Reinforced Concrete: Basic Theory and Standards

Preface
Contents
1 Introduction
1.1 General Concepts
1.2 History and Development of Reinforced Concrete
1.3 Materials
1.4 Application of Reinforced Concrete
2 Mechanical Behavior of Materials
2.1 Concrete
2.1.1 Grade of Concrete Strength
2.1.2 Axial Compressive Strength
2.1.3 Axial Tensile Strength
2.2 Concrete Behaviors in Compression and Failure Mechanism
2.2.1 Structure of Hardened Concrete
2.2.2 Properties of Concrete Under Short-Term Uniaxial Compressive Loading
2.3 Elasticity Modulus of Concrete Ec and Poisson’s Ratio
2.3.1 Modulus of Elasticity of Concrete
2.3.2 Two Methods for Evaluation of Ec
2.3.3 Poisson’s Ratio of Concrete
2.4 Constitutive Relation and Deformation of Concrete
2.5 Effect of Lateral Confinement of Transverse Reinforcement on the σ–ε Relationship of Concrete Under Compression
2.6 Mechanical Properties of Concrete Subjected to Multiaxial Stress States
2.7 Time-Dependent Strains of Concrete/Shrinkage and Creep of Concrete
2.7.1 Shrinkage of Concrete
2.7.2 Creep of Concrete
2.8 Reinforcement
2.8.1 Types of Steel Reinforcement
2.8.2 Prestressing Steel Products
2.8.3 Characteristic Strength and Modulus of Elasticity of Reinforcing Steel and Prestressing Steel
2.8.4 Thermal Expansion
2.8.5 Relaxation
2.9 Bond Between Steel and Concrete
3 Limit State Design
3.1 Development of the Design Method
3.2 Limit State of Structure
3.2.1 Limit State Design Based on the Probability Theory
3.2.2 Limit State Design Philosophy
3.2.3 Brief Review of Statistical Concepts
3.3 Function of the Structure
3.3.1 Ultimate Limit State (ULS)
3.3.2 Serviceability Limit State (SLS)
3.4 Action Effect, Resistance Effect, and Reliability
3.4.1 Failure Probability and Reliability
3.4.2 Characteristic Value of Action Effect Sk and Resistance Effect Rk
3.5 Discussion of “Limit State Design” and “Design Value” Based on BS 8110 [14]
4 Reinforced Concrete Beams
4.1 A General Theory for Flexural Behavior
4.1.1 Bending Elements
4.1.2 Bending Experiment
4.2 General Theory for Flexural Behavior of RC Beam
4.2.1 Three Stages of RC Beam Under Bending
4.2.2 Effect of Steel Ratio on the Failure Pattern of RC Beam Under Bending
4.3 Analysis of Section Stress Subjected to Bending
4.3.1 Characteristics of Stress Block of the Beam in Stage I
4.3.2 Equivalent Rectangular Stress Distribution
4.4 Balanced-, Over-Reinforced, and Under-Reinforced Beams
4.5 Calculation of Rectangular Beams with Reinforcement
4.5.1 Singly Reinforced Section
4.5.2 Doubly Reinforced Beams—Section with Compression Reinforcement
4.5.3 Derivation of Design Formulae Referring to Ref. [13] Based on BS 8110 [14]
4.6 Flanged Beam and T-beam
4.6.1 Effective Flange Width of T-Section
4.6.2 Analysis and Design of T-Section
5 Diagonal Section Strength Under Flexure
5.1 Introduction
5.2 Diagonal Tension and Formation of the Diagonal Cracks in Concrete Beam
5.3 Failure Pattern of Beams Without Shear Reinforcement
5.3.1 Shear–Span Ratio of Diagonal Section
5.3.2 Failure Pattern of Diagonal Section Based on GB 50010-2010
5.3.3 Stress State Before and After Diagonal Cracks
