## Description

The main objective of a basic mechanics course should be to develop in the student the ability to analyze a given problem in a simple and logical manner and to apply to its solution a few fundamental and well-understood principles. This text is designed for the first course in mechanics of materials—or of materials—offered to engineering students in the sophomore or junior year. The authors hope that it will help instructors achieve this goal in that particular course in the same way that their other texts may have helped them in statics and dynamics.

In this text the study of the mechanics of materials is based on the understanding of a few basic concepts and on the use of simplified models. This approach makes it possible to develop all the necessary in a rational and logical manner, and to clearly indicate the conditions under which they can be safely applied to the of actual structures and components.

Free-body diagrams are used extensively throughout the text to determine external or internal forces. The use of “picture equations” will also help the students understand the superposition of loadings and the resulting stresses and deformations.

Each chapter begins with an introductory section setting the purpose and goals of the chapter and describing in simple terms the material to be covered and its application to the solution of problems. The body of the text has been divided into units, each consisting of one or several theory sections followed by sample problems and a large number of problems to be assigned. Each unit corresponds to a well-defined topic and generally can be covered in one lesson. Each chapter ends with a review and summary of the material covered in the chapter.

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• 1 INTRODUCTION—CONCEPT OF STRESS 2
1.1 Introduction 2
1.2 A Short Review of the Methods of Statics 2
1.3 Stresses in the Members of a Structure 5
1.4 Analysis and Design 6
1.6 Shearing Stress 9
1.7 Bearing Stress in Connections 11
1.8 Application to the Analysis and Design of Simple Structures 12
1.9 Method of Problem Solution 14
1.10 Numerical Accuracy 15
1.13 Design Considerations 27
Review and Summary for Chapter 1 38

2.1 Introduction 47
2.3 Stress-Strain Diagram 50
2.4 True Stress and True Strain 55
2.5 Hooke’s Law; Modulus of Elasticity 56
2.6 Elastic versus Plastic Behavior of a Material 57
2.9 Statically Indeterminate Problems 70
2.10 Problems Involving Temperature Changes 74
2.11 Poisson’s Ratio 84
2.13 Dilatation; Bulk Modulus 87
2.14 Shearing Strain 89
2.15 Further Discussion of Deformations under AxialLoading; Relation among E, , and G 92
2.16 Stress-Strain Relationships for Fiber-Reinforced Composite Materials 95
2.18 Stress Concentrations 107
2.19 Plastic Deformations 109
2.20 Residual Stresses 113
Review and Summary for Chapter 2 121

3 TORSION 132
3.1 Introduction 132
3.2 Preliminary Discussion of the Stresses in a Shaft 134
3.3 Deformations in a Circular Shaft 136
3.4 Stresses in the Elastic Range 139
3.5 Angle of Twist in the Elastic Range 150
3.6 Statically Indeterminate Shafts 153
3.7 Design of Transmission Shafts 165
3.8 Stress Concentrations in Circular Shafts 167
3.9 Plastic Deformations in Circular Shafts 172
3.10 Circular Shafts Made of an Elastoplastic Material 174
3.11 Residual Stresses in Circular Shafts 177
3.12 Torsion of Noncircular Members 186
3.13 Thin-Walled Hollow Shafts 189
Review and Summary for Chapter 3 198

4 PURE BENDING 209
4.1 Introduction 209
4.2 Symmetric Member in Pure Bending 211
4.3 Deformations in a Symmetric Member in Pure Bending 213
4.4 Stresses and Deformations in the Elastic Range 216
4.5 Deformations in a Transverse Cross Section 220
4.6 Bending of Members Made of Several Materials 230
4.7 Stress Concentrations 234
4.8 Plastic Deformations 243
4.9 Members Made of an Elastoplastic Material 246
4.10 Plastic Deformations of Members with a Single Plane of Symmetry 250
4.11 Residual Stresses 250
4.13 Unsymmetric Bending 270
4.15 Bending of Curved Members 285
Review and Summary for Chapter 4 298

