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Control of Cracking in Reinforced Concrete Structures
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Foreword xi Notations xv Introduction xxi Chapter 1. CEOS.fr Project Presentation 1 1.1. CEOS.fr work program 1 1.2. Testing 2 1.2.1. Tests on prismatic full-scale blocks 2 1.2.2. Tests on 1/3-scale beams 10 1.2.3. Tests on 1/3-scale shear walls 13 1.2.4. Tests on ties 17 1.3. Modeling and simulation 21 1.3.1. MEFISTO research program 21 1.3.2. Benchmarks and workshops 23 1.3.3. Numerical experiments 24 1.4. Engineering 25 1.5. Database and specimen storage 26 1.5.1. Database CHEOPS 26 1.5.2. Specimen storage (Renardieres site) 26 Chapter 2. Hydration Effects of Concrete at an Early Age and the Scale Effect 27 2.1. Hydration effects of concrete at an early age 27 2.1.1. Global heating and cooling of a concrete element 28 2.1.2. Differential temperature between concrete core and surface 29 2.2. Scale effect 32 2.2.1. Scale effect principle 32 2.2.2. Calculating scale effect according to Weibull theory 33 2.2.3. Worked examples of calculation with the scale effect according to the Weibull model 37 2.2.4. Application of Weibull integral in bending and in tension 44 Chapter 3. Cracking of Ties 47 3.1. Design values and limit values 47 3.2. Adjusting the design value for verification purposes 47 3.3. Crack spacing equation 48 3.3.1. Linear equation 48 3.3.2. Relationship between the maximum spacing Sr,max and the mean spacing Sr,m 49 3.3.3. Equation based on the MC2010 bond-slip relationship 49 3.4. Equation for the mean differential strain 50 3.5. Model accuracy when calculating the strain and crack width 51 3.6. Example of the application of the cracking equations to a concrete tie in tension 53 Chapter 4. Cracking of Beams Under Mechanical Flexural Loading 59 4.1. Crack spacing 59 4.2. Crack width 60 4.2.1. Tensile stress-strain curve 60 4.2.2. Calculating the crack width from the relative strain 61 4.2.3. Calculating the crack width by interpolation between uncracked and fully cracked conditions (the method) 62 4.3. Examples 69 4.3.1. Example 1: calculation of crack spacing and crack width in a thick concrete slab under heavy loads 69 4.3.2. Example 2: calculation of crack spacing and crack width in a double thick beam 71 Chapter 5. Cracking in Walls 75 5.1. Current status of the reference texts 75 5.2. Validity of the physical model and calculating of the crack angle 77 5.3. Calculation model 78 5.4. Crack spacing and slippage length 79 5.5. Mean differential strain 82 5.6. Calculating the crack width from reinforcing bar strains 87 5.7. Calculating the crack width in accordance with the strut and tie model 89 5.8. Recommendations for evaluating the cracking in walls subject to earthquake situations 91 5.9. Examples of application of cracking equations in a wall subjected to a shear stress in the plane of the wall 92 5.9.1. Example 1 94 5.9.2. Example 2 102 5.9.3. Example 3 103 Chapter 6. Minimum Reinforcement of Thick Concrete Elements 105 6.1. Reinforcement of reinforced concrete ties 106 6.1.1. Detailed calculation from a 3D approach 106 6.1.2. Simplified methodology for calculating concrete reinforcement 106 6.2. Reinforcement of prestressed concrete ties 111 6.2.1. Crack formation in an element in tension 112 6.2.2. Stabilized cracking stage in an element in tension 113 6.2.3. Conclusion 114 6.3. Reinforcement of beams 115 6.3.1. Beams under monotonic mechanical loading 115 6.3.2. Beams under imposed deformation and monotonic mechanical loading 115 6.4. Reinforcement of walls 116 6.4.1. Walls without specific requirements for cracking 116 6.4.2. Walls with specific requirements for cracking 