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Andrew Pytel, Jaan Kiusalaas
التاريخ
28 يناير 2023
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Engineering Mechanics – Statics 4th Edition
Andrew Pytel
The Pennsylvania State University
Jaan Kiusalaas
The Pennsylvania State University
CONTENTS
Preface x
Chapter 1 Introduction to Statics 1
1.1 Introduction I
1.2 Newtonian Mechanics 3
1.3 Fundamental Properties of Vectors 11
1,4 Representation of Vectors Using Rectangular Components 19
1.5 Vector Multiplication 28
Chapter 2 Basic Operations with Force Systems
2.1 Introduction 39
2.2 Equivalence of Vectors 40
2.3 Force 40
2.4 Reduction of Concurrent Force Systems 41
2.5 Moment of a Force about a Point 52
2.6 Moment of a Force about an Axis 63
2.7 Couples 76
2.8 Changing the Line of Action of a Force 89
39
Chapter 3 Resultants of Force Systems 101
3.1 Introduction 101
3.2 Reduction of a Force System to a Force and a Couple 102
3.3 Definition of Resultant 109
3.4 Resultants of Coplanar Force Systems 110
3.5 Resultants of Three-Dimensional Systems 120
3.6 Introduction to Distributed Normal Loads 132
Chapter 4 Coplanar Equilibrium Analysis 147
4.1 Introduction 147
4.2 Definition of Equilibrium 148
Part A: Analysts of Single Bodies 148
4.3 Free-Body Diagram of a Body 148
4.4 Coplanar Equilibrium Equations 157
4.5 Writing and Solving Equilibrium Equations 159
4.6 Equilibrium Analysis for Single-Body Problems 170
Part B: Analysis of Composite Bodies 183
4 7 Free-Body Diagrams Involving Internal Reactions 183
4.8 Equilibrium Analysis of Composite Bodies 194
■ ■
VIIVJIt ■ ■ ■ CONTENTS
4.9 Special Cases: Two-Force and Three-Force Bodies 204
Pan C: Analysis of Plane Trusses 218
4.10 Description of a Truss 218
4.11 Method of Joints 219
4112 Method of Sections 228
Chapter 5 Three-Dimensional Equilibrium 241
5.1 Introduction 241
5.2 Definition of Equilibrium 242
5.3 Free-Body Diagrams 242
5.4 Independent Equilibrium Equations 253
5.5 Improper Constraints 256
5.6 Writing and Solving Equilibrium Equations 257
5.7 Equilibrium Analysis 268
Chapter 6 Beams and Cables 287
*6.1 Introduction 287
Part A: Beams 288

• 6.2 Interna] Force Systems 288
• 6.3 Analysis of Internal Forces 297
• 6.4 Area Method for Drawing K- and .W-Diagrams 309
Part B: Cables 324
*6.5 Cables under Distributed Loads 324
*6.6 Cables under Concentrated Loads 336
Chapter 7 Dry Friction 347
7.1 Introduction 347
7.2 Coulomb’s Theory of Dry Friction 348
7.3 Problem Classification and Analysis 351
7.4 Impending Tipping 367
7.5 Angle of Friction: Wedges and Screws 375
• 7.6 Ropes and Flat Belts 385
• 7.7 Disk Friction 392
• 7.8 Rolling Resistance 397
Chapter 8 Centroids and Distributed Loads 407
8.1 Introduction 407
8.2 Centroids of Plane Areas and Curves 408
8.3 Centroids of Curved Surfaces. Volumes, and Space Curves 425
• Indicates option^} articlesCONTENTS IX
8,4 Theorems of Pappus-Guldinus 444
8.5 Center of Gravity and Center of Mass 448
Chapter 9 Moments and Products of Inertia of Areas 477
9.1 Introduction 477
9.2 Moments of Inertia of Areas and Polar Moments of Inertia 478
9.3 Products of Inertia of Areas 498
9.4 Transformation Equations and Principal Moments
of Inertia of Areas 505
*9.5 Mohr’s Circle for Moments and Products of Inertia 514
Chapter 10 Virtual Work and Potential Energy 529
• 10.1 Introduction 529
• 10.2 Virtual Displacements 530
• 10.3 Virtual Work 531
• 10.4 Method of Virtual Work 534
• 10.5 Instant Center of Rotation 545
• 10.6 Equilibrium and Stability of Conservative Systems 554
Appendix A Numerical Integration 565
A.l Introduction 565
A.2 Trapezoidal Rule 566
A.3 Simpson’s Rule 566
Appendix В Finding Roots of Functions 569
B.l Introduction 569
B.2 Newton’s Method 569
B.3 Secant Method 570
Appendix C Densities of Common Materials 573
Index 583INDEX ■
A
Absolute system (4 units, 4
Acceleration. Newton’s second law for, 4
Aclnenforce diagram. 53ft
of couples, 79
of sectors:
poly gon rule for addition. 13
Angle, between vectors. 28-29
Angle ol friction;
angle of kinetic Ind ion. 377
angle of static Inchon. 37ft
cute of к in и he friction, 377
cute of Malic friction. 376-377
Applied forces, 148
Area method,
concentгак-d forces and couples, 313
equations for. 314
theorems for. 3111-3! I
Areas, plane (.Vfr Plane areas)
Axial forces;
definition of. 219
in disk friction, 392
Aos. centroidal, 2X9
Axis of the wrench. 123
В
Ball and socket joint. 243-244
Beams.
