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Vector Mechanics for Engineers


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Table of Contents

List of Symbols

Chapter 1: Introduction
1.1 What Is Mechanics?
1.2 Fundamental Concepts and Principles
1.3 Systems of Units
1.4 Conversion from One System of Units to Another
1.5 Method of Problem Solution
1.6 Numerical Accuracy

Chapter 2: Statics of Particles
2.1 Introduction
2.2 Force on a Particle. Resultant of Two Forces
2.3 Vectors
2.4 Addition of Vectors
2.5 Resultant of Several Concurrent Forces
2.6 Resolution of a Force into Components
2.7 Rectangular Components of a Force. Unit Vectors
2.8 Addition of Forces by Summing x and y Components
2.9 Equilibrium of a Particle
2.10 Newton's First Law of Motion
2.11 Problems Involving the Equilibrium of a Particle.
2.12 Rectangular Components of a Force in Space
2.13 Force Defined by Its Magnitude and Two Points on Its Line of Action
2.14 Addition of Concurrent Forces in Space
2.15 Equilibrium of a Particle in Space

Chapter 3: Rigid Bodies: Equivalent Systems of Forces
3.1 Introduction
3.2 External and Internal Forces
3.3 Principle of Transmissibility. Equivalent Forces
3.4 Vector Product of Two Vectors
3.5 Vector Products Expressed in Terms of Rectangular Components
3.6 Moment of a Force about a Point
3.7 Varignon's Theorem
3.8 Rectangular Components of the Moment of a Force
3.9 Scalar Product of Two Vectors
3.10 Mixed Triple Product of Three Vectors
3.11 Moment of a Force about a Given Axis
3.12 Moment of a Couple
3.13 Equivalent Couples
3.14 Addition of Couples
3.15 Couples Can Be Represented by Vectors
3.16 Resolution of a Given Force Into a Force at O and a Couple
3.17 Reduction of a System of Forces to One Force and One Couple
3.18 Equivalent Systems of Forces
3.19 Equipollent Systems of Vectors
3.20 Further Reduction of a System of Forces
3.21 Reduction of a System of Forces to a Wrench

Chapter 4: Equilibrium of Rigid Bodies
4.1 Introduction
4.2 Free-Body Diagram
4.3 Reactions at Supports and Connections for a Two-Dimensional Structure
4.4 Equilibrium of a Rigid Body in Two Dimensions
4.5 Statically Indeterminate Reactions. Partial Constraints
4.6 Equilibrium of a Two-Force Body
4.7 Equilibrium of a Three-Force Body Equilibrium in Three Dimensions
4.8 Equilibrium of a Rigid Body in Three Dimensions
4.9 Reactions at Supports and Connections for a Three-Dimensional Structure

Chapter 5: Distributed Forces: Centroids and Centers of Gravity
5.1 Introduction
5.2 Center of Gravity of a Two-Dimensional Body
5.3 Centroids of Areas and Lines
5.4 First Moments of Areas and Lines
5.5 Composite Plates and Wires
5.6 Determination of Centroids by Integration
5.7 Theorems of Pappus-Guldinus
5.8 Distributed Loads on Beams
5.9 Forces on Submerged Surfaces
5.10 Center of Gravity of a Three-Dimensional Body.
5.11 Composite Bodies
5.12 Determination of Centroids of Volumes by

Chapter 6: Analysis of Structures
6.1 Introduction
6.2 Definition of a Truss
6.3 Simple Trusses
6.4 Analysis of Trusses by the Method of Joints
6.5 Joints under Special Loading Conditions
6.6 Space Trusses
6.7 Analysis of Trusses by the Method of Sections
6.8 Trusses Made of Several Simple Trusses
6.9 Structures Containing Multiforce Members
6.10 Analysis of a Frame
6.11 Frames Which Cease to Be Rigid When Detached from Their Supports
6.12 Machines

Chapter 7: Forces in Beams and Cables
7.1 Introduction
7.2 Internal Forces in Members
7.3 Various Types of Loading and Support
7.4 Shear and Bending Moment in a Beam
7.5 Shear and Bending-Moment Diagrams
7.6 Relations among Load, Shear, and Bending Moment
7.7 Cables with Concentrated Loads
7.8 Cables with Distributed Loads
7.9 Parabolic Cable
7.10 Catenary

