STATICS AND DYNAMICS—7TH EDITION
1
INTRODUCTION
1.1
1.2
1.3
1.4
1.5
1.6
What is Mechanics?
Fundamental Concepts and Principles
Systems of Units
Conversion from One System of Units to Another
Method of Problem Solution
Numerical Accuracy
2
STATICS OF PARTICLES
2.1
Introduction
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
Forces in a Plane
Force on a Particle. Resultant of Two Forces
Vectors
Addition of Vectors
Resultant of Several Concurrent Forces
Resolution of a Force into Components
Rectangular Components of a Force. Unit Vectors
Addition of Forces by Summing x and y Components
Equilibrium of a Particle
Newton's First Law of Motion
Problems Involving the Equilibrium of a Particle. Free-Body Diagrams
2.12
2.13
2.14
2.15
Forces in Space
Rectangular Components of a Force in Space
Force Defined by Its Magnitude and Two Points on Its Line of Action
Addition of Concurrent Forces in Space
Equilibrium of a Particle in Space
Review and Summary
Review Problems
Computer Problems
2
RIGID BODIES: EOUIVALENT SYSTEMS OF FORCES
3.1
3.2
Introduction
External and Internal Forces
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
3.20
3.21
Principle of Transmissibility. Equivalent Forces
Vector Product of Two Vectors
Vector Products Expressed in Terms of Rectangular Components
Moment of a Force about a Point
Varignon's Theorem
Rectangular Components of the Moment of a Force
Scalar Product of Two Vectors
Mixed Triple Product of Three Vectors
Moment of a Force about a Given Axis
Moment of a Couple
Equivalent Couples
Addition of Couples
Couples Can Be Represented by Vectors
Resolution of a Given Force Into a Force at O and a Couple
Reduction of a System of Forces to One Force and One Couple
Equivalent Systems of Forces
Equipollent Systems of Vectors
Further Reduction of a System of Forces
Reduction of a System of Forces to a Wrench
Review and Summary
Review Problems
Computer Problems
4
EQUILIBRIUM OF RIGID BODIES
4.1
4.2
Introduction
Free-Body Diagram
4.3
4.4
4.5
4.6
4.7
Equilibrium in Two Dimensions
Reactions at Supports and Connections for a Two-Dimensional Structure
Equilibrium of a Rigid Body in Two Dimensions
Statically Indeterminate Reactions. Partial Constraints
Equilibrium of a Two-Force Body
Equilibrium of a Three-Force Body
4.8
4.9
Equilibrium in Three Dimensions
Equilibrium of a Rigid Body in Three Dimensions
Reactions at Supports and Connections for a Three-Dimensional Structure
Review and Summary
Review Problems
Computer Problems
5
DISTRIBUTED FORCES: CENTROIDS AND CENTERS OF GRAVITY
5.1
Introduction
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
Areas and Lines
Center of Gravity of a Two-Dimensional Body
Centroids of Areas and Lines
First Moments of Areas and Lines
Composite Plates and Wires
Determination of Centroids by Integration
Theorems of Pappus-Guldinus
Distributed Loads on Beams
Forces on Submerged Surfaces
5.10
5.11
5.12
Volumes
Center of Gravity of a Three-Dimensional Body. Centroid of a Volume
Composite Bodies
Determination of Centroids of Volumes by Integration
Review and Summary
Review Problems
Computer Problems
6
ANALYSIS OF STRUCTURES
6.1
Introduction
6.2
6.3
6.4
6.5
6.6
6.7
6.8
Trusses
Definition of a Truss
Simple Trusses
Analysis of Trusses by the Method of Joints
Joints under Special Loading Conditions
Space Trusses
Analysis of Trusses by the Method of Sections
Trusses Made of Several Simple Trusses
6.9
6.10
6.11
6.12
Frames and Machines
Structures Containing Multiforce Members
Analysis of a Frame
Frames Which Cease to Be Rigid When Detached from Their Supports
Machines
Review and Summary
Review Problems
Computer Problems
7
FORCES IN BEAMS AND CABLES
7.1
7.2
Introduction
Internal Forces in Members
7.3
7.4
7.5
7.6
7.4
7.5
7.6
Beams
Various Types of Loading and Support
Shear and Bending Moment in a Beam
