Vector Mechanics for Engineers: Statics

by Beer, Ferdinand P.; Johnston, Russell E., Jr.

• ISBN13: 9780071140577
• ISBN10: 0071140573
• Edition: 6th
• Format: Paperback
• Copyright: 2000-04-01
• Publisher: MCGRAW HILL BOOK CO LTD

Table of Contents

Preface	xvii
List of Symbols	xxiii
Introduction	1	(14)
What Is Mechanics?	2	(1)
Fundamental Concepts and Principles	2	(3)
Systems of Units	5	(5)
Conversion from One System of Units to Another	10	(2)
Method of Problem Solution	12	(1)
Numerical Accuracy	13	(2)
Statics of Particles	15	(56)
Introduction	16	(1)
Forces In a Plane	16	(1)
Force on a Particle. Resultant of Two Forces	16	(1)
Vectors	17	(1)
Addition of Vectors	18	(2)
Resultant of Several Concurrent Forces	20	(1)
Resolution of a Force into Components	21	(6)
Rectangular Components of a Force. Unit Vectors	27	(3)
Addition of Forces by Summing x and y Components	30	(5)
Equilibrium of a Particle	35	(1)
Newton's First Law of Motion	36	(1)
Problems Involving the Equilibrium of a Particle. Free-Body Diagrams	36	(9)
Forces in Space	45	(1)
Rectangular Components of a Force in Space	45	(3)
Force Defined by Its Magnitude and Two Points on Its Line of Action	48	(1)
Addition of Concurrent Forces in Space	49	(8)
Equilibrium of a Particle in Space	57	(14)
Review and Summary for Chapter 2	64	(3)
Review Problems	67	(4)
Rigid Bodies: Equivalent Systems of Forces	71	(82)
Introduction	72	(1)
External and Internal Forces	72	(1)
Principle of Transmissibility. Equivalent Forces	73	(2)
Vector Product of Two Vectors	75	(2)
Vector Products Expressed in Terms of Rectangular Components	77	(2)
Moment of a Force about a Point	79	(2)
Varignon's Theorem	81	(1)
Rectangular Components of the Moment of a Force	81	(10)
Scalar Product of Two Vectors	91	(2)
Mixed Triple Product of Three Vectors	93	(2)
Moment of a Force about a Given Axis	95	(10)
Moment of a Couple	105	(1)
Equivalent Couples	106	(2)
Addition of Couples	108	(1)
Couples Can Be Represented by Vectors	108	(1)
Resolution of a Given Force Into a Force at O and a Couple	109	(11)
Reduction of a System of Forces to One Force and One Couple	120	(2)
Equivalent Systems of Forces	122	(1)
Equipollent Systems of Vectors	122	(1)
Further Reduction of a System of Forces	123	(2)
Reduction of a System of Forces to a Wrench	125	(28)
Review and Summary for Chapter 3	144	(5)
Review Problems	149	(4)
Equilibrium of Rigid Bodies	153	(56)
Introduction	154	(1)
Free-Body Diagram	155	(1)
Equilibrium in Two Dimensions	156	(1)
Reactions at Supports and Connections for a Two-Dimensional Structure	156	(2)
Equilibrium of a Rigid Body in Two Dimensions	158	(2)
Statically Indeterminate Reactions. Partial Constraints	160	(17)
Equilibrium of a Two-Force Body	177	(1)
Equilibrium of a Three-Force Body	178	(7)
Equilibrium in Three Dimensions	185	(1)
Equilibrium of a Rigid Body in Three Dimensions	185	(1)
Reactions at Supports and Connections for a Three-Dimensional Structure	185	(24)
Review and Summary for Chapter 4	202	(2)
Review Problems	204	(5)
Distributed Forces: Centroids and Centers of Gravity	209	(65)
Introduction	210	(1)
Areas and Lines	210	(1)
Center of Gravity of a Two-Dimensional Body	210	(2)
Centroids of Areas and Lines	212	(1)
First Moments of Areas and Lines	213	(3)
Composite Plates and Wires	216	(11)
Determination of Centroids by Integration	227	(2)
