كتاب Statics and Mechanics of Materials

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Statics and Mechanics of Materials 5th Edition
R. C. Hibbeler
SI Conversion by
Kai Beng Yap

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CONTENTS
General Principles 21
Chapter Objectives 21
1.1 Mechanics 21
1.2 Fundamental Concepts 22
1.3 The International System of Units 26
1.4 Numerical Calculations 28
1.5 General Procedure for Analysis 29
1
Force Vectors 35
Chapter Objectives 35
2.1 Scalars and Vectors 35
2.2 Vector Operations 36
2.3 Vector Addition of Forces 38
2.4 Addition of a System of Coplanar Forces 49
2.5 Cartesian Vectors 58
2.6 Addition of Cartesian Vectors 61
2.7 Position Vectors 70
2.8 Force Vector Directed Along a Line 73
2.9 Dot Product 81
2
Force System
Resultants 97
Chapter Objectives 97
3.1 Moment of a Force—Scalar Formulation 97
3.2 Cross Product 101
3.3 Moment of a Force—Vector Formulation 104
3.4 Principle of Moments 108
3.5 Moment of a Force about a
Specified Axis 119
3.6 Moment of a Couple 128
3.7 Simplification of a Force and Couple
System 138
3.8 Further Simplification of a Force and
Couple System 149
3.9 Reduction of a Simple Distributed
Loading 161
3
Equilibrium of a
Rigid Body 175
Chapter Objectives 175
4.1 Conditions for Rigid-Body Equilibrium 175
4.2 Free-Body Diagrams 177
4.3 Equations of Equilibrium 187
4.4 Two- and Three-Force Members 193
4.5 Free-Body Diagrams 203
4.6 Equations of Equilibrium 208
4.7 Characteristics of Dry Friction 218
4.8 Problems Involving Dry Friction 222
4
Structural Analysis 241
Chapter Objectives 241
5.1 Simple Trusses 241
5.2 The Method of Joints 244
5.3 Zero-Force Members 250
5.4 The Method of Sections 257
5.5 Frames and Machines 266
5
Center of Gravity,
Centroid, and Moment
of Inertia 287
Chapter Objectives 287
6.1 Center of Gravity and the Centroid
of a Body 287
6.2 Composite Bodies 301
6.3 Moments of Inertia for Areas 310
6.4 Parallel-Axis Theorem for an Area 311
6.5 Moments of Inertia for Composite Areas 319
616 contents
Torsion 471
Chapter Objectives 471
10.1 Torsional Deformation of a
Circular Shaft 471
10.2 The Torsion Formula 474
10.3 Power Transmission 482
10.4 Angle of Twist 492
10.5 Statically Indeterminate Torque-Loaded
Members 506
10
Bending 517
Chapter Objectives 517
11.1 Shear and Moment Diagrams 517
11.2 Graphical Method for Constructing
Shear and Moment Diagrams 524
11.3 Bending Deformation of a
Straight Member 543
11.4 The Flexure Formula 547
11.5 Unsymmetric Bending 562
11
Transverse Shear 577
Chapter Objectives 577
12.1 Shear in Straight Members 577
12.2 The Shear Formula 578
12.3 Shear Flow in Built-Up Members 596
12
Combined Loadings 609
Chapter Objectives 609
13.1 Thin-Walled Pressure Vessels 609
13.2 State of Stress Caused by Combined
Loadings 616
13
Mechanical Properties
of Materials 397
Chapter Objectives 397
8.1 The Tension and Compression Test 397
8.2 The Stress–Strain Diagram 399
8.3 Stress–Strain Behavior of Ductile and
Brittle Materials 403
8.4 Strain Energy 407
8.5 Poisson’s Ratio 416
8.6 The Shear Stress–Strain Diagram 418
8
Axial Load 429
Chapter Objectives 429
9.1 Saint-Venant’s Principle 429
9.2 Elastic Deformation of an Axially
Loaded Member 431
9.3 Principle of Superposition 446
9.4 Statically Indeterminate Axially Loaded
Members 446
9.5 The Force Method of Analysis for Axially
Loaded Members 453
9.6 Thermal Stress 459
9
Stress and Strain 329
Chapter Objectives 329
7.1 Introduction 329
7.2 Internal Resultant Loadings 330
7.3 Stress 344
7.4 Average Normal Stress in an
Axially Loaded Bar 346
7.5 Average Shear Stress 353
7.6 Allowable Stress Design 364
7.7 Deformation 379
7.8 Strain 380
7contents 17
Stress and Strain
Transformation 637
Chapter Objectives 637
14.1 Plane-Stress Transformation 637
14.2 General Equations of Plane-Stress
Transformation 642
14.3 Principal Stresses and Maximum
In-Plane Shear Stress 645
14.4 Mohr’s Circle—Plane Stress 661
14.5 Absolute Maximum Shear Stress 673
14.6 Plane Strain 679
14.7 General Equations of Plane-Strain
Transformation 680
*14.8 Mohr’s Circle—Plane Strain 688
*14.9 Absolute Maximum Shear Strain 696
14.10 Strain Rosettes 698
14.11 Material Property Relationships 700
14
Design of Beams and
Shafts 717
Chapter Objectives 717
15.1 Basis for Beam Design 717
15.2 Prismatic Beam Design 720
15
Deflection of Beams
and Shafts 735
Chapter Objectives 735
16.1 The Elastic Curve 735
16.2 Slope and Displacement by
Integration 739
*16.3 Discontinuity Functions 757
16.4 Method of Superposition 768
16.5 Statically Indeterminate Beams and
Shafts—Method of Superposition 776
16
17 Buckling of Columns 795
Chapter Objectives 795
17.1 Critical Load 795
17.2 Ideal Column with Pin Supports 798
17.3 Columns Having Various Types of
Supports 804
*17.4 The Secant Formula 816
Appendix
A Mathematical Review and Expressions 828
B Geometric Properties of An Area and
Volume 832
C Geometric Properties of Wide-Flange
Sections 834
D Slopes and Deflections of Beams 837
Preliminary Problems Solutions 839
Fundamental Problems
Solutions and Answers 858
Selected Answers 891
Index 916
INDEX
A
Absolute maximum shear strain, 696–697, 713
Absolute maximum shear stress, 673–676, 712
Allowable stress (sallow), 364–365, 723, 733
Allowable stress design (ASD), 364–371, 393
Angle of twist, 472–473, 492–499, 513
circular shafts, 472–473
constant cross-sectional area (A), 493–494
internal torque and, 492–493, 496
multiple torques, 494
procedure for analysis of, 496
sign convention for, 495
torsion and, 472–473, 492–499, 513
torsional deformation and, 472–473
Angles (u), 35, 59–61, 82, 92–93, 219–221.
See also Angle of twist
Cartesian vectors, 58–61
coordinate direction (a, b, g), 59–60, 92–93
dot products and, 82, 93
dry friction (f), 219–220
horizontal, 60–61
kinetic friction (fk), 220–221
line of action (direction) and, 35
static friction (fs), 219, 221
vertical (f), 60–61
Anisotropic material, 346
Area (A), 290, 310–314, 319–321, 325–326, 403, 432–433,
467, 832–833
centroid (C) of, 290, 325, 832–833
composite, 319–321, 326
constant cross-sectional, 432–433, 467
moment of inertia (I ) for, 310–314,
319–321, 326, 832–833
parallel-axis theorem for, 311–314, 326
percent reduction in, 403
procedures for analysis of, 312, 319
Arrow notation, 35, 49, 91
Axes, 98, 119–123, 161–165, 170, 543–546, 548, 562–563
bending applied to, 543–546
direction and, 98
distributed loading along single, 161–165
line of action, 119, 170
longitudinal, 543–545
moment, 98
moment of force about, 119–123, 170
neutral, 543, 548, 562, 565
principal, 562–563
projection, 120
resultant force on, 119–123, 170
scalar analysis of, 119
unsymmetric bending and, 562–563
vector analysis of, 120–121
Axial loads, 346–352, 392, 428–469, 795–797, 816–821, 825
bars, 346–352, 392
buckling from, 795–797, 816–821, 825
columns, 795–797, 816–821, 825
constant cross-sectional area (A),
432–433, 467
cross section of, 346
displacement (d), 431–438, 447–452, 467
eccentric applications, 816–821, 827
elastic deformation in members,
431–438, 467
force (flexibility) method of analysis, 453–454
principle of superposition for, 446, 467
procedures for analysis of, 434, 448, 453–454
relative displacement (d), 431–438, 466
Saint-Venant’s principle for, 429–431, 466
sign convention for, 433, 467
statically indeterminate members,
446–452, 467
stress (s) and, 346–352, 392
thermal stress and, 459–462, 467
Axis of symmetry, 543, 562
B
Ball-and-socket joints, 203
Base units, 26
Beams, 516–575, 576–607, 716–733, 734–793, 834–839
bearing plates, 718
bending, 516–575
built-up members, 596–600, 605, 722, 733
cantilevered, 839
concentrated forces and moments, 526
deflection of, 718, 734–793, 838–839
deformation of, 543–546
design of, 716–733
discontinuity functions for, 757–765, 790
distributed loads, 524–526
equations for, 838–839
fastener spacing, 597, 605
flexure formula for, 547–553, 573
force (flexibility) method for, 777–780
glulam, 722
graphical representations of, 524–533, 572
load-displacement relationships, 777–780
longitudinal shear stress in, 577–578
916Index 917
Beams (continued)
method of integration for, 739–749, 790
method of superposition for, 768–772, 776–785, 791
moment diagrams, 735–749, 790
plate girders, 719
prismatic, 720–727
procedures for analysis of, 519, 527, 550, 584, 723,
742, 762, 780
section modulus (S), 720
shear and moment diagrams, 517–533, 572
shear flow (q), 596–600, 605
shear formula for, 578–589, 605
sign convention for, 518, 526, 572
simply supported, 838
statically indeterminate members,
776–785, 791
steel sections, 721
stress trajectories, 719
transverse shear, 576–607
unsymmetric bending, 562–568, 573
warping, 578
wide-flange sections, 834–837
wood sections, 721
Bearing plates, 718
Bearing supports, 203
Bending, 516–575
axis of symmetry, 543, 562
beams, 516–575
deformation, 543–546
flexure formula for,
547–553, 573
neutral axis, 543, 548, 562, 565
neutral surface, 543, 562
principal axis, 562–563
procedures for analysis of, 519, 527, 550
shear and moment diagrams,
517–533, 572
straight members, 543–546, 573
unsymmetric, 562–568, 573
Bending moment (M), 331–332, 526, 543–546, 548–549,
562–568, 572–573
arbitrarily applied, 564
deformation of straight members,
543–546, 572
flexure formula for, 548–549, 573
internal resultant loadings, 331–332
principal axis, applied to, 562–563, 573
shear and moment diagram regions of concentration, 526
unsymmetric bending, 562–568, 573
Bending stress, 723, 733
Biaxial stress, 611
Bifurcation point, 797
Bridge trusses, 242
Brittle materials, 405, 424
Buckling, 794–827
axial loads, 795–797, 816–821, 825
bifurcation point, 797
columns, 794–827
critical load (Pcr) for, 795–797, 825
eccentric loading, 816–821, 825
equilibrium and, 796–797
lateral deflection, 795–797
Built-up members, 596–600, 605, 722–723, 733
design of, 722–723, 733
fastener spacing, 597, 605, 723
plate girders for, 722
shear flow (q) in, 596–600, 605
Bulk modulus (k), 703, 713
C
Cartesian stress and strain components, 381
Cartesian vectors, 50, 58–64, 70–75, 81, 92–93, 102–103,
105–107, 169
addition of, 61
coordinate direction angles (a), 59–60
coplanar forces, notation of, 50
cross product, formulation of,
102–103, 169
direction of, 58–61, 92–93
dot product and, 81, 93
force vectors, 73–75
horizontal angle (u), 60–61
magnitude of, 59, 92
position vectors for, 70–72, 169
rectangular components, 58
resultant forces, formulation of, 61–62, 93
resultant moments, formulation of,
105–107, 169
right-hand rule for, 58, 101–102
three-dimensional components, 58–61
unit vectors, 58–61, 73–75, 92
vertical angle (f), 60–61
x, y, z coordinates, 59–60, 70
Center of gravity (G), 180, 287–289, 291, 301–302, 325
composite bodies, 301–302, 325
free-body diagram location, 180
procedures for analysis of, 291, 302
rigid-body equilibrium and, 180
specific weight (constant density) and, 301
weight (W) and, 180, 287–289, 325
Centroid (C), 162, 171, 289–294, 325,
832–833
area (A), 290, 325, 832–833
distributed loading, 162, 171
procedure for analysis of, 291
volume (V), 289, 325, 832–833918 Index
Circular shafts, torsional deformation of, 471–473, 513
Coefficients of friction (μ), 219–221, 237
Cohesive material, 344
Collinear vectors, 37, 91
Columns, 794–827
critical load (Pcr) of, 795–797,
