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An Engineering Companion to the Mechanics of Materials - A Systems Approach
Christopher H. Jenkins, Sanjeev K. Khanna
Mechanical & Industrial Engineering Department
Montana State University
و المحتوى كما يلي :
CONTENTS
Preface . ix
Chapter 1 Fundamentals 1
Learning objectives . 1
Clarifications 1
Importance 1
1.0 Representative Problems . 2
1.1 Mechanics and materials 2
1.2 Loads and Structures 3
1.3 Strength and Stiffness . 16
1.4 Modeling and Analysis . 18
1.5 Structural Design . 20
1.6 C3 Clarified 24
1.7 Developing Engineering Intuition 25
1.8 Resources . 27
Chapter 2 Basic Structures Level I 29
Learning objectives . 29
Clarifications 29
Importance 29
2.0 Representative Problems . 30
2.1 Definitions . 32
2.2 Geometry, Boundary Conditions, and Loads 38
2.3 Equilibrium under Simple Loading 46
2.4 Uniaxial Material Response 57
2.5 Structural Design . 64
2.6 C3 Clarified 73
2.7 Developing Engineering Intuition 75
Chapter 3 Basic Structures Level II . 77
Learning objectives . 77
Clarifications 77
Importance 77x CONTENTS
3.0 Representative Problems 79
3.1 Body Loads and Axial Response . 80
3.2 Equilibrium under General Loading I . 83
3.3 Flexural Structure Deformation I 94
3.4 Material Response in Flexure . 98
3.5 Flexural Structure Deformation II . 101
3.6 Structural design . 106
3.7 C3 Clarified . 112
3.8Developing Engineering Intuition 114
Chapter 4 Basic Structures Level III . 115
Learning objectives 115
Clarifications . 115
Importance 115
4.0 Representative Problems 117
4.1 General State of Stress and Strain 118
4.2 Analysis of Thin-Walled Torsion Structures 128
4.3 Three-Dimensional Stress-Strain Relationship . 138
4.4 Combined Axial, Torsional and Flexural Loading 145
4.5 Structural Design under Combined Loading . 164
4.6 Design III 170
4.7 C3 Clarified . 174
Appendices
A1. System of Units 177
A2. Free Body Diagrams . 179
A3. Centroid and Second Moment of Area 181
A4. Sign Conventions in Mechanics of Materials . 185
A5. Vectors and Tensors 195
Index 201
Index
American Institute for Steel
Construction (AISC), 17
Area moment of inertia, 42
Areas, sign conventions, 190
Axial structures, 32–37
compact compressive, 33
constitution, 58–59
equilibrium, 48–52
geometry and boundary
conditions, 38–39
strength, 60–61
Beams, 8, 35
beam-column, 84
bending sign conventions, 192–193
cantilever, 37
prismatic, 42
Bending moment, 35
Basis vector, 197
Biaxial stress field, 168
Body loads, 3
and axial response, 80–83
Boundary conditions, 9–14
axial structure, 38–39
flexural structure, 42–45
torsion structure, 39–41
Buckling
slender compressive axial structure,
33
Cables, 8
Cantilever beams, 37
Carrying loads, 5
Cartesian stress components, 174
Cauchy’s Stress Principal, 49, 50
Centroid, 183–184
Circular bending, 104
Co-axial loading, 45
Combined axial and flexural loading,
92–94
Combined loading
stress analysis for, 145–151
structural design under, 164–169
Compact compressive axial structure,
33
Constitution
axial structure, 58–59
flexural structure, 98–99
Coordinate degree of freedom
(CDOF), 38, 40, 43
Coordinate sign convention, 188
Couple, 175
Crane(s)
failure, 78
types of, 78
Deformation, 18–19, 124
elastic, 60
flexural structure, 94–98, 101–106
inelastic, 165
plastic, 165
stress/strain effects on, 127–128
uniaxial, 57–58
Density, 15, 24–25
Determinacy, 9–14
Direct stiffness method, 19
Displacement, 124
Dynamic loads, 4
Elastic curve, 101
Elastic deformation, 60
Elastic material, three-dimensional,
138–142
Elastic modulus, 59
Energetics, 142–145
Equilibrium, 2, 18, 20–23
axial structure, 48–52
flexural structure, 55–56, 83–92
global versus local, 73–74
under simple loading, 46–56202 INDEX
stress/strain effects on, 127–128
torsion structure, 52–55
Euler-Bernoulli assumptions, 94–95
Experimental analysis, 19
Factor of safety (FS), 17, 64
Finite element method, 19
First moment of area, 183
Flexural energetics, 99–100
Flexural structures, 35–37
constitution, 98–99
deformation, 94–98, 101–106
equilibrium, 55–56, 83–92
geometry and boundary
conditions, 42–45
Forces
sign conventions, 188–190
Free body diagram (FBD), 19, 48,
55, 86, 87, 90, 181–182,
193–194
Gravity loads, 80–83
Hooke’s Law, 59, 63, 98–99, 113, 138
Hyatt Regency walkway collapse, 29
Inelastic deformation, 165
