By Ploutarchos John Yannopoulos B.Sc.(Eng.)
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FATIGUE, BOND AND CRACKING CHARACTERISTICS' OF REINFORCED CONCRETE TENSION MEMBERS by Ploutarchos John Yannopoulos B.Sc.(Eng.), A.C.G.I., M.Sc.(Eng.), D.I.C. a thesis submitted for the .degree of Doctor of Philosophy in the Faculty of Engineering . of the University of London Department of Civil Engineering imperial College of Science and Technology London January 1976 2 ABSTRACT This thesis describes an investigation of the fatigue, bond and cracking characteristics of reinforced concrete tension members. To improve the state of knowledge on the behaviour of reinforced concrete beams under fatigue loading, an experi- mental investigation of the fatigue life of hot rolled de- formed bars, as affected by their embedment in concrete, their test length in air and identification marks within their length, was carried out. An extensive number of statistically planned fatigue tests were performed on a large proportion of the hot rolled deformed bar types marketed in the United Kingdom, which were either free in air or embedded axially in concrete tension members. The fatigue test results were analysed and compared statistically and curves of stress range against number of cycles to failure were determined by regression analyses, for different probabilities of survival. Extensive numbers of tests were also carried out to determine the bond stress-slip relations for hot rolled de- deformed bars and mild steel plain bars, from specimens with a concrete embedment length of 38 mm. The effect of bar back load, bar pull relative to the settlement of concrete, concrete cover to bar and different intensity repeated loading on the bond stress-slip relationships was also statistically determined. Load-crack width and load-end slip data determined by testing concrete tension and long pull-out members res- pectively, reinforced with a hot rolled deformed bar, were compared with the results of a finite element computer program developed for the analysis of axi-symmetric reinforced concrete members. The non-linear bond stress-slip characteristics between steel and concrete determined from the short pull- out specimens were incorporated into the program by using special bond linkage elements. The non-linear reponse of the members under load and the formation and propagation of cracks in the concrete matrix were handled by specially adapted non- linear finite element techniques. 4 ACKNOWLEDGE1ENTS The author wishes to express his gratitude to the following persons and associations that helped in carrying out this research project : Professor A.J. Harris, head of the Concrete Structures and Technology section of the Civil Engineering Department of Imperial College of Science and Technology, for his general supervision of the project. Dr.A.D. Edwards, who supervised this work, for his valuable advice, guidance and help during the research period and during the preparation of the thesis. The Road Research Laboratory of the Department of the Environment under whose sponsorship the research was carried. The technical staff of the Concrete Structures and Technology Laboratories without whose experience and technical expertise the experimental part of the project would not have been possible. Special mention must be made in this context of Mr.J. Baulch for his skilled and continuous assistance during the laboratory work, Mr. R. Loveday for his technical advice and Messrs. C. Mortlock, J. Turner and H. Wilson for their general help. CONTENTS ABSTRACT 2 ACKNOWLEDGEMENTS ...... 4 CONTENTS 5 LIST OF TABLES, FIGURES AND PLATES 15 NOTATION • 24 CHAPTER 1. : INTRODUCTION 1.1. Introduction 6 26 1.2. Object and scope of present investigation . 29 CHAPTER 2 : CRITICAL REVIEW OF PAST WORK 2.1. Critical review of past work on fatigue . 30 2.1.1. Fatigue behaviour of steel 30 2.1.2. Fatigue properties of hot-rolled deformed reinforcing steel bars . 31 2.1.2.1. General 31 2.1.2.2. Factors affecting fatigue strength 33 2.1.3. Type of fatigue specimen 0 • • 39 2.1.3.1. Fatigue behaviour of deformed bars as affected by their embedment in concrete • . ..... 39 2.1.3.2. Gripping arrangement of bars tested free in air . 44 2.2. Critical review of past work on bond and cracking 46 2.2.1. General . .. .. 46 2.2.2. Nature of bond and mechanism of bond failure ...... • ... 