Design of Structural Elements PDF

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Design of Structural Elements W.M.C. McKenzie Design of Structural Elements W.M.C. McKenzie BSc, PhD, CPhys, MInstP, CEng. Teaching Fellow, Napier University, Edinburgh © W. M. C. McKenzie 2004 All rights reserved. No reproduction, copy or transmission of this publication may be made without written...

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Design of Structural Elements W.M.C. McKenzie

Design of Structural Elements W.M.C. McKenzie BSc, PhD, CPhys, MInstP, CEng. Teaching Fellow, Napier University, Edinburgh

© W. M. C. McKenzie 2004 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, 90 Tottenham Court Road, London W1T 4LP. Any person who does any unauthorised act in relations to this publication may be liable to criminal prosecution and civil claims for damages. The author(s) has/have asserted his/her/their right(s) to be identified as the author(s) of this work in accordance with the Copyright, Designs and Patents Act 1988. First published 2004 by PALGRAVE MACMILLAN Houndmills, Basingstoke, Hampshire RG21 6XS and 175 Fifth Avenue, New York, N.Y. 10010 Companies and representatives throughout the world PALGRAVE MACMILLAN is the global academic imprint of the Palgrave Macmillan division of St. Martin’s Press LLC and of Palgrave Macmillan Ltd. Macmillan© is a registered trademark in the United States, United Kingdom and other countries. Palgrave is a registered trademark in the European Union and other countries. ISBN 1–4039–1224–6 paperback This book is printed on paper suitable for recycling and made from fully managed and sustained forest sources A catalogue record for this book is available from the British Library. Library of Congress Cataloging-in-Publication Data p. cm. Includes bibliographical references and index. ISBN 0−333−00000−0 1. 10

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Printed in Great Britain by Antony Rowe Ltd, Chippenham and Eastbourne

Contents Preface Acknowledgements

1. Structural Analysis Techniques

xvii xix

1

1.1

Resumé of Analysis Techniques

1

1.2

Method of Sections for Pin-Jointed Frames

1

1.2.1 Example 1.1: Pin-Jointed Truss

2

1.3

Method of Joint Resolution for Pin-Jointed Frames

4

1.4

Unit Load Method to Determine the Deflection of Pin-Jointed Frames

6

1.4.1 Example 1.2: Deflection of a Pin-Jointed Truss

6

1.5

Shear Force and Bending Moment

10

1.5.1 Shear Force Diagrams

13

1.5.2 Bending Moment Diagrams

16

1.5.3 Example 1.3: Beam with Uniformly Distributed Load (UDL)

20

1.5.4 Example 1.4: Beam with Combined Point Loads and UDLs

23

McCaulay’s Method for the Deflection of Beams

25

1.6.1 Example 1.5: Beam with Point Loads

26

1.6.2 Example 1.6: Beam with Combined Point Loads and UDLs

29

1.7

Equivalent UDL Technique for the Deflection of Beams

32

1.8

Elastic Shear Stress Distribution

33

1.8.1 Example 1.7: Shear Stress Distribution in a Rectangular Beam

34

Elastic Bending Stress Distribution

36

1.9.1 Example 1.8: Bending Stress Distribution in a Rectangular Beam

38

1.6

1.9

1.10 Transformed Sections 1.10.1 Example 1.9: Composite Timber/Steel Section 1.11 Moment Distribution

39 40 42

1.11.1 Bending (Rotational) Stiffness

44

1.11.2 Carry-Over Moment

45

1.11.3 Pinned End

45

1.11.4 Free and Fixed Bending Moments

45

iv

Contents 1.11.5 Example 1.10: Single-span Encastre Beam

47

1.11.6 Propped Cantilevers

49

1.11.7 Example 1.11: Propped Cantilever

50

1.11.8 Distribution Factors

53

1.11.9 Application of the Method

54

1.11.10 Example 1.12: Three-span Continuous Beam

55

2. Design Philosophies

63

2.1

Introduction

63

2.2

Permissible Stress Design

63

2.3

Load Factor Design

63

2.4

Limit State Design

64

2.5

Design Codes

65

2.6

Eurocodes

67

2.6.1

National Annex

67

2.6.2

Normative and Informative

68

2.6.3

Terminology, Symbols and Conventions 2.6.3.1 Decimal Point 2.6.3.2 Symbols and Subscripts