5 ANALYSIS AND DESIGN OF BEAMS FOR BENDING 308
5.1 Introduction 308
5.2 Shear and Bending-Moment Diagrams 311
5.3 Relations among Load, Shear, and Bending Moment 322
5.4 Design of Prismatic Beams for Bending 332
5.5 Using Singularity Functions to Determine Shear and Bending Moment in a Beam 343
5.6 Nonprismatic Beams 354
Review and Summary for Chapter 5 363

6 SHEARING STRESSES IN BEAMS AND THIN-WALLED MEMBERS 372
6.1 Introduction 372
6.2 Shear on the Horizontal Face of a Beam Element 374
6.3 Determination of the Shearing Stresses in a Beam 376
6.4 Shearing Stresses in Common Types of Beams 377
*6.5 Further Discussion of the Distribution of Stresses in a Narrow Rectangular Beam 380
6.6 Longitudinal Shear on a Beam Element of Arbitrary Shape 388
6.7 Shearing Stresses in Thin-Walled Members 390
6.8 Plastic Deformations 392
Review and Summary for Chapter 6 414

7 TRANSFORMATIONS OF STRESS AND STRAIN 423
7.1 Introduction 423
7.2 Transformation of Plane Stress 425
7.3 Principal Stresses: Maximum Shearing Stress 428
7.4 Mohr’s Circle for Plane Stress 436
7.5 General State of Stress 446
7.6 Application of Mohr’s Circle to the Three-Dimensional Analysis of Stress 448
7.7 Yield Criteria for Ductile Materials under Plane Stress 451
7.8 Fracture Criteria for Brittle Materials under Plane Stress 453
7.9 Stresses in Thin-Walled Pressure Vessels 462
7.10 Transformation of Plane Stress 470
7.11 Mohr’s Circle for Plane Strain 473
7.12 Three-Dimensional Analysis of Strain 475
7.13 Measurements of Strain; Strain Rosette 478
Review and Summary for Chapter 7 486

8.1 Introduction 496
8.2 Principal Stresses in a Beam 497
8.3 Design of Transmission Shafts 500
Review and Summary for Chapter 8 521

9 DEFLECTION OF BEAMS 530
9.1 Introduction 530
9.3 Equation of the Elastic Curve 533
9.4 Direct Determination of the Elastic Curve from the Load Distribution 538
9.5 Statically Indeterminate Beams 540
9.6 Using Singularity Functions to Determine the Slope and Deflection of a Beam 549
9.7 Method of Superposition 558
9.8 Application of Superposition to Statically Indeterminate Beams 560
9.9 Moment-Area Theorems 569
9.11 Bending-Moment Diagrams by Parts 573
9.13 Maximum Deflection 584
9.14 Use of Moment-Area Theorems with Statically Indeterminate Beams 586
Review and Summary for Chapter 9 594

10 COLUMNS 607
10.1 Introduction 607
10.2 Stability of Structures 608
10.3 Euler’s Formula for Pin-Ended Columns 610
10.4 Extension of Euler’s Formula to Columns with Other End Conditions 614
10.6 Design of Columns under a Centric Load 636
10.7 Design of Columns under an Eccentric Load 652
Review and Summary for Chapter 10 662

11 ENERGY METHODS 670
11.1 Introduction 670
11.2 Strain Energy 670
11.3 Strain-Energy Density 672
11.4 Elastic Strain Energy for Normal Stresses 674
11.5 Elastic Strain Energy for Shearing Stresses 677
11.6 Strain Energy for a General State of Stress 680
11.8 Design for Impact Loads 695
11.9 Work and Energy under a Single Load 696
11.10 Deflection under a Single Load by the Work-Energy Method 698
11.11 Work and Energy under Several Loads 709
11.12 Castigliano’s Theorem 711
11.13 Deflections by Castigliano’s Theorem 712
11.14 Statically Indeterminate Structures 716
Review and Summary for Chapter 11 726

APPENDICES
A Moments of Areas 736
B Typical Properties of Selected Materials Used in Engineering 746
C Properties of Rolled-Steel Shapes 750
D Beam Deflections and Slopes 762
E Fundamentals of Engineering Examination 763

Photo Credits 765
Index 766
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