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.

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.)

• Foreword by Manfred Curbach vForeword by Werner Sobek ixPreface xiiiList of Examples xixAcronyms xxiAbout the Authors xxiiiAcknowledgments xxv1 Introduction 11.1 Preliminaries 11.2 Outer and Inner Shaping 21.3 Environmental Demands 61.4 Optimization Aided Design (OAD) 111.5 Structure of the Book 14References 152 Fundamentals of Reinforced Concrete (RC) Design 192.1 Basic Principles 192.2 Verification Concept 212.3 Safety Concept 222.4 Materials 232.4.1 Plain Concrete 232.4.2 Fiber-Reinforced Concrete (FRC) 242.4.3 Ultra-High Performance Concrete (UHPC) 262.4.4 Reinforcement 272.5 Load-Bearing Behavior 282.5.1 Bending Design 282.5.1.1 Fundamentals 282.5.1.2 Equilibrium for Composite Sections 292.5.2 Strut-and-Tie Models (STMs) 32References 353 Fundamentals of Structural Optimization 373.1 Structural Optimization Approaches 373.1.1 General Procedure 373.1.2 Classification of Methods 383.2 Problem Statement 403.3 Lagrange Function 433.4 Sensitivity Analysis 443.4.1 Numerical Approach 443.4.2 Analytical Approach 453.5 Solution Methods 463.5.1 Mathematical Programming 463.5.2 Optimality Conditions (OC) 47References 474 Identification of Structures 514.1 One-material Structures 524.1.1 Problem Statement 524.1.2 Sensitivity Analysis 544.1.3 Filtering 544.1.4 Solving 564.1.5 Optimization Process 574.1.6 Multiple Load Cases 584.2 One-material Stress-biased Structures 594.2.1 Problem Statement 594.2.2 Sensitivity Analysis and Stress Bias 604.2.3 Solving 624.2.4 Optimization Process 634.3 Bi-material Structures 644.3.1 Problem Statement 644.3.2 Sensitivity Analysis and Stress Differentiation 654.3.3 Bi-material Filtering 684.3.4 Solving 694.3.5 Optimization Process 704.4 Examples 714.4.1 One-material Structures 714.4.2 One-material Stress-biased Structures 814.4.3 Bi-material Structures 834.5 Applications 894.5.1 Solar Thermal Collectors 894.5.1.1 Parabolic Trough Collectors 904.5.1.2 Heliostats 954.5.2 Ultra-light Beams 100References 1025 Internal Force Flow 1095.1 Preliminaries 1105.2 Continuum Topology Optimization (CTO) Approach 1115.3 Truss Topology Optimization (TTO) Approach 1125.3.1 Problem Statement 1125.3.2 Sensitivity Analysis and Solving 1175.3.3 Optimization Process 1195.3.4 Recommendations for Practical Application 1205.3.4.1 Setting Up the Optimization Problem 1205.3.4.2 Procedure 1235.4 Continuum-Truss Topology Optimization (CTTO) Approach 1245.4.1 Problem Statement 1255.4.2 Sensitivity Analysis and Solving 1285.4.3 Post-Processing 1305.4.4 Optimization Process 1325.5 Examples 1335.5.1 CTO Approach 1335.5.2 TTO Approach 1385.6 Applications 1515.6.1 Joints in Tunnel Linings 1515.6.2 Partial Area Loading in Tunnel Linings 153References 1536 Design of Cross-sections 1576.1 Problem Statement 1596.2 Equilibrium Iteration 1616.3 Sectional Optimization 1636.3.1 Reinforcement Amounts 1656.3.2 Cross-sectional Layout 1656.3.3 Material Weighting 1656.4 Solving 1666.4.1 Stress Integrals 1666.4.2 Optimization Problem 1676.5 Parameterization 1676.5.1 Plane Case 1676.5.2 Spatial Case 1686.5.3 Parameterization with Intentional Steering 1696.6 Examples 1706.6.1 Equilibrium Iteration 1706.6.2 Sectional Optimization 175References 183

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.