800–801, 804, 820, 825
deflection equations for, 798–801,
817–818
design of, 820
eccentric loading, 816–821, 825
effective length, 805
Euler load, 800, 825
fixed-supported (braced), 804
ideal, 798–803
lateral deflection of, 795–797
pin-supported, 798–803
Secant formula for, 816–821, 825
Combined loadings, 608–635
biaxial stress, 611
cylindrical (hoop) stress, 610–611, 632
cylindrical vessels, 610–611, 632
procedure for analysis of, 616–617
radial stress, 611
spherical vessels, 611, 632
state of stress caused by, 616–623, 632
thin-walled pressure vessels, 609–612, 632
Compatibility (kinematic)
conditions, 447
Component vectors, 36, 38–39, 49–54
Composite bodies, 301–304, 319–321, 325–326
area (A), 319–321, 326
center of gravity (G) and centroid of, 301–302, 325
moment of inertia for, 319–321, 326
procedures for analysis of, 302, 319
specific weight and, 301
Compression test, 397–398
Compressive forces, 243–244, 257–258
Concentrated force, 22
Concurrent forces, 50, 61, 93, 149, 193
couple system simplification, 149
resultants, 50, 92
three-force member equilibrium, 193
Continuous material, 344
Coplanar forces, 49–54, 92, 138–140, 149, 161, 177–185,
187–194, 332
Cartesian vector notation, 50
couple system simplification,
138–140, 149
distributed loads, 161
equations of equilibrium for, 187–192
internal resultant loadings, 332
procedures for analysis of, 182, 188
resultants, 50–51, 92
rigid-body equilibrium and, 177–185, 187–194
scalar notation, 49
support reactions for, 177–185
three-force members, 193–194
two-force members, 193–194
Cosine law, 40
Coulomb friction, 218. See also
Dry friction
Couple, 128–133, 138–143, 149–154,
170–171, 177
concurrent force systems, 149
coplanar force systems, 138–140,
149, 177
equivalent, 129
moment of, 128–133, 170
parallel force systems, 150
procedures for analysis of, 140, 150
resultant moment (MR), 129–130
rigid-body equilibrium and, 177
scalar formulation, 128
system simplification, 138–143,
149–154, 171
vector formulation, 128, 170
Critical load (Pcr), 795–797, 800–801, 804, 820, 825
bifurcation point, 797
buckling and, 795–797, 825
column design and, 820
deflection and, 798–801
equilibrium and, 796–797
Euler load, 800, 825
fixed supported (braced), 804
pin-supported columns, 800–801, 825
Cross product, 101–103, 169
Cross sections, 330–332, 344–348, 392, 432–433, 467
axially loads, 346–348, 432–433, 467
constant area (A), 432–433, 467
internal resultant loading,
330–332, 392
stress distribution, 344–348
transverse shear moment (Q), 580–581
Cylindrical (hoop) stress, 610–611, 632
Cylindrical vessels, 610–611, 632
D
Deflection, 718, 734–793, 795–797,
816–821, 825, 838–839. See also Buckling
beams, 718, 734–793, 838–839
boundary conditions, 740
cantilevered beams, 838
column buckling, 795–797,
816–821, 825
continuity conditions, 740
coordinates for, 741
critical load (Pcr), 795–797, 825Index 919
Deflection (continued)
discontinuity functions for,
757–765, 790
eccentric loading, 816–821, 825
elastic curve, 735–739, 790, 838–839
flexural rigidity (EI ), 740
lateral (buckling), 795–797
method of integration for,
739–749, 790
method of superposition for, 768–772, 776–785, 791
moment–curvature relationship, 738
moment diagrams, 735–749, 790
procedures for analysis of, 742, 762, 780
Secant formula for, 816–821, 825
sign conventions for, 751
simply supported beams, 838
slope equations, 739–749, 790, 838–839
statically indeterminate members,
776–785, 791
Deformation, 346, 379–385, 393, 397–398, 400–401,
403–417, 424–425, 429–438, 543–546, 573, 578
axially loaded members, 431–438
bending, 543–546, 573
brittle materials, 405, 424
circular shafts, 471–473, 513
displacement (d) and, 431–438,
447, 452, 467
ductile materials, 403–404, 424
elastic, 431–438, 467
localized, 429–430
necking, 401
permanent, 400, 424
plastic, 400
Poisson’s ratio (ν) for, 416–417, 425
relative displacement (d), 431–438
Saint-Venant’s principle for,
429–431, 466
small strain analysis, 382
straight members (beams), 543–546, 573
strain and, 380–385, 393
strain energy from, 407–411, 425
strain hardening, 401
stress–strain diagrams for,
400–401, 424
tension and compression tests for,
397–398
torsional, 471–473, 513
twisting, 471–473
uniform, 346
warping, 578
yielding, 400
Degree of indeterminacy, 776
Derivatives, 830
Design. See Structural design
Determinant notation, 103
Dilatation (e), 702–703, 713
Dimensional homogeneity, 28
Dimensionless quantity, 380, 393
Direction, 35, 38, 49, 58–61, 70–71, 73, 91–93, 98, 101–102,
104, 128, 169–170, 244, 250, 258, 719
angle (u) for, 35, 60–61
arrow notation for, 49
Cartesian vectors, 58–61, 92–93
coordinate angles (a, b, g), 59–60, 92–93
cosines, 59–60
couple moments, 128
cross product, 101–102
force and, 73–75, 82, 92–93, 98, 102–103, 104, 169–170
by inspection, 244, 250, 258
line of action, 35
moment axis, 98, 170
position vectors, 70–71
resultant forces, 38–39
resultant moments (MR), 98, 102–103, 169–170
right-hand rule for, 58, 98, 102–103, 104, 128, 169
scalar formulation and, 98, 169
sense of, 35, 91
sign convention for, 98
stress trajectories, 719
truss member forces, 244, 250, 258
unit vectors, 50, 58, 73–75, 92
vectors and, 35, 38, 49, 58–61, 70–71, 73, 91–92,
102–103, 104
Discontinuity functions, 757–765, 790
applications of, 761
deflection and, 757–765, 790
Macaulay functions, 758
procedure for analysis of, 762
singularity functions, 759–760
Displacement (d), 431–438, 447–452, 467
axially loaded members, 431–438, 448–452
compatibility (kinematic) conditions for, 447–452, 467
constant cross-sectional area (A),
432–433, 467
principle of superposition for, 446, 467
procedure for analysis of, 434
relative, 431–438
statically indeterminate members, 447–452, 467
Distributed loading, 161–165, 171, 344–345, 477, 524–526,
757–765, 790
axially loaded members, 346–348
axis (single), along, 161–165
centroid (C) location, 162, 171
coplanar, 161–165, 171
cross sections for, 344–348
deflection and, 757–765, 790
discontinuity functions for, 757–765, 790
Macaulay functions and, 758920 Index
magnitude of resultant force, 161
resultant forces of, 162–165
shear and moment diagram regions, 524–526
shear stress (t), 477
singularity functions, 759–760
stress (s) and, 344–348
torsion and, 477
Dot notation, 27
Dot product, 81–85, 93, 120
Dry friction, 218–235, 237
angles (f) of, 219–221
coefficients of (μ), 219–221, 237
distributed and frictional loads, 218
impending motion (static) and, 219, 221, 222–228, 237
motion (kinetic), 220–221, 237
normal forces and, 218
procedure for analysis of, 225
rigid-body equilibrium and, 218–235, 237
rolling and, 221
slipping (sliding) and, 219–223, 237
theory of, 218
tipping and, 218, 224
Ductile materials, 403–404, 424
E
Eccentric loading, 816–821, 825
Effective length, 805
Elastic behavior, 399–401, 431–438, 467
axially loaded members, 431–438, 467
deformation and, 431–438, 467
stress–strain diagrams for, 399–401
stress/strain transformation and, 702–703
Elastic curve, 735–739, 790, 838–839
Electrical-resistance strain gage, 398
Engineering notation, 28
Engineering (nominal) stress/strain, 399
Equilibrium, 174–239, 347–348, 354, 796–797
bifurcation point, 797
column buckling and, 796–797
column buckling and, 796–797
conditions for, 175–176
dry friction and, 218–235
equations of, 187–192, 208–211
free-body diagrams for, 177–185, 203–207
friction force equations and, 218, 223
neutral, 797
procedures for analysis of, 182, 188,
209, 225
rigid bodies, 174–239
scalar equations of, 208
shear stress (t) and, 354
stable, 796
stress (s) and, 347–348, 354
support reactions, 177–179, 203–207, 236–237
three-dimensional rigid-bodies, 203–217, 237
two-dimensional rigid bodies, 176–202, 237
unstable, 219, 796
vector equations of, 208
zero force for, 176
Equivalent system, 138–143
Euler load, 800, 825
Extensometer, 398
External effects of force systems, 138. See also Rotation;
Translation
F
Factor of safety (F.S.), 364–365, 393
Fastener spacing in built-up beams, 597, 605, 723
Fixed supports, 177, 804
Flexibility (force) method, 777–780
Flexural rigidity (EI), 740
Flexure formula, 547–553, 573
bending moment (M) for, 548–549, 573
bending stress from, 547–553, 573
moment of inertia (I) for, 549
neutral axis location for, 548
procedure of analysis for, 550
Force (F), 22–26, 34–95, 119–123, 128–133, 169–170,
176–180, 193–194, 218–237, 243–244, 257–258, 331–332,
379, 392–393, 526. See also Dry friction; Frictional
forces; Weight
addition of, 38–43
axis, moment of about, 119–123, 170
component vectors of, 38–39
compressive, 243–244, 257–258
concentrated, 23
concept of, 22
concurrent, 50, 61, 93, 193
coplanar, 49–54, 92, 332
couple, moment of, 128–133, 170
deformation from, 379, 393
directed along a line, 73–75, 82, 93
free-body diagrams for, 177–180
frictional, 218–235, 237
gravitational, 25
internal, 180
internal resultant loadings, 331–332, 392
moment (MO) of, 119–123, 170
Newton’s laws and, 24–25
normal (N), 218, 331–332
parallelogram laws for, 36, 40
position vectors and, 70–72, 93
procedure for analysis of, 40
resultants of, 38–39, 50–51, 61, 91–93, 129, 170
rigid-body equilibrium and, 176–180
scalar determination of, 35–36, 119, 128, 169Index 921
Force (continued)
shear (V), 331–332
shear and moment diagram regions
of concentration, 526
tensile, 243–244, 257–258
triangle rule for, 36–37, 91
two-and three-force members, equilibrium of, 193–194
units of, 26
unknown forces, 177, 188, 203, 206, 209, 236–237, 244
vector determination of, 34–95, 120–121, 128, 169
zero, 176
Force (flexibility) method of analysis, 453–454, 777–780
Force systems, 96–173, 174–239, 242–243, 282
axis, moment of about, 119–123, 170
Cartesian vector formulation, 102–103, 105–107, 169
concurrent, 149, 171, 193, 242, 282
coplanar, 139–140, 149, 161, 177–185, 187–194, 242
couple moments, 128–133, 138–143, 149–154,
170–171, 177
cross product, 101–103, 169
distributed loads, 161–165, 171
dry friction and, 218–235, 243
equilibrium of, 174–239
equivalent, 138–143, 171
external effects from, 138
free-body diagrams for, 177–185, 203–207
frictional forces on, 218–235, 237
moments (MO), 97–107, 119–123, 128–133, 169
parallel, 150, 171, 193
perpendicular, 149
principle of moments, 108–110, 169
principle of transmissibility, 104, 138
procedures for analysis of, 140, 150, 182, 188, 209
resultants, 96–173
rigid-bodies, 174–239
rotational motion and, 138–140, 177, 203
scalar formulation of, 97–100, 119, 128, 169
simplification of, 138–143, 149–154, 171
support reactions and, 177–179, 203–207, 236–237
three-dimensional rigid-bodies, 203–217, 237
translational motion and, 138–140, 177, 203
truss members, 242–243, 282
two-dimensional (coplanar) rigid bodies, 176–202, 236
vector formulation of, 103–105, 120–121, 128, 169
Fracture stress (sf), 401
Frames, 266–281, 283
free-body diagrams for, 266–273, 283
multiforce members of, 266
procedure for analysis of, 269
structural analysis of, 266–281, 283
Free-body diagrams, 177–185, 188, 203–207, 209, 218–219,
236–237, 244–251, 257–262, 266–273, 282–283
center of gravity (G), 180
frames and machines, 266–273, 283
frictional forces, 218–219, 237
idealized models, 180–181
internal forces and, 180
procedures for analysis using, 182, 188, 209
springs, 180
structural analysis using, 244–251, 257–262, 266–273,
