كتاب Engineering Mechanics - Statics - Fifteenth Edition
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منتدى هندسة الإنتاج والتصميم الميكانيكى
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 كتاب Engineering Mechanics - Statics - Fifteenth Edition

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Engineering Mechanics - Statics
Fifteenth Edition in SI Units
R. C. Hibbeler
Si Conversion by
Jun Hwa Lee  

كتاب Engineering Mechanics - Statics - Fifteenth Edition R_c_h_10
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Contents
1
General Principles 25
Chapter Objectives 25
1.1 Mechanics 25
1.2 Fundamental Concepts 26
1.3 The International System of Units 29
1.4 Numerical Calculations 32
1.5 General Procedure for Analysis 34
2
Force Vectors 39
Chapter Objectives 39
2.1 Scalars and Vectors 39
2.2 Vector Operations 40
2.3 Vector Addition of Forces 42
2.4 Addition of a System of Coplanar
Forces 54
2.5 Cartesian Vectors 65
2.6 Addition of Cartesian Vectors 68
2.7 Position Vectors 76
2.8 Force Vector Directed Along a Line 78
2.9 Dot Product 8618 contents
3
Equilibrium of a
Particle 103
Chapter Objectives 103
3.1 Condition for the Equilibrium
of a Particle 103
3.2 The Free-Body Diagram 104
3.3 Coplanar Force Systems 107
3.4 Three-Dimensional Force Systems 120
4
Force System
Resultants 135
Chapter Objectives 135
4.1 Moment of a Force—Scalar
Formulation 135
4.2 Principle of Moments 137
4.3 Cross Product 145
4.4 Moment of a Force—Vector
Formulation 148
4.5 Moment of a Force about a
Specified Axis 158
4.6 Moment of a Couple 167
4.7 Simplification of a Force and Couple
System 179
4.8 Further Simplification of a Force and
Couple System 190
4.9 Reduction of a Simple Distributed
Loading 202contents 19
5
Equilibrium of a
Rigid Body 217
Chapter Objectives 217
5.1 Conditions for Rigid-Body
Equilibrium 217
5.2 Free-Body Diagrams 219
5.3 Equations of Equilibrium 230
5.4 Two- and Three-Force Members 240
5.5 Free-Body Diagrams 253
5.6 Equations of Equilibrium 258
5.7 Constraints and Statical Determinacy 259
6
Structural Analysis 279
Chapter Objectives 279
6.1 Simple Trusses 279
6.2 The Method of Joints 282
6.3 Zero-Force Members 288
6.4 The Method of Sections 296
6.5 Space Trusses 306
6.6 Frames and Machines 31020 contents
7
Internal Forces 347
Chapter Objectives 347
7.1 Internal Loadings 347
7.2 Shear and Moment Equations and
Diagrams 363
7.3 Relations among Distributed Load, Shear,
and Moment 372
7.4 Cables 383
8
Friction 403
Chapter Objectives 403
8.1 Characteristics of Dry Friction 403
8.2 Problems Involving Dry Friction 408
8.3 Wedges 430
8.4 Frictional Forces on Screws 432
8.5 Frictional Forces on Flat Belts 439
8.6 Frictional Forces on Collar Bearings, Pivot
Bearings, and Disks 447
8.7 Frictional Forces on Journal Bearings 450
8.8 Rolling Resistance 452contents 21
9
Center of Gravity and
Centroid 465
Chapter Objectives 465
9.1 Center of Gravity, Center of Mass, and the
Centroid of a Body 465
9.2 Composite Bodies 488
9.3 Theorems of Pappus and Guldinus 502
9.4 Resultant of a General Distributed
Loading 511
9.5 Fluid Pressure 512
10
Moments of Inertia 529
Chapter Objectives 529
10.1 Definition of Moments of Inertia for
Areas 529
10.2 Parallel-Axis Theorem for an Area 530
10.3 Radius of Gyration of an Area 531
10.4 Moments of Inertia for Composite
Areas 540
10.5 Product of Inertia for an Area 548
10.6 Moments of Inertia for an Area about
Inclined Axes 552
10.7 Mohr’s Circle for Moments of Inertia 555
10.8 Mass Moment of Inertia 56322 contents
11
Virtual Work 581
Chapter Objectives 581
11.1 Definition of Work 581
11.2 Principle of Virtual Work 583
11.3 Principle of Virtual Work for a System of
Connected Rigid Bodies 585
11.4 Conservative Forces 597
11.5 Potential Energy 598
11.6 Potential-Energy Criterion for
Equilibrium 600
11.7 Stability of Equilibrium Configuration 601
Appendix
A. Mathematical Review and
Formulations 616
Fundamental Problem
Solutions and
Answers 620
Review Problem
Answers 637
Selected Answers 640
Index
Index
A
Acceleration, dynamics and, 25
Active force, 105
Angles, 56, 66–67, 86–88, 90, 98–99, 405–407, 432, 616–617
Cartesian force vectors, 66–67
coordinate direction, 66, 98–99
dot product used for, 86–88, 90, 99
dry friction and, 405–407, 432
formed between intersecting lines, 90
horizontal (u), 67
impending motion and, 405, 407
kinetic friction (uk), 406–407
lead, 432
mathematical review of, 616–617
projection, parallel and perpendicular, 87
Pythagorean’s theorem and, 56, 87, 617
resultant forces from, 56
screws, 432
static friction (us), 405, 407
vectors and, 56, 66–67, 86–88, 90, 98–99
vertical (f), 67
Applied force (P), 404–407, 430–431, 459–460
Area (A), 468, 470, 474–476, 502–505, 523–524, 530–535,
540–542, 548–557, 576–577
axial symmetry and rotation, 502–505, 524, 548–551,
577
centroid (C) of an, 468, 470, 474–476, 502–505, 523–524,
576
centroidal axis of, 530–531
composite bodies (shapes), 503, 524, 540–542, 576–577
inclined axis, about, 552–554
integration for, 468, 474–476, 523, 529–530
Mohr’s circle for, 555–557
moments of inertia (I) for, 530–535, 540–542, 548–557,
576–577
Pappus and Guldinus, theorems of, 502–505, 524
parallel-axis theorem for, 530–532, 540, 549, 576
plane, volume generated revolution of, 503
polar moment of inertia, 530–531
principal moments of inertia, 553–554, 577
procedures for analysis of, 470, 532, 540
product of inertia for, 548–551, 553, 576
radius of gyration of, 531
surface of revolution, 502, 504–505, 524
transformation equations for, 552, 577
volume of revolution, 503–505, 524
Associative law, 146
Axes, 158–162, 202, 212, 529–535, 540–542, 548–557, 563–570,
576–577
area moments of inertia for, 529–535, 548–554, 576
centroidal axis of, 530–531, 576
composite bodies, 540–542, 568–570, 576–577
distributed load reduction, 202
inclined, area about, 552–554
line of action for, 158–160, 212
mass moments of inertia for, 563–570, 577
Mohr’s circle for, 555–557
moment of a force about specified, 158–162, 212
moments of inertia (I), 529–535, 540–542, 552–557,
563–570, 576–577
parallel-axis theorem for, 530–532, 540, 549, 567, 576
principal, 553–557, 577
procedures for analysis of, 532, 556, 564
product of inertia and, 548–551, 553, 576
radius of gyration for, 531, 568
resultant forces and, 158–162, 202, 212
right-hand rule for, 158–160
scalar analysis, 158, 212
transformation equations for, 552
vector analysis, 159–162, 212
Axial loads, friction analysis of, 447–449
Axial revolution, 502–505, 524
Axial symmetry, 502–505, 524–525
axial revolution and, 502–505, 525
centroid (C) and, 502–505, 524
composite bodies, 503
Pappus and Guldinus, theorems of, 502–505, 525
rotation and, 502–505, 525
surface area and, 502, 504–505, 525
volume and, 503–505, 525
Axis of symmetry, 469, 488–489, 524, 548–551, 553, 576
area (A) of, 548–551
centroid (C) and, 469, 488–489, 524, 576
parallel-axis theorem for, 549, 576
principal axes, 553
product of inertia, 548–551, 553, 576
B
