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TitleIntroduction to Engineering Mechanics
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Total Pages491
Table of Contents
                            Cover
Title Page
Copyright
Contents
Preface
About the Authors
1 Introduction
	1.1 A Motivating Example: Remodeling an Underwater Structure
	1.2 Newton’s Laws: The First Principles of Mechanics
	1.3 Equilibrium
	1.4 Definition of a Continuum
	1.5 Mathematical Basics: Scalars and Vectors
	1.6 Problem Solving
	1.7 Examples
		Example 1.1
		Example 1.2
	1.8 Problems
	Notes
2 Strain and Stress in One Dimension
	2.1 Kinematics: Strain
		2.1.1 Normal Strain
		2.1.2 Shear Strain
		2.1.3 Measurement of Strain
	2.2 The Method of Sections and Stress
		2.2.1 Normal Stresses
		2.2.2 Shear Stresses
	2.3 Stress–Strain Relationships
	2.4 Equilibrium
	2.5 Stress in Axially Loaded Bars
	2.6 Deformation of Axially Loaded Bars
	2.7 Equilibrium of an Axially Loaded Bar
	2.8 Indeterminate Bars
		2.8.1 Force (Flexibility) Method
		2.8.2 Displacement (Stiffness) Method
	2.9 Thermal Effects
	2.10 Saint-Venant’s Principle and Stress Concentrations
	2.11 Strain Energy in One Dimension
	2.12 A Road Map for Strength of Materials
	2.13 Examples
		Example 2.1
		Example 2.2
		Example 2.3
		Example 2.4
		Example 2.5
		Example 2.6
		Example 2.7
		Example 2.8
		Example 2.9
	2.14 Problems
	Case Study 1: Collapse of the Kansas City Hyatt Regency Walkways
		Problems
	Notes
3 Strain and Stress in Higher Dimensions
	3.1 Poisson’s Ratio
	3.2 The Strain Tensor
	3.3 Strain as Relative Displacement
	3.4 The Stress Tensor
	3.5 Generalized Hooke’s Law
	3.6 Limiting Behavior
	3.7 Properties of Engineering Materials
		Ferrous Metals
		Nonferrous Metals
		Nonmetals
	3.8 Equilibrium
		3.8.1 Equilibrium Equations
		3.8.2 The Two-Dimensional State of Plane Stress
		3.8.3 The Two-Dimensional State of Plane Strain
	3.9 Formulating Two-Dimensional Elasticity Problems
		3.9.1 Equilibrium Expressed in Terms of Displacements
		3.9.2 Compatibility Expressed in Terms of Stress Functions
		3.9.3 Some Remaining Pieces of the Puzzle of General Formulations
	3.10 Examples
		Example 3.1
		Example 3.2
	3.11 Problems
	Notes
4 Applying Strain and Stress in Multiple Dimensions
	4.1 Torsion
		4.1.1 Method of Sections
		4.1.2 Torsional Shear Stress: Angle of Twist and the Torsion Formula
		4.1.3 Stress Concentrations
		4.1.4 Transmission of Power by a Shaft
		4.1.5 Statically Indeterminate Problems
		4.1.6 Torsion of Inelastic Circular Members
		4.1.7 Torsion of Solid Noncircular Members
		4.1.8 Torsion of Thin- Walled Tubes
	4.2 Pressure Vessels
	4.3 Transformation of Stress and Strain
		4.3.1 Transformation of Plane Stress
		4.3.2 Principal and Maximum Stresses
		4.3.3 Mohr’s Circle for Plane Stress
		4.3.4 Transformation of Plane Strain
		4.3.5 Three-Dimensional State of Stress
	4.4 Failure Prediction Criteria
		4.4.1 Failure Criteria for Brittle Materials
		4.4.2 Yield Criteria for Ductile Materials
	4.5 Examples
		Example 4.1
		Example 4.2
		Example 4.3
		Example 4.4
		Example 4.5
		Example 4.6
		Example 4.7
		Example 4.8
		Example 4.9
		Example 4.10
		Example 4.11
	4.6 Problems
	Case Study 2: Pressure Vessel Safety
		Why Are Pressure Vessels Spheres and Cylinders?
		Why Do Pressure Vessels Fail?
		Problems
	Notes
5 Beams
	5.1 Calculation of Reactions
	5.2 Method of Sections: Axial Force, Shear, Bending Moment
		Axial Force in Beams
		Shear in Beams
		Bending Moment in Beams
	5.3 Shear and Bending Moment Diagrams
		Rules and Regulations for Shear and Bending Moment Diagrams
	5.4 Integration Methods for Shear and Bending Moment
	5.5 Normal Stresses in Beams
	5.6 Shear Stresses in Beams
	5.7 Examples
		Example 5.1
		Example 5.2
		Example 5.3
		Example 5.4
		Example 5.5
		Example 5.6
	5.8 Problems
	Case Study 3: Physiological Levers and Repairs
		The Forearm Is Connected to the Elbow Joint
		Fixing an Intertrochanteric Fracture
		Problems
	Notes
6 Beam Deflections
	6.1 Governing Equation
	6.2 Boundary Conditions
	6.3 Solution of Deflection Equation by Integration
	6.4 Singularity Functions
	6.5 Moment Area Method
	6.6 Beams with Elastic Supports
	6.7 Strain Energy for Bent Beams
	6.8 Flexibility Revisited and Maxwell- Betti Reciprocal Theorem
	6.9 Examples
		Example 6.1
		Example 6.2
		Example 6.3
		Example 6.4
	6.10 Problems
	Notes
7 Instability: Column Buckling
	7.1 Euler’s Formula
	7.2 Effect of Eccentricity
	7. 3 Examples
		Example 7.1
		Example 7.2
	7.4 Problems
	Case Study 4: Hartford Civic Arena
	Notes
8 Connecting Solid and Fluid Mechanics
	8.1 Pressure
	8.2 Viscosity
	8.3 Surface Tension
	8.4 Governing Laws
	8.5 Motion and Deformation of Fluids
		8.5.1 Linear Motion and Deformation
		8.5.2 Angular Motion and Deformation
		8.5.3 Vorticity
		8.5.4 Constitutive Equation (Generalized Hooke’s Law) for Newtonian Fluids
	8.6 Examples
		Example 8.1
		Example 8.2
		Example 8.3
		Example 8.4
	8.7 Problems
	Case Study 5: Mechanics of Biomaterials
		Nonlinearity
		Composite Materials
		Viscoelasticity
		Problems
	Notes
9 Fluid Statics
	9.1 Local Pressure
	9.2 Force Due to Pressure
	9.3 Fluids at Rest
	9.4 Forces on Submerged Surfaces
	9.5 Buoyancy
	9.6 Examples
		Example 9.1
		Example 9.2
		Example 9.3
		Example 9.4
		Example 9.5
	9.7 Problems
	Case Study 6: St. Francis Dam
		Problems
	Note
10 Fluid Dynamics: Governing Equations
	10.1 Description of Fluid Motion
	10.2 Equations of Fluid Motion
	10.3 Integral Equations of Motion
		10.3.1 Mass Conservation
		10.3.2 F = ma, or Momentum Conservation
		10.3.3 Reynolds Transport Theorem
	10.4 Differential Equations of Motion
		10.4.1 Continuity, or Mass Conservation
		10.4.2 F = ma, , or Momentum Conservation
	10.5 Bernoulli Equation
	10.6 Examples
		Example 10.1
		Example 10.2
		Example 10.3
		Example 10.4
		Example 10.5
		Example 10.6
	10.7 Problems
	Notes
11 Fluid Dynamics: Applications
	11.1 How Do We Classify Fluid Flows?
	11.2 What’s Going on Inside Pipes?
	11.3 Why Can an Airplane Fly?
	11.4 Why Does a Curveball Curve?
	11.5 Problems
	Notes
12 Solid Dynamics: Governing Equations
	12.1 Continuity, or Mass Conservation
	12.2 F = ma, or Momentum Conservation
	12.3 Constitutive Laws: Elasticity
	Note
References
Appendix A: Second Moments of Area
Appendix B: A Quick Look at the Del Operator
	Divergence
		Physical Interpretation of the Divergence
		Example
	Curl
		Physical Interpretation of the Curl
		Examples
	Laplacian
Appendix C: Property Tables
Appendix D: All the Equations
Index
                        
