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 |  موضوع: كتاب Engineering Statics with MATLAB الأربعاء 05 يونيو 2024, 4:28 am | |
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أخواني في الله
أحضرت لكم كتاب
Engineering Statics with MATLAB
Lester W. Schmerr Jr.
و المحتوى كما يلي :
Contents
Preface .ix
1. Introduction to Statics and the Concept of Force 1
1.1 About This Book 1
1.2 Quantities and Units . 2
1.3 Numerical Calculations 4
1.4 Forces and Vectors . 5
1.5 Scalars, Vectors, and Matrices . 10
1.6 Unit Vectors and Cartesian (Rectangular) Components 12
1.7 Oblique Components 18
1.8 The Dot Product and Direction Cosines 24
1.8.1 The Dot Product . 24
1.8.2 Direction Cosines . 28
1.9 Position Vectors 31
1.10 Problems 34
1.10.1 Review Problems 41
2. Moments and Couples 44
2.1 Moment of a Force about a Point . 44
2.1.1 The Vector Cross Product . 47
2.2 Couples 57
2.3 Moment of a Force about a Line 61
2.4 Problems 68
2.4.1 Review Problems 73
3. Equivalent Systems and Resultants 76
3.1 Resultants of Two-Dimensional Force Systems . 78
3.2 Resultants of Three-Dimensional Force Systems . 81
3.3 Reduction to a Wrench . 84
3.4 Resultants and the Center of Gravity 87
3.5 Resultants of Distributed Forces . 92
3.6 Problems 95
3.6.1 Review Problems 100
4. Equilibrium . 103
4.1 Free Body Diagrams 104
4.2 Reaction Forces at Supports . 110
v4.3 Solving Equilibrium Problems – I 116
4.4 Alternate Systems of Equilibrium Equations 135
4.5 Problems 138
4.5.1 Review Problems 146
5. Trusses 149
5.1 The Method of Pins . 151
5.1.1 Summary 157
5.2 Zero-Force Members . 157
5.3 The Method of Sections 159
5.4 Space Trusses 161
5.5 Problems 165
5.5.1 Review Problems 171
6. Frames and Machines . 173
6.1 Solving Equilibrium Problems – II . 173
6.2 Problems 196
6.2.1 Review Problems 201
7. Centroids 204
7.1 Centroids of Volumes, Areas, and Lines . 204
7.1.1 Integration with Strips 210
7.2 Composite Areas 215
7.3 Distributed Line Loads . 218
7.4 Problems 220
7.4.1 Review Problems 227
7.5 Tables of Centroids 228
8. Beams 232
8.1 Internal Forces and Moments 232
8.2 Singularity Functions 246
8.3 Problems 256
8.3.1 Review Problems 259
9. Frictional Forces . 261
9.1 Slipping and Tipping 261
9.2 Flat Belts or Ropes in Contact with Rough Surfaces 281
9.3 Wedges . 286
9.4 Problems 287
9.4.1 Review Problems 291
10. Statically Indeterminate Structures . 294
10.1 Solving a Statically Indeterminate Problem 295
vi Contents10.2 A Matrix-Vector Force-Based Method . 299
10.3 Steps in the Force-Based Method . 309
10.4 Examples of the Force-Based Method 311
10.5 Problems 332
10.5.1 Review Problems 336
11. Area Moments and Mass Moments of Inertia 339
11.1 Area Moments 340
11.2 Polar Area Moment and the Radius of Gyration 347
11.2.1 Polar Area Moment . 347
11.2.2 Radius of Gyration . 347
11.3 Composite Areas 348
11.4 Rotation of Coordinates 350
11.5 Principal Area Moments and Principal Axes . 351
11.6 Area Moment Matrices . 356
11.7 Mass Moments of Inertia 363
11.7.1 Parallel Axis Theorem . 365
11.7.2 Radius of Gyration . 367
11.8 Problems 367
11.8.1 Review Problems 371
11.9 Tables of Mass Moments of Inertia and Area
Moments 372
Appendices . 375
A MATLAB Overview . 375
A.1 Constants, Operations, and Built-in Functions . 375
A.2 Vectors 377
A.3 Matrices 382
A.4 Solutions of Simultaneous Linear Equations . 388
A.4.1 Numerical Solution 389
A.4.2 Symbolic Solution in Terms of Numerical
Variables 390
A.4.3 Symbolic Solution in Terms of Symbolic
Variables 391
A.5 Element-by-Element Operations, Plotting, and
Logical Vectors 397
A.5.1 Element-by-Element Operations 397
A.5.2 Plotting . 398
A.5.3 Logical Vectors . 401
A.5.4 Constants eps and inf 402
A.6 Functions and Scripts . 403
A.7 Anonymous Functions . 405
Contents viiA.8 Symbolic Calculations 406
A.8.1 Symbolic Integration 406
A.8.2 Symbolic Differentiation . 407
A.8.3 Substitution . 408
