Engineering Mechanics Statics

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Engineering Mechanics Statics

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Engineering mechanics is both a foundation and a framework for most of the branches of engineering. Many of the topics in such areas as civil, mechanical, aerospace, and agricultural engineering, and of course engineering mechanics itself, are based upon the subjects of statics and dynamics. Even in a discipline such as electrical engineering, practitioners, in the course of considering the electrical components of a robotic device or a manufacturing process, may find themselves first having to deal with the mechanics involved.

Thus, the engineering mechanics sequence is critical to the engineering curriculum. Not only is this sequence needed in itself, but courses in engineering mechanics also serve to solidify the student’s understanding of other important subjects, including applied mathematics, physics, and graphics. In addition, these courses serve as excellent settings in which to strengthen problem-solving abilities.

The primary purpose of the study of engineering mechanics is to develop the capacity to predict the effects of force and motion while carrying out the creative design functions of engineering. This capacity requires more than a mere knowledge of the physical and mathematical principles of mechanics; also required is the ability to visualize physical configurations in terms of real materials, actual constraints, and the practical limitations which govern the behavior of machines and structures. One of the primary objectives in a mechanics course is to help the student develop this ability to visualize, which is so vital to problem formulation. Indeed, the construction of a meaningful mathematical model is often a more important experience than its solution. Maximum progress is made when the principles and their limitations are learned together within the context of engineering application.

There is a frequent tendency in the presentation of mechanics to use problems mainly as a vehicle to illustrate theory rather than to develop theory for the purpose of solving problems. When the first view is allowed to predominate, problems tend to become overly idealized and unrelated to engineering with the result that the exercise becomes dull, academic, and uninteresting. This approach deprives the student of valuable experience in formulating problems and thus of discovering the need for and meaning of theory. The second view provides by far the stronger motive for learning theory and leads to a better balance between theory and application. The crucial role played by interest and purpose in providing the strongest possible motive for learning cannot be overemphasized.

Furthermore, as mechanics educators, we should stress the understanding that, at best, theory can only approximate the real world of mechanics rather than the view that the real world approximates the theory. This difference in philosophy is indeed basic and distinguishes the engineering of mechanics from the science of mechanics.

Over the past several decades, several unfortunate tendencies have occurred in engineering education. First, emphasis on the geometric and physical meanings of prerequisite mathematics appears to have diminished. Second, there has been a significant reduction and even elimination of instruction in graphics, which in the past enhanced the visualization and representation of mechanics problems. Third, in advancing the mathematical level of our treatment of mechanics, there has been a tendency to allow the notational manipulation of vector operations to mask or replace geometric visualization. Mechanics is inherently a subject which depends on geometric and physical perception, and we should increase our efforts to develop this ability.

A special note on the use of computers is in order. The experience of formulating problems, where reason and judgment are developed, is vastly more important for the student than is the manipulative exercise in carrying out the solution. For this reason, computer usage must be carefully controlled. At present, constructing free-body diagrams and formulating governing equations are best done with pencil and paper. On the other hand, there are instances in which the solution to the governing equations can best be carried out and displayed using the computer. Computer-oriented problems should be genuine in the sense that there is a condition of design or criticality to be found, rather than “makework” problems in which some parameter is varied for no apparent reason other than to force artificial use of the computer. These thoughts have been kept in mind during the design of the computer-oriented problems in the Seventh Edition. To conserve adequate time for problem formulation, it is suggested that the student be assigned only a limited number of the computer-oriented problems.

As with previous editions, this Seventh Edition of Engineering Mechanics is written with the foregoing philosophy in mind. It is intended primarily for the first engineering course in mechanics, generally taught in the second year of study. Engineering Mechanics is written in a style which is both concise and friendly. The major emphasis is on basic principles and methods rather than on a multitude of special cases. Strong effort has been made to show both the cohesiveness of the relatively few fundamental ideas and the great variety of problems which these few ideas will solve.

