Reinforced Concrete Design: Limit State Method and Beyond

✍ Scribed by Santanu Bhanja

• Publisher: CRC Press
• Year: 2024
• Tongue: English
• Leaves: 415
• Edition: 1
• Category: Library

✦ Synopsis

Reinforced Concrete Design (RC) is performed mostly by the limit state method throughout the world. This book covers the fundamental concepts and principles of RC design developing the topics from the basic theories and assumptions. Building upon the possible revisions to the mother code of concrete in India, IS:456-2000, it explains the RC design provisions of IRC:112-2020, which are in line with international standards. In addition to strength design, serviceability and ductility design are also covered.

Features:

• Highlights the basic philosophy of RC design and behaviour of the sections up to and beyond limit state.
• Clarifies limit state theory from the basic assumptions provided in relevant Indian and international standards, IS:456, IRC:112 and Eurocode:2.
• Includes design aids or tools for standard and high strength concrete up to M90 grade as per different codes of practice.
• Explains the concept of ductility of reinforced concrete sections subjected to flexure with or without axial loads from fundamental principles.
• Covers fundamentals on serviceability requirements in reinforced concrete structures.
• Illustrates the design methodology of shear walls and includes design aids developed using basic principles as per relevant codes of practice.
• Explains reinforced concrete design provisions as per latest national and international standards and these are expected to be in line with those to be included in the forthcoming revision of IS:456.

This book is aimed at graduate students, researchers and professionals in civil engineering, construction engineering and concrete.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
About the Author
Acknowledgements
1 Introduction
1.1 Reinforced Concrete – Definition
1.2 Plain and Structural Concrete
1.3 Advantages and Disadvantages of Reinforced Concrete
1.3.1 Advantages of Concrete
1.3.2 Disadvantages of Concrete
1.4 Role of Concrete and Reinforcement On the Properties of Reinforced Concrete
1.5 Grades of Structural Concrete Permitted By IS:456 and Grades of Steel Permitted in IS:1786
1.6 Summary
Bibliography
2 Basic Material: Concrete
2.1 Introduction
2.2 Ingredients of Concrete – Cement, Aggregates, Water and Admixtures
2.2.1 Cement
2.2.1.1 Manufacture
2.2.1.2 Chemical Composition
2.2.1.3 Hydration of Cement
2.2.1.4 Fineness
2.2.1.5 Structure of Hydrated Cement Paste
2.2.2 Aggregates
2.2.2.1 Influence of Aggregates On the Properties of Concrete
2.2.3 Water
2.2.4 Admixtures
2.2.4.1 Benefits of Admixtures
2.2.4.2 Reasons for Using Admixtures
2.2.4.3 Different Types of Admixtures as Per Indian Standard IS:9103
2.3 Properties of Concrete
2.3.1 Properties of Fresh Concrete
2.3.2 Properties of Hardened Concrete
2.3.2.1 Strength of Concrete
2.3.2.2 Water–cement Ratio
2.3.2.3 Factors Affecting Strength of Concrete
2.3.2.4 Stress–strain Relationship
2.3.2.5 Durability of Concrete
2.4 Basics of Concrete Mix Design
2.4.1 Economy
2.4.2 Workability
2.4.3 Strength and Durability
2.4.4 Parameters Considered in Concrete Mix Design
2.4.5 Methods of Concrete Mix Design
2.4.6 Purpose/objectives of Mix Design
2.4.7 Approach to Concrete Mix Design
2.4.8 Mix Design of Ordinary and Standard Grades of Concrete as Per Indian Standard IS: 10262-2019
2.4.9 Concept of Trial Mixes
2.5 High-Performance Concrete (HPC) – Definition, Materials and Properties
2.5.1 High-Performance Concrete Principle
2.5.2 High-Performance Concrete: Requirements for Constituent Materials and Mix Proportioning
2.5.3 Selection of Materials
2.5.4 Ratio of Coarse to Fine Aggregate
2.5.5 Admixtures
2.6 Summary
Bibliography