Theorems of Pappus-Guldinus	229	(11)
Distributed Loads on Beams	240	(1)
Forces on Submerged Surfaces	241	(10)
Volumes	251	(1)
Center of Gravity of a Three-Dimensional Body. Centroid of a Volume	251	(3)
Composite Bodies	254	(1)
Determination of Centroids of Volumes by Integration	254	(20)
Review and Summary for Chapter 5	266	(4)
Review Problems	270	(4)
Analysis of Structures	274	(67)
Introduction	275	(1)
Trusses	276	(1)
Definition of a Truss	276	(2)
Simple Trusses	278	(1)
Analysis of Trusses by the Method of Joints	279	(2)
Joints under Special Loading Conditions	281	(2)
Space Trusses	283	(10)
Analysis of Trusses by the Method of Sections	293	(1)
Trusses Made of Several Simple Trusses	294	(11)
Frames and Machines	305	(1)
Structures Containing Multiforce Members	305	(1)
Analysis of a Frame	305	(1)
Frames Which Cease to Be Rigid When Detached from Their Supports	306	(15)
Machines	321	(20)
Review and Summary for Chapter 6	333	(3)
Review Problems	336	(5)
Forces in Beams and Cables	341	(55)
Introduction	342	(1)
Internal Forces in Members	342	(7)
Beams	349	(1)
Various Types of Loading and Support	349	(1)
Shear and Bending Moment in a Beam	350	(2)
Shear and Bending-Moment Diagrams	352	(8)
Relations among Load, Shear, and Bending Moment	360	(11)
Cables	371	(1)
Cables with Concentrated Loads	371	(1)
Cables with Distributed Loads	372	(1)
Parabolic Cable	373	(9)
Catenary	382	(14)
Review and Summary for Chapter 7	390	(3)
Review Problems	393	(3)
Friction	396	(59)
Introduction	397	(1)
The Laws of Dry Friction. Coefficients of Friction	397	(3)
Angles of Friction	400	(1)
Problems Involving Dry Friction	401	(16)
Wedges	417	(1)
Square-Threaded Screws	417	(9)
Journal Bearings. Axle Friction	426	(2)
Thrust Bearings. Disk Friction	428	(1)
Wheel Friction. Rolling Resistance	429	(7)
Belt Friction	436	(19)
Review and Summary for Chapter 8	447	(3)
Review Problems	450	(5)
Distributed Forces: Moments of Inertia	455	(84)
Introduction	456	(1)
Moments of Inertia of Areas	457	(1)
Second Moment, or Moment of Inertia, of an Area	457	(1)
Determination of the Moment of Inertia of an Area by Integration	458	(1)
Polar Moment of Inertia	459	(1)
Radius of Gyration of an Area	460	(7)
Parallel-Axis Theorem	467	(1)
Moments of Inertia of Composite Areas	468	(13)
Product of Inertia	481	(1)
Principal Axes and Principal Moments of Inertia	482	(8)
Mohr's Circle for Moments and Products of Inertia	490	(6)
Moments of Inertia of Masses	496	(1)
Moment of Inertia of a Mass	496	(2)
Parallel-Axis Theorem	498	(1)
Moments of Inertia of Thin Plates	499	(1)
Determination of the Moment of Inertia of a Three-Dimensional Body by Integration	500	(1)
Moments of Inertia of Composite Bodies	500	(15)
Moment of Inertia of a Body with Respect to an Arbitrary Axis through O. Mass Products of Inertia	515	(1)
Ellipsoid of Inertia. Principal Axes of Inertia	516	(2)
Determination of the Principal Axes and Principal Moments of Inertia of s Body of Arbitrary Shape	518	(21)
Review and Summary for Chapter 9	529	(6)
Review Problems	535	(4)
Method of Virtual Work	539	(42)
Introduction	540	(1)
Work of a Force	540	(3)
Principle of Virtual Work	543	(1)
Applications of the Principle of Virtual Work	544	(2)
Real Machines. Mechanical Efficiency	546	(14)
Work of a Force during a Finite Displacement	560	(2)
