Analysis and Design of Concrete Structures

1 Introduction 1-1
1.1 Concrete structures 1-1
1.2 History of concrete 1-1
1.3 Building regulations and design codes of practice 1-2
1.4 Cost of concrete 1-4
2 Properties of Reinforced Concrete 2-1
2.1 Introduction 2-1
2.2 Concrete Material Properties 2-2
2.2.1 Compressive strength 2-2
2.2.2 Stress-strain relationship 2-3
2.2.3 Tensile strength 2-4
2.2.4 Modulus of elasticity 2-5
2.2.5 Poisson’s ratio 2-7
2.2.6 Shear modulus 2-8
2.2.7 Unit weight 2-8
2.2.8 Time-dependent behaviour 2-9
2.2.9 Durability 2-15
2.2.10 Concrete specification 2-15
2.3 Material Properties of Steel Reinforcement 2-16
2.3.1 Stress-strain relationship 2-16
2.3.2 Modulus of elasticity 2-17
2.3.3 Time-dependent behaviour 2-17
2.3.4 Corrosion 2-17
2.3.5 Specification 2-17
2.3.6 Identification 2-18
3 Limit States Design 3-1
3.1 Introduction 3-1
3.2 Limit States 3-2
3.2.1 Ultimate limit state 3-2
3.2.2 Serviceability limit state 3-3
3.2.3 Special limit states 3-3
3.2.4 Limit states design 3-4
3.3 Characteristics Material Strengths 3-5
3.4 Nominal Loads 3-6
3.5 Partial Factors of Safety 3-6
3.5.1 Partial factors of safety for metrials ?m 3-6
3.5.2 Partial factors of safety for loads ?f? 3-7
3.6 Examples 3-9
3.7 Structural Reliability 3-9
3.8 Partial Safety Factors Used by BS 8110 (1997) 3-12
3.9 ACI 318 Approach 3-14
3.10 Demonstration Problems 3-17
Examples 3-18
4 Analysis of the Structure 4-1
4.1 Introduction 4-1
4.2 Load combinations to consider 4-1
4.3 Simplification of the structure 4.-2
4.3.1 Braced frames 4-4
4.3.2 Unbraced frames 4-5
4.4 Section properties of elements 4-6
4.5 Moment Redistribution 4-8
4.6 Requirements for Moment Redistribution 4-12
4.7 Demonstration Problems 4-13
5 Analysis and Design for Flexure 5-1
5.1 Introduction 5-1
5.2 Fundamental Principles 5-1
5.3 Stress-strain Relationship for Concrete in Bending 5-2
5.4 Stress-strain Relationship for Reinforcement 5-4
5.5 Distribution of Strain and Stress at a Section 5-6
5.6 Relationship Between Strains and Neutral Axis Depth 5-8
5.7 Limits on Neutral Axis Depth 5-8
5.8 Bending and the Equivalent Rectangular Stress Block 5-10
5.9 Singly Reinforced Rectangular Sections 5-11
5.9.1 Design 5-11
5.9.2 Analysis 5-14
5.10 Doubly Reinforced Rectangular Sections 5-15
5.10.1 Design 5-15
5.10.2 Non-yielding compression reinforcement 5-17
5.10.3 Analysis 5-19
5.11 Design Charts 5-20
5.12 Moment Redistribution and the Design Equations 5-21
5.13 Flanged Beams 5-25
5.13.1 Analysis 5-26
5.13.2 Design 5-27
5.13.3 Simplified design 5-28
5.14 Elastic Analysis and Design 5-29
5.14.1 Elastic analysis of a cracked section 5-29
15.4.2 Elastic design of a cracked section 5-31
5.15 Elastic Analysis Using the Transformed Section 5-32
5.15.1 Cracked rectangular section 5-32
5.15.2 Cracked T-section 5-34
5.15.3 Compression reinforcement 5-35
5.15.4 Uncracked section 5-36
5.16 Demonstration Problems 5-37
Examples 5-41
6 Design of Beams for Shear 6-1
6.1 Introduction 6-1
6.2 Beams Without Shear Reinforcement 6-1
6.2.1 Elastic behaviour of uncracked beams 6-1
6.2.2 Behaviour of cracked beams 6-5
6.2.3 The principal mechanisms of shear resistance 6-7
6.2.4 Influence of shear span/effective depth ration on failure mode 6-9
6.2.4 Mechanisms of shear transfer 6-13
6.2.5 Factors influencing shear strength 6-13
6.3 Beams With Shear Reinforcement 6-14
6.3.1 Shear components 6-14
6.3.2 Truss analogy 6-15
6.4 Design for Shear to BS 8110 6-18
