Cover Page
Reactions at Supports and Connections for a Two-Dimensional Structure
Reactions at Supports and Connections for a Three-Dimensional Structure
Title Page
Copyright Page
About the Authors
Brief Contents
Table of Content
Preface
Guided Tour
What Resources Support This Textbook?
Acknowledgments
Connect
List of Symbols
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
2 Statics of Particles
2.1 Introduction
Forces in a Plane
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 Newtonโs First Law of Motion
2.11 Problems Involving the Equilibrium of a Particle. Free-Body Diagrams
Forces in Space
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
Review and Summary for Chapter 2
Review Problems
Computer Problems
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 Varignonโs 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
Review and Summary for Chapter 3
Review Problems
Computer Problems
4 Equilibrium of Rigid Bodies
4.1 Introduction
4.2 Free-Body Diagram
Equilibrium in Two Dimensions
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
Review and Summary for Chapter 4
Review Problems
Computer Problems
5 Distributed Forces: Centroids and Centers of Gravity
5.1 Introduction
Areas and Lines
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
Volumes
5.10 Center of Gravity of a Three-Dimensional Body. Centroid of a Volume
5.11 Composite Bodies
5.12 Determination of Centroids of Volumes by Integration
Review and Summary for Chapter 5
Review Problems
Computer Problems
6 Analysis of Structures
6.1 Introduction
Trusses
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
Frames and Machines
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
Review and Summary for Chapter 6
Review Problems
Computer Problems
7 Forces in Beams and Cables
7.1 Introduction
7.2 Internal Forces in Members
Beams
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
Cables
7.7 Cables with Concentrated Loads
7.8 Cables with Distributed Loads
7.9 Parabolic Cable
7.10 Catenary
Review and Summary for Chapter 7
Review Problems
Computer Problems
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 Resistance
8.10 Belt Friction
Review and Summary for Chapter 8
Review Problems
Computer Problems
9 Distributed Forces: Moments of Inertia
9.1 Introduction
Moments of Inertia of Areas
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 Mohrโs Circle for Moments and Products of Inertia
Moments of Inertia of a Mass
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
Review and Summary for Chapter 9
Review Problems
Computer Problems
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
Review and Summary for Chapter 10
Review Problems
Computer Problems
11 Kinematics of Particles
11.1 Introduction to Dynamics
Rectilinear Motion of Particles
11.2 Position, Velocity, and Acceleration
11.3 Determination of the Motion of a Particle
11.4 Uniform Rectilinear Motion
11.5 Uniformly Accelerated Rectilinear Motion
11.6 Motion of Several Particles
11.7 Graphical Solution of Rectilinear-Motion Problems
11.8 Other Graphical Methods
Curvilinear Motion of Particles
11.9 Position Vector, Velocity, and Acceleration
11.10 Derivatives of Vector Functions
11.11 Rectangular Components of Velocity and Acceleration
11.12 Motion Relative to a Frame in Translation
11.13 Tangential and Normal Components
11.14 Radial and Transverse Components
Review and Summary for Chapter 11
Review Problems
Computer Problems
12 Kinetics of Particles: Newtonโs Second Law
12.1 Introduction
12.2 Newtonโs Second Law of Motion
12.3 Linear Momentum of a Particle. Rate of Change of Linear Momentum
12.4 Systems of Units
12.5 Equations of Motion
12.6 Dynamic Equilibrium
12.7 Angular Momentum of a Particle. Rate of Change of Angular Momentum
12.8 Equations of Motion in Terms of Radial and Transverse Components
12.9 Motion Under a Central Force. Conservation of Angular Momentum
12.10 Newtonโs Law of Gravitation
12.11 Trajectory of a Particle Under a Central Force
12.12 Application to Space Mechanics
12.13 Keplerโs Laws of Planetary Motion
Review and Summary for Chapter 12
Review Problems
Computer Problems
13 Kinetics of Particles: Energy and Momentum Methods
13.1 Introduction
13.2 Work of a Force
13.3 Kinetic Energy of a Particle. Principle of Work and Energy
13.4 Applications of the Principle of Work and Energy
13.5 Power and Efficiency
13.6 Potential Energy
13.7 Conservative Forces
