Engineering Mechanics : Statics

by Soutas-Little, Robert; Inman, Daniel J.

• ISBN13: 9780137690015
• ISBN10: 0137690010
• Format: Hardcover
• Copyright: 1999-01-01
• Publisher: Pearson College Div

Summary

This progressive guide emphasizes the use of vector mechanics and vector mathematics in its treatment of statistics, and is the first engineering mechanics book of its kind to address the use of computational software for computing solutions and for visualizing physical properties - reflecting the latest developments in the methods of analysis of mechanics problems by incorporating the highly sophisticated computational software packages currently available. Uses computational software as a vector calculator (so readers can perform vector manipulations quickly and accurately, allowing them more time to focus on the fundamentals), and provides direct vector calculations throughout (presenting systematic methods to solve some vector equations without expanding into scalar components). Offers a Matrix Solution of Systems of Equations using computational software; uses discontinuity functions to make shear and moment calculations and plots; and provides such powerful computational tools as symbolic manipulation and plotting for visualization of forces and the effects of geometry, and other parameters on internal and reaction forces and moments. Approximately 1,000 problems and 95 worked sample problems help foster understanding, and all sample problems and the use of computational software (Mathcad, MATLAB, Mathematica and Maple) are presented in four separate manuals (one for each software program).

Table of Contents

Preface	x
Chapter 1. Introduction	1	(15)
1.1 Mechanics	1	(1)
1.2 Basic Concepts	2	(4)
Problems 1.1-1.4	5	(1)
1.3 Units	6	(7)
SI Units	6	(1)
U.S. Customary Units	7	(2)
Conversion between Systems of Units	9	(3)
Problems 1.5-1.9	12	(1)
1.4 Numerical Calculations	13	(1)
1.5 Problem-Solving Strategy	14	(1)
1.6 Computational Software	15	(1)
Chapter 2. Vectors and Force Systems Acting on a Particle	16	(90)
2.1 Introduction	16	(1)
2.2 Vectors	17	(17)
Definition of a Scalar and Vector	17	(1)
Vector Addition	18	(4)
Multiplication of a Vector by a Scalar	22	(1)
Vector Components	22	(7)
Resolution of a Vector into Components	29	(5)
2.3 Forces and Their Characteristics	34	(8)
Concurrent Coplanar Forces	36	(2)
Problems 2.1-2.21	38	(4)
2.4 Three-dimensional Cartesian Coordinates and Unit Base Vectors	42	(9)
Unit Base Vectors	43	(2)
Vector Equality in Component Notation	45	(1)
Vector Addition by Components	45	(1)
Multiplication of a Vector by a Scalar	46	(1)
Vector Subtraction	46	(1)
General Unit Vectors	46	(1)
Vector Directions in Space	47	(2)
Matrix Notation for Vectors	49	(2)
2.5 Computation of Vector Operations	51	(8)
Problems 2.2-2.59	54	(5)
2.6 Components of a Vector in Nonorthongonal Directions	59	(3)
2.7 Systems of Linear Equations	62	(9)
Matrices	64	(5)
Problems 2.60-2.77	69	(2)
2.8 Scalar Product of Two Vectors	71	(8)
Applications of the Scalar Product	72	(4)
Problems 2.78-2.94	76	(3)
2.9 Free-body Diagrams of a Particle	79	(6)
Problems 2.95-2.104	83	(2)