Shear and Bending-Moment Diagrams
Relations among Load, Shear, and Bending Moment
Shear and Bending Moment in a Beam
Shear and Bending-Moment Diagrams
Relations among Load, Shear, and Bending Moment
7.7
7.8
7.9
7.10
Cables
Cables with Concentrated Loads
Cables with Distributed Loads
Parabolic Cable
Catenary
Review and Summary
Review Problems
Computer Problems
8
FRICTION
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10
Introduction
The Laws of Dry Friction. Coefficients of Friction
Angles of Friction
Problems Involving Dry Friction
Wedges
Square-Threaded Screws
Journal Bearings. Axle Friction
Thrust Bearings. Disk Friction
Wheel Friction. Rolling Resistance
Belt Friction
Review and Summary
Review Problems
Computer Problems
9
DISTRIBUTED FORCES: MOMENTS OF INERTIA
9.1
Introduction
9.2
9.3
9.4
9.5
9.6
9.7
9.8
9.9
9.10
Moments of Inertia of Areas
Second Moment, or Moment of Inertia, of an Area
Determination of the Moment of Inertia of an Area by Integration
Polar Moment of Inertia
Radius of Gyration of an Area
Parallel-Axis Theorem
Moments of Inertia of Composite Areas
Product of Inertia
Principal Axes and Principal Moments of Inertia
Mohr's Circle for Moments and Products of Inertia
9.11
9.12
9.13
9.14
9.15
9.16
9.17
9.18
Moments of Inertia of Masses
Moment of Inertia of a Mass
Parallel-Axis Theorem
Moments of Inertia of Thin Plates
Determination of the Moment of Inertia of a Three-Dimensional Body by
Integration
Moments of Inertia of Composite Bodies
Moment of Inertia of a Body with Respect to an Arbitrary Axis through O. Mass
Products of Inertia
Ellipsoid of Inertia. Principal Axes of Inertia
Determination of the Principal Axes and Principal Moments of Inertia of a Body
of Arbitrary Shape
Review and Summary
Review Problems
Computer Problems
10
METHOD OF VIRTUAL WORK
10.1
10.2
10.3
10.4
10.5
10.6
10.7
Introduction
Work of a Force
Principle of Virtual Work
Applications of the Principle of Virtual Work
Real Machines. Mechanical Efficiency
Work of a Force during a Finite Displacement
Potential Energy
10.8
10.9
Potential Energy and Equilibrium
Stability of Equilibrium
Review and Summary
Review Problems
Computer Problems
11
KINEMATICS OF PARTICLES
11.1
Introduction to Dynamics
11.2
11.3
11.4
11.5
11.6
11.7
11.8
Rectilinear Motion of Particles
Position, Velocity, and Acceleration
Determination of the Motion of a Particle
Uniform Rectilinear Motion
Uniformly Accelerated Rectilinear Motion
Motion of Several Particles
Graphical Solution of Rectilinear-Motion Problems
Other Graphical Methods
11.9
11.10
11.11
11.12
11.13
11.14
Curvilinear Motion of Particles
Position Vector, Velocity, and Acceleration
Derivatives of Vector Functions
Rectangular Components of Velocity and Acceleration
Motion Relative to a Frame in Translation
Tangential and Normal Components
Radial and Transverse Components
Review and Summary
Review Problems
Computer Problems
12
KINETICS OF PARTICLES: NEWTON’S SECOND LAW
12.1
12.2
12.3
12.4
12.5
12.6
Introduction
Newton’s Second Law of Motion
Linear Momentum of a Particle. Rate of Change of Linear Momentum
Systems of Units
Equations of Motion
Dynamic Equilibrium
12.7
12.8
12.9
12.10
12.11
12.12
12.13
Angular Momentum of a Particle. Rate of Change of Angular Momentum
Equations of Motion in Terms of Radial and Transverse Components
Motion under a Central Force. Conservation of Angular Momentum.
Newton’s Law of Gravitation
Trajectory of a Particle under a Central Force
Application to Space Mechanics
Kepler’s Laws of Planetary Motion
Review and Summary
Review Problems
Computer Problems
13
KINETICS OF PARTICLES: ENERGY AND MOMENTUM METHODS
13.1
13.2
13.3
13.4
13.5
13.6
13.7
13.8
13.9
13.10
13.11
13.12
13.13
13.14
13.15
Introduction
Work of Force
Kinetic Energy of a Particle. Principle of Work and Energy.
