Optimization Aided Design: Reinforced Concrete
Concrete is the most used building material. Its main component, cement, however, accounts production- related for up to 10 % of global CO2 emissions and is therefore a major contributor to human-induced climate change. Due to its low tensile strength, concrete must be further enhanced in tension with adequate reinforcement, such as steel. Producing the latter therefore additionally impacts the environment. Consequently, reducing the material amount for design and construction of structures, thus lowering material- and transport-induced emissions, represents a key element to climate protection. In this context, meeting the essential requirements - sustainability, serviceability, durability - is yet indispensable.
The book presents innovative optimization aided design methods for concrete structures. Mathematical optimization is applied to practical problems of structural concrete at each level: from external, through internal structure identification to cross-section design. It is shown how to design resource-efficient structures following the flux of forces, how to optimally adapt reinforcement layouts to the internal force flow, and how to efficiently cope with demanding cross-sectional design tasks such as biaxial bending.
The optimization aided design methods are discussed in detail and described vividly. They are independent of standards, concrete material (normal to ultra-high performance) and reinforcement type (steel fibers to carbon bars), thus universally applicable. The book illustrates the different approaches with numerous figures and calculation examples. Existing applications in structural engineering are presented to demonstrate the potential of optimization aided design concepts, including ultra-lightweight hybrid beams, thin concrete solar collectors, and improved reinforcement layouts for tunnel lining segments.
Table of Contents:
Foreword by Manfred Curbach v
Foreword by Werner Sobek ix
Preface xiii
List of Examples xix
Acronyms xxi
About the Authors xxiii
Acknowledgments xxv
1 Introduction 1
1.1 Preliminaries 1
1.2 Outer and Inner Shaping 2
1.3 Environmental Demands 6
1.4 Optimization Aided Design (OAD) 11
1.5 Structure of the Book 14
2 Fundamentals of Reinforced Concrete (RC) Design 19
2.1 Basic Principles 19
2.2 Verification Concept 21
2.3 Safety Concept 22
2.4 Materials 23
2.4.1 Plain Concrete 23
2.4.2 Fiber-Reinforced Concrete (FRC) 24
2.4.3 Ultra-High Performance Concrete (UHPC) 26
2.4.4 Reinforcement 27
2.5 Load-Bearing Behavior 28
2.5.1 Bending Design 28
2.5.1.1 Fundamentals 28
2.5.1.2 Equilibrium for Composite Sections 29
2.5.2 Strut-and-Tie Models (STMs) 32
3 Fundamentals of Structural Optimization 37
3.1 Structural Optimization Approaches 37
3.1.1 General Procedure 37
3.1.2 Classification of Methods 38
3.2 Problem Statement 40
3.3 Lagrange Function 43
3.4 Sensitivity Analysis 44
3.4.1 Numerical Approach 44
3.4.2 Analytical Approach 45
3.5 Solution Methods 46
3.5.1 Mathematical Programming 46
3.5.2 Optimality Conditions (OC) 47
4 Identification of Structures 51
4.1 One-material Structures 52
4.1.1 Problem Statement 52
4.1.2 Sensitivity Analysis 54
4.1.3 Filtering 54
4.1.4 Solving 56
4.1.5 Optimization Process 57
4.1.6 Multiple Load Cases 58
4.2 One-material Stress-biased Structures 59
4.2.1 Problem Statement 59
4.2.2 Sensitivity Analysis and Stress Bias 60
4.2.3 Solving 62
4.2.4 Optimization Process 63
4.3 Bi-material Structures 64
4.3.1 Problem Statement 64
4.3.2 Sensitivity Analysis and Stress Differentiation 65
4.3.3 Bi-material Filtering 68
4.3.4 Solving 69
4.3.5 Optimization Process 70
4.4 Examples 71
4.4.1 One-material Structures 71
4.4.2 One-material Stress-biased Structures 81
4.4.3 Bi-material Structures 83
4.5 Applications 89
4.5.1 Solar Thermal Collectors 89
4.5.1.1 Parabolic Trough Collectors 90
4.5.1.2 Heliostats 95
4.5.2 Ultra-light Beams 100
5 Internal Force Flow 109
5.1 Preliminaries 110
5.2 Continuum Topology Optimization (CTO) Approach 111
5.3 Truss Topology Optimization (TTO) Approach 112
5.3.1 Problem Statement 112
5.3.2 Sensitivity Analysis and Solving 117
5.3.3 Optimization Process 119
5.3.4 Recommendations for Practical Application 120
5.3.4.1 Setting Up the Optimization Problem 120
5.3.4.2 Procedure 123
5.4 Continuum-Truss Topology Optimization (CTTO) Approach 124
5.4.1 Problem Statement 125
5.4.2 Sensitivity Analysis and Solving 128
5.4.3 Post-Processing 130
5.4.4 Optimization Process 132
5.5 Examples 133
5.5.1 CTO Approach 133
5.5.2 TTO Approach 138
5.6 Applications 151
5.6.1 Joints in Tunnel Linings 151
5.6.2 Partial Area Loading in Tunnel Linings 153
6 Design of Cross-sections 157
6.1 Problem Statement 159
6.2 Equilibrium Iteration 161
6.3 Sectional Optimization 163
6.3.1 Reinforcement Amounts 165
6.3.2 Cross-sectional Layout 165
6.3.3 Material Weighting 165
6.4 Solving 166
6.4.1 Stress Integrals 166
6.4.2 Optimization Problem 167
6.5 Parameterization 167
6.5.1 Plane Case 167
6.5.2 Spatial Case 168
6.5.3 Parameterization with Intentional Steering 169
6.6 Examples 170
6.6.1 Equilibrium Iteration 170
6.6.2 Sectional Optimization 175
References 183
About the Author :
Georgios Gaganelis is a structural designer for civil engineering structures and a freelance consultant in structural optimization. 2020 he received his PhD at the Ruhr University Bochum, Germany in the field of optimization strategies for concrete and steel-concrete-composite structures. His research interest focus on topology optimization and material driven steering. A special focus lies on ultra-light structures requiring minimal material efforts.
