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Theory of Structures: Fundamentals, Framed Structures, Plates and Shells

Overview

This book provides the reader with a consistent approach to theory of structures on the basis of applied mechanics. It covers framed structures as well as plates and shells using elastic and plastic theory, and emphasizes the historical background and the relationship to practical engineering activities. This is the first comprehensive treatment of the school of structures that has evolved at the Swiss Federal Institute of Technology in Zurich over the last 50 years.

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Overview

This book provides the reader with a consistent approach to theory of structures on the basis of applied mechanics. It covers framed structures as well as plates and shells using elastic and plastic theory, and emphasizes the historical background and the relationship to practical engineering activities. This is the first comprehensive treatment of the school of structures that has evolved at the Swiss Federal Institute of Technology in Zurich over the last 50 years.

The many worked examples and exercises make this a textbook ideal for in-depth studies. Each chapter concludes with a summary that highlights the most important aspects in concise form. Specialist terms are defined in the appendix.

There is an extensive index befitting such a work of reference. The structure of the content and highlighting in the text make the book easy to use. The notation, properties of materials and geometrical properties of sections plus brief outlines of matrix algebra, tensor calculus and calculus of variations can be found in the appendices.

This publication should be regarded as a key work of reference for students, teaching staff and practising engineers. Its purpose is to show readers how to model and handle structures appropriately, to support them in designing and checking the structures within their sphere of responsibility.

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Editorial Reviews

From the Publisher
“However, it would be a wonderful resource for academic and professional libraries and could replace a shelf full of textbooks for the practicing structural engineer. Summing Up: Highly recommended. Upper-division undergraduates, graduate students, researchers/faculty, and professionals/practitioners. (Choice, 1 November 2013)
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Product Details

  • ISBN-13: 9783433029916
  • Publisher: Wiley
  • Publication date: 4/1/2013
  • Edition number: 1
  • Pages: 696
  • Product dimensions: 8.60 (w) x 11.20 (h) x 1.70 (d)

Meet the Author

Prof. Dr. sc. techn. Peter Marti has been professor for theory of structures and structural design at the Swiss Federal Institute of Technology in Zurich since 1990, lecturing in theory of structures and reinforced concrete. Peter Marti has served as chairman on various technical commissions, e.g. ACI-ASCE Joint Committee 445 Shear and Torsion and fib Commission 4 Modelling of Structural Behaviour and Design. He was also president of Swiss standards commission SIA 162 Concrete construction, project manager for Swisscodes and president of the Society for the Art of Civil Engineering. In his role as consulting engineer, reviewer and jury member for competitions, he is responsible for many challenging building, bridge and tunnel projects.