Ball and socket connections, 253–254, 256
Base units, 29, 31
Beams, 347–382, 398–400
bending moments (M) and, 348–349, 373–377, 398
cantilevered, 347–348, 363
centroid (C), 348
couple moment (M) and, 374
distributed loads and, 372–377, 400
force equilibrium, 372–373
free-body diagrams, 347–349, 398
internal forces, 347–382, 398–400
internal loads of, 347–354, 372–377
method of sections for, 347–354, 364
moments, 348–349, 372–377, 398
normal force (N) and, 348–349, 398
procedures for analysis of, 349, 364654 Index
Beams (Continued)
resultant loadings, 348, 398
shear and moment diagrams, 363–366, 372–377, 399–400
shear force (V) and, 348–349, 372–377, 398
sign convention for, 349, 399
simply supported, 363
torsional (twisting) moment, 348, 398
Bearings, 253–257, 447–451, 461
axial loads, 447–449
collar, 447–449, 461
free-body diagrams, 253–257
frictional analysis of, 447–451, 461
journal, 254–256, 450–451, 461
lateral loads, 450–451
pivot, 447–449, 461
rigid-body support reactions, 253–257
thrust, 255, 256
Belts (flat), frictional analysis of, 439–441, 460
Bending moment diagrams, 363–366. See also Shear and
moment diagrams
Bending moments (M), 348–349, 373–377, 398–400
distributed loads and, 373–377, 400
internal forces and, 348–349, 372–377, 398, 400
method of sections for, 348–349
shear (V) and, 373
shear and moment diagrams, 372–377, 399–400
Body at rest (zero), 218
By inspection, determination of forces, 282, 288–289
C
Cables, 104, 109, 131, 220, 221, 254, 383–397, 400
concentrated loads, 383–385, 400
connections, 220, 221
continuous, 131
distributed loads, 386–389, 400
equilibrium of, 104, 109, 131
flexibility of, 383
free-body diagram for, 104, 109, 131, 220, 254
inextensible, 383
internal forces of, 109, 383–397, 400
sagging, 383
support reactions, 220, 254
weight of as force, 390–393, 400
Calculations, engineering importance of, 32–33
Cantilevered beam, 347–348, 363
Cartesian coordinate system, 55–58, 65–70, 76–81, 86, 98–99,
145–152, 211
addition of vectors, 55–58, 68
concurrent force resultants, 55, 65–70, 99
coordinate direction angles, 66–67, 98–99
coplanar force resultants, 55–58
cross product for, 145–147
direction and, 66–68, 98–99, 145, 148
dot product in, 86, 99
force vector directed across a line, 78–81
horizontal angles (u), 67
magnitude of, 55, 66–68, 98, 145, 148
moment of a force, calculations by, 148–152, 211
position vectors (r), 76–77, 79–80, 99
rectangular components, 55–58, 65–70, 98
right-hand rule, 65, 145–146, 148
sign convention for, 146
three-dimensional systems, 65–70
two-dimensional systems, 55–58
unit vectors, 55, 65–66, 78, 98
vector formulation, 146–152, 211
vector representation, 65–66, 98–99
vertical angles (f), 67
Cartesian vector notation, 55
Center of gravity (G), 29, 222, 464–527
center of mass (Cm) and, 467, 524
centroid (C) as, 222, 464–527
composite bodies, 488–492, 525
constant density and, 488
coplanar forces, 222
free-body diagrams of, 222
location of, 465–466, 469–478, 524
Newton’s law of gravitational attraction and, 29
procedure for analysis of, 470, 489
rigid-body equilibrium and, 222
specific weight and, 488
weight (W) and, 29, 222, 465–466, 488, 524
Center of mass (Cm), 467, 470, 478, 523
Center of pressure (P), 513, 525
Centroid (C), 203, 222, 348, 464–527
area in x–y plane, 468, 470, 474–476, 523
axis of symmetry, 469, 488–489, 523
axial symmetry, 502–505, 523–524
beam cross-section location, 348
center of gravity (G) as, 222, 464–527
center of mass (Cm) of a body, 467, 470, 478, 523
composite bodies, 488–492, 524
composite shapes, 503
coplanar forces, 222
distributed loads and, 511–518, 525
distributed loads, 203
flat surfaces, 511
fluid pressure and, 512–518, 525
free-body diagrams for, 222
integration for determination of, 467–478, 523
line in x-y plane, 468–473, 523
line of action for, 203, 513, 520, 525
location of, 203, 467–478, 523Index 655
mass of a body (Cm), 467, 469, 478
method of sections and, 348
Pappus and Guldinus, theorems of, 502–505, 524
plates, 511–518
procedure for analysis of, 470, 489
Pythagorean’s theorem for, 469
resultant forces and, 203, 348, 511–518, 525
rigid-body equilibrium and, 222
rotation of an axis, 502–505, 524
surface area and, 502, 504–505, 524
volume, of a, 467, 470, 503–505, 524
Centroidal axis, 530–531, 576
Coefficient of kinetic friction (μk), 406–407
Coefficient of rolling resistance, 452–453
Coefficient of static friction (μs), 405, 407, 447–448
Collar bearings, frictional analysis of, 447–449, 461
Collinear couple moment, 192
Collinear vectors, 41, 97
Commutative law, 41, 86, 146
Component vectors of a force, 40, 42–48, 97
Composite bodies, 488–492, 503, 524, 540–542, 568–570,
576–577
area (A) of, 503, 540–542, 576
axial symmetry and, 488–489, 503
center of gravity (G), 488–492, 524
centroid (C) of, 488–492, 503, 524
constant density and, 488
mass moments of inertia, 568–570, 577
moments of inertia (I), 540–542, 568–570, 576
procedure for analysis of, 489, 540
theorem of Pappus and Guldinus for parts of, 503
specific weight and, 488
weight (W) and, 488, 524
Compressive forces (C), 280–283, 296–297
method of joints and, 282–283
method of sections and, 296–297
truss members, 280–281
Concentrated force, 27
Concentrated loads, 372–373, 383–385, 399–400
cables subjected to, 383–385, 400
distributed loads, 372–373
sagging from, 383
shear and moment discontinuities from, 373, 399
Concurrent forces, 40, 55, 65–70, 105, 120–124, 131, 190–192,
240–241, 260
addition of vectors, 40, 65–70
Cartesian coordinate system for, 55, 65–70
constraints and, 260
equilibrium of, 108, 120–124, 131, 260
equivalent systems of, 190–192
free-body diagrams, 108, 120–124, 131
force and couple systems, simplification of, 190–192
lines of action for, 190
procedure for analysis of, 192
resultant couple moment, 190
statical determinacy and, 260
three-dimensional systems, 65–70, 120–124, 190–192
three-force members, 240–241
two-dimensional coplanar resultants, 55
Connections, free-body diagrams of, 219–221. See also Joints;
Support reactions
Conservative forces, 597–598
friction as nonconservative, 598
spring force, 597
virtual work (U) and, 597–598
weight, 597
Constant density, center of gravity (G) and, 488
Constraints, 259–267, 276
improper, 260–261, 276
procedure of analysis of, 262
redundant, 259
statical determinacy and, 259–267, 276
support reactions and, 259–267
rigid-body equilibrium and, 259–267, 276
Continuous cables, 131
Coordinate direction angles, 66–67, 98–99
Coordinates, 65–70, 76–80, 98–99, 585–590, 600, 612. See also
Cartesian coordinate system
Cartesian, 65–70, 76–77, 79–80, 98–99
frictionless systems, 600
position, 76–77, 79–80, 585–590, 600, 612
potential energy and, 600
right-hand rule for, 65
vector representation, 65–70, 76–78
virtual work for rigid-body connections, 585–590,
600, 612
x, y, z positions, 65–66, 76, 98–99
Coplanar distributed loads, 202–206
Coplanar forces, 54–59, 98, 107–111, 131, 179–184, 190–196,