area method for.
cottocntriled forces, 313
couples. 313
distributed кккк309-312
equations for. 314
bending moment equations and dutrams for,
299
deTimlKm uL 297
differential equilibrium equations for. 310
internal forces systems in
aulysb of. 2X7-290
determination of. 2XX
load * and the support. 297
shear force equations and diagrams for. 299
sign convention lor analysis of internal forces
in. 297-298
Bending moment;
area method diagram and. 3(1 * 1
definition of. 2X9
diagram * t M-diugrtuns ) for, 31 j9
equations (M-cqu.ihouM for. 309
Built-in (cantilever) support, 245.24ft
c
Cables:
catenary. 327
honrontal spacing given. 337-338
segment length given. 338
signconventions for, 337
flexible:
definition
parabolic.325
(See ufso Flexible cable)
Catenary cable, 327-328
Center of gravity
as centroid of volume for homoccncous bosh
149.450
Гог composite bodies. 450
contrasted with center of mass. 448-450
definition of, 448
weight and.449
(.See afro Center uf mass)
Center of mass:
of composite bodies. 450
contrasted with center of gravity. 44S-449
definition of, 450
Center of weight (See Center of gravity i
Centroidal axis. 218,289
Centroids:
center of gravity and. 149.448-450
center of mass and. 448—150
of common geometric shapes. 135
of composite shapes:
method of composite areas. 411
method ofcomposite curves. JI i
coordinates for three-dimensional shapes and.
425
of curved surfaces, volumes, and space curves
first moment of the area fur threedimensional shapes.
425-427
method of composite 4iapc> for, 42
symmetry an± 42“
of plane areas and plane curves
centroid of the area. 4438
centroid of the cun c.409
first moments of the area. Jus
first moments of the curve. 4 M
integration techniques for. 409-41iI
moment of inertia. 478
table of plane figures. 412
Coefficient of kinetic friction. 349
Coefficient of static friction. 348
Components:
definition of 12
orthogonal. 29
rectangular. 19-21
scalar. 19
vector, 20
Composite areas. 411.427.482.499
Composite bodies:
center of gravity of. 450
center of mass of. 450
coplanar equilibrium analysis of, 183-188
Composite curves,411.427
Composite shapes.411.42“
Composite volumes. 427
Compression. 218
Concentrated force:
in beams. 313
in cables.336-338
contrasted with distributed normal loads, 132
definition of 40
(,Vr Concentrated force)
Concurrent force systems:
cophrur. J 03
reduction oC 41-42
resultant forces of. IШ
three-dimensional. 110.120.253
Cone ofkinetic friction, 377
Cone <4 static fnction. 377 Concernalive systems, 554 Constraint * ; improper. 256 kinematic. 535 t”onversion factors, units,6 Coordinate systems kinematically independent CLNlfdinales, 535 left-handed, 31 rectangular reference frame and, 19 right-handed. 31 (Afrtffco Reference frames) ( oplan.ir equilibrium analysis: composite body: analysis. 183-188 equation * fur; concurrent force systems, 158 general coplanar force systems, 157 parallel coplanar force systems. IS tree-body diagram for. 148-151 plane trusses: assumptions fur, 218 method of joints, 220 method of pins. 221 method of sections. 228 yngk’bodv analysis, 170 support reactions in. 148-151 three-force bodies 206 twiHorce bodies, 205 Coplanar force systems: concurrent. 111 general. 1Ю. 157 parallel. 112.158 ( ophrur loads: bending moment. 289.297-299 normal force. 289.297-299 shear force. 2X9.297-299 torque. 289 Coplanar support reactions: built-in support, 151 flexible cable. 149 I riel ion les * surface, 149 pin support, 151 roller support. 