47 2.2.3. Measurement of anchorage and flexural bond strengths .... • • 49 2.2.4. Experimental determination of bond stress and slip between concrete and reinforcing bars 50 2.2.4.1. Average bond stress 50 2.2.4.2. Bond stress distribution • • 52 2.2.4.3. Slip between concrete and a reinforcing bar ...,... • 54 2.2.4.4. Bond stress - slip relationships 56 2.2.5. Investigations related to cracking . 62 2.2.5.1. General 62 2.2.5.2. Empirical studies on cracking 63 2.2.5.3. Classical analytical methods on cracking 65 2.2.5.4. Finite element studies on cracking 66 2.2.6. Investigations on the effect of repeated loading on bond 73 CHAPTER 3 EXPERIMENTAL TECHNIQUES AND PROCEDURE 3.1. Materials and their properties 94 3.1.1. Concrete 94 3.1.2. Hot rolled deformed bars 96 3.1.3. Hot rolled mild steel plain bars . 97 3.2. Details of specimens 97 3.2.1. Specimens for fatigue tests 97 3.2.1.1. Specimens free in air . 97 3.2.1.2. Specimens embedded in concrete . 99 3.2.2. Specimens for bond tests 99 3.2.2.1. Specimens details 99 3.2.2.2. Casting and curing . 101 3.3. Description of test rig 102 3.4. Static tests on hot rolled deformed bars and mild steel plain bars 103 3.5. Fatigue tests on hot rolled deformed bars free in air and on hot rolled deformed bars embedded in concrete 104 3.5.1. Loading equipment 104 3.5.2. Static and dynamic calibration of loading equipment 106 3.5.3. Testing procedure . ..... 109 3.6. Bond tests on hot rolled deformed bars and mild steel plain bars 111 3.6.1. Loading equipment 111 3.6.2. Instrumentation and testing procedure 111 CHAPTER 4 : TECHNIQUES OF STATISTICAL ANALYSIS OF FATIGUE DATA 4.1. Introduction 139 4.2. Fatigue life frequency distribution 139 4.2.1. Choice of life distribution shape and point estimates of parameters . 140 4.2.2. The normal distribution . ..... 141 4.2.3. Level of significance of a statistical hypothesis 144 4.2.4. X2 - test for goodness of fit .144 4.3. Confidence intervals for the mean and the variance 147 4.4. Tests of significance for normal populations 148 4.4.1. Test for the equality of the variances of k populations 148 4.4.2. Test for the equality of the variances of two populations . • • . 150 4.4.3. Test for the equality of the means of k populations 150 4.4.4. Test for the equality of the means of two populations 152 4.4 4.1. Variances not significantly different . 152 4.4.4.2. Variances significantly different 153 4.5. Regression analysis 154 4.5.1. Hypothesis underlying regression analysis 154 4.5.2. Linear regression analysis 156 4.5.2.1. Estimates of parameters a, b, and of linear regression analysis 157 4.5.2.2. Testing of linearity of regression curve and confidence limits 158 4 5.2.3. Blom's test 161 4.5.3. Comparison of two regression lines 161 4.5.3.1. Comparison of two regression lines of not significantly different variances 162 ▪▪• 4.5.3.2• Comparison of two regression lines of significantly, different variances 164 4.5.4. Linear regression for fatigue data 166 4.6. Probability curves 167 4.7. Computer programs 168 CHAPTER 5 : EXPERIMENTAL INVESTIGATION OF THE FATIGUE PROPERTIES OF HOT-ROLLED DEFORMED BARS AND STATISTICAL ANALYSIS OF THE RESULTS 5.1. Object and scope of tests 169 5.2. Definitions and notation 170 5.3. Static tests on hot rolled deformed bars . • 171 5.4. Fatigue tests on hot rolled deformed bars . 172 5.4.1. General 172 5.4.2. Fatigue tests on bars free in air test series WEL-F-900-NI 174 5.4.3• Fatigue tests on bars embedded in concrete. Test =series WEL-C-900-NI• • • 175 5.4.4. Fatigue tests on bars free in air. Test series WEL-F-400-WI, JON-F-400-WI, SHE-F-400-WI, UNI-F-400-WI and WEL-F-400-NI, JON-F-400-NI, SHE-F-400-NI . 176 5.5• Description of static and fatigue failures of hot rolled deformed bars 177 5.6. Statistical analysis of fatigue test data . • 180 2 5.6.1. X - test for goodness of fit . 182 5.6.2. Regression analysis, Blom's test and comparison of regression lines 183 5.6.2.1. Regression analysis 183 10 5.6.2.2. Blom's test 184 5.6.2.3. Comparison of regression lines . 185 5.7. Interpretation of results of statistical analysis and conclusions 187 CHAPTER EXPERIMENTAL INVESTIGATION OF THE BOND PROPERTIES OF HOT ROLLRD DEFORMED BARS AND MILD STEEL PLAIN BARS 6.1. General 237 6.2. Bond-slip relation for hot-rolled deformed bars and mild steel plain bars 238 6.2.1. Test results 238 6.2.2. Statistical analysis of Welbond deformed bar bond-slip data and discussion of results 241 6.2.2.1. Bond-slip curves for Welbond deformed bar . 241 6.2.2.2. X2 - test for goodness of fit 243 6.2.2.3. Effect of bar back load on maximum bond stress . 244 6.2.2.4. Effect of concrete cover on maximum bond stress 245 6.2.2.5.