Engineering Mechanics: Statics and Dynamics, 3rd Education

Cover
Title Page
Bookmarks
About the Authors
Dedications
Brief Contents
Statics Table of Contents
Dynamics Table of Contents
Preface
Acknowledgments
1 Introduction to Statics
1.1 Engineering and Statics
1.2 Topics That Will Be Studied in Statics
1.3 ABriefHistory of Statics
Galileo Galilei
Isaac Newton
1.4 Fundamental Principles
Newton’s laws of motion
1.5 Force
1.6 Units and Unit Conversions
Dimensional homogeneity and unit conversions
Prefixes
Angular measure
Small angle approximations
Accuracy of calculations
1.7 Newton’s Law of Gravitation
Relationship between specific weight and
density
1.8 Failure
1.9 Chapter Review
2 Vectors: Force and Position
2.1 Basic Concepts
Introduction—force, position, vectors, and tides
Denoting vectors in figures
Basic vector operations
Performing vector operations
Resolution of a vector into vector components
2.2 Cartesian Representation of Vectors in Two
Dimensions
Introduction—Cartesian representation and a walk
to work
Unit vectors
Cartesian coordinate system
Cartesian vector representation
Addition of vectors using Cartesian components
Position vectors
2.3 Cartesian Representation of Vectors in Three
Dimensions
Right-hand Cartesian coordinate system
Cartesian vector representation
Direction angles and direction cosines
Position vectors
Use of position vectors to write expressions for
force vectors
Some simple structural members
2.4 Vector Dot Product
Dot product using Cartesian components
Determination of the angle between two vectors
Determination of the component of a vector in a particular direction
Determination of the component of a vector perpendicular to a direction
2.5 Vector Cross Product
Cross product using Cartesian components
Evaluation of cross product using determinants
Determination of the normal direction to a
plane
Determination of the area of a parallelogram
Scalar triple product
2.6 Chapter Review
3 Equilibrium of Particles
3.1 Equilibrium of Particles in Two
Dimensions
Free body diagram (FBD)
Modeling and problem solving
Cables and bars
Pulleys
Reactions
3.2 Behavior of Cables, Bars, and Springs
Equilibrium geometry of a structure
Cables
Bars
Modeling idealizations and solution of Σ ?⃗ = 0 ⃗
Springs
3.3 Equilibrium of Particles in Three
Dimensions
Reactions
Solution of algebraic equations
Summing forces in directions other than ?, ?, or ?
3.4 Engineering Design
Objectives of design
Particle equilibrium design problems
3.5 Chapter Review
4 Moment of a Force and Equivalent Force
Systems
4.1 Moment of a Force
Scalar approach
Vector approach
Varignon’s theorem
Which approach should I use: scalar or vector?
4.2 Moment of a Force About a Line
Vector approach
Scalar approach
4.3 Moment of a Couple
Vector approach
Scalar approach
Comments on the moment of a couple
Equivalent couples
Equivalent force systems
Resultant couple moment
Moments as free vectors
4.4 Equivalent Force Systems
Transmissibility of a force
Equivalent force systems
Some special force systems
Wrench equivalent force systems
Why are equivalent force systems called
equivalent
4.5 Chapter Review
5 Equilibrium of Bodies
5.1 Equations of Equilibrium
5.2 Equilibrium of Rigid Bodies in Two
Dimensions
Reactions
Free body diagram (FBD
Alternative equilibrium equations
Gears
Examples of correct FBDs
Examples of incorrect and/or incomplete FBDs
5.3 Equilibrium of Bodies in Two Dimensions—Additional Topics
Why are bodies assumed to be rigid
Treatment of cables and pulleys
Springs
Superposition
Supports and fixity
Static determinacy and indeterminacy
Two-force and three-force members
5.4 Equilibrium of Bodies in Three Dimensions?
Reactions
More on bearings
Scalar approach or vector approach
Solution of algebraic equations
Examples of correct FBDs
Examples of incorrect and/or incomplete FBDs
5.5 Engineering Design
Codes and standards
Design problems
5.6 ChapterReview
6 Structural Analysis and Machines
Structures and machines
6.1 Truss Structures and the Method
of Joints
When may a structure be idealized as a
truss
Method of joints
Zero-force members
Typical truss members
6.2 Truss Structures and the Method of
Sections
Treatment of forces that are not at joints
Static determinacy and indeterminacy
Design considerations
6.3 Trusses in ThreeDimensions
Stability of space trusses and design
considerations
6.4 Frames andMachines
Analysis procedure and free body diagrams (FBDs)
Examples of correct FBDs
Examples of incorrect and/or incomplete FBDs
6.5 Chapter Review
7 Centroids and Distributed Force Systems
7.1 Centroid
Introduction—center of gravity
Centroid of an area
Centroid of a line
Centroid of a volume
Unification of concepts
Which approach should I use: composite shapes or integration?
