Computational Methods for Reinforced Concrete Structures.

Cover -- Title Page -- Preface -- Contents -- Notations -- 1 Finite Elements Overview -- 1.1 Modeling Basics -- 1.2 Discretization Outline -- 1.3 Elements -- 1.4 Material Behavior -- 1.5 Weak Equilibrium and Spatial Discretization -- 1.6 Numerical Integration and Solution Methods for Algebraic Systems -- 1.7 Convergence -- 2 Uniaxial Structural Concrete Behavior -- 2.1 Scales and Short-Term Stress-Strain Behavior of Homogenized Concrete -- 2.2 Long-Term Behavior - Creep and Imposed Strains -- 2.3 Reinforcing Steel Stress-Strain Behavior -- 2.4 Bond between Concrete and Reinforcing Steel -- 2.5 The Smeared Crack Model -- 2.6 The Reinforced Tension Bar -- 2.7 Tension Stiffening of Reinforced Tension Bar -- 3 Structural Beams and Frames -- 3.1 Cross-Sectional Behavior -- 3.1.1 Kinematics -- 3.1.2 Linear Elastic Behavior -- 3.1.3 Cracked Reinforced Concrete Behavior -- 3.1.3.1 Compressive Zone and Internal Forces -- 3.1.3.2 Linear Concrete Compressive Behavior with Reinforcement -- 3.1.3.3 Nonlinear Behavior of Concrete and Reinforcement -- 3.2 Equilibrium of Beams -- 3.3 Finite Element Types for Plane Beams -- 3.3.1 Basics -- 3.3.2 Finite Elements for the Bernoulli Beam -- 3.3.3 Finite Elements for the Timoshenko Beam -- 3.4 System Building and Solution Methods -- 3.4.1 Elementwise Integration -- 3.4.2 Transformation and Assemblage -- 3.4.3 Kinematic Boundary Conditions and Solution -- 3.5 Further Aspects of Reinforced Concrete -- 3.5.1 Creep -- 3.5.2 Temperature and Shrinkage -- 3.5.3 Tension Stiffening -- 3.5.4 Shear Stiffness for Reinforced Cracked Concrete Sections -- 3.6 Prestressing -- 3.7 Large Deformations and Second-Order Analysis -- 3.8 Dynamics of Beams -- 4 Strut-and-Tie Models -- 4.1 Elastic Plate Solutions -- 4.2 Modeling -- 4.3 Solution Methods for Trusses -- 4.4 Rigid-Plastic Truss Models -- 4.5 More Application Aspects.

5 Multiaxial Concrete Material Behavior -- 5.1 Basics -- 5.1.1 Continua and Scales -- 5.1.2 Characteristics of Concrete Behavior -- 5.2 Continuum Mechanics -- 5.2.1 Displacements and Strains -- 5.2.2 Stresses and Material Laws -- 5.2.3 Coordinate Transformations and Principal States -- 5.3 Isotropy, Linearity, and Orthotropy -- 5.3.1 Isotropy and Linear Elasticity -- 5.3.2 Orthotropy -- 5.3.3 Plane Stress and Strain -- 5.4 Nonlinear Material Behavior -- 5.4.1 Tangential Stiffness -- 5.4.2 Principal Stress Space and Isotropic Strength -- 5.4.3 Strength of Concrete -- 5.4.4 Phenomenological Approach for the Biaxial Anisotropic Stress-Strain Behavior -- 5.5 Isotropic Plasticity -- 5.5.1 A Framework for Multiaxial Elastoplasticity -- 5.5.2 Pressure-Dependent Yield Functions -- 5.6 Isotropic Damage -- 5.7 Multiaxial Crack Modeling -- 5.7.1 Basic Concepts of Crack Modeling -- 5.7.2 Multiaxial Smeared Crack Model -- 5.8 The Microplane Model -- 5.9 Localization and Regularization -- 5.9.1 Mesh Dependency -- 5.9.2 Regularization -- 5.9.3 Gradient Damage -- 5.10 General Requirements for Material Laws -- 6 Plates -- 6.1 Lower Bound Limit Analysis -- 6.1.1 The General Approach -- 6.1.2 Reinforced Concrete Contributions -- 6.1.3 A Design Approach -- 6.2 Crack Modeling -- 6.3 Linear Stress-Strain Relations with Cracking -- 6.4 2D Modeling of Reinforcement and Bond -- 6.5 Embedded Reinforcement -- 7 Slabs -- 7.1 A Placement -- 7.2 Cross-Sectional Behavior -- 7.2.1 Kinematic and Kinetic Basics -- 7.2.2 Linear Elastic Behavior -- 7.2.3 Reinforced Cracked Sections -- 7.3 Equilibrium of Slabs -- 7.3.1 Strong Equilibrium -- 7.3.2 Weak Equilibrium -- 7.3.3 Decoupling -- 7.4 Structural Slab Elements -- 7.4.1 Area Coordinates -- 7.4.2 A Triangular Kirchhoff Slab Element -- 7.5 System Building and Solution Methods -- 7.6 Lower Bound Limit Analysis.

7.6.1 General Approach and Principal Moments -- 7.6.2 Design Approach for Bending -- 7.6.3 Design Approach for Shear -- 7.7 Kirchhoff Slabs with Nonlinear Material Behavior -- 8 Shells -- 8.1 Approximation of Geometry and Displacements -- 8.2 Approximation of Deformations -- 8.3 Shell Stresses and Material Laws -- 8.4 System Building -- 8.5 Slabs and Beams as a Special Case -- 8.6 Locking -- 8.7 Reinforced Concrete Shells -- 8.7.1 The Layer Model -- 8.7.2 Slabs as Special Case -- 8.7.3 The Plastic Approach -- 9 Randomness and Reliability -- 9.1 Basics of Uncertainty and Randomness -- 9.2 Failure Probability -- 9.3 Design and Safety Factors -- Appendix A: Solution of Nonlinear Algebraic Equation Systems -- Appendix B: Crack Width Estimation -- Appendix C: Transformations of Coordinate Systems -- Appendix D: Regression Analysis -- Appendix E: Reliability with Multivariate Random Variables -- Appendix F: Programs and Example Data -- Bibliography -- Index.

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