Engineering Mechanics – Statics 4th Edition
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Andrew Pytel, Jaan Kiusalaas
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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
    8.6 Distributed Normal Loads 456
    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
    Answers to Even-Numbered Problems 575
    Index 583INDEX ■
    A
    Absolute system (4 units, 4
    Acceleration. Newton’s second law for, 4
    Aclnenforce diagram. 53ft
    Addition;
    of couples, 79
    of sectors:
    parallelogram law foe addition. 11-13
    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
    distributed loading. 3(W
    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
    under concentrated loads:
    honrontal spacing given. 337-338
    segment length given. 338
    signconventions for, 337
    under distributed loads. 324
    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
    of surface loads. 132
    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
    Concentrated loads
    (,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)
    Curves, space (See Spade 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
    load diagram:
    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
    Distributed loads:
    beams. 3(19-312
    flexible cables. 324-328
    Distributed normal loads:
    compulation of. 132-133
    contrasted with concentrated forces, 132
    for fluid pressure, 460—461
    general case of, 456—157
    line loads along plane curves:
    load diagram for. 134.458-459
    load intensity for. 134. 458-459
    line loads along straight Lnes:
    load diagram for. 134-335
    load intensity for. 134
    pressure as example of. 132
    resultants of. 132
    surface loads:
    centroid of the volume and. 133
    on flat surfaces. 457-458
    load area of, 132
    load intensity oil 132
    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 square—threaded screws378
    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)
    distributed normal loads (See Distributed
    normal loads)
    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
    distributed normal loads, 132. 142
    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
    Graphic addition, 13
    Grav national potential energy. 554
    Gravitational system of measureme nt. 4
    Gravity, weight and. 449 (See also Center of gravity)
    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
    loading and supports, 297
    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
    Line leads:
    along plane carves:
    load diagram. 458—159
    load intensity. 458
    along straight lines:
    I oad diagra m. ! 34
    load intensity, 134
    Line of action of a force:
    changing. 89
    couple of transfer. 90
    force-couple system. 90
    definition of, 40
    Load arcar 132
    Load diagram:
    area method. 309
    line loads along plane curves. 456-461
    fine loads along straight Lines. 134
    Load intensity:
    definition of. 132, 134
    distributed normal loads, 456-561
    line loads along plane curves. -158-459
    line loads along straight Lines. 134
    uniform pressure on curs ed surfaces.
    459-460
    Load surface, 132-133
    Loads:
    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
    (See also Distributed normal loads)
    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
    Moment about a point Moment of a force about
    a pointj
    Moment about an axis (5« Moment of a force about
    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:
    about the centroidal axis, 479—180
    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
    radius of gyration. 481
    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
    Normal loads (.Set Distributed normal loads)
    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
    Parallelogram Law for addition:
    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
    Polygon rule for addition, 13
    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:
    distributed normal loads and, 132
    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
    Quad raturc (.See Numerical integration)
    tjuuntum mechanics. 3
    R
    Radius of gyration, 481
    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
    vector addition with.20
    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
    d 1strihaled normal loads
    line loads. 134-1.35
    surface loads. 132-133
    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:
    about a fixed point, 530
    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:
    lead angle of. 378-379
    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
    loads, 297
    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
    Surface loads:
    centroid of the volume. 133
    load area. 132
    load intensity. 132
    load surface, 132
    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
    Гог load. 309-314
    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
    Three-dimensional support readions:
    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
    Uniform pressure.distributed normal loads. 459-46(1
    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:
    addition of:
    parallelogram law for addition. 12
    polygon rule far addition. 13
    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
    virtual rotation about a fixed
    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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