6.5 Design for Shear to SABS 0100 6-21
6.6 Shear in One-Way Spanning Solid Slabs 6-25
6.7 Demonstration Problems 6-25
Examples 6-27
7 Analysis and Design for Torsion 7.1
7.1 Introduction 7.1
7.1.1 Equilibrium torsion 7.1
7.1.2 Compatibility torsion 7.1
7.2 Unreinforced Concrete 7.3
7.2.1 Elastic behaviour 7.3
7.2.2 Plastic behaviour 7.7
7.2.3 SABS 0100 approach 7.10
7.3 Influence of Reinforcement 7.10
7.4 Torsion Combined with Bending and Shear 7.14
7.5 Design for Torsion to SABS 0100 7.14
7.6 Demonstration Problems 7.19
Examples 7-20
8 Bond and Anchorage 8-1
8.1 Introduction 8-1
8.2 Design Ultimate Bond Stress 8-1
8.3 Anchorage of Hooks and Bends 8-4
8.4 Lapping of Bars 8-5
8.5 Bearing Stress Inside a Bend 8-7
8.6 Demonstration Problems 8-9
9 Design for Serviceability 9-1
9.1 Introduction 9-1
9.1.1 Equivalent diameter 9-1
9.2 Cover to Concrete 9-1
9.2.1 Nominal cover 9-1
9.2.2 Conditions of exposure 9-2
9.3 Maximum Clear Spacing of Reinforcement 9-2
9.3.1 Beams 9-3
9.3.2 Slabs 9-5
9.4 Minimum Spacing of Reinforcement 9-6
9.5 Minimu Area of Reinforcement 9-6
9.6 Maximum Area of Reinforcement 9-9
9.7 Reinforcement at Sides of Beams Exceeding 750mm in Depth 9-9
9.8 Span-Effective Depth Ratio 9-10
9.8.1 Basic L/d ratios 9-11
9.8.2 Influence of tension reinforcement and service stress 9-12
9.8.3 Influence of compression reinforcement 9-13
9.8.4 Influence of creep and shrinkage 9-14
9.9 Demonstration Problems 9-15
Examples 9-16
10 Design of Beams 10-1
10.1 Design Process 10-1
10.2 Preliminary design and member dimensions 10-1
10.3 Effective Span Length 10-4
10.4 Analysis of Continuous Beams 10-4
10.5 Flanged Beams 10-6
10.5.1 Effective flange width 10-6
10.5.2 Transverse reinforcement in the flange 10-8
10.6 Beams With Compression Reinforcement 10-8
10.7 Curtailment of Reinforcement 10-10
10.7.1 Introduction 10-10
10.7.2 Curtailment anchorage length 10-11
10.7.3 Simply supported ends 10-13
10.7.4 Simplified curtailment rules 10-14
10.8 Demonstration Problems 10-15
Examples 10-16
11 Analysis and Design of Columns 11-1
11.1 Introduction 11-1
11.2 Short columns subjected to axial loads only 11-1
11.3 Combined bending moment and axial force at the ultimate limit state 11-4
11.3.1 Basic theory – symmetrical rectangular section 11-4
11.3.2 Allowing for the concrete replaced by compression reinforcement 11-6
11.3.3 Development of design charts 11-6
11.3.4 Characteristics of the interaction diagram 11-8
11.3.5 Alternative design charts 11-10
11.3.6 Asymmetrical sections 11-11
11.4 Design of short columns 11-13
11.5 Biaxial bending 11-13
11.5.1 Major and minor axes of bending 11-13
11.5.2 Interaction surface 11-14
11.6 Definitions and conventions for slender columns 11-16
11.6.1 Braced and unbraced columns 11-16
11.6.2 Effective lengths 11-17
11.6.3 Walls 11-20
11.6.4 Short and slender columns 11-20
11.6.5 Slenderness limits 11-23
11.7 Moments and forces in columns 11-24
11.7.1 Column moments from subframes 11-24
11.7.2 Minimum eccentricity 11-26
11.7.3 Additional moments in slender columns 11-27
11.7.4 Braced slender columns 11-28
11.7.5 Unbraced slender columns 11-30
11.7.6 Additional moments in members supporting slender columns 11-32
11.7.7 Slender columns bent uniaxially 11-32
11.7.8 Slender columns bent about both axes 11-32
11.8 Conclusions 11-32
11.9 Demonstration Problems 11-34
Examples 11-35
12 Foundations 12.1
12.1 Bearing Capacity 12.1
12.2 Foundation types 12.4