202–206, 218–252, 275–276
addition of systems of, 54–59, 107
Cartesian vector notation, 55
center of gravity, 222
centroid (geometric center), 222
couple moments of, 179–184, 190–196
direct solution for unknowns, 230–239, 276
direction of, 54–55, 107
distributed load reduction, 202–206
equations of equilibrium, 107, 131, 230–239, 275
equilibrium of, 107–111, 131, 218–252, 275–276
equivalent systems of, 179–184, 190–196
free-body diagrams, 107–111, 219–228, 275
idealized models of, 222–223
internal forces and, 222656 Index
Coplanar forces (Continued)
lines of action, 179, 190–196
magnitude of, 55, 56, 107
particles subjected to, 107–111, 131
procedure for analysis of, 108, 181, 192, 224, 231
rectangular components, 54–59, 98
resultant couple moment, 190
resultants, 55–59, 179–184, 190–196, 202–206
rigid bodies, 218–252, 275–276
scalar notation, 54, 55
support reactions, 219–221, 275
system components, 54–59
systems, simplification of, 179–184, 190–196
two-and three-force members, 240–241
vectors for, 54–59, 98
weight and, 222
Cosine functions, 617
Cosine law, 42, 44, 97
Cosines, direction of, 66–67
Coulomb friction, 403. See also Dry friction
Couple, 167
Couple moments (M0), 167–172, 179–184, 190–196, 212–213,
217–219, 374, 582–583
collinear, 192
concurrent force system simplification, 190–192, 213
coplanar force system simplification, 179–184, 190–196,
212–213
distributed loading, 179–184, 190–196, 212–213, 374
equivalent couples, 168
equivalent systems, 179–184, 190–196, 212–213
force systems and, 167–172, 217–218
free vectors, 167
internal forces and, 374
parallel force system simplification, 191–192, 213
procedure for analysis of, 181, 192
resultants, 168–169, 190–196
right-hand rule for, 167
rigid bodies, equilibrium of, 217–218
rotation of, 219, 582–583
scalar formulation of, 167
shear and moment diagrams, 374
shear load (V) relationships, 374
support reactions and, 219
systems, simplification of, 179–184, 190–196, 212–213
three-dimensional systems, 179–184, 190–196, 213
translation of, 219, 582
vector formulation of, 167–172
virtual work of, 583
work of, 582
wrench, reduction of forces to, 192, 213
Cross product, 145–147
Cartesian vector formulation, 146–147
direction for, 145
laws of operation, 146
magnitude for, 145
right-hand rule for, 145–146
vector multiplication using, 145–147
Curved plates, fluid pressure and, 514
Cylinders, rolling resistance of, 452–453
D
Deformation, rolling resistance and, 452, 461
Derivatives, 618
Derived units, 29–31
Dimensional homogeneity, 32
Direct solution for unknowns, 230–239, 276
Direction, 39, 55–56, 66–68, 76–78, 87–90, 97–99, 105, 107,
136, 145, 148, 158–160, 167, 211, 219, 407, 409, 430,
432–434, 460
axis, moment of a force about, 158–160
Cartesian coordinate vectors, 66–68, 76–78, 98
Cartesian vector notation, 55
coordinate direction angles, 66–67, 98
coplanar force systems, 55–56, 107
cross product and, 145
dot product applications, 87–90
equilibrium and, 105, 107, 219
force vector along a line, 78
free-body diagrams, 105, 107, 219
frictional forces, 407, 409, 430, 432–434, 460
horizontal angle u, 56
impending motion and, 432–434, 460
line of action, 39–40, 78, 99, 148, 158–160
moment of a couple, 167
moment of a force (MO), 136, 148, 158–160, 211
position vectors, 76–77, 99
right-hand rule for, 65, 145, 148, 158–160, 167, 211
screws, impending motion of, 432–434, 460
three-dimensional systems, 66–68
translation, 219
vector sense of, 39, 55–56, 97
vertical angle f, 56
Direction cosines, 66–67
Disks, 447–449, 461, 564, 566, 577
frictional analysis of, 447–449, 461
mass moments of inertia, 564, 566, 577
Displacement (d), 583–590, 600, 612
frictionless systems, 600
potential energy and, 600
principle of virtual work and, 583–590, 612Index 657
procedure for analysis of, 586
rigid bodies, connected systems of, 585–590
virtual work (U) and, 583–590, 600, 612
virtual work equations for, 583–584, 586
Distributed loads, 202–206, 213, 372–377, 386–389, 399–400,
511–518, 525
axis (single) loading, 202
beams subjected to, 372–377, 399–400
bending moment (M) relationships, 372–377, 400
cables subjected to, 386–389, 400
center of pressure (P), 512, 525
centroid (C) of, 203, 213, 511–518, 525
concentrated loads and, 372–373, 399–400
coplanar, 202, 213
couple moment (M0) relationships, 374
fluid pressure from, 512–518, 525
force equilibrium, 372–374
force system resultants, 202–206, 213
incompressible fluids, 512
internal forces, 372–377, 386–389, 399–400
linearly, 513, 525
line of action of, 203, 213
loading curve for, 203, 213
magnitude and, 202, 511, 525
reduction of forces, 202–206, 213
resultant forces of, 202–206, 213, 511, 525
shear and moment diagrams, 372–377, 399–400
shear force (V) relationships, 372–377, 400
uniform, 372, 525
Distributive law, 86, 146, 150
Dot notation, 31
Dot product, 86–90, 99, 159
angles between intersecting lines, 87, 99
applications of, 87–90
Cartesian vector formulation, 86, 99
laws of operation, 86
moment about a specified axis, 159
projections, parallel and perpendicular, 87–88, 99
unit vectors and, 86–87, 99
vector angles and direction from, 86–90, 99
Dry friction, 403–463
angles (u) of, 405–406
applied force (P) and, 404–407, 459–461
bearings, analysis of, 447–451, 461
belts (flat), analysis of, 439–441, 460
collar and pivot bearings, analysis of, 447–449, 461
characteristics of, 403–407, 459
coefficients of (μ), 405–407, 459
direction of force, 407, 409
disks, analysis of, 447–449, 461
equations for friction versus equilibrium, 409–416
equilibrium and, 404–405, 409
frictional force, 404–407, 450
impending motion, 405, 408–416, 432–434, 459–460
journal bearings, analysis of, 450–451, 461
kinetic force (Fk), 406–407, 459
motion and, 405–416, 432–434, 447–453
problems involving, 408–416
procedure for analysis of, 411
rolling resistance and, 452–453, 461
screws, forces on, 432–434, 460
sliding and, 406–416, 459
slipping and, 405, 407–409, 459
static force (Fs), 405, 407, 459
theory of, 404
tipping effect, balance of, 404, 459
wedges and, 430–431, 460
Dynamics, study of, 24–26
E
Elastic potential energy (Ve), 598
Engineering notation, 32
Equations of equilibrium, 103, 107–108, 120–124, 218,
230–239, 258, 275–276, 409–416
alternative sets for, 230–231
body at rest (zero), 218
coplanar force systems, 107–108, 230–239, 275–276
direct solution, 230–239, 276
direction and, 107
frictional equations and, 409–416
magnitude and, 107
particles, 103, 107–108, 120–124
procedure for analysis using, 108, 120, 231, 411
rigid bodies, 218, 230–239, 275–276
scalar form, 258, 275–276
three-dimensional force systems, 120–124, 258, 276
two-and three-force members, 240–241
vector form, 258, 276
Equilibrium, 25, 102–133, 216–277, 372–373, 404–405, 409,
600–606, 613
concurrent forces, 105, 120–124, 131, 260
conditions for, 103, 217–218, 230
constraints, 259–267
coplanar force systems, 107–111, 131, 218–252, 275–276
direction and, 105, 107, 219
distributed load relationships, 372–373
