Engineering Mechanics – Statics – Fifteenth Edition

Engineering Mechanics – Statics
Fifteenth Edition in SI Units
R. C. Hibbeler
Si Conversion by
Jun Hwa Lee
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, 78–81
     forces and, 38–101
     free, 167, 224
     line of action, 39–40, 78, 99, 148–149, 159–160
     magnitude and, 39, 42–48, 54–56, 66–68, 145, 148
     moments of a force, formulation by, 148–152,
     159–162, 211
     multiplication by scalars, 40, 86, 97
     operations, 40–41
     parallelogram law for, 40, 42–44, 97
     physical quantity requirements, 39
     position (r), 76–77, 79–80, 99
     principle of transmissibility, 148
     procedure for analysis of, 44
     projections, parallel and perpendicular, 87–88, 169
     rectangular components, 54–70, 98–99
     resultant couple moment, 168–169
     resultant of a force, 40, 42–48, 97, 149
     rigid-body equilibrium and, 258, 276
     scalar notation for, 54
     scalar triple product, 159
     scalars and, 39, 40, 86, 97
     sliding, 148, 224
     subtraction of forces, 41
     systems of coplanar forces, 54–59
     three-dimensional systems, 65–70, 76–81, 86–90, 98–99, 276
     triangle rule for, 41, 97
     two-dimensional systems, 54–59, 98
     unit, 55–56, 65–66, 78, 86–87, 98–99
     Virtual movement, 583
     Virtual work (U), 580–615
     conservative forces and, 597–598
     couple moment, work of, 582–583
     displacement (d) and, 583–590, 600, 612
     equations for, 583–584, 586
     equilibrium and, 600–606, 613
     force (F) and, 581–582, 585–590, 597–598, 612
     friction and, 598
     frictionless systems, 600
     movement as, 583
     position coordinates for, 585–590, 600, 612
     potential energy (V) and, 598–606, 613
     principle of, 581, 583–590, 612
     procedures for analysis using, 586, 603
     rigid-bodies, connected systems of, 585–590
     single (one) degree-of-freedom systems, 599, 602–603
     spring force (Fs) and, 597
     stability of a system, 601–606, 613
     weight (W) and, 597
     work (W) of a force, 581–583
     Volume (V), 467, 470, 477, 503–505, 523–524
     axial rotation and symmetry, 503–505, 524
     centroid of (C), 467, 470, 477, 503–505, 523–524
     integration of, 467, 477, 523
     Pappus and Guldinus, theorems of, 503–505, 524
     plane area revolution and, 503
     procedure for analysis of, 470
     W
     Wedges, 430–431, 460
     Weight (W), 29, 222, 390–393, 400, 465–466, 488, 523–524, 597
     cables subjected to own, 390–393, 400
     center of gravity (G) and, 222, 465–466, 488, 523–524
     composite body parts, 488, 524Index 669
     conservative force of, 597
     gravitational attraction and, 29
     internal force of, 390–393, 400
     rigid-body equilibrium and, 222
     virtual work (U) and, 597
     Weightless link, support reactions of, 220
     Work (W) of a force, 581–583. See also Virtual work
     couple moment, of a, 582
     force, of a, 581–582
     virtual movement and, 583
     Wrench, reduction of force and moment to,
     192, 213
     X
     x, y, z position coordinates, 65–66, 76, 98–99
     Z
     Zero condition of equilibrium, 103, 131, 218
     Zero-force members, method of joints and, 288–290

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