282–283
support reactions, 177–179, 203–207
three-dimensional rigid bodies, 203–207, 209, 237
trusses, 244–251, 257–262, 282–283
two-dimensional rigid bodies, 177–185, 188, 236
unknown forces, 177, 188, 203, 206, 209, 236–237
weight (W), 180
Free vector, 128, 138–139
Friction, 218. See also Frictional forces; Dry friction
Frictional forces, 218–235, 237. See also Dry friction
angles (f) of, 219–221
coefficients of (μ), 219–221, 237
dry friction and, 218–235
equilibrium equations and, 218, 223, 237
free-body diagrams for, 218–219, 237
kinetic (motion), 220–221, 237
normal (N), 218
procedure for analysis of, 225
rigid-body equilibrium and, 218–235, 237
static (impending motion), 219, 221, 222–228
G
Gage-length distance (L0), 398
Glulam beams, 722
Gravitational attraction, 25
Gravity. See Center of gravity; Weight
Gusset plate, 242
H
Hinge supports, 203
Homogeneous material, 346
Hooke’s law, 400, 402, 407–418, 424, 700–701, 713
linear elastic behavior and, 407–418
modulus of elasticity from, 400, 402, 424
shear modulus of elasticity from, 418
stress/strain transformation and, 700–701, 713
Hoop (cylindrical) stress, 610–611, 632
Horizontal angle (u), 60–61
Hydrostatic loading, 703, 713
Hyperbolic functions, 830
I
Idealized models of rigid bodies, 180–181
Impending motion, 219, 221, 222–228
Inertia. See Moment of inertia
Inflection point, 736–737
In-plane shear strain, 684
In-plane shear stress, 645–651, 711922 Index
Integrals, 831
Integration. See Method of integration
Internal forces, 180
Internal resultant loadings, 330–343, 392
bending moment (M) in, 331–332
coplanar systems, 332
cross sections for, 330–332, 392
normal force (N) in, 331–332
procedure for analysis of, 333
shear force (V) in, 331–332
three-dimensional components, 331
torsional moment (T) in, 331
Internal torque, 474–475, 492–493, 496
International System (SI) of units, 26–27
Isotropic material, 346
J
Joint connections, 242
K
Kilogram (kg), unit of, 26
Kinetic frictional forces (motion), 220–221, 237
L
Lateral contraction, 416
Lateral deflection, 795–797
Length, units of, 26
Line of action, 35, 119, 138, 149, 162, 169
Linear coefficient of thermal expansion (a), 459
Load-displacement relationships, 444–452, 467, 777–780
axially loaded members, 444–452, 467
beam deflection and, 777–780
statically indeterminate members, 444–452, 467, 777–780
Loads. See Axial loads; Combined loadings; Distributed
loadings; Internal resultant loadings
Longitudinal axis, 543–545
Longitudinal elongation, 416
Longitudinal shear stress, 577–578
M
Macaulay functions, 758
Machines, 266. See also Frames; Structural analysis
Magnitude, 35, 38–39, 49, 59, 91–92, 98, 101, 104, 128, 161,
169
arrow notation for, 35, 49
Cartesian vectors, 59, 92
coplanar force systems, 49
couple moments, 128
cross product and, 101
distributed loadings and, 161
moments of a force and, 98, 101, 104
resultant forces, 38–39, 161
scalar determination of, 35, 91, 98, 169
vectors and, 35, 38–39, 49, 59, 91–92, 104
Mass, quantity of, 22
Mass, units of, 26
Material properties, 397–427, 700–707
brittle materials, 405, 424
compression test for, 397–398
dilatation (e), 702–703, 713
ductile materials, 403–404, 424
elastic behavior, 399–401, 702–703
Hooke’s law, 400, 402, 418, 424, 700–701, 713
necking, 401
Poisson’s ratio (ν) for, 416–417, 425
shear stress–strain diagrams for, 418–421, 425
stiffness, 406
strain energy, 407–411, 425
strain hardening, 401, 406
stress and strain transformation effects,
700–707
stress–strain diagrams for, 399–406, 418–421,
424–425
tension test for, 397–398
volume (hydrostatic loading), 703, 713
yielding, 400
Mechanics of materials, 21–25, 328–395.
See also Material properties
deformation, 379, 393
engineering study of, 21–22, 329
fundamental concepts of, 23–25
internal resultant loadings, 330–343, 392
Newton’s laws for, 24–25
procedure for analysis of problems, 29–30
strain (P), 380–390, 393
stress (s), 344–378, 392–393
Meter (m), unit of, 26
Method of integration, 739–749, 790
boundary conditions, 740
continuity conditions, 740
flexural rigidity (EI), 740
procedure for analysis of, 742
slope equations, 739–749, 790
Method of joints, 244–249, 282
Method of sections, 257–262, 283
Method of superposition. See Superposition
Modulus of elasticity (E), 400, 702–703
Modulus of resilience (ur), 407
Modulus of rigidity (G), 418
Modulus of toughness (ut), 408
Mohr’s circle, 661–667, 688–692, 712–713
plane strain, 688–692, 713
plane stress, 661–667, 712
Moment arm (distance), 98
Moment axis (direction), 98
Moment–curvature relationship, 738
Moment diagrams, 735–749, 790
elastic curve, 735–739, 790
inflection point, 736–737Index 923
Moment of inertia (I), 310–314, 319–321, 326, 474, 549,
562–563, 573, 801, 832–833
area (A), 310–314, 319–321, 326, 832–833
column buckling, 801
composite bodies, 319–321, 326
flexure formula and, 549
least, 801
parallel-axis theorem for, 311–314, 326
polar, 310, 326, 475–476
principal axis of, 562–563, 573
procedures for analysis of, 312, 319
product of, 563
torsion formula and, 474
unsymmetric bending and, 562–563, 573
Moments (M), 96–173, 331–332, 526, 580–581. See also
Bending moment; Moment of inertia
Cartesian vector formulation, 102–103,
105–107, 169
couple, 128–133, 138–143, 149–154, 170–171
cross product for, 101–103
cross-sectional (Q), 580–581
direction of, 98, 101–102, 104, 169
dot product for, 120
force about an axis, 119–123, 170
force and couple systems, simplification of, 138–143,
149–154, 171
internal (M0) loadings, 331–332
magnitude of, 98, 101, 104, 169
principle of, 108–110
principle of transmissibility, 104, 138
procedures for analysis of, 140, 150
resultant (MR), 98–100, 105–107
right-hand rule for, 98, 101–102, 169–170
scalar formulation of, 97–100, 119, 128, 169
shear and moment diagram regions
of concentration, 526
sign convention for, 98
torque as, 97
torsional (T ), 331
transverse shear and, 580–581
vector formulation of, 104–107, 120–121, 128, 169
Motion, 24, 138–143, 177, 203, 218–235, 222–228
force and couple system simplification,
138–143
frictional forces and, 218–235, 237
impending, 219, 221, 222–228, 237
kinetic frictional forces, 220–221, 237
Newton’s laws of, 24
rigid-body equilibrium and, 218–235
rolling, 221
rotational, 138–140, 177, 203
slipping (sliding), 219–223
static frictional force and, 219, 221
supports for prevention of, 177, 203
tipping, 218, 224
translational, 138–140, 177, 203
Multiforce members, 266
N
Necking, 401
Neutral axis, 543, 548, 562, 565
Neutral equilibrium, 797
Newton (N), unit of, 26
Newton’s law of gravitational attraction, 25
Newton’s laws of motion, 24
Nominal (engineering) stress/strain, 399
Nominal dimensions, 721
Normal force (N), internal resultant loadings, 331–332
Normal strain (P), 380–382, 393
Normal stress (s), 345–352, 392, 642–643
Numerical calculations, engineering use of, 28–29
O
Offset method, 403
P
Parallel force systems, 150, 193
Parallel-axis theorem, 311–314, 326
Parallelogram law, 36–37, 40, 91
Particles, concept of, 23
Pascal (Pa), unit of, 345
Percent elongation, 403, 424
Percent reduction in area, 403, 424
Perfectly plastic materials, 400
Permanent set, 406
Perpendicular force systems, 149
Pin connections, 242–243
Pin supports, 203, 798–803
Planar trusses, 241
Plane strain, 679–697, 713
absolute maximum shear strain, 696–697, 713
equations for transformation, 680–688
maximum in-plane shear strain, 684
Mohr’s circle for, 688–692, 713
normal and shear strain components, 681–683
principle strains, 684
procedures for analysis of, 688–689
sign convention for, 680
transformation of, 679–688
Plane stress, 637–676, 711–712
absolute maximum shear stress, 673–676, 712
equations for transformation, 642–644
in-plane shear stress, 645–651, 711
Mohr’s circle for, 661–667, 712
normal and shear stress components, 642–643
principle stresses, 645–651
procedures for analysis of, 639, 643, 663–664
sign convention for, 642
transformation of, 637–644924 Index
Plastic deformation, 400
Plate girders, 719
Poisson’s ratio (ν), 416–417, 425
Polar moment of inertia, 310, 326, 475–476
Position vectors, 70–72, 93, 169
Power transmission, 482–483, 513
Power-series expansion, 830
Primary beam, 777
Principal axis, 562–563, 573
Principle of moments, 108–110, 169
Principle of transmissibility, 104, 138
Principle strains, 684
Principle stresses, 645–651
Prismatic beams, 720–727
Product of inertia (I), 563
Projection of a moment, 120
Proportional limit (spl), 399, 418
Purlins, 241
Pythagorean theorem, 829
Q
Quadratic formula, 830
R
Radial stress, 611
Radius of gyration, 801
Rectangular components, 50–51, 58–64, 70–71, 92–93
three dimensional, 58–64, 70–71, 92–93
two dimensional, 50–51, 92
Redundants, 776–779, 791
Relative displacement (d), 431–438
Resultants, 36–39, 50–51, 61–64, 91–93, 96–173, 330–343,
392
axis, moment of force about, 119–123, 161–165
Cartesian vector formulation, 61–62, 93, 102–103, 105–
107, 169
centroid (C) location and, 162
collinear vectors, 37, 91
concurrent forces, 50, 61, 93, 149
coplanar force, 50–51, 92, 149
couple moments, 128–133, 138–143, 149–154, 170–171
cross product, 101–103, 169
direction of, 98, 101–102, 104, 169
distributed loadings, 161–165
equivalent force systems, 138–143
force components, 38–39
force and couple moments,simplification of, 138–143,
149–154, 171
force systems, 96–173
internal loadings, 330–343, 392
magnitude of, 98, 101, 104, 161
moments (MR), 98–100, 105–107, 129–130, 138–143
parallel force systems, 150
parallelogram law for, 36, 40, 91
perpendicular force systems, 149
principle of moments, 108–110
principle of transmissibility, 104, 138
procedures for analysis of, 140, 150
rectangular components, 50–51, 92
right-hand rule for, 98, 101–102, 104, 128
scalar formulation of moment, 98, 128, 169
triangle rule for, 36–37, 91
vector addition for, 36–38, 61–64, 93
vector formulation of moment, 104–107, 128, 169
vector subtraction for, 37
Right-hand rule, 58, 98, 101–102, 104, 128
Rigid bodies, 23, 174–239
center of gravity (G), 180
concept of, 23
dry friction and, 218–235, 237
equations of equilibrium for, 187–192, 208–211
equilibrium of, 174–239
free-body diagrams for, 177–185, 203–207, 236, 237
frictional forces on, 218–235, 237
idealized models of, 180–181
impending motion (static) of, 219, 221, 222–228
internal forces and, 180
procedures for analysis of, 182, 188, 209, 225
rotational motion of, 177, 203
springs, 180
support reactions, 177–179, 203–207, 236–237
three-dimensional, equilibrium of, 203–217, 237
three-force members, 193–194
translational motion of, 177, 203
two-dimensional (coplanar), equilibrium of,
176–202, 236
two-force members, 193–194
weight (W), 180
Rolled shapes, 721
Roller supports, 177
Rolling motion, 221
Roof trusses, 241–242
Rotational motion, 138–140, 177, 203
force and couple system simplification, 138–140
supports for prevention of, 177, 203
Rounding off numbers, 29
S
Saint-Venant’s principle, 429–431, 466
Scalar triple product, 120
Scalars, 35–36, 49, 91, 97–100, 119, 128, 169, 208
coplanar forces, notation for, 49
couple moments, 128
division of a vector by, 36
equations of equilibrium, 208
moment of force about an axis, 119
moment of a force, formulation of, 97–100, 119, 128, 169
multiplication of a vector by, 36
quantity, 35, 91