3 General Overview of IS:456-2000 and IRC:112-2020: General Provisions of Indian Standards On Concrete
3.1 Introduction
3.2 Provisions for Plain Concrete and Reinforcements
3.2.1 Materials and General Considerations
3.2.2 Workmanship
3.2.3 Inspection and Testing
3.3 Provisions of IS:456-2000 On Structural Concrete
3.4 Provisions of IRC:112-2020 – Code of Practice for Concrete Road Bridges
3.4.1 Provisions for Plain Concrete and Reinforcements (Untensioned)
3.5 Summary
Bibliography
4 Provisions of Standards Or Codes of Practice On Reinforcement: IS:1786-2008, IS:456-2000, SP:16-1980, IRC:112-2020 and Eurocode-2
4.1 Introduction
4.2 General Requirements as Per Indian Standards: IS:456-2000, IS:1786-2008, IRC:112-2020, and Eurocode 2
4.3 Mechanical Properties
4.4 Stress–strain Relationship
4.4.1 Engineering Stress–strain Curves
4.4.1.1 Determination of the Engineering Stress–strain Curve
4.4.2 Behaviour of Steel Under Stress
4.4.3 Stress–strain Relationships as Per IS:456
4.4.4 Stress–strain Relationships as Per IRC:112
4.4.5 Stress–strain Relationship as Per Eurocode 2
4.5 Summary
Bibliography
5 General Considerations for Analysis of RC Structures
5.1 Introduction
5.2 Loading
5.2.1 Dead Loads
5.2.2 Imposed Loads
5.2.3 Wind Load
5.2.4 Earthquake Force
5.2.5 Snow Loads
5.2.6 Special Loads
5.3 Characteristic and Design Loads
5.4 Combinations of Loads
5.5 Analysis Considerations
5.6 Methods of Analysis
5.7 Guidelines for Analysis as Per Indian Standards
5.8 Stress Resultants of RC Structural Elements
5.9 Summary
Bibliography
6 General Considerations for Design of RC Structures
6.1 Introduction
6.2 Basis of Structural Design – Design Process
6.3 Aims and Objectives of Design
6.4 General Requirements
6.5 Prescriptive Method of Design as Per Standards
6.6 Strength and Serviceability Design Based On Loads
6.7 Summary
Bibliography
7 Philosophy of Reinforced Concrete Design
7.1 Introduction
7.2 Basic Assumptions of RC Design
7.3 Unconfined and Confined Stress–strain Diagrams of Concrete
7.4 Strain Distribution Diagrams Across the Cross-Section
7.5 Development of Stress Blocks From the Stress–strain Diagram
7.6 Historical Development of Design Methods
7.7 Working Stress Method (WSM)
7.8 Ultimate Load Method (ULM)
7.9 Limit State Method (LSM)
7.10 Summary
Bibliography
8 Working Stress Method
8.1 Introduction
8.2 Design Philosophy – Strength and Serviceability Design
8.3 Provisions as Per IS:456-2000
8.4 Assumptions
8.5 Stress Blocks in Concrete
8.6 Permissible Stresses
8.7 Flexural Members
8.8 Singly Reinforced Section
8.8.1 Balanced Section
8.8.2 Under-Reinforced Section
8.8.3 Over-Reinforced Section
8.9 Types of Sections – Balanced, Under-Reinforced and Over-Reinforced
8.10 Mode of Failure in WSM – Single-Stage Failure
8.11 Doubly Reinforced Sections
8.12 Examples
8.12.1 Analysis Type of Problem
8.12.2 Design Type of Problem
8.12.3 Analysis Type Problem
8.12.4 Design Type Problem
8.13 Compression Members
8.14 Member Subjected to Direct Tension
8.15 Serviceability Requirements
8.16 Shortcomings of WSM
8.17 Why WSM Is Getting Outdated Throughout the Globe
8.18 Summary
Bibliography
9 Limit State Method as Per IS:456
9.1 Introduction
9.2 Objectives of LSM of Design
9.3 Limit States
9.4 Types and Classification of Limit States
9.5 Characteristic and Design Values of Loads and Material Strengths
9.6 Provision of IS:456 for LSM of Design
9.7 Mode of Failure – Multistage Failure
9.8 Summary
Bibliography
10 Limit State of Collapse in Flexure as Per IS:456
10.1 Introduction
10.2 Stress–strain Relationships of Concrete and Steel
10.2.1 Stress–strain Relationships of Concrete
10.2.2 Stress–strain Relationships of Reinforcing Steel
10.3 Strain Distribution Diagram and Stress Blocks
10.4 Assumptions
10.5 Failure Modes in Balanced, Under-Reinforced and Over-Reinforced Sections – Yield and Ultimate Stages (two-Stage Failure)