117 Chapter 7. Shrinkage, Creep and Other Concrete Properties 119 7.1. Introduction 119 7.2. Strain 121 7.2.1. Definition 121 7.2.2. Range of applicability 121 7.2.3. Initial strain at loading 122 7.3. Shrinkage 124 7.3.1. Autogenous shrinkage 125 7.3.2. Drying shrinkage 125 7.4. Creep 129 7.4.1. Assumptions and related basic equation 129 7.4.2. Basic creep 131 7.4.3. Drying creep 131 7.5. Experimental identification procedures 133 7.5.1. Initial strain at loading time 134 7.5.2. Shrinkage 134 7.5.3. Basic creep 134 7.5.4. Drying creep 134 7.5.5. Estimation of long-term delayed strain 134 7.6. Temperature effects on concrete properties 135 7.6.1. Temperature effects on instantaneous concrete characteristics 136 7.6.2. Maturity 136 7.6.3. Thermal expansion 136 7.6.4. Compressive strength 137 7.6.5. Tensile strength 137 7.6.6. Fracture energy 138 7.6.7. Elasticity modulus 138 7.6.8. Temperature effects on the delayed deformations 139 7.6.9. Autogenous shrinkage 141 7.6.10. Drying shrinkage 141 Chapter 8. Cracking of Beams and Walls Subject to Restrained Deformations at SLS 143 8.1. Evaluation of shrinkage with bulk heating and cooling of concrete 144 8.2. Estimating and limiting crack widths 145 8.3. Estimating restraints at SLS 146 8.3.1. Approximate calculation of external restraint 146 8.3.2. Detailed calculation of a restraint on a wall 147 8.4. Estimation of stiffness 152 8.4.1. General comments 152 8.4.2. Simplified method 153 8.4.3. Principles of the detailed method 154 8.4.4. Worked example of a massive element thermal gradient 158 Chapter 9. Effects of Various Phenomena in Combination 163 9.1. Estimating crack width 163 9.2. Combining effects due to imposed deformations and deformations resulting from in-service loadings 164 9.2.1. Structures with water or air tightness requirements 165 9.2.2. Structures with durability requirements 167 9.2.3. Minimum reinforcement 169 Chapter 10. Numerical Modeling: a Methodological Approach 171 10.1. Scope 171 10.2. Methodology 172 10.3. Thermal and hydration effects 173 10.4. Drying 175 10.5. Mechanics 177 10.5.1. Hydration 177 10.5.2. Permanent basic creep 178 10.5.3. Reversible basic creep 180 10.5.4. Influence of temperature on the creep velocity 181 10.5.5. Shrinkage 182 10.5.6. Drying creep 182 10.5.7. Steel-concrete composite modeling 183 10.5.8. Statistical scale effect 184 10.6. Example simulation 185 10.6.1. Thermal and hydration simulation 185 Chapter 11. Recommendations for the use of Measurements on Mock-up Test Facilities and Structures 189 11.1. General methodology of the measurements 190 11.1.1. Preliminary general approach 192 11.1.2. Selection and choice of measuring devices 193 11.1.3. Method of measurement selection 194 11.1.4. Measurement data-mining and analysis 194 11.2. Mock-up measurements 196 11.2.1. Measurement of parameters 197 11.2.2. Data acquisition and storage 207 11.3. Measurement of structures 208 11.3.1. Preliminary measurements 210 11.3.2. Parameters to be measured 210 11.3.3. Equipment of the measurements 211 11.3.4. Formwork 212 11.4. Example of measurement instrumentation on massive structures 212 11.5. Example of mock-up test instrumentation 213 11.6. Conclusion 216 Bibliography 217 Index 225

About the Author

Francis Barre, G odynamique et Structure.Philippe Bisch, Egis Industries.Dani le Chauvel, EDF SEPTEN.Jacques Cortade, Consultant.Jean-Fran ois Coste, IESF.Jean-Philippe Dubois, Consultant.Silvano Erlicher, Egis.Etienne Gallitre, EDF SEPTEN.Pierre Labb , EDF.Jacky Mazars, University of Grenoble.Claude Rospars, IFSTTAR - EDF SEPTEN.Alain Sellier, LMDC, University of Toulouse.Jean-Michel Torrenti, IFSTTAR.

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