sign convention for, 98, 169Index 925
Secant formula, 816–821, 825
Seconds (s), unit of, 26
Section modulus (S), 720
Shafts, 471–473, 482–483, 492–499, 506–509, 513
angle of twist, 472–473, 492–499, 513
circular, 471–473, 513
internal torque, 492–493, 496
power transmission, design for, 482–483
procedures for analysis of, 496, 507
statically indeterminate, 506–509, 513
torsional deformation, 471–473, 513
Shear and moment diagrams, 517–533, 572
beams, 517–533, 572
concentrated forces and moments, 526
distributed loads, 524–526
graphical methods for, 524–533, 572
procedures for analysis of, 519, 527
sign convention for, 518, 526, 572
Shear flow (q), 596–600, 605
Shear force (V), internal resultant loadings, 331–332
Shear formula, 578–589, 605
Shear modulus (G), 418, 425, 702, 713
Shear strain (g), 381, 393, 474, 679–687, 696–697, 713
absolute maximum, 696–697, 713
deformation and, 381, 393
linear variation in, 474
maximum in-plane, 684
plane strain components, 681–683
plane strain transformation and, 679–687, 696–697, 713
Shear stress (t), 345, 353–357, 392, 474, 477, 577–579,
642–651, 673–676, 711–712. See also Transverse shear
absolute maximum, 673–676, 712
beams 577–579
direct (simple), 353
distribution of, 345, 477, 578–579
equilibrium, 354
in-plane, 645–651, 711
linear variation in, 474
longitudinal, 577–578
plane stress components, 642–643
plane stress transformation and, 642–651, 673–676,
711–712
procedure for analysis of, 355
torsion and, 474, 477
Shear stress–strain diagrams, 418–421, 425
Significant figures, 28–29
Sine law, 40
Singularity functions, 759–760
Slenderness ratio, 801–802
Sliding vector, 104, 138
Slipping (sliding), 219–223, 237
Slope equations, 739–749, 790, 838–839
Small strain analysis, 382
Specific weight (constant density), 301
Spherical vessels, 611, 632
Springs, free-body diagrams of, 180
Stable equilibrium, 796
Static frictional forces (impending motion), 219, 221,
222–228, 237
Statically indeterminate members, 446–454, 467, 506–509,
513, 776–785, 791
axially loaded, 446–454, 467
beams, 776–785, 791
compatibility (kinematic) conditions for, 447–452, 467
deflection of, 776–785, 791
degree of indeterminacy, 776
force (flexibility) method of analysis, 453–454, 777–780
load-displacement relationships, 447–452, 467, 777–780
method of superposition for, 446–452, 776–785, 791
procedures for analysis of, 448, 507, 780
redundants (reactions) of, 776–779, 791
shafts, 506–509, 513
torque loaded, 506–509, 513
Steel, stress–strain diagram for, 402
Steel sections, structural design and, 721
Stiffness, 406
Straight members. See Beams
Strain (P), 380–390, 393, 399, 684. See also Plane strain
Cartesian components, 381
deformation and, 380–385, 393
dimensionless quantity of, 380, 393
nominal (engineering), 399
normal (P), 380–382, 393
principle, 684
shear (g), 381, 393
small strain analysis, 382
units of, 380
Strain energy, 407–411, 425
Strain hardening, 401, 406
Strain rosettes, 698–699
Stress (s), 344–378, 392–393, 399–400, 459–462, 467,
610–611, 616–623, 632, 645–651, 700, 723, 733. See also
Plane stress
allowable (sallow), 364–365, 723, 733
allowable stress design (ASD), 364–371, 393
axially loaded bars, 346–352, 392
bending, 723, 733
biaxial, 611
combined loadings and, 610–611, 616–623, 632
cylindrical (hoop), 610–611, 632
equilibrium and, 347–348, 354
factor of safety (F.S.), 364–365, 393
loading distribution and, 344–345
nominal (engineering), 399
normal (s), 345–352, 392
principle, 645–651
procedure for analysis of, 349, 355, 366
radial, 611926 Index
shear (t), 345, 353–357, 392, 723, 733
state of, 345, 616–623, 632
thermal, 459–462, 467
triaxial, 700
ultimate (su), 400
uniaxial, 348
units of, 345
Stress and strain transformation, 636–715
absolute maximum shear strain, 696–697, 713
absolute maximum shear stress, 673–676, 712
bulk modulus (k) and, 703, 713
dilatation (e), 702–703, 713
equations for, 642–644, 680–688
Hooke’s law and, 700–701, 713
in-plane shear stress, 645–651, 711
material property relationships, 700–707
modulus of elasticity (E) and, 702–703
Mohr’s circle for, 661–667, 688–692, 712–713
plane strain, 679–697, 713
plane stress, 637–676, 711–712
principle stresses, 645–651
procedures for analysis of, 639, 643, 663–664,
688–689
shear modulus (G) and, 702, 713
strain rosettes, 698–699
triaxial stress, 700
Stress–strain diagrams, 399–421, 424–425
brittle material behavior from, 405, 424
conventional, 399–406, 424
ductile material behavior from, 403–404, 424
elastic behavior, 399–401
fracture stress (sf), 401
modulus of resilience (ur), 407
modulus of rigidity (G), 418
modulus of toughness (ut), 408
nominal (engineering) stress/strain for, 399
proportional limit (spl), 399, 418
shear, 418–421, 425
steel, 402
true, 401
ultimate stress (su), 401, 418
yield point (sY), 400, 406, 408, 424–425
Young’s modulus of elasticity (E), 400
Stress trajectories, 719
Structural analysis, 240–285
frames, 266–281, 283
free-body diagrams for, 244–251, 257–262, 266–273,
282–283
machines, 266–281, 283
method of joints, 244–249, 282
method of sections, 257–262, 283
procedures for, 245, 259, 269
trusses, 241–265, 282–283
zero-force members, 250–252
Structural design, 242–243, 364–371, 393, 482–483,
716–733
allowable bending and shear stress, 723, 733
allowable stress design (ASD), 364–371, 393
beams, 716–733
prismatic beams, 720–727
section modulus (S), 720
shafts, 482–483
stress trajectories, 719
trusses, 242–243
Superposition, 446–452, 467, 768–772, 776–785, 791
axial loads and, 446–452, 467
beams, 768–772, 776–785, 791
deflection and, 768–772, 776–785, 791
displacement (d) and, 446, 467
force (flexibility) method for, 777–780
load-displacement relationships, 446–452, 467, 777–780
method of, 768–772, 776–785, 791
primary beam for, 777
principle of, 446, 467
procedure for analysis of, 780
redundants (reactions) from, 776–779, 791
statically indeterminate members, 447–452, 467,
776–785, 791
Support reactions, 177–179, 203–207, 236–237
free-body diagrams for, 177–179, 203–207
prevention of motion by, 177, 203
three-dimensional rigid-bodies, 203–207, 237
two-dimensional rigid bodies, 177–179, 236
types of, 178–179, 204–205
T
Tensile forces, 243–244, 257–258
Tension test, 397–398
Thermal stress, 459–462, 467
Thin-walled pressure vessels, 609–612, 632
Three-dimensional rigid-bodies, 203–217, 237
equations of equilibrium, 208–211, 237
equilibrium of, 203–217
free-body diagrams for, 203–207
procedure for analysis of, 209
support reactions, 203–207, 237
unknown forces in, 203, 206, 209, 237
Time, units of, 26
Tipping, 218, 224
Torque, 97, 471. See also Moments (M)
Torsion, 470–515
angle of twist, 472–473, 492–499, 513
circular shafts, 471–473, 513
constant cross-sectional area (A), 493–494
deformation, 471–473, 513
internal torque and, 474–475, 492–493, 496
polar moment of inertia and, 310, 326, 475–476
power transmission, 482–483, 513Index 927
Torsion (continued)
procedures for analysis of, 478, 496, 507
shafts, 471–473, 482–483, 506–509, 513
shear stress distribution, 477
statically indeterminate members, 506–509, 513
torsion formula, 474–481, 513
Torsional moment (T), internal resultant loadings, 331
Translational motion, 138–140, 159, 177, 203
force and couple system simplification, 138–140
supports for prevention of, 177, 203
Transmissibility, principle of, 104, 138
Transverse shear, 576–607
beams, 576–607
built-up members, 596–600, 605
cross-sectional moment (Q), 580–581
longitudinal shear stress and, 577–578
procedures for analysis of, 584
shear flow (q), 596–600, 605
shear formula for, 578–589, 605
shear-stress distribution, 578–579, 605
Triangle rule, 36–37, 91
Triaxial stress, 700
Trigonometric functions and identities, 829–830
True stress–strain diagram, 401
Trusses, 241–265, 282–283
compressive forces, 243–244, 257–258
design assumptions, 242–243
forces determined by inspection, 244, 250, 258
free-body diagrams for, 244–251, 257–262, 282–283
joint connections, 242
method of joints, 244–249, 282
method of sections, 257–262, 283
procedures for analysis of, 245, 259
simple, 241–243, 282
structural analysis of, 241–265, 282–283
tensile forces, 243–244, 257–258
zero-force members, 250–252
Twisting, 471–473
Two-dimensional (coplanar) rigid bodies, 176–202, 236
equations of equilibrium, 187–192
equilibrium of, 176–202, 236
free-body diagrams for, 177–185
procedures for analysis of, 182, 188
support reactions, 177–179, 236
three-force members, 193–194
two-force members, 193–194
unknown forces in, 177, 188, 236
U
Ultimate stress (su), 401, 418
Uniaxial stress, 348
Uniform deformation, 346
Unit vectors, 50, 58–61, 73, 73–75, 92
Units of measurement, 26–27, 28, 345, 380, 393, 482, 721
base units, 26
derived units, 26
dimensional homogeneity, 28
dimensionless quantity and, 380, 393
foot-pound-second system, 345
force, 26
International System (SI), 26–27
length, 26
mass, 26
nominal dimensions, 721
power, 482
rules for use, 27
SI prefixes, 26–27
strain, 380
stress, 345
time, 26
weight, 26
Unstable equilibrium, 219, 796
Unsymmetric bending, 562–568, 573
bending moment (M) of, 562–568, 573
moment arbitrarily applied, 564
neutral axis orientation, 565
principal axis, moment applied to, 562–563, 573
product of inertia (I ) for, 563
V
Varignon’s theorem, 108–110
Vectors, 34–95, 101–107, 120–121, 128, 138–143,
169–170, 208
addition, 36–37, 38–43, 49–54, 61–64, 91–93
angle (u), 35, 59–61, 82, 92–93
arrow notation, 35, 49, 91
Cartesian, 50, 58–64, 70–75, 81, 92–93, 102–103,
105–107, 169
collinear, 37, 91
component, 36, 38–39, 49–54
coplanar forces, 49–54
couple moments, 128, 170
cross product for, 101–103, 169–170
directed along a line, 73–75, 82, 93
direction of, 35, 38, 49, 58–61, 70–71, 73, 101–102, 104
division of by a scalar, 36, 91
dot product, 81–85, 93, 120
equations of equilibrium, 208
force and, 34–95, 128, 169
force and couple systems, 138–143
free, 128, 138–139
line of action, 35, 119, 138, 169
magnitude of, 35, 49, 59, 91–92, 101, 104
moment of force about an axis, 120–121, 169
multiplication by a scalar, 36, 91
parallelogram law for, 36–37, 40, 91
position, 70–72, 93, 169
procedures of analysis for, 40928 Index
rectangular components, 50–51, 58–64, 70–71, 92–93
resultant moments and, 105–107, 169
resultants of a force, 36–38, 50–51, 91, 93, 101–107, 129–
130, 169
right-hand rule for, 58
scalars and, 35–36, 49, 91
several forces, 39
sliding, 104, 138
subtraction, 37
three-dimensional components, 58–64, 70–71, 92–93
triangle rule for, 36–37, 91
two-dimensional components, 50–51, 92
unit, 50, 58–61, 73–75, 92
x, y, z coordinates, 58–60, 70, 92–93
Vertical angle (f), 60–61
Volume (V), centroid of, 289, 325, 832–833
Volume changes (hydrostatic loading), 703, 713
W
Warping, 578
Weight (W), 25, 26, 180, 287–289, 325
center of gravity (G) and, 180, 287–289, 325
free-body diagrams and, 180
gravitational force and, 25
rigid-body equilibrium and, 180
units of, 26
Wide-flange sections, 834–837
Wood, ductility of, 404
Wood sections, structural design and, 721
X
x, y, z coordinates, 58–60, 70, 92–93
Y
Yield point (sY), 400, 406, 408, 424–425
Yield strength, 403–404
Yielding, 400
Young’s modulus (E), 400
Z
Zero force, 176. See also Equilibrium
Zero-force members, 250–252

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كتاب Statics and Mechanics of Materials - صفحة 2 761752

