIPlainConcretePull-out 19.5 18.7 0.8 45.5 45.4 0.1Push-in 26.6 26.0 0.6 49.8 49.7 0.1PFConcretePull-out 19.9 18.9 1.0 46.0 45.6 0.4Push-in 27.6 26.8 0.8 50.2 49.9 0.3SFConcretePull-out 28.7 27.5 1.2 64.6 64.3 0.3Push-in 38.6 37.3 1.3 71.5 71.2 0.3IIIPlainConcretePull-out 19.1 18.2 0.9 47.8 47.6 0.2Push-in 28.5 27.4 1.1 52.6 52.4 0.2PFConcretePull-out 19.2 18.2 1.0 48.6 48.4 0.2Push-in 28.4 27.6 0.8 53.0 52.7 0.3SFConcretePull-out 28.1 26.8 1.3 66.7 66.4 0.3Push-in 40.3 39.1 1.2 74.0 73.8 0.2IIIIPlainConcretePull-out 18.4 17.2 1.2 50.9 50.7 0.2Push-in 31.0 30.0 1.0 54.5 54.4 0.1PFConcretePull-out 18.5 17.4 1.1 51.1 50.8 0.3Push-in 31.3 29.9 1.4 60.8 60.6 0.2SFConcretePull-out 27.9 26.5 1.4 71.7 71.6 0.1Push-in 41.0 39.5 1.5 75.3 75.1 0.2/ I = 0.5 • 10 -4^III =PF - Polypropylene0.5 • 10 -3^/ III = 0.5 • 10 -2^(MPa/s)Fibre^SF - Steel FibreChapter 6. Energy Transfer and Balance^ 278Table 6.12: Energy Balance at Bond FailureType ofSpecimenEnergies^(Nnt)Smooth Bars Deformed BarsWha Wb E yield Wha Wb E yieldIIPlainConcretePull-out 18.7 18.6 0.1 45.4 45.2 0.2Push-in 26.0 26.0 0.0 49.7 49.4 0.3PFConcretePull-out 18.9 18.7 0.2 45.6 45.5 0.1Push-in 26.8 26.7 0.1 49.9 49.6 0.3SFConcretePull-out 27.5 27.3 0.2 64.3 63.9 0.4Push-in 37.3 37.1 0.2 71.2 70.8 0.4IIIPlainConcretePull-out 18.2 18.1 0.1 47.6 47.3 0.3Push-in 27.4 27.3 0.1 52.4 51.9 0.5PFConcretePull-out 18.2 18.1 0.1 48.4 48.0 0.4Push-in 27.6 27.4 0.2 52.7 52.2 0.5SFConcretePull-out 26.8 26.5 0.3 66.4 65.8 0.6Push-in 39.1 38.9 0.2 73.8 73.2 0.6IIIIPlainConcretePull-out 17.2 17.2 0.0 50.7 50.2 0.5Push-in 30.0 29.9 0.1 54.4 53.8 0.6PFConcretePull-out 17.4 17.2 0.2 50.8 50.5 0.3Push-in 29.9 29.8 0.1 60.6 60.1 0.5SFConcretePull-out 26.5 26.2 0.3 71.6 70.9 0.7Push-in 39.5 39.1 0.4 75.1 74.3 0.8/ I = 0.5 • 10 -4^/ II = 0.5 • 10'^1 111 = 0.5 • 10 -2^(MPa/.9)PF - Polypropylene Fibre^SF - Steel Fibre6.6 Energy Absorbtion and Dissipation CapacityIn structural engineering design, it is expected that a structure subjected to dynamicloading should resist such loading without collapse, though with some structural and non-structural damage. To avoid collapse, the structural members must he ductile enoughto absorb and dissipate energy. For reinforced concrete structures it is essential that thebond between the reinforcing bar and the concrete exhibit a certain 'ductility' duringChapter 6. Energy Transfer and Balance^ 279dynamic loading. That is, the bond resistance in the member should decrease graduallyinstead of suddenly failing, so that the dynamic energy can largely be transferred, ab-sorbed and dissipated to the entire structure member over a relatively long time period.This bond 'ductility' may be represented by the fracture energy, which is calculated asthe work done by the bond stress. A larger value of fracture energy means a 'ductile'bond. The fracture energy results for different types of specimens are presented in Tables6.13 and 6.14. The following conclusions may be drawn:1. The fracture energy during the bond failure process for deformed bars was muchgreater than that for smooth bars. In this experimental work, in which smooth barswith a diameter of 12.7 mm and No.10 deformed bars (diameter = 11.7 mm) wereused, the fracture energy for the deformed bars was 2 to 3 times that for smoothbars.2. Concrete of high compressive strength absorbed more fracture energy during bondfailure than concrete with normal compressive strength.3. The fracture energy for the push-in case was 10 ti 20 % higher than that for thepull-out case.4. The addition of polypropylene fibers did not have much effect on the fracture energyduring bond failure.5. Steel fibers significantly increased the fracture energy during bond failure by about100% (for static loading) to about 300 % (for impact loading), i.e. they made theconcrete matrix more ductile with regard to bond. Higher fiber contents were moreeffective in this regard.Chapter G. Energy Transfer and Balance^ 2806. Generally the fracture energy increased with an increase in loading rate, especiallyfor the specimens made with steel fibres.Chapter 6. Energy Transfer and Balance^ 281Table 6.13: Fracture Energy in Bond Failure (Smooth Bars)Type ofConcretePull-out Tests^(Nm) Push-in Tests^(Nm)Normal High Normal HighSPlain Concrete 20.2 21.3 23.9 24.9PolypropyleneFibre Concrete0.1% 20.2 21.3 23.8 25.00.5% 20.2 21.4 24.0 24.9SteelFibre Concrete0.5% 29.3 30.5 :35.4 :37.81.0% 36.7 39.8 43.2 45.6MIPlain Concrete 19.6 21.1 23.9 25.1PolypropyleneFibre Concrete0.1% 19.6 21.1 23.9 25.10.5% 19.7 21.1 23.9 25.1SteelFibre Concrete0.5% 28.7 29.:3 35.7 36.71.0% 36.4 39.5 43.2 45.9MIIPlain Concrete 18.8 20.5 24.9 26.4PolypropyleneFibre Concrete0.1% 18.9 20.5 24.9 26.50.5% 18.9 20.6 24.9 26.3SteelFibre Concrete0.5% 27.3 28.4 36.5 :36.11.0% :36.4 38.9 44.1 47.2IIPlain Concrete 18.6 20.5 26.0 28.2PolypropyleneFibre Concrete0.1% 18.6 20.5 26.8 28.10.5% 18.7 20.6 26.7 28.1SteelFibre Concrete0.5% 27.3 28.5 :37.1 :35.21.0% :35.9 38.0 45.1 48.1IIIPlain Concrete 18.1 20.4 27.3 29.0PolypropyleneFibre Concrete0.1% 18.1 20.3 27.4 29.10.5% 18.1 20.3 27.4 29.1SteelFibre Concrete0.5% 26.5 27.5 :38.9 :34.81.0% 35.2 38.1 46.8 48.9IIIIPlain Concrete 17.2 20.1 29.9 :32.0PolypropyleneFibre Concrete0.1% 17.2 20.1 29.9 :32.80.5% 17.2 20.1 29.8 :32.8SteelFibre Concrete0.5% 26.2 27.2 39.1 34.61.0% 35.1 :38.2 47.8 50.2S - Static^M - Medium^I - ImpactChapter C. Energy Transfer and Balance^ 282Table 6.14: Fracture Energy in Bond Failure (Deformed Bars)Type ofConcretePull-out Tests^(Nrn) Push-in Tests^(Nni)Normal High Normal High'Plain Concrete 40.2 42.1 44.0 45.1PolypropyleneFibre Concrete0.1% 40.6 42.4 44.3 45.20.5% 40.7 44.2 44.5 46.0SteelFibre Concrete0.5% 54.6 58.4 62.3 65.61.0% 71.5 75.3 80.2 86.1MIPlain Concrete 42.1 43.3 46.4 48.1PolypropyleneFibre Con crete0.1% 42.2 43.5 46.5 48.20.5% 42.3 44.1 46.8 49.3SteelFibre Concrete0.5% 58.2 63.5 65.9 70.21.0% 73.3 78.6 84.1 90.9MIIPlain Concrete 42.8 45.2 47.3 49.8PolypropyleneFibre Concrete0.1% 42.9 45.3 47.5 50.30.5% 4:3.2 45.5 47.6 50.5SteelFibre Concrete0.5% 60.3 64.2 68.2 77.41.0% 75.9 80.7 88.6 94.7IIPlain Concrete 45.2 47.4 49.4 5:3.2PolypropyleneFibre Concrete0.1% 45.4 47.7 49.5 54.20.5% 45.5 47.8 49.6 54.6SteelFibre Concrete0.5% 63.9 68.5 70.8 78.71.0% 79.5 85.4 93.5 100.3IIIPlain Con crete 47.3 50.1 51.9 56.7PolypropyleneFibre Concrete0.1% 47.9 .50.2 52.1 56.90.5% 48.0 50.5 52.2 58.2SteelFibre Concrete0.5% 65.8 71.4 7:3.2 80.21.0% 87.9 93.4 97.9 107.3IIIIPlain Concrete 50.2 52.3 5:3.8 58.7Polypropylene 0.1% 50.3 52.5 54.2 61.:3Fibre Concrete 0.5% 50.5 52.6 60.1 64.6Steel 0.5% 70.9 76.5 74.3 85.2Fibre Concrete 1.0% 94.6 100.5 103.4 110.3' - Static^M - Medium^I - ImpactChapter 7Analytical Study7.1 IntroductionThe mechanism of bond between steel rebars and concrete is a highly complex, non-linear process involving progressive cracking, crushing, nonlinearity and inhomogeneityof the concrete, especially under high rate (impact) loading. So far no studies have beencarried out which use fracture mechanics and finite element methods to establish thebond stress-slip relationship analytically. Previous studies regarding the application offinite element method to the bond problem simply introduced the local bond stress-sliprelationships which were obtained from tests. However, in spite of much useful infor-mation obtained from extensive experimental studies, there are still many unansweredquestions regarding the bond phenomenon. Many variables in bond behaviour are diffi-cult to measure experimentally, and it is hard to design an experimental program to takeinto account all relevant factors.There is not enough information available in the literature from which the bondstress-slip characteristics can be derived analytically. Theoretically, there is a uniquerelationship between bond stress and slip at the interface between a steel bar and concretefor which the geometric and mechanical properties are known. The problem can be solved28:3Chapter 7. Analytical Study^ 284by reasonably modelling the mechanical properties at the interface between the rebar andthe concrete, as well as the constitutive laws for both materials and appropriate crackingand crushing criteria.This chapter is devoted to a nonlinear fracture mechanics analysis of pull-out andpush-in bond tests under high rate loading conditions, and the finite element methodis used in the numerical calculation. The aim of the analysis is to obtain quantitativeinformation to help explain the physical phenomena occurring around the reinforcingbar.The chemical adhesion and frictional resistance between the rebar and the concreteare considered only during early loading in the elastic stage. After that only the ribbearing mechanism is taken into account. The fiber concrete composite and the highstrength concrete are appropriately modelled. In the finite element analysis quadraticsolid isoparametric elements with 20 nodes and 60 degree of freedom are employed for therebar and the concrete before cracking. After cracking, the concrete elements are replacedby quadratic singularity elements, which are quarter-point elements able to model curvedcrack fronts.The dynamic constitutive laws of both steel and concrete, the criteria for crack for-mation and propagation in concrete based on the energy release rate theorem for mixedmode fracture, and the criterion for concrete crushing are used in the finite elementprocess (see below). It is an iterative program with rapid convergence. Not only canthe bond stress and crack distribution be found through the analysis, but also a bondstress-slip relationship under high rate loading can be established analytically.The most important part of the finite element analysis is to develop appropriateChapter 7. Analytical Study^ 285types of elements suitable to the specific problem, and then to choose reasonably accurate`shape functions' for these elements and to establish the corresponding stiffness matrixes.After that, the assembly of the global stiffness matrix and the external load matrix, andthe strategy for equation solving, etc., are similar for all finite element processes.Another important part of the finite element analysis in this study is the setting up ofthe criteria for evaluating the mechanical behaviours of the elements, such as the contactconditions between the rebar and the concrete, and the cracking and crushing in theconcrete.7.2 Finite Element Models7.2.1 Steel ElementsThe elements representing the steel rebar are quadratic solid isoparametric elementswith 20 nodes and 60 d.o.f. (degrees of freedom), as shown in Fig 7.1. The formulation ofthe stiffness matrix for this type of element can be found in any book of advanced finiteelement methods (for example, reference [100]). The shape function is shown in Fig. 7.2,and may be expressed as:.hapte• 7. Analytical Study^ 286- (1 +^(1 + 7)1/i) (1 + (Ci)^+7Pii^(Ci — 2) (i = 1, 2, • • 8)=1—4 — 2 )( 1 WO ( 1 +— 71 2 ) (I + ((z) ( 1 +(1 - ( 2 ) (1 +^(1 + 7p)i)(i = 9, 10, 11, 12)(i = 13, 14, 15, 16)(i = 17, 18, 19, 20)(7.1)where^= +1.The stiffness matrix is[k] =^[B]T[E][B] R.111 d clq c1(^(7.2)where0 0aN,ayChapter 7. Analytical Study287^- aNi^aN20 ^0^o^0^0ax ax0^DN20ay0^0aN, aN200^0az^ az(7.3)aN20 aN200ay^ax^ay^ax^0aN, aN,00 a^N, aN,^aN20 aN20az^ay az^ay0 ^0aN20^aN20 ax az OX -tt^p^0^0^01—p 1 —fi 1 ft 1 — 0^0^01 — ,u,az1[13) =E(1 — it)[E] = ^( 1^2p)p^f2 1 — ft 1 — ft0^0^011 — 2tt2(1 — 0^01 — 2p2(1 — 11) 00^0^0^0^0 1 —2f12(1 — it)(7.4)Chapter 7. Analytical Study^ 28820 aAri^20 aN^20 aN,^x t E^ y, E — zi20 aNi^20 aNi y, 20 aNix t E^E^zii=1 an^07720 aN .