149 surface with friction, 149 Coulomb * theory of dry friction: dynamic ease. 349 impending sliding ease, 348 impending tipping ease, 367-368 hnu ration * rtf. 350 static case, 348 (5« nfw Dry friction1 Couple of transfer. 90 Couple-vector. 79 Couple * : addition of, 79 INDEX 583584 INDEX in beams: area method and. 313 bending moment in. 289 torque in. 289 couplu-i ector. 79 definition of. 76 equivalent. 7S line of action of a force changing: 89-90 couple of transfer. 90 force-couple system., 89-90 moment of a couple about a point. 76-““ moment of a couple as a free vector. 77 notation and terminology for. 78-79 plane of a couple. 76 resolution of, 79 scalar method for.76 vector method for. 77 virtual work of. 532 Cross (vector! product, 3(>-31
Curs ed surfaces:
centroids of. 425
uniform pressure on459—46(1
Curves, plane {Sec Plane curves)
Cylindrical roller on friction surface or on guide
rail, 242
D
Densities table. 573
Diagrams:
active-force di agram. 536
bending moment (M-diagrams). 299
area method and. 309
line loads along plane curves. 458
line loads along straight lines. 134-135
shear force (V-diagramsj. 299
Differential equilibrium equations. 310
Dimensions.in Newtonian mechanics.4
Direction cosines:
definition of. 19-20
и riling vectors in rectangular form, 22
Disk friction:
axial force in. 392
new surfaces. 393
torque requirements in. 392
worn surfaces,393
beams. 3(19-312
flexible cables. 324-328
compulation of. 132-133
contrasted with concentrated forces, 132
for fluid pressure, 460—461
general case of, 456—157
pressure as example of. 132
resultants of. 132
centroid of the volume and. 133
on flat surfaces. 457-458
uniform pressure on cun cd surfaces.459-46(1
Dot (scalar) product:
definition of 28
finding angle between two vectors. 29
orthogonal components and. 29
Dry friction:
angle of kinetic friction,37“
angle of st at ic friction, 376-377
coefficient of kinetic friction. 349
coefficient of static friction. 348
cone of kinetic friction. 377
cone of static friction. 376
Coulomb’s theory of. 378
dynamic case. 349
impending sliding case. 348-349
impending lipping case.367—368
limitations of. 348
sialic case. 348-349
disk friction;
axial force in. 392
new surfaces, 393
Lorqae requirements in.392
worn surfaces, 393-394
for flat belts, 385
method of analysis by problem type. 351-352
for ropes.385
for wedges, 377
Dy namic friction force.349 (.Sec also Kinetic friction i
E
Elastic potential energy. 555
Engm c c ri n g. defined. I -2
Engineer ng mechanics:
definition of. 1
problem analysis in.2-3
Equal and opposite pin reactions. 187-188
Equality of vectors. 12
Equations:
for area method. 309-314
for bending moment (M-aq nations}- 299
for composite volumes.427
equilibrium:
coplanar. 148, 157-158
differential equilibrium equalions for beams.
310
three-dimensional. 242
for flexible cable, 324-328
independent equilibrium equalions:
all forces intersect an axis. 256
concurrent force systems. 158
concurrent, three-dimensional force svstem.
254
general, coplanar force systems. 157
general, three-dimensional force svstem.
253-254
parallel, coplanar force systems. 158
parallel, three-dimensional force svstem.
255-256
for moment of a couple about a point, 76
for moment of a force about a point.52-53
for moment of a force about an axis. 63-67
for reducing force system to force-couple
system. 89-90
for resultant of concurrent force systems. 41
transformation equalions for moments and
products of inertia. 505-507
Equalions of const rain t. 535
Equilibrium analysis:
coplanar
composite bodies. 194
concurrent force systems, 158
tree-body diagrams for. 148-151
general coplanar force systems. 157
independent equilibrium equations for.
