Engineering Mechanics: Statics and Dynamics

by Shames, Irving H.

• ISBN13: 9780133569247
• ISBN10: 0133569241
• Edition: 4th
• Format: Hardcover
• Copyright: 1996-04-01
• Publisher: Prentice Hall

Summary

For Combined Statics and Dynamics courses. This edition of the highly respected and well-known book for Engineering Mechanics focuses on developing a solid understanding of basic principles rather than rote learning of specific methodologies. It covers fundamental principles instead of "cookbook" problem-solving, and has been refined to make it more readable. It includes over 500 new problems rigorously checked for accuracy. Statics topics covered include fundamentals of mechanics, elements of vector algebra, important vector quantities, equivalent force systems, equations of equilibrium, introduction to structural mechanics, friction forces, properties of surfaces, moments and products of inertia, and methods of virtual work and stationary potential energy. Dynamics topics include kinematics of a particle, particle dynamics, energy methods for particles, methods of momentum for particles, kinematics of rigid bodies, kinetics of plane motion of rigid bodies, energy and impulse-momentum methods for rigid bodies, dynamics of general rigid-body motion, and vibrations.

Table of Contents

Preface	ix
1 Fundamentals of Mechanics Review I	3	(20)
1.1 Introduction	3	(1)
1.2 Basic Dimensions and Units of Mechanics	4	(3)
1.3 Secondary Dimensional Quantities	7	(1)
1.4 Law of Dimensional Homogeneity	8	(1)
1.5 Dimensional Relation between Force and Mass	9	(1)
1.6 Units of Mass	10	(2)
1.7 Idealizations of Mechanics	12	(2)
1.8 Vector and Scalar Quantities	14	(3)
1.9 Equality and Equivalence of Vectors	17	(2)
1.10 Laws of Mechanics	19	(3)
1.11 Closure	22	(1)
2 Elements of Vector Algebra Review II	23	(38)
2.1 Introduction	23	(1)
2.2 Magnitude and Multiplication of a Vector by a Scalar	23	(1)
2.3 Addition and Subtraction of Vectors	24	(6)
2.4 Resolution of Vectors; Scalar Components	30	(3)
2.5 Unit Vectors	33	(2)
2.6 Useful Ways of Representing Vectors	35	(6)
2.7 Scalar or Dot Product of Two Vectors	41	(6)
2.8 Cross Product of Two Vectors	47	(4)
2.9 Scalar Triple Product	51	(3)
2.10 A Note on Vector Notation	54	(2)
2.11 Closure	56	(5)
3 Important Vector Quantities	61	(32)
3.1 Position Vector	61	(1)
3.2 Moment of a Force about a Point	62	(7)
3.3 Moment of a Force about an Axis	69	(8)
3.4 The Couple and Couple Moment	77	(2)
3.5 The Couple Moment as a Free Vector	79	(1)
3.6 Addition and Subtraction of Couples	80	(2)
3.7 Moment of a Couple About a Line	82	(7)
3.8 Closure	89	(4)
4 Equivalent Force Systems	93	(58)
4.1 Introduction	93	(1)
4.2 Translation of a Force to a Parallel Position	94	(8)
4.3 Resultant of a Force System	102	(4)
4.4 Simplest Resultants of Special Force Systems	106	(1)
4.5 Distributed Force Systems	107	(36)
4.6 Closure	143	(8)
5 Equations of Equilibrium	151	(70)
5.1 Introduction	151	(1)
5.2 The Free-body Diagram	152	(2)
5.3 Free Bodies Involving Interior Sections	154	(4)
*5.4 Looking Ahead--Control Volumes	158	(4)
5.5 General Equations of Equilibrium	162	(2)
5.6 Problems of Equilibrium I	164	(19)
5.7 Problems of Equilibrium II	183	(16)
5.8 Two Point Equivalent Loading	199	(1)
5.9 Problems Arising from Structures	200	(4)
5.10 Static Indeterminacy	204	(6)
5.11 Closure	210	(11)
6 Introduction to Structural Mechanics	221	(60)
Part A: Trusses	221	(26)
6.1 The Structural Model	221	(3)
6.2 The Simple Truss	224	(1)
6.3 Solution of Simple Trusses	225	(1)
6.4 Method of Joints	225	(13)
6.5 Method of Sections	238	(4)
*6.6 Looking Ahead--Deflection of a Simple, Linearly Elastic Truss	242	(5)
Part B: Section Forces in Beams	247	(19)
6.7 Introduction	247	(1)