13.8 Conservation of Energy
13.9 Motion Under a Conservative Central Force. Application to Space Mechanics
13.10 Principle of Impulse and Momentum
13.11 Impulsive Motion
13.12 Impact
13.13 Direct Central Impact
13.14 Oblique Central Impact
13.15 Problems Involving Energy and Momentum
Review and Summary for Chapter 13
Review Problems
Computer Problems
14 Systems of Particles
14.1 Introduction
14.2 Application of Newtonโs Laws to the Motion of a System of Particles. Effective Forces
14.3 Linear and Angular Momentum of a System of Particles
14.4 Motion of the Mass Center of a System of Particles
14.5 Angular Momentum of a System of Particles About Its Mass Center
14.6 Conservation of Momentum for a System of Particles
14.7 Kinetic Energy of a System of Particles
14.8 Work-Energy Principle. Conservation of Energy for a System of Particles
14.9 Principle of Impulse and Momentum for a System of Particles
14.10 Variable Systems of Particles
14.11 Steady Stream of Particles
14.12 Systems Gaining or Losing Mass
Review and Summary for Chapter 14
Review Problems
Computer Problems
15 Kinematics of Rigid Bodies
15.1 Introduction
15.2 Translation
15.3 Rotation About a Fixed Axis
15.4 Equations Defining the Rotation of a Rigid Body About a Fixed Axis
15.5 General Plane Motion
15.6 Absolute and Relative Velocity in Plane Motion
15.7 Instantaneous Center of Rotation in Plane Motion
15.8 Absolute and Relative Acceleration in Plane Motion
15.9 Analysis of Plane Motion in Terms of a Parameter
15.10 Rate of Change of a Vector with Respect to a Rotating Frame
15.11 Plane Motion of a Particle Relative to a Rotating Frame. Coriolis Acceleration
15.12 Motion About a Fixed Point
15.13 General Motion
15.14 Three-Dimensional Motion of a Particle Relative to a Rotating Frame. Coriolis Acceleration
15.15 Frame of Reference in General Motion
Review and Summary for Chapter
Review Problems
Computer Problems
16 Plane Motion of Rigid Bodies: Forces and Accelerations
16.1 Introduction
16.2 Equations of Motion for a Rigid Body
16.3 Angular Momentum of a Rigid Body in Plane Motion
16.4 Plane Motion of a Rigid Body. DโAlembertโs Principle
16.5 A Remark on the Axioms of the Mechanics of Rigid Bodies
16.6 Solution of Problems Involving the Motion of a Rigid Body
16.7 Systems of Rigid Bodies
16.8 Constrained Plane Motion
Review and Summary for Chapter 16
Review Problems
Computer Problems
17 Plane Motion of Rigid Bodies: Energy and Momentum Methods
17.1 Introduction
17.2 Principle of Work and Energy for a Rigid Body
17.3 Work of Forces Acting on a Rigid Body
17.4 Kinetic Energy of a Rigid Body in Plane Motion
17.5 Systems of Rigid Bodies
17.6 Conservation of Energy
17.7 Power
17.8 Principle of Impulse and Momentum for the Plane Motion of a Rigid Body
17.9 Systems of Rigid Bodies
17.10 Conservation of Angular Momentum
17.11 Impulsive Motion
17.12 Eccentric Impact
Review and Summary for Chapter 17
Review Problems
Computer Problems
18 Kinetics of Rigid Bodies in Three Dimensions
18.1 Introduction
18.2 Angular Momentum of a Rigid Body in Three Dimensions
18.3 Application of the Principle of Impulse and Momentum to the Three-Dimensional Motion of a Rigid Body
18.4 Kinetic Energy of a Rigid Body in Three Dimensions
18.5 Motion of a Rigid Body in Three Dimensions
18.6 Eulerโs Equations of Motion. Extension of DโAlembertโs Principle to the Motion of a Rigid Body in Three Dimensions
18.7 Motion of a Rigid Body About a Fixed Point
18.8 Rotation of a Rigid Body About a Fixed Axis
18.9 Motion of a Gyroscope. Eulerian Angles
18.10 Steady Precession of a Gyroscope
18.11 Motion of an Axisymmetrical Body Under No Force
Review and Summary for Chapter 18
Review Problems
Computer Problems
19 Mechanical Vibrations
19.1 Introduction
Vibrations Without Damping
19.2 Free Vibrations of Particles. Simple Harmonic Motion
19.3 Simple Pendulum (Approximate Solution)
19.4 Simple Pendulum (Exact Solution)
19.5 Free Vibrations of Rigid Bodies
19.6 Application of the Principle of Conservation of Energy
19.7 Forced Vibrations
Damped Vibrations
19.8 Damped Free Vibrations
19.9 Damped Forced Vibrations
*19.10 Electrical Analogues
Review and Summary for Chapter 19
Review Problems
Computer Problems
Appendix
Photo Credits
Index
Answers to Problems
Centroids of Common Shapes of Areas and Lines
Moments of Inertia of Common Geometric Shapes
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