157-158
parallel coplanar force systems. 158
plane lrusses.218
single-body problems. 170
support reactions in. 148-151
three-force bodies. 206
two-force bodies, 205
definition of equilibrium. 148,242
equalions of equilibrium. 148.242
frcc-bod\ diagram:
applied forces on, 148
definition of. 1.47
determining support reactions, 149-1511
procedure for constructing. 149
reactive forces on, 148
three-dimensional:
tree-body diagrams lor. 242-246
improper constraints in. 256
independent equilibrium equations for.
253-256
method for, 268
steps in analysis. 257
support reactions in. 242-246
trusses, equilibrium of pins. 221
trusses. method of j oi nts. 219-221
trusses, method of sections, 228-23{)
writing Bud solving cqua Itons:
method of analysis, 159
statically determinate force Systems, 159
statically indeterminate force systems. 159
Equilibrium and stability of conservative systems:
definition of conservative systems. 556
elastic potential energy. 555
grav national potential energy, 555
polenli al c nergy. 555
stationary potential energy and stability.555
Equilibrium, defined, 148.242
Equilibrium equations:
coplanar. 148
differentia] equilibrium equations for beams. 309
three-dimensional. 242
Equivalence:
of couples, 78
definition of. 40
of force systems:
general. 40
statically equivalent force systems. 110
of vectors:
fixed vectors. 40
free vectors. 40
sliding vectors. 40
Expansion by minors using the first row. 32
Externa] effects:
in beams. 288
of a force. 41
icsuhanlof a force system and. 109
First moments of an area:
Fappus-Guldinus theorems and. 444-445
for plane figures, 408—J11
for three-dimensional shapes. 425-426
First moments of a curve:
Fappus-Ciuldinus theorems and. 444-445
for plane cuncs. 409-412
Fixed vector:
definition of. 40
force as. 40-41
Fat th.1 Ils. dry friction ana lysis, 385
Flat surfaces, distributed normal loads. 457
Flexible cable:
catenary. 327-328
coplanar support reactions. 149-150
definition of flexible, 242
equations for. 324-327
guidelines for problem solution, 328INDEX 585
parabolic. 325
three-dimensional support reactions and. 242.
344
Fluid friction, 347-3+8
Fluid pressure, distributed normal loads. 46′ i—161
Force-couple system:
changing line of action of a force. 89-90
reduction lo, 102
scalar equations for determining. 103
vector equations for detenu ini ng. 102
wrench, 120,122-123
Force systems:
ah forces intersect an axis, 256
concurrent force systems:
reduction of,41-42
resultant forces of. 42
coplanar:
concurrent. 111.158
general. 110.157
parallel. 112,158
resultants in, 110-112
equivalence of, 41
force-couple system. 89-90
slulically determinate. 159
Statically equivalent. LIO
statically indeterminate. 159
three-dimensional:
concurrent. 120.254-255
general. 122. 253-255
parallel. 12.1-122.255-256
resultants in. 120-123
wrench, 120,121-123
(5« aiao Dnee)
Force:
applied. 148
concentrated. 41)
definition of. 4l)
as external effects. 41
as fixed vectors. 40
friction. 348-350
generalized. 554
line of action of:
changing. 89-90
definition of. 40
moment of a force about a point. 52-54
definition of. 52
geometric interpretation of. 52-53
moment arm. 53
moment center. 52
Newton’s second law and. 52
principle of moments (Varignons theorem I
for. 54
scalar method for. 54
vector method for. 54
moment of a force about an axis:
definition of. 63—M
geometric interpretation of, 66-67
scalar method for. 67
vector method for. 67
Newton’s laws. 3—1
point of application of. 40
reactive (reactions):
compared w ilh applied forces, 148
interna] reactions al connections. 183
internal reactions in members. 183
resultants:
coplanar systems. 110-112
definition oL 109
reduction lo a force and a couple, 102-103
three-dimensional systems. 120-123
as sliding vectors. 4(1
virtual work oL531-534
work ing comроп c nt of. 532
(Str irfra Foret svstems)
Frames. 147,183
Frames, reference:
inertial. 4
rectangular. 19
Frcc-body diagram:
applied forces. 148
coplanar support reactions:
built’in (cantilever) support. 150
flexible cable i negligible weight). 149
frictionLess surface {simile point of contact ),
149
pin support. 151
roller support. 149
surface with friction (single point of contact >.