Potential Energy	562	(1)
Potential Energy and Equilibrium	563	(1)
Stability of Equilibrium	564	(17)
Review and Summary for Chapter 10	574	(3)
Review Problems	577	(4)
Kinematics of Particles	581	(86)
Introduction to Dynamics	582	(1)
Rectilinear Motion of Particles	583	(1)
Position, Velocity, and Acceleration	583	(4)
Determination of the Motion of a Particle	587	(9)
Uniform Rectilinear Motion	596	(1)
Uniformly Accelerated Rectilinear Motion	597	(1)
Motion of Several Particles	598	(12)
Graphical Solution of Rectilinear-Motion Problems	610	(1)
Other Graphical Methods	611	(10)
Curvilinear Motion of Particles	621	(1)
Position Vector, Velocity, and Acceleration	621	(2)
Derivatives of Vector Functions	623	(2)
Rectangular Components of Velocity and Acceleration	625	(1)
Motion Relative to a Frame in Translation	626	(17)
Tangential and Normal Components	643	(3)
Radial and Transverse Components	646	(21)
Review and Summary for Chapter 11	659	(4)
Review Problems	663	(4)
Kinetics of Particles: Newton's Second Law	667	(62)
Introduction	668	(1)
Newton's Second Law of Motion	669	(1)
Linear Momentum of a Particle. Rate of Change of Linear Momentum	670	(1)
Systems of Units	671	(2)
Equations of Motion	673	(2)
Dynamic Equilibrium	675	(20)
Angular Momentum of a Particle. Rate of Change of Angular Momentum	695	(1)
Equations of Motion in Terms of Radial and Transverse Components	696	(1)
Motion under a Central Force. Conservation of Angular Momentum	697	(1)
Newton's Law of Gravitation	698	(9)
Trajectory of a Particle under a Central Force	707	(1)
Application to Space Mechanics	708	(3)
Kepler's Laws of Planetary Motion	711	(18)
Review and Summary for Chapter 12	720	(4)
Review Problems	724	(5)
Kinetics of Particles: Energy and Momentum Methods	729	(98)
Introduction	730	(1)
Work of a Force	730	(4)
Kinetic Energy of a Particle. Principle of Work and Energy	734	(2)
Applications of the Principle of Work and Energy	736	(1)
Power and Efficiency	737	(18)
Potential Energy	755	(2)
Conservative Forces	757	(1)
Conservation of Energy	758	(2)
Motion under a Conservative Central Force, Application to Space Mechanics	760	(19)
Principle of Impulse and Momentum	779	(3)
Impulsive Motion	782	(12)
Impact	794	(1)
Direct Central Impact	794	(3)
Oblique Central Impact	797	(3)
Problems Involving Energy and Momentum	800	(27)
Review and Summary for Chapter 13	816	(6)
Review Problems	822	(5)
Systems of Particles	827	(58)
Introduction	828	(1)
Application of Newton's Laws to the Motion of a System of Particles. Effective Forces	828	(3)
Linear and Angular Momentum of a System of Particles	831	(1)
Motion of the Mass Center of a System of Particles	832	(2)
Angular Momentum of a System of Particles about Its Mass Center	834	(2)
Conservation of Momentum for a System of Particles	836	(9)
Kinetic Energy of a System of Particles	845	(2)
Work-Energy Principle. Conservation of Energy for a System of Particles	847	(1)
Principle of Impulse and Momentum for a System of Particles	847	(11)
Variable Systems of Particles	858	(1)
Steady Stream of Particles	858	(3)
Systems Gaining or Losing Mass	861	(24)
Review and Summary for Chapter 14	876	(4)
Review Problems	880	(5)
Kinematics of Rigid Bodies	885	(105)
Introduction	886	(2)
Translation	888	(1)
Rotation about a Fixed Axis	889	(3)