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Statics and Mechanics of Materials 5th Edition
R. C. Hibbeler
SI Conversion by
Kai Beng Yap

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CONTENTS
General Principles 21
Chapter Objectives 21
1.1 Mechanics 21
1.2 Fundamental Concepts 22
1.3 The International System of Units 26
1.4 Numerical Calculations 28
1.5 General Procedure for Analysis 29
1
Force Vectors 35
Chapter Objectives 35
2.1 Scalars and Vectors 35
2.2 Vector Operations 36
2.3 Vector Addition of Forces 38
2.4 Addition of a System of Coplanar Forces 49
2.5 Cartesian Vectors 58
2.6 Addition of Cartesian Vectors 61
2.7 Position Vectors 70
2.8 Force Vector Directed Along a Line 73
2.9 Dot Product 81
2
Force System
Resultants 97
Chapter Objectives 97
3.1 Moment of a Force—Scalar Formulation 97
3.2 Cross Product 101
3.3 Moment of a Force—Vector Formulation 104
3.4 Principle of Moments 108
3.5 Moment of a Force about a
Specified Axis 119
3.6 Moment of a Couple 128
3.7 Simplification of a Force and Couple
System 138
3.8 Further Simplification of a Force and
Couple System 149
3.9 Reduction of a Simple Distributed
Loading 161
3
Equilibrium of a
Rigid Body 175
Chapter Objectives 175
4.1 Conditions for Rigid-Body Equilibrium 175
4.2 Free-Body Diagrams 177
4.3 Equations of Equilibrium 187
4.4 Two- and Three-Force Members 193
4.5 Free-Body Diagrams 203
4.6 Equations of Equilibrium 208
4.7 Characteristics of Dry Friction 218
4.8 Problems Involving Dry Friction 222
4
Structural Analysis 241
Chapter Objectives 241
5.1 Simple Trusses 241
5.2 The Method of Joints 244
5.3 Zero-Force Members 250
5.4 The Method of Sections 257
5.5 Frames and Machines 266
5
Center of Gravity,
Centroid, and Moment
of Inertia 287
Chapter Objectives 287
6.1 Center of Gravity and the Centroid
of a Body 287
6.2 Composite Bodies 301
6.3 Moments of Inertia for Areas 310
6.4 Parallel-Axis Theorem for an Area 311
6.5 Moments of Inertia for Composite Areas 319
616 contents
Torsion 471
Chapter Objectives 471
10.1 Torsional Deformation of a
Circular Shaft 471
10.2 The Torsion Formula 474
10.3 Power Transmission 482
10.4 Angle of Twist 492
10.5 Statically Indeterminate Torque-Loaded
Members 506
10
Bending 517
Chapter Objectives 517
11.1 Shear and Moment Diagrams 517
11.2 Graphical Method for Constructing
Shear and Moment Diagrams 524
11.3 Bending Deformation of a
Straight Member 543
11.4 The Flexure Formula 547
11.5 Unsymmetric Bending 562
11
Transverse Shear 577
Chapter Objectives 577
12.1 Shear in Straight Members 577
12.2 The Shear Formula 578
12.3 Shear Flow in Built-Up Members 596
12
Combined Loadings 609
Chapter Objectives 609
13.1 Thin-Walled Pressure Vessels 609
13.2 State of Stress Caused by Combined
Loadings 616
13
Mechanical Properties
of Materials 397
Chapter Objectives 397
8.1 The Tension and Compression Test 397
8.2 The Stress–Strain Diagram 399
8.3 Stress–Strain Behavior of Ductile and
Brittle Materials 403
8.4 Strain Energy 407
8.5 Poisson’s Ratio 416
8.6 The Shear Stress–Strain Diagram 418
8
Axial Load 429
Chapter Objectives 429
9.1 Saint-Venant’s Principle 429
9.2 Elastic Deformation of an Axially
Loaded Member 431
9.3 Principle of Superposition 446
9.4 Statically Indeterminate Axially Loaded
Members 446
9.5 The Force Method of Analysis for Axially
Loaded Members 453
9.6 Thermal Stress 459
9
Stress and Strain 329
Chapter Objectives 329
7.1 Introduction 329
7.2 Internal Resultant Loadings 330
7.3 Stress 344
7.4 Average Normal Stress in an
Axially Loaded Bar 346
7.5 Average Shear Stress 353
7.6 Allowable Stress Design 364
7.7 Deformation 379
7.8 Strain 380
7contents 17
Stress and Strain
Transformation 637
Chapter Objectives 637
14.1 Plane-Stress Transformation 637
14.2 General Equations of Plane-Stress
Transformation 642
14.3 Principal Stresses and Maximum
In-Plane Shear Stress 645
14.4 Mohr’s Circle—Plane Stress 661
14.5 Absolute Maximum Shear Stress 673
14.6 Plane Strain 679
14.7 General Equations of Plane-Strain
Transformation 680
*14.8 Mohr’s Circle—Plane Strain 688
*14.9 Absolute Maximum Shear Strain 696
14.10 Strain Rosettes 698
14.11 Material Property Relationships 700
14
Design of Beams and
Shafts 717
Chapter Objectives 717
15.1 Basis for Beam Design 717
15.2 Prismatic Beam Design 720
15
Deflection of Beams
and Shafts 735
Chapter Objectives 735
16.1 The Elastic Curve 735
16.2 Slope and Displacement by
Integration 739
*16.3 Discontinuity Functions 757
16.4 Method of Superposition 768
16.5 Statically Indeterminate Beams and
Shafts—Method of Superposition 776
16
17 Buckling of Columns 795
Chapter Objectives 795
17.1 Critical Load 795
17.2 Ideal Column with Pin Supports 798
17.3 Columns Having Various Types of
Supports 804
*17.4 The Secant Formula 816
Appendix
A Mathematical Review and Expressions 828
B Geometric Properties of An Area and
Volume 832
C Geometric Properties of Wide-Flange
Sections 834
D Slopes and Deflections of Beams 837
Preliminary Problems Solutions 839
Fundamental Problems
Solutions and Answers 858
Selected Answers 891
Index 916
INDEX
A
Absolute maximum shear strain, 696–697, 713
Absolute maximum shear stress, 673–676, 712
Allowable stress (sallow), 364–365, 723, 733
Allowable stress design (ASD), 364–371, 393
Angle of twist, 472–473, 492–499, 513
circular shafts, 472–473
constant cross-sectional area (A), 493–494
internal torque and, 492–493, 496
multiple torques, 494
procedure for analysis of, 496
sign convention for, 495
torsion and, 472–473, 492–499, 513
torsional deformation and, 472–473
Angles (u), 35, 59–61, 82, 92–93, 219–221.
See also Angle of twist
Cartesian vectors, 58–61
coordinate direction (a, b, g), 59–60, 92–93
dot products and, 82, 93
dry friction (f), 219–220
horizontal, 60–61
kinetic friction (fk), 220–221
line of action (direction) and, 35
static friction (fs), 219, 221
vertical (f), 60–61
Anisotropic material, 346
Area (A), 290, 310–314, 319–321, 325–326, 403, 432–433,
467, 832–833
centroid (C) of, 290, 325, 832–833
composite, 319–321, 326
constant cross-sectional, 432–433, 467
moment of inertia (I ) for, 310–314,
319–321, 326, 832–833
parallel-axis theorem for, 311–314, 326
percent reduction in, 403
procedures for analysis of, 312, 319
Arrow notation, 35, 49, 91
Axes, 98, 119–123, 161–165, 170, 543–546, 548, 562–563
bending applied to, 543–546
direction and, 98
distributed loading along single, 161–165
line of action, 119, 170
longitudinal, 543–545
moment, 98
moment of force about, 119–123, 170
neutral, 543, 548, 562, 565
principal, 562–563
projection, 120
resultant force on, 119–123, 170
scalar analysis of, 119
unsymmetric bending and, 562–563
vector analysis of, 120–121
Axial loads, 346–352, 392, 428–469, 795–797, 816–821, 825
bars, 346–352, 392
buckling from, 795–797, 816–821, 825
columns, 795–797, 816–821, 825
constant cross-sectional area (A),
432–433, 467
cross section of, 346
displacement (d), 431–438, 447–452, 467
eccentric applications, 816–821, 827
elastic deformation in members,
431–438, 467
force (flexibility) method of analysis, 453–454
principle of superposition for, 446, 467
procedures for analysis of, 434, 448, 453–454
relative displacement (d), 431–438, 466
Saint-Venant’s principle for, 429–431, 466
sign convention for, 433, 467
statically indeterminate members,
446–452, 467
stress (s) and, 346–352, 392
thermal stress and, 459–462, 467
Axis of symmetry, 543, 562
B
Ball-and-socket joints, 203
Base units, 26
Beams, 516–575, 576–607, 716–733, 734–793, 834–839
bearing plates, 718
bending, 516–575
built-up members, 596–600, 605, 722, 733
cantilevered, 839
concentrated forces and moments, 526
deflection of, 718, 734–793, 838–839
deformation of, 543–546
design of, 716–733
discontinuity functions for, 757–765, 790
distributed loads, 524–526
equations for, 838–839
fastener spacing, 597, 605
flexure formula for, 547–553, 573
force (flexibility) method for, 777–780
glulam, 722
graphical representations of, 524–533, 572
load-displacement relationships, 777–780
longitudinal shear stress in, 577–578
916Index 917
Beams (continued)
method of integration for, 739–749, 790
method of superposition for, 768–772, 776–785, 791
moment diagrams, 735–749, 790
plate girders, 719
prismatic, 720–727
procedures for analysis of, 519, 527, 550, 584, 723,
742, 762, 780
section modulus (S), 720
shear and moment diagrams, 517–533, 572
shear flow (q), 596–600, 605
shear formula for, 578–589, 605
sign convention for, 518, 526, 572
simply supported, 838
statically indeterminate members,
776–785, 791
steel sections, 721
stress trajectories, 719
transverse shear, 576–607
unsymmetric bending, 562–568, 573
warping, 578
wide-flange sections, 834–837
wood sections, 721
Bearing plates, 718
Bearing supports, 203
Bending, 516–575
axis of symmetry, 543, 562
beams, 516–575
deformation, 543–546
flexure formula for,
547–553, 573
neutral axis, 543, 548, 562, 565
neutral surface, 543, 562
principal axis, 562–563
procedures for analysis of, 519, 527, 550
shear and moment diagrams,
517–533, 572
straight members, 543–546, 573
unsymmetric, 562–568, 573
Bending moment (M), 331–332, 526, 543–546, 548–549,
562–568, 572–573
arbitrarily applied, 564
deformation of straight members,
543–546, 572
flexure formula for, 548–549, 573
internal resultant loadings, 331–332
principal axis, applied to, 562–563, 573
shear and moment diagram regions of concentration, 526
unsymmetric bending, 562–568, 573
Bending stress, 723, 733
Biaxial stress, 611
Bifurcation point, 797
Bridge trusses, 242
Brittle materials, 405, 424
Buckling, 794–827
axial loads, 795–797, 816–821, 825
bifurcation point, 797
columns, 794–827
critical load (Pcr) for, 795–797, 825
eccentric loading, 816–821, 825
equilibrium and, 796–797
lateral deflection, 795–797
Built-up members, 596–600, 605, 722–723, 733
design of, 722–723, 733
fastener spacing, 597, 605, 723
plate girders for, 722
shear flow (q) in, 596–600, 605
Bulk modulus (k), 703, 713
C
Cartesian stress and strain components, 381
Cartesian vectors, 50, 58–64, 70–75, 81, 92–93, 102–103,
105–107, 169
addition of, 61
coordinate direction angles (a), 59–60
coplanar forces, notation of, 50
cross product, formulation of,
102–103, 169
direction of, 58–61, 92–93
dot product and, 81, 93
force vectors, 73–75
horizontal angle (u), 60–61
magnitude of, 59, 92
position vectors for, 70–72, 169
rectangular components, 58
resultant forces, formulation of, 61–62, 93
resultant moments, formulation of,
105–107, 169
right-hand rule for, 58, 101–102
three-dimensional components, 58–61
unit vectors, 58–61, 73–75, 92
vertical angle (f), 60–61
x, y, z coordinates, 59–60, 70
Center of gravity (G), 180, 287–289, 291, 301–302, 325
composite bodies, 301–302, 325
free-body diagram location, 180
procedures for analysis of, 291, 302
rigid-body equilibrium and, 180
specific weight (constant density) and, 301
weight (W) and, 180, 287–289, 325
Centroid (C), 162, 171, 289–294, 325,
832–833
area (A), 290, 325, 832–833
distributed loading, 162, 171
procedure for analysis of, 291
volume (V), 289, 325, 832–833918 Index
Circular shafts, torsional deformation of, 471–473, 513
Coefficients of friction (μ), 219–221, 237
Cohesive material, 344
Collinear vectors, 37, 91
Columns, 794–827
critical load (Pcr) of, 795–797,