149
definition of. 148
internal reactions:
al connections. 184-188
in members. 183,220
pin reactions. 184
procedure for constructing. 148, 246
reactive forces on, 148
three-dimensional support reactions:
ball and socket joint. 243
built-in (cantilever) support.245-246
cylindrical roller on friction surface or on
guide
rail. 242-2+4
flexible cable i negligible weight). 242.244
friction surface (single point of contact). 243
slider (radial) bearing or hinge. 245
spherical roller Ctf single point of contact on
frictionLess
surface. 242-244
thrust bearing or hinge. 245
Univcrsal joint. 245-246
Free vectors:
definition of. 40
moment of a couple as a free vector, 77
Friction:
angle of, 375-377
Coulomb. 348
disk, 392
drv I Sire Drv friction)
fluid. 347-348
friction surfaces (single point of contact). 149.
242-243
frictionlcss surfaces. 149.347
kinetic or dynamic, 349
static. 348-349
Friction force:
analysis of. 348-350
definition of.348-350
(Jee also Dry friction)
Friction surface (single point of contact). 149-150.
242-243
Frictionless surface (single point of contact). 149-151).
347
G
Galilean reference frames. 4
General force systems:
coplanar. 1IQ. 157-] 58
three-dimensional, 122-123.253-254
General virtual plane motion. 531
Generalized forces. 554
Gcomelric center of the region (Are Centroids)
Geometric interpretation:
of moment of a force about a point. 52-53
of moment of a force about an axis. 63-65
Geometric tables:
centroids of common shapes. 135
inertial properties of plane areas. 483-484
plane Ugures. 412
surfaces and volumes. 428
Grav national potential energy. 554
Gravitational system of measureme nt. 4
Impending sliding:
in dry friction. 348-349
method of analysis by problem type. 351-352
Impending lipping:
in dry friction. 367-368
method of analysis by problem type. 368
Improper constraints, 256
Independent equilibrium equations:
all forces intersect an axis. 256
concurrent coplanar force systems. 157
concurrent, three-dimensional force system. 253
general coplanar force systems. 157-158
general, thrcc’dimcnsional force system. 253-254
parallel coplanar force system^ 158
parallel.ihree-dimensionLil force system. 253-256
Inertia (.S’fc Moment of inertia of a plane area;Product
of inertia of a plane area)
Inertial reference frames. 4
Instant center of rotation:
body extended in.546
definition of.545
Internal force systems:
analysis in beams:
bending moment equation.^ and diagrams. 299
shear force equations and diagrams, 299
bending moment. 289
normal force, 289
shear force. 289
torque, 289
Internal forces (5ff Internal reactions)
Interna] reactions:
in beams. 288-290
al connections. 184-185
in members, 183-184
normal force, 289
shear forces, 289
in trusses:
m c thod о Г joints. 219-223
method of sections. 228-230
in [wo-forcc body:
compression. 218
tension. 218
J
Joi nls. i n trusses. 218
К
Kinematic constraints, 535
Kinematically independent coordinates. 535
Kinematics:
equations of constraint. 535
к inematicail у i ndc pc ndc n L coordi nates. 535
number of degrees of freedom f DOF).. 535
planar kincmatics cf a rigid body. 530-531586 INDEX
Kinetic friction:
angjc oL377
cone of 377
;n dry friction. 347
L
Law of universal gravitation. 6
Laws of partick- motion, 3-4
Left’handed coordinate systems, 31
along plane carves:
along straight lines:
I oad diagra m. ! 34
Line of action of a force:
changing. 89
couple of transfer. 90
force-couple system. 90
definition of, 40
area method. 309
line loads along plane curves. 456-461
fine loads along straight Lines. 134
definition of. 132, 134
line loads along plane curves. -158-459
line loads along straight Lines. 134
uniform pressure on curs ed surfaces.