2.10 Equilibrium of a Particle	85	(8)
Problems 2.105-2.113	90	(3)
2.11 Springs	93	(4)
2.12 Statically Indeterminate Problems	97	(4)
Problems 2.114-2.118	100	(1)
Chapter Summary	101	(5)
Vectors	101	(1)
Free-body Diagrams and Equilibrium of a Particle	102	(1)
Review Problems 2.119-2.131	103	(3)
Chapter 3. Rigid Bodies: Equivalent Force Systems	106	(66)
3.1 Rigid Bodies	106	(2)
3.2 Modeling of Rigid Bodies and Moment of a Force	108	(6)
Problems 3.1-3.10	112	(2)
3.3 Vector Product or Cross Product	114	(8)
Multiple Products of Vectors	117	(4)
Problems 3.11-3.20	121	(1)
3.4 Moment of a Force about a Point in Space	122	(5)
Direct Vector Solutions	124	(3)
3.5 Varignon's Theorem	127	(7)
Problems 3.21-3.47	130	(4)
3.6 Moment of a Force about an Axis	134	(5)
Problems 3.48-3.60	137	(2)
3.7 Moment of a Couple	139	(5)
Problems 3.61-3.70	142	(2)
3.8 Equivalent Force Systems	144	(4)
Problems 3.71-3.74	147	(1)
3.9 Special Equivalent Force Systems	148	(9)
Concurrent Force Systems	150	(1)
Coplanar Force Systems	150	(2)
Parallel Force Systems	152	(5)
3.10 General Equivalent Force Systems	157	(13)
The Wrench	159	(7)
Problems 3.75-3.94	166	(4)
Chapter Summary	170	(2)
Chapter 4. Distributed Forces: Centroids and Center of Gravity	172	(47)
4.1 Introduction	172	(3)
4.2 Center of Mass and Center of Gravity	175	(4)
Center of Mass	175	(2)
Center of Gravity	177	(2)
4.3 Centroids of Areas, Volumes, and Lines; The First Moment	179	(13)
Centroids of an Area	179	(4)
Centroid of a Volume	183	(2)
Centroid of a Line	185	(1)
Centroid of a Curve in Space	186	(3)
Problems 4.1-4.25	189	(3)
4.4 Theorems of Pappus and Guldinus Problems 4.26-4.32	192	(4)
4.5 Centroids of Composite Bodies	196	(10)
Problems 4.33-4.32	202	(4)
4.6 Distributed Loads on Beams	206	(4)
Problems 4.52-4.62	208	(2)
4.7 Forces Due to Fluid Pressure Acting on a Submerged Surface	210	(6)
Buoyancy	211	(3)
Problems 4.63-4.70	214	(2)
Chapter Summary	216	(3)
Centroid	216	(1)
Center of Mass	216	(1)
Centroids of Composite Bodies	217	(1)
Distributed Loads on a Beam	217	(1)
Focus on a Submerged Surface	218	(1)
Buoyancy	218	(1)
Chapter 5. Equilibrium of Rigid Bodies	219	(65)
5.1 Introduction	219	(2)
5.2 Supports for a Two-dimensional Model	221	(4)
5.3 Supports for a Three-dimensional Model	225	(4)
5.4 Free-Body Diagram	229	(7)
Problems 5.1-5.10	233	(3)
5.5 Equilibrium of a Rigid Body in Two Dimensions	236	(21)
Solution Strategy	237	(1)
A Two-Force Member	238	(1)
A Three-Force Member	238	(8)
Problems 5.11-5.51	246	(11)
5.6 Equilibrium of a Rigid Body in Three Dimensions	257	(7)
Constraints	258	(6)
5.7 Statically Indeterminate Reactions and Improper Constraints	264	(18)
Problems 5.52-5.80	272	(10)
Chapter Summary	282	(2)
Equilibrium	282	(1)
Free-body Diagram	282	(1)
Two-force Member	282	(1)
Three-force Member	282	(1)
Equilibrium of a Rigid Body in Three Dimensions	283	(1)
Chapter 6. Analysis of Structures	284	(52)
6.1 Introduction	284	(2)
6.2 Planar Trusses	286	(3)
6.3 Simple Trusses	289	(1)
6.4 Method of Joints	290	(6)
6.5 Method of Joints Using Matrix Techniques	296	(9)
Problems 6.1-6.30	300	(5)
6.6 Method of Sections	305	(7)
Problems 6.31-6.55	308	(4)
6.7 Space Trusses	312	(7)