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Table of Contents

Preface V

I INTRODUCTION

1 THE PURPOSE AND SCOPE OF THEORY OF STRUCTURES 1

1.1 General 1

1.2 The basis of theory of structures 1

1.3 Methods of theory of structures 2

1.4 Statics and structural dynamics 3

1.5 Theory of structures and structural engineering 3

2 BRIEF HISTORICAL BACKGROUND 5

II FUNDAMENTALS

3 DESIGN OF STRUCTURES 11

3.1 General 11

3.2 Conceptual design 11

3.3 Service criteria agreement and basis of design 14

3.4 Summary 26

3.5 Exercises 27

4 STRUCTURAL ANALYSIS AND DIMENSIONING 29

4.1 General 29

4.2 Actions 29

4.2.1 Actions and action effects 29

4.2.2 Models of actions and representative values 30

4.3 Structural models 31

4.4 Limit states 31

4.5 Design situations and load cases 32

4.6 Verifications 33

4.6.1 Verification concept 33

4.6.2 Design values 33

4.6.3 Verification of structural safety 34

4.6.4 Verification of serviceability 35

4.7 Commentary 35

4.8 Recommendations for the structural calculations 36

4.9 Recommendations for the technical report 38

4.10 Summary 40

4.11 Exercises 41

5 STATIC RELATIONSHIPS 43

5.1 Force systems and equilibrium 43

5.1.1 Terminology 43

5.1.2 Force systems 44

5.1.3 Equilibrium 45

5.1.4 Overall stability 45

5.1.5 Supports 47

5.1.6 Hinges 50

5.1.7 Stress resultants 51

5.2 Stresses 53

5.2.1 Terminology 53

5.2.2 Uniaxial stress state 53

5.2.3 Coplanar stress states 54

5.2.4 Three-dimensional stress states 57

5.3 Differential structural elements 61

5.3.1 Straight bars 61

5.3.2 Bars in single curvature 62

5.4 Summary 68

5.5 Exercises 69

6 KINEMATIC RELATIONSHIPS 71

6.1 Terminology 71

6.2 Coplanar deformation 72

6.3 Three-dimensional deformation state 74

6.4 Summary 76

6.5 Exercises 77

7 CONSTITUTIVE RELATIONSHIPS 79

7.1 Terminology 79

7.2 Linear elastic behaviour 81

7.3 Perfectly plastic behaviour 83

7.3.1 Uniaxial stress state 83

7.3.2 Three-dimensional stress states 84

7.3.3 Yield conditions 85

7.4 Time-dependent behaviour 90

7.4.1 Shrinkage 90

7.4.2 Creep and relaxation 91

7.5 Thermal deformations 94

7.6 Fatigue 94

7.6.1 General 94

7.6.2 S-N curves 95

7.6.3 Damage accumulation under fatigue loads 96

7.7 Summary 98

7.8 Exercises 99

8 ENERGY METHODS 101

8.1 Introductory example 101

8.1.1 Statically determinate system 101

8.1.2 Statically indeterminate system 103

8.1.3 Work equation 104

8.1.4 Commentary 105

8.2 Variables and operators 105

8.2.1 Introduction 105

8.2.2 Plane framed structures 107

8.2.3 Spatial framed structures 109

8.2.4 Coplanar stress states 110

8.2.5 Coplanar strain state 111

8.2.6 Slabs 111

8.2.7 Three-dimensional continua 113

8.2.8 Commentary 114

8.3 The principle of virtual work 115

8.3.1 Virtual force and deformation variables 115

8.3.2 The principle of virtual deformations 115

8.3.3 The principle of virtual forces 115

8.3.4 Commentary 116

8.4 Elastic systems 118

8.4.1 Hyperelastic materials 118

8.4.2 Conservative systems 119

8.4.3 Linear elastic systems 125

8.5 Approximation methods 128

8.5.1 Introduction 128

8.5.2 The RITZ method 129

8.5.3 The GALERKIN method 132

8.6 Summary 134

8.7 Exercises 135

III LINEAR ANALYSIS OF FRAMED STRUCTURES 9 STRUCTURAL ELEMENTS AND TOPOLOGY 137

9.1 General 137

9.2 Modelling of structures 137

9.3 Discretised structural models 140

9.3.1 Description of the static system 140

9.3.2 Joint equilibrium 141

9.3.3 Static determinacy 142

9.3.4 Kinematic derivation of the equilibrium matrix 144

9.4 Summary 147

9.5 Exercises 147

10 DETERMINING THE FORCES 149

10.1 General 149

10.2 Investigating selected free bodies 150

10.3 Joint equilibrium 154

10.4 The kinematic method 156

10.5 Summary 158

10.6 Exercises 158

11 STRESS RESULTANTS AND STATE DIAGRAMS 159

11.1 General 159

11.2 Hinged frameworks 160

11.2.1 Hinged girders 161

11.2.2 Hinged arches and frames 163

