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 |  موضوع: كتاب Engineering Mechanics - Volume 1 - Statics الأحد 23 أغسطس 2020, 11:21 pm | |
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أحضرت لكم كتاب
Engineering Mechanics - Volume 1 - Statics
Ninth Edition
J.L. Meriam
L.G. Kraige
Virginia Polytechnic Institute and State University
J.N. Bolton
Bluefield State College
و المحتوى كما يلي :
Contents
1 Introduction to Statics 1
1/1 Mechanics 1
1/2 Basic Concepts 2
1/3 Scalars and Vectors 2
1/4 Newton’s Laws 5
1/5 Units 6
1/6 Law of Gravitation 9
1/7 Accuracy, Limits, and Approximations 10
1/8 Problem Solving in Statics 11
1/9 Chapter Review 14
2 Force Systems 17
2/1 Introduction 17
2/2 Force 17
Section A Two-Dimensional Force Systems 20
2/3 Rectangular Components 20
2/4 Moment 26
2/5 Couple 31
2/6 Resultants 34
Section B Three-Dimensional Force Systems 37
2/7 Rectangular Components 37
2/8 Moment and Couple 41
2/9 Resultants 48
2/10 Chapter Review 54
3 Equilibrium 55
3/1 Introduction 55
Section A Equilibrium in Two Dimensions 56
3/2 System Isolation and the Free-Body
Diagram 56
3/3 Equilibrium Conditions 66
Section B Equilibrium in Three Dimensions 74
3/4 Equilibrium Conditions 74
3/5 Chapter Review 82
4 Structures 83
4/1 Introduction 83
4/2 Plane Trusses 84
4/3 Method of Joints 86
4/4 Method of Sections 92
4/5 Space Trusses 96
4/6 Frames and Machines 99
4/7 Chapter Review 105
5 Distributed Forces 106
5/1 Introduction 106
Section A Centers of Mass and Centroids 108
5/2 Center of Mass 108
5/3 Centroids of Lines, Areas, and Volumes 110
5/4 Composite Bodies and Figures;
Approximations 118
5/5 Theorems of Pappus 122
Section B Special Topics 125
5/6 Beams—External Effects 125
5/7 Beams—Internal Effects 128
5/8 Flexible Cables 135
5/9 Fluid Statics 143
5/10 Chapter Review 153
6 Friction 154
6/1 Introduction 154
Section A Frictional Phenomena 155
6/2 Types of Friction 155
6/3 Dry Friction 155
xiSection B Applications of Friction in Machines 164
6/4 Wedges 164
6/5 Screws 165
6/6 Journal Bearings 169
6/7 Thrust Bearings; Disk Friction 169
6/8 Flexible Belts 172
6/9 Rolling Resistance 173
6/10 Chapter Review 176
7 Virtual Work 177
7/1 Introduction 177
7/2 Work 177
7/3 Equilibrium 180
7/4 Potential Energy and Stability 188
7/5 Chapter Review 197
APPENDIX A Area Moments of Inertia 198
A/1 Introduction 198
A/2 Definitions 199
A/3 Composite Areas 206
A/4 Products of Inertia and Rotation of Axes 209
APPENDIX B Mass Moments of Inertia 214
APPENDIX C Selected Topics of Mathematics 215
C/1 Introduction 215
C/2 Plane Geometry 215
C/3 Solid Geometry 216
C/4 Algebra 216
C/5 Analytic Geometry 217
C/6 Trigonometry 217
C/7 Vector Operations 218
C/8 Series 221
C/9 Derivatives 221
C/10 Integrals 222
C/11 Newton’s Method for Solving Intractable
Equations 225
C/12 Selected Techniques for Numerical
Integration 227
APPENDIX D Useful Tables 230
Table D/1 Physical Properties 230
Table D/2 Solar System Constants 231
Table D/3 Properties of Plane Figures 232
Table D/4 Properties of Homogeneous Solids 234
Table D/5 Conversion Factors; SI Units 238
PROBLEMS P-1
INDEX I-1
PROBLEM ANSWERS PA-1
Index
A
Absolute system of units, 7
Acceleration, of a body, 5, 66