^20 aNi^20 aNiE^x t E^y, E zt1=1^C^1=1 UC^1=1 ut,Figure 7.1: The Quadratic Solid Isoparametric Element with 20 Nodes and 60D.O.F.7.2.2 Concrete Elementsand[J]= (7.5)Before cracking, the elements in the concrete are same as those in the steel, i.e.quadratic solid isoparametric elements with 20 nodes and 60 d.o.f. After cracking, theChapter 7. Analytical Study^ 289quadratic singularity elements for solids are adopted. These are quarter-point elementsand can model a curved crack front ([100],[101]), as shown in Fig. 7.3. By placing themid-side node near the crack tip at the quarter point, the singularities, both lkg and1/r, in these elements are achieved. The proof of this involves a tedious mathematicalderivation ([101], [102]) and will not be given here. The formulation of the stiffnessmatrix is the same as for the regular quadratic solid isoparametric element.Chapter 7. Analytical Study^ 290==- 118192013CRACK 7 8 1 2FRONT1717^3h1417Figure 7.2: The Shape Function of the Quadratic Solid IsoparametricElementFigure 7.3: The Quadratic Singularity Isoparametric ElementChapter 7. Analytical Study^ 2917.2.3 Interface ElementsA special interface element, the 'bond-link element', has been adopted to model thebond slip phenomena in this analytical study. It connects two nodes but has no physicalthickness at all. As shown in Fig. 7.4, it can be thought of conceptually as consistingof two orthogonal springs, which simulate the mechanical properties in the connection,i.e. transmit the shear and normal forces between nodes i and j. This kind of interfaceelement has been commonly used in the finite element analysis of reinforced concretemembers. However, various bond stress-slip relationships which were determined ex-perimentally have been used to establish the stiffness matrix of the element (i.e. theconstitutive relationship for the element to relate the node forces to the node displace-ments). A new approach is proposed in this study for the establishment of the stiffnessmatrix of the 'bond-link element'. A bond stress-slip relationship at the interface be-tween the rebar and the concrete is one of the output results of the present finite elementanalysis, rather than an input parameter required before the analysis can proceed.•-, z' .i• e4/./Z .,,, ilr•••w•■••aw.4111■•,,/,,,,-'.,/t17,--/, ',/1-../Figure 7.4: The Interface Element (Bond-Link Element)iChapter 7. Analytical Study^ 292The vertical spring relates to the force transfer by dowel action between the rebar andthe concrete. It also accounts for the chemical adhesion. This means that the spring cantransfer a certain amount of tensile stress which is equal to the unit chemical adhesionbefore the relative displacement of two nodes, i and j, reaches a critical value. After thatno tensile force can be transmitted. In the case in which these two nodes are pushingagainst each other, especially if there is good confinement for the concrete (such as thespecimens used in this research program), the pushing force can be of a large magnitude,great value, which is proportional to the relative deformation between the rebar and theconcrete, and to the elastic modulus in tension of the concrete. A laboratory test canbe carried out to determine the related coefficient which governs this pushing force. Themechanical model of the linkage can be expressed as0^if (v i — vj) > 0.1 mznav =^Co^if 0 < (v i — vj ) < 0.1 mm^(7.6)- v; )^if (v i — vj ) < 0where= the interface normal stress^(MPa)a= the vertical displacements of nodes i and j, respectively,^(ntin)Co = the unit chemical adhesion force, which is determined from laboratorytests^(MPa)fa = the normal stress factor at the interface, which is determined fromlaboratory tests^(M Pa/min){Co + frgvIT Cryif (u i — uj) < 0.1 77i7nif (u i — uj ) > 0.1 inn/ah (7.7)Chapter 7. Analytical Study^ 293The horizontal spring takes into account the chemical adhesion and the frictional resis-tance at the interface between the steel and the concrete. When the relative displacementbetween the two nodes exceeds the critical value, the chemical adhesion is destroyed andonly the frictional effect remains. This mechanical model can be expressed aswhere= the interface shear stress (or the bond stress)^(MPa)= the frictional factor at the interface, which is determined from laboratorytests^u„ uj = the horizontal displacements of node i and j, respectively,^(Tim)Therefore the node forces of the 'bond-link element' can be expressed asU7= [k]F:v3and the stiffness matrix of the 'bond-link element' is different for different stages of thebond process, which is governed by the constitutive laws expressed in Eqs. 7.6 and 7.7.For example, in the case for which the chemical adhesion has been destroyed and there(7.8)hapter 7. Analytical Study^ '294is no separation between the steel and the concrete, the stiffness matrix is[k] = o fr fp 0 — fr fp^(7.9)0 fp 0 — fpIn the case in which both the chemical adhesion and the frictional resistance no longerexist, the stiffness of the interface element should become zero (Technically, each of theeight elements inside the matrix is given a very small value to ensure that the mathe-matical operations continue smoothly).7.3 Constitutive Laws of the Materials7.3.1 Constitutive Law of SteelSo far no :3-dimensional constitutive models for steel under high rates of strain havebeen established. The present specimens were designed so that the stress in the reharwas relatively low throughout the entire bond process. Therefore an elastic constitutivematrix, which is based on Hooke's law, was adopted in this analytical study.7.3.2 Constitutive Law of ConcreteThere have been many models proposed for the 3-dimensional constitutive law forconcrete. Most of them have been determined empirically, and all are controversialto sonic extent. However, none of these take into account the effects of strain rate.Soroushian e t al ([10:3D proposed a one-dimensional constitutive model for concrete,Chapter 7. Analytical Study^ 295which takes into consideration the strain rate,.f =K 1 K2 E. ^[ 2'^( 0.002K1 K3 )2]{^^e 0.002K i Kfor F < 0.002K1 K3K i K2 1„[1 — z(e — 0.002K 1 K3 )]^for 0.002K 1 K3 < C < 0.2111 .K2,f ic.(7.10)wheref = the concrete compressive stress= the concrete compressive strainPs .fy i,11 1 = 1 +p s = the volume ratio of the transverse reinforcement to the concrete core= 28-day compressive strength of concretefyh = the yield strength of transverse reinforcement0.53+0.29 fc^3^h'n145 P c —1000 +4_ 4 r s 0.002K1 K3h' = the width of concrete core measured to outside of the transverse reinforcement= the centre-to-centre spacing of transverse reinforcementK2 = 1.48 + 0.206 log 10 E + 0.0221 (log 10 E ) 2Iii = 1.08 + 0.112 log io + 0.0193 (log io ) 2Chapter 7. Analytical Study^ 296Note: for E < 10 -5 /sec, k 2 = K3 = 1.07.4 Criteria of Cracking, Crack Propagation and Crushing in ConcreteWhen the principal tensile stress in the concrete element exceeds the tensile strengthof the concrete, the element cracks. That is, whenac,1^fc,r^ (7.11)the crack will initiate, where= the principal tensile stress in the concrete element= the tensile strength of concreteFor mixed mode fractures, i.e. fractures with combinations of the opening mode,sliding mode and tearing mode, an energy release rate criterion will apply ([104], [105]).According to this criterion, a crack will propagate whenK/ ) 2^K// 2^K/// ) 2 = 1.,d1C (7.12)whereK 1 , K11 , Km = the stress intensity factors for fracture modes I, II, III, respec-tively.Chapter 7. Analytical Study^ 997K1 c , Ku c , Kin c = the critical stress intensity factors for fracture modes I, II,III, respectively.According to Hannant [106], the criterion for concrete crushing can be written asif^at — 50.2 + a3 > acyor a2 — 50-3 +^> o-cyor a3 — 5o 1^a2 > acyfor a1 + a2 + a3 > 5.5ac y (7.13)andif^a1 — 4a2^a3 > 1.75ac3or^a2 — 40-3 + a 3 > 1.750-cyor^a3 — 4a 1^a2 > 1.750-cyfor^5.5acy < a l^a2^0-3 < 12.17a cy (7.14)wherea2 . a3 = the principal stresses in the concrete elementacy = the crushing strength of the concrete cylinder7.5 The Algorithm for the Finite Element AnalysisThe finite element analysis involves an iterative process. First, a small increment ofload is applied to the specimen and all the elements are assumed to be elastic. Withfurther increases in the load, the state of the connection between the steel elements andChapter 7. Analytical Study^ 298the concrete elements changes and the stiffness matrix of the interface elements mustalso change. Cracks may initiate in the concrete specimens and the quadratic solidisoparametric elements must then be replaced by the quadratic singularity elements.Then the energy release rate criterion is applied to determine the possibility of crackpropagation. It is always necessary to check whether the outputs of each step coincidewith the assumed conditions in the previous step. The algorithm is given in Figs. 7.5and 7.6.Input Geometric & Material Property DataMIRApply Load IncrementAssume Loading RateCheck if the Concrete CrackCheck if the Strain RateCoincides with the assumed valueSolve for Node displacementsCalculate Strains & StressesAssume Perfect BondNo Crack DevelopsCalculate Stiffness Matrixfor Each ElementAssemble Global Stiffness Matrixand Load VectorNo, Assume Strain Rate Again —Check if the Perfect Bond ExistsCheck if the Concrete Crushed— Yes, Next Load IncrementOutput Bond Stress vs. Slip RelationModify Interface Element ParameterCheck if the Concrete CrushedNo, Reduce Load Increment YesNoYesYes No, Next Load IncrementChapter 7. Analytical Study^ 299Figure 7.5: Algorithm of Finite Element Analysis — IChapter 7. Analytical Study^ 300Use Fracture Mechanics ElementsModify Global Stiffness MatrixiCalculate Kr, Kil and K111at Crack TipsCalculate the Energy Release Ratefor Each Cracki^^Check if the Crack Is Stableor It Will DevelopDevelop Stable, Next Load Increment —^I^Check if the Applied Load Decline— No, Modify the Previous Crack Length YesI Stop IterationOutput Bond Stress vs. Slip Relation,Load vs. Displacement Relation.Fracture Energy etc.Assume New Crack Increment AiModify Finite Element Meshi Update the GlobalStiffness Matrix`Go to Next Load IncrementFigure 7.6: Algorithm of Finite Element Analysis — II(lapter 7. Analytical Study^ 3017.6 The Results of the Finite Element Analysis7.6.1 The Mechanical Parameters of the SpecimensThe finite element analysis was carried out for seven specimens, and compared withthe experimental results. They are as follows (note that No. 1 ti 6 are normal strengthconcrete and No. 7 is high strength concrete),1. Plain concrete under push-in impact loading (0.5 • 10_ 2 MPa/s, equivalent toImpact III);2. Polypropylene fibre reinforced concrete (0.5% by volume) under push-in impactloading (0.5 • 10 -2 MPa/s, equivalent to Impact III);3. Steel fibre reinforced concrete (0.5% by volume) under push-in impact loading(0.5 • 10 -2 MPa/s, equivalent to Impact III);4. Steel fibre reinforced concrete (1.0% by volume) under push-in impact loading(0.5 . 