Vector Mechanics for Engineers: Statics (in SI Units)

Target AudienceThis text is designed for the first course in Statics offered in the sophomore year. OverviewThe main objective of a first course in mechanics should be to develop in the engineering student the ability to analyze any problem in a simple and logical manner and to apply to its solution a few, well-understood, basic principles. This text is designed to help the instructor achieve this goal. Vector analysis is introduced early in the text and is used in the presentation and discussion of the fundamental principles of mechanics. Vector methods are also used to solve many problems, particularly three-dimensional problems where these techniques result in a simpler and more concise solution. The emphasis in this text, however, remains on the correct understanding of the principles of mechanics and on their application to the solution of engineering problems, and vector analysis is presented chiefly as a convenient tool. In order to achieve the goal of being able to analyze mechanics problems, the text employs the following pedagogical strategy: Practical applications are introduced early. New concepts are introduced simply. Fundamental principles are placed in simple contexts. Students are given extensive practice through: sample problems, special sections entitled Solving Problems on Your Own, extensive homework problem sets, review problems at the end of each chapter, and computer problems designed to be solved with computational software. Resources Supporting This Textbook Instructor’s and Solutions Manual features typeset, one-per-page solutions to the end of chapter problems. It also features a number of tables designed to assist instructors in creating a schedule of assignments for their course. The various topics covered in the text have been listed in Table I and a suggested number of periods to be spent on each topic has been indicated. Table II prepares a brief description of all groups of problems. Sample lesson schedules are shown in Tables III, IV, and V, together with various alternative lists of assigned homework problems. For additional resources related to users of this SI edition, please visit http://www.mheducation.asia/olc/beerjohnston. McGraw-Hill Connect Engineering, a web-based assignment and assessment platform, is available at http://www.mhhe.com/beerjohnston, and includes algorithmic problems from the text, Lecture PowerPoints, an image bank, and animations. Hands-on Mechanics is a website designed for instructors who are interested in incorporating three-dimensional, hands-on teaching aids into their lectures. Developed through a partnership between the McGraw-Hill Engineering Team and the Department of Civil and Mechanical Engineering at the United States Military Academy at West Point, this website not only provides detailed instructions for how to build 3-D teaching tools using materials found in any lab or local hardware store, but also provides a community where educators can share ideas, trade best practices, and submit their own original demonstrations for posting on the site. Visit http://www.handsonmechanics.com. McGraw-Hill Tegrity, a service that makes class time available all the time by automatically capturing every lecture in a searchable format for students to review when they study and complete assignments. To learn more about Tegrity watch a 2-minute Flash demo at http://tegritycampus.mhhe.com.

Table of Contents:
Contents Preface xix Guided Tour xxiii What Resources Support This Textbook? xxv Acknowledgments xxvii Connect xxviii List of Symbols xxx 1 Introduction 1 1.1 What Is Mechanics? 2 1.2 Fundamental Concepts and Principles 2 1.3 Systems of Units 5 1.4 Conversion from One System of Units to Another 10 1.5 Method of Problem Solution 11 1.6 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 27 2.8 Addition of Forces by Summing X and Y Components 30 2.9 Equilibrium of a Particle 35 2.10 Newton’s First Law of Motion 36 2.11 Problems Involving the Equilibrium of a Particle. Free-Body Diagrams 36 Forces in Space 45 2.12 Rectangular Components of a Force in Space 45 2.13 Force Defined by Its Magnitude and Two Points on Its Line of Action 49 2.14 Addition of Concurrent Forces in Space 50 2.15 Equilibrium of a Particle in Space 58 Review and Summary for Chapter 2 66 Review Problems 69 Computer Problems 72 3 Rigid Bodies: Equivalent Systems of Forces 74 3.1 Introduction 76 3.2 External and Internal Forces 76 3.3 Principle of Transmissibility. Equivalent Forces 77 3.4 Vector Product of Two Vectors 79 3.5 Vector Products Expressed in Terms of Rectangular Components 81 3.6 Moment of a Force about a Point 83 3.7 Varignon’s Theorem 85 3.8 Rectangular Components of the Moment of a Force 85 3.9 Scalar Product of Two Vectors 96 3.10 Mixed Triple Product of Three Vectors 98 3.11 Moment of a Force about a Given Axis 99 3.12 Moment of a Couple 110 3.13 Equivalent Couples 111 3.14 Addition of Couples 113 3.15 Couples Can Be