800–801, 804, 820, 825
deflection equations for, 798–801,
817–818
design of, 820
eccentric loading, 816–821, 825
effective length, 805
Euler load, 800, 825
fixed-supported (braced), 804
ideal, 798–803
lateral deflection of, 795–797
pin-supported, 798–803
Secant formula for, 816–821, 825
Combined loadings, 608–635
biaxial stress, 611
cylindrical (hoop) stress, 610–611, 632
cylindrical vessels, 610–611, 632
procedure for analysis of, 616–617
radial stress, 611
spherical vessels, 611, 632
state of stress caused by, 616–623, 632
thin-walled pressure vessels, 609–612, 632
Compatibility (kinematic)
conditions, 447
Component vectors, 36, 38–39, 49–54
Composite bodies, 301–304, 319–321, 325–326
area (A), 319–321, 326
center of gravity (G) and centroid of, 301–302, 325
moment of inertia for, 319–321, 326
procedures for analysis of, 302, 319
specific weight and, 301
Compression test, 397–398
Compressive forces, 243–244, 257–258
Concentrated force, 22
Concurrent forces, 50, 61, 93, 149, 193
couple system simplification, 149
resultants, 50, 92
three-force member equilibrium, 193
Continuous material, 344
Coplanar forces, 49–54, 92, 138–140, 149, 161, 177–185,
187–194, 332
Cartesian vector notation, 50
couple system simplification,
138–140, 149
distributed loads, 161
equations of equilibrium for, 187–192
internal resultant loadings, 332
procedures for analysis of, 182, 188
resultants, 50–51, 92
rigid-body equilibrium and, 177–185, 187–194
scalar notation, 49
support reactions for, 177–185
three-force members, 193–194
two-force members, 193–194
Cosine law, 40
Coulomb friction, 218. See also
Dry friction
Couple, 128–133, 138–143, 149–154,
170–171, 177
concurrent force systems, 149
coplanar force systems, 138–140,
149, 177
equivalent, 129
moment of, 128–133, 170
parallel force systems, 150
procedures for analysis of, 140, 150
resultant moment (MR), 129–130
rigid-body equilibrium and, 177
scalar formulation, 128
system simplification, 138–143,
149–154, 171
vector formulation, 128, 170
Critical load (Pcr), 795–797, 800–801, 804, 820, 825
bifurcation point, 797
buckling and, 795–797, 825
column design and, 820
deflection and, 798–801
equilibrium and, 796–797
Euler load, 800, 825
fixed supported (braced), 804
pin-supported columns, 800–801, 825
Cross product, 101–103, 169
Cross sections, 330–332, 344–348, 392, 432–433, 467
axially loads, 346–348, 432–433, 467
constant area (A), 432–433, 467
internal resultant loading,
330–332, 392
stress distribution, 344–348
transverse shear moment (Q), 580–581
Cylindrical (hoop) stress, 610–611, 632
Cylindrical vessels, 610–611, 632
D
Deflection, 718, 734–793, 795–797,
816–821, 825, 838–839. See also Buckling
beams, 718, 734–793, 838–839
boundary conditions, 740
cantilevered beams, 838
column buckling, 795–797,
816–821, 825
continuity conditions, 740
coordinates for, 741
critical load (Pcr), 795–797, 825Index 919
Deflection (continued)
discontinuity functions for,
757–765, 790
eccentric loading, 816–821, 825
elastic curve, 735–739, 790, 838–839
flexural rigidity (EI ), 740
lateral (buckling), 795–797
method of integration for,
739–749, 790
method of superposition for, 768–772, 776–785, 791
moment–curvature relationship, 738
moment diagrams, 735–749, 790
procedures for analysis of, 742, 762, 780
Secant formula for, 816–821, 825
sign conventions for, 751
simply supported beams, 838
slope equations, 739–749, 790, 838–839
statically indeterminate members,
776–785, 791
Deformation, 346, 379–385, 393, 397–398, 400–401,
403–417, 424–425, 429–438, 543–546, 573, 578
axially loaded members, 431–438
bending, 543–546, 573
brittle materials, 405, 424
circular shafts, 471–473, 513
displacement (d) and, 431–438,
447, 452, 467
ductile materials, 403–404, 424
elastic, 431–438, 467
localized, 429–430
necking, 401
permanent, 400, 424
plastic, 400
Poisson’s ratio (ν) for, 416–417, 425
relative displacement (d), 431–438
Saint-Venant’s principle for,
429–431, 466
small strain analysis, 382
straight members (beams), 543–546, 573
strain and, 380–385, 393
strain energy from, 407–411, 425
strain hardening, 401
stress–strain diagrams for,
400–401, 424
tension and compression tests for,
397–398
torsional, 471–473, 513
twisting, 471–473
uniform, 346
warping, 578
yielding, 400
Degree of indeterminacy, 776
Derivatives, 830
Design. See Structural design
Determinant notation, 103
Dilatation (e), 702–703, 713
Dimensional homogeneity, 28
Dimensionless quantity, 380, 393
Direction, 35, 38, 49, 58–61, 70–71, 73, 91–93, 98, 101–102,
104, 128, 169–170, 244, 250, 258, 719
angle (u) for, 35, 60–61
arrow notation for, 49
Cartesian vectors, 58–61, 92–93
coordinate angles (a, b, g), 59–60, 92–93
cosines, 59–60
couple moments, 128
cross product, 101–102
force and, 73–75, 82, 92–93, 98, 102–103, 104, 169–170
by inspection, 244, 250, 258
line of action, 35
moment axis, 98, 170
position vectors, 70–71
resultant forces, 38–39
resultant moments (MR), 98, 102–103, 169–170
right-hand rule for, 58, 98, 102–103, 104, 128, 169
scalar formulation and, 98, 169
sense of, 35, 91
sign convention for, 98
stress trajectories, 719
truss member forces, 244, 250, 258
unit vectors, 50, 58, 73–75, 92
vectors and, 35, 38, 49, 58–61, 70–71, 73, 91–92,
102–103, 104
Discontinuity functions, 757–765, 790
applications of, 761
deflection and, 757–765, 790
Macaulay functions, 758
procedure for analysis of, 762
singularity functions, 759–760
Displacement (d), 431–438, 447–452, 467
axially loaded members, 431–438, 448–452
compatibility (kinematic) conditions for, 447–452, 467
constant cross-sectional area (A),
432–433, 467
principle of superposition for, 446, 467
procedure for analysis of, 434
relative, 431–438
statically indeterminate members, 447–452, 467
Distributed loading, 161–165, 171, 344–345, 477, 524–526,
757–765, 790
axially loaded members, 346–348
axis (single), along, 161–165
centroid (C) location, 162, 171
coplanar, 161–165, 171
cross sections for, 344–348
deflection and, 757–765, 790
discontinuity functions for, 757–765, 790
Macaulay functions and, 758920 Index
magnitude of resultant force, 161
resultant forces of, 162–165
shear and moment diagram regions, 524–526
shear stress (t), 477
singularity functions, 759–760
stress (s) and, 344–348
torsion and, 477
Dot notation, 27
Dot product, 81–85, 93, 120
Dry friction, 218–235, 237
angles (f) of, 219–221
coefficients of (μ), 219–221, 237
distributed and frictional loads, 218
impending motion (static) and, 219, 221, 222–228, 237
motion (kinetic), 220–221, 237
normal forces and, 218
procedure for analysis of, 225
rigid-body equilibrium and, 218–235, 237
rolling and, 221
slipping (sliding) and, 219–223, 237
theory of, 218
tipping and, 218, 224
Ductile materials, 403–404, 424
E
Eccentric loading, 816–821, 825
Effective length, 805
Elastic behavior, 399–401, 431–438, 467
axially loaded members, 431–438, 467
deformation and, 431–438, 467
stress–strain diagrams for, 399–401
stress/strain transformation and, 702–703
Elastic curve, 735–739, 790, 838–839
Electrical-resistance strain gage, 398
Engineering notation, 28
Engineering (nominal) stress/strain, 399
Equilibrium, 174–239, 347–348, 354, 796–797
bifurcation point, 797
column buckling and, 796–797
column buckling and, 796–797
conditions for, 175–176
dry friction and, 218–235
equations of, 187–192, 208–211
free-body diagrams for, 177–185, 203–207
friction force equations and, 218, 223
neutral, 797
procedures for analysis of, 182, 188,
209, 225
rigid bodies, 174–239
scalar equations of, 208
shear stress (t) and, 354
stable, 796
stress (s) and, 347–348, 354
support reactions, 177–179, 203–207, 236–237
three-dimensional rigid-bodies, 203–217, 237
two-dimensional rigid bodies, 176–202, 237
unstable, 219, 796
vector equations of, 208
zero force for, 176
Equivalent system, 138–143
Euler load, 800, 825
Extensometer, 398
External effects of force systems, 138. See also Rotation;
Translation
F
Factor of safety (F.S.), 364–365, 393
Fastener spacing in built-up beams, 597, 605, 723
Fixed supports, 177, 804
Flexibility (force) method, 777–780
Flexural rigidity (EI), 740
Flexure formula, 547–553, 573
bending moment (M) for, 548–549, 573
bending stress from, 547–553, 573
moment of inertia (I) for, 549
neutral axis location for, 548
procedure of analysis for, 550
Force (F), 22–26, 34–95, 119–123, 128–133, 169–170,
176–180, 193–194, 218–237, 243–244, 257–258, 331–332,
379, 392–393, 526. See also Dry friction; Frictional
forces; Weight
addition of, 38–43
axis, moment of about, 119–123, 170
component vectors of, 38–39
compressive, 243–244, 257–258
concentrated, 23
concept of, 22
concurrent, 50, 61, 93, 193
coplanar, 49–54, 92, 332
couple, moment of, 128–133, 170
deformation from, 379, 393
directed along a line, 73–75, 82, 93
free-body diagrams for, 177–180
frictional, 218–235, 237
gravitational, 25
internal, 180
internal resultant loadings, 331–332, 392
moment (MO) of, 119–123, 170
Newton’s laws and, 24–25
normal (N), 218, 331–332
parallelogram laws for, 36, 40
position vectors and, 70–72, 93
procedure for analysis of, 40
resultants of, 38–39, 50–51, 61, 91–93, 129, 170
rigid-body equilibrium and, 176–180
scalar determination of, 35–36, 119, 128, 169Index 921
Force (continued)
shear (V), 331–332
shear and moment diagram regions
of concentration, 526
tensile, 243–244, 257–258
triangle rule for, 36–37, 91
two-and three-force members, equilibrium of, 193–194
units of, 26
unknown forces, 177, 188, 203, 206, 209, 236–237, 244
vector determination of, 34–95, 120–121, 128, 169
zero, 176
Force (flexibility) method of analysis, 453–454, 777–780
Force systems, 96–173, 174–239, 242–243, 282
axis, moment of about, 119–123, 170
Cartesian vector formulation, 102–103, 105–107, 169
concurrent, 149, 171, 193, 242, 282
coplanar, 139–140, 149, 161, 177–185, 187–194, 242
couple moments, 128–133, 138–143, 149–154,
170–171, 177
cross product, 101–103, 169
distributed loads, 161–165, 171
dry friction and, 218–235, 243
equilibrium of, 174–239
equivalent, 138–143, 171
external effects from, 138
free-body diagrams for, 177–185, 203–207
frictional forces on, 218–235, 237
moments (MO), 97–107, 119–123, 128–133, 169
parallel, 150, 171, 193
perpendicular, 149
principle of moments, 108–110, 169
principle of transmissibility, 104, 138
procedures for analysis of, 140, 150, 182, 188, 209
resultants, 96–173
rigid-bodies, 174–239
rotational motion and, 138–140, 177, 203
scalar formulation of, 97–100, 119, 128, 169
simplification of, 138–143, 149–154, 171
support reactions and, 177–179, 203–207, 236–237
three-dimensional rigid-bodies, 203–217, 237
translational motion and, 138–140, 177, 203
truss members, 242–243, 282
two-dimensional (coplanar) rigid bodies, 176–202, 236
vector formulation of, 103–105, 120–121, 128, 169
Fracture stress (sf), 401
Frames, 266–281, 283
free-body diagrams for, 266–273, 283
multiforce members of, 266
procedure for analysis of, 269
structural analysis of, 266–281, 283
Free-body diagrams, 177–185, 188, 203–207, 209, 218–219,
236–237, 244–251, 257–262, 266–273, 282–283
center of gravity (G), 180
frames and machines, 266–273, 283
frictional forces, 218–219, 237
idealized models, 180–181
internal forces and, 180
procedures for analysis using, 182, 188, 209
springs, 180
structural analysis using, 244–251, 257–262, 266–273,