11.2.3 Stiffened beams with intermediate hinges 165

11.3 Trusses 166

11.3.1 Prerequisites and structural topology 166

11.3.2 Methods of calculation 169

11.3.3 Joint equilibrium 169

11.3.4 CREMONA diagram 171

11.3.5 RITTER method of sections 172

11.3.6 The kinematic method 173

11.4 Summary 174

11.5 Exercises 175

12 INFLUENCE LINES 177

12.1 General 177

12.2 Determining influence lines by means of equilibrium conditions 178

12.3 Kinematic determination of influence lines 179

12.4 Summary 183

12.5 Exercises 183

13 ELEMENTARY DEFORMATIONS 185

13.1 General 185

13.2 Bending and normal force 185

13.2.1 Stresses and strains 185

13.2.2 Principal axes 187

13.2.3 Stress calculation 189

13.2.4 Composite cross-sections 190

13.2.5 Thermal deformations 192

13.2.6 Planar bending of curved bars 193

13.2.7 Practical advice 194

13.3 Shear forces 194

13.3.1 Approximation for prismatic bars subjected to pure bending 194

13.3.2 Approximate coplanar stress state 196

13.3.3 Thin-wall cross-sections 197

13.3.4 Shear centre 199

13.4 Torsion 200

13.4.1 Circular cross-sections 200

13.4.2 General cross-sections 201

13.4.3 Thin-wall hollow cross-sections 204

13.4.4 Warping torsion 207

13.5 Summary 216

13.6 Exercises 218

14 SINGLE DEFORMATIONS 221

14.1 General 221

14.2 The work theorem 222

14.2.1 Introductory example 222

14.2.2 General formulation 223

14.2.3 Calculating the passive work integrals 223

14.2.4 Systematic procedure 226

14.3 Applications 226

14.4 MAXWELL’s theorem 230

14.5 Summary 231

14.6 Exercises 231

15 DEFORMATION DIAGRAMS 233

15.1 General 233

15.2 Differential equations for straight bar elements 233

15.2.1 In-plane loading 233

15.2.2 General loading 235

15.2.3 The effect of shear forces 235

15.2.4 Creep, shrinkage and thermal deformations 235

15.2.5 Curved bar axes 235

15.3 Integration methods 236

15.3.1 Analytical integration 236

15.3.2 MOHR’s analogy 238

15.5 Exercises 243

16 THE FORCE METHOD 245

16.1 General 245

16.2 Structural behaviour of statically indeterminate systems 245

16.2.1 Overview 245

16.2.2 Statically determinate system 246

16.2.3 System with one degree of static indeterminacy 247

16.2.4 System with two degrees of static indeterminacy 249

16.2.5 In-depth analysis of system with one degree of static indeterminacy 250

16.2.6 In-depth analysis of system with two degrees of static indeterminacy 253

16.3 Classic presentation of the force method 254

16.3.1 General procedure 254

16.3.2 Commentary 255

16.3.3 Deformations 257

16.3.4 Influence lines 259

16.4 Applications 262

16.5 Summary 272

16.6 Exercises 274

17 THE DISPLACEMENT METHOD 277

17.1 Independent bar end variables 277

17.1.1 General 277

17.1.2 Member stiffness relationship 277

17.1.3 Actions on bars 278

17.1.4 Algorithm for the displacement method 280

17.2 Complete bar end variables 281

17.2.1 General 281

17.2.2 Member stiffness relationship 282

17.2.3 Actions on bars 283

17.2.4 Support force variables 283

17.3 The direct stiffness method 284

17.3.1 Incidence transformation 284

17.3.2 Rotational transformation 285

17.3.3 Algorithm for the direct stiffness method 286

17.4 The slope-deflection method 290

17.4.1 General 290

17.4.2 Basic states and member end moments 292

17.4.3 Equilibrium conditions 293

17.4.4 Applications 294

17.4.5 Restraints 298

17.4.6 Influence lines 303

17.4.7 CROSS method of moment distribution 305

17.5 Summary 309

17.6 Exercises 310

18 CONTINUOUS MODELS 311

18.1 General 311

18.2 Bar extension 311

18.2.1 Practical examples 311

18.2.2 Analytical model 312

18.2.3 Residual stresses 314

18.2.4 Restraints 315

18.2.5 Bond 316

18.2.6 Summary 320

18.3 Beams in shear 321

18.3.1 Practical examples 321

18.3.2 Analytical model 321

18.3.3 Multi-storey frame 321

18.3.4 VIERENDEEL girder 323

18.3.5 Sandwich panels 324

18.3.6 Summary 326

18.4 Beams in bending 326

18.4.1 General 326