due to gravity, 8
Accuracy, 10
Action and reaction, principle of, 5, 19,
56, 83, 99, 105, 128
Active force, 182
Active-force diagram, 183
Addition of vectors, 3, 20, 22, 218
Aerostatics, 143
Angle, of friction, 158
of repose, 160
Approximations, 11, 118
Archimedes, 1
Area, first moment of, 111
second moment of, 111, 198
Area moments of inertia, see Moments
of inertia of areas
Atmospheric pressure, 144
Axes, choice of, 21, 38, 60, 89, 110, 112
rotation of, 210
Axis, moment, 26, 41
B
Beams, concentrated loads on, 125
definition of, 125
distributed loads on, 126
external effects, 126
internal effects, 128
loading-shear relation for, 129, 130
resultant of forces on cross section
of, 128
shear-moment relation for, 129,
130, 131
statically determinate and
indeterminate, 125
types of, 125
Bearing friction, 169
Belt friction, 172
Bending moment, 128
Bending-moment diagram, 129
Bodies, interconnected, 99, 181
Body, deformable, 2
rigid, 2
Body force, 18, 107
Boundary conditions, 136
British system of units, 7
Buoyancy, center of, 149
force of, 148
principle of, 148
C
Cables, catenary, 138
flexible, 135
length of, 138, 140
parabolic, 136
tension in, 137, 140
Cajori, F., 5
Center, of buoyancy, 149
of gravity, 19, 108
of mass, 108, 109, 234
of pressure, 144
Centroids, 110
of composite figures, 118
by integration, 110
of irregular volumes, 119
table of, 232
by theorems of Pappus, 122
Coefficient, of friction, 157, 158, 230
of rolling resistance, 173
Collinear forces, equilibrium of, 66
Components, of a force, 20, 21, 22
rectangular, 4, 20, 21, 22, 37
scalar, 21
of a vector, 4, 20, 21, 22, 37
Composite areas, moment of inertia
of, 206
Composite bodies, center of mass
of, 118
Composite figures, centroid of, 118
Compression in truss members, 86, 88
Concentrated forces, 19, 106
on beams, 125
Concurrent forces, equilibrium of,
66, 75
resultant of, 19, 22, 35, 49
Cone of friction, 158
Constant of gravitation, 9, 231
Constraint, 69, 77
adequacy of, 70, 78
partial, 78
proper and improper, 70
redundant, 70, 78
Coordinates, choice of, 21, 38, 60, 112,
153, 200
Coplanar forces, equilibrium of, 66, 67
resultant of, 22, 34
Coulomb, 155
Couple, 31, 43
equivalent, 31
moment of, 31, 43
resolution of, 32, 49
resultant, 34, 48, 49
vector representation of, 31, 43
work of, 179
Cross or vector product, 27, 41, 219
D
D’Alembert, J., 2
da Vinci, 2
Deformable body, 2
Degrees of freedom, 183, 193, 197
Density, 109, 230
Derivative of vector, 220
Derivatives, table of, 221
Diagram, active-force, 183, 190
bending-moment, 129
free-body, 13, 56, 59, 75
shear-force, 129
Differential element, choice of, 112
Differentials, order of, 10, 112, 153
Dimensions, homogeneity of, 14
Direction cosines, 5, 37
Disk friction, 169
Displacement, 178
virtual, 180
Distributed forces, 19, 106, 107, 153
on beams, 125, 126
Distributive law, 28, 219
Dot or scalar product, 38, 178, 219
Dynamics, 2, 5
E
Efficiency, mechanical, 184
Elastic potential energy, 188
Energy, criterion for equilibrium, 192
criterion for stability, 192
elastic, 188
potential, 188, 190, 191
Equilibrium, alternative equations of, 68
categories of, 66, 75
of collinear forces, 66
of concurrent forces, 66, 75
