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استاتیک و مقاومت مصالح.ویرایش1.بیر جانسون

(statics and mechanics of materials1st (p.beer & e.rassell johnston

 

1 Introduction 1

1.1 What is Mechanics? 2

1.2 Fundamental Concepts and Principles—

Mechanics of Rigid Bodies 2

1.3 Fundamental Concepts—Mechanics of

Deformable Bodies 5

1.4 Systems of Units 5

1.5 Conversion from One System of Units to Another 10

1.6 Method of Problem Solution 11

1.7 Numerical Accuracy 13

2 Statics of Particles 14

2.1 Introduction 16

Forces in a Plane 16

2.2 Force on a Particle. Resultant of Two Forces 16

2.3 Vectors 17

2.4 Addition of Vectors 18

2.5 Resultant of Several Concurrent Forces 20

2.6 Resolution of a Force into Components 21

2.7 Rectangular Components of a Force. Unit Vectors 26

2.8 Addition of Forces by Summing x and y Components 29

2.9 Equilibrium of a Particle 33

2.10 Newton’s First Law of Motion 34

2.11 Problems Involving the Equilibrium of a Particle.

Free-Body Diagrams 34

Forces in Space 42

2.12 Rectangular Components of a Force in Space 42

2.13 Force Defined by its Magnitude and

Two Points on Its Line of Action 45

2.14 Addition of Concurrent Forces in Space 46

2.15 Equilibrium of a Particle in Space 52

Review and Summary 58

Review Problems 61

3 Rigid Bodies: Equivalent

Systems of Forces 64

3.1 Introduction 66

3.2 External and Internal Forces 66

3.3 Principle of Transmissibility. Equivalent Forces 67

3.4 Vector Product of Two Vectors 69

3.5 Vector Products Expressed in Terms of

Rectangular Components 71

3.6 Moment of a Force about a Point 73

3.7 Varignon’s Theorem 75

3.8 Rectangular Components of the Moment of a Force 75

3.9 Scalar Product of Two Vectors 84

3.10 Mixed Triple Product of Three Vectors 86

3.11 Moment of a Force about a Given Axis 87

3.12 Moment of a Couple 94

3.13 Equivalent Couples 95

3.14 Addition of Couples 97

3.15 Couples Can be Represented by Vectors 97

3.16 Resolution of a Given Force into a Force at O

and a Couple 98

3.17 Reduction of a System of Forces to One Force and

One Couple 108

3.18 Equivalent Systems of Forces 109

3.19 Equipollent Systems of Vectors 110

3.20 Further Reduction of a System of Forces 110

Review and Summary 122

Review Problems 127

4 Equilibrium of Rigid Bodies 130

4.1 Introduction 132

4.2 Free-Body Diagram 133

Equilibrium in Two Dimensions 134

4.3 Reactions at Supports and Connections for a

Two-Dimensional Structure 134

4.4 Equilibrium of a Rigid Body in Two Dimensions 136

4.5 Statically Indeterminate Reactions. Partial Constraints 138

4.6 Equilibrium of a Two-Force Body 149

4.7 Equilibrium of a Three-Force Body 150

Equilibrium in Three Dimensions 155

4.8 Equilibrium of a Rigid Body in Three Dimensions 155

4.9 Reactions at Supports and Connections

for a Three-Dimensional Structure 155

4.10 Friction Forces 167

4.11 The Laws of Dry Friction. Coefficients of Friction 167

4.12 Angles of Friction 170

4.13 Problems Involving Dry Friction 171

Review and Summary 179

Review Problems 183

5 Distributed Forces: Centroids

and Centers of Gravity 186

5.1 Introduction 188

Areas and Lines 188

5.2 Center of Gravity of a Two-Dimensional Body 188

5.3 Centroids of Areas and Lines 190

5.4 First Moments of Areas and Lines 191

5.5 Composite Plates and Wires 194

5.6 Determination of Centroids by Integration 201

5.7 Theorems of Pappus-Guldinus 203

*5.8 Distributed Loads on Beams 210

Volumes 213

*5.9 Center of Gravity of a Three-Dimensional Body.

