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    Yield Design

    Jean Salenç\;on|2013.12.01

    Preface xi

    Chapter 1. Origins and Topicality of a Concept 1

    1.1. Historical milestones 1

    1.2. Topicality of the yield design approach 8

    1.3. Bibliography 11

    Chapter 2. An Introductory Example of the Yield Design Approach 19

    2.1. Setting the problem 19

    2.2. Potential stability of the structure 22

    2.3. To what extent potential stability is a relevant concept? 24

    2.4. Bibliography 28

    Chapter 3. The Continuum Mechanics Framework 29

    3.1. Modeling the continuum 29

    3.2. Dynamics 34

    3.3. The theory of virtual work 41

    3.4. Statically and kinematically admissible fields 46

    3.5. Bibliography 48

    Chapter 4. Primal Approach of the Theory of Yield Design 51

    4.1. Settlement of the problem 51

    4.2. Potentially safe loads 57

    4.3. Comments 60

    4.4. Some usual isotropic strength criteria 66

    4.5. Bibliography 70

    Chapter 5. Dual Approach of the Theory of Yield Design 73

    5.1. A static exterior approach 73

    5.2. A kinematic necessary condition 76

    5.3. The π functions 78

    5.4. π functions for usual isotropic strength criteria 84

    5.5. Bibliography 88

    Chapter 6. Kinematic Exterior Approach 91

    6.1. Equation of the kinematic exterior approach 91

    6.2. Relevant virtual velocity fields 94

    6.3. One domain, two approaches 100
     
    6.4. Bibliography 107

    Chapter 7. Ultimate Limit State Design from the Theory of Yield Design 111

    7.1. Basic principles of ultimate limit state design 111

    7.2. Revisiting the yield design theory in the context of ULSD 113

    7.3. The yield design theory applied to ULSD 114

    7.4. Conclusion 117

    7.5. Bibliography 118

    Chapter 8. Optimality and Probability Approaches of Yield Design 119

    8.1. Optimal dimensioning and probabilistic approach 119

    8.2. Domain of potential stability 120

    8.3. Optimal dimensioning 130

    8.4. Probabilistic approach of yield design 133

    8.5. Bibliography 141

    Chapter 9. Yield Design of Structures 145

    9.1. The curvilinear one-dimensional continuum 145

    9.2. Implementation of the yield design theory 157

    9.3. Typical strength criteria 164

    9.4. Final comments 172

    9.5. Bibliography 174

    Chapter 10. Yield Design of Plates: the Model 177

    10.1. Modeling plates as two-dimensional continua 177

    10.2. Dynamics 182

    10.3. Theorem/principle of virtual work 191

    10.4. Plate model derived from the three-dimensional continuum 198

    10.5. Bibliography 204

    Chapter 11. Yield Design of Plates Subjected to Pure Bending 205

    11.1. The yield design problem 205

    11.2. Implementation of the yield design theory 208

    11.3. Strength criteria and π functions 213

    11.4. Final comments 226

    11.5. Bibliography 234

    Index 237

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