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.)

• Foreword by Manfred Curbach vForeword by Werner Sobek ixPreface xiiiList of Examples xixAcronyms xxiAbout the Authors xxiiiAcknowledgments xxv1 Introduction 11.1 Preliminaries 11.2 Outer and Inner Shaping 21.3 Environmental Demands 61.4 Optimization Aided Design (OAD) 111.5 Structure of the Book 14References 152 Fundamentals of Reinforced Concrete (RC) Design 192.1 Basic Principles 192.2 Verification Concept 212.3 Safety Concept 222.4 Materials 232.4.1 Plain Concrete 232.4.2 Fiber-Reinforced Concrete (FRC) 242.4.3 Ultra-High Performance Concrete (UHPC) 262.4.4 Reinforcement 272.5 Load-Bearing Behavior 282.5.1 Bending Design 282.5.1.1 Fundamentals 282.5.1.2 Equilibrium for Composite Sections 292.5.2 Strut-and-Tie Models (STMs) 32References 353 Fundamentals of Structural Optimization 373.1 Structural Optimization Approaches 373.1.1 General Procedure 373.1.2 Classification of Methods 383.2 Problem Statement 403.3 Lagrange Function 433.4 Sensitivity Analysis 443.4.1 Numerical Approach 443.4.2 Analytical Approach 453.5 Solution Methods 463.5.1 Mathematical Programming 463.5.2 Optimality Conditions (OC) 47References 474 Identification of Structures 514.1 One-material Structures 524.1.1 Problem Statement 524.1.2 Sensitivity Analysis 544.1.3 Filtering 544.1.4 Solving 564.1.5 Optimization Process 574.1.6 Multiple Load Cases 584.2 One-material Stress-biased Structures 594.2.1 Problem Statement 594.2.2 Sensitivity Analysis and Stress Bias 604.2.3 Solving 624.2.4 Optimization Process 634.3 Bi-material Structures 644.3.1 Problem Statement 644.3.2 Sensitivity Analysis and Stress Differentiation 654.3.3 Bi-material Filtering 684.3.4 Solving 694.3.5 Optimization Process 704.4 Examples 714.4.1 One-material Structures 714.4.2 One-material Stress-biased Structures 814.4.3 Bi-material Structures 834.5 Applications 894.5.1 Solar Thermal Collectors 894.5.1.1 Parabolic Trough Collectors 904.5.1.2 Heliostats 954.5.2 Ultra-light Beams 100References 1025 Internal Force Flow 1095.1 Preliminaries 1105.2 Continuum Topology Optimization (CTO) Approach 1115.3 Truss Topology Optimization (TTO) Approach 1125.3.1 Problem Statement 1125.3.2 Sensitivity Analysis and Solving 1175.3.3 Optimization Process 1195.3.4 Recommendations for Practical Application 1205.3.4.1 Setting Up the Optimization Problem 1205.3.4.2 Procedure 1235.4 Continuum-Truss Topology Optimization (CTTO) Approach 1245.4.1 Problem Statement 1255.4.2 Sensitivity Analysis and Solving 1285.4.3 Post-Processing 1305.4.4 Optimization Process 1325.5 Examples 1335.5.1 CTO Approach 1335.5.2 TTO Approach 1385.6 Applications 1515.6.1 Joints in Tunnel Linings 1515.6.2 Partial Area Loading in Tunnel Linings 153References 1536 Design of Cross-sections 1576.1 Problem Statement 1596.2 Equilibrium Iteration 1616.3 Sectional Optimization 1636.3.1 Reinforcement Amounts 1656.3.2 Cross-sectional Layout 1656.3.3 Material Weighting 1656.4 Solving 1666.4.1 Stress Integrals 1666.4.2 Optimization Problem 1676.5 Parameterization 1676.5.1 Plane Case 1676.5.2 Spatial Case 1686.5.3 Parameterization with Intentional Steering 1696.6 Examples 1706.6.1 Equilibrium Iteration 1706.6.2 Sectional Optimization 175References 183