Peter Mark is a full professor for Structural Concrete at the Ruhr University Bochum, Germany. He is researching on applied optimization methods and lightweight concrete structures since 20 years. He received his PhD in 1994 and the post-doctoral degree in 2006. He is Consultant Engineer and Independent Checking Engineer since 2008 and involved in several bridge, tunnel and building construction projects.
Patrick Forman is a post-doctoral research fellow at the Institute of Concrete Structures at Ruhr University Bochum, Germany. He received his PhD in 2016. More than 10 years he is researching on lightweight shell and beam structures made of high-performance materials using various structural optimization techniques. Currently, he is technical and managing director of an interdisciplinary research centre on adaptive modularized construction methods.
Georgios Gaganelis ist Planungsingenieur für Ingenieurbauwerke und freiberuflicher Berater im Bereich der Strukturoptimierung. Seine Promotion erhielt er 2020 an der Ruhr-Universität Bochum mit einer Arbeit über Optimierungsstrategien für Beton- und Stahl-Beton-Verbundtragwerke. Seine Forschungsinteressen liegen in der topologischen Optimierung und der baustoffgerechten Steuerung der Formfindung. Ein Schwerpunkt liegt auf ultra-leichten Konstruktionen, die mit minimalen Materialmengen auskommen.
Peter Mark ist Universitätsprofessor für Massivbau an der Ruhr-Universität in Bochum. Er forscht auf den Gebieten der angewandten Optimierungsmethoden und des Betonleichtbaus seit 20 Jahren. Er promovierte 1994 und habilitierte sich 2006. Er ist Beratender Ingenieur und Prüfingenieur für Baustatik seit 2008 und maßgeblich beteiligt an zahlreichen Projekten des Brücken-, Tunnel- und Hochbaus.
Patrick Forman ist Oberingenieur am Lehrstuhl für Massivbau an der Ruhr-Universität Bochum. Seine Promotion schloss er 2016 ab. Seit über 10 Jahren forscht er zu leichten Schalen und Stabstrukturen aus Hochleistungsmaterialien mit verschiedenartigen Optimierungsmethoden. Aktuell ist er Geschäftsführer und technischer Leiter eines interdisziplinären Großforschungsprogramms zu adaptiven Modulbauweisen.
Review :
There is hardly a topic among building professionals that is discussed more intensively than sustainable construction. (?) In view of the continuing increase in the world's population, we will not build less, but more. Contrary to this, we need to radically limit resource consumption and CO2 emissions. It is obvious that in the future, building will have to be completely different, not just marginally, but fundamentally. (?)
The methods, procedures and calculations described in this book represent an important step towards a kind of building that has little to do with the way we know it today. And this is a good thing.
(Prof. Dr.-Ing. Dr.-Ing. E. h. Manfred Curbach in his foreword.)
The introduction of state-of-the-art optimization methods [to concrete design] and the resulting minimum-material component shapes, which also have a minimized need for reinforcing steel (?), promote construction with concrete that is characterized by considerable material savings and thus considerable emission savings for the same utility value and durability. Supported by clearly understandable descriptions and a large number of examples, readers will find their way around quickly and easily. This makes it much easier to understand the subject matter, which is not always simple.
This book provides a significant contribution to establishing a new foundation for building with concrete, this wonderful building material for everyone and for almost everything.
(Prof. em. Dr. Dr. E. h. Dr. h. c. Werner Sobek in his foreword.)