Equations Defining the Rotation of a Rigid Body about a Fixed Axis	892	(10)
General Plane Motion	902	(2)
Absolute and Relative Velocity in Plane Motion	904	(11)
Instantaneous Center of Rotation in Plane Motion	915	(11)
Absolute and Relative Acceleration in Plane Motion	926	(2)
Analysis of Plane Motion in Terms of a Parameter	928	(12)
Rate of Change of a Vector with Respect to a Rotating Frame	940	(2)
Plane Motion of a Particle Relative to a Rotating Frame. Coriolis Acceleration	942	(11)
Motion about a Fixed Point	953	(3)
General Motion	956	(11)
Three-Dimensional Motion of a Particle Relative to a Rotating Frame. Coriolis Acceleration	967	(1)
Frame of Reference in General Motion	968	(22)
Review and Summary for Chapter 15	979	(7)
Review Problems	986	(4)
Plane Motion of Rigid Bodies: Forces and Accelerations	990	(55)
Introduction	991	(1)
Equations of Motion for a Rigid Body	992	(1)
Angular Momentum of a Rigid Body in Plane Motion	993	(1)
Plane Motion of a Rigid Body. D'Alembert's Principle	994	(1)
A Remark on the Axioms of the Mechanics of Rigid Bodies	995	(1)
Solution of Problems Involving the Motion of a Rigid Body	996	(1)
Systems of Rigid Bodies	997	(19)
Constrained Plane Motion	1016	(29)
Review and Summary for Chapter 16	1039	(2)
Review Problems	1041	(4)
Plane Motion of Rigid Bodies: Energy and Momentum Methods	1045	(61)
Introduction	1046	(1)
Principle of Work and Energy for a Rigid Body	1046	(1)
Work of Forces Acting on a Rigid Body	1047	(1)
Kinetic Energy of a Rigid Body in Plane Motion	1048	(1)
Systems of Rigid Bodies	1049	(1)
Conservation of Energy	1050	(1)
Power	1051	(17)
Principle of Impulse and Momentum for the Plane Motion of a Rigid Body	1068	(3)
Systems of Rigid Bodies	1071	(1)
Conservation of Angular Momentum	1071	(13)
Impulsive Motion	1084	(1)
Eccentric Impact	1084	(22)
Review and Summary for Chapter 17	1098	(4)
Review Problems	1102	(4)
Kinetics of Rigid Bodies in Three Dimensions	1106	(65)
Introduction	1107	(1)
Angular Momentum of a Rigid Body in Three Dimensions	1108	(4)
Application of the Principle of Impulse and Momentum to the Three-Dimensional Motion of a Rigid Body	1112	(1)
Kinetic Energy of a Rigid Body in Three Dimensions	1113	(13)
Motion of a Rigid Body in Three Dimensions	1126	(1)
Euler's Equations of Motion. Extension of d'Alembert's Principle to the Motion of a Rigid Body in Three Dimensions	1127	(1)
Motion of a Rigid Body about a Fixed Point	1128	(1)
Rotation of a Rigid Body about a Fixed Axis	1129	(15)
Motion of a Gyroscope. Eulerian Angles	1144	(2)
Steady Precession of a Gyroscope	1146	(1)
Motion of an Axisymmetrical Body under No Force	1147	(24)
Review and Summary for Chapter 18	1160	(5)
Review Problems	1165	(6)
Mechanical Vibrations	1171	(72)
Introduction	1172	(1)
Vibrations without Damping	1172	(1)
Free Vibrations of Particles. Simple Harmonic Motion	1172	(4)
Simple Pendulum (Approximate Solution)	1176	(1)
Simple Pendulum (Exact Solution)	1177	(9)
Free Vibrations of Rigid Bodies	1186	(12)
Application of the Principle of Conservation of Energy	1198	(11)
Forced Vibrations	1209	(10)
Damped Vibrations	1219	(1)
Damped Free Vibrations	1219	(3)
Damped Forced Vibrations	1222	(1)
Electrical Analogues	1223	(20)
Review and Summary for Chapter 19	1234	(5)
Review Problems	1239	(4)
Index	1243	(12)
Answers to Problems	1255