5.3.4 Effect of the λ on the Loading Transfer Mechanism and the Failure Mode Based on GB 50010-2010 and BS
5.3.5 Analyzing the Influence Factors on the Strength of Diagonal Section Based on Different Codes
5.3.6 Reliable Shear Resistance of a Member Without Web Reinforcement
5.4 Shear Behavior of Beams with Web Reinforcement
5.5 Some Detailing Notation of Web Reinforcement
5.6 Design Procedure of Web Reinforcement
5.7 Moment Resistance of the Diagonal Section
5.7.1 Moment of the Diagonal Section
5.7.2 Ultimate Moment Diagram
5.7.3 Cut-Off and Fully Developed Sections of Bars
5.7.4 Anchorage Length
5.7.5 Bending Resistance of a Diagonal Section
6 Torsion
6.1 Introduction
6.2 Torsion Members
6.3 Cracking Torque
6.3.1 Stress State Before Cracking of Beam
6.3.2 Torsional Cracking
6.4 Hollow Section, I Section, and T Section
6.4.1 Torsion Modulus of Hollow Section
6.4.2 Torsion Modulus of I-Section and T-Section/Section with Flange
6.4.3 Reinforcement of the Pure Torsion Member
6.5 Failure Mode Under Torsion
6.5.1 Torsional Stiffness
6.5.2 Failure Mode Under Torsion
6.6 Space Truss Analogy for the Ultimate Torsional Strength
6.7 Detailing Requirement of Torsion Resisting Reinforcement According to GB 50010–2010
6.8 Interaction of Torsion, Bending, and Shear
6.9 Failure Mode of a Member Under Combined Actions
6.10 Provision for Reinforcement
7 Compression Members––Columns
7.1 Introduction
7.2 Behavior of Axial Compression Member
7.2.1 Column Under the Axial Load N
7.2.2 Axially Loaded Column with Rectangular Cross-Section
7.2.3 Axially Loaded Spiral Column
7.3 Eccentrically Loaded Columns
7.3.1 Tension Column and Compression Column Sections
7.3.2 Column Section Subjected to Combined Compression and Bending
7.4 Moment Magnifying Coefficient
7.5 Second-Order Effect Due to Sway or Lateral Deflection of the Slender Column
7.5.1 Failure Pattern of Column
7.5.2 Brief Introduction of Second-Order Effect Induced by Sway
7.5.3 Second-Order Effect Induced by the Own Lateral Deflection of a Slender Column
7.6 Calculation of the Rectangular Column Section Subjected to Eccentrically Loading
7.6.1 Design of Section with Asymmetrical Reinforcement
7.6.2 Checking of a Column Section with Asymmetrical Reinforcement
7.6.3 Eccentrically Loaded Column Section with Symmetrical Reinforcement
7.7 Brief Introduction of Biaxial Eccentrically Loaded Column Section
7.7.1 Evaluation of Ultimate Load Nu Based on GB 50010–2010
7.7.2 Evaluation of Ultimate Load Nu According to BS
7.7.3 Circular Column with Symmetrical Reinforcement
7.8 Ductility and Detailing Requirement of Column
7.8.1 Ductility of Column
7.8.2 Detailing Requirement
8 Tension Members
8.1 Behavior of RC Member Subjected to the Uniaxial Tensile Force
8.1.1 Before Cracking (N < Ncr), the Tensile Force Is Carried by Concrete and Steel Bars
8.1.2 At Cracking and After Cracking
8.2 Behavior of RC Member Subjected to the Eccentric Tension Loading
8.2.1 Full Tension Section
8.2.2 Partial Tension Section
8.3 Shear Capacity of the Diagonal Section of the RC Tension Member
9 Limit State of Serviceability
9.1 General Concept
9.2 Deflection Control of the Flexural Member