10.5.1 Modes of Failure
10.5.1.1 Balanced Section Or Critical Section
10.5.1.2 For Under-Reinforced Sections
10.6 Shortcomings/limitations of the Assumptions as Per Indian Standards
10.7 Assumptions of LSM of Design as Per International Guidelines
10.8 Singly Reinforced Sections
10.9 Computation of Design Parameters for Flexural Members
10.9.1 Balanced Section
10.9.1.1 Limiting Values of Neutral Axis Depth
10.9.1.2 Balanced Percentage of Tension Reinforcement (Table 10.2)
10.9.1.3 Computation of Limiting Moment of Resistance
10.9.2 Maximum Under-Reinforced Section
10.10 Singly Reinforced Sections – an Idealized Or Purely Theoretical Condition
10.11 Doubly Reinforced Sections
10.12 Introduction and Need for Doubly Reinforced Sections
10.13 Assumptions
10.14 Are All Doubly Reinforced Sections Balanced in Nature?
10.15 Basic Principles of Under-Reinforced Doubly Reinforced Sections
10.16 Determination of Strain Distribution and Stress Blocks
10.17 Real-Life Beams – All Are Doubly Reinforced
10.18 Load Design – Ignore Reinforcements On Compression Side
10.19 Capacity Design Approach – Considering Reinforcement Both On the Tension and Compression Sides
10.20 In RC Sections Only Flexure Failure Can Be Made Ductile
10.21 Illustrative Examples
10.22 Numerical Examples
10.22.1 Problem 10.1
10.22.2 Problem 10.2
10.22.2.1 Capacity Design Approach
10.23 Summary
Bibliography
11 Limit State of Collapse in Compression as Per IS:456
11.1 Introduction
11.2 Classification and Definitions
11.3 Braced and Unbraced Columns
11.4 Longitudinal Reinforcement
11.5 Transverse Reinforcement
11.6 Desirable Choices of Section
11.7 Difference Between Flexure Design and Compression Design
11.8 Why Design Charts Are Needed for Column Design
11.9 Design of Axially Loaded Columns
11.10 Columns Under Axial Load and Uniaxial Bending
11.11 Modes of Failure in Columns
11.12 Failure Under Balanced Condition
11.13 Failure in Over-Reinforced Condition Or Compression Failure
11.14 Failure in Under-Reinforced Condition Or Tension Failure
11.15 Equilibrium Equations for Column Design
11.16 Need for P–M Interaction Charts for Column Design
11.17 Development of Strain Distribution Diagram and Stress Blocks for Different Arbitrary Positions of the Neutral Axis
11.17.1 When Neutral Axis Is Outside the Section
11.17.2 When the Neutral Axis Is Within the Section
11.18 Development of Safety Profile of a Column Section From Pure Axial Load to Steel Beam Condition With a Certain Percentage of Longitudinal Reinforcement
11.18.1 Determination of Stress and Strain Values in Reinforcements From Stress–strain Relationships
11.18.2 Development of the Safety Profile of a Column Section With Typical Percentage of Longitudinal Reinforcements
11.18.3 Different Arbitrary Positions of the Neutral Axis
11.19 P–M Interaction Diagrams
11.19.1 Different Steps for the Preparation of Charts
11.19.2 Problem Example
11.20 Design Aids for Compression Design and Shortcomings of SP16
11.20.1 Shortcomings of SP16 With Respect to Design Charts in Compression
11.21 Interaction Charts for Rectangular Column Sections Valid for M20–M60 Grades of Concrete and Fe 415, Fe 500, Fe 550 and Fe 600 Steel With D’/D Values of 0.05–0.20 as Per the Fundamental Principles of the Limit State Method
11.22 Interactions Charts for a Rectangular Section With Reinforcement Distributed On Two Sides (Charts 11.1–11.16)
11.23 Interaction Charts for a Rectangular Column Section With Reinforcements Equally Distributed On Four Sides (Charts 11.17–11.32)
11.24 Columns Under Axial Load With Biaxial Bending
11.25 Summary
Bibliography
12 Limit State of Collapse in Shear
12.1 Introduction
12.2 Shear Strength of RC Sections
12.3 Action of Shear Reinforcements
12.4 Present-Day Concept of Shear Design
12.5 Effect of Stirrup in Confinement of Core Concrete
