Unified Theory of Concrete Structures

2. Auflage 2010
ISBN: 978-0-470-68874-8
Verlag: Wiley

Buch, Englisch, 520 Seiten, Format (B × H): 175 mm x 249 mm, Gewicht: 1016 g

Unified Theory of Concrete Structures develops an integrated theory that encompasses the various stress states experienced by both RC & PC structures under the various loading conditions of bending, axial load, shear and torsion. Upon synthesis, the new rational theories replace the many empirical formulas currently in use for shear, torsion and membrane stress.


The unified theory is divided into six model components: a) the struts-and-ties model, b) the equilibrium (plasticity) truss model, c) the Bernoulli compatibility truss model, d) the Mohr compatibility truss model, e) the softened truss model, and f) the softened membrane model. Hsu presents the six models as rational tools for the solution of the four basic types of stress, focusing on the significance of their intrinsic consistencies and their inter-relationships. Because of its inherent rationality, this unified theory of reinforced concrete can serve as the basis for the formulation of a universal and international design code.
- Includes an appendix and accompanying website hosting the authors’ finite element program SCS along with instructions and examples
- Offers comprehensive coverage of content ranging from fundamentals of flexure, shear and torsion all the way to non-linear finite element analysis and design of wall-type structures under earthquake loading.
- Authored by world-leading experts on torsion and shear

Autoren/Hrsg.

Hsu, Thomas T C

Mo, Yi-Lung

Fachgebiete

• Technische Wissenschaften Bauingenieurwesen Baukonstruktion, Baufachmaterialien

Inhaltsverzeichnis

About the Authors xi

Preface xv

Instructors’ Guide xvii

1 Introduction 1

1.1 Overview 1

1.2 Structural Engineering 2

1.2.1 Structural Analysis 2

1.2.2 Main Regions vs Local Regions 3

1.2.3 Member and Joint Design 5

1.3 Six Component Models of the Unified Theory 6

1.3.1 Principles and Applications of the Six Models 6

1.3.2 Historical Development of Theories for Reinforced Concrete 7

1.4 Struts-and-ties Model 13

1.4.1 General Description 13

1.4.2 Struts-and-ties Model for Beams 14

1.4.3 Struts-and-ties Model for Knee Joints 15

1.4.4 Comments 20

2 Equilibrium (Plasticity) Truss Model 23

2.1 Basic Equilibrium Equations 23

2.1.1 Equilibrium in Bending 23

2.1.2 Equilibrium in Element Shear 24

2.1.3 Equilibrium in Beam Shear 33

2.1.4 Equilibrium in Torsion 34

2.1.5 Summary of Basic Equilibrium Equations 37

2.2 Interaction Relationships 38

2.2.1 Shear–Bending Interaction 38

2.2.2 Torsion–Bending Interaction 41

2.2.3 Shear–Torsion–Bending Interaction 44

2.2.4 Axial Tension–Shear–Bending Interaction 51

2.3 ACI Shear and Torsion Provisions 51

2.3.1 Torsional Steel Design 52

2.3.2 Shear Steel Design 55

2.3.3 Maximum Shear and Torsional Strengths 56

2.3.4 Other Design Considerations 58

2.3.5 Design Example 60

2.4 Comments on the Equilibrium (Plasticity) Truss Model 67

3 Bending and Axial Loads 71

3.1 Linear Bending Theory 71

3.1.1 Bernoulli Compatibility Truss Model 71

3.1.2 Transformed Area for Reinforcing Bars 77

3.1.3 Bending Rigidities of Cracked Sections 78

3.1.4 Bending Rigidities of Uncracked Sections 82

3.1.5 Bending Deflections of Reinforced Concrete Members 84

3.2 Nonlinear Bending Theory 88

3.2.1 Bernoulli Compatibility Truss Model 88

3.2.2 Singly Reinforced Rectangular Beams 93

3.2.3 Doubly Reinforced Rectangular Beams 101

3.2.4 Flanged Beams 105

3.2.5 Moment–Curvature (M–f) Relationships 108

3.3 Combined Bending and Axial Load 112

3.3.1 Plastic Centroid and Eccentric Loading 112

3.3.2 Balanced Condition 115

3.3.3 Tension Failure 116

3.3.4 Compression Failure 118

3.3.5 Bending–Axial Load Interaction 121

3.3.6 Moment–Axial Load–Curvature (M-N- f) Relationship 122

4 Fundamentals of Shear 125

4.1 Stresses in 2-D Elements 125

4.1.1 Stress Transformation 125

4.1.2 Mohr Stress Circle 127

4.1.3 Principal Stresses 131

4.2 Strains in 2-D Elements 132

4.2.1 Strain Transformation 132

4.2.2 Geometric Relationships 134

4.2.3 Mohr Strain Circle 136

4.2.4 Principle Strains 137

4.3 Reinforced Concrete 2-D Elements 138

4.3.1 Stress Condition and Crack Pattern in RC 2-D Elements 138

4.3.2 Fixed Angle Theory 140

4.3.3 Rotating Angle Theory 142

4.3.4 ‘Contribution of Concrete’ (Vc) 143

4.3.5 Mohr Stress Circles for RC Shear Elements 145

5 Rotating Angle Shear Theories 149

5.1 Stress Equilibrium of RC 2-D Elements 149

5.1.1 Transformation Type of Equilibrium Equations 149

5.1.2 First Type of Equilibrium Equations 150

5.1.3 Second Type of Equilibrium Equations 152

5.1.4 Equilibrium Equations in Terms of Double Angle 153

5.1.5 Example Problem 5.1 Using Equilibrium (Plasticity) Truss Model 154

5.2 Strain Compatibility of RC 2-D Elements 158

5.2.1 Transformation Type of Compatibility Equations 158

5.2.2 First Type of Compatibility Equations 159

5.2.3 Second Type of Compatibility Equations 160

5.2.4 Crack Control 161

5.3 Mohr Compatibility Truss Model (MCTM) 165

5.3.1 Basic Principles of MCTM 165

5.3.2 Summary of Equations 166

5.3.3 Solution Algorithm 167

5.3.4 Example Problem 5.2 using MCTM 168

5.

Über Autor(innen)

Thomas Hsu & Yi-Lung Mo, University of Houston, USA
Thomas Hsu is Moores Professor of Civil Engineering in the department of civil and environmental engineering at the University of Houston. Professor Hsu has been Principal and Co-Principal Investigator on funded projects for over 30 years, and has received project funding amounting to over $3.5 million, including 14 grants from National Science Foundation totaling $2.2 million. He established the University of Houston's Structural Research Laboratory, which is widely recognized and has supported over thirty Ph. D., M. S., and post-doctoral students. His research work has formed the basis for the shear and torsion design provisions in the American concrete Institute Building Code. His current research interests are in concrete, concrete structures, and structural mechanics. He has won numerous awards for his teaching and research, and has authored? or edited 3 books on reinforced concrete.
Yi-Lung Mo is Professor of Civil Engineering in the Department of Civil and Environmental Engineering at the University of Houston. His primary research interests are related to the behavior and design of reinforced/ pre-stressed concrete, steel, hybrid and composite structures subjected to seismic and blast loads. He has authored or edited 3 books on the topics of construction materials and concrete.