459-460
concentrated, on cables. 336-338
coplanar:
bending moment. 289.297-299
normal force. 289.297-299
shear force.289.297-299
torque, 289
distributed:
on beams. 309-312
on cables. 324-328
line. 134-135
surface. 132-133
transverse. 297
M
M-diagrams. 299
M-equaLions.299
Machines: 183
Mass tenter (Sec Center of mass)
Mass, Newton’s second law and, 5
Measurement:
conversion factors for. 6
dimensions. 4
standards:
Svsk7?re irtternationafe d’unites (SI). 4
l.’.S. Customary system. 4
systems:
absolute. 4
gravitational. 4
units. 4
Mechanics:
definition of. I
Newton tan, 3
quantum. 3
relativistic, 3
Method of composite areas:
determining centroids with. 411
for moment of inertia of a plane area. 482
for product of inertia of a plane area. 499
Method of composite curves. 411
Mel hod of composite shapes:
applied to curved surfaces. volumes. and space
runes. 427
center of gravity and. 450
centroids by. 411
Method of joints:
equilibrium analysis of joints. 219-221
equilibrium unal\sL of pins.221
support reactions. 219
zero-force members. 22 2
Method of sections. 228-230
Method of virtual work:
active-force diagram for. 536
generalized forces in, 536
implemenlation of. 535—536
Mohr’s circle:
construeLion of, 515
properties of. 5 i 6
verification oL 517-518
a pointj
an axis)
Moment arm.53
Moment axis (5’w Moment of u force about an axis)
Moment center. 52
Moment of u couple about a point. 76-77
Moment of u couple as a free vector. 77
Moment of a force about a point:
definition of, 52
geometric interpretation of, 52-53
moment arm and. 53
moment center and. 52
New Lon’s second law ал d, 54
principle of moments (Varignon’s theorem! for. 54
scalar method for. 54
special case: moment axis perpendicular to
force, 65
vector method for. 54
MomcnL of a force about an axis:
definition of. 63-64
geometric interpretation of. 66—67
rec Langular components of. 64-65
scalar method for. 67
special case: moment axis perpendicular to
force, 65
vector method for. 67
MomcnL of couple (See Couples)
Moment of inertia of a plane area:
definition of, 478-479
integration techniques for, 481-482
method of composite ureas for. 482—484
Mohr’s circle for. 514-518
parallel-axis theorems for. 479—481
polar moment of inertia using.479
principal moments of inertia:
principal axes. 507
principal directions. 51 )7
transformation equations for.505-507
Moments:
bend ing momen 1.289
first moments of an urea:
Pappus-Guldinus theorems and, 444
for plane figures. 408
for three-dimensional shapes. 425
first moments of a curve:
Pappus-Guldinus theorems and. 444
for plane curves. 409
moment of inertia of a plane area, 478
polar moment of inertia. 479
twisting moment or torque. 289
N
Newton. Sir Isaac.3
Newtonian mechanics:
conversion of units in. 6
inertial reference frames in, 4
law of universal gravitation. 6
] a ws of part ide motion. 3
Newton’s second law. 3
scope of 3
units and dimensions in. 4
New toman reference frames (Sff Inertial reference
frames)
New Lon’s method, for roots. 569-5 70
New ton’s second law:
acceleration in. 5
force in. 5
mass in.5
moment of force about a point and.52-53
weight in. 5
Newton’s third law.3. 183
Normal force. 149,289
Number of degrees of freedom (DOF).535
Numerical integration:
definition of. 565
Simpson’s rule. 566
trapezoidal rule. 566
when to use. 565
О
Orthogonal components. 29
p
Pappus-Guldinus:
Theorem 1.444
Theorem 11.444
Parabolic cable. 325-328
Para lie!-axis theorem:
for moments of snertia. 479
for polar moments of inertia. 481
for products of inertia. 499
transfer distance. 480
Parallel force system:
coplanar, i 12, 158
three-dimensional. 121.255
components of 12
resolution and, 12
resultants of. 12
triangle law and. 12
Pins:
equilibrium analysis in trusses.
220-222,228-230
pin reactions:
equal and opposite. 184-185
not equal and opposite. IBS
pin support. 15!