68 68 68

2.6.4

Limit State Design

69

2.6.5

Design Values 2.6.5.1 Partial Safety Factors

70 71

2.6.6

Conventions

73

3. Structural Loading 3.1

Introduction

74 74

3.1.1

Dead loads: BS 648:1964

74

3.1.2

Imposed Loads: BS 6399-1:1996

74

3.1.3

Imposed Roof Loads: BS 6399-3:1988

75

3.1.4

Wind Loads: BS 6399-2:1997

75

3.2

Floor Load Distribution

75

3.3

Example 3.1: Load Distribution − One-way Spanning Slabs

76

3.4

Example 3.2: Load Distribution − Two-way Spanning Slabs

77

Contents

v

3.5

Example 3.3: Load Distribution − Secondary Beams

78

3.6

Example 3.4: Combined One-way/Two-way Slabs and Beams −1

79

3.7

Example 3.5: Combined One-way/Two-way Slabs and Beams – 2

80

3.8

Example 3.6: Combined One-way/Two-way Slabs and Beams – 3

83

4. Structural Instability, Overall Stability and Robustness

86

4.1

Introduction

86

4.2

Overall Buckling

86

4.2.1

Short Elements

87

4.2.2

Slender Elements

87

4.2.3

Intermediate Elements

88

4.2.4

Secondary Stresses 4.2.4.1 Effect on Short Elements 4.2.4.2 Effect on Slender Elements 4.2.4.3 Effect on Intermediate Elements

88 89 90 90

4.2.5

Critical Stress 4.2.5.1 Critical Stress for Short Columns 4.2.5.2 Critical Stress for Slender Columns 4.2.5.3 Effective Buckling Length 4.2.5.4 Critical Stress for Intermediate Columns

90 90 90 92 94

4.3

Local Buckling

100

4.4

Lateral Torsional Buckling

100

4.5

4.4.1

Lateral Restraint 4.4.1.1 Full Lateral Restraint 4.4.1.2 Intermittent Lateral Restraint 4.4.1.3 Torsional Restraint 4.4.1.4 Beams without Torsional Restraint

101 101 102 102 103

4.4.2

Effective Length

103

Overall Structural Stability

103

4.5.1

Structural Form

106

4.5.2

Braced Frames

106

4.5.3

Unbraced Frames

107

4.5.4

Shear Cores/Walls

108

4.5.5

Cross-Wall Construction

110

4.5.6

Cellular Construction

110

4.5.7

Diaphragm Action

111

vi

Contents 4.5.8

Accidental Damage and Robustness

111

5. Design of Reinforced Concrete Elements 5.1

Introduction

113

5.2

Material Properties

116

5.3

5.4

5.2.1

Concrete Compressive Strength

116

5.2.2

Concrete Tensile Strength

116

5.2.3

Concrete Stress-Strain Relationship

116

5.2.4

Concrete Modulus of Elasticity

118

5.2.5

Concrete Poisson’s Ratio

118

5.2.6

Steel Reinforcement Strength

118

5.2.7

Steel Reinforcement Stress-Strain Relationship

118

5.2.8

Steel Reinforcement Modulus of Elasticity

120

5.2.9

Material Partial Safety Factors

120

5.2.10 Durability 5.2.10.1 Minimum Dimensions

120 123

5.2.11 Example 5.1: Nominal Cover 1

123

5.2.12 Example 5.2: Nominal Cover 2

124

5.2.13 Example 5.3: Nominal Cover 3

126

Flexural Strength of Sections

126

5.3.1

Singly-reinforced Sections

131

5.3.2

Example 5.4: Singly-reinforced Rectangular Beam 1

133

5.3.3

Example 5.5: Singly-reinforced Rectangular Beam 2

133

5.3.4

Example 5.6: Singly-reinforced Rectangular Beam 3

134

5.3.5

Example 5.7: Singly-reinforced Rectangular Slab 1

135

5.3.6

Doubly-reinforced Sections

140

5.3.7

Example 5.8: Doubly-reinforced Rectangular Beam 1

142

5.3.8

Example 5.9: Doubly-reinforced Rectangular Beam 2

143

5.3.9

Example 5.10: Doubly-reinforced Rectangular Beam 3

145

Shear Strength of Sections

147

5.4.1

Example 5.11: Shear Links Beam 1

151

5.4.2

Example 5.12: Shear Links Beam 2

153

Contents 5.5

Deflection of Beams

vii 156

5.5.1

Example 5.13: Deflection − Beam 1

158

5.5.2

Example 5.14: Deflection − Beam 2

159

5.5.3

Example 5.15: Deflection − Rectangular Slab

162

5.6

Effective Span of Beams

163

5.7

Detailing of Sections

163

5.8

5.7.1

Minimum Areas of Steel 5.7.1.1 Example 5.16: Minimum Areas of Steel

164 164

5.7.2

Maximum Areas of Steel

167

5.7.3

Minimum Spacing of Bars

167

5.7.4

Maximum Spacing of Bars

168

5.7.5

Bond and Anchorage

170

5.7.6

Lap Lengths

172

5.7.7

Curtailment of Bars and Anchorage at Supports 5.7.7.1 Simplified Detailing Rules for Beams

