Computational Structural Concrete: Theory and Applications

Description

Concrete is by far the most used building material due to its advantages: it is shapeable, cost-effective and available everywhere. Combined with reinforcement it provides an immense bandwidth of properties and may be customized for a huge range of purposes. Thus, concrete is the building material of the 20th century. To be the building material of the 21th century its sustainability has to move into focus. Reinforced concrete structures have to be designed expending less material whereby their load carrying potential has to be fully utilized. Computational methods such as Finite Element Method (FEM) provide essential tools to reach the goal. In combination with experimental validation, they enable a deeper understanding of load carrying mechanisms. A more realistic estimation of ultimate and serviceability limit states can be reached compared to traditional approaches. This allows for a significantly improved utilization of construction materials and a broader horizon for innovative structural designs opens up. However, sophisticated computational methods are usually provided as black boxes. Data is fed in, the output is accepted as it is, but an understanding of the steps in between is often rudimentary. This has the risk of misinterpretations, not to say invalid results compared to initial problem definitions. The risk is in particular high for nonlinear problems. As a composite material, reinforced concrete exhibits nonlinear behaviour in its limit states, caused by interaction of concrete and reinforcement via bond and the nonlinear properties of the components. Its cracking is a regular behaviour. The book aims to make the mechanisms of reinforced concrete transparent from the perspective of numerical methods. In this way, black boxes should also become transparent. Appropriate methods are described for beams, plates, slabs and shells regarding quasi-statics and dynamics. Concrete creeping, temperature effects, prestressing, large displacements are treated as examples. State of the art concrete material models are presented. Both the opportunities and the pitfalls of numerical methods are shown. Theory is illustrated by a variety of examples. Most of them are performed with the ConFem software package implemented in Python and available under open-source conditions. Cover Half-Title Page Title Page Copyright Page Contents Preface List of Examples Notation 1 Introduction Why Read This Book? Topics of the Book How to Read This Book 2 Finite Elements Overview 2.1 Modelling Basics 2.2 Discretisation Outline 2.3 Elements 2.4 Material Behaviour 2.5 Weak Equilibrium 2.6 Spatial Discretisation 2.7 Numerical Integration 2.8 Equation Solution Methods 2.8.1 Nonlinear Algebraic Equations 2.8.2 Time Incrementation 2.9 Discretisation Errors 3 Uniaxial Reinforced Concrete Behaviour 3.1 Uniaxial Stress–Strain Behaviour of Concrete 3.2 Long–Term Behaviour – Creep and Imposed Strains 3.3 Reinforcing Steel Stress–Strain Behaviour 3.4 Bond between Concrete and Reinforcement 3.5 Smeared Crack Model 3.6 Reinforced Tension Bar 3.7 Tension Stiffening of Reinforced Bars 4 Structural Beams and Frames 4.1 Cross-Sectional Behaviour 4.1.1 Kinematics 4.1.2 Linear Elastic Behaviour 4.1.3 Cracked Reinforced Concrete Behaviour 4.2 Equilibrium of Beams 4.3 Finite Elements for Plane Beams 4.3.1 Timoshenko Beam 4.3.2 Bernoulli Beam 4.4 System Building and Solution 4.4.1 Integration 4.4.2 Transformation and Assembling 4.4.3 Kinematic Boundary Conditions and Solution 4.4.4 Shear Stiffness 4.5 Creep of Concrete 4.6 Temperature and Shrinkage 4.7 Tension Stiffening 4.8 Prestressing 4.9 Large Displacements – Second-Order Analysis 4.10 Dynamics 5 Strut-and-Tie Models 5.1 Elastic Plate Solutions 5.2 Strut-and-Tie Modelling 5.3 Solution Methods for Trusses 5.4 Rigid Plastic Truss Models 5.5 Application Aspects 6 Multi-Axial Concrete Behaviour 6.1 Basics 6.1.1 Continua and Scales 6.1.2 Characteristics of Concrete Behaviour 6.2 Continuum Mechanics 6.2.1 Displacements and Strains 6.2.2 Stresses and Material Laws 6.2.3 Coordinate Transformations and Principal States 6.3 Isotropy, Linearity, and Orthotropy 6.3.1 Isotropy and Linear Elasticity 6.3.2 Orthotropy 6.3.3 Plane Stress and Strain 6.4 Nonlinear Material Behaviour 6.4.1 Tangential Stiffness 6.4.2 Principal Stress Space and Isotropic Strength 6.4.3 Strength of Concrete 6.4.4 Nonlinear Material Classification 6.5 Elasto-Plasticity 6.5.1 A Framework for Multi-Axial Elasto-Plasticity 6.5.2 Pressure-Dependent Yield Functions 6.6 Damage 6.7 Damaged Elasto-Plasticity 6.8 The Microplane Model 6.9 General Requirements for Material Laws 7 Crack Modelling and Regularisation 7.1 Basic Concepts of Crack Modelling 7.2 Mesh Dependency 7.3 Regularisation 7.4 Multi-Axial Smeared Crack Model 7.5 Gradient Methods 7.5.1 Gradient Damage 7.5.2 Phase Field 7.5.3 Assessment of Gradient Methods 7.6 Overview of Discrete Crack Modelling 7.7 The Strong Discontinuity Approach 7.7.1 Kinematics 7.7.2 Equilibrium and Material Behaviour 7.7.3 Coupling 8 Plates 8.1 Lower Bound Limit State Analysis 8.1.1 General Approach 8.1.2 Reinforced Concrete Resistance 8.1.3 Reinforcement Design 8.2 Cracked Concrete Modelling 8.3 Reinforcement and Bond 8.4 Integrated Reinforcement 8.5 Embedded Reinforcement with a Flexible Bond 9 Slabs 9.1 Classification 9.2 Cross-Sectional Behaviour 9.2.1 Kinematics 9.2.2 Internal Forces 9.3 Equilibrium of Slabs 9.3.1 Strong Equilibrium 9.3.2 Weak Equilibrium 9.3.3 Decoupling 9.4 Reinforced Concrete Cross-Sections 9.5 Slab Elements 9.5.1 Area Coordinates 9.5.2 Triangular Kirchhoff Slab Element 9.6 System Building and Solution Methods 9.7 Lower Bound Limit State Analysis 9.7.1 Design for Bending 9.7.2 Design for Shear 9.8 Nonlinear Kirchhoff Slabs 9.8.1 Basic Approach 9.8.2 Simple Moment–Curvature Behaviour 9.8.3 Extended Moment–Curvature Behaviour 9.9 Upper Bound Limit State Analysis 10 Shells 10.1 Geometry and Displacements 10.2 Deformations 10.3 Shell Stresses and Material Laws 10.4 System Building 10.5 Slabs and Beams as a Special Case 10.6 Locking 10.7 Reinforced Concrete Shells 10.7.1 Layer Model 10.7.2 Slabs As a Special Case 11 Randomness and Reliability 11.1 Uncertainty and Randomness 11.2 Failure Probability 11.2.1 Linear Limit Condition 11.2.2 Nonlinear Limit Condition 11.2.3 Multiple Limit Conditions 11.3 Design and Safety Factors 11.3.1 Safety Factor Basics 11.3.2 Partial Safety Factor Application 12 Concluding Remarks Appendix A Solution Methods A.1 Nonlinear Algebraic Equations A.2 Transient Analysis A.3 Stiffness for Linear Concrete Compression A.4 The Arc Length Method Appendix B Material Stability Appendix C Crack Width Estimation Appendix D Transformations of Coordinate Systems Appendix E Regression Analysis References Index