free-body diagrams, 104–111, 120–124, 219–228, 253–257,
275–276
friction and, 404–405, 409
frictionless systems, 600658 Index
Equilibrium (Continued)
idealized models for, 222–223
impending motion and, 409
improper constraints and, 260–261, 276
neutral, 601–602, 613
one (single) degree-of-freedom system, 602–603
particles, 102–133
potential-energy (V) criterion for, 600, 613
procedures for analysis of, 108, 120, 224, 231, 262, 603
redundant constraints and, 259
rigid bodies, 216–277
shear and moment diagrams, 372–373
stability of systems, 260–261, 276, 601–606, 613
stable, 601–603, 613
statical determinacy and, 259–267, 276
statics and, 25
support reactions, 219–221, 253–257, 259–267, 275–276
three-dimensional force systems, 120–124, 131, 253–267,
276
tipping effect, balance of, 404, 459
two-and three-force members, 240–241
two-dimensional force systems, 107–111, 131
unstable, 602–603, 613
virtual work (U) and, 600–606, 613
zero condition, 103, 107, 131, 218
Equivalent couples, 168
Equivalent systems, 179–184, 190–196
concurrent force systems, 190–192
coplanar force systems, 179–184, 190–196
external effects of, 179
force and couple moment simplification, 179–184,
190–196
lines of action of, 179, 190–196
parallel force systems, 191–192
principle of transmissibility for, 179
procedures for analysis, 181, 192
system of force and couple moments, 180
three-dimensional systems, 179–184, 190–196
wrench, reduction to, 192
Exponential notation, 31
External effects for equivalent systems, 179
External forces, 217, 283, 296
F
Fixed supports, 219, 221, 255
Flat belts, frictional analysis of, 439–441, 460
Flat plates, 511, 513, 515–516, 525
constant width, 513
distributed loads on, 511, 525
fluid pressure and, 513, 515–516, 525
variable width, 515
Floor beams, truss analysis and, 280
Fluid pressure, 512–518, 525
acceleration due to gravity (g), 513
center of pressure (P), 513
centroid (C), 512–518, 525
curved plate of constant width, 514
flat plate of constant width, 513
flat plate of variable width, 515
incompressible fluids, 512
line of action, 513
Pascal’s law, 512
plates, 512–518, 525
resultant forces and, 512–518, 525
Force, 25–29, 38–215, 217–218, 222, 240–241, 279–305,
310–341, 346–463, 511–518, 525, 581–583, 585–590,
597–598
active, 105
addition of vectors, 40–48, 54–59, 68–70
applied (P), 404–407, 430–431, 459–460
axis, about a specified, 158–162, 202, 212
basic quantity of mechanics, 26
beams, 347–382, 398–399
bending moments (M) and, 348–349, 372–377, 398, 400
by inspection, 282, 288–289
cables, 104, 109, 383–397, 400
Cartesian vector notation for, 55, 76–81, 149
components of, 42–48, 54–59, 97
compressive (C), 280–283, 296–297
concentrated, 27, 372–373, 383–385, 399–400
concurrent, 40, 55, 65–70, 99, 190–192, 260
conservative, 597–598
coplanar, 54–59, 98, 107–111, 131, 179–184, 190–196,
202–206, 213
couple moments and, 167–172, 179–184, 190–196, 212–213,
217–218
cross product, 145–147
directed along a line, 78–81
displacements from, 585–590
distributed loads, 202–206, 213, 372–377, 386–389, 400,
511–518
dot product, 86–90, 99
equilibrium and, 102–133, 217–218, 240–241, 372–373
equivalent systems, reduction to, 179–184, 190–196
external, 217, 283, 296
fluid pressure, 512–518, 525
frames, 310–325
free-body diagrams, 104–111, 120–124, 131, 222, 310–341,
347–349
friction as, 402–463, 598
frictional, 404–407, 459
gravitational, 29
idealized models for, 222–223
internal, 222, 296–298, 346–401Index 659
kinetic frictional (Fk), 406–407, 459
line of action, 39–40, 78, 99, 148–149, 158–160, 179,
190–196, 203, 212
machines, 310–325
mechanics of, 25
method of joints and, 282–290
method of sections for, 296–301, 347–354, 364
moment (M) of, 135–139, 148–152, 158–162, 167–172,
179–184, 190–199, 211–212, 348–349, 398, 400
motion and, 405–407
multiforce members, 310
Newton’s laws, 28–29
nonconservative, 598
normal (N), 104, 348–349, 398, 404–406
parallel systems, 191–192
parallelogram law for, 40, 42–44, 97
particles subjected to, 102–133
position vectors and, 76–77, 79–80, 99
principle of moments, 137–139, 150
principle of transmissibility, 148, 179
procedures for analysis of, 44, 105, 108, 181, 192, 231, 316,
349
pulleys, 104, 110
reactive, 105
rectangular components, 54–70, 98–99
resultant, 40, 42–48, 55–59, 97, 99, 134–215, 348–349,
511–518, 525
rigid bodies, equilibrium of, 217–218, 222–223
scalar notation for, 54, 55
scalar formulation, 39, 40, 86, 97, 135–136, 158, 167, 211
shear (V), 348–349, 372–377, 398, 400
simplification of systems, 179–184, 190–196, 213
smooth surface contact, 104
spring (Fs), 104, 597
springs, 104, 111
static frictional (Fs), 405, 407, 459
structural analysis and, 279–305, 310–341, 347–354
structural members, 240–241, 279–290, 296–301, 347–382
systems of, 54–59, 134–215
tensile (T), 280–283, 296–297, 439–441
three-dimensional systems, 65–70, 76–80, 120–124, 131,
179–184, 190–196, 212
trusses, 279–305, 342–343
two-and three-force members, 240–241
unbalanced, 28
units of, 30–31
unknown, 282–287, 296–301
vector formulation, 38–133, 145–152, 159–162, 167–172, 211
virtual work (U) and, 581–583, 585–590, 597–598
weight, 29, 222, 390–393, 400, 597
work (W) of, 581–583
wrench, reduction to, 192
Frames, 310–325, 343
free-body diagrams for, 310–316, 343
multiforce members of, 310, 343
procedure for analysis of, 316
structural analysis of, 310–325, 343
Free-body diagrams, 104–116, 120–124, 131, 219–228,
230–239, 253–257, 259–267, 275–276, 296–301, 310–316,
342–343, 347–354, 398, 585–590
beams, 347–354, 398
cables, 104, 109
center of gravity, 222
centroid (geometric center), 222, 348, 398
concurrent forces, 120–124
coplanar force systems, 107–111, 131, 219–228, 230–239,
275–276
constraints, 259–267, 276
direction and, 105, 107, 219
equilibrium and, 104–116, 120–124, 131, 219–228, 230–239,
253–257, 259–267, 275–276
external forces and, 296–297
frames, 310–316, 343
idealized models of, 222–223
internal forces and, 222, 296–297, 347–354, 398
machines, 310–316, 343
method of sections using, 296–301, 347–354
particle equilibrium, 104–106
procedures for analysis using, 105, 108, 120, 224, 231, 262,
298, 316
pulleys, 104, 110
rigid bodies, 219–228, 230–239, 253–257, 259–267,
275–276
smooth surface contact, 104
springs, 104, 111
statical determinacy and, 259–267, 276
structural analysis using, 296–301, 310–316, 342–343
support reactions, 219–221, 253–257, 259–267,
275–276
three-dimensional systems, 120–124, 131, 253–257, 276
trusses, 296–301
virtual work, 585–590
weight and, 222
Free vector, 167, 224
Friction (F), 402–463, 598
angles (u) of, 405–406
applied force (P), 404–407, 430–431, 459–460
axial loads and, 447–449
bearings, analysis of, 447–451, 461
belts (flat), forces on, 439–441, 460
characteristics of, 403–407, 459
coefficients of (μ), 405–407, 447–448, 459
collar bearings, analysis of, 447–449, 461
Coulomb, 403660 Index
Friction (F) (Continued)
disks, analysis of, 447–449, 461
dry, 403–463