Applications of the Principle of Work and Energy
Power and Efficiency
Potential Energy
Conservative Forces
Conservation of Energy
Motion under a Conservative Central Force. Application to Space Mechanics
Principle of Impulse and Momentum
Impulsive Motion
Impact
Direct Central Impact
Oblique Central Impact
Problems Involving Energy and Momentum
Review and Summary
Review Problems
Computer Problems
14
SYSTEMS OF PARTICLES
14.1
14.2
14.3
14.4
14.5
Introduction
Application of Newton’s Laws to the Motion of a System of Particles. Effective
forces.
Linear and Angular Momentum of a System of Particles
Motion of the Mass Center of a System of Particles
Angular Momentum of a System of Particles about Its Mass Center
14.6
14.7
14.8
14.9
14.10
14.11
14.12
Conservation of Momentum for a System of Particles
Kinetic Energy of a System of Particles
Work-Energy Principle. Conservation of Energy for a System of Particles.
Principles of Impulse and Momentum for a System of Particles
Variable Systems of Particles
Steady Stream of Particles
Systems Gaining or Losing Mass
Review and Summary
Review Problems
Computer Problems
15
KINEMATICS OF RIGID BODIES
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
15.9
15.10
15.11
15.12
15.13
15.14
Introduction
Translation
Rotation about a Fixed Angle
Equations Defining the Rotation of a Rigid Body about a Fixed Axis
General Plane Motion
Absolute and Relative Velocity in Plane Motion
Instantaneous Center of Rotation in Plane Motion
Absolute and Relative Acceleration in Plane Motion
Analysis of Plane Motion in Terms of a Parameter
Rate of Change of a Vector with Respect to a Rotating Frame
Plane Motion of a Particle Relative to a Rotating Frame. Coriolis Acceleration.
Motion about a Fixed Point
General Motion
Three-Dimensional Motion of a Particle Relative to a Rotating Frame. Coriolis
Acceleration.
15.15 Frame of Reference in General Motion
Review and Summary
Review Problems
Computer Problems
16
PLANE MOTION OF RIGID BODIES: FORCES AND ACCELERATIONS
16.1
16.2
16.3
16.4
16.5
Introduction
Equations of Motion for a Rigid Body
Angular Momentum of a Rigid Body
Plane Motion of a Rigid Body. D’Alembert’s Principle
A Remark on the Axioms of the Mechanics of Rigid Bodies
16.6
16.7
16.8
Solution of Problems Involving the Motion of a Rigid Body
Systems of Rigid Bodies
Constrained Plane Motion
Review and Summary
Review Problems
Computer Problems
17
Plane Motion of Rigid Bodies: Energy and Momentum Methods
17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9
17.10
17.11
17.12
Introduction
Principle of Work and Energy for a Rigid Body
Work of Forces Acting on a Rigid Body
Kinetic Energy of a Rigid Body in Plane Motion
Systems of Rigid Bodies
Conservation of Energy
Power
Principle of Impulse and Momentum for the Plane Motion of a Rigid Body
Systems of Rigid Bodies
Conservation of Angular Momentum
Impulsive Motion
Eccentric Impact
Review and Summary
Review Problems
Computer Problems
18
Kinetics of Rigid Bodies in Three Dimensions
18.1
18.2
18.3
Introduction
Angular Momentum of a Rigid Body in Three Dimensions
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 Euler’s Equations of Motion. Extension of d’Alembert’s 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 Axisymmetical Body under No Force
Review and Summary
Review Problems
Computer Problems
19
MECHANICAL VIBRATIONS
19.1
Introduction
Vibrations without Damping
Free Vibrations of Particles. Simple Harmonic Motion
Simple Pendulum (Approximate Solution)
Simple Pendulum (Exact Solution)
Free Vibrations of Rigid Bodies
Application of the Principle of Conservation of Energy
Forced Vibrations
Damped Vibrations
19.8 Damped Free Vibrations
19.9 Damped Forced Vibrations
19.10 Electrical Analogues
19.2
19.3
19.4
19.5
19.6
19.7
Review and Summary
Review Problems
Computer Problems
Appendix: Fundamentals of Engineering Appendix
Index
Answers to Problems