| Preface |
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ix | |
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1 | (6) |
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Chapter 2 Prerequisites of the Mini-Max Principle |
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7 | (34) |
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2.1 History of the Principle |
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7 | (4) |
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11 | (2) |
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2.3 Bearing Capacity of Continuous Beam at Complicated Loading Configuration |
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13 | (2) |
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2.4 Horn's Theorem and Its Review |
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15 | (3) |
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2.5 Solving Certain Problems Using Ultimate Equilibrium Method |
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18 | (14) |
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2.6 Convexity of a Region, Defined by Plasticity Equations for Compressed Elements |
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32 | (3) |
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2.7 Duality Theorems for Simple Plastic Failure |
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35 | (1) |
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2.8 Consequence of the Ultimate Equilibrium theorems |
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36 | (2) |
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2.9 Unity of Internal Forces' Fields at Realization of the Kinematic Failure Mechanism |
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38 | (1) |
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39 | (2) |
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Chapter 3 Mini-Max Principle as a Tool for Calculation of RC Structural Bearing Capacity |
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41 | (32) |
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3.1 Two Groups of Parameters for Calculating the Structural Bearing Capacity |
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41 | (3) |
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3.2 Mini-Max Principle and an Alternative Maxi-Min Principle |
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44 | (4) |
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3.3 Presenting the Two-Parametric Structural Bearing Capacity Function As a Functional |
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48 | (2) |
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3.4 Some Definitions from the Theory of Sets |
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50 | (1) |
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3.5 The Basic Concepts in the Theory of Antagonistic Games with a Zero Sum |
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51 | (3) |
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3.6 Two-Parametric Function of Structural Bearing Capacity in Games' Theory Terms |
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54 | (16) |
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3.8 Difference between Mini-Max Principle and Optimization Problems |
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70 | (3) |
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Chapter 4 Using the Mini-Max Principle in Calculating the Bearing Capacity of RC Structures |
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73 | (40) |
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4.1 Interaction between the Internal Forces in Thin-Walled Elasto-Plastic Shells |
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73 | (3) |
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4.2 Calculating the Bearing Capacity of an RC Shell Using a Five Disks Failure Scheme |
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76 | (3) |
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4.3 Calculating the Bearing Capacity of a Ribbed RC Shell Using a Five Disks Failure Scheme |
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79 | (2) |
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4.4 Calculating the Bearing Capacity of a Ribbed RC Shell with Variable Ribs' Height Using a Five Disks Failure Scheme |
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81 | (4) |
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4.5 Calculating Bearing Capacity of an RC Tube |
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85 | (2) |
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4.6 Calculating the Bearing Capacity of a Polygonal RC Plate Under Concentrated Load |
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87 | (4) |
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4.7 Calculating the Bearing Capacity of a Ferro-Cement Shell Panel |
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91 | (3) |
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4.8 Calculating the Bearing Capacity of a Pre-Cast RC Shell Element |
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94 | (2) |
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4.9 Critical Impulse on Statically Loaded Shell |
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96 | (5) |
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4.10 Precising the Bearing Capacity of RC Dome under Concentrated Loading |
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101 | (3) |
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4.11 Calculating Parameters of Drift Shapes in Statically Pre-Loaded RC Shells under Seismic Excitation |
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104 | (4) |
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4.12 Using the Mini-Max Principle for Verifying Existing Design Approaches for RC Shells |
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108 | (1) |
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4.13 Approximate Estimation of the Compressed Concrete Zone Depth in RC Shell Section |
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109 | (2) |
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4.14 Maximization by Section Compressed Zone Depth As Additional Condition for Design of Compressed RC Elements with Double Reinforcement |
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111 | (2) |
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113 | (4) |
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Appendix 1 Variation Principles, Forming a Basis for the Mini-Max Principle |
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113 | (1) |
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Appendix 2 The Only Possible Rigid Body Stress Condition As a Basis for the Mini-Max Principle |
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114 | (3) |
| References |
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117 | (4) |
| Authors' Contact Information |
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121 | (2) |
| Index |
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123 | |