173 175

Example 5.17: Slab and Beam Design 5.8.1

5.9

Solution to Example 5.17

Example 5.18: Doubly Reinforced Beam 5.9.1

Solution to Example 5.18

5.10 T and L Beams

177 178 186 186 188

5.10.1 Introduction

188

5.10.2 Bending

189

5.10.3 Shear

189

5.10.4 Deflection

189

5.10.5 Transverse Reinforcement

189

5.10.6 Example 5.19: Single-Span T-Beam Design

189

5.10.7 Solution to Example 5.19

191

5.11 Multi-Span Beams and Slabs 5.11.1 Analysis 5.11.1.1 Example 5.20: Analysis of a Typical Sub-Frame

195 195 201

5.11.2 Re-Distribution of Moments 203 5.11.2.1 Example 5.21: Redistribution of Moments in a Two-Span Beam 204

viii

Contents 5.11.3 Example 5.22: Multi-Span Floor System Design

207

5.11.4 Solution to Example 5.22

208

5.12 Ribbed Slabs (with Solid Blocks, Hollow Blocks or Voids)

221

5.12.1 Introduction

221

5.12.2 Spacing and Size of Ribs

223

5.12.3 Thickness of Structural Topping

223

5.12.4 Deflection

223

5.12.5 Arrangement of Reinforcement

223

5.12.6 Links in Ribs

224

5.12.7 Design Resistance Moments

224

5.12.8 Design Shear Stress

224

5.12.9 Example 5.23: Single-Span Hollow- Tile Floor

224

5.12.10 Solution to Example 5.23

225

5.13 Two-Way Spanning Slabs

229

5.13.1 Introduction

229

5.13.2 Simply-Supported Slabs

230

5.13.3 Deflection

231

5.13.4 Restrained Slabs

231

5.13.5 Torsion

232

5.13.6 Loads on Supporting Beams

233

5.13.7 Example 5.24: Simply-Supported Two-Way Spanning Slab

233

5.13.8 Solution to Example 5.24

234

5.13.9 Example 5.25: Two-Way Spanning Restrained Slab

237

5.13.10 Solution to Example 5.25

238

5.14 Design Charts for Bending Moments

243

5.14.1 Example 5.26: Singly-Reinforced Rectangular Beam

243

5.14.2 Example 5.27: Singly-Reinforced Rectangular Slab

244

5.14.3 Example 5.28: Doubly-Reinforced Rectangular Beam

245

5.15 Columns 5.15.1 Design Resistance of Columns 5.15.1.1 Short Columns Resisting Moments and Axial Forces 5.15.1.2 Short Braced Columns Supporting an Approximately Symmetrical Arrangement of Beams

246 248 249 249

Contents

ix

5.15.2 Example 5.29: Axially Loaded Short Column

249

5.15.3 Solution to Example 5.29

250

5.15.4 Example 5.30: Reinforced Concrete Multi-Storey Braced Column

251

5.15.5 Solution to Example 5.30

252

5.16 Foundations

256

5.16.1 Introduction

256

5.16.2 Pad Foundations

256

5.16.3 Combined Foundations

256

5.16.4 Strip Footings

257

5.16.5 Raft Foundations

257

5.16.6 Piled Foundations

258

5.16.7 Loading Effects

259

5.16.8 Base Pressures 5.16.8.1 Case 1: Uniform Pressure (compression throughout) 5.16.8.2 Case 2: Varying Pressure (compression throughout) 5.16.8.3 Case 3: Varying Pressure (compression over part of the base)

259 259 260

5.16.9 Design of Pad Foundations 5.16.9.1 Critical Section for Bending 5.16.9.2 Critical Sections for Shear 5.16.9.3 Design Procedure