Inertia, 184
Kinetic energy, 61
Lagrangian mechanics approach, 61
Line-forming elements (LFEs), 6–8
Line load, 24
Load(s/ing), 45–46
body, 3
carrying, 5
co-axial, 45
dynamic, 4
gravity, 80–83
line, 24
orientation of, 4, 5
path, 25–27
point, 24
simple, 45, 46–56
static, 3–4
steady-state, 4
structural, 3–5
surface, 3
transient, 4
transverse, 35
Load and resistance factor design
(LRFD), 17
Mass, 15–16
Materials, properties of, 14–16
Materials science, 2
Maximum moment
from beam theory, 89
by statics alone, 86–89
Maximum shear stress theory, 166–169
Mechanics, 2
Mechanics of materials, 24
sign conventions in, 187–195
Modulus of toughness, 144
Mohr’s circle, for plane stress
problems, 151–160
Moment of inertia (MOI), 73, 184–185
Moments, 174–175
diagram, 86
sign conventions, 188–190
Multi-axial stresses, yielding under,
164–165
Newtonian mechanics, 19
Normal force, 121
Normal strain, 124–125
Normal stress, 190
Oblique plane, stresses on, 148
Parallel Axis Theorem, 184
Plane stress, 146
problems, Mohr’s circle for,
151–160
stress transformation in, 147
in three-dimensional stress state,
161–164INDEX 203
Plastic deformation, 165
Plates, 8
Point load, 24
Polar moment of inertia, 39, 54
Position vector, 197
Potential energy, 61
Primary structure, 1
Principal normal stress, 149
Principle of minimum potential
energy, 63
Principle of superposition, 5, 144
Prismatic beams, 42
Representative problems, 2
Rods, 8
Secondary structure, 1
Second moment of area (SMoA), 73,
184–185
Shear
deformation, 105
diagram, 86
flow, in thin-walled torsion
structures, 129–131
force, 74, 121
strain, 125–126
stress, 50, 191
Shell, 8
Sign conventions in mechanics of
materials, 187–195
areas, 190
coordinate sign convention, 188
forces and moments, 188–190
stress sign convention, 190–195
Simple loading, 45
equilibrium under, 46–56
Slender compressive axial structure, 33
Static loads, 3–4
Steady-state loads, 4
Stiffness, 16–17, 58
Strain, 46
at a point, general states of, 124–127
effects on equilibrium and
deformation, 127–128
energy, 61, 142–145
energy density, 143–145
engineering, 57, 59
extensional, 96
measurement of, 74
normal, 124–125
shear, 125–126
Strain-curvature relationship, 97, 101
Strain–displacement relation, 57
Strength, 16–17
design problems, 30–31
Stress, 46, 175
analysis, for combined loading,
145–151
at a point, general states of, 118–124
Cartesian components of, 122
effects on equilibrium and
deformation, 127–128
engineering, 59
failure, 60
invariants, 161, 162
measurement of, 74
normal, 50, 190
shear, 50, 191
sign convention, 190–195
vector, 74
yield, 166
Stress-couple, 101
Stress–strain relations, 19
Structural analysis
characteristic tasks in, 18
methods of, 18–20
Structural design, 20–23, 64–73
stiffness, 106–112, 113
Structural elements, 7
Structural loads, 3–5
Structure(s), 3, 24
axial. See Axial structures
definition of, 1
flexural. See Flexural structures
primary, 1
secondary, 1
taxonomy of, 5–8
torsion. See Torsion structures204 INDEX
Superposition, principle of, 5, 144
Surface-forming elements (SFEs), 7, 8
Surface loads, 3
System of units, 177–179
Tacoma Narrows Bridge, torsion
collisions of, 35
Taxonomy of structures, 5–8
Tensors, 46, 121, 200–201
strain, 127
Thin-walled torsion structures, 128–137
closed cross-section, shafts of,
131–134
open cross-section, shafts of,
136–137
shear flow in, 129–131
torsional shape factor, 134–135
Three-dimensional stress–strain
relationship, 138–145
elastic material, 138–142
energetics, 142–145
Torque, 174–175
Torsional shape factor, 134–135
Torsion constant, 132
Torsion structures, 34–35
equilibrium, 52–55
geometry and boundary
conditions, 39–41
Traction vector, 74
Transient loads, 4
Transverse load, 35
Two concentrated loads, 90–92
Uniaxial deformation, 57–58
Uniaxial energy, 61–64
Uniaxial material response, 57–64
axial structure constitution, 58–59
axial structure strength, 60–61
uniaxial deformation, 57–58
uniaxial energy, 61–64
Unit vector, 197
Vectors
addition of, 198
basis, 197
definition of, 197
multiplication by scalar, 198–199
position, 197
product of two vectors, 200
subtraction of, 198
unit, 197
Volume force, 74
Weight, 15
Yielding
criteria, 165–166
under multi-axial stresses, 164–165
Yield stress, 166
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