equations for friction and equilibrium, 409–416
equilibrium and, 404–405, 409
impending motion, 405, 408–416, 432–434, 459–460
journal bearings, analysis of, 450–451, 461
kinetic force (Fk), 406–407, 459
lateral loads and, 450–451
nonconservative force, as a, 598
point of contact, 403–409, 452–453, 459
pivot bearings, analysis of, 447–449, 461
procedure for analysis of, 411
rolling resistance and, 452–453, 461
screws, forces of, 432–434, 460
shaft rotation and, 447–451, 461
sliding and, 406–416, 459
slipping and, 405, 407–409, 459
static force (Fs), 405, 407, 459
virtual work (U) and, 598
wedges and, 430–431, 460
Frictional circle, 450
Frictional force, 404–407, 459
Frictionless systems, 600
G
Geometric center, 203, 222, 348. See also Centroid (C)
Gravitational attraction, Newton’s law of, 29
Gravitational potential energy (Vg), 598
Gravity, see Center of gravity (G)
Gusset plate, 280–281
H
Hinge connections, 221, 253, 255–256
Hyperbolic functions, 618
I
Idealizations (models) for mechanics, 27, 222–223
Impending motion, 405, 408–416, 432–434, 459–460
all points of contact, 408
angle of static friction for, 405
coefficient of static friction (μs) for, 405, 459
downward, 433, 460
dry friction problems due to, 408–416
equilibrium and frictional equations for, 409–416
friction and, 405, 408–416, 432–434, 459–460
no apparent, 408
points of contact, 405, 408–409
procedure for analysis of, 411
screws and, 432–434, 460
slipping, verge of, 405
tipping and, 409
upward, 432–433, 460
Inclined axes, moment of inertia for area about, 552–554
Incompressible fluids, 512
Inertia, see Moments of inertia
Integrals, 529, 619
Integration, 467–478, 511, 515, 525, 529–535, 563, 576–577
area (A), centroid of, 468, 474–476, 529–535
center of mass (Cm), determination of using, 467, 478
centroid (C), determination of using, 467–478, 511, 515,
525, 576
distributed loads, 511, 515, 525
fluid pressure distribution from, 515, 525
line, centroid of, 468–469, 471–473
mass moments of inertia, determination of using, 563, 577
moments of inertia, determination of using, 529–535, 576
parallel-axis theorem, 530–531, 576
procedure for analysis using, 470, 532
resultant forces determined by, 511, 515
volume (V), centroid of, 467, 477
volume elements for, 563
Internal forces, 222, 296–297, 346–401
beams subjected to, 347–382, 398–399
bending moments (M) and, 348–349, 372–377, 398, 400
cables subjected to, 383–397, 400
compressive (C), 296
concentrated loads, 372–373, 383–385, 399–400
couple moment (M0) and, 374
distributed loads, 372–377, 386–390, 399–400
force equilibrium, 372–373
free-body diagrams, 222, 296–297, 347–354, 398
method of sections and, 296–297, 347–354, 364
moments (M) and, 348–349, 372–377, 398–400
normal force (N) and, 348–349, 398
procedures for analysis of, 349, 364
resultant loadings, 348–349, 398
rigid-body equilibrium and, 222
shear and moment diagrams, 363–366, 372–377, 399–400
shear force (V) and, 348–349, 372–377, 398, 400
sign convention for, 349, 399
structural members with, 296–297, 347–354, 398
tensile (T), 296
torsional (twisting) moment, 348, 398
weight, 390–393, 400
International System (SI) of units, 29–31
J
Joints, 279–282, 290. See also Method of joints
equilibrium of, 282–283
loadings at, 280–281
pin connections, 280–281
procedure for analysis of, 283
truss analysis and, 279–290
unknown forces, 282–287Index 661
zero-force members, 288–290
Joules (J), unit of, 582
Journal bearings, 254–256, 450–451, 461
free-body diagrams, 254–256
frictional analysis of, 450–451, 461
support reactions, 254–256
K
Kinetic frictional force (Fk), 406–407, 459
L
Lateral loads, friction analysis of, 450–451
Lead of a screw, 432
Lead angle, 432
Length, 26, 30–31, 468–473, 523
basic quantity of mechanics, 26
centroid (C) of lines, 468–473, 523
integration for, 468–469, 471–473, 523
procedure for analysis of, 470
Pythagorean theorem for, 469
units of, 30–31
Line of action, 39–40, 78, 99, 148–149, 158–160, 179, 190–196,
212, 511, 513, 525
centroid (C) location from, 203, 511
collinear vectors, 40
distributed loads, 511, 513, 525
fluid pressure and, 513
force and couple system simplification, 179, 190–196
force vector directed along, 78, 99
moment force-vector formulation, 148–149
moment of a force about an axis, 158–160, 212
perpendicular to force resultants, 190–196
principle of transmissibility, 148, 179
resultant force, 203, 511
vector representation of, 39–40, 78, 99, 159–160
Linear elastic behavior, 104
Linear load distribution, 513, 525
Lines, centroid (C) of, 468–473. See also Length
integration for, 468–469, 471–473
procedure for analysis of, 470
Loading curve, 203, 213
Loads, 202–206, 279–281, 347–354, 372–377, 383–400,
447–451, 511–518, 525. See also Distributed loads
axial, 447–449
beams, 347–354, 372–377, 398–399
cables, 383–397, 400
concentrated, 372–373, 383–385, 399–400
distributed, 202–206, 372–377, 386–389, 399–400,
511–518
fluid pressure, 512–518
friction (F) and, 447–451
internal, 347–354
lateral, 450–451
linear distribution of, 513, 525
moment (M) relations with, 373–377, 400
plates, 511–518, 525
resultant forces, 202–206, 511–518
reduction of distributed, 202–206
shaft rotation and, 447–451
shear (V), 372–377, 398, 400
single axis representation, 202
structural analysis and, 279–281
three-dimensional, 348, 398
truss joints, 279–281
uniform, 525
units of, 202
weight, 390–393, 400
M
Machines, 310–325, 343
free-body diagrams for, 310–316, 343
multiforce members of, 310, 343
vector formulation, 38–133, 145–152, 159–162, 167–172, 211
procedure for analysis of, 316
structural analysis of, 310–325, 343
Magnitude, 39, 42–48, 54–56, 66–67, 105, 107, 131, 136, 145,
148, 167, 202–203, 211, 511, 525
Cartesian vectors, 55, 66–68
coplanar force systems, 54–56, 107
constant, 131
couple moments, 167
cross product and, 145
distributed load reduction and, 202–203, 511, 525
equilibrium and, 105, 107
force components, 42, 44, 54–56, 105
free-body diagrams, 105, 107
integration for, 511, 525
moments and, 136, 145, 148, 211
Pythagorean theorem for, 56
resultant forces, 42, 44, 202–203, 511, 525
right-hand rule for, 148
sine and cosine laws for, 42, 44
vector force addition and, 42, 44–48
vector representation of, 39, 42, 44, 54–56, 66
units of, 136
Mass, 26, 30, 467, 470, 478, 523
basic quantity of mechanics, 26
center of (Cm), 467, 470, 478, 523
integration of, 467, 478, 523
units of, 30
Mass moments of inertia, 563–570, 577
axis systems, 563–570, 577
composite bodies, 568–570, 577
disk elements, 564, 566, 577662 Index
Mass moments of inertia (Continued)
integration for, 563, 577
parallel-axis theorem for, 567
procedure for analysis of, 564
Pythagorean theorem for, 567
radius of gyration for, 568
shell elements, 564–565, 577
volume elements for integration, 563
Mathematical expressions, 616–619
Mechanics, study of, 25
Members, 240–241, 279–290, 296–301, 310–325, 343, 347–354,
398. See also Beams
compressive force (C), 280–282, 296–297
equilibrium of forces, 240–241