18.4.2 Analytical model 327

18.4.3 Restraints 327

18.4.4 Elastic foundation 329

18.4.5 Summary 332

18.5 Combined shear and bending response 333

18.5.1 General 333

18.5.2 Shear wall - frame systems 334

18.5.3 Shear wall connection 338

18.5.4 Dowelled beams 342

18.5.5 Summary 344

18.6 Arches 345

18.6.1 General 345

18.6.2 Analytical model 345

18.6.3 Applications 346

18.6.4 Summary 350

18.7 Annular structures 350

18.7.1 General 350

18.7.2 Analytical model 351

18.7.3 Applications 352

18.7.4 Edge disturbances in cylindrical shells 353

18.7.5 Summary 354

18.8 Cables 354

18.8.1 General 354

18.8.2 Analytical model 355

18.8.3 Inextensible cables 357

18.8.4 Extensible cables 358

18.8.5 Axial stiffness of laterally loaded cables 360

18.8.6 Summary 360

18.9 Combined cable-type and bending response 361

18.9.1 Analytical model 361

18.9.2 Bending-resistant ties 362

18.9.3 Suspended roofs and stress ribbons 363

18.9.4 Suspension bridges 368

18.9.5 Summary 368

18.10 Exercises 369

19 DISCRETISED MODELS 371

19.1 General 371

19.2 The force method 372

19.2.1 Complete and global bar end forces 372

19.2.2 Member flexibility relation 372

19.2.3 Actions on bars 374

19.2.4 Algorithm for the force method 374

19.2.5 Comparison with the classic force method 376

19.2.6 Practical application 376

19.2.7 Reduced degrees of freedom 376

19.2.8 Supplementary remarks 379

19.3 Introduction to the finite element method 381

19.3.1 Basic concepts 381

19.3.2 Element matrices 381

19.3.3 Bar element rigid in shear 381

19.3.4 Shape functions 385

19.3.5 Commentary 386

19.4 Summary 386

19.5 Exercises 387

IV NON-LINEAR ANALYSIS OF FRAMED STRUCTURES

20 ELASTIC-PLASTIC SYSTEMS 389

20.1 General 389

20.2 Truss with one degree of static indeterminacy 389

20.2.1 Single-parameter loading 389

20.2.2 Dual-parameter loading and generalisation 395

20.3 Beams in bending 398

20.3.1 Moment-curvature diagrams 398

20.3.2 Simply supported beams 399

20.3.3 Continuous beams 403

20.3.4 Frames 404

20.3.5 Commentary 405

20.4 Summary 406

20.5 Exercises 407

21 LIMIT ANALYSIS 409

21.1 General 409

21.2 Upper- and lower-bound theorems 410

21.2.1 Basic concepts 410

21.2.2 Lower-bound theorem 410

21.2.3 Upper-bound theorem 411

21.2.4 Compatibility theorem 411

21.2.5 Consequences of the upper- and lower-bound theorems 411

21.3 Static and kinematic methods 412

21.3.1 General 412

21.3.2 Simply supported beams 413

21.3.3 Continuous beams 415

21.3.4 Plane frames 416

21.3.5 Plane frames subjected to transverse loads 421

21.4 Plastic strength of materials 426

21.4.1 General 426

21.4.2 Skew bending 426

21.4.3 Bending and normal force 428

21.4.4 Bending and torsion 432

21.4.5 Bending and shear force 434

21.5 Shakedown and limit loads 435

21.6 Dimensioning for minimum weight 437

21.6.1 General 437

21.6.2 Linear objective function 438

21.6.3 FOULKES mechanisms 438

21.6.4 Commentary 440

21.7 Numerical methods 441

21.7.1 The force method 441

21.7.2 Limit load program 442

21.7.3 Optimum design 444

21.8 Summary 446

21.9 Exercises 447

22 STABILITY 449

22.1 General 449

22.2 Elastic buckling 449

22.2.1 Column deflection curve 449

22.2.2 Bifurcation problems 453

22.2.3 Approximation methods 454

22.2.4 Further considerations 460

22.2.5 Slope-deflection method 465

22.2.6 Stiffness matrices 469

22.3 Elastic-plastic buckling 471

22.3.1 Concentrically loaded columns 471

22.3.2 Eccentrically loaded columns 474

22.3.3 Limit loads of frames according to second-order theory 477

22.4 Flexural-torsional buckling and lateral buckling 480

22.4.1 Basic concepts 480

22.4.2 Concentric loading 482

22.4.3 Eccentric loading in the strong plane 483

22.4.4 General loading 485

22.5 Summary 488

22.6 Exercises 489

V PLATES AND SHELLS

23 PLATES 491

23.1 General 491

23.2 Elastic plates 491

23.2.1 Stress function 491

23.2.2 Polar coordinates 493