10 -2 MPa/s, equivalent to Impact III);5. Steel fibre reinforced concrete (1.0% by volume) under push-in impact loading(0.5 • 10 -3 MPa/s, equivalent to Impact II); and6. Steel fibre reinforced concrete (1.0% by volume) under pull-out impact loading(0.5 • 10 -2 MPa/s, equivalent to Impact III);7. Steel fibre reinforced high strength concrete (1.0% by volume) under push-in impactloading (0.5 • 10 -2 MPa/s, equivalent to Impact III);Chapter 7. Analytical Study^ :302The mechanical parameters of the interface elements, C o , f,. and L„ which were de-termined experimentally, are given in Table 7.1. The tests for C o and fr are conventionaltests in physics, and the test for f p is a simple mechanical tests (see Appendix H fordetails). As stated earlier, these parameters are defined asCo = the unit chemical adhesion force, which is determined from laboratorytests (MPa)= the normal stress factor at the interface, which is determined fromlaboratory tests (111 Pa / zurn)= the frictional factor at the interface, which is determined from laboratorytestsFor steel fibre reinforced concrete, the critical stress intensity factor for mode I (ten-sion) under impact loading, Kjc , was determined by :3-point loaded beam impact tests(Mindess ct al [107]); the values for the plain concrete and polypropylene fibre reinforcedconcrete were directly adapted from the results of their tests. So far no impact tests havebeen carried out to determine the dynamic critical stress intensity factors for mode II(sliding) and mode III (tearing) for concrete. It was assumed that the conclusion con-cerning the relationships of the critical stress intensity factors among mode I, mode IIand mode III by Ba2ant ct al [108, 109] can apply also to the impact case. That is thevalue of fracture energy obtained from mode III tests is about 3 times larger than themode I fracture energy and about 9 times smaller than the mode II fracture energy. Inlinear elastic fracture mechanics there exists a linear relationship between the fractureenergy and the stress intensity factor. Therefore, the critical stress intensity factors formode II and Mode and Kim., can be determined by multiplying K1, by 27 and('hapter 7. Analytical Study^ :303:3, respectively. Table 7.2 gives these values.The finite element meshes for the push-in and pull-out cases are shown in Figs. 7.7and 7.8, respectively.Table 7.1: Parameters of Mechanical Properties of Interface ElementsThe unit chemicaladhesion force Co(M Pa)The frictionalfactor L.The normal stressfactor fp(M Pa/min)NPlain concrete 4.36 0.72 1008Polypropylenefibre Concrete(0.5% by volume)4.02 0.72 1051Steel fibreconcrete(0.5% by volume)3.95 0.71 120:3Steel fibreconcrete(1.0% by volume):3.87 0.71 1417HSteel fibreconcrete(0.5% by volume)4.82 0.75 1109N — Normal Strength^ H — High StrengthChapter 7. Analytical Study^ 304Table 7.2: Dynamic Critical Stress Intensity Factors for ConcreteMode I (Tension)Kic(MP(“/TT21)Mode II (Sliding)Km c a (MPa0n)Mode III (Tearing)Km c b(M.PaN/TT)NPlain concrete 3.54 95.6 10.6Polypropylenefibre Concrete(0.5% by volume)3.75 101.3 11.3Steel fibreconcrete(0.5% by volume)4.65 125.6 14.0Steel fibreconcrete(1.0% by volume)5.23 141.2 15.7HSteel fibreconcrete(0.5% by volume)4.48 121.0 13.4N - Normal Strength^H - High Strengtha, b Calculated using Ba2ant et al ([108, 109]) relationships, i.e.= 27 Ki= 3 K.! cIINMIIN^Jewl■11111 I^1■1 1 1 1 1^I^1^IN Ulm SpiralSteel elementOnly half shownChapter 7. Analytical Study^ 305Interface elementConcrete element-rFigure 7.7: The Finite Element Mesh (Fracture Mechanics, Pull-out)Chapter 7. Analytical Study^ 306UT •Only half shownSteel elementSpiralInterface element^Concrete elementa 1^1 I^• _ A •Figure 7.8: The Finite Element Mesh (Fracture Mechanics, Push-in)aChapter 7. Analytical Study^ 3077.6.2 The Stress Distribution and Crack DevelopmentThe calculated results showed that at very low levels of the steel stress (about 30 -- 40MPa) the chemical adhesion between the rebar and the concrete was destroyed, and forthe case of pull-out loading the frictional resistance reduced rapidly with the separationbetween the rebar and the concrete when the steel stress increased. At that point the ribbearing became the main factor providing resistance in the bond process. These seem toagree well with the experimental results.It was found from the finite element analysis that at a relatively low level of appliedload, the distribution of the stress in the rebar was not much different from that obtainedby the experimental method. With further increases in the applied load, however, thedifferences in the distributions between the two method became larger and larger. Theresults of the experimental method were obtained directly from the strain gauge mea-surements and are considered to be more reliable. Although the grooving of the rebar(in order to place the strain gauges) had an effect on this comparison, this indicates thatthe nonlinear modelling of the concrete, which was introduced at a relatively high levelof the applied load during the finite element process, needs to be improved.It was also found that relatively high values of the principal tensile stresses developedin the concrete in the vicinity of the tips of the ribs, especially for the pull-out case,which indicated that the secondary cracks would form first. For the plain concrete andthe polypropylene fibre concrete, some crushing of the concrete also took place at thetips of the ribs. This resulted in a great decrease in the bond strength, or, from the viewpoint of energy, in the capacity of energy transfer. On the other hand there was seldomcrushing in the concrete for the steel fibre concrete. This may help to explain why theChapter 7. Analytical Study^ 308specimens made of plain concrete and polypropylene fibre concrete consumed much lessfracture energy during the entire bond-slip process.The calculated results also indicated that there were more cracking elements for thesteel fibre concrete than for the plain and polypropylene fibre concrete. Because of this,the bond slips in the former case were always found to be larger than in the latter casesin the calculations, which, in turn, made the fracture energy for the steel fibre concretemuch larger than for the other types of concrete. This is also in agreement with theexperimental results.As expected, the bond strength and the fracture energy for push-in loading were foundto be greater than for pull-out loading. This indicates that by adopting the :3-dimensionalelastic matrix in the constitutional law, the Poisson effect was properly considered, andthat the modelling of the frictional resistance at the contact surface between the rebarand the concrete by the 'bond-link element' was reasonable.7.6.3 The Bond Stress-Slip RelationshipThe bond stress-slip relationships determined by the finite element method are given inFigs. 7.9 to 7.14. Similar to the method adopted in Chapter 6, these curves also refer tothe average data over the time period and the embedment length. In these figures thecurves from experiments are also given for comparison. Fig. 7.15 represents one of theapplied load vs. the displacement of the rebar, which is also determined based on theresults of the finite element method. These results can be summarized as:Chapter 7. Analytical Study^ 3091. The shapes of the curves obtained by the finite element method are different fromthose from the experimental measurements. There is only a very small linear por-tion from the beginning of the loading in those curves obtained by the finite elementmethod. This may be because for the finite element models the chemical adhesionis destroyed at a very low level of loading, and the contribution of the frictionalresistance to the bond strength depends on the calculated stress state at the inter-face to a great extent. This difference is most obvious for the pull-out case, as canbe seen in Fig. 7.14.9. Both the peak and average bond stress are larger for the analytical than for theexperimental results. From the viewpoint of mechanics, the models of the finiteelements make the specimen more 'rigid', i.e. its stiffness becomes larger eventhough the modelling of the chemical adhesion and the frictional force may lessenthe stiffness of the interface between the rebar and the concrete to some extent. Theincrease in the bond resistance and the relatively smaller local slip correspondingto the same bond stress may also attribute to this.3. Although there are great differences in the curves between the finite element methodand the experimental method, the total displacements of the rebars from bothmethod are relatively close, as shown in Fig. 7.15. This suggests that the modelsadopted in the finite element analysis were reasonable.4. By comparing the differences between the curves obtained by the two methods inFig. 7.10 and Fig. 7.11 it can be seen that the polypropylene fibre addition didnot have much effect on the results of the two difference approaches, in terms ofthe bond stress-slip relationship.Chapter 7. Analytical Study^ 3105. As expected, the influence of steel fibre additions on the bond stress-slip relationshipin the finite element analysis is significant, which can be seen by the comparisonof two corresponding curves in Fig. 7.10 and Fig. 7.13, respectively. Both of theseresults are from the finite element method, but one is for a plain concrete specimenand the other for a steel fibre reinforced concrete specimen.6. The result for high strength concrete (with 1.0% by volume steel fibres) is illustratedin Fig. 7.14. The difference between this result and that by experimental method isquite large. This may indicate that with the combined effects of concrete strength,Young's modulus, and a significant content of steel fibres, the modelling of thefinite element method could introduce a considerable uncertainty in the analysis.Further research work needs to be carried out for more realistic modelling.7. The effect of the loading rate on the bond stress-slip relationship can be reflectedin this analytical study, as can be found by comparison of Fig. 7.12 and Fig. 7.13,which represent the results of same specimen subjected to loading at two differentrates..4.••■••■■•••••\"\"\"SS 4020I02 1Chapter 7. Analytical Study^ 3111^2^9^4^5Local Slip (0.01 mm)Finite Element Method^Experiment0111•1■ ••■•■ •••••■••• 01••■■ .