Planar kinematics of a rigid body:
virtual displacements:
definition of. 530
general virtual plane motion. 531
notation for. 530
virtual rotation about a fixed point. 530
virtual translation.530INDEX 587
Pliinc artas:
centroid of an area.408
fi rsl moment s of an area. 408
inertial properties of 483-484
second moments of an area (moments of
inertia). 408
Plane curves:
centroid of a curve. 409
first moments of a curve, 409
Pappus-tiuldinus theorems and. 444
Plane figures, properly tables of. 412
Plane mo I ion (Sre Planar kinematics of a rigid
body)
Plane of the couple. 76
Point of application of a force. 4il
Polar moment of inertia:
moments of inertia and. 479-481
parallel-axis theorems Jbr. 479-481
Position vector. 21
Potential energy:
definition of.554
clastic. 555
gravitational. 555
principle of minimum potential energy. 556
principle of stationary potential energy.556
Pressure:
lluid, 460-461
uniform. 459-460
Principal moments of inertia:
principal axes, 507
principal directions 507
Principia [.\fathematicni Principlea ofNatural
Philosophyк 3
Principle of minimum potential energy. 556
Principle of moments. 54
Principle of stationary potential energy. 556
Principle of transmissibility. 41
Principle of virtual work.534-535
Product of area (Sre Product of inertia of a plane
area)
Product of inertia of a plane area:
definition oL 498
inertial properties. tables for. 483—184
method of composite areas for. 499
Mohr’s circle and.514-518
parallel-axis theorem for. 499
transformation equations Гог. 505-506
Q
tjuuntum mechanics. 3
R
Reactive forces (reactionsк
coplanar supports 149-151
internal reactions:
al connections, 184-185
in members. 183-184
pin reactions. 151.184-188
support reactions in trusses. 219
three-dimensional supports. 242-246
Rectangular components:
of moment of a force about an axis. 64-65
representation of vectors with. 19-22
writing vectors wilh. 22
Rectangular coordinate systems:
left-handed. 31
right-handed. 31
Rectangular reference frame. 19
Reduction of concurrent force systems. 41—42
Reference frames:
inertial. 4
rectangular. 19
Relative position vector:
definition of.21
using to write a vector in rectangular
form. 22
Relativistic mechanics. 3
Resolution:
of couples, 79
of forces. 12
Resultants of force systems:
concurrent force systems. 41-42
coplanar systems:
concurrent. Ill
general. 110
parallel. 112
definition of. 12.110-111
external effects and. 41
redaction to a force and a couple.
102-103
l h гес-dimensional systems:
concurrent, 120
general. 122-123
parallel. 121-122
Right-handed coordinate systems. 31
Rigid bodies:
equri ah’nt couples and. 78
equivalent force systems and. 41
general virtual plane motion for.531
instant center of rotation in.545
resultant of a force system for. 109
virtual work for a system of. 534
Rigid-body eq u tvalenl. 41
Roller support. 149
Roots:
definition of.569
Newton’s method for finding. 569-570
secant method for finding. 570-571
Ropes,dry friction analysis. 385-387
Rotation:
instant center of. 545-547
virtual, 530
s
Scalar equations:
for moment of a couple about a point. 76-77
for momc nt of a force about a point, 54
for moment of a force about an axis 63
noncoplttnar, 242
for reducing force system to force-couple system,
103
for resultant of concurrent force systems. 42
Scalar method (5re Scalar equations)
Scalar triple product. 32
Scalar-Sector multiplication, 12
Scalars:
compared with vectors. 11
as components, 19-21
dot (scalar) product and. 28
notation for. 11
scalar-vector multiplication. 12
Screws:
pitch of 378-379
self-locking. 379
torque required by. 378-379
Secant method. 571 j-571
Second moment of the area (Sec Moment of inertia of
a plane area)
Shear force:
definition of 289
diagram (V-diagramj for. 299.309-314
equations (V-cquation) for. 299
as part of interna] force system of cuplanar
SI system {.See Systerne internationale tPttniles’)
Simpson’s rule. 566-567
Single bodies, coplanar equilibrium analysis of.
148-151
Slider (radial j bearing or hi ngc. 2 45
Sliding (Sire Impending sliding)
Sliding vector
definition of.40
treating force ate 40
Slug, as mass unit, 5
Space curves, 425-427
Spherical roller or single point ofcontact on friclionIcss surface. 242
Spring constant.555
Standards of measurement:
Sv.src??!? internutionale J ‘unites (SI),4
U.S. Customary system.4
Static friction:
angle of. 375
coefficient of. 348
cone of 376-377
Statically de terminate force ss stems:
beams. 297-298
definition of, 159
Statically Equivalent force
systems. 110
Statically in detenu in ate force systems:
beams, 297-299
definition of. 159
Stationary potential energy.554-555
Stiffness, 555
Support reactions:
in beams 297-298
coplanar:
b ailt-in i canlilc ver) s upport. 151
determining. 148-151
friclionlcss surface (single point of contact).
149
pin support. 151
roller support. 149
surface with friction (single point of contact).
149
th re c-dimensiona 1.242-246
in trusses, 219
Surface friction:
friction less surface (single point of contact), 149
new surfaces and. 393
surface Wilh friction {single point of
contact), 149
worn surfaces and.