Finer points: surfaces and lines in three
dimensions
7.2 Center of Mass and Center of Gravity
Center of mass
Center of gravity
7.3 Theorems of Pappus and Guldinus
Area of a surface of revolution
Volume of a solid of revolution
Proof of the Pappus–Guldinus theorems
7.4 Distributed Forces, Fluid and Gas Pressure
Loading
Distributed forces
Distributed forces applied to beams
Fluid and gas pressure
Forces produced by fluids
Forces produced by gases
7.5 Chapter Review
8 Internal Forces
8.1 Internal Forces in Structural Members
Why are internal forces important
Internal forces for slender members in two
dimensions
Internal forces for slender members in three
dimensions
Determination of internal forces
8.2 Internal Forces in Straight Beams
Determination of ? and ? using equilibrium
Shear and moment diagrams
8.3 Relations Among Shear, Moment, and
Distributed Force
Relations among ?, ?, and ?
Determination of ? and ? using integration
Which approach should I use?
Tips and shortcuts for drawing shear and moment
diagrams
Design considerations
8.4 Chapter Review
9 Friction
9.1 Basic Concepts
A brief history of tribology
A simple experiment
Coulomb’s law of friction
Coefficients of friction
Dry contact versus liquid lubrication
Angle of friction
Problems with multiple contact surfaces
Wedges
Coulomb’s law of friction in three
dimensions
Design considerations
9.2 Problems with Multiple Contact Surfaces
Determination of sliding directions
9.3 Belts and Cables Contacting Cylindrical
Surfaces
Equilibrium analysis
9.4 Chapter Review
10 Moments of Inertia
10.1 AreaMoments of Inertia
An example—test scores
An example—beam loading
Definition of area moments of inertia
What are area moments of inertia used for?
Radius of gyration
Evaluation of moments of inertia using
integration
10.2 Parallel Axis Theorem
Use of parallel axis theorem in integration
Use of parallel axis theorem for composite
shapes
10.3 MassMoments of Inertia
An example—figure skating
Definition of mass moments of inertia
What are mass moments of inertia used for?
Radius of gyration
Parallel axis theorem
Evaluation of moments of inertia using
integration
Evaluation of moments of inertia using composite
shapes
10.4 Chapter Review
Preface
11 Introduction to Dynamics
11.1 The Newtonian Equations
11.2 Fundamental Concepts in Dynamics
Space and time
Force, mass, and inertia
Particle and rigid body
Vectors and their Cartesian representation
Useful vector “tips and tricks”
Units
11.3 Dynamics and Engineering Design
System modeling
12 Particle Kinematics
12.1 Position, Velocity, Acceleration, and Cartesian Coordinates
Position vector
Trajectory
Velocity vector and speed
Acceleration vector
Cartesian coordinates
12.2 One-Dimensional Motion
Rectilinear motion relations
Circular motion and angular velocity
12.3 ProjectileMotion
12.4 Planar Motion: Normal-Tangential
Components
Normal-tangential components
12.5 Planar Motion: Polar Coordinates
The time derivative of a vector
Polar coordinates and position, velocity, and
acceleration
12.6 Relative Motion Analysis and Differentiation of Geometrical Constraints
Relative motion
Differentiation of geometrical constraints
12.7 Motion in Three Dimensions
Cartesian coordinates
Tangent-normal-binormal components
Cylindrical coordinates
Spherical coordinates
12.8 Chapter Review
13 Force and Acceleration Methods for
Particles
13.1 Rectilinear Motion
Applying Newton’s second law
Force laws
Equation(s) of motion
Inertial reference frames
Degrees of freedom
13.2 Curvilinear Motion
Newton’s second law in 2D and 3D component systems
13.3 Systems of Particles
Engineering materials one atom at a time
Newton’s second law for systems of particles
13.4 Chapter Review
14 Energy Methods for Particles
14.1 Work-Energy Principle for a Particle
Work-energy principle and its relation
with
Work of a force
14.2 Conservative Forces and Potential Energy
Work done by the constant force of gravity
Work of a central force
Conservative forces and potential energy
Work-energy principle for any type of force
When is a force conservative
