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 |  موضوع: كتاب Statics with MATLAB السبت 24 أغسطس 2019, 11:31 am | |
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أخوانى فى الله
أحضرت لكم كتاب
Statics with MATLAB
Dan B. Marghitu , Mihai Dupac , Nels H. Madsen
و المحتوى كما يلي :
Contents
1 Operation with Vectors 1
1.1 Introduction . 1
1.2 Vector Addition 3
1.3 Linear Independence 4
1.4 Resolution of Vectors 4
1.5 Angle Between Two Vectors . 7
1.6 Position Vector 8
1.7 Scalar Product of Vectors . 9
1.8 Vector Product of Vectors . 11
1.9 Scalar Triple Product of Three Vectors 13
1.10 Vector Triple Product of Three Vector 14
1.11 Derivative of a Vector Function . 15
1.12 Examples 17
1.13 Problems . 29
1.14 Programs . 32
1.14.1 Program 1.1 32
1.14.2 Program 1.2 35
1.14.3 Program 1.3 38
References 41
2 Moments, Couples, Equipollent Systems 45
2.1 Moment of a Vector About a Point 45
2.2 Couples . 54
2.3 Force Vectors . 55
2.4 Equipollent Force Systems 57
2.5 Examples 61
2.6 Problems . 77
2.7 Programs . 80
2.7.1 Program 2.1 80
2.7.2 Program 2.2 82
2.7.3 Program 2.3 84
vii2.7.4 Program 2.4 87
2.7.5 Program 2.5 87
References 90
3 Centers of Mass 93
3.1 First Moment 93
3.2 Center of Mass of a Set of Particles 94
3.3 Center of Mass of a Body . 94
3.4 First Moment of an Area . 96
3.5 Center of Gravity . 97
3.6 Theorems of Guldinus-Pappus 98
3.7 Examples 100
3.8 Problems . 124
3.9 Programs . 130
3.9.1 Program 3.1 130
3.9.2 Program 3.2 131
3.9.3 Program 3.3 133
3.9.4 Program 3.4 134
3.9.5 Program 3.5 136
3.9.6 Program 3.6 137
3.9.7 Program 3.7 139
3.9.8 Program 3.8 141
3.9.9 Program 3.9 142
3.9.10 Program 3.10 146
3.9.11 Program 3.11 147
References 148
4 Equilibrium . 151
4.1 Equilibrium Equations . 151
4.2 Supports . 153
4.2.1 Planar Supports 153
4.2.2 Three-Dimensional Supports . 155
4.3 Free-Body Diagrams 155
4.4 Two-Force and Three-Force Members 159
4.5 Plane Trusses . 160
4.6 Particle on a Smooth Surface and on a Smooth Curve . 164
4.7 Examples 166
4.8 Problems . 185
4.9 Programs . 188
4.9.1 Program 4.2 188
4.9.2 Program 4.3 191
4.9.3 Program 4.4 194
4.9.4 Program 4.5 196
viii Contents4.9.5 Program 4.6 199
4.9.6 Program 4.7 201
4.9.7 Program 4.8 205
References 208
5 Friction 211
5.1 Introduction . 211
5.2 Static Coefficient of Friction . 212
5.3 Kinetic Coefficient of Friction 213
5.4 Angle of Friction . 213
5.5 Technical Applications of Friction: Screws . 222
5.5.1 Power Screws . 224
5.5.2 Force Analysis for a Square-Threaded Screw . 227
5.6 Problems . 230
5.7 Programs . 232
5.7.1 Program 5.1 232
5.7.2 Program 5.2 236
5.7.3 Program 5.3 239
References 241
6 Virtual Work and Stability 243
6.1 Virtual Displacement and Virtual Work . 243
6.2 Elastic Potential Energy 245
6.3 Gravitational Potential Energy 247
6.4 Stability of Equilibrium 248
6.5 Examples 250
6.6 Problems . 263
6.7 Programs . 266
6.7.1 Program 6.1 266
6.7.2 Program 6.2 270
6.7.3 Program 6.3 275
6.7.4 Program 6.4 277
6.7.5 Program 6.5 279
References 280
Index .