393-394
centroid of the volume. 133
Surfaces:
fiat. 457
geometric tables for, 425
Syriiftne international?d’unites
(Sl).4588 INDEX
T
ТсШ1йщ218
Theorems:
area method diagrams and. 309-314
far bending moment, 3(19-314
Pappus-Guldinus iheorcms. 44-1—44?
parallel-axis Lheortm. 479
far shear farce. 309-314
theorem far virtual wort performed on a rigid
body. 533
Varignon’s theorem. 54
Three ‘dimcnsional equilibri urn an alysis:
free’body diagram t»C 242-246
improper constraints in. 256
independent equilibrium equations of. 253-254
method far, 268
support reactions in.242-246
uriling and solving equations for. 257
Three’dimensional shapes:
centroids of. 425-428
coordinate systems for. 425
first moments far. 425
ball and socket joint, 243
built-in (canliliger I support. 246
cylindrical roller on friction surface or on guide
’ rail, 242
flexible cable I negligible weight). 242
friction surface (single point of contact). 245
slider {radial) bearing or hinge. 245
spherical roller or single point of con!act on
fricl ion less surface. 242
thrust bearing or hinge. 245
universal joint. 246
Three’dimensional systems:
concurrent. 120.254
genera!. 122-123.253-254
parallel 121-122,255-256
wrench.120.122-123
Three-farce principle. 206
Thrust bearing or hinge. 243
Tipping (.Vet’ Impending lipping)
Torque:
definition oL289
required by screws. 375
requirements in disk friction. 392
Transfer distance. 480
Transformation equations for moments and products
of inertia:
definition of.505-5(16
properties of. 516
verification of. 517
Translation, rigid bodies. 530
Trapezoidal rule, 410.566
Triangle law. 12-13
Truss:
asutm plions for a nalysis.. 218-219
description of. 2 IS
members as Iwo-force bodies.2R—239
method of joints:
equilibrium analysis of joints. 219-221
cquilibrEum analysis of pins. 221
support re actions.219
zero-force members. 222
method of sections. 228-230
Twisting moment (5й₽Torque)
Two-dimensional shapes.40S-4I2
Two-farce body:
compression. 218
equilibrium, 2(M
tension. 218
Two-farce principle. 205
u
Unit vectors, 12.21-22
Units:
conversion:
factor list for. 6
method for. 6
in Newtonian mechanics. 4
Universal joint, 246
U.S. Customary system.-I
V
V-diagrams. V-cqualions. 299
Varignon’s theorem, 54
Vector equations:
far moment of a couple about a point, 76
far moment of a farce about a point.52
far moment of a farce about an axis. 63-67
far reducing farce system to farce-couple
system. 1GQ
Lhree-di mcnsional, 242
Vector method
1 See Vector equations)
Vector product. 30
Vectors:
triangle law. 13
using rectangular components. 19-21
compared with scalars. 11
as components. 12.19
couple-vector. 79
as directed line segments. 1J
equality of vectors. 12
equivalent:
fixed vectors. 40
free vectors. 40
sliding vectors. 40
multiplication of:
cross (vector) product. 30-32
dot (scalar) product.28-30
scalar triple product. 32
scalar-тссlor multiplication. 12
notation far. 11
position vector21-22
relative position vector. 21-22
representation:
with direction cosines, 19-20
by rectangular components. 19-20
resolution of. 12
resullanl. 12
unit. 12,2(4-22
writing a vector in rectangular farm:
using direction cosines. 19-20
using relative position vector. 21
Virtual displacements:
definition of. 530
general virtual plane molion. 531
notation far. 530
point. 530
virtual translation. 530
Virtual work:
of a couple, 532
of a farce:
work-absorbing component. 532
working component. 532
к inc malic con si mints and independent
coordinal cs for. 535
method ok 534-536
principle of, 534-535
for a system of rigid bodies 534
theorem for virtual work performed on a rigid
body, 533-534
Vol umes:
centroids oil35,425-428
composite. 427
gcontelric tables for. 428
Plippus-Guldinus theorems for. 444—145
w
Wedge angle.377
Wedg.es, 377
Weighl:
Newton’s second law and. 5
as resultant force of gravity. 448
Work-absorbing compone nt of a force.532
Working component of a force. 532
Wrench” 120,122-123
z
Zero-force members. 222

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