9.2.1 Allowable Deflection f ≤ [f]
9.2.2 Evaluation of Deflection
9.3 Section Stiffness Under Short-Term and Long-Term Loading
9.3.1 Section Stiffness Under Short-Term Loading
9.3.2 Discussion of Factors ƞ, Ζ, and Ψ
9.3.3 Section Stiffness Under Long-Term Loading
9.3.4 Deflection Control
9.4 Crack Control
9.4.1 Crack
9.4.2 Causes and Types of Cracks
9.4.3 Limitation of Crack Width
9.5 Bond Between Steel Rebar and Concrete
9.5.1 Bond Stress–Slip (τb - s) Relationship
9.5.2 Bond Stress τb and Steel Stress σs
9.6 Analysis for Crack Control in RC Member
9.6.1 Crack Formation Phase
9.6.2 Crack Spacing Based on the Bond–Slip Theory
9.6.3 Stabilized Cracking Phase
9.7 Discussion of Cracking of RC
9.7.1 Cracking, Stiffness, and Load–Elongation Relationship
9.7.2 Crack Spacing Based on Traditional Theory
9.7.3 Crack Width Based on the Bond–Slip Theory
10 Prestressed Concrete
10.1 Introduction
10.2 Concept of Prestressing
10.3 Pretensioning Versus Posttensioning Method
10.3.1 Pretensioned Method
10.3.2 Posttensioned Method
10.4 Establishing of the Prestressing
10.4.1 Stress Transfer Between Tendons and Concrete
10.4.2 Bond Properties of Prestressing Steel
10.4.3 Stress State of the Cross-Section
10.5 Materials of Prestressed Concrete
10.5.1 Tendons
10.5.2 Concrete
10.6 Anchorage Systems
10.6.1 Anchorage Systems for Posttensioned Reinforcement
10.6.2 Anchorage Systems for Pretensioned Reinforcement
10.7 Control Stress of Prestress
10.7.1 Stress State of the Prestressed Beam Section
10.7.2 Control Stress of Prestress
10.7.3 Loss of Prestress
10.8 Combination of Prestress Losses
10.8.1 Estimation of Prestress Losses
10.8.2 Pretensioned Member [6]
10.8.3 Posttensioned Member
10.9 Prestressed Bending Members
10.9.1 Calculation of Pre-compressive Stress of Concrete Under Bending
10.9.2 Tendon Stress in the Tension Zone at the Ultimate State
10.9.3 Tendon Stress in the Compression Zone
11 Girder–Beam–Slab System
11.1 Load of Girder–Beam–Slab System
11.2 Some Major Types of Slab
11.3 One-Way and Two-Way Slabs
11.4 Elastic Analysis of RC Continuous Beam
11.4.1 Combination of Live Loads and Dead Loads
11.4.2 Moment and Shear Envelop Diagrams
11.4.3 Stiffness of the Supports
11.4.4 Plastic Redistribution of Internal Force
11.4.5 Moment and Shear Coefficients
11.4.6 Restrictions of Moment Redistribution
11.5 Calculation and Detailing Requirements of  One-Way Slab
11.5.1 Detailing of Steel Rebar of One-Way Slab
11.6 Design of Beams
11.6.1 Basic Characteristics
11.6.2 Detailing of Beams
11.7 Design of Girder
11.7.1 Basic Characteristics
11.7.2 Evaluation of Loading
11.7.3 Strength Design of Girder
11.7.4 Detailing of Girder
11.8 Example of One-Way Slab Design
11.8.1 Design of One-Way Slab
11.8.2 Design of Beams
11.8.3 Design of Girder
11.9 RC Slabs and Yield-Line Analysis
11.9.1 Flexural Strength of Slabs
11.9.2 Yield-Line Analysis
11.9.3 Hillerborg’s Strip Method
11.9.4 Shear Strength of Slabs
11.9.5 Design of Slabs
Appendix A Main Parameters of Concrete, Bars, and Tendons
Appendix B Internal Force Factors of Continues Beam with Equal Span Subjected to Uniformly Distributed Load and Concentrated Load
References