■■••■•Figure 7.9: The Bond Stress-slip Relationship by the Finite Element Method(Plain Concrete, Push-in, Impact III - 0.5 • 10 -2 Mpa/s)so512 4030r4hd 20100 0^1^2^3^4Local Slip (0.01 mm)Finite Element Method^ExperimentFigure 7.10: The Bond Stress-slip Relationship by the Finite Element Method(Polypropylene Concrete, Push-in, Impact III - 0.5 • 10 -2 Mpa/s)Chapter 7. Analytical Study^ 312,soX40040 0^ 1^ 2^ 3Local Slip (0.01 mm)Finite Element Method^ExperimentFigure 7.11: The Bond Stress-slip Relationship by the Finite Element Method(Steel Fibre Concrete, Push-in, Impact II - 0.5 • 10 -3 Mpa/s)Local Slip (0.01 mm)Finite Element Method^Experiment4Figure 7.12: The Bond Stress-slip Relationship by the Finite Element Method(Steel Fibre Concrete, Push-in, Impact III - 0.5 • 10 -2 Mpa/s)2^3^4Local Slip (0.01 mm)Finite Element Method^Experiment4■■11 ••■■•• ■■■■■ ■■■■•■ ■■•Chapter 7. Analytical Study^ 3130 4061 20\"100 12^ 4Local Slip (0.01 mm)Finite Element Method^ExperimentFigure 7.13: The Bond Stress-slip Relationship by the Finite Element Method(Steel Fibre High Strength Concrete, Push-in, Impact III — 0.5.10 -2 Mpa/s)Figure 7.14: The Bond Stress-slip Relationship by the Finite Element Method(Steel Fibre Concrete, Pull-out, Impact III — 0.5 • 10_ 2 Mpa/s)Chapter 7. Analytical Study^ 314End Displacement (mm)Finite Element Method^Experiment■■••■■ ■■•■■■■ •••■• ••••■■ •■=1,M,Figure 7.15: The Applied Load vs. Displacement Curve the Finite ElementMethod (Steel Fibre Concrete, Push-in, Impact III — 0.5 • 10 -2 Mpa/s)Chapter 8Conclusions and Recommendations8.1 ConclusionsThe purpose of this research work has been to provide a more fundamental under-standing of the bond behaviour of rebars in concrete subjected to high rate loading,to develop appropriate techniques to investigate the bond phenomenon using both ex-perimental and analytical approaches, and to study the feasibility of using steel fibres,high strength concrete and other measures for better bond performance under impactloading. Based on the experimental investigation and the analytical study, the followingimportant conclusions may be drawn:1. The entire testing program as designed was suitable for the experimental investiga-tion of the bond behaviour under impact loading. The testing machines was able toprovide a wide range of high rate loading with a considerable amount of energy; thetransducers and instrumentation used were able to measure and record the basicdata, such as the applied load, the accelerations and the strains, at a sufficientlyhigh rate with an acceptable level of error; the mechanical and mathematical mod-els for processing the test data to obtain the most important parameters, such as:315Chapter 8. Conclusions and Recommendations^ 316the external forces, displacements, stresses, slips and the fracture energy, are appro-priate and accurate: the specimens used are satisfactory and most of the importantvariables, which may affect the bond behaviour under high rate loading, have beenconsidered.2. For smooth bars, the bond resistance is due to the chemical adhesion and the fric-tional force at the interface between the rebar and the concrete. There exists alinear bond stress-slip relationship under both static and high rate loading. Dif-ferent compressive strengths, types of fibres, fibre contents, and loading rates werefound to have no great influence on this relationship or the stresses in both thesteel bar and the concrete.3. For deformed rebars, the chemical adhesion and the frictional force at the interfacebetween the rebar and the concrete are less important for the bond resistance. Theshear mechanism due to the ribs bearing on the concrete plays a major role in thebond-slip process.4. For deformed rebars, the bond stress-slip relationship under a dynamic (high rate)loading changes with time and is different at different points along the reinforcingbar. An average bond stress-slip relationship over the time period and the em-bedded length is necessary and useful for evaluation and comparison of differenttests.5. Higher loading rate significantly increases the bond resistance capacity. Under highrate loading, the stress distribution along the rebar is not uniform, and is not evenlinear; there is more stress concentration along the rebar than under static loading.Higher stresses both in the rebar and in the concrete, greater slips, higher bondstresses, and larger fracture energy during the bond failure were developed withChapter 8. Conclusions and Recommendations^ :317an increase in the loading rate. These effects are especially noticeable when steelfibres are added to the concrete mixture.6. The steel fibre additions greatly increased the bond strength. Steel fibres causereduced stress concentrations along the rebar, and higher stresses in the concrete.The crack resistance is improved, thus the stiffness of the concrete surroundingthe rebar increases. More fracture energy is needed for the bond failure. The bondstress-slip relationship of steel fibre concrete is quite different from that of the plainconcrete and polypropylene fibre concrete, in terms of the peak value, the averagevalue and the slope of the curve. These effects are more significant when subjectedto high rate loading. A sufficient steel fibre content could help us to achieve themaximum improvement in the bond behaviour.7. The high strength concrete exhibits higher bond strength and absorbs more fractureenergy in the bond process, especially when steel fibres are added.8. Under the same conditions, there is always higher bond resistance and more stressconcentrations along the rebar for push-in loading than for pull-out loading. Thestress distribution both in the rebar and the concrete is quite different for these twoloading cases, and thus the patterns of cracking and bond failure are also different.A bond stress-slip relationship for the pull-out loading cannot simply be appliedto the push-in case with only a change of the symbol of force. Since more fractureenergy is needed for push-in loading than for pull-out loading, a reinforce concretemember can be expected to be tougher when the rebars are subjected to push-inforces.9. The addition of polypropylene fibres to the concrete has no significant effect onthe bond behaviour, in terms of the bond strength, the stress distributions bothChapter 8. Conclusions and Recommendations^ :318in the rebar and the concrete, the crack development, the slip, the bond stress-sliprelationship, and the fracture energy during the bond failure.10. For epoxy-coated rebar the bond resistance and the fracture energy decrease tosome extent, and wider cracks are developed. The influence of epoxy-coated rebarson the bond strength for push-in loading is much more significant than for pull-out loading. However, high rate loading, high concrete strength, and the steelfibre additions at a sufficient content will effectively reduce these negative effects ofepoxy coating on the bond behaviour. Polypropylene fibre has little effect on thisbehaviour.11. The study of the energy transfer, energy dissipation and energy balance during thebond-slip process can help us to achieve a better physical understanding of the bondmechanism. The concept of fracture energy could be an effective and convenientway of evaluating the importance of certain variables, such as fibres in the concretemixture, the concrete compressive strength, etc. to the bond improvement.12. An analytical method based on fracture mechanics and the finite element analysismethod is an effective and powerful approach for the study of bond behaviourunder impact loading. By reasonably modelling the mechanical properties at theinterface between the rebar and the concrete, the fracture characteristics in theconcrete, the constitutive laws of both materials, and the cracking and crushingcriteria, the stresses in the rebar and the concrete and the crack development canbe predicted, and in addition the bond stress-slip relationship can be establishedanalytically. It is relatively easy for an analytical method to take into account all ofthe important variables in the bond process, though this is difficult experimentally.Chapter 8. Conclusions and Recommendations^ 3198.2 Recommendations for Further StudyThe experimental program and the analytical study carried out in this investigation haveprovided greater insight into the bond behaviour of the rebar under high rate loading.However, there are some areas connected to this study which need to be explored further.Based on the results of this study, the following suggestions are made for further researchon the bond behaviour of deformed bars under impact loading:I. A more extensive experimental investigation should be carried out for the bondbehaviour under high rate loading, in which the following variables need to beconsidered:• size of the specimen• size and geometry of the deformed bar, such as the rib angle, rib height, andrib spacing• embedment length of the rebar• confining pressure• shape, size and content of steel fibre• concrete compressive strength2. Internal cracking in the concrete needs further study, similar to the method de-veloped by Goto [30], to investigate the pattern and the extent of the cracking.In order to study crack propagation in plain or fibre reinforced concretes, certaintechniques can be used to detect the fracture process zone (Mindess [110]); Theinfluence of the bond resistance on the crack propagation and the width of thecrack in the concrete should also be studied.Chapter S. Conclusi ons and Recommendations^ 3203. More precise finite elements, capable of handling cracking. crack opening andclosing in a composite of steel fibres and concrete, need to be developed in theanalytical approach.4. The 3-dimensional constitutive laws of both the steel and the concrete under dy-namic loading should be determined and applied in the finite element analysis.5. More reasonable crushing and crack propagation criteria in the concrete underdynamic loading should be established.Appendix AMaximum Length of Rebar at the Struck EndFrom the theory of buckling and stability [111], the critical stress in a column undercompression is governed by the equationsE(Al Pa)^ (A.1)acr = (^7 71,)Ir =^A^(7n 777 )^ (A.2)7r d4I = 64^(nim4) (A.3)r d2A = ^4(7777712) (A.4)where(7,7. = the critical stress in the column7' = the minimum rotational radiusE = Young's modulus of the material321Appendix A. Maximum Length of Rebar at the Struck End^322K = the effective length coefficientL = the length of the column^(mm)I = the inertial moment of the section^(m7 m 4)A = the cross-sectional area^(7117712)d = the diameter of the rebar^(mm)For the specimens used in this experimental work, one end of the column (rebar)is considered to be free while the other end is fixed. In this case the effective lengthcoefficient K = 2.0. The other parameters for smooth and deformed bars are listed inthe following tableTable A.1: Geometrical and Mechanical Parameters of the RebarParameter Straight bar Deformed barDiameter^d^(mm) 12.7 11.3Area^A^(mm 2 ) 126.7 100.0Inertial Moment^/^(mm 4 ) 1276.9 800.3Minimum Rotational Radius^r^(mm) 3.17 2.83Young's modulus^E,^(CPa) 207.0 212.0Critical Stress^u ^(M Pa) 286.5 423.9For this case the critical stress a„ can be taken as the yield stresses of the smoothand deformed bars. From Eq. A.1, Eq. A.2 and Eq. A.3 the maximum length of therebar at the struck end can be calculated from the following1'L =KEacr(A.5)The results areAppendix A. Maximum Length of Rebar at the Struck End^ 323Lamooth = 133.8 777772L de. f armed = 99.4 717777After consideration of