Index
A
Absolute
value, 1, 2
Angle
of friction, 213, 227
Associative, 3
B
Ball and socket
support, 155
Bearing, 155, 182, 186
forces, 181
loads, 187
Bound vector, 2, 57
C
Cartesian, 5, 24, 89, 131, 174
Centroid, 97, 124, 147
Centroidal
axis, 97
coordinate, 99
Circular, 108, 123, 155
area, 123, 147
cross section, 123
helix, 135
shaft, 135
Collinear, 55, 164, 243
Commutative, 3, 10, 12
Concurrent
force, 59, 152, 161
Constraint, 243
bilateral, 164
unilateral, 164
Coordinates, 9, 20, 101, 112, 165
cartesian, 95, 135
centroidal, 99
independent, 249
spatial, 56
Coplanar, 159
Coulomb
friction, 212
law, 211
Couple, 45
arbitrary, 59
clockwise, 179
null, 57
simple, 54
Cross product, 11, 13, 28
Curve, 95, 109, 170
planar, 122
smooth, 164, 165
spatial, 108
uniform, 95
D
Decomposition, 96
Degrees, 1, 40, 68
of freedom, 164, 249
Density, 95
Derivative, 15, 249, 261
Determinant, 12, 14
Diagonal, 3, 13, 160
Differential
arc length, 103, 108
displacement, 245
element, 95, 100, 111
Direction, 12, 55, 161, 247
angle, 24
cosines, 5, 22, 72
horizontal, 252
proper, 161, 177
receding, 223
upward, 181
D. B. Marghitu et al., Statics with MATLAB,
DOI: 10.1007/978-1-4471-5110-4, Springer-Verlag London 2013
283Displacement, 1, 243, 253
differential, 245
vector, 1
virtual, 243, 246
Distributive, 3, 12
Dot product, 10, 11
E
Elastic, 34
constant, 245
force, 245
moment, 246
potential energy, 245, 251
Equilibrium, 151, 174, 225
condition
equations, 145, 160, 170, 211
force, 163, 167
moment, 169
neutral, 249
position, 170, 176, 197, 254, 263
scalar, 165
stable, 249, 255, 263
unstable, 249, 255
vectorial, 165
Equipollent, 57, 60, 70
External force, 161, 215, 244
F
First moment, 93, 112, 120
Fixed
point, 170, 191
support, 154, 181, 245
surface, 213
Force(s), 1, 55, 161, 211, 245
conservative, 246
elastic, 245
external, 220, 233
friction, 211
gravitational, 248
internal, 243
normal, 211
reaction, 171
resultant, 53, 71
parallel, 59
Frame, 5, 23, 78, 160, 215
Free
body diagram, 155, 216
vector, 2, 55
Friction, 211
angle, 213, 214
dry, 225
force, 211, 233
static, 220, 230
thread, 226, 239
G
Generating, 68
area, 100
circle, 123
curve, 98, 147
equation, 122
plane, 99, 147
surface, 98, 99
Gradient, 16
Gravity, 97, 173, 256, 279
force, 170, 174, 279
Guldinus-Pappus, 94, 119, 143
H
Helical
thread, 222
trajectory, 256
I
Improper
support, 158
Independent
coordinate, 249
equations, 156, 161
equilibrium, 156
linearly, 4
variable, 262
vector, 4
Inertial reference frame, 151
Instant, 55
Invariant, 52
J
Joint, 157, 161, 178, 265
force, 217, 251
pin, 153, 160
reaction, 157
slider, 157
K
Kilogram, 1, 55
Kinematic chain, 157
284 IndexKinetic
angle of friction, 214
coefficient of friction, 213
L
Lead, 222, 232
Left-handed, 12, 163, 223
Linear
combination, 4
dependent, 156
independent, 4
motion, 218
spring, 248
Line of action, 1, 45, 64, 77