12.6 IS Codal Requirements
12.7 Summary
Bibliography
13 Development Length of Reinforcement in RC Sections
13.1 Introduction
13.2 Concept of Development Length
13.3 Bends, Hooks and Mechanical Anchorages
13.4 Critical Sections for Checking Development Length
13.5 IS Codal Requirements
13.6 Calculations of Breaking Strength of Concrete and Its Effect
13.7 Summary
Bibliography
14 Limit State of Serviceability
14.1 Introduction
14.2 Serviceability Design of Commonly Used Structural Elements
14.3 Calculation of Deflection
14.3.1 Deflection Behaviour of Beams
14.3.2 Deflection By Elastic Theory
14.3.3 Tension Stiffening Effect
14.3.4 Calculation of Flexural Rigidity
14.3.5 Effective Moment of Inertia Formulation
14.3.6 Long-Term Deflection
14.3.6.1 Deflection Due to Creep
14.3.6.2 Deflection Due to Shrinkage
14.4 Control of Deflection
14.5 Deflection Limits/requirements as Per Indian Standards
14.6 Calculations of Crack Width
14.7 Guidelines to Provide Crack Control
14.8 Limits On Cracking as Per Indian Standards
14.9 Summary
Bibliography
15 Limit State Method as Per IRC:112-2020 for RC Sections
15.1 Introduction
15.2 Stress–strain Relationships of Concrete and Steel
15.3 Stress Blocks for Concrete
15.4 Assumptions in Ultimate Limit State for Design of Members
15.5 Design for Flexural Members – Singly Reinforced Sections
15.6 For Factored Simplified Bilinear Stress–strain Relationship of Steel (Horizontal Plastic Branch)
15.6.1 Computation of Design Parameters for Concrete Grades From M20 to M90 and Grades of Steel From Fe 415 to Fe 600 for Balanced Condition
15.6.1.1 Compressive Force
15.6.1.2 Line of Action of the Compressive Force
15.6.1.3 Tensile Force
15.6.1.4 Balanced/limiting Moment of Resistance
15.6.2 Computation of Design Parameters for Concrete Grades From M20 to M90 and Grades of Steel From Fe 415 to Fe 600 for Maximum Under-Reinforced Condition
15.6.3 Computation of Design Parameters for Concrete Grades From M20 to M90 and Grades of Steel From Fe 415 to Fe 600 for Maximum Percentage of Tension Reinforcement
15.7 For Factored Idealized Bilinear Stress–strain Diagram of Steel With Inclined Plastic Branch
15.7.1 Computation of Design Parameters for Concrete Grades From M20 to M90 and Grades of Steel From Fe415 to Fe600
15.7.1.1 Balanced Condition
15.7.1.2 Under-Reinforced Condition
15.7.1.3 Maximum Under-Reinforced Condition
15.7.1.4 Maximum Over-Reinforced Condition Or Section With Maximum Percentage of Tension Reinforcement
15.8 Doubly Reinforced Sections
15.9 Design for Compression Members
15.10 Columns Under Axial Load and Uniaxial Bending
15.11 Development of Strain Distribution Diagrams and Stress Blocks
15.12 Numerical Example (For Concrete Grade Up to M60)
15.13 Sample Design Aids for Compression Design
15.14 Numerical Example (Higher Grades of Concrete Beyond M60)
15.15 Sample Design Aids for Compression Members Beyond M60 Grade of Concrete
15.16 Summary
Bibliography
16 Design Beyond Limit State
16.1 Introduction
16.2 Limit State Corresponds to Failure Under Design Load
16.3 Overloading Beyond Design Loads
16.4 Limit State Method Fails Beyond Design Loads
16.5 Behaviour of Structural Elements Beyond Limit State, I.e., Under Overloading
16.6 Load-Based Design Failures
16.7 Displacement-Based Design
16.8 Ductility Design
16.9 Introduction to Performance-Based Design (PBD)
16.10 Summary
Bibliography
17 Ductility Design
17.1 Introduction
17.2 Need for Ductility Design
17.3 Significance of Ductility
17.4 Role of Ductility in Design
17.5 Moment Curvature Relationship in RC Members
17.6 Determination of Yield and Ultimate Curvature
17.7 Limit State Method and Maximum Under-Reinforced Sections
17.8 Calculation and Interpretation of Strain Ductility Values
17.9 Ductility of Under-Reinforced Sections
17.10 Measures of Ductility