the alignment of the specimen and the striking head and thecontact condition during impact, a safety factor of 2.0 was applied to the lengths. Themaximum lengths of the struck end should then beLs,„0071, = 66.9 717717L de f ormed = 49.7 717777Appendix BThe Effect of Stress Wave Propagation on Outputs of TransducersFrom the theory of elasticity, the stress waves which propagate to the transducers usedin the impact tests in this experimental investigation can be considered as simple planelongitudinal waves [112]. The governing equation for the waves isn2(I 2 02u^ =C ^t2^ax2(B.1)wheret = the time variableu = the variable of the axial displacementThe coefficient c turns out to be the velocity of the stress wave and is given byc = E^(inis)^ (B.2)whereE = Young's modulus^(M Pa)324Appendix B. The Effect of Stress Wave Propagation on Outputs of Transducers^:325p = the density of the material^(kg/inin2 • in)For steel, E = 210,000 MPa and p= 7800 ksint3 = 0.0078 kg/min 2 • in, so the wavevelocity c isc =2100000.0078 = 5190 tn/sThe time, T, which takes for the stress waves to reach the sensors isT_ L^(s )^(B.3)whereL = the distance between the striking point and the location of the sensors(m )The sensors could be either strain gauges for the load cell and the strain measurementunit or piezoelectric crystals for the accelerometers.For the bolt load cell, L = 0.08 m , so the travailing time of the stress waves is0.08Toad = ^ = 0.000015 .9 = 15 /L85190For the strain measurement, L = 0.30 in (pull-out) and 0.05 in (push-in), so thetravailing time of the stress waves isAppendix B. The Effect of Stress Wave Propagation on Outputs of Transducers^:3 2 60.30TPull =-7 5190 = 0.000058 8 = 58 /is0.000010 s = 10 psFor the accelerometer, L = 0.19 in, so the travelling time of the stress waves is0.19Lea ^ = 0.000037 s = 37 its5190The preliminary tests showed that the duration of an impact test ranged from 5 711.S to30 in.s and the sampling rate for data collection was 200 /is. It is obvious that the effectof stress waves on the time delay of the signal outputs from the transducers is negligible.andTpush0.05 5190bout(R 1 + 120.0 +^)^(R2 + 120.0 + K2R2(2)(V)^(C.1)E^+ R1) E • 120.0Appendix CDesign of Electric Circuit for Strain MeasurementThe electricity the output voltage (signal) is (see Fig. 3.4 in Section :3.3.1.5)whereVout = the output signal^(V)E = the excitation voltage^(V)K1 K2 = the gauge factors of a pair of strain gauges (gauge 1 and gauge 2)R 1 , B2 = the electric resistances of a pair of strain gauges^(C/)( 1 . ( 2 = the strains at two opposite sides of the rebarThe two dummy resistances were 120.0 ft precision resistances. After operation andrearrangement, Eq. C.1 becomes:327Appendix C. Design of Electric Circuit for Strain Measurement^ 328t —Ii1 Ri R2E1 + K2 RI R2E2 + Ri R2 — 120.0 2 + KI K2R1R2 6 1€2 (V)^(('.2)(R 1 + 120.0 + KiRiei)(R2 + 120.0 + K2R2(2)In this test the strains would not exceed 2000 x 10 -6 , i.e. the maximum values for t iand E2 were less than 0.002, while the gauge factors, K 1 and A2, were about 2.050 andthe electric resistances, R 1 and R2, were about 120.0 Q. This means that in Eq. C.2K1 R 1 ( 1 and K2R2E2 are higher order terms compared to (R 1 + 120.0) and (R2 + 120.0),so they are negligible. The same thing happens to the term K i K2 R 1 R2 e 1 t 2 . Thus Eq.('.2 becomesRl R2 1 1 + K2 R1 R2 E2 + Rl R2 — 120.0 2OutThe manufacture of the strain gauges guarantees an accuracy of ±0.3% for the electricresistance and ±0.5% for the gauge factor. This means that for all the strain gauges R 1and B2 are 120.0± 0.36 f2, K 1 and K2 are 2.050± 0.01025. From the theory of error [113]if we take all electric resistances as 120.0 ft and all gauge factors as 2.050 the possibleerror for the output signal will be01/00 di/out avout aVout 6Vont = 6R1 + 6R2 + 6K1+ 6K2 (C.4)O i O 2 dlkl OK2The maximum absolute error for the output signal is(RA^120.0)(R2 + 120.0) (V)^(('.3) 1 W,,it = i)t ro„t 6 R i + Vo„ t 6R2 avout 6K 1 + 1 00 6K2^(('.5)DR 1 DR2 O K I dK22.050E (€ 1 + (2)govt = 2(VandAppendix C. Design of Electric Circuit for Strain Measurement^329where the increments 6R 1 , 6R 2 , 6K1 and bK2 are positive numbers.From Eqs. C.3 and C.4 it was clear that the evaluation of 1/0 ,a and (5' V0ut involved ex-tremely tedious mathematical operations. However, by means of numerical differentiationit was possible to evaluate these values at the specified point where= R2 = 120.0 5.2= K2 = 2.050with the increments of variables6R i = 6R2 = 0.36 fl6Ki = 6K2 = 2.050The results were161/0 .0 1 = 0.0015 2.050E (El + (2) 2The relative error was16vo. t I = 0.15%VontAppendix C. Design of Electric Circuit for Strain Measurement^:330Since the average (6 1 + t 2 )/2 represents the actual strain ( at the section, any bendingmoment in the longitudinal loading plane where the strain gauges were mounted wouldcancel out automatically.It can be concluded that for the electric circuit of an 'opposite arm' Wheatstonebridge there exists a linear relationship between the actual strain and the output signaland that this can be represented by a simple equationIi E(fi + (2)Vopt = 2(V)Or, in a. more practical form,=ER^(1 0-6)^(C.9)One calibration based on Eq. C.8 applies to all the strain gauge measurements.Appendix DThe Effect of Inertial ForceThe inertial force of the rebar, F.. can be determined by the following equation= I paA d.5^(N)^ (D.1)where= the inertial force of the rebar^(N)1 = the location of the calculated section^(mm)p = the density of the rebar^(Ns 2 /7727n 4 )a = the acceleration of the rebar^(77/77//s 2 )= the cross-sectional area of the rebar^( 7117712)The experimental data showed that the acceleration a can be assumed to be the samealong the whole bar. Thus Eq. D.1 becomes331Appendix D. The Effect of Inertial Force^ 332= paAls^(N)^ (D.2)whereIs = the length of the rebar^(mm)The deformed rebar used had a cross-sectional areaa l engthand a density of steelA3 = 100.0 77/ 771 2 ,is = 190.5 mmp = 7.8 x 10 -6 kg/mm 3. The maximum acceleration measured was a s = 29.3 g (g is the gravitational accelera-tion). Thus the inertial force of the rebar Ft is= 7.8 x 10 -6 x 29.3g x 100.0 x 190.5 = 42.7 NThis inertial force is negligible when compared to the contact load Ft , the peak value ofwhich could be as high as 50.0 -- 80.0 kN. The same conclusion applies to the smoothbar.Appendix ETests for Determining Characteristics of Signal NoiseE.1 Noise in Acceleration and Strain MeasurementE.1.1 Test DesignA longitudinal impact test of two bars was carried out to determine the characteristicsof signal noise in the acceleration and the strain measurement. As shown in Fig. E.1, a.rod (Bar 1) made of plastic with a. length 11 = 200.0 mm, fell from a height, h = 150.0717.111, and struck another rod (Bar 2) made of the same material with a length 1 2 = 400.0711111 longitudinally. Bar 2 was instrumented with an accelerometer and a pair of straingauge to record the acceleration waves at its bottom and the stress waves at the topduring the impact.Both the compression waves and velocities of particles induced by the impact wereplane longitudinal waves and would travel at the wave velocity, c, given by Eq. B.2 inAppendix B,C^E^(m/s)^ (E.1):33 :3400 0 Bar 2i200 0150.0Bar 1Strain GaugeAccelerometerAppendix E. Tests for Determining Characteristics of Signal Noise^334V=0V/2V/2V/2t=0^t= 400.0/cAll in mmFigure E.1: Longitudinal Impact of BarsAppendix E. Tests for Determining Characteristics of Signal Noise^335E.1.2 Acceleration WavesE.1.2.1 Analytical SolutionAt the instant of impact two identical compression waves started to travel along bothbars. The corresponding velocities of the particles relative to the unstressed portionsof the moving bars were equal and were directed in each bar away from the surface ofcontact [112, 114, 115]. Let v be the velocity of the falling bar (Bar 1) at the momentof impact: the magnitude of the velocities of the particles must be equal to v/2 in orderto have the absolute velocities of the particles of the two bars at the surface of contactequal. After an interval of time equal toT= 12^(s)^(E.2)the absolute velocity of the particle at the bottom of Bar 2 would reach v/2. Physi-cally, the absolute velocity history would increase gradually, as shown in Fig. E.2. Thusthe acceleration at the bottom during the period [0, A(t), is a constant (see Fig. E.3),i.e.A(t) = dvdtA(t) =(.0TVC2l 2[0, ( 771/8 2 ) (E.3)Appendix E. Tests for Determining Characteristics of Signal Noise^3360.8osg 0.4020 ^0 40^80^120^103^2C0Time (micro second);4.Figure E.2: Absolute Velocity History at the Bottom (Analytic)40^03^120^100^200Time (micro second)Figure E.3: Acceleration History at the Bottom (Analytic)Applying FFT (Fast Fourier Transform) to the acceleration function A(t) in Eq. E.3yieldsAppendix E. Tests for Determining characteristics of Signal Noise^337▪ 00C oa (w) =^l^A (t) e - iw t dt,+ 00 yeJ ^2 /2 dtT vC--^dtfo 212ye 1 ^—iwTC 2 /2 )ve^1 [ s .7--) — in wT + (cos coT — 1) i^(in/.s2 • Hz)^(E.4)212Eq. E.4 is the equation of the amplitude spectrum of the analytic solution for the ac-celeration. In order to get the spectrum curve it is necessary to determine the magnitudeof the complex function—1 ] 1wI ca (-') I = 212 sin coT +(cos LoT — 1)ye21.2 )(ye12)1wsin 2 coT + (cos coT — 1) 2sin wT(in/s 2 • Hz)^(E.5)Ca)The plastic had a density, p = 1500 ky/in 3 = 0.0015 kg /iiiin 2 • in, and Young'smodulus. E = 7000 111 Pa, so the wave velocity c isAppendix E. Tests for Determining Characteristics of Signal Noise^:3:387000= 2160 misand the velocity of the particle v is2g h =^x 9.81 x 0.91 x 0.15 = 1.64 misthe interval of time T is (Eq. E.2)/2^0.40T = — = ^ = 1.85 • 10 -4 sc^2160Substituting these value in Eq. E.5 yieldsCa (w) I = 8856 sin 1.85 • 10 -4 cv(7n/s2 • Hz)^(E.6)wBased on Eq. E.6, the amplitude spectrum of the acceleration can then be drawn, asshown in Fig. E.5.E.1.2.2 Experimental ApproachAn acceleration history curve based on the acceleration data recorded by the dataacquisition system is shown in Fig. E.4. It may be noticed that the curve obtained bythe experimental method is a bit different from that by the analytic method, with thepeak value about 10% higher than the analytic peak value. Applying FFT to the curve,one get the amplitude spectrum shown in Fig. E.6.Ec =0.0015- t - • t-.L...4-^-1-1•..L.10^20^30 40^50^60Frequecy (kHz)Appendix E. Tests for Determining Characteristics of Signal Noise^339o ^0 40^SO^120^103^203Time (micro second)-4-Figure E.4: Acceleration History at Bottom (Experimental)Figure E.5: The Amplitude Spectrum of Acceleration (Analytic)Appendix E. Tests for Determining . Characteristics of Signal Noise^340E.1.2.3 Characteristics of Noise in the Acceleration MeasurementBy the comparing the two amplitude spectra (see Figs. E.5 and E.6) it was found thatthe significant frequencies of the noise in the acceleration measurement were higher than2.4 kHz. Therefore a low pass filter, with a 2.4 kHz cut limit, was suitable for filteringthe acceleration signal data. Fig. E.7 shows the filtered signal of the acceleration, whichis considered to be a \"true\" signal and is close to