Chapter 8: Friction
8.1 Introduction
8.2 The Laws of Dry Friction. Coefficients of Friction
8.3 Angles of Friction
8.4 Problems Involving Dry Friction
8.5 Wedges
8.6 Square-Threaded Screws
8.7 Journal Bearings. Axle Friction
8.8 Thrust Bearings. Disk Friction
8.9 Wheel Friction. Rolling
8.10 Belt Friction

Chapter 9: Distributed Forces: Moments of Inertia
9.1 Introduction
9.2 Second Moment, or Moment of Inertia, of an Area
9.3 Determination of the Moment of Inertia of an Area by Integration
9.4 Polar Moment of Inertia
9.5 Radius of Gyration of an Area
9.6 Parallel-Axis Theorem
9.7 Moments of Inertia of Composite Areas
9.8 Product of Inertia
9.9 Principal Axes and Principal Moments of Inertia
9.10 Mohr's Circle for Moments and Products of Inertia
9.11 Moment of Inertia of a Mass
9.12 Parallel-Axis Theorem
9.13 Moments of Inertia of Thin Plates
9.14 Determination of the Moment of Inertia of a Three-Dimensional Body by Integration
9.15 Moments of Inertia of Composite Bodies
9.16 Moment of Inertia of a Body with Respect to an Arbitrary Axis through O. Mass Products of Inertia
9.17 Ellipsoid of Inertia. Principal Axes of Inertia
9.18 Determination of the Principal Axes and Principal Moments of Inertia of a Body of Arbitrary Shape

Chapter 10: Method of Virtual Work
10.1 Introduction
10.2 Work of a Force
10.3 Principle of Virtual Work
10.4 Applications of the Principle of Virtual Work
10.5 Real Machines. Mechanical Efficiency
10.6 Work of a Force during a Finite Displacement
10.7 Potential Energy
10.8 Potential Energy and Equilibrium
10.9 Stability of Equilibrium

Appendix: Fundamentals of Engineering Examination
Photo Credits
Answers to Problems

About the Author

Born in France and educated in France and Switzerland, Ferdinand Beer held an M.S. degree from the Sorbonne and an Sc.D. degree in theoretical mechanics from the University of Geneva. He came to the United States after serving in the French army during the early part of World War II and taught for four years at Williams College in the Williams-MIT joint arts and engineering program. Following his service at Williams College, Beer joined the faculty of Lehigh University, where he taught for thirty-seven years. He held several positions, including the University Distinguished Professors Chair and Chairman of the Mechanical Engineering and Mechanics Department. In 1995, Beer was awarded an honorary Doctor of Engineering degree by Lehigh University. Born in Philadelphia, Russ holds a B.S. degree in civil engineering from the University of Delaware and an Sc.D. degree in the field of structural engineering from The Massachusetts Institute of Technology (MIT). He taught at Lehigh University and Worchester Polytechnic Institute (WPI) before joining the faculty of the University of Connecticut where he held the position of Chairman of the Civil Engineering Department and taught for twenty-six years. In 1991 Russ received the Outstanding Civil Engineer Award from the Connecticut Section of the American Society of Civil Engineers. David Mazurek holds a B.S. in ocean engineering and an M.S. in civil engineering from the Florida Institute of Technology, and a Ph.D. in civil engineering from the University of Connecticut. Employed by the General Dynamics Corporation Electric Boat Division for five years, he provided submarine construction support and conducted engineering design and analysis associated with pressure hull and other structures. He then taught for one year at Lafayette College prior to joining the civil engineering faculty at the U.S. Coast Guard Academy, where he has been since 1990. Mazurek is currently a member of the American Railway Engineering & Maintenance-of-way Association Committee 15, and the American Society of Civil Engineers Committee on Blast, Shock, and Vibratory Effects. He has also worked with the Federal Railroad Administration on their bridge-inspection training program. He is a licensed professional engineer in Connecticut and Pennsylvania. Elliot holds a B.S. degree in engineering and an M.E. degree, both from Cornell University. He has focused his scholarly activities on professional service and teaching, and he was recognized for this work in 1992 when the American Society of Mechanical Engineers (ASME) awarded him the Ben C. Sparks Medal for his contributions to mechanical engineering and mechanical engineering technology education and for service to the American Society for Engineering Education (ASEE). Elliot taught for thirty-two years, including twenty-nine years at Penn State where he was recognized with awards for both teaching and advising.

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