CHAPTER 1
INTRODUCTION TO STATICS 3
1/1 Mechanics 3
1/2 Basic Concepts 4
1/3 Scalars and Vectors 4
1/4 Newton’s Laws 7
1/5 Units 8
1/6 Law of Gravitation 12
1/7 Accuracy, Limits, and Approximations 13
1/8 Problem Solving in Statics 14
1/9 Chapter Review 18
CHAPTER 2
FORCE SYSTEMS 23
2/1 Introduction 23
2/2 Force 23
SECTION A TWO-DIMENSIONAL FORCE SYSTEMS 26
2/3 Rectangular Components 26
2/4 Moment 38
2/5 Couple 50
2/6 Resultants 58
SECTION B THREE-DIMENSIONAL FORCE SYSTEMS 66
2/7 Rectangular Components 66
2/8 Moment and Couple 74
2/9 Resultants 88
2/10 Chapter Review 99
CHAPTER 3
EQUILIBRIUM 109
3/1 Introduction 109
SECTION A EQUILIBRIUM IN TWO DIMENSIONS 110
3/2 System Isolation and the Free-Body Diagram 110
3/3 Equilibrium Conditions 121
SECTION B EQUILIBRIUM IN THREE DIMENSIONS 145
3/4 Equilibrium Conditions 145
3/5 Chapter Review 163
CHAPTER 4
STRUCTURES 173
4/1 Introduction 173
4/2 Plane Trusses 175
4/3 Method of Joints 176
4/4 Method of Sections 188
4/5 Space Trusses 197
4/6 Frames and Machines 204
4/7 Chapter Review 224
CHAPTER 5
DISTRIBUTED FORCES 233
5/1 Introduction 233
SECTION A CENTERS OF MASS AND CENTROIDS 235
5/2 Center of Mass 235
5/3 Centroids of Lines, Areas, and Volumes 238
5/4 Composite Bodies and Figures; Approximations 254
5/5 Theorems of Pappus 264
SECTION B SPECIAL TOPICS 272
5/6 Beams—External Effects 272
5/7 Beams—Internal Effects 279
5/8 Flexible Cables 291
5/9 Fluid Statics 306
5/10 Chapter Review 325
CHAPTER 6
FRICTION 335
6/1 Introduction 335
SECTION A FRICTIONAL PHENOMENA 336
6/2 Types of Friction 336
6/3 Dry Friction 337
SECTION B APPLICATIONS OF FRICTION IN MACHINES 357
6/4 Wedges 357
6/5 Screws 358
6/6 Journal Bearings 368
6/7 Thrust Bearings; Disk Friction 369
6/8 Flexible Belts 377
6/9 Rolling Resistance 378
6/10 Chapter Review 387
CHAPTER 7
VIRTUAL WORK 397
7/1 Introduction 397
7/2 Work 397
7/3 Equilibrium 401
7/4 Potential Energy and Stability 417
7/5 Chapter Review 433
APPENDICES
APPENDIX A AREA MOMENTS OF INERTIA 441
A/1 Introduction 441
A/2 Definitions 442
A/3 Composite Areas 456
A/4 Products of Inertia and Rotation of Axes 464
APPENDIX B MASS MOMENTS OF INERTIA 477
APPENDIX C SELECTED TOPICS OF MATHEMATICS 479
C/1 Introduction 479
C/2 Plane Geometry 479
C/3 Solid Geometry 480
C/4 Algebra 480
C/5 Analytic Geometry 481
C/6 Trigonometry 481
C/7 Vector Operations 482
C/8 Series 485
C/9 Derivatives 485
C/10 Integrals 486
C/11 Newton’s Method for Solving Intractable Equations 489
C/12 Selected Techniques for Numerical Integration 491
APPENDIX D USEFUL TABLES 495
Table D/1 Physical Properties 495
Table D/2 Solar System Constants 496
Table D/3 Properties of Plane Figures 497
Table D/4 Properties of Homogeneous Solids 499
INDEX 503
PROBLEM ANSWERS 507