Represented by Vectors 113 3.16 Resolution of a Given Force into a Force at O and a Couple 114 3.17 Reduction of a System of Forces to One Force and One Couple 125 3.18 Equivalent Systems of Forces 126 3.19 Equipollent Systems of Vectors 127 3.20 Further Reduction of a System of Forces 128 *3.21 Reduction of a System of Forces to a Wrench 130 Review and Summary for Chapter 3 148 Review Problems 153 Computer Problems 156 4 Equilibrium of Rigid Bodies 158 4.1 Introduction 160 4.2 Free-Body Diagram 161 Equilibrium in Two Dimensions 162 4.3 Reactions at Supports and Connections for a Two-Dimensional Structure 162 4.4 Equilibrium of a Rigid Body in Two Dimensions 164 4.5 Statically Indeterminate Reactions. Partial Constraints 166 4.6 Equilibrium of a Two-Force Body 183 4.7 Equilibrium of a Three-Force Body 184 Equilibrium in Three Dimensions 191 4.8 Equilibrium of a Rigid Body in Three Dimensions 191 4.9 Reactions at Supports and Connections for a Three-Dimensional Structure 191 Review and Summary for Chapter 4 210 Review Problems 213 Computer Problems 216 5 Distributed Forces: Centroids and Centers of Gravity 218 5.1 Introduction 220 Areas and Lines 220 5.2 Center of Gravity of a Two-Dimensional Body 220 5.3 Centroids of Areas and Lines 222 5.4 First Moments of Areas and Lines 223 5.5 Composite Plates and Wires 226 5.6 Determination of Centroids by Integration 236 5.7 Theorems of Pappus-Guldinus 238 *5.8 Distributed Loads on Beams 248 *5.9 Forces on Submerged Surfaces 249 Volumes 258 5.10 Center of Gravity of a Three-Dimensional Body. Centroid of a Volume 258 5.11 Composite Bodies 261 5.12 Determination of Centroids of Volumes by Integration 261 Review and Summary for Chapter 5 274 Review Problems 278 Computer Problems 280 6 Analysis of Structures 282 6.1 Introduction 284 Trusses 285 6.2 Definition of a Truss 285 6.3 Simple Trusses 287 6.4 Analysis of Trusses by the Method of Joints 288 *6.5 Joints Under Special Loading Conditions 290 *6.6 Space Trusses 292 6.7 Analysis of Trusses by the Method of Sections 302 *6.8 Trusses Made of Several Simple Trusses 303 Frames and Machines 314 6.9 Structures Containing Multiforce Members 314 6.10 Analysis of a Frame 314 6.11 Frames Which Cease to Be Rigid When Detached from Their Supports 315 6.12 Machines 330 Review and Summary for Chapter 6 344 Review Problems 347 Computer Problems 350 7 Forces in Beams and Cables 352 *7.1 Introduction 354 *7.2 Internal Forces in Members 354 Beams 361 *7.3 Various Types of Loading and Support 361 *7.4 Shear and Bending Moment in a Beam 363 *7.5 Shear and Bending-Moment Diagrams 365 *7.6 Relations Among Load, Shear, and Bending Moment 373 Cables 383 *7.7 Cables with Concentrated Loads 383 *7.8 Cables with Distributed Loads 384 *7.9 Parabolic Cable 385 *7.10 Catenary 395 Review and Summary for Chapter 7 403 Review Problems 406 Computer Problems 408 8 Friction 410 8.1 Introduction 412 8.2 The Laws of Dry Friction. Coefficients of Friction 412 8.3 Angles of Friction 413 8.4 Problems Involving Dry Friction 416 8.5 Wedges 429 8.6 Square-Threaded Screws 430 *8.7 Journal Bearings. Axle Friction 439 *8.8 Thrust Bearings. Disk Friction 441 *8.9 Wheel Friction. Rolling Resistance 442 *8.10 Belt Friction 449 Review and Summary for Chapter 8 460 Review Problems 463 Computer Problems 466 9 Distributed Forces: Moments of Inertia 468 9.1 Introduction 470 Moments of Inertia of Areas 471 9.2 Second Moment, or Moment of Inertia, of an Area 471 9.3 Determination of the Moment of Inertia of an Area by Integration 472 9.4 Polar Moment of Inertia 473 9.5 Radius of Gyration of an Area 474 9.6 Parallel-Axis Theorem 481 9.7 Moments of Inertia of Composite Areas 482 *9.8 Product of Inertia 495 *9.9 Principal Axes and Principal Moments of Inertia 496 *9.10 Mohr’s Circle for Moments and Products of Inertia 504 Moments of Inertia of a Mass 510 9.11 Moment of Inertia of a Mass 510 9.12 Parallel-Axis Theorem 512 9.13 Moments of Inertia of Thin Plates 513 9.14 Determination of the Moment of Inertia of a Three-Dimensional Body by Integration 514 9.15 Moments of Inertia of Composite Bodies 514 *9.16 Moment of Inertia of a Body with Respect to an Arbitrary Axis Through O . Mass Products of Inertia 530 *9.17 Ellipsoid of Inertia. Principal Axes of Inertia 531 *9.18 Determination of the Principal Axes and Principal Moments of Inertia of a Body of Arbitrary Shape 533 Review and Summary for Chapter 9 545 Review Problems 551 Computer Problems 554 10 Method of Virtual Work 556 *10.1 Introduction 558 *10.2 Work of a Force 558 *10.3 Principle of Virtual Work 561 *10.4 Applications of the Principle of Virtual Work 562 *10.5 Real Machines. Mechanical Efficiency 564 *10.6 Work of a Force During a Finite Displacement 578 *10.7 Potential Energy 580 *10.8 Potential Energy and Equilibrium 581 *10.9 Stability of Equilibrium 582 Review and Summary for Chapter 10 592 Review Problems 595 Computer Problems 598 Appendix Fundamentals of Engineering Examination A1 Photo Credits C1 Index I1 Answers to Problems AN1