282–283
support reactions, 177–179, 203–207
three-dimensional rigid bodies, 203–207, 209, 237
trusses, 244–251, 257–262, 282–283
two-dimensional rigid bodies, 177–185, 188, 236
unknown forces, 177, 188, 203, 206, 209, 236–237
weight (W), 180
Free vector, 128, 138–139
Friction, 218. See also Frictional forces; Dry friction
Frictional forces, 218–235, 237. See also Dry friction
angles (f) of, 219–221
coefficients of (μ), 219–221, 237
dry friction and, 218–235
equilibrium equations and, 218, 223, 237
free-body diagrams for, 218–219, 237
kinetic (motion), 220–221, 237
normal (N), 218
procedure for analysis of, 225
rigid-body equilibrium and, 218–235, 237
static (impending motion), 219, 221, 222–228
G
Gage-length distance (L0), 398
Glulam beams, 722
Gravitational attraction, 25
Gravity. See Center of gravity; Weight
Gusset plate, 242
H
Hinge supports, 203
Homogeneous material, 346
Hooke’s law, 400, 402, 407–418, 424, 700–701, 713
linear elastic behavior and, 407–418
modulus of elasticity from, 400, 402, 424
shear modulus of elasticity from, 418
stress/strain transformation and, 700–701, 713
Hoop (cylindrical) stress, 610–611, 632
Horizontal angle (u), 60–61
Hydrostatic loading, 703, 713
Hyperbolic functions, 830
I
Idealized models of rigid bodies, 180–181
Impending motion, 219, 221, 222–228
Inertia. See Moment of inertia
Inflection point, 736–737
In-plane shear strain, 684
In-plane shear stress, 645–651, 711922 Index
Integrals, 831
Integration. See Method of integration
Internal forces, 180
Internal resultant loadings, 330–343, 392
bending moment (M) in, 331–332
coplanar systems, 332
cross sections for, 330–332, 392
normal force (N) in, 331–332
procedure for analysis of, 333
shear force (V) in, 331–332
three-dimensional components, 331
torsional moment (T) in, 331
Internal torque, 474–475, 492–493, 496
International System (SI) of units, 26–27
Isotropic material, 346
J
Joint connections, 242
K
Kilogram (kg), unit of, 26
Kinetic frictional forces (motion), 220–221, 237
L
Lateral contraction, 416
Lateral deflection, 795–797
Length, units of, 26
Line of action, 35, 119, 138, 149, 162, 169
Linear coefficient of thermal expansion (a), 459
Load-displacement relationships, 444–452, 467, 777–780
axially loaded members, 444–452, 467
beam deflection and, 777–780
statically indeterminate members, 444–452, 467, 777–780
Loads. See Axial loads; Combined loadings; Distributed
loadings; Internal resultant loadings
Longitudinal axis, 543–545
Longitudinal elongation, 416
Longitudinal shear stress, 577–578
M
Macaulay functions, 758
Machines, 266. See also Frames; Structural analysis
Magnitude, 35, 38–39, 49, 59, 91–92, 98, 101, 104, 128, 161,
169
arrow notation for, 35, 49
Cartesian vectors, 59, 92
coplanar force systems, 49
couple moments, 128
cross product and, 101
distributed loadings and, 161
moments of a force and, 98, 101, 104
resultant forces, 38–39, 161
scalar determination of, 35, 91, 98, 169
vectors and, 35, 38–39, 49, 59, 91–92, 104
Mass, quantity of, 22
Mass, units of, 26
Material properties, 397–427, 700–707
brittle materials, 405, 424
compression test for, 397–398
dilatation (e), 702–703, 713
ductile materials, 403–404, 424
elastic behavior, 399–401, 702–703
Hooke’s law, 400, 402, 418, 424, 700–701, 713
necking, 401
Poisson’s ratio (ν) for, 416–417, 425
shear stress–strain diagrams for, 418–421, 425
stiffness, 406
strain energy, 407–411, 425
strain hardening, 401, 406
stress and strain transformation effects,
700–707
stress–strain diagrams for, 399–406, 418–421,
424–425
tension test for, 397–398
volume (hydrostatic loading), 703, 713
yielding, 400
Mechanics of materials, 21–25, 328–395.
See also Material properties
deformation, 379, 393
engineering study of, 21–22, 329
fundamental concepts of, 23–25
internal resultant loadings, 330–343, 392
Newton’s laws for, 24–25
procedure for analysis of problems, 29–30
strain (P), 380–390, 393
stress (s), 344–378, 392–393
Meter (m), unit of, 26
Method of integration, 739–749, 790
boundary conditions, 740
continuity conditions, 740
flexural rigidity (EI), 740
procedure for analysis of, 742
slope equations, 739–749, 790
Method of joints, 244–249, 282
Method of sections, 257–262, 283
Method of superposition. See Superposition
Modulus of elasticity (E), 400, 702–703
Modulus of resilience (ur), 407
Modulus of rigidity (G), 418
Modulus of toughness (ut), 408
Mohr’s circle, 661–667, 688–692, 712–713
plane strain, 688–692, 713
plane stress, 661–667, 712
Moment arm (distance), 98
Moment axis (direction), 98
Moment–curvature relationship, 738
Moment diagrams, 735–749, 790
elastic curve, 735–739, 790
inflection point, 736–737Index 923
Moment of inertia (I), 310–314, 319–321, 326, 474, 549,
562–563, 573, 801, 832–833
area (A), 310–314, 319–321, 326, 832–833
column buckling, 801
composite bodies, 319–321, 326
flexure formula and, 549
least, 801
parallel-axis theorem for, 311–314, 326
polar, 310, 326, 475–476
principal axis of, 562–563, 573
procedures for analysis of, 312, 319
product of, 563
torsion formula and, 474
unsymmetric bending and, 562–563, 573
Moments (M), 96–173, 331–332, 526, 580–581. See also
Bending moment; Moment of inertia
Cartesian vector formulation, 102–103,
105–107, 169
couple, 128–133, 138–143, 149–154, 170–171
cross product for, 101–103
cross-sectional (Q), 580–581
direction of, 98, 101–102, 104, 169
dot product for, 120
force about an axis, 119–123, 170
force and couple systems, simplification of, 138–143,
149–154, 171
internal (M0) loadings, 331–332
magnitude of, 98, 101, 104, 169
principle of, 108–110
principle of transmissibility, 104, 138
procedures for analysis of, 140, 150
resultant (MR), 98–100, 105–107
right-hand rule for, 98, 101–102, 169–170
scalar formulation of, 97–100, 119, 128, 169
shear and moment diagram regions
of concentration, 526
sign convention for, 98
torque as, 97
torsional (T ), 331
transverse shear and, 580–581
vector formulation of, 104–107, 120–121, 128, 169
Motion, 24, 138–143, 177, 203, 218–235, 222–228
force and couple system simplification,
138–143
frictional forces and, 218–235, 237
impending, 219, 221, 222–228, 237
kinetic frictional forces, 220–221, 237
Newton’s laws of, 24
rigid-body equilibrium and, 218–235
rolling, 221
rotational, 138–140, 177, 203
slipping (sliding), 219–223
static frictional force and, 219, 221
supports for prevention of, 177, 203
tipping, 218, 224
translational, 138–140, 177, 203
Multiforce members, 266
N
Necking, 401
Neutral axis, 543, 548, 562, 565
Neutral equilibrium, 797
Newton (N), unit of, 26
Newton’s law of gravitational attraction, 25
Newton’s laws of motion, 24
Nominal (engineering) stress/strain, 399
Nominal dimensions, 721
Normal force (N), internal resultant loadings, 331–332
Normal strain (P), 380–382, 393
Normal stress (s), 345–352, 392, 642–643
Numerical calculations, engineering use of, 28–29
O
Offset method, 403
P
Parallel force systems, 150, 193
Parallel-axis theorem, 311–314, 326
Parallelogram law, 36–37, 40, 91
Particles, concept of, 23
Pascal (Pa), unit of, 345
Percent elongation, 403, 424
Percent reduction in area, 403, 424
Perfectly plastic materials, 400
Permanent set, 406
Perpendicular force systems, 149
Pin connections, 242–243
Pin supports, 203, 798–803
Planar trusses, 241
Plane strain, 679–697, 713
absolute maximum shear strain, 696–697, 713
equations for transformation, 680–688
maximum in-plane shear strain, 684
Mohr’s circle for, 688–692, 713
normal and shear strain components, 681–683
principle strains, 684
procedures for analysis of, 688–689
sign convention for, 680
transformation of, 679–688
Plane stress, 637–676, 711–712
absolute maximum shear stress, 673–676, 712
equations for transformation, 642–644
in-plane shear stress, 645–651, 711
Mohr’s circle for, 661–667, 712
normal and shear stress components, 642–643
principle stresses, 645–651
procedures for analysis of, 639, 643, 663–664
sign convention for, 642
transformation of, 637–644924 Index
Plastic deformation, 400
Plate girders, 719
Poisson’s ratio (ν), 416–417, 425
Polar moment of inertia, 310, 326, 475–476
Position vectors, 70–72, 93, 169
Power transmission, 482–483, 513
Power-series expansion, 830
Primary beam, 777
Principal axis, 562–563, 573
Principle of moments, 108–110, 169
Principle of transmissibility, 104, 138
Principle strains, 684
Principle stresses, 645–651
Prismatic beams, 720–727
Product of inertia (I), 563
Projection of a moment, 120
Proportional limit (spl), 399, 418
Purlins, 241
Pythagorean theorem, 829
Q
Quadratic formula, 830
R
Radial stress, 611
Radius of gyration, 801
Rectangular components, 50–51, 58–64, 70–71, 92–93
three dimensional, 58–64, 70–71, 92–93
two dimensional, 50–51, 92
Redundants, 776–779, 791
Relative displacement (d), 431–438
Resultants, 36–39, 50–51, 61–64, 91–93, 96–173, 330–343,
392
axis, moment of force about, 119–123, 161–165
Cartesian vector formulation, 61–62, 93, 102–103, 105–
107, 169
centroid (C) location and, 162
collinear vectors, 37, 91
concurrent forces, 50, 61, 93, 149
coplanar force, 50–51, 92, 149
couple moments, 128–133, 138–143, 149–154, 170–171
cross product, 101–103, 169
direction of, 98, 101–102, 104, 169
distributed loadings, 161–165
equivalent force systems, 138–143
force components, 38–39
force and couple moments,simplification of, 138–143,
149–154, 171
force systems, 96–173
internal loadings, 330–343, 392
magnitude of, 98, 101, 104, 161
moments (MR), 98–100, 105–107, 129–130, 138–143
parallel force systems, 150
parallelogram law for, 36, 40, 91
perpendicular force systems, 149
principle of moments, 108–110
principle of transmissibility, 104, 138
procedures for analysis of, 140, 150
rectangular components, 50–51, 92
right-hand rule for, 98, 101–102, 104, 128
scalar formulation of moment, 98, 128, 169
triangle rule for, 36–37, 91
vector addition for, 36–38, 61–64, 93
vector formulation of moment, 104–107, 128, 169
vector subtraction for, 37
Right-hand rule, 58, 98, 101–102, 104, 128
Rigid bodies, 23, 174–239
center of gravity (G), 180
concept of, 23
dry friction and, 218–235, 237
equations of equilibrium for, 187–192, 208–211
equilibrium of, 174–239
free-body diagrams for, 177–185, 203–207, 236, 237
frictional forces on, 218–235, 237
idealized models of, 180–181
impending motion (static) of, 219, 221, 222–228
internal forces and, 180
procedures for analysis of, 182, 188, 209, 225
rotational motion of, 177, 203
springs, 180
support reactions, 177–179, 203–207, 236–237
three-dimensional, equilibrium of, 203–217, 237
three-force members, 193–194
translational motion of, 177, 203
two-dimensional (coplanar), equilibrium of,
176–202, 236
two-force members, 193–194
weight (W), 180
Rolled shapes, 721
Roller supports, 177
Rolling motion, 221
Roof trusses, 241–242
Rotational motion, 138–140, 177, 203
force and couple system simplification, 138–140
supports for prevention of, 177, 203
Rounding off numbers, 29
S
Saint-Venant’s principle, 429–431, 466
Scalar triple product, 120
Scalars, 35–36, 49, 91, 97–100, 119, 128, 169, 208
coplanar forces, notation for, 49
couple moments, 128
division of a vector by, 36
equations of equilibrium, 208
moment of force about an axis, 119
moment of a force, formulation of, 97–100, 119, 128, 169
multiplication of a vector by, 36
quantity, 35, 91