261 261 262 262

5.16.10 Example 5.31: Axially Loaded Pad Foundation

263

5.16.11 Solution to Example 5.31

263

5.16.12 Example 5.32: Pad Foundation with Axial Load and Moment

268

5.16.13 Solution to Example 5.32

268

5.16.14 Example 5.33: Inverted T-Beam Combined Foundation

275

5.16.15 Solution to Example 5.33

275

6. Design of Structural Steelwork Elements

260

282

6.1

Introduction

282

6.2

Material Properties

283

6.2.1

Stress-Strain Characteristics

283

6.2.2

Ductility 6.2.2.1 Example 6.1 6.2.2.2 Example 6.2

284 285 286

6.2.3

Fatigue

287

x

Contents

6.3

6.2.4

Elastic Properties

287

6.2.5

Section Classification 6.2.5.1 Aspect Ratio 6.2.5.2 Type of Section 6.2.5.3 Plastic Sections 6.2.5.4 Compact Sections 6.2.5.5 Semi-compact Sections 6.2.5.6 Slender Sections 6.2.5.7 Example 6.3: Classification of Sections

287 288 289 291 291 291 292 292

6.2.6

Cross-Section Properties 6.2.6.1 Gross Cross-sectional Properties 6.2.6.2 Net Cross-sectional Area 6.2.6.3 Example 6.4: Net Cross-sectional Area 6.2.6.4 Effective Net Cross-sectional Area 6.2.6.5 Example 6.5: Effective Net Cross-sectional Area 6.2.6.6 Effective Plastic Section Modulus for Class 3 Sections 6.2.6.7 Example 6.6: Effective Plastic Section Modulus for Class 3 Sections 6.2.6.8 Effective Cross-sectional Area and Section Modulus for Class 4 Sections 6.2.6.9 Example 6.7: Effective Plastic Section Properties for Class 4 Sections

295 295 295 296 297 297 297

Axially Loaded Elements

298 300 301 302

6.3.1

Introduction

302

6.3.2

Tension Members 6.3.2.1 Effects of Eccentric Connections 6.3.2.2 Single Angle, Channels and T-Sections 6.3.2.3 Double Angles, Channels and T-Sections Connected Both Sides of a Gusset Plate 6.3.2.4 Other Simple Ties 6.3.2.5 Example 6.8: Plate with Staggered Holes − Single and Double Angle Sections 6.3.2.6 Solution to Example 6.8

306 306 307

Compression Members 6.3.3.1 Compressive Strength 6.3.3.2 Compressive Resistance 6.3.3.3 Slenderness 6.3.3.4 Example 6.9: Single Angle Strut 6.3.3.5 Solution to Example 6.9 6.3.3.6 Example 6.10: Double Angle Strut 6.3.3.7 Solution to Example 6.10 6.3.3.8 Example 6.11: Side Column with Lateral Restraint to Flanges 6.3.3.9 Solution to Example 6.11

312 312 313 313 314 315 316 316

6.3.3

307 308 309 309

318 318

Contents

6.3.4

6.3.5

6.3.6

xi

6.3.3.10 Example 6.12: Concentrically Loaded Column 6.3.3.11 Solution to Example 6.12 6.3.3.12 Column Base Plates 6.3.3.13 Example 6.13: Column Base Plate 6.3.3.14 Solution to Example 6.13

319 320 321 323 323

Flexural Elements 6.3.4.1 Section Classification 6.3.4.2 Shear Capacity 6.3.4.3 Example 6.14: Shear Check of a Simply Supported Beam 6.3.4.4 Moment Capacity 6.3.4.5 Example 6.15: Moment Capacity of Beam with Full Lateral Restraint 6.3.4.6 Solution to Example 6.15 6.3.4.7 Moment Capacity of Beams with Intermittent Lateral Restraint 6.3.4.8 Example 6.16: Beam with No Lateral Restraint 6.3.4.9 Solution to Example 6.16 6.3.4.10 Example 6.17: Beam 1 with Intermittent Lateral Restraint 6.3.4.11 Solution to Example 6.17 6.3.4.12 Example 6.18: Rectangular Hollow Section 6.3.4.13 Solution to Example 6.18 6.3.4.14 Deflection − Example 6.19 6.3.4.15 Web Bearing and Web Buckling − Example 6.20 6.3.4.16 Example 6.21: Beam 2 with Intermittent Lateral Restraint 6.3.4.17 Solution to Example 6.21 6.3.4.18 Example 6.22: Beam 3 Beam with Cantilever S...