Link, 70, 160, 264
M
Magnitude, 1, 6, 74, 159, 212
Mass, 1, 112, 185, 264
body, 95
center, 110, 112
density, 95
of a particle, 93
per unit of area, 95
per unit of length, 95
per unit volume, 95
MATLAB, 6, 63, 103, 171, 259
Maximum, 4, 212, 249
friction force, 213
value, 212
Member
three-force, 159
two-force, 159
force, 159, 177
Method
of decomposition, 96
of joints, 161, 163, 177, 199
of sections, 163
of virtual work, 244
Module, 1, 2
Moment
about a line
about a point, 74
of a couple, 54
equilibrium, 169
first, 96, 111
of a force, 56, 61
minimum, 53
reaction, 179
resultant, 52
of a system of vectors, 50
of a vector, 45, 49
Motion
linear, 224
relative, 212
rotary, 224
uniform, 213
N
Newton, 55, 77
first principle, 55
second law, 55
third law, 55
Norm, 1, 19
Normal
component, 53, 61, 167
force, 213, 220
reaction, 164, 173, 221
thread load, 227
O
Orientation, 1, 2, 6, 96, 230
Orthogonal
axes, 97
cartesian coordinates, 25, 95
component, 6
reference frame, 6
P
Parallel, 1, 14
component, 61
directions, 56
forces, 60
Parallelogram law, 3
Particle, 55, 97, 164, 245, 259
Period, 11
Perpendicular, 1, 12, 57, 164, 181
Pin, 153, 160, 186
connections, 160
joint, 157
support, 161
Point of application, 2, 61, 79
Pound, 55, 246
Power, 224, 228
Principle
of action, 55
first, 55
of virtual work, 243, 248
Product
of the area, 99
cross, 11, 56, 66
dot, 9
scalar, 9, 52
Index 285of static coefficient, 215
triple, 13, 24
vector, 11
Projection, 24, 31, 53
R
Radius, 100, 121, 147, 186, 262
Rectangular component, 6
Redundant, 158, 160
Reference frame
axes, 97
frame, 23, 77, 215
Relative
angle, 264
motion, 212
sliding, 213
translation, 151
Resolution
of components, 6
of vectors, 3, 6
Resultant, 3, 18, 55, 97
direction, 52
force, 53, 78
moment, 53, 56
vector, 26, 30, 52
Resultant, 4, 31, 53, 97
Right-hand(ed), 1, 12, 56, 163, 223
Roller support, 154, 155, 161
Revolution
axis, 98
body, 99, 100
surface, 99, 123, 147
volume, 100, 123, 147
S
Scalar
component, 6
equations, 5, 71
equilibrium equations, 155, 165, 216
function, 15
invariant, 52
product, 9, 52
quantity, 1
triple product, 13, 24, 29
Screw, 222, 224, 227
right handed, 12
Sense, 1, 2, 12, 56, 163
SI, 55, 223, 248
Sliding vector, 2, 46
Slip, 211, 215, 230
Socket, 155
Solid, 96
Spatial
coordinates, 6
curve, 108
Strength, 93, 158
Symbolic, 6, 15, 38, 100, 115
Symmetry, 97
Surface, 70, 96, 123, 164,
211, 222
T
Tangential components, 166
Temperature, 1, 160
Transitivity, 57
Translation, 151
Transmissible vector, 2
Transpose, 16, 19, 34
Triangle, 97, 160, 225
Truss plane, 160, 163
U
Unit vector, 5, 22, 163
V
Varignon theorem, 12
Vector
addition, 13
(cross) product, 11
function, 15
position, 9
unit, 8
Velocity, 1, 211
Volume, 94, 124, 147
W
Weight, 24
Work, 243, 268
Wrench, 57, 61, 76, 187
Z
Zero vector, 2, 4, 9
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