Advanced Mechanics of Materials /

Incluye Referencias Bibliográficas

FUNDAMENTAL CONCEPTS

1 Introduction

1.1 The Role of Design 3

1.2 Topics Treated in This Book

4

1.3 Load-Stress and Load-Deflection Relations

5

1.4 Stress-Strain Relations

8

1.5 Failure and Limits on Design

17

Problems 24

References 26

2 Theories of Stress and Strain

2.1 Definition of Stress at a Point

28

2.2 Stress Notation 30

2.3 Symmetry of the Stress Array and Stress on an Arbitrarily Oriented Plane 32

2.4 Transformation of Stress. Principal Stresses.

Other Properties 35

2.5 Differential Equations of Motion of a Deformable Body

52

2.6 Deformation of a Deformable Body

56

2.7 Strain Theory. Transformation of Strain.

Principal Strains 57

2.8 Small-Displacement Theory

64

2.9 Strain Measurement. Strain Rosettes.

73

Problems 75

References

84

3 Linear Stress-Strain-Temperature Relations

3.1 First Law of Thermodynamics. Internal-Energy Density. Complementary Internal-Energy Density 85

3.2 Hooke's Law: Anisotropic Elasticity

3.3 Hooke's Law: Isotropic Elasticity

90

92

3.4 Equations of Thermoelasticity for Isotropic 99

Materials

3.5 Hooke's Law: Orthotropic Materials

101

Problems

References

110

112

4 Inelastic Material Behavior

4.1 Limitations of the Use of Uniaxial Stress-Strain Data

4.2 Nonlinear Material Response

116

4.3 Yield Criteria: General Concepts

126

4.4 Yielding of Ductile Metals

130

4.5 Alternative Yield Criteria

140

4.6 Comparison of Failure Criteria for General Yielding

Problems

References

154

162

113

113

144

5 Applications of Energy Methods

163

5.1 Principle of Stationary Potential Energy

163

5.2 Castigliano's Theorem on Deflections

169

5.3 Castigliano's Theorem on Deflections for Linear

Load-Deflection Relations 173

5.4 Deflections of Statically Determinate Structures

5.5 Statically Indeterminate Structures

196

Problems 208

References 232

PART II

CLASSICAL TOPICS IN ADVANCED MECHANICS

235

237

6 Torsion

179

6.1 Torsion of a Prismatic Bar of Circular

Cross Section 237

6.2 Saint-Venant's Semiinverse Method 243

6.3 Linear Elastic Solution 248

6.4 The Prandtl Elastic-Membrane (Soap-Film) Analogy

253

6.5 Narrow Rectangular Cross Section

257

6.6 Hollow Thin-Wall Torsion Members. Multiply Connected 260

Cross Section

6.7 Thin-Wall Torsion Members with Restrained Ends 266

6.8 Numerical Solution of the Torsion Problem

6.9 Fully Plastic Torsion 277

274

Problems

283

References

291

7 Nonsymmetrical Bending of Straight Beams

7.1 Definition of Shear Center in Bending. Symmetrical and Nonsymmetrical Bending 293

7.2 Bending Stresses in Beams Subjected to Nonsymmetrical Bending 302

7.3 Deflections of Straight Beams Subjected to Nonsymmetrical Bending 312

7.4 Effect of Inclined Loads 316

7.5 Fully Plastic Load for Nonsymmetrical Bending

Problems

References

320

330

318

8 Shear Center for Thin-Wall Beam Cross Sections

8.1 Approximations for Shear in Thin-Wall Beam Cross Sections 331

8.2 Shear Flow in Thin-Wall Beam Cross Sections

8.3 Shear Center for a Channel Section 336

334

8.4 Shear Center of Composite Beams Formed from Stringers and

Thin Webs 342

8.5 Shear Center of Box Beams

346

Problems

350

References

361

9. Curved Beams

9.1 Introduction 362

9.2 Circumferential Stresses in a Curved Beam

363

9.3 Radial Stresses in Curved Beams 373

9.4 Correction of Circumferential Stresses in Curved Beams Having I-, T-, or Similar Cross Sections 379

9.5 Defections of Curved Beams 385

9.6 Statically Indeterminate Curved Beams. Closed Ring Subjected to a Concentrated Load 391

INTRODUCTION

In this chapter, we present general concepts and definitions that are fundamental to many of the topics discussed in this book. The chapter serves also as a brief guide and introduction to the remainder of the book. The reader may find it fruitful to refer to this chapter, from time to time, in conjunction with the study of topics in other chapters.

THE ROLE OF DESIGN

This book emphasizes the methods of mechanics of materials and applications to the analysis and design of components of structural/machine systems. As such, it is directed to aeronautical, civil, mechanical, and nuclear engineers, as well as to specialists in the field of theoretical and applied mechanics. As engineers, we are problem solvers. The problems that we solve encompass practically all fields of human activity. We solve problems related to buildings, transportation (including automotive, rail, water, air and outer-space travel), water systems (e.g., dams and pipelines), manufacturing, specialized medical equipment, communication systems, computers, hazardous wastes, etc. These problems are generally encountered in the design, manufacture, and construction of engineering systems. Ordinarily, these systems are not built or manufactured before the design process is completed. The design process usually involves the development of many drawings and/or CAD files to describe the final system. One of the major purposes of the design process is to analyze or evaluate various design alternatives before a final design is selected. One of the simplest objectives of the analysis is to ensure that all components of the system will fit together and function properly. More complicated analysis involves the evaluation of forces in the proposed design to ensure that each component of the system functions properly (for instance, safely withstands loads or does not undergo excessive displacements). This analysis is essential in the process of refining the design to meet required conditions such as adequate strength, minimum weight, and minimum cost of production.

The process of refining the design can be very complicated and extremely time-consuming. For example, consider the design of a space vehicle, such as the shuttle. After the shuttle's mission or use has been established, the designer must decide on the shape of the vehicle and the materials to be used. The designer must analyze the vehicle's structure to determine if it is strong and stiff enough to withstand the aerodynamic and thermal loads to which it will be subjected.