sign convention for, 98, 169Index 925
Secant formula, 816–821, 825
Seconds (s), unit of, 26
Section modulus (S), 720
Shafts, 471–473, 482–483, 492–499, 506–509, 513
angle of twist, 472–473, 492–499, 513
circular, 471–473, 513
internal torque, 492–493, 496
power transmission, design for, 482–483
procedures for analysis of, 496, 507
statically indeterminate, 506–509, 513
torsional deformation, 471–473, 513
Shear and moment diagrams, 517–533, 572
beams, 517–533, 572
concentrated forces and moments, 526
distributed loads, 524–526
graphical methods for, 524–533, 572
procedures for analysis of, 519, 527
sign convention for, 518, 526, 572
Shear flow (q), 596–600, 605
Shear force (V), internal resultant loadings, 331–332
Shear formula, 578–589, 605
Shear modulus (G), 418, 425, 702, 713
Shear strain (g), 381, 393, 474, 679–687, 696–697, 713
absolute maximum, 696–697, 713
deformation and, 381, 393
linear variation in, 474
maximum in-plane, 684
plane strain components, 681–683
plane strain transformation and, 679–687, 696–697, 713
Shear stress (t), 345, 353–357, 392, 474, 477, 577–579,
642–651, 673–676, 711–712. See also Transverse shear
absolute maximum, 673–676, 712
beams 577–579
direct (simple), 353
distribution of, 345, 477, 578–579
equilibrium, 354
in-plane, 645–651, 711
linear variation in, 474
longitudinal, 577–578
plane stress components, 642–643
plane stress transformation and, 642–651, 673–676,
711–712
procedure for analysis of, 355
torsion and, 474, 477
Shear stress–strain diagrams, 418–421, 425
Significant figures, 28–29
Sine law, 40
Singularity functions, 759–760
Slenderness ratio, 801–802
Sliding vector, 104, 138
Slipping (sliding), 219–223, 237
Slope equations, 739–749, 790, 838–839
Small strain analysis, 382
Specific weight (constant density), 301
Spherical vessels, 611, 632
Springs, free-body diagrams of, 180
Stable equilibrium, 796
Static frictional forces (impending motion), 219, 221,
222–228, 237
Statically indeterminate members, 446–454, 467, 506–509,
513, 776–785, 791
axially loaded, 446–454, 467
beams, 776–785, 791
compatibility (kinematic) conditions for, 447–452, 467
deflection of, 776–785, 791
degree of indeterminacy, 776
force (flexibility) method of analysis, 453–454, 777–780
load-displacement relationships, 447–452, 467, 777–780
method of superposition for, 446–452, 776–785, 791
procedures for analysis of, 448, 507, 780
redundants (reactions) of, 776–779, 791
shafts, 506–509, 513
torque loaded, 506–509, 513
Steel, stress–strain diagram for, 402
Steel sections, structural design and, 721
Stiffness, 406
Straight members. See Beams
Strain (P), 380–390, 393, 399, 684. See also Plane strain
Cartesian components, 381
deformation and, 380–385, 393
dimensionless quantity of, 380, 393
nominal (engineering), 399
normal (P), 380–382, 393
principle, 684
shear (g), 381, 393
small strain analysis, 382
units of, 380
Strain energy, 407–411, 425
Strain hardening, 401, 406
Strain rosettes, 698–699
Stress (s), 344–378, 392–393, 399–400, 459–462, 467,
610–611, 616–623, 632, 645–651, 700, 723, 733. See also
Plane stress
allowable (sallow), 364–365, 723, 733
allowable stress design (ASD), 364–371, 393
axially loaded bars, 346–352, 392
bending, 723, 733
biaxial, 611
combined loadings and, 610–611, 616–623, 632
cylindrical (hoop), 610–611, 632
equilibrium and, 347–348, 354
factor of safety (F.S.), 364–365, 393
loading distribution and, 344–345
nominal (engineering), 399
normal (s), 345–352, 392
principle, 645–651
procedure for analysis of, 349, 355, 366
radial, 611926 Index
shear (t), 345, 353–357, 392, 723, 733
state of, 345, 616–623, 632
thermal, 459–462, 467
triaxial, 700
ultimate (su), 400
uniaxial, 348
units of, 345
Stress and strain transformation, 636–715
absolute maximum shear strain, 696–697, 713
absolute maximum shear stress, 673–676, 712
bulk modulus (k) and, 703, 713
dilatation (e), 702–703, 713
equations for, 642–644, 680–688
Hooke’s law and, 700–701, 713
in-plane shear stress, 645–651, 711
material property relationships, 700–707
modulus of elasticity (E) and, 702–703
Mohr’s circle for, 661–667, 688–692, 712–713
plane strain, 679–697, 713
plane stress, 637–676, 711–712
principle stresses, 645–651
procedures for analysis of, 639, 643, 663–664,
688–689
shear modulus (G) and, 702, 713
strain rosettes, 698–699
triaxial stress, 700
Stress–strain diagrams, 399–421, 424–425
brittle material behavior from, 405, 424
conventional, 399–406, 424
ductile material behavior from, 403–404, 424
elastic behavior, 399–401
fracture stress (sf), 401
modulus of resilience (ur), 407
modulus of rigidity (G), 418
modulus of toughness (ut), 408
nominal (engineering) stress/strain for, 399
proportional limit (spl), 399, 418
shear, 418–421, 425
steel, 402
true, 401
ultimate stress (su), 401, 418
yield point (sY), 400, 406, 408, 424–425
Young’s modulus of elasticity (E), 400
Stress trajectories, 719
Structural analysis, 240–285
frames, 266–281, 283
free-body diagrams for, 244–251, 257–262, 266–273,
282–283
machines, 266–281, 283
method of joints, 244–249, 282
method of sections, 257–262, 283
procedures for, 245, 259, 269
trusses, 241–265, 282–283
zero-force members, 250–252
Structural design, 242–243, 364–371, 393, 482–483,
716–733
allowable bending and shear stress, 723, 733
allowable stress design (ASD), 364–371, 393
beams, 716–733
prismatic beams, 720–727
section modulus (S), 720
shafts, 482–483
stress trajectories, 719
trusses, 242–243
Superposition, 446–452, 467, 768–772, 776–785, 791
axial loads and, 446–452, 467
beams, 768–772, 776–785, 791
deflection and, 768–772, 776–785, 791
displacement (d) and, 446, 467
force (flexibility) method for, 777–780
load-displacement relationships, 446–452, 467, 777–780
method of, 768–772, 776–785, 791
primary beam for, 777
principle of, 446, 467
procedure for analysis of, 780
redundants (reactions) from, 776–779, 791
statically indeterminate members, 447–452, 467,
776–785, 791
Support reactions, 177–179, 203–207, 236–237
free-body diagrams for, 177–179, 203–207
prevention of motion by, 177, 203
three-dimensional rigid-bodies, 203–207, 237
two-dimensional rigid bodies, 177–179, 236
types of, 178–179, 204–205
T
Tensile forces, 243–244, 257–258
Tension test, 397–398
Thermal stress, 459–462, 467
Thin-walled pressure vessels, 609–612, 632
Three-dimensional rigid-bodies, 203–217, 237
equations of equilibrium, 208–211, 237
equilibrium of, 203–217
free-body diagrams for, 203–207
procedure for analysis of, 209
support reactions, 203–207, 237
unknown forces in, 203, 206, 209, 237
Time, units of, 26
Tipping, 218, 224
Torque, 97, 471. See also Moments (M)
Torsion, 470–515
angle of twist, 472–473, 492–499, 513
circular shafts, 471–473, 513
constant cross-sectional area (A), 493–494
deformation, 471–473, 513
internal torque and, 474–475, 492–493, 496
polar moment of inertia and, 310, 326, 475–476
power transmission, 482–483, 513Index 927
Torsion (continued)
procedures for analysis of, 478, 496, 507
shafts, 471–473, 482–483, 506–509, 513
shear stress distribution, 477
statically indeterminate members, 506–509, 513
torsion formula, 474–481, 513
Torsional moment (T), internal resultant loadings, 331
Translational motion, 138–140, 159, 177, 203
force and couple system simplification, 138–140
supports for prevention of, 177, 203
Transmissibility, principle of, 104, 138
Transverse shear, 576–607
beams, 576–607
built-up members, 596–600, 605
cross-sectional moment (Q), 580–581
longitudinal shear stress and, 577–578
procedures for analysis of, 584
shear flow (q), 596–600, 605
shear formula for, 578–589, 605
shear-stress distribution, 578–579, 605
Triangle rule, 36–37, 91
Triaxial stress, 700
Trigonometric functions and identities, 829–830
True stress–strain diagram, 401
Trusses, 241–265, 282–283
compressive forces, 243–244, 257–258
design assumptions, 242–243
forces determined by inspection, 244, 250, 258
free-body diagrams for, 244–251, 257–262, 282–283
joint connections, 242
method of joints, 244–249, 282
method of sections, 257–262, 283
procedures for analysis of, 245, 259
simple, 241–243, 282
structural analysis of, 241–265, 282–283
tensile forces, 243–244, 257–258
zero-force members, 250–252
Twisting, 471–473
Two-dimensional (coplanar) rigid bodies, 176–202, 236
equations of equilibrium, 187–192
equilibrium of, 176–202, 236
free-body diagrams for, 177–185
procedures for analysis of, 182, 188
support reactions, 177–179, 236
three-force members, 193–194
two-force members, 193–194
unknown forces in, 177, 188, 236
U
Ultimate stress (su), 401, 418
Uniaxial stress, 348
Uniform deformation, 346
Unit vectors, 50, 58–61, 73, 73–75, 92
Units of measurement, 26–27, 28, 345, 380, 393, 482, 721
base units, 26
derived units, 26
dimensional homogeneity, 28
dimensionless quantity and, 380, 393
foot-pound-second system, 345
force, 26
International System (SI), 26–27
length, 26
mass, 26
nominal dimensions, 721
power, 482
rules for use, 27
SI prefixes, 26–27
strain, 380
stress, 345
time, 26
weight, 26
Unstable equilibrium, 219, 796
Unsymmetric bending, 562–568, 573
bending moment (M) of, 562–568, 573
moment arbitrarily applied, 564
neutral axis orientation, 565
principal axis, moment applied to, 562–563, 573
product of inertia (I ) for, 563
V
Varignon’s theorem, 108–110
Vectors, 34–95, 101–107, 120–121, 128, 138–143,
169–170, 208
addition, 36–37, 38–43, 49–54, 61–64, 91–93
angle (u), 35, 59–61, 82, 92–93
arrow notation, 35, 49, 91
Cartesian, 50, 58–64, 70–75, 81, 92–93, 102–103,
105–107, 169
collinear, 37, 91
component, 36, 38–39, 49–54
coplanar forces, 49–54
couple moments, 128, 170
cross product for, 101–103, 169–170
directed along a line, 73–75, 82, 93
direction of, 35, 38, 49, 58–61, 70–71, 73, 101–102, 104
division of by a scalar, 36, 91
dot product, 81–85, 93, 120
equations of equilibrium, 208
force and, 34–95, 128, 169
force and couple systems, 138–143
free, 128, 138–139
line of action, 35, 119, 138, 169
magnitude of, 35, 49, 59, 91–92, 101, 104
moment of force about an axis, 120–121, 169
multiplication by a scalar, 36, 91
parallelogram law for, 36–37, 40, 91
position, 70–72, 93, 169
procedures of analysis for, 40928 Index
rectangular components, 50–51, 58–64, 70–71, 92–93
resultant moments and, 105–107, 169
resultants of a force, 36–38, 50–51, 91, 93, 101–107, 129–
130, 169
right-hand rule for, 58
scalars and, 35–36, 49, 91
several forces, 39
sliding, 104, 138
subtraction, 37
three-dimensional components, 58–64, 70–71, 92–93
triangle rule for, 36–37, 91
two-dimensional components, 50–51, 92
unit, 50, 58–61, 73–75, 92
x, y, z coordinates, 58–60, 70, 92–93
Vertical angle (f), 60–61
Volume (V), centroid of, 289, 325, 832–833
Volume changes (hydrostatic loading), 703, 713
W
Warping, 578
Weight (W), 25, 26, 180, 287–289, 325
center of gravity (G) and, 180, 287–289, 325
free-body diagrams and, 180
gravitational force and, 25
rigid-body equilibrium and, 180
units of, 26
Wide-flange sections, 834–837
Wood, ductility of, 404
Wood sections, structural design and, 721
X
x, y, z coordinates, 58–60, 70, 92–93
Y
Yield point (sY), 400, 406, 408, 424–425
Yield strength, 403–404
Yielding, 400
Young’s modulus (E), 400
Z
Zero force, 176. See also Equilibrium
Zero-force members, 250–252

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