condition of, 34, 66, 74, 181, 182
of coplanar forces, 66, 67
energy criterion for, 191, 192
equations of, 66, 74
of interconnected rigid bodies, 99, 181
of machines, 99
necessary and sufficient conditions
for, 66, 74
neutral, 192
of parallel forces, 66, 75
of a particle, 180
of a rigid body, 181
stability of, 70, 191
with two degrees of freedom, 183
by virtual work, 180, 181, 182
Euler, 2
External effects of force, 18
F
First moment of area, 111
Fixed vector, 3, 18
Flexible cables, 135
differential equation for, 136
Fluids, 143
friction in, 155
incompressible, 144
pressure in, 143
Foot, 6, 7
Force, action of, 17, 56, 57, 58, 75, 76
active, 182I-2 Index
body, 18, 107
buoyancy, 148
components of, 20, 21, 37
concentrated, 19, 104
concept of, 2
contact, 18
coplanar system of, 34
distributed, 19, 106, 107, 153
effects of, 17
external, 18
friction, 57, 154
gravitational, 9, 19, 59, 107
inertia, 199
intensity of, 107
internal, 18, 107, 128, 182
kinds of, 18
magnetic, 19, 59
measurement of, 19
mechanical action of, 57, 58, 76
moment of, 26, 41
polygon, 34, 68
reactive, 18, 182
remote action of, 59
resolution of, 20, 21, 37, 38
resultant, 34, 48, 49, 108, 153
shear, 128, 143
specifications of, 18
unit of, 6, 7
work of, 178
Force–couple system, 32, 34, 44
Force system, concurrent, 35, 43, 49,
66, 75
coplanar, 34
general, 17, 49
parallel, 20, 35, 49
Formulation of problems, 11
Frames, defined, 99, 105
equilibrium of, 99
Frames and machines, rigidity of, 99
Free-body diagram, 13, 56, 59, 75
Freedom, degrees of, 183, 193, 197
Free vector, 3, 4, 31, 43
Friction, angle of, 158
bearing, 169, 170
belt, 172
circle of, 169
coefficients of, 157, 158, 230
cone of, 158
disk, 169
dry or Coulomb, 155, 156
fluid, 155
internal, 155
journal bearing, 169
kinetic, 157
limiting, 157
in machines, 164
mechanism of, 156
pivot, 169
problems in dry friction, 159, 176
rolling, 173
screw thread, 165
static, 157
types of, 155
wedge, 164
work of, 183
G
Gage pressure, 144
Galileo, 1
Gas, 143
Graphical representation, 12, 19, 20, 34
Gravitation, constant of, 9, 231
law of, 9
Gravitational force, 9, 19, 59, 107
Gravitational potential energy, 189
Gravitational system of units, 7
Gravity, acceleration due to, 8
center of, 19, 108
Guldin, Paul, 122
Gyration, radius of, 200
H
Homogeneity, dimensional, 14
Hydrostatic pressure, 144, 146, 147
Hydrostatics, 143
Hyperbolic functions, 140
I
Ideal systems, 181
Impending motion, 157, 158, 159
Inclined axes, area moments of inertia
about, 210
Inertia, 2, 199
area moments of, see Moments of
inertia of areas
principal axes of, 211
products of, 209
Inertia force, 199
Integrals, table of selected, 222
Integration, choice of element for,
112, 153
numerical techniques for, 227, 228
of vectors, 220
Interconnected bodies, 99, 181
Internal effects of force, 18, 107, 128, 182
Internal friction, 155
International System of units, 6
J
Joints, method of, 86, 97, 105
Joule, 180
Journal bearings, friction in, 169
K
Kilogram, 6, 7, 9
Kilopound, 7
Kinetic friction, 157
coefficient of, 157, 230
L
Lagrange, 2
Laplace, 2
Law, associative, 218
commutative, 218, 219
of cosines, 218
distributive, 28, 219
of gravitation, 9