frame analysis, 310–325, 343
internal loads(forces) in, 296, 347–354, 398
joint connections, 279–290
machine analysis, 310–325, 343
method of sections for, 296–301
multiforce, 310, 343
pin connections, 280–281
procedure for analysis of, 349
tensile force (T), 280–281
three-force, 240–241
truss analysis, 279–290, 296–301
two-force, 240–241
unknown forces, 282–287, 296–301
zero-force, 288–290
Method of joints, 282–290, 306–307, 342
compressive forces, 282–283
procedures for analysis using, 283, 306
space truss analysis, 306–307
structural analysis using, 282–290, 306–307, 342
tensile forces, 282–283
truss analysis, 282–290, 306–307, 342
unknown forces, 282–287
zero-force members for, 288–290
Method of sections, 296–301, 306, 342, 347–354, 364
beam analysis using, 347–354, 364
compressive forces (C), 296–297
external forces and, 296–297
internal forces and, 296–297, 347–354
free-body diagrams for, 296–301, 347–354
procedures for analysis using, 298, 306, 349
shear and moment diagrams from, 364
space truss analysis, 306
structural analysis using, 296–301, 306, 342, 347–354
tensile forces (T), 296–297
truss analysis, 296–301, 306, 342
unknown member forces, 296–301
Models (idealizations), 27, 222–223
Mohr’s circle, 555–557
Moment arm (perpendicular distance), 135–137, 158, 212
Moment axis, 136, 148, 158–162, 212
direction and, 136, 148
force about a, 158–162, 212
force-vector formulation and, 148
right-hand rule for, 136, 148, 158–160
scalar analysis of, 158
vector analysis of, 159–162
Moments (M), 134–215, 348–349, 372–377, 398, 400. See also
Couple moments
bending (M), 348–349, 372–377, 398, 400
concentrated load discontinuities, 373
couple (M0), 167–172, 179–184, 190–196, 212–213, 374
cross product for, 145–147
direction and, 136, 145, 148, 211
distributed loads and, 202–206, 213, 372–377, 400
equivalent systems, reduction to, 179–184, 190–196
force, of, 134–215
force-vector formulation, 148–152
free vector, 167
internal forces and, 348–349, 372–377, 398, 400
magnitude and, 136, 145, 148, 211
normal force (N) and, 348–349
parallel force systems, 191–192
perpendicular to force resultants, 190–196
principle of moments, 137–139, 150, 211
principle of transmissibility, 148, 179
procedures for analysis of, 181, 192
right-hand rule for, 136–137
resultant forces and, 136, 149, 168–169, 202–206
scalar formulation of, 135–136, 158, 167, 211
shear loads (V) and, 348–349, 372–377, 400
sign convention for, 136, 146
system simplification of, 179–184, 190–196, 212–213
torque, 136
torsional (twisting), 348, 398
Varignon’s theorem, 137–139
vector formulation of, 148–152, 159–162, 167–172, 211
wrench, reduction of force and couple to, 192
Moments of inertia (I), 529–579
algebraic sum of, 540
area (A), 530–535, 540–542, 548–554, 576
axis of symmetry, 548–551, 563–570, 596
axis systems, 529–535, 540–542, 563–570
composite bodies, 540–542, 568–570, 576–577
disk elements, 564, 566
inclined axis, area about, 552–554
integrals, 529
integration and, 529–535
mass, 563–570, 577Index 663
Mohr’s circle for, 555–557
parallel-axis theorem for, 530–532, 540, 549, 567, 576
polar, 530–531
principle, 553–554, 556, 577
procedures for analysis of, 532, 540, 556, 564
product of inertia and, 548–551, 555–556, 576
radius of gyration for, 531, 568
shell elements, 564–565, 577
transformation equations for, 552–553, 577
Motion, 28, 405–416, 430–434, 439–441, 447–453, 459–461.
See also Revolution; Shaft rotation
bearings, 447–451, 461
belt drives, 439–441, 460
coefficients of friction (μ) and, 405–407, 452–453, 459
downward, 433, 460
equilibrium and frictional equations for, 409–416
friction and, 405–416, 430–434, 439–441, 447–453,
459–461
impending, 405, 408–416, 432–434, 459–460
kinetic frictional force (Fk), 406–407, 459
Newton’s laws of, 28
points of contact, 405–409
procedure for analysis of, 411
rolling resistance and, 452–453, 461
screws and, 432–434, 460
self-locking mechanisms, 430, 433
shaft rotation, 447–451, 461
sliding, 406–416, 459
slipping (impending), 405, 408–409, 459
static frictional force (Fs), 405, 407, 459
upward, 432–433, 460
verge of sliding, 405
wedges, 430–431, 460
Movement, virtual, 583
Multiforce members, 310. See also Frames; Machines
N
Neutral equilibrium, 601–602
Newton, unit of, 30
Newton’s laws, 26, 28–29
dynamics and, 26
gravitational attraction, 29
motion, 28
Nonconservative force, friction as a, 598
Normal force (N), 348–349, 398, 404–406
dry friction and, 404–406
equilibrium and, 404
impending motion and, 405–406
internal forces as, 348–349, 398
method of sections for, 348–349, 398
Numerical calculations, importance of, 32–33
P
Pappus and Guldinus, theorems of, 502–505, 524
axial revolution and symmetry, 502–505, 524
centroid (C) and, 502–505, 524
composite shapes, 503
surface area and, 502, 504–505, 524
volume and, 503–505, 524
Parallel-axis theorem, 530–532, 540, 549, 567, 576
area (A) and, 530–532, 540, 549, 576
centroidal axis for, 530–532, 576
composite parts, 540
mass moments of inertia determined by, 567
moments of inertia determined by, 530–532, 540, 567, 576
product of inertia determined by, 549, 576
Parallel force systems, 191–192, 240
equilibrium of, 240, 260–261
improper constraints, 260–261
reactive, 260–261
three-force members, 240
simplification of, 191–192
Parallelogram law, 40, 42–44, 97
Particles, 27–29, 102–133
coplanar force systems, 107–111, 131
defined, 27
equations of equilibrium, 103, 107–108, 120–124
equilibrium of, 102–133
free-body diagrams, 104–106
gravitational attraction, 29
idealized model of, 27
Newton’s laws applied to, 28–29
nonaccelerating reference of motion, 28
procedures for analysis of, 105, 120
three-dimensional force systems, 120–124, 131
two-dimensional force systems, 107–111, 131
zero condition, 103, 131
Pascal’s law, 512
Perpendicular distance (moment arm), 135–137,
158, 212
Pin connections, 219–221, 223, 253, 255–256, 280–281
concurrent forces of, 280–281
coplanar systems, 219–221, 223
free-body diagrams of, 219–221, 253, 255–256
three-dimensional systems, 253, 255–256
truss member analysis, 280–281
Pivot bearings, frictional analysis of, 447–449
Planar truss, 279
Plates, 511–518, 525
flat of constant width, 513
distributed loads on, 511, 525
centroid (C), 511–518, 525
curved of constant width, 514664 Index
Plates (Continued)
flat of constant width, 513
flat of variable width, 515
fluid pressure and, 512–518, 525
linear distribution on, 513, 525
resultant forces acting on, 511–518, 525
Point of contact, 403–409, 452–453, 459
friction and, 403–409, 452–453, 459
impending motion (slipping), 405, 408–409
kinetic friction and, 406–407
motion (sliding), 406–407
rolling resistance and, 452–453
static friction and, 405, 407
Polar moments of inertia, 530–531
Position coordinates, 585–590, 600, 612
Position vectors (r), 76–77, 79–80, 99
Cartesian vector form, 76–77, 79–80, 99
head-to-tail addition, 76–77
x, y, z coordinates, 76, 99
Potential energy (V), 598–606, 613