the analytic curve.E.1.3 Stress WavesThe procedure used to determine the characteristics of the noise for the strain mea-surement was similar to that for the acceleration measurement, described in the abovesection. The analytic function of the stress at the top of the bar in the time-domain is(1)^E^E^2c^[0, 2T]^(10-6)^(E.7)and the amplitude spectrum of the strain is sin 2wTc((w) l = ' (10 -6 /Hz)^(E.8)wThe amplitude spectra of the strain from both analytic and experimental methodsare given in Figs. E.8 and E.11. Similar to the analysis of the characteristics of the noisein the acceleration measurement, a low pass filter with 1.5 kHz was found suitable forthe strain measurement. Figs. E.8 and E.10 show the strain history obtained by ther^—t—12ih o!10^20^30^40Frequecy (kHz)E 411s450 sor-40^80^120Time (micro second)160 lxAppendix E. Tests for Determining Characteristics of Signal Noise^341Figure E.6: The Amplitude Spectrum of Acceleration (Experimental)Figure E.7: Acceleration History at the Bottom (Filtered)Appendix E. Tests for Determining Characteristics of Signal Noise^342403I•1 243•1 16010t0 0^80^1E0^240^320^403Time (micro second)Figure E.8: Strain History at the Top (Analytic)analytic and experimental methods, respectively. The filtered signal (\"true\" signal) isgiven in Fig. E.12.E.2 Noise in Load MeasurementLet a relatively rigid mass made of cast iron fall under gravity from a height, h = 200.0mm, and strike the bolt load cell (described in Section 3.3.1.3), as shown in Fig. E.13.The mass of the block was M = 2.0 kg. The velocity of the particles at the tup of thebolt at the instant of impact, vo , isvo = I2g h^(m/s)^(E.9)4-Appendix E. Tests for Determining Characteristics of Signal Noise^3437;1^i!1^1 1i I-/ ..' .1:77.\\\\. .i.i i i4.1 6004C02C0•Cla! 0 0^5^10^15^20^25^30Frequecy (kHz)Figure E.9: The Amplitude Spectrum of the Strain (Analytic)4C03202°I 243leoBO93^163^243^4C0Time (micro second)Figure E.10: Strain History at the Top (Experimental)j10^16^20^25^soFrequecy (kHz)Appendix E. Tests for Determining Characteristics of Signal Noise^344Figure E.11: The Amplitude Spectrum of The Strain (Experimental)3202240I 1 03C73BO..-..-.._... • ._—..-80^180^240^320^4C0Time (micro second)Figure E.12: Strain History at the Top (Filtered)Appendix E. Tests for Determining Characteristics of Signal Noise^345and the initial compressive stress cc, is given by [112]cro = vo E P^(Mpa)^ (E.10)All in rnrnM200.0Figure E.13: Longitudinal Impact of Bar and BlockOwing to the resistance of the block, the velocity of the bolt load cell, and hence thepressure on the tup of the bolt gradually decreased. A compressive wave with a decreasingstress started to travel along the length of the bolt. The change in compression with timecan easily be found from the equation of motion of the block,Appendix E. Tests for Determining Characteristics of Signal Noise^:346whereMkt + Ao- = 0 (E.11)M = the mass of the iron block^(kg)v = the variable velocity of the mass^(m/s)= the cross-sectional area of the bolt (7n77/2)a = the variable stress at the tup of the bolt^(MPa)With the initial condition, Eq. E.10, the solution for the ordinary differential equationEq. E.11 isa(t) = V2g hEp c - A ATP- ^(MPa)^(E.12)The force exerted on the bolt isF(t) = Aa(t) = A/2g hEp e - AVNiEP t^(N)^(E.1:3)Let T be the time interval between the instant of impact and the instant at whichthe compressive wave with a front pressure a 0 returns to the tup of the bolt that is incontact with the moving block, T is given by2 1 boltT =Appendix E. Tests for Determining Characteristics of Signal Noise^347wherebolt = the length of the bolt load cell^(inn)c = 5190 nt/s, the wave velocity of steel (see Eq. B.2 in Appendix B)The above solution Eq. E.13 can be used as long as 0 < t < T, as shown in Fig. E.14.From Eq. E.13, the spectrum equation of the load isf +DOCF (U)^L 00 F(t) c- iwt di CCJ-00 A 2g hEp^A MEP i e zw t dt= IT ^^A 2g hE pc A MVT7 C -iWt dt1 ^[ (AM +,w)7,— 11 (MPa/Hz) (E.14)— AV2g hEp fAvEpMThe magnitude of this complex function is (ANTET w)T— 1ICT--(,))1 = A\\/2g hEp (MPa/Hz)^(E.15)A VEp wMAppendix E. Tests for Determining Characteristics of Signal Noise^348Given all of the known parameters,A = 1 718 2 = 254.5 mrn 24h = 0.20 7-nE = 210000 M Pap = 7800 kg/7n3and2 x 0.12T =^ = 46.2 its5190it was possible to evaluate ICa (w)1 for the variable frequency w; the load history and itsspectrum of frequencies are shown in Fig. E.14 and Fig. E.15, respectively.On the other hand, the load history was also recorded by the data acquisition system,as shown in Fig. E.16 and the amplitude spectrum based on the recorded data is givenin Fig. EAT.Similar to the procedure of analyzing the characteristics of the noise in the accelerationmeasurement which is described in the above section, a low pass filter with 2.0 kHz wasfound suitable for the strain measurement. Figs. E.18 shows the filtered signal of theload.i!!— .1 —10^20^30^40^50^soFrequecy (kHz)Z °Ao4.1OSis) 0.4S.•C 02a0Appendix E. Tests for Determining Characteristics of Signal Noise^34925 '^ 0••■■15! 0'^0 10^20^30^40^50Time (micro second)soFigure E.14: Load History (Analytic)Figure E.15: The Amplitude Spectrum of the Load (Analytic)10^20^ao^40Time (micro second)50 so1.5 1050 '^0i!2520151 0 50 so1•■••■.Z °A^ OS•=14.0V 0.4V°C 02O00 20^30^40Frequecy (kHz)Appendix E. Tests for Determining Characteristics of Signal Noise^350Figure E.16: Load History (Experimental)Figure E.17: The Amplitude Spectrum of The Load (Experimental)50 50-ri20^30^40Time (micro second)0 ^0 102520151.2\"01141 105••■■Figure E.18: Load History (Filtered)Appendix E. Tests for Determining Characteristics of Signal Noise^351Appendix FThe Solution of Three-dimensional, Axisymmetric ProblemsIt was noted that the specimen tested was axially symmetric because its geometry,loading and material properties were independent of the circumferential coordinate O.There were only u (axial) and w (radial) displacement components inside the body, sothe problem was physically three dimensional but mathematically two dimensional. Evenso, it is hard to find an analytic solution. The finite element method, therefore, was usedto analyze the stresses in the rebar and the concrete [116, 117, 118, 100].The element employed was a ring of constant rectangular cross section, as shown inFig. F.1. Centers of all nodal circles lie on the Z-axis, which is the axis of the rebar.The body and its elements were solids of revolution about the Z-axis. This is a linearisoparametric element and the displacement field {f} has only z and r components,{f}^{u w} = [N]{d}^ (F.1)where [N] is a function of the coordinates,NI 0 N2 0 N3 0 N4 0[N] =^ ( F . 2 )0 N1 0 N2 0 N3 0 N4352Appendix F.^The Solution of Three-dimensional, Axisyinmetric Problems^353and {d} contains the 'it's and w's of the nodal circles,{CI} =^Ul^WI^U2^W2^U3^W3^U4^W4 }^ (F.3)The individual shape functions areN1 =^( 1 —^( 1 — 71 )^ N2 =^+ 0 ( 1^7i) (F.4)AT3^14 (1 +)(1 +^N4 =4 (^—^(^+^)The strains are0dz10E rEB a(F.5)007'0^0Or^d ZThe stresses are{ 0 ^0-r Cr() Tzr }^[E]^{ (z Er 6 0 Yzr }^{60}^{ cro }^ (FM)where {c o } and fcr o l are the initial strains and the initial stresses respectively, and thematrix of the modulus of elasticity isAppendix F. The Solution of Three-dimensional, Axisymmetric Problems^354{E} = E 1^ft^ftP^1 —^1.1,^1 — ft0^0^000(F.7)(1 + it) (1 — 21,t) 01 —2^-The above matrix of the elastic modulus can be either for the steel or for the concrete,by substituting E and p with the corresponding values for the materials.To calculate the stresses in the steel and the concrete in the elastic stage, two reason-ably fine meshes for the finite element calculation, as shown in Fig. F.2 (for the pull-outcalculation) and Fig. F.3 (for the push-in calculation), were used. The applied load wastaken as 30.0 kN and the specimen was normal strength concrete with polypropylenefibers and a deformed bar. The values of the material properties were those given inSection :3.2.5 in Chapter 4. Some results are given in Tables F.1 and F.2. It can be foundfrom the results of the calculations that the radial strain and the tangential strain do notplay much of a role in the terms of the total strain either in the steel or in the concrete.For example, for the elements at the interface between the steel and the concrete in thecross-section I under pull-out case, the ratios are[,^ (^+^(9)= 4.3% < 5% (in the steel)z^is,z]1-2p,andNe )]^ = 4.9% < 5% (in the concrete)[i —\"2s „^c E c,z JAppendix F. The Solution of Three-dimensional, Axisymmetric Problems^:355It was also found that for elements at a distance of 85% of the diameter away fromthe rebar, the axial strain decreases to zero. This means that the effective cross-sectionalarea can given by multiplying the total area by a factor, 7, given by47r(0.85 D) 2D2^= 0.57where= the length of the square of the specimen^(non)The aboVe conclusions were used to simplify some equations in the calculations ofstrains and stresses in the data processing.Table F.1: Strains in the Rebar (by the Finite Element Method)Cross-Section aLoadingTypeCentral Elements Outer Elementsfs,z C s ,r E5,0 C s,z Es,r 6 s,9I Pull-out 1058 b 40 26 1041 65 57Push-in -1064 -29 -27 -1045 -59 -51II Pull-out 557 21 18 548 :34 30Push-in -560 -15 -14 -550 -31 -27III Pull-out 56 3 2 51 0 2Push-in -60 0 0 -54 0°The load the rebar part carries for Section I, II and III is 95%, 50% and 5% respectively'Positive number represents the tensile strain and negative the compressive strain; all numbers arein 10 -6Appendix F. The Solution of Three-dimensional, Axisymmetric Problems^356Local coordinate (x, y)Global coordinate (Z, R)Figure F.1: Finite Elements of a RingTable F.2: Strains in the Concrete (By the Finite Element Method)Cross-Section 'LoadingTypeCentral Elements a Outer Elements bE-s,z r-s,r es,e fs,z es,r fs,0I Pull-out 721 d 62 58 0 0 0Push-in -732 -55 -49 0 0 0II Pull-out 403 34 30 30 5 4Push-in -466 -30 -28 -23 -2 -2III Pull-out 59 2 2 59 1 2Push-in -58 -3 -1 -55 -1 0'Elements in the vicinity of the rebarbElements at about 70% of the radius away from the rebar`The load the concrete part carries for Section I, II and III is 5%, 50% and 95% respectivelydPositive number represents the tensile strain and negative the compressive strain; all numbers arein 10 -6illININ111111^111111^1^1^1INN SpiralReberOnly half shownAppendix F. The Solution of Three-dimensional, Axisymmetric Problems^357ConcreteFFigure F.2: The Finite Element Mesh (Pull-out)Appendix F. The Solution of Three-dimensional, Axisymmetric Problems^358Only half shownRebarElm SpiralConcreteMI■MIA^IAA^414.4 4Figure F.3: The Finite Element Mesh (Push-in)Appendix GThe Calculation of the Hammer ReboundAs soon as the hammer rebounds it starts to decelerate at a constant rate. Fromkinetics, the rebound height is given byg t 2h rf bound = 2 (1 + 0.09)^up (nun)^ (G.1)wheret up = the time that the hammer takes to reach its highest point^(s )and the deceleration (1 + 0.09)g includes the gravitational deceleration, and thefrictional and air resistance effect.When the hammer falls down again, it has a constantly accelerating motion. Assum-ing that the friction and air resistance losses remain the same, the equation of motionIS1h fbounci =^— 0 . 