parallelogram, 3, 19, 34
of sines, 218
Pascal’s, 143
triangle, 4, 19
Laws of motion, Newton’s, 5
Length, standard unit of, 7
Limit, mathematical, 11
Line of action, 18
Liquids, 144
Loading-shear relation for beams,
129, 130
M
Mach, Ernst, 28
Machines, defined, 99, 105
equilibrium of, 99
friction in, 164
ideal or real, 155
Mass, 2, 7
center of, 108, 109, 234
unit of, 6, 7
Mathematical limit, 10
Mathematical model, 12
Mathematics, selected topics in, 215
Mechanical efficiency, 184
Mechanical system, 56
Mechanics, 1
Metacenter, 149
Metacentric height, 149
Meter, 7
Method, of joints, 86, 97, 105
of problem solution, 13, 54, 59, 82,
105, 153, 176, 197
of sections, 92, 97, 105
of virtual work, 177
Metric units, 6
Minimum energy, principle of, 192
Mohr’s circle, 211
Moment, bending, 128
components of, 42
of a couple, 31, 43
of a force, 26, 41
torsional, 128, 199
units of, 26
vector representation of, 27, 41
Moment arm, 26
Moment axis, 26, 41
Moments, principle of, 35, 48, 108,
113, 153
Moments of inertia of areas, 198
for composite areas, 206
dimensions and units of, 200
about inclined axes, 210
by integration, 199
maximum and minimum, 210, 211
Mohr’s circle representation of, 211
polar, 199
principal axes of, 211
radius of gyration for, 200
rectangular, 199
table of, 232
tabular computation of, 206
transfer of axes for, 201, 209
Morin, 155
Motion, impending, 157, 158, 159
Multi-force members, 99
Force, action of (Continued)Index I-3
N
Neutral equilibrium, 192
Newton, Isaac, 1
Newton’s laws, 5
Newton (unit), 6
Newton’s method, 225
Numerical integration, 227, 228
O
Order of differentials, 10, 112, 153
P
Pappus, 122
theorems of, 122
Parallel-axis theorems, for area
moments of inertia, 201
Parallel forces, equilibrium of, 66, 75
resultant of, 20, 35, 49
Parallelogram law, 3, 19, 34
Particle, 2
Particles, equilibrium of, 181
Pascal (unit), 107
Pascal’s law, 143
Pivot friction, 169
Polar moment of inertia, 199
Polygon, of forces, 34, 68
Potential energy, 188, 190, 191
datum for, 189
units of, 189, 190
Pound, standard, 7
Pound force, 7
Pound mass, 7
Pressure, 107, 143
atmospheric, 144
center of, 144
fluid, 143
gage, 144
hydrostatic, 144, 146, 147
on submerged surfaces, 144, 146, 147
Principal axes of inertia, 211
Principia, 5
Principle, of action and reaction, 5, 19, 56,
83, 99, 105, 128
of buoyancy, 148
of concurrency of forces, 67
of minimum energy, 192
of moments, 35, 48, 108, 113, 153
of transmissibility, 3, 18, 34
of virtual work, 181, 182, 191
Products of inertia, 209
about inclined axes, 210
Products of vectors, 27, 38, 41, 42,
178, 219
R
Radius of gyration, 200
Reactive forces, 18, 182
Rectangular components, 4, 20, 21,
22, 37
Rectangular moments of inertia, 199
Redundancy, external and internal,
88, 96
Redundant supports, 69, 78
Repose, angle of, 160
Resolution, force, 20, 21, 37, 38
force and couple, 32, 34, 44
Resultant, of concurrent forces, 19, 22,
35, 49
of coplanar forces, 22, 34
couple, 34, 48, 49
of fluid pressure, 144, 146, 147
force, 34, 48, 49, 108, 153
of forces on beam cross section, 128
of general force system, 49
of parallel forces, 20, 35, 49
Right-hand rule, 26, 38, 41, 219
Rigid bodies, interconnected, 99, 181