12.3 Simple Footings 12.6
12.3.1 The case where the M=O 12.6
12.3.2 For the case where e? D/6 12.6
12.3.3 The case where e? D/6 12.7
12.3.4 Detailing of reinforcement 12.8
12.3.5 Critical sections for design 12.1
12.3.6 Design approach 12.12
12.3.7 Footing subjected to a combined axial force and moment 12.13
12.4 Combined footings 12.14
12.4.1 Footing layout 12.14
12.4.2 Detailing 12.15
12.5 Strap footings 12.17
12.6 Strip footings 12.20
Examples 12-22
13 Design of Suspended Floors 13-1
13.1 Introduction 13-1
13.2 One-way spanning slabs 13-3
13.2.1 Behaviour 13-3
13.2.2 Analysis 13-6
13.2.3 Simplified rules for curtailment of bars 13-9
13.2.4 Cracking control 13-10
13.2.5 Concentrated loads 13-12
13.2.6 Examples of one-way spanning slabs 13-13
13.3 Two-way spanning edge supported slabs 13-13
13.3.1 Behaviour 13-13
13.3.2 Analysis of simply supported slabs 13-15
13.3.3 Analysis of slabs with restrained edges 13-17
13.3.4 Deflections in two-way spanning slabs 13-24
13.3.5 Example of a two-way spanning slab 13-25
13.4 Flat slabs 13-25
13.4.1 Introduction 13-25
13.4.2 Equivalent frame analysis 13-25
13.4.3 Column heads 13-32
13.4.4 Moment transfer at slab-column connection 13-34
13.4.5 Simplified analysis method 13-35
13.4.6 Slab thickness 13-37
13.4.7 Effective depth 13-37
13.4.8 Deflections 13-38
13.4.9 Openings in panels 13-38
13.4.10 Detailing of reinforcement 13-39
13.5 Punching shear in slabs 13-40
13.5.1 Shear stresses in solid slabs under concentrated loads 13-40
13.5.2 Design of shear reinforcement for punching 13-43
13.5.3 Effects of moment transfer on shear 13-44
13.5.4 Punching shear examples 13-46
13.6 Flat slab example 13-46
13.7 Ribbed slabs 13-47
13.7.1 Structural topping 13-47
13.7.2 Non-structural topping 13-47
13.7.3 Properties of blocks and formers 13-48
13.7.4 Dimensional requirements 13-48
13.7.5 Design 13-50
13.8 Demonstration Problems 13-51
Examples 13-55
14 Design of Stairs 14-1
14.1 Introduction 14-1
14.2 General Requirements 14-1
14.3 Transverse spanning stairs 14-5
14.4 Stairs spanning longitudinally 14-5
14.4.1 Determining span and loading 14-5
14.4.2 Flights of landings built into a wall 14-7
14.4.3 Landings spanning at right angles to the stair 14-8
14.4.4 Stairs with quarter landings 14-8
14.5 Demonstration Problems 14-10
Examples 14-12
15 Cracking Deflections 15-1
15.1 Tension Stiffening 15-1
15.1.1 Strain reduction 15-1
15.1.2 Effective tensile stress in the concrete 15-6
15.1.3 Effective secant stiffness 15-8
15.2 Cracking in Concrete Structures 15-11
15.2.1 Introduction 15-11
15.2.2 Maximum crack widths and probality of exeedence 15-11
15.2.3 Calculating crack widths 15-12
15.3 Deflections in Concrete Structure 15-15
15.3.1 Introduction 15-15
15.3.2 Calculating instantaneous deflections 15-15
15.3.3 Calculating long-term deflections 15-18
Examples 15-21
16 Introduction to Prestressed Concrete
16.1 The Basic Idea of Prestressed Concrete 16-1
16.2 Effects of Prestressing 16-3
16.3 General Principles 16-5
16.4 Basic Definitions 16-10
16.5 Prestressed Versus Reinforced Concrete 16-12
16.6 History of Prestressed Concrete 16-13
16.7 References to Prestressed Concrete 16-15
17 References
Appendix A: Design Charts for Beams
A.1 Design Charts for Flexure A-1
Appendix B: Design of Charts for Columns
B.1 Rectangular Columns B-1
Appendix C: Reinforcement Areas
C.1 Reinforcement for a given spacing C-1
C.2 Reinforcement for a given number of bars C-2