6.8 Shear Force, Axial Force, and Bending Moment	247	(12)
6.9 Differential Relations for Equilibrium	259	(7)
Part C: Chains and Cables	266	(15)
6.10 Introduction	266	(1)
6.11 Coplanar Cables; Loading is a Function of x	266	(4)
6.12 Coplanar Cables: Loading is the Weight of the Cable Itself	270	(7)
6.13 Closure	277	(4)
7 Friction Forces	281	(50)
7.1 Introduction	281	(1)
7.2 Laws of Coulomb Friction	282	(2)
*7.3 A Comment Concerning the Use of Coulomb's Law	284	(1)
7.4 Simple Contact Friction Problems	284	(15)
7.5 Complex Surface Contact Friction Problems	299	(2)
7.6 Belt Friction	301	(16)
7.7 The Square Screw Thread	317	(2)
*7.8 Rolling Resistance	319	(4)
7.9 Closure	323	(8)
8 Properties of Surfaces	331	(48)
8.1 Introduction	331	(1)
8.2 First Moment of an Area and the Centroid	331	(11)
8.3 Other Centers	342	(5)
8.4 Theorems of Pappus-Guldinus	347	(8)
8.5 Second Moments and the Product of Area of a Plane Area	355	(1)
8.6 Transfer Theorems	356	(1)
8.7 Computations Involving Second Moments and Products of Area	357	(9)
8.8 Relation Between Second Moments and Products of Area	366	(3)
8.9 Polar Moment of Area	369	(1)
8.10 Principal Axes	370	(5)
8.11 Closure	375	(4)
9 Moments and Products of Inertia	379	(34)
9.1 Introduction	379	(1)
9.2 Formal Definition of Inertia Quantities	379	(7)
9.3 Relation Between Mass-Inertia Terms and Area-Inertia Terms	386	(6)
9.4 Translation of Coordinate Axes	392	(3)
*9.5 Transformation Properties of the Inertia Terms	395	(5)
*9.6 Looking Ahead--Tensors	400	(7)
*9.7 The Inertia Ellipsoid and Principal Moments of Inertia	407	(3)
9.8 Closure	410	(3)
10 *Methods of Virtual Work and Stationary Potential Energy	413	(38)
10.1 Introduction	413	(1)
Part A: Method of Virtual Work	414	(18)
10.2 Principle of Virtual Work for a Particle	414	(1)
10.3 Principle of Virtual Work for Rigid Bodies	415	(3)
10.4 Degrees of Freedom and the Solution of Problems	418	(6)
10.5 Looking Ahead--Deformable Solids	424	(8)
Part B: Method of Total Potential Energy	432	(19)
10.6 Conservative Systems	432	(2)
10.7 Condition of Equilibrium for a Conservative System	434	(7)
10.8 Stability	441	(2)
10.9 Looking Ahead--More on Total Potential Energy	443	(3)
10.10 Closure	446	(5)
11 Kinematics of a Particle--Simple Relative Motion	451	(60)
11.1 Introduction	451	(1)
Part A: General Notions	452	(2)
11.2 Differentiation of a Vector with Respect to Time	452	(2)
Part B: Velocity and Acceleration Calculations	454	(38)
11.3 Introductory Remark	454	(1)
11.4 Rectangular Components	455	(10)
11.5 Velocity and Acceleration in Terms of Path Variables	465	(15)
11.6 Cylindrical Coordinates	480	(12)
Part C: Simple Kinematical Relations and Applications	492	(19)
11.7 Simple Relative Motion	492	(2)
11.8 Motion of a Particle Relative to a Pair of Translating Axes	494	(10)
11.9 Closure	504	(7)
12 Particle Dynamics	511	(68)
12.1 Introduction	511	(1)
Part A: Rectangular Coordinates; Rectilinear Translation	512	(24)
12.2 Newton's Law for Rectangular Coordinates	512	(1)
12.3 Rectilinear Translation	512	(16)
12.4 A Comment	528	(8)
Part B: Cylindrical Coordinates; Central Force Motion	536	(25)
12.5 Newton's Law for Cylindrical Coordinates	536	(2)
12.6 Central Force Motion--An Introduction	538	(1)
*12.7 Gravitational Central Force Motion	539	(5)
*12.8 Applications to Space Mechanics	544	(17)
Part C: Path Variables	561	(3)
12.9 Newton's Law for Path Variables	561	(3)
Part D: A System of Particles	564	(15)
12.10 The General Motion of a System of Particles	564	(7)
12.11 Closure	571	(8)
13 Energy Methods for Particles	579	(58)
Part A: Analysis for a Single Particle	579	(30)
13.1 Introduction	579	(6)
13.2 Power Considerations	585	(9)
13.3 Conservative Force Field	594	(4)
