Computational Structural Concrete

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.
Beton ist aufgrund seiner Vorteile der mit Abstand meistverwendete Baustoff: er ist formbar, preiswert und überall verfügbar. Kombiniert mit Bewehrung bietet dies eine immense Bandbreite an Eigenschaften und kann für eine Vielzahl von Zwecken angepasst werden. Damit ist Beton der Baustoff des 20. Jahrhunderts. Um der Baustoff des 21. Jahrhunderts zu sein, muss seine Nachhaltigkeit in den Fokus rücken. Bewehrte Betonkonstruktionen müssen mit geringerem Materialaufwand konstruiert werden, wobei ihr Tragfähigkeitspotential optimal ausgeschöpft werden muss.
Computergestützte Methoden wie die Finite-Elemente-Methode (FEM) bieten wesentliche Werkzeuge, um das Ziel zu erreichen. In Kombination mit experimenteller Validierung ermöglichen sie ein tieferes Verständnis der Tragmechanismen. Im Vergleich zu herkömmlichen Ansätzen kann eine realistischere Abschätzung der Grenzzustände der Tragfähigkeit und der Gebrauchstauglichkeit erreicht werden. Dies ermöglicht eine deutlich verbesserte Ausnutzung der Baustoffe. Damit eröffnet sich auch ein weiterer Horizont für innovative Tragwerksentwürfe.
Anspruchsvolle numerische Rechenverfahren werden aber in der Regel als "Black Boxes" bereitgestellt. Daten werden eingegeben, die Ausgaben ungeprüft übernommen, aber das Verständnis für die dazwischenliegenden Schritte ist oft rudimentär. Dies birgt die Gefahr von Fehlinterpretationen, um nicht zu sagen ungültigen Ergebnissen im Vergleich zu den getroffenen Problemdefinitionen. Das Risiko ist insbesondere bei nichtlinearen Problemen hoch. Bewehrter Beton weist als Verbundmaterial in seinen Grenzzuständen ein nichtlineares Verhalten auf, verursacht durch Verbund und nichtlineare Eigenschaften seiner Bestandteile. Seine Rissbildung ist ein reguläres Verhalten. In diesem Buch werden die Mechanismen des bewehrten Betons unter dem Blickwinkel numerischer Methoden aufgezeigt. So sollen auch "Black Boxes" transparent werden.
Das Buch beschreibt entsprechende Methoden für Balken, Scheiben, Platten und Schalen im Rahmen von Quasi-Statik und Dynamik. Betonkriechen, Temperatureinwirkungen, Vorspannung, große Verformungen werden beispielhaft behandelt. Weiterhin werden aktuelle Materialmodelle für Beton dargestellt. Dabei werden sowohl die Möglichkeiten als auch die Fallstricke numerischer Methoden aufgezeigt. Die Theorie wird durch eine Vielzahl von Beispielen veranschaulicht. Die meisten von ihnen werden mit dem in Python implementierten und unter Open-Source-Bedingungen verfügbaren Softwarepaket ConFem durchgeführt. Preface
Notations
List of Examples
1 INTRODUCTION
2 FINITE ELEMENTS OVERVIEW
2.1 Modeling Basics
2.2 Discretization Outline
2.3 Elements
2.4 Material Behavior
2.5 Weak Equilibrium
2.6 Spatial Discretization
2.7 Numerical Integration
2.8 Equation Solution Methods
2.9 Discretization Errors
3 UNIAXIAL STRUCTURAL CONCRETE BEHAVIOR
3.1 Uniaxial Stress-Strain Behavior of Concrete
3.2 Long-Term Behavior -
Creep and Imposed Strains
3.3 Reinforcing Steel Stress-Strain Behavior
3.4 Bond between Concrete and Reinforcement
3.5 The Smeared Crack Model
3.6 The Reinforced Tension Bar
3.7 Tension Stiffening of Reinforced Bar
4 STRUCTURAL BEAMS AND FRAMES
4.1 Cross-Sectional Behavior
4.2 Equilibrium of Beams
4.3 Finite Element Types for Plane Beams
4.4 System Building and Solution
4.5 Creep of Concrete
4.6 Temperature and Shrinkage
4.7 Tension Stiffening
4.8 Prestressing
4.9 Large Displacements -
2nd-Order Analysis
4.10 Dynamics
5 STRUT-AND-TIE MODELS
5.1 Elastic Plate Solutions
5.2 Strut-and-Tie Modeling
5.3 Solution Methods for Trusses
5.4 Rigid-Plastic Truss Models
5.5 Application Aspects
6 MULTIAXIAL CONCRETE MATERIAL BEHAVIOR
6.1 Basics
6.1.1 Continua and Scales
6.1.2 Characteristics of Concrete Behavior
6.2 Continuum Mechanics
6.3 Isotropy, Linearity, and Orthotropy
6.4 Nonlinear Material Behavior
6.5 Elastoplasticity
6.6 Damage
6.7 Damaged Elastoplasticity
6.8 The Microplane Model
6.9 General Requirements for Material Laws
7 CRACK MODELING AND REGULARIZATION
7.1 Basic Concepts of Crack Modeling
7.2 Mesh Dependency
7.3 Regularization
7.4 Multiaxial Smeared Crack Model
7.5 Gradient Methods