09 )g2,t2own (inm)^ (G.2)Where:359Appendix G. The Calculation of the Hammer Rebound^ :360td,„, = the tune that the hammer takes to start to fall for the second timeWhat the data acquisition system records is the total time of the rebound, t rebound,t rebound = tup^tdown^(s )^(G.3)Solving Eqs. G.1, G.2 and G.3 simultaneously yields(•)1tup = ^1 + 11.09 rebound = 0.4775 t rebound51 (A) (G.4)After the rising time fur is known, the rebound velocity and the rebound height canall he determined from kinetics.Appendix HDeterminations of Parameters, C o , fr and frH.1 The Unit Chemical Adhesion ForceA simple tension tests was carried out using a universal testing machine to determinethe unit chemical adhesion force. The specimen is shown in Fig. 1-1.1. The unit chemicaladhesion force, C o , is calculated by^Co = —A^(MPa)^ (H.1)whereF = the break force^(N)A = the cross-sectional area of^the specimen^(77/7n2)H.2 The Frictional Factor at the InterfaceThe test for determining the frictional factor at the interface is shown in Fig. H.2. Itwas carried out using a universal testing machine. The applied vertical force varied from361Appendix H. Determinations of Parameters, C o , fp and fr^3620 to 4.0^7.0 kN, depending on the compressive strength of the concrete. The factor,fr , is given bydFh^\" Fig fr = ^ =D f, n `74 Fui(H.2)whereEh = the horizontal force corresponding to the point where a 0.1 mmhorizontal displacement takes place.^(N)F„ = the applied vertical force^(N)n = the number of data pointsH.3 The Normal Stress Factor at the InterfaceThe test for determining the normal stress factor at the interface is shown in Fig. H.3.It was carried out using a universal testing machine. The applied vertical force variedfrom 0 to 4.0 7.0 kAT, depending on the compressive strength of the concrete. Thefactor, fr , is given bydv1 ,\"f''= ^ =dF^2_, Fn^v • (H.3)wherez. = the vertical deformation^(mm)Appendix H. Determinations of Parameters, co , fp and fT^36:3F„ = the applied vertical force^(N)I? = the number of data points 4050A — AAll in mmFigure I-1.1: Test Specimen for the Unit Chemical Adhesion ForceApp(-wdix H. Determinations of Parameters. Co , fp and L.^ :3641111 1111 1111 1111 11 5050111111111111111111^All in mm150 -1'1Figure H.2: Test for the Frictional Factor at the Interface_Appendix H. Determinations of Parameters, C o , fp and fr^365AConcrete45RebarAAll in mmA—AFigure H.3: Test for the Normal Stress Factor at the InterfaceBibliography[1] Wastlund, George, Odman and Aven, \"Subjects of the Symposium,\" RILEM Sym-posium on Bond and Crack Formation in Reinforced Concrete, Vol. I, Stockholm,1957.[2] CAN3-A23.3-M70, \"Design of Concrete Structures for Building,\" Canadian Stan-dards Association, Toronto, 1970. 252 pp.[3] ACI Committee 318, \"Building Code Requirements for Reinforced Concrete (ACI318-63),\" American Concrete Institute, Detroit, 1963, 144 pp.[4] CANS-A23.3-M73, \"Design of Concrete Structures for Building,\" Canadian Stan-dards Association, Toronto, 1973. 263 pp.[5] CANS-A23.3-M84, \"Design of Concrete Structures for Building,\" Canadian Stan-dards Association, Toronto, 1984. 281 pp.[6] ACI Committee 318, \"Building Code Requirements for Reinforced Concrete (ACI318-70,\" American Concrete Institute, Detroit, 1971, 78 pp.[7] ACI Committee 318, \"Building Code Requirements for Reinforced Concrete (ACI318-89/ACI 318R-89),\" American Concrete Institute, Detroit, 1989, 353 pp.[8] ASTM C 234-91a, \"Standard Test Method for Comparing Concretes on the Basisof the Bond Developed with Reinforced Steel,\" ASTM Annual Book of Standard,Section 4, (onstruction, 1991.[9] Ba2ant, C.P. and Sener, S., \" Size Effect in Pullout Tests,\" ACI Materials Journal,Vol. 85, No. 5, Sept.-Oct. 1988, pp. 347-351.[10] Abrams, D.A., \"Readers Writes: Section,\" Civil Engineering, V.21, No.6, June 1951,pp. 51-52.[11] Abrams, D.A.. \"Tests of Bond Between concrete and Steel,\" Engineering ExperimentStation, Bulletin No. 71, University of Illinois, Urbana, Dec. 1913.[12] ACI Committee 408, \"Bond Stress — The State of the Art,\" ACI Journal, Proceed-ings V.63, No.11, Nov. 1966, pp. 1161-1188.366Bibliography^ 367[13] ACI Committee 408, \"State of the Art ^ Bond under Cyclic Loading,\" ACI MaterialJournal, V.88, No.6, Nov./Dec. 1991, pp. 669-673.[14] Mindess, S., \"Effects of Dynamic Loading on Bond,\" ACI Committee 446: State-of-the Art Report, Section 4.2.3., 1989[15] CEB Task Group VI, \"Bond Action Behaviour of Reinforcement — State of the ArtReport,\" Dec. 1981.[16] Myirea, T.D., \"Bond and Anchorage,\" ACI Journal, Vol.44, March 1948, pp. 521-552.[17] Watstein, D., \"Bond Stress in Concrete Pull-out Specimens,\" ACI Journal, Vo1.13,No.1, Sep. 1941.[18] Watstein, D., \"Distribution of Bond Stress in Concrete Pull-out Specimens,\" ACIJournal, Proceedings Vol.43, May 1947.[19] Mains, R.M., \"Measurement of the Distribution of Tensile and Bond Stresses AlongReinforcing Bars,\" ACI Journal, Proceedings Vol. 48, No. 3, Nov. 1951, pp. 225-252.[20] Gilkey, H.J., Chamberlin, S.J., and Beal, R.W., \"Bond between Concrete and Steel,\"Iowa. Engineering Experiment Station, Bulletin 147, 1940.[21] Ferguson, P.M., Turpin, R.D. and Thomson, .J.N., \"Minimum Bar Spacing as aFunction of Bond and Shear Strength,\" ACI Journal, June 1954, pp. 869-888.[22] Ferguson, P.M. and Thomson, J.N., \"Development Length for High Strength Rein-forcing Bars in Bond,\" ACI Journal, Proceedings, Vol.59, July. 1962, pp. 887-922.[23] Ferguson, P.M. and Thomson, J.N., \"Development Length for Large High StrengthReinforcing Bars,\" ACI Journal, Proceedings, Vol.62, No.1, Jan. 1965, pp. 71-94.[24] Ferguson, P.M., \"Bond Stress - The State of the Art,\" Report by ACI Committee408, ACI .Journal, Proceedings, V.63, No.11, Nov. 1966, pp. 408-422.[25] Bresler, B. and Bertero, V.V., \"Behaviour of Reinforced Concrete Under RepeatedLoad,\" Proceedings of the ASCE, V.94, ST6, June 1968, pp. 1567-1590.[26] Bresler, B. and Bertero, V.V., \"Reinforced Concrete Prism Under Repeated Loads.\"International Symposium on the Effects of Repeated Loading of Materials and Struc-tures, Proceedings, Mexico City, 1966, Vol.3, pp. 1-30.[27] Lutz, L.A. and Gergley, P., \"The Mechanics of Bond and Slip of Deformed Bars inConcrete,\" ACI .Journal proceedings, Vol.64, No.11, Nov. 1967, pp. 711-721.Bibliography^ :368[28] Lutz, L.A., \"The Mechanics of Bond and Slip of Deformed Reinforcing Bars inConcrete,\" Ph.D. Thesis, Cornell University, Sep. 1966.[29] Rehm, G., \"The Basic Principles of Bond Between Steel and Concrete,\" TranslationNo.134, Cement and Concrete Associations, London, pp. 1-31.[30] Coto. Y., \"Crack Formed in Concrete around Deformed Tension Bars,\" ACI .Journalproceedings, Vol.68, No.4, April 1971, pp. 244-251.[31] Nilson, A.H., \"Non-linear Analysis of Reinforced Concrete by the Finite ElementMethod,\" ACI Journal, Vol. 65, No.9, Sep. 1968.[32] Nilson, A.H., \"Finite Element Analysis of Reinforced Concrete,\" Ph.D. Thesis, Uni-versity of California at Berkeley, 1968.[33] Nilson, A.H., \"Internal Measurement of Bond Slip,\" ACI Journal, Vol. 69, No.7, Jul.1972, pp. 439-441.[34] Nilson. A.H., \"Bond Stress Slip Relations in Reinforced Concrete Report,\" No.345,Dept. of Structural Engineering, Cornell University, Dec. 1971.[35] Honde, J., \"Study of Force-Displacement Relationships for the Finite Element Anal-ysis of Reinforced Concrete,\" Ph.D. Thesis, McGill University, 1974.[36] Richart, F.E. and Jensen, V.P., \"Tests of Plain Reinforced Concrete Made withHaydite Aggregates,\" Bulletin No.237, Engineering Experiment Station, Universityof Illinois, 1931.[37] Menzel, C.A., \"Some Factors Influencing Results of Pull-out Bond Test,\" ACI Jour-nal, Proceedings, Vol. 35, June 1939, pp. 517-544.[:38] Gilkey, H.J., Chamberlin, S.J. and Beal, R.W., \"Bond with Reinforcing Steel,\" IowaState College Bulletin, Engineering Report No.26, 1955-56.[39] Watstein, I). and Seese, N.A., \"Effect of Type of Bar on Width of Cracks in Rein-forced Concrete Subjected to Tension,\" ACI Journal em Proceedings, Vol.41, No.4,Feb. 1945, pp. 293-304.[40] Clark. A.P., \"Comparative Bond Efficiency of Deformed Concrete Reinforcing Bars.\"ACI Journal em Proceedings, Vol.18, No.4, Dec. 1946, pp. :381-400.[41] Konyi, N.H., Bond between Concrete and Steel,\" Structural Concrete, ReinforcedConcrete Association, VoLl, No.9, May/June 1963, pp. 373-390.Bibliography^ 369[42] Mathey, R.M. and Watstein, D., \" Investigation of Bond in Beam and Pull-outSpecimens with High Yield Strength Deformed Bars,\" ACI .Journal Proceedings,Vol.57, No.9, March 1961, pp. 1071-1090.[43] Vos, I.E. and Reinhardt, H.W., \"Bond Resistance of Deformed Bars, Plain Bars, andStrands under Impact Loading,\" Report 5-80-6, Department of Civil Engineering,Delft University of Technology, Netherlands, August, 1980.[44] Rehm, G., \"The fundamental Law of Bond,\" RILEM Symposium on Bond and CrackFormation in Reinforced Concrete, Vol. I, Stockholm, 1957.[45] Bernander, E.G., \"An Investigation of Bond by Means of Strain Measurement inHigh Tensile Bars Embedded in Long Cylindrical Pullout Specimens,\" RILEM Sym-posium, Vol. I, Stockholm, 1957.[46] Tassios, T.P. and Koroneos, E.G., \"Local Bond-Slip Relationships by Means of theMoire Method,\" ACI Journal em Proceedings, Vo1.81, No.4, 1984, pp. 27-34.[47] .Jiang, D.H., Shah, S.P. and Andonian, A.T., \"Study of the Transfer of Tensile Forcesby Bond,\" ACI .Journal Proceedings, Vol. 81, No. 4, 1984, pp. 251-259.[48] Abrishami, H.H. and Mitchell, D., \"Simulation of Uniform Bond Stress,\" ACI Ma-terial .Journal, Vol.86, No.:3, March/April 1992, pp. 161-168.[49] Robin, R.I. and Standish, I.G., \"The Influence of Lateral Pressure upon AnchorageBond,\" Magazine of Concrete Research, Vol.36, No.129, Dec. 1984, pp. 195-202.[50] Bentur, A. and Mindess, S., \"Fiber Reinforced Cementitious Materials,\" ElsevierScience Publishers, U.K., 1990.[51] Swamy, R.N. and Al-Noori, K., \"Bond Strength of Steel Fibres Reinforced Con-crete,\" Concrete (Great Britain), Vol. 8, No. 8, Aug. 1974, pp. :36-37.[52] Yerex, Lowell 11, Wenzel, Thomas H. and Davies, Robert, \"Bond Strength of MildSteel in Polypropylene Fiber Reinforced Concrete,\" ACI .Journal Proceedings, Vol.82,No.1, Jan./Feb. 1985, pp. 40-45.[53] Clifton, J.R. and Mathey, R.G., \"Bond and Creep Characteristics of Coated Rein-forcing Bars in Concrete,\" ACI Journal Proceedings, Vol.80, No.4, July/Aug. 1983,pp. 288-293.[54] Treece, R.A. and Jirsa, J.0., \"Bond Strength of Epoxy-Coated Reinforcing Bars.\"ACI Materials Journal, V.86, No.2, Mar-Apr. 1989, pp. 167-174.Bibliography^ 370[55] Cleary, D.B. and Ramirez, J.A., \"Bond Strength of Epoxy-Coated Reinforcement,\"ACI Materials .Journal, V.88, No.2, Mar-Apr. 1991, pp. 146-149.[56] Takeda, T., Sozen, M.A. and Nielsen, N.N., \"Reinforced Concrete Response to Sim-ulated Earthquakes,\" Proceedings of ASCE, V.96, ST12, Dec. 1970, pp. 2557-257:3.[57] Hassan, F.M. and Hawkins, N.W., \"Effect of Post-Yield Loading Reversals on Bondbetween Reinforcing Bars and Concrete,\" Report SM73-2, Dept. of Civil Engineer-ing, University of Washington, Seattle, March 1973.