B MATLAB Files . 409
Problem Answers 411
Index 417
Index
alternate equilibrium equations, 135
anonymous functions (MATLAB),
252, 405
area moments, 340
area moment matrix, 356
beams, 232
bending moment, 233
bending moment diagram, 238
Cartesian components, 12
Cartesian coordinates, 12
center of gravity, 87
center of mass, 216, 365
centroid (line, area, volume), 204
compatibility equations, 297
compatibility matrix, 300
composite body (line, area, volume),
215, 216
constants, operations, and built-in
functions (MATLAB), 375
coplanar force system, 77
couple, 57
cross product, 47
deformation, 297
deformation-displacement
relationship, 301
determinant, 50, 51
direction cosines, 5, 24
direction cosine matrix, 357
displacements, 294
distributed line loads, 92, 218
dot product, 24
eigenvalue, 359
eigenvalue problem, 359, 361
eigenvector, 359
elastic spring constant (see stiffness)
element-by-element operations
(MATLAB), 397
equationsToMatrix function
(MATLAB), 322, 396
equilibrium, 103
equilibrium equations, 103
equilibrium matrix, 121
equipollent system (see equivalent
system)
equivalent system, 76
finite element method, 305
first moments (area, volume), 206, 209
flat belt or rope, 281
flexibility, 294, 298
flexibility matrix, 300
force-based method, 299
force system, 76
frames and machines, 173
free body diagram, 105
free vector, 58
frictional forces, 261
functions (MATLAB), 403
fzero function (MATLAB), 253
homogeneous solutions, 301, 394
internal forces and moments, 104
International System of Units, 3
kinetic coefficient of friction, 263
law of cosines, 6
law of sines, 6
linear equations solution
(MATLAB), 388
logical vectors (MATLAB), 401
Macaulay bracket function
(see singularity function)
magnitude of a vector, 10, 15
mass moments of inertia matrix,
339, 363
matrices (MATLAB), 382
417matrix determinant (see determinant)
matrix multiplication (MATLAB), 386
method of pins (joints), 151
method of sections, 159
mixed area moment, 340
moment about a line, 61
moment about a point, 44
Navier’s table problem, 311
null function (MATLAB), 394
oblique force components, 18
parallel axis theorem, 342, 343
parallel force system, 81
parallelogram law of addition, 6
planar truss, 149
plotting (MATLAB), 398
polar area moment, 347
position vector, 31
principal area moments, 351
principal directions (principal axes or
coordinates), 352
radius of gyration, 347, 367
reaction forces, 104, 110
rectangular components (see Cartesian
components)
rectangular coordinates (see Cartesian
coordinates)
resultant force, 6
resultant (of a force system), 76
right-handed coordinate system, 48, 49
right-hand-rule, 46
rotation of coordinates, 350
scalar product (see dot product)
scientific notation, 4
scripts (MATLAB), 403
second moments (see area moments)
self-locking, 272
shear force, 232
shear force diagram, 232
SI System (see International System of
Units)
significant digits, 4
simple truss, 149
singularity functions, 232, 246
sliding vector, 52
slipping, 261
solution of linear equations (MATLAB)
(see linear equations solution
(MATLAB))
solve function (MATLAB), 390
space truss, 149
static coefficient of friction, 262
statically determinate system, 116,
149, 150
statically indeterminate system, 117,
149, 150, 294
statically overdetermined, 149, 150
stiffness, 297
stiffness matrix, 304
strip integrals, 210, 344
symbolic calculations (MATLAB), 406
three-force member, 115
tipping, 261
transpose (matrix), 383
trusses, 149
two-dimensional force system
(see coplanar force system)
two-force member, 114
underdetermined system of equations
(see statically indeterminate)
unit vector, 12
U.S. Customary System of Units, 3
vector cross product (see cross product)
vectors (MATLAB), 377
wedge, 286
weightless link (see two-force member)
wrench, 84
Young’s modulus, 256, 297
zero-force member, 157
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