Rigid body, 2
equilibrium of, 181
Rolling resistance, coefficient of, 173
S
Scalar, 2
Scalar components, 21
Scalar or dot product, 38, 178, 219
Screw, friction in, 165
Second moment of area, 111, 198
Sections, method of, 92, 97, 105
Series, selected expansions, 221
Shear force, 128, 143
Shear-force diagram, 129
Shear-moment relation for beams, 129,
130, 131
Shear stress, 199
Singularity functions, 131
SI units, 6, 238, 239
Sliding vector, 3, 18, 26, 43
Slug, 6, 7
Space, 2
Space trusses, 96, 105
Specific weight, 107, 230
Spring, linear and nonlinear, 58, 59
potential energy of, 188
stiffness of, 59, 188
torsional, 58, 59
Stability, of equilibrium, 70, 191
of floating bodies, 149
for single-degree-of-freedom system,
192
of trusses, 88, 96
Statically determinate structures, 69,
77, 83, 88, 96
Statically indeterminate structures, 69,
78, 88, 96, 99
Static friction, 157
coefficient of, 157, 230
Statics, 2
Stevinus, 1
Stiffness of spring, 188
Stress, 107
shear, 199
Structures, statical determinacy of, 69, 77,
83, 88, 96, 99
types of, 83
Submerged surfaces, pressure on, 144,
146, 147
Subtraction of vectors, 4, 218
Symmetry, considerations of, 110, 209
System, with elastic members, 188
force–couple, 32, 34, 44
of forces, concurrent, 19, 35, 43, 49,
66, 75
coplanar, 34
general, 17, 48
parallel, 35, 49, 66, 75
ideal, 181
of interconnected bodies, 99, 181
mechanical, 56
real, 183
of units, 6
T
Table, of area moments of inertia, 232
of centroids, 232
of coefficients of friction, 230
of densities, 230
of derivatives, 221
of mass centers, 234
of mathematical relations, 215
of solar system constants, 231
Tension in truss members, 86, 87, 88
Theorem, of Pappus, 122
of Varignon, 27, 35, 43
Three-force member, 67
Thrust bearing, friction in, 169
Time, 2, 8
Ton, 7
Torque, see Moment, of force
Torsional moment, 128, 199
Transfer of axes, for moments of
inertia, 201
for products of inertia, 209
Transmissibility, principle of, 3, 18, 34
Triangle law, 4, 19
Triple scalar product, 42, 220
Triple vector product, 220
Trusses, definition, 84
plane, 84
simple, 84, 96
space, 96, 105
stability of, 88, 96
statical determinacy of, 88, 96, 105
types of, 85
Two-force members, 67, 85
U
U.S. customary units, 7
Units, 6, 26, 180, 238, 239
Unit vectors, 4, 21, 37, 38, 42
Unstable equilibrium, 192
V
Varignon, 2
Varignon’s theorem, 27, 35, 43
Vector equation, 5
Vectors, 2, 17
addition of, 3, 19, 22, 218
components of, 4, 20, 21, 22, 37
couple, 31, 43
cross or vector product of, 27, 41, 219
derivative of, 220I-4 Index
dot or scalar product of, 38, 178, 219
fixed, 3, 18
free, 3, 4, 31, 43
moment, 27, 41
notation for, 3
resolution of, 20, 21, 37, 38
sliding, 3, 18, 26, 43
subtraction of, 4, 218
unit, 4, 21, 37, 38, 42
Vector sum, of couples, 43, 48
of forces, 19, 22, 34, 48
Virtual displacement, 180
Virtual work, 177, 180
for elastic systems, 191
for ideal systems, 181, 182
for a particle, 180
for a rigid body, 181
Viscosity, 155
W
Wear in bearings, 170
Wedges, friction in, 164
Weight, 9, 10, 19, 59, 107
Work, of a couple, 179
of a force, 178
units of, 179
virtual, 177, 180
Wrench, 49
Vectors (Continued)
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