7.6 Discrete Crack Modeling Overview
7.7 A Strong Discontinuity Approach
8 PLATES
8.1 Lower Bound Limit Analysis
8.2 Cracked Concrete Modeling
8.3 Reinforcement and Bond
8.4 Integrated Reinforcement
8.5 Embedded Reinforcement with Flexible Bond
9 SLABS
9.1 Classification
9.2 Cross-Sectional Behavior
9.3 Equilibrium of Slabs
9.4 Reinforced Concrete Cross Sections
9.5 Slab Elements
9.6 System Building and Solution Methods
9.7 Lower Bound Limit State Analysis
9.8 Nonlinear Kirchhoff Slabs
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
11 RANDOMNESS AND RELIABILITY
11.1 Uncertainty and Randomness
11.2 Failure Probability
11.3 Design and Safety Factors
12 CONCLUDING REMARKS
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
B MATERIAL STABILITY
C CRACK WIDTH ESTIMATION
D TRANSFORMATIONS OF COORDINATE SYSTEMS
E REGRESSION ANALYSIS
INDEX
LIST OF EXAMPLES
3.1 Tension bar with localization
3.2 Tension bar with creep and imposed strains
3.3 Simple uniaxial smeared crack model
3.4 Reinforced concrete tension bar
4.1 Moment-curvature relations for given normal forces
4.2 Simple reinforced concrete (RC) beam
4.3 Creep deformations on RC beam
4.4 Effect of temperature actions on a RC beam
4.5 Effect of tension stiffening on a RC beam with external and temperature loading
4.6 Prestressed RC beam
4.7 Stability limit of cantilever column
4.8 Ultimate limit for RC cantilever column
4.9 Beam under impact load
5.1 Continuous interpolation of stress fields with the quad element
5.2 Deep beam with strut-and-tie model
5.3 Corbel with an elastoplastic strut-and-tie model
6.1 Mises elastoplasticity for uniaxial behavior
6.2 Uniaxial stress-strain relations with Hsieh-Ting-Chen damage
6.3 Stability of Hsieh-Ting-Chen uniaxial damage
6.4 Microplane uniaxial stress-strain relations with de Vree damage
7.1 Plain concrete plate with notch
7.2 Plain concrete plate with notch and crack band regularization
7.3 2D smeared crack model with elasticity
7.4 Gradient damage formulation for the uniaxial two-node bar
7.5 Phase field formulation for the uniaxial tension bar
7.6 Plain concrete plate with notch and SDA crack modeling
8.1 Reinforcement design for a deep beam with a limit state analysis
8.2 Simulation of cracked reinforced deep beam
8.3 Simulation of a single fiber connecting a dissected continuum
8.4 Reinforced concrete plate regarding flexible bond
9.1 Linear elastic rectangular slab with opening and free edges
9.2 Reinforcement design for a slab with opening and free edges with a limit state analysis
9.3 Computation of shear forces and shear design
9.4 Elastoplastic slab with opening and free edges
9.5 Simple RC slab under concentrated loading
9.6 Simple RC slab with yield line method and distributed loading
9.7 Simple RC slab with yield line method and concentrated loading
10.1 Convergence study for linear simple slab
10.2 Simple RC slab with interaction of normal forces and bending
11.1 Analytical failure probability of cantilever column
11.2 Approximate failure probability of cantilever column with a Monte Carlo integration
11.3 Simple partial safety factor derivation

Ulrich Häussler-Combe studied structural engineering at the Technical University Dortmund and gained his doctorate from the University Karlsruhe. Following ten years of construction engineering and development in computational engineering, he came back to the University Karlsruhe as a lecturer for computer aided design and structural dynamics. In 2003 he was appointed as professor for special concrete structures at the Technical University Dresden. He retired in 2021 and currently is still active as guest professor at the Technical University Munich.

Ulrich Häussler-Combe studierte Bauingenieurwesen mit Vertiefung Konstruktiver Ingenieurbau an der TU Dortmund und promovierte an der TH Karlsruhe. Nach zehn Jahren Ingenieurpraxis und Programmentwicklung in der Industrie kehrte er zurück an die Universität Karlsruhe und lehrte dort CAD und Praktische Baudynamik. Im Jahr 2003 wurde er Universitätsprofessor für Spezielle Massivbauwerke am Institut für Massivbau der TU Dresden. Seit 2021 ist er im Ruhestand, dabei noch als Gastprofessor an der Technischen Universität München aktiv.