elastic (Ve), 598
equilibrium, criterion for, 600, 613
equilibrium configurations, 601–606
frictionless systems, 600
gravitational (Vg), 598
position coordinates for, 600
potential function equations, 599
procedure for analysis of, 603
single (one) degree-of-freedom systems, 599, 602–603
stability of systems and, 601–606, 613
virtual work (V) and, 598–606, 613
Power-series expansions, 618
Pressure, see Fluid pressure
Principal axes, 553–557, 576
Mohr’s circle for, 555–557
principal moment of inertia and, 553–557
procedure for analysis of, 556
product of inertia for, 553, 576
Principle moments of inertia, 553–554, 556, 577
Mohr’s circle for, 555–557
principal axes, 553–554, 556, 577
procedure for analysis of, 556
transformation equations for, 553, 577
Principle of moments, 137–139, 150, 211
Principle of transmissibility, 148, 179
Principle of virtual work, 581, 583–590, 612
Product of inertia, 548–551, 553, 555–556, 576
axis of symmetry for, 548–551
centroid for, 549, 576
Mohr’s circle and, 555–556
parallel-axis theorem for, 549, 576
procedure for analysis of, 556
principal axes and, 553
Procedure for analysis, 34–36
Projections, parallel and perpendicular, 87–88, 99, 159
Pulleys, free-body diagram of, 104, 110, 131
Purlins, 279
Pythagorean theorem, 56, 87, 469, 567, 617
Q
Quadratic formula, 618
R
Radius of gyration, 531, 568
Reactive force, 105, 260–261
Rectangular components, 54–70, 98–99
coplanar force systems, 54–59, 98–99
force vectors of, 54–70, 98–99
resultant force, 55–56, 98
Resultant forces, 40, 42–48, 55–59, 65–71, 97–98, 134–215,
348–349, 398, 511–518, 525
axis, moment of force about, 158–162, 202, 212
beams, 348–349
Cartesian vector components, 65–70
Cartesian vector notation for, 55
centroid (C) and, 203, 348, 511–518, 525
concurrent forces, 55, 65–70, 99, 190–192
coplanar forces, 55–56, 98, 179–184, 190–196
couple moments, 167–172, 179–184, 190–196, 213
cross product for, 146–147
direction of, 146, 211
distributed loads, 511–518, 525
fluid pressure and, 512–518, 525
force components and, 40, 42–44, 97
force system, 55–59, 99, 134–215
integration for, 511, 525
internal forces, 348–289, 398
lines of action, 158–160, 179, 190–196, 203, 511, 513
magnitude of, 146, 202, 211, 511, 525
method of sections for, 348–349
moments of a force, 135–139, 149, 158–162, 211, 348–349
parallel force systems, 191–192
parallelogram law for, 40, 42–44, 97
perpendicular to moments, 190–196
plates, 511–518, 525
principle of moments, 137–139, 211
procedure for analysis of, 44, 192
reduction of distributed loads, 202–206, 213
scalar formulation of, 135–136, 158, 167, 211
scalar notation for, 55
system reduction for, 179–184, 190–196, 213
vector addition for, 40–44, 55–59
vector formulation of, 42–48, 97, 148–152, 167–172, 211–212
vector subtraction for, 41
wrench, reduction to, 192, 213Index 665
Revolution, 502–505, 524
axial symmetry and, 502–505
centroid (C) and, 502–505, 524
composite shapes, 503
Pappus and Guldinus, theorems of, 502–505, 524
plane area, 503
surface area, 502, 504–505, 524
volume from, 503–505, 524
Right-hand rule, 65, 136–137, 145–146, 148, 158–160, 167
axis, moment of a force about, 158–160
cross product direction, 145–146
force-vector formulation, 146, 148
moment of a couple, 167
moment of a force, 136–137, 158–160
three-dimensional coordinate systems, 65
Rigid bodies, 25, 27, 216–277, 585–590, 600–606, 612
center of gravity, 222
centroid (geometric center), 222
conditions for, 217–218
connected systems of, 585–590, 612
constraints of, 259–267
coplanar force systems, 218–252, 275–276
defined, 27
displacement (d) and, 585–590, 600, 612
equations of equilibrium for, 218, 230–239, 275–276
equilibrium of, 216–277, 600–606
external forces and, 217
force and couple systems acting on, 217–218
free-body diagrams, 219–228, 253–257, 259–267,
275–276
frictionless systems, 600
idealized models of, 27, 222–223
internal forces and, 222
improper constraints for, 260–261, 276
mechanics, study of, 25
position coordinates for, 585–590, 600, 612
potential energy and, 600–606
procedures for analysis of, 224, 231, 262, 586, 603
redundant constraints for, 259
statical determinacy and, 259–267, 276
support reactions, 219–221, 253–257, 259–267, 275–276
three-dimensional systems, 253–267, 276
two-and three-force members, 240–241
uniform, 222
virtual work (V) for, 585–590, 600–606, 612
weight and, 222
Rocker connections, 220, 221
Roller connections, 219–220, 223, 254, 256
Rolling resistance, frictional forces and, 452–453, 461
Roof truss, 279–280, 342
Rotation, 219, 447–448, 450, 461, 582–583. See also
Revolution; Shaft rotation
Rounding off numbers, 33
S
Scalar notation, 54, 55
Scalar product, 86
Scalar triple product, 159
Scalars, 39, 40, 54, 86, 107, 135–136, 158, 167, 211, 258,
275–276, 582
axis, moment of force about, 158
couple moments, formulation by, 167
division of vectors by, 40
dot product and, 86
equations of equilibrium, 258, 275–276
magnitude of, 39
moment of a force, formulation by, 135–136, 158, 211
multiplication of vectors by, 40, 86
negative, 54, 107
torque, 135
vectors and, 39, 40, 86
work of a couple moment, 582
Screws, frictional forces on, 432–434, 460
Self-locking mechanisms, 430, 433
Sense of direction, 39
Shaft rotation, 447–451, 461
axial loads, 447–449
collar and pivot bearings, 447–449, 460
disks, 447–449, 460
frictional analysis of, 447–451, 460
frictional circle, 450
journal bearings, 450–451, 460
lateral loads, 450–451
Shear and moment diagrams, 363–366, 372–377, 399–400
beam analysis using, 363–366, 372–377, 399
couple moment (M0) and, 374
discontinuities in, 373
distributed load relations and, 372–377, 400
internal forces and, 363–366, 372–377, 399–400
method of sections for, 364
moment (M) relations in, 373–377, 399–400
procedure for analysis of, 364
shear force (V) relations in, 372–377, 399–400
Shear force (V), 348–349, 372–377, 398–400
beams, 348–349, 372–377, 398
bending moments (M) and, 348–349, 372–377, 398, 400
concentrated load discontinuities, 373
couple moment (M0) and, 374
distributed load relations, 372–377, 400
internal forces, 348–349, 372–377, 398–400
method of sections for, 348–349
shear and moment diagrams, 372–377, 399–400
Shell elements, mass moments of inertia, 564–565, 577
Significant figures, 32–33
Simple trusses, 279–281, 342
Simply supported beam, 363
Sine functions, 617666 Index
Sine law, 42, 44, 97
Single degree-of-freedom systems, 599, 602–603
Sliding, 405–416, 459–460
friction and, 405–416
kinetic frictional force (Fk), 406–407, 459
motion of, 406–416
problems involving, 408–416
verge of, 405
Sliding vector, 148, 179, 224
Slipping, 405, 407–416, 459
friction and, 405, 407–416, 459
impending motion of, 405, 408–409, 459
points of contact, 405, 408–409
problems involving, 408–416
static frictional force (Fs), 405, 407, 459
Smooth surface contact (support), 104, 254
Solving problems, procedure for, 34–36
Space trusses, structural analysis of, 306–307, 343