[58] Viwathanatepa, S., Popov, E.P. and Bertero, V.V., \"Deterioration of ReinforcedConcrete Bond under Generalized Loading,\" ACI Annual Conference, San Diego,California, March 1977.[59] Hungspreug, S., \"Local Bond between a Reinforcing Bar and Concrete under HighIntensity Cyclic. Load,\" Ph.D Thesis, Cornell University, .Jan. 1981.[60] Morita, S and Kaku, T., \"Local Bond Stress-Slip Relationship under Repeated Load-ing,\" IA B,SE Symposium, V.13, Lisbon, 1973, pp. 221-226.[61] Rehm, G. and Eligehausen, R., \"Einfluss Einer Nicht Ruhenden Belastung auf dasVerbundverhalten von Rippenstahlen,\" Betonwerk and Fertigteil Technik, Hert 6,1977, pp. 295-299.[62] Edwards, A.D. and Yannopoulos, P.J., \"Local Bond Stress-Slip Relationship underRepeated Loading,\" Magazine of Concrete Research, V.30, No.103, .June 1978. •[6:3] Perry, E.S. and .Jundi, N., \"Pull-out Bond Stress Distribution under Static andDynamic Repeated Loading,\" ACI Journal Proceedings, Vo1.66, No.5, May. 1969,pp. :377-380.[64] Panda, A.K., \"Investigations of Bond of Deformed Bars in Plain and Steel FibreReinforced Concrete Under Reverse Cyclic Loading,\" M.A.Sc. Thesis, University ofBritish Columbia, Vancouver, B.C., Sep. 1980.[65] Spencer, R.A., Panda, A.K. and Mindess, S., \"Bond of Deformed Bars in Plain andFibre Reinforced Concrete Under Reversal Cyclic Loading,\" International Journalof Cement Composites and Lightweight Concrete, Vol.4, No.1, Feb. 1982.[66] Panda, A.K., \"Bond of Deformed Bars in Steel Fibre-Reinforced Concrete UnderCyclic Loading,\" Ph.D. Thesis, University of British Columbia, Vancouver, Apr.1984.[67] ACI Committee 408.2R \"State-of-the-Art-Report: Bond under Cyclic Loads,\" ACIMaterials .Journal, Vol.88, No.6, Nov.-Dec. 1991, pp. 669-67:3.Bibliography^ 371[68] Mindess, S.. \"Rate of Loading Effects on The Fracture of Cementitious Materials,\" inShah, S.P. (ed.), \"Application of Fracture Mechanics to Cementitious Composites,\"Proceedings of the NATO Advanced Research Workshop, Northwestern University,1984, Martnus Njhoff Publishers, The Netherlands, 1985, pp. 617-636.[69] Mindess, S., Banthia, N.P. and Bentur, A, \"The Response of Reinforced ConcreteBeams with a Fibrous Concrete Matrix to Impact Loading,\" International Journalof Cement Composites and Lightweight Concrete, Vol.8, No.3, 1986, pp. 165-170.[70] Mindess, S., Bentur, A. Yam C. and Vondran, C., \"Impact Resistance of ConcreteContaining Both Conventional Steel Reinforcement and Fibrillated PolypropyleneFibres,\" ACI .Journal, Vo1.86, No.6, 1989, pp. 545-549.[71] Mindess, S., \"Fracture Toughness Testing of Cement and Concrete,\" in Carpinteri,A. and Ingraffea, A.R. (eds.), \"Fracture Mechanics of Concrete: Material Char-acterization and Testing,\" Martnus Njhoff Publishers, The Netherlands, 1984, pp.67-110.[72] Shah, S.P. and John, R., \"International Conference on Fracture Mechanics of Con-crete,\" Lausanne, 1985, pp. 373-385.[73] Mindess, S., Banthia, N.P., Ritter, A. and Skalny, J.P., \"Crack Development inCementitious Materials under Impact Loading,\" in Mindess, S. and Shah, S. P. (eds.),\"Cement-Based Composites: Strain Rate Effects on Fracture,\" Vol.64, 1986, pp.217-223.[74] Banthia, N.P., Mindess, S. and Bentur, A, \"High Stress Rate Testing of Concrete:An Overview,\" Indian Concrete Journal, Vo1.60, No.10, 1986, pp. 265-272.[75] Hansen, R..J. and Liepins, A.A., \"Behaviour of Bond Under Dynamic Loading,\" ACIJournal Proceedings, Vol.59, No.4, April 1962, pp. 56:3-582.[76] Hjorth. 0., \"Ein Beitrag zur Frage der Festigkeiten and des Verbundverhaltensvon Stahl and Beton bei Hohen Beanspruchungsgeschwindigkeiten,\" Dissertation,Technische Universitk Braunschweig, 1976.[77] Vos, I.E. and Reinhardt, H.W., \"Influence of Loading Rate on Bond Behaviour ofReinforcing Steel and Prestressing Strands,\" Materiaux et Constructions, Vol.15,No.85, 1982, pp. 3-10.[78] Takeda, Jin-Ichi, \"Strain Rate Effects on Concrete and Reinforcements and TheirContributions to Structures,\" in S. Mindess and S.P. Shah (Eds.), \"Cement-BasedComposites: Strain-Rate Effects on Fracture,\" Vol.64, 1986, pp. 15-20.Bibliography^ :372[79] Bentur, A., Mindess, S. and Banthia, N.P., \"The Fracture of Reinforced ConcreteUnder Impact Loading,\" in S. Mindess and S.P. Shah (Eds.), \"Cement-Based Com-posites: Strain Rate Effects on Fracture,\" Vol.64, 1986. pp. 225-234.[80] Banthia, N.P., \"Impact Resistance of Concrete,\" Ph.D. Thesis, University of BritishColumbia, Vancouver, B.C., Canada, 1987.[81] Banthia, N.P., Mindess, S. and Bentur, A., \"Impact Behaviour of Concrete Beams, \"Materiaux et Constructions, Vol. 20, No. 118, 1987 pp. 293-302.[82] Rehm, G, \"Stress Distribution in Reinforcing Bars Embedded in Concrete,\" RILEMSymposium on Bond and Crack Formation in Reinforced Concrete, Vol. II, Stock-holm, 1957.[83] (Mihail, T.A., \"Slip between Reinforcement and Concrete,\" RILEM Symposium onBond and Crack Formation in Reinforced Concrete, Vol. II, Stockholm, 1957.[84] .Jonsson, P.O., \"Investigation of Bond between Reinforcement and concrete,\"Swedish Cement and Concrete Research Institute, Proceedings, No.29, Stockholm,1957.[85] Kuuskoski, V., \"Uber die Haftung Zwischen Beton and Stahl,\" The State Institutefor Technical Research, 19, Helsinki, 1950.[86] Broms, B.B., \"Mechanics of Tension Cracking in Reinforced Member,\" Phase II,Dept. of Structure Engineering, Cornell University, Report No.311, 196:3.[87] Bresler, B. and Bertero, V., \"Behaviour of Reinforced Concrete under RepeatedLoad,\" Journal of Structure Division, ASE Proceedings, June 1968.[88] Gerstle, W.H., Ingraffea, A.R. and Gergely, P., \"The Fracture Mechanics of Bond inReinforced Concrete,\" Dept. of Structural Engineering, Cornell University, Report82-7, .June 1982.[89] Ingraffea, A.R., Gerstle, W.H., Gergley, P. and Saouma, V., \"Fracture Mechanics ofBond in Reinforced Concrete,\" Journal of Structural Engineering, A,SVE, Vol. 110,No. 4, Apr. 1984. pp. 871-889.[90] Yankelevsky. D.Z., \"Bond Action Between Concrete and a Deformed Bar — A NewModel,\" ACI .Journal Proceedings, Vol.82, No.13, 1984, pp. 154-161.[91] Yankelevsky, D.Z., \"New Finite Element for Bond-Slip Analysis,\" Journal of Struc-tural Engineering, ASCE, Vol. 111, No.7, Jul. 1985, pp. 15:33-1542.Bibliography^ 373[92] Keuser, M. and Mehlhorn, G., \"Finite Element Models for Bond Problems,\" Journalof Structural Engineering, ASE, Vol.113, No.10, 1987, pp. 2160-2173.[9:3] Rots, J.G., \"Bond-slip Simulations Using Smeared Cracks and/or Interface Ele-ments,\" Research Report 85-01, Struct. Mech., Dept. of Civil Engineering, DelftUniversity of Technology, 1985, 56 pp.[94] Rots, J.G., \"Chapter 12: Bond of Reinforcement,\" in Elfgren, L., (ed.) \"FractureMechanics of Concrete Structures: From theory to Applications,\" RILEM Report,Chapman and Hall, 1989, pp. 245-262.[95] Society for Experimental Mechanics Inc., \"Handbook on Experimental Mechanics,\"Kobayashi, A.S., (ed.), Prentice-Hall, Englewood Cliffs, N.J., 1987, 1002 pp.[96] Somaakanthan, N., \"Investigation of the Dynamic Fracture Behaviour of Concrete,\"Master Thesis, Department of Civil Engineering, University of British Columbia,1989, pp. 40-41.[97] Bentur, A., Mindess, S. and Banthia, N.P., \"The behaviour of Concrete under Im-pact Loading: Experimental Procedures and Method of Analysis,\" Materiaux etConstructions, Vol.19, No.11:3, 1986, pp. 371-378.[98] Window. A.L. and Holister, G.S. (eds.), \"Strain Gauge Technology,\" Applied SciencePublisher, London, England, 1982.[99] Blinchikoff, Hi. and Zverev, A.I., \"Filtering in Time and Frequency Domains,\" JohnWiley and Sons, New York, 1976.[100] Cook, R.D., \"Concept and Applications of Finite Element Analysis,\" (Second Edi-tion), John Wiley and Sons Inc., 1981.[101] Barsoum, R.S., \"Triangular Quarter-Point Elements as Elastic and Perfectly-Plastic Crack Tip Elements,\" IJNME, Vol. 11, No. 1, 1977, pp. 85-98.[102] Barsoum, R.S., \"On the Use of Isoparametric Finite Elements in Linear FractureMechanics,\" LINME, Vol. 10, No. 1, 1976, pp. 25-37.[10:3] Soroushian, P., Choi, K.B. and Alhamad, A., \"Dynamic Constitutive Behaviour ofConcrete,\" ACI Journal Proceedings, March/April 1986, pp. 251-259.[104] Nuismer, R..1., \"An Energy Release Rate Criterion for Mixed Mode Fracture,\" Int.J. Fracture, 11 (1975). pp. 245-250.[105] Brock, David, \"Elementary Engineering Fracture Mechanics,\" Martinus NijhoffPublishers. 1982.Bibliography^ 374[106] Hannant, D.J., \"Failure Criteria for Concrete in Compression,\" Magazine of Con-crete Research, Vol. 20, No. 64, Sep. 1968, pp. 137-144.[107] Mindess, S., Banthia, N. and Yan, C., \"The Fracture Toughness of Concrete UnderImpact Loading,\" Cement and Concrete Research, Vol. 17, 1987, pp. 231-241.[108] Ba2ant, Z.P. and Pfeiffer, P.A., \"Shear Fracture Tests of Concrete,\" RILEM Ma-terials and Structures, Vol 19, No. 110, 1986, pp. 111-121.[109] Ba2ant, Z.P. and Prat, P.C., \"Measurement of Mode III Fracture Energy of Con-crete,\" Nuclear Engineering and Design, Vol. 106, 1988, pp. 1-8.[110] Mindess, S., \"Fracture Process Zone Detection,\" in Shah, S.P. and Carpinteri, A.,(eds.) \"Fracture Mechanics Tests Method for Concrete,\" RILEM Report 5, Chapmanand Hall, 1991, pp. 231-261.[111] Timoshenko, S.P. and Gere, J., \"Mechanics of Materials,\" Chapter 10, Van Nos-trand Reinhold Company, 1972.[112] Timoshenko, S.P. and Goodier, J.N., \"Theory of Elasticity,\" (Third Edition), Chap-ter 14, McGraw-Hill Book Company, New York, 1970.[113] Barry, B.A., \"Errors in Practical Measurement in Science, Engineering and Tech-nology,\" Morris, M.D., (ed.), Wiley, New York, 1978, 183 pp.[114] Miklowitz, .J.,\"Elastic Wave Propagation,\" in Abramson, H.N., Liebowitz, H.,Crowley, J.M. and Juhasz, S. (eds.), \"Applied Mechanics Survey,\" Spartan Books,Washington, D.C. 1966, pp. 809-839.[115] Davies, R.M., \"Stress Waves in Solids,\" in Abramson, H.N., Liebowitz, H., Crowley,J.M. and Juhasz, S. (eds.), \"Applied Mechanics Survey,\" Spartan Books, Washing-ton, D.C. 1966. pp. 803-807.[116] Zienkiewicz,^\"The Finite Element Method in Engendering Science,\" McGraw-Hill Book Company, New York, 1971.[117] Crose, J.G., \"Stress analysis of Axisymmetric Solid with Axisymmetric Properties,\"AIAAJ, Vol.10, No.7, 1972, pp.866-871.[118] Pardoen, J.C., \"Axisymmetric Stress Analysis of Axisymmtric Solids with An-isotropic Material Properties,\" AIAAJ, Vol.15, No.10, 1977, pp. 1498-1500."@en ; edm:hasType "Thesis/Dissertation"@en ; vivo:dateIssued "1993-05"@en ; edm:isShownAt "10.14288/1.0050492"@en ; dcterms:language "eng"@en ; ns0:degreeDiscipline "Civil Engineering"@en ; edm:provider "Vancouver : University of British Columbia Library"@en ; dcterms:publisher "University of British Columbia"@en ; dcterms:rights "For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use."@en ; ns0:scholarLevel "Graduate"@en ; dcterms:title "Bond between reinforcing bars and concrete under impact loading"@en ; dcterms:type "Text"@en ; ns0:identifierURI "http://hdl.handle.net/2429/2097"@en .