17.11 Plastic Hinge in Reinforced Concrete Sections
17.12 Expression of Plastic Rotation and Curvature Ductility of Balanced Sections
17.12.1 Determination of Xy
17.12.2 Determination of Xu,max Or Xu,balanced
17.13 Expressions for Plastic Rotation and Curvature Ductility of Maximum Under-Reinforced Sections
17.13.1 Determination of Xu,min
17.13.2 Determination of Xy,min
17.14 Expressions for Plastic Rotation and Curvature Ductility of Doubly Reinforced Sections
17.14.1 Calculation of Neutral Axis at Yield
17.14.2 Calculation of Depth of Neutral Axis at Ultimate Stage (xu)
17.15 Discussions On Ductility and Plastic Rotations
17.15.1 Prescriptive Design as Per Indian Standards
17.16 Desirable Ductility Values of Reinforced Concrete Sections
17.17 Evaluation of Ductility for Columns
17.18 Effect of Axial Compressive Force On Curvature Ductility
17.19 Performance-Based Design
17.20 Summary
Bibliography
18 Earthquake-Resistant Design of Structures
18.1 Introduction
18.2 Philosophy of Design
18.3 Elements Which Need Ductility Design
18.4 Provisions for Ductility Design and Detailing as Per IS:13920-2016
18.5 Summary
Bibliography
19 Design of Shear Walls Following the Fundamental Principles of Limit State Method as Per Indian and International Standards
19.1 Introduction
19.2 Definition and Classifications
19.3 Advantages of Shear Walls
19.4 Braced and Unbraced Walls
19.5 Stiffness of Shear Walls
19.6 Stress Resultants in Shear Walls
19.7 Modes of Failure in Walls
19.8 Design of Shear Wall Subjected to Axial Load and Uniaxial Bending
19.9 Development of Strain Distribution Diagrams and Stress Blocks
19.9.1 Under Pure Axial Load Only
19.9.2 Stress Blocks for Concrete and Steel in Balanced Condition
19.9.2.1 Stress Block for Concrete
19.9.2.2 Stress Blocks for Steel
19.9.2.3 Stress Blocks for HYSD Steel
19.9.3 For Failure in Over-Reinforced Condition
19.9.3.1 Area of Stress Block in Concrete
19.9.3.2 Stress Block of Steel in Compression
19.9.3.3 Stress Block of Steel in Tension
19.9.4 For Failure in Under-Reinforced Condition
19.9.5 Failure Under Pure Flexure Only When the Wall Acting as a Steel Beam
19.10 Development of Force and Moment Equilibrium Equation
19.11 Solutions of the Equations for Arbitrary Depths of Neutral Axis
19.12 Illustrative Example
19.13 Development of P–M Interaction Diagrams for Shear Wall for Nine Grades of Concrete (M20 to M60) and Four Grades of Steel (Fe415 to Fe600)
19.13.1 Inferences From the Proposed Charts as Per IS:456-2000
19.14 Design Provisions as Per Indian Standard IS:13920-2016
19.15 Limitations of the Standard
19.16 Development of Interaction Charts for Shear Walls as Per IRC Standard/Eurocode Requirements
19.16.1 Flexure Design as Per IRC:112-2020
19.16.2 Development of Interaction Diagrams as Per IRC:112-2020
19.17 Summary
Bibliography
20 Design of Staircases
20.1 Introduction
20.2 Types of Staircases
20.2.1 Based On the Geometrical Configurations
20.2.2 Structurally, Staircases Can Be Classified Into Two Groups Depending Upon the Direction of Load Transfer
20.3 IS Codal Requirements
20.4 Structural Analysis and Design Consideration
20.5 Illustrative Example
20.6 Summary
Bibliography
21 Design of Foundations
21.1 Introduction
21.2 Effect of Wind Force as Per NBC-2016
21.3 Effect of Earthquake Force as Per IS:1893 – Part 1, 2016
21.4 Types of Footing
21.5 Distribution of Soil Pressure and Behaviour of Isolated Footing
21.6 General Design Considerations and IS Codal Requirements
21.6.1 Thickness at the Edge of the Footing
21.6.2 Bending Moment
21.6.3 Shear and Bond
21.6.4 Critical Section
21.6.5 Tensile Reinforcements
21.6.6 Transfer of Load at the Base of Column
21.6.7 Nominal Reinforcement
21.7 Proportioning of Footings
21.8 Structural Design of Footings
21.9 Illustrative Example
21.10 Summary
Bibliography
Index