Specific weight, center of gravity (G) and, 488
Spring constant (k), 104
Spring force (Fs), virtual work and, 597
Springs, free-body diagram of, 104, 111, 131
Stable equilibrium, 601–603, 613
Stability of a system, 260–261, 276, 601–606, 613. See also
Equilibrium
equilibrium configurations for, 601–606, 613
free-body diagrams for, 260–261, 276
improper constraints and, 260–261
neutral equilibrium, 601–602, 613
one (single) degree-of-freedom system,
602–603
potential energy and, 601–606
procedure for analysis of, 603
reactive parallel forces, 260–261
rigid-body equilibrium and, 260–261, 276
stable equilibrium, 601–603, 613
statical determinacy and, 260–261, 276
unstable equilibrium, 601–603, 613
virtual work and, 601–606, 613
Static frictional force (Fs), 405, 407, 459
Statical determinacy, 259–267, 276
equilibrium and, 259–267
procedure for analysis of, 262
improper constraints and, 260–261
indeterminacy, 259, 276
redundant constraints and, 259
rigid-body equilibrium and, 259–267, 276
stability and, 260–261, 276
Statically indeterminate bodies, 259, 276
Statics, 24–37
basic quantities, 26
concentrated force, 27
equilibrium and, 25
force, 26–30
gravitational attraction, 29
historical development of, 26
idealizations, 27
length, 26, 29–31
mass, 26, 29–31
mechanics study of, 24–25
motion, 28
Newton’s laws, 28–29
numerical calculations for, 32–33
particles, 27
procedure for analysis of, 34–36
rigid bodies, 27
study of, 24–37
time, 26, 30
units of measurement, 29–31
weight, 29
Stiffness factor (k), 104
Stringers, 280
Structural analysis, 278–345, 347–382
beams, 347–382
compressive forces (C), 280–283, 296–297
frames, 310–325, 343
free-body diagrams, 296–301, 310–316, 342–343
internal forces and, 296–297, 347–382
machines, 310–325, 343
method of joints, 282–290, 306–307, 342
method of sections, 296–301, 306, 342, 347–354, 364
multiforce members, 310, 343
procedures for analysis of, 283, 298, 306, 316, 349, 364
shear and moment diagrams for, 363–366
space trusses, 306–307, 343
tensile forces (T), 280–283, 296–297
trusses, 279–309, 342–343
unknown forces, 282–287, 296–301
zero-force members, 288–290
Structural members, see Members
Support reactions, 219–221, 223, 253–257, 259–267,
275–276
coplanar force systems, 219–221, 223, 275
free-body diagrams, 219–221, 223, 253–257, 259–267,
275–276
improper constraints, 260–261
procedure for analysis of, 262
redundant constraints, 259
rigid-body equilibrium and, 219–221, 223, 253–257,
259–267
statical determinacy and, 259–267, 276
three-dimensional force systems, 253–257, 259–267, 276
Surface area, centroid (C) and, 502, 504–505, 524
Symmetry, see Axial symmetry; Axis of symmetryIndex 667
System simplification, 179–184, 190–196
concurrent force system, 190–192
coplanar force systems, 179–184, 190–196
equivalent system, reduction to, 179–184, 190–196
lines of action and, 179, 190–196
parallel force systems, 191–192
procedures for analysis, 181, 192
reduction to a wrench, 192
system of force and couple moments, 180
three-dimensional systems, 179–184, 190–196
T
Tangent functions, 617
Tensile forces (T), 280–283, 296–297, 439–441
flat belts, 439–441
method of joints and, 282–283
method of sections and, 296–297
truss members, 280–281, 296–297
Tetrahedron form, 306
Thread of a screw, 432
Three-dimensional systems, 65–70, 76–81, 86–90, 98–99,
120–124, 131, 179–184, 190–196, 253–267, 276. See also
Concurrent forces
addition of vectors, 68
Cartesian coordinate system for, 65–70, 98–99
Cartesian unit vectors, 65–66, 78, 98–99
Cartesian vector representation, 65–66
concurrent forces, 65–70, 99, 120–124, 131, 190–192, 276
constraints for, 259–267, 276
coordinate direction angles, 66–67, 98–99
direction angles for, 66–67
dot product for, 86–90, 99
equations of equilibrium, 120, 258, 276
equilibrium of, 120–124, 131, 253–267, 276
equivalent systems, 179–184, 190–196
force and couple moment system simplification, 179–184,
190–196
force vectors, 65–70, 78–81, 99
free-body diagrams, 120–124, 253–257, 276
magnitude of, 66
parallel system simplification, 191–192
particles, 120–124, 131
position vectors, 76–77, 79–80, 99
procedure for analysis of, 120
reactive parallel forces, 261
rectangular components, 65–70, 98–99
resultants, 65–70
right-hand rule, 65
rigid bodies, 253–267, 276
statical determinacy and, 259–267, 276
support reactions for, 253–257, 259–267, 276
x, y, z position coordinates, 65–66, 76, 98–99
Three-force member equilibrium, 240–241
Thrust bearing connections, 255, 256
Time, 26, 30
basic quantity of mechanics, 26
units of, 30
Tipping effect, balance of, 404, 459
Torque, 135. See also Moments (M)
Torsional (twisting) moment, 348, 398
Transformation equations, moments of inertia (I) and,
552–553, 577
Translation, 219, 582
Trapezoid, distributed loading of, 206
Triangle rule, 41, 97
Triangular truss, 281
Trigonometric identities, 618
Trusses, 279–309, 342–343
assumptions for design, 280–281, 306
bridges, 279–280
compressive force (C) and, 280–283,
296–297
floor beams, 280
gusset plate for, 280–281
joints, 279–290
method of joints, 282–290, 306–307, 342
method of sections, 296–301, 306, 342
planar, 279
procedures for analysis of, 283, 298, 306
purlins, 279
roof, 279–280, 342
simple, 279–281, 342
space trusses, 306–307, 343
stringers, 280
structural analysis for, 279–309, 342–343
tensile force (T) and, 280–283, 296–297
triangular, 281
zero-force members, 288–290
Two-dimensional systems, 54–59, 98, 107–111, 218–252.
See also Coplanar forces
Cartesian unit vectors, 55, 98
coplanar force vectors, 54–59, 98
free-body diagrams for, 107–111
particle equilibrium, 107–111
procedure for analysis of, 108, 224, 231
rigid-body equilibrium, 218–252
scalar notation for, 54
Two-force member equilibrium,
240–241
U
Unbalanced force, 28
Uniform distributed load, 372, 525
Uniform rigid bodies, 222668 Index
Unit vector (u), 55–56, 65–66, 78, 86–87, 98–99. See also
Cartesian coordinates
Cartesian vectors, 55–56, 65–66, 78, 98
dot product and, 86–87, 99
three-dimensional, 65–66, 78, 98–99
force components, 55–56
force vectors, 78, 99
Units of measurement, 29–31
base, 29, 31
derived, 29–31
International System (SI) of, 30–31
prefixes, 30
rules for use, 31
Unknown member forces, 282–287,
296–301
Unstable equilibrium, 601–603, 613
V
Varignon’s theorem, 137–139
Vectors, 38–101, 145–152, 159–162, 167–172, 211, 258, 276
addition of, 40–48, 54–59, 68–70
addition of forces, 42–48, 54–59
axis, moment of a force about, 159–162
Cartesian coordinate system, 55–58, 65–70, 76–81, 98,
145–152, 211
Cartesian notation for, 55
components of a force, 40, 42–48, 97
concurrent forces, 40, 55, 65–70, 99
coplanar force systems, 54–59
cross product method of multiplication, 145–147
collinear, 41, 97
couple moments, formulation by, 167–172
direction and, 39, 55–56, 66–68, 145, 148
division by scalars, 40, 97
dot product, 86–90, 99, 169
equations of equilibrium, 258, 276
force directed along a line


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