13.4 Conservation of Mechanical Energy	598	(5)
13.5 Alternative Form of Work-Energy Equation	603	(6)
Part B: Systems of Particles	609	(28)
13.6 Work-Energy Equations	609	(5)
13.7 Kinetic Energy Expression Based on Center of Mass	614	(5)
13.8 Work-Kinetic Energy Expressions Based on Center of Mass	619	(12)
13.9 Closure	631	(6)
14 Methods of Momentum for Particles	637	(70)
Part A: Linear Momentum	637	(38)
14.1 Impulse and Momentum Relations for a Particle	637	(6)
14.2 Linear-Momentum Considerations for a System of Particles	643	(5)
14.3 Impulsive Forces	648	(11)
14.4 Impact	659	(6)
*14.5 Collision of a Particle with a Massive Rigid Body	665	(10)
Part B: Moment of Momentum	675	(32)
14.6 Moment-of-Momentum Equation for a Single Particle	675	(3)
14.7 More on Space Mechanics	678	(8)
14.8 Moment-of-Momentum Equation for a System of Particles	686	(8)
*14.9 Looking Ahead--Basic Laws of Continua	694	(6)
14.10 Closure	700	(7)
15 Kinematics of Rigid Bodies: Relative Motion	707	(80)
15.1 Introduction	707	(1)
15.2 Translation and Rotation of Rigid Bodies	707	(2)
15.3 Chasles' Theorem	709	(2)
15.4 Derivative of a Vector Fixed in a Moving Reference	711	(12)
15.5 Applications of the Fixed-Vector Concept	723	(20)
15.6 General Relationship Between Time Derivatives of a Vector for Different References	743	(1)
15.7 The Relationship Between Velocities of a Particle for Different References	744	(11)
15.8 Acceleration of a Particle for Different References	755	(18)
15.9 A New Look at Newton's Law	773	(3)
15.10 The Coriolis Force	776	(5)
15.11 Closure	781	(6)
16 Kinetics of Plane Motion of Rigid Bodies	787	(66)
16.1 Introduction	787	(1)
16.2 Moment-of-Momentum Equations	788	(3)
16.3 Pure Rotation of a Body of Revolution About its Axis of Revolution	791	(6)
16.4 Pure Rotation of a Body with Two Orthogonal Planes of Symmetry	797	(3)
16.5 Pure Rotation of Slablike Bodies	800	(10)
16.6 Rolling Slablike Bodies	810	(6)
16.7 General Plane Motion of a Slablike Body	816	(18)
16.8 Pure Rotation of an Arbitrary Rigid Body	834	(4)
*16.9 Balancing	838	(8)
16.10 Closure	846	(7)
17 Energy and Impulse-Momentum Methods for Rigid Bodies	853	(58)
17.1 Introduction	853	(1)
Part A: Energy Methods	853	(25)
17.2 Kinetic Energy of a Rigid Body	853	(7)
17.3 Work-Energy Relations	860	(18)
Part B: Impulse-Momentum Methods	878	(33)
17.4 Angular Momentum of a Rigid Body About Any Point in the Body	878	(4)
17.5 Impulse-Momentum Equations	882	(13)
17.6 Impulsive Forces and Torques: Eccentric Impact	895	(12)
17.7 Closure	907	(4)
18 *Dynamics of General Rigid-Body Motion	911	(50)
18.1 Introduction	911	(3)
18.2 Euler's Equations of Motion	914	(2)
18.3 Application of Euler's Equations	916	(14)
18.4 Necessary and Sufficient Conditions for Equilibrium of a Rigid Body	930	(1)
18.5 Three-Dimensional Motion About a Fixed Point; Euler Angles	930	(4)
18.6 Equations of Motion Using Euler Angles	934	(11)
18.7 Torque-Free Motion	945	(13)
18.8 Closure	958	(3)
19 Vibrations	961
19.1 Introduction	961	(1)
19.2 Free Vibration	961	(12)
19.3 Torsional Vibration	973	(9)
*19.4 Examples of Other Free-Oscillating Motions	982	(2)
*19.5 Energy Methods	984	(6)
19.6 Linear Restoring Force and a Force Varying Sinusoidally with Time	990	(9)
19.7 Linear Restoring Force with Viscous Damping	999	(8)
19.8 Linear Restoring Force, Viscous Damping, and a Harmonic Disturbance	1007	(7)
*19.9 Oscillatory Systems with Multi-Degrees of Freedom	1014	(8)
19.10 Closure	1022
APPENDIX I Integration Formulas	xvii	(2)
APPENDIX II Computation of Principal Moments of Inertia	xix	(2)
APPENDIX III Additional Data For the Ellipse	xxi	(2)
APPENDIX IV Proof that Infinitesimal Rotations Are Vectors	xxiii	(2)
Projects	xxv	(37)
Answers	lxii	(15)
Index	lxxvii