Centroid of a Volume 213

*5.10 Composite Bodies 214

Review and Summary 221

Review Problems 224

6 Analysis of Structures 226

6.1 Introduction 228

Trusses 229

6.2 Definition of a Truss 229

6.3 Simple Trusses 231

6.4 Analysis of Trusses by the Method of Joints 232

6.5 Joints under Special Loading Conditions 234

6.6 Analysis of Trusses by the Method of Sections 240

*6.7 Trusses Made of Several Simple Trusses 241

Frames and Machines 248

6.8 Structures Containing Multiforce Members 248

6.9 Analysis of a Frame 248

6.10 Frames Which Cease to Be Rigid when

Detached from Their Supports 249

6.11 Machines 260

Review and Summary 271

Review Problems 274

Contents v

7 Distributed Forces: Moments of

Inertia of Areas 276

7.1 Introduction 278

7.2 Second Moment, or Moment of Inertia, of an Area 278

7.3 Determination of the Moment of Inertia

of an Area by Integration 279

7.4 Polar Moment of Inertia 281

7.5 Radius of Gyration of an Area 282

7.6 Parallel-Axis Theorem 287

7.7 Moments of Inertia of Composite Areas 288

Review and Summary 295

Review Problems 297

8 Concepts of Stress 300

8.1 Introduction 302

8.2 Stresses in the Members of a Structure 302

8.3 Axial Loading. Normal Stress 303

8.4 Shearing Stress 305

8.5 Bearing Stress in Connections 306

8.6 Application to the Analysis of a Simple Structure 307

8.7 Design 312

8.8 Stress on an Oblique Plane under Axial Loading 320

8.9 Stress under General Loading Conditions.

Components of Stress 321

8.10 Design Considerations 324

Review and Summary 335

Review Problems 338

9 Stress and Strain—Axial

Loading 342

9.1 Introduction 344

9.2 Normal Strain under Axial Loading 345

9.3 Stress-Strain Diagram 346

9.4 Hooke’s Law. Modulus of Elasticity 351

*9.5 Elastic versus Plastic Behavior of a Material 352

*9.6 Repeated Loadings. Fatigue 354

9.7 Deformations of Members under Axial Loading 355

9.8 Statically Indeterminate Problems 364

9.9 Problems Involving Temperature Changes 368

9.10 Poisson’s Ratio 379

9.11 Multiaxial Loading: Generalized Hooke’s Law 380

9.12 Shearing Strain 382

*9.13 Further Discussion of Deformations under

Axial Loading. Relation Among E, n, and G 385

9.14 Stress and Strain Distribution under

Axial Loading. Saint-Venant’s Principle 391

9.15 Stress Concentrations 393

Review and Summary 397

Review Problems 402

10 Torsion 406

10.1 Introduction 408

10.2 Preliminary Discussion of the Stresses in a Shaft 409

10.3 Deformations in a Circular Shaft 411

10.4 Stresses 413

10.5 Angle of Twist 423

10.6 Statically Indeterminate Shafts 427

Review and Summary 437

Review Problems 439

11 Pure Bending 442

11.1 Introduction 444

11.2 Symmetric Member in Pure Bending 446

11.3 Deformations in a Symmetric Member in Pure Bending 448

11.4 Stresses and Deformations 451

11.5 Bending of Materials Made of Several Materials 461

11.6 Eccentric Axial Loading in a Plane of Symmetry 471

*11.7 Unsymmetric Bending 479

*11.8 General Case of Eccentric Axial Loading 485

Review and Summary 493

Review Problems 496

12 Analysis and Design of

Beams for Bending 500

12.1 Introduction 502

12.2 Shear and Bending-Moment Diagrams 505

12.3 Relations among Load, Shear, and Bending Moment 514

12.4 Design of Prismatic Beams for Bending 524

Review and Summary 531

Review Problems 533

Contents vii

13 Shearing Stresses in Beams and

Thin-Walled Members 536

13.1 Introduction 538

13.2 Shear on the Horizontal Face of a Beam Element 540

13.3 Determination of the Shearing Stresses in a Beam 542

13.4 Shearing Stresses txy in Common Types of Beams 543

13.5 Longitudinal Shear on a Beam Element of Arbitrary

Shape 552

13.6 Shearing Stresses in Thin-Walled Members 554

Review and Summary 564

Review Problems 566

14 Transformations of Stress 570

14.1 Introduction 572

14.2 Transformation of Plane Stress 574

14.3 Principal Stresses. Maximum Shearing Stresses 575

14.4 Mohr’s Circle for Plane Stress 582

14.5 Stresses in Thin-Walled Pressure Vessels 592

Review and Summary 599

Review Problems 602

15 Deflection of Beams 604

15.1 Introduction 606

15.2 Deformation of a Beam under Transverse Loading 607

15.3 Equation of the Elastic Curve 608

15.4 Direct Determination of the Elastic

Curve from the Load Distribution 614

15.5 Statically Indeterminate Beams 616

15.6 Method of Superposition 624

15.7 Application of Superposition to Statically

Indeterminate Beams 626

Review and Summary 634

Review Problems 637

viii Contents

16 Columns 640

16.1 Introduction 642

16.2 Stability of Structures 642

16.3 Euler’s Formula for Pin-Ended Columns 644

16.4 Extension of Euler’s Formula to Columns

with Other End Conditions 648

*16.5 Design of Columns under a Concentric Load 658

Review and Summary 670

Review Problems 672

Appendices 675

A Typical Properties of Selected Materials

Used in Engineering 676

B Properties of Rolled-Steel Shapes 680

C Beam Deflections and Slopes 692

Photo Credits 693

Index 695

Answers to Problems 705

Contents ix

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