Problems 6.56-6.66	316	(3)
6.8 Compound Trusses	319	(1)
6.9 Frames and Machines	319	(16)
Problems 6.67-6.97	324	(11)
Chapter Summary	335	(1)
Trusses	335	(1)
Frames and Machines	335	(1)
Chapter 7. Internal Forces in Structural Members	336	(47)
7.1 Introduction	336	(1)
7.2 Internal Forces in a Member	337	(9)
Problems 7.1-7.17	343	(3)
7.3 Types of Loading and Supports in Beams	346	(1)
7.4 Shear and Bending Moments in Beams	347	(12)
Relationship between the Load Distribution, the Shear Force, and the Bending Moment	349	(6)
Problems 7.18-7.41	355	(4)
7.5 Discontinuity Functions for Beam Equations	359	(9)
Problems 7.42-7.53	366	(2)
7.6 Cables	368	(12)
Cable Subjected to Concentrated Loads	368	(3)
Cables Supporting Loads Distributed Uniformly along a Horizontal Line	371	(2)
Cables Supporting Loads Distributed Uniformly along Its Own Length	373	(3)
Problems 7.54-7.70	376	(4)
Chapter Summary	380	(3)
Beams	380	(1)
Discontinuity Functions	380	(1)
Cables	381	(2)
Chapter 8. Friction	383	(54)
8.1 Introduction	383	(4)
8.2 Coulomb Friction	387	(19)
Problems 8.1-8.70	396	(10)
8.3 Wedges	406	(7)
Problems 8.71-8.89	411	(2)
8.4 Square-Threaded Screws	413	(8)
Problems 8.90-8.104	418	(3)
8.5 Belt Friction	421	(4)
V-belts	423	(2)
8.6 Bearings	425	(3)
8.7 Thrust Bearings, Collars, and Clutches	428	(1)
8.8 Rolling Resistance	429	(6)
Problems 8.105-8.125	432	(3)
Chapter Summary	435	(2)
Belt Friction	436	(1)
Roller Bearings	436	(1)
Thrust Bearings, Collars, and Clutches	436	(1)
Chapter 9. Moments of Inertia	437	(44)
9.1 Introduction	437	(1)
9.2 Second Moment of an Area	438	(1)
Determination of the Second Moment of an Area by Integration	439	(1)
9.3 Polar Moment of Inertia	439	(2)
9.4 Second Moment of an Area about Centroidal Axes for Specific Areas	441	(3)
Problems 9.1-9.21	442	(2)
9.5 Parallel-Axes Theorem for the Second Moment of Area	444	(2)
9.6 Radius of Gyration of an Area	446	(3)
Problems 9.22-9.32	448	(1)
9.7 Second Moments of Composite Areas	449	(5)
Problems 9.33-9.45	452	(2)
9.8 Principal Second Moments of Area	454	(8)
Product Moment of an Area, or Product Moment of Inertia	454	(1)
Rotation of Axes	455	(5)
Problems 9.46-9.59	460	(2)
9.9 Mohr's Circle to Determine Principal Second Moments of Area	462	(5)
Problems 9.60-9.73	465	(2)
9.10 Eigenvalue Problem	467	(5)
Problems 9.74-9.87	470	(2)
9.11 Mass Moments of Inertia	472	(6)
Parallel-Axis Theorem	473	(3)
Problems 9.88-9.102	476	(2)
Chapter Summary	478	(3)
Principal Second Moment of Area	479	(1)
Mass Moments of Inertia	480	(1)
Chapter 10. Virtual Work	481	(33)
10.1 Introduction	481	(2)
Work-By a Force or Moment	481	(2)
10.2 Virtual Work	483	(1)
10.3 Principle of Virtual Work for a System of Connected Rigid Bodies	484	(10)
Problems 10.1-10.28	489	(5)
10.4 Finite Work of a Force and Moment	494	(5)
Problems 10.29-10.34	498	(1)
10.5 Conservative Forces and Potential Energy	499	(4)
10.6 Potential Energy and Equilibrium	503	(1)
10.7 Stability of Equilibrium	504	(7)
Problems 10.35-10.60	508	(3)
Chapter Summary	511	(3)
Conservative Forces	512	(2)
Appendix: Solution of Systems of Linear Equations	514	(9)
Glossary	523	(11)
Problem Statements	534	(26)
Index	560