Engineering Mechanics: Statics and Dynamics, 3rd Edition

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 𝐹⃗ = 0 ⃗ Springs 3.3 Equilibrium of Particles in Three Dimensions Reactions Solution of algebraic equations Summing forces in directions other than 𝒙, 𝒚, or 𝒛 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 𝑉 and 𝑀 using equilibrium Shear and moment diagrams 8.3 Relations Among Shear, Moment, and Distributed Force Relations among 𝑉, 𝑀, and 𝑤 Determination of 𝑉 and 𝑀 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 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 F⃗ = 0 ⃗ Springs 3.3 Equilibrium of Particles in Three Dimensions Reactions Solution of algebraic equations Summing forces in directions other than x, y, or z 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 V and M using equilibrium Shear and moment diagrams 8.3 Relations Among Shear, Moment, and Distributed Force Relations among V, M, and w Determination of V and M 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 Engineering Mechanics: Statics and Dynamics is the Problem Solver's Approach for Tomorrow's Engineers. Based upon a great deal of classroom teaching experience, authors Plesha, Gray, & Costanzo provide a rigorous introduction to the fundamental principles of statics and dynamics in a visually appealing framework for students.This title is available in Connect with SmartBook, featuring Application-Based Activities, the Free Body Diagram Tool, and Process Oriented Problems. Instructor resources for this title include: an Image Library, Lecture PPTs, and an Instructor Solutions Manual.