14.3 Work-Energy Principle for Systems of
Particles
Internal work and work-energy principle for a
system
Kinetic energy for a system of particles
14.4 Power and Efficiency
Power developed by a force
Efficiency
14.5 Chapter Review
15 Momentum Methods for Particles
15.1 Momentumand Impulse
Impulse-momentum principle
Conservation of linear momentum
15.2 Impact
Impacts are short, dramatic events
Definition of impact and notation
Line of impact and contact force between impacting
objects
Impulsive forces and impact-relevant FBDs
Coefficient of restitution
Unconstrained direct central impact
Unconstrained oblique central impact
Impact and energy
15.3 Angular Momentum
Moment-angular momentum relation for a
particle
Angular impulse-momentum for a system of
particles
Euler’s first and second laws of motion
15.4 Orbital Mechanics
Determination of the orbit
Energy considerations
15.5 Mass Flows
Steady flows
Variable mass flows and propulsion
15.6 Chapter Review
16 Planar Rigid Body Kinematics
16.1 Fundamental Equations, Translation, and
Rotation About a Fixed Axis
Crank, connecting rod, and piston motion
Qualitative description of rigid body motion
General motion of a rigid body
Elementary rigid body motions: translations
Elementary rigid body motions: rotation about a
fixed axis
Planar motion in practice
16.2 Planar Motion: Velocity Analysis
Vector approach
Differentiation of constraints
Instantaneous center of rotation
16.3 Planar Motion: Acceleration Analysis
Vector approach
Differentiation of constraints
Rolling without slip: acceleration analysis
16.4 Rotating Reference Frames
The general kinematic equations for the motion of a
point relative to a rotating reference frame
Coriolis component of acceleration
16.5 Chapter Review
17 Newton-Euler Equations for Planar Rigid
BodyMotion
17.1 Newton-Euler Equations: Bodies
Symmetric with Respect to the Plane
ofMotion
Linear momentum: translational equations
Angular momentum: rotational equations
Graphical interpretation of the equations of
motion
17.2 Newton-Euler Equations: Translation
17.3 Newton-Euler Equations: Rotation About a FixedAxis
17.4 Newton-Euler Equations: General Plane
Motion
Newton-Euler equations for general plane
motion
17.5 Chapter Review
18 Energy and Momentum Methods for
Rigid Bodies
18.1 Work-Energy Principle for Rigid Bodies
Kinetic energy of rigid bodies in planar motion
Work-energy principle for a rigid body
Work done on rigid bodies
Potential energy and conservation of energy
Work-energy principle for systems
Power
18.2 Momentum Methods for Rigid Bodies
Impulse-momentum principle for a rigid
body
Angular impulse-momentum principle for a rigid body
18.3 Impact of Rigid Bodies
Rigid body impact: basic nomenclature and
assumptions
Classification of impacts
Central impact
Eccentric impact
Constrained eccentric impact
18.4 Chapter Review
19 Mechanical Vibrations
19.1 Undamped Free Vibration
Oscillation of a railcar after coupling
Standard form of the harmonic oscillator
Linearizing nonlinear systems
Energy method
19.2 Undamped Forced Vibration
Standard form of the forced harmonic oscillator
19.3 Viscously Damped Vibration
Viscously damped free vibration
Viscously damped forced vibration
19.4 ChapterReview
20 Three-Dimensional Dynamics of
Rigid Bodies
20.1 Three-Dimensional Kinematics of
Rigid Bodies
Computation of angular accelerations
Summing angular velocities
20.2 Three-Dimensional Kinetics of
Rigid Bodies
Newton-Euler equations for three-dimensional motion
Kinetic energy of a rigid body in three-dimensional motion
20.3 Chapter Review
A Technical Writing
B Answers to Even-Numbered Problems
C Mass Moments of Inertia
Definition of mass moments and products of inertia
How are mass moments of inertia used
Radius of gyration
Parallel axis theorem
Principal moments of inertia
Moment of inertia about an arbitrary axis
Evaluation of moments of inertia using composite
shapes
D Angular Momentum of a Rigid Body
Angular momentum of a rigid body undergoing three-dimensional motion
Angular momentum of a rigid body in planar
motion
Index