23.2.3 Approximating functions for displacement components 496

23.3 Reinforced concrete plate elements 496

23.3.1 Orthogonal reinforcement 496

23.3.2 General reinforcement 500

23.4 Static method 501

23.4.1 General 501

23.4.2 Truss models 501

23.4.3 Discontinuous stress fields 505

23.4.4 Stringer-panel model 511

23.5 Kinematic method 512

23.5.1 Applications in reinforced concrete 512

23.5.2 Applications in geotechnical engineering 517

23.6 Summary 520

23.7 Exercises 522

24 SLABS 525

24.1 Basic concepts 525

24.1.1 General 525

24.1.2 Static relationships 525

24.1.3 Kinematic relationships 531

24.2 Linear elastic slabs rigid in shear with small deflections 533

24.2.1 Fundamental relationships 533

24.2.2 Methods of solution 535

24.2.3 Rotationally symmetric problems 536

24.2.4 Rectangular slabs 539

24.2.5 Flat slabs 543

24.2.6 Energy methods 546

24.3 Yield conditions 547

24.3.1 VON MISES and TRESCA yield conditions 547

24.3.2 Reinforced concrete slabs 550

24.4 Static method 557

24.4.1 Rotationally symmetric problems 557

24.4.2 Moment fields for rectangular slabs 560

24.4.3 Strip method 563

24.5 Kinematic method 567

24.5.1 Introductory example 567

24.5.2 Calculating the dissipation work 568

24.5.3 Applications 569

24.6 The influence of shear forces 572

24.6.1 Elastic slabs 572

24.6.2 Rotationally symmetric VON MISES slabs 574

24.6.3 Reinforced concrete slabs 575

24.7 Membrane action 575

24.7.1 Elastic slabs 575

24.7.2 Perfectly plastic slab strip 577

24.7.3 Reinforced concrete slabs 578

24.8 Summary 581

24.9 Exercises 583

25 FOLDED PLATES 587

25.1 General 587

25.2 Prismatic folded plates 588

25.2.1 Sawtooth roofs 588

25.2.2 Barrel vaults 589

25.2.3 Commentary 593

25.3 Non-prismatic folded plates 594

25.4 Summary 594

25.5 Exercises 594

26 SHELLS 595

26.1 General 595

26.2 Membrane theory for surfaces of revolution 596

26.2.1 Symmetrical loading 596

26.2.2 Asymmetric loading 600

26.3 Membrane theory for cylindrical shells 601

26.3.1 General relationships 601

26.3.2 Pipes and barrel vaults 602

26.3.3 Polygonal domes 604

26.4 Membrane forces in shells of any form 606

26.4.1 Equilibrium conditions 606

26.4.2 Elliptical problems 607

26.4.3 Hyperbolic problems 608

26.5 Bending theory for rotationally symmetric cylindrical shells 613

26.6 Bending theory for shallow shells 615

26.6.1 Basic concepts 615

26.6.2 Differential equation for deflection 616

26.6.3 Circular cylindrical shells subjected to asymmetric loading 617

26.7 Bending theory for symmetrically loaded surfaces of revolution 620

26.7.1 Basic concepts 620

26.7.2 Differential equation for deflection 620

26.7.3 Spherical shells 621

26.7.4 Approximation for shells of any form 623

26.8 Stability 623

26.8.1 General 623

26.8.2 Bifurcation loads 624

26.8.3 Commentary 626

26.9 Summary 627

26.10 Exercises 628

APPENDIX

A1 DEFINITIONS 631

A2 NOTATION 637

A3 PROPERTIES OF MATERIALS 643

A4 GEOMETRICAL PROPERTIES OF SECTIONS 645

A5 MATRIX ALGEBRA 649

A5.1 Terminology 649

A5.2 Algorithms 650

A5.3 Linear equations 652

A5.4 Quadratic forms 652

A5.5 Eigenvalue problems 653

A5.6 Matrix norms and condition numbers 654

A6 TENSOR CALCULUS 655

A6.1 Introduction 655

A6.2 Terminology 655

A6.3 Vectors and tensors 656

A6.4 Principal axes of symmetric second-order tensors 658

A6.5 Tensor fields and integral theorems 658

A7 CALCULUS OF VARIATIONS 661

A7.1 Extreme values of continuous functions 661

A7.2 Terminology 661

A7.3 The simplest problem of calculus of variations 662

A7.4 Second variation 663

A7.5 Several functions required 664

A7.6 Higher-order derivatives 664

A7.7 Several independent variables 665

A7.8 Variational problems with side conditions 665

A7.9 The RITZ method 666

A7.10 Natural boundary conditions 667

REFERENCES 669

NAME INDEX 671

SUBJECT INDEX 673

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