Document Text Contents
Page 2

Introduction to

Engineering
Mechanics

A Continuum Approach

Page 245

226 Introduction to Engineering Mechanics: A Continuum Approach

L

kx

x

Figure 5.25

For Figure 5.25, we start with the external reactions, using the equivalent
concentrated load in place of the distributed one (Figure 5.26).

3
1– kL3

2
1 kL2

2
1 kL  L = 2

1 kL2

Figure 5.26

Since the distributed load is linearly distributed, the shear distribution is
parabolic, and the moment distribution is cubic. Or we may proceed either by
integrating the distributed load q(x) = kx once for V(x) and twice for M(x) or by
making our imaginary cut at some distance x from the end of the beam and find-
ing the internal shear and moment. Both methods provide the same results.

Integration



V x qdx kxdx kx C

V kL C

V x

( ) .

( ) .

( )

=− = =− +

= =

∫ ∫ 12 2
1
2

20

== −1
2

2 1
2

2kL kx .



M x Vdx kL x kx C

M kL C

M x

( ) .

( ) .

( )

= = − +

=− =

∫ 12 2 16 3
1
3

30

== − −1
2

2 1
6

3 1
3

3kL x kx kL .

Page 246

Beams 227

Method of Sections

x

x/3

2
1 kx2

3
1 kL3

2
1 kL2

V(x)

M(x)

Figure 5.27

ΣFz = 0 = − +12
2 1

2
2kL kx + V(x).

so V(x) = 1
2

2 1
2

2kL kx− .

ΣMx = 0 = M(x)+ − + ( )13
3 1

2
2 1

2
2

3
kL kL x kx x .

We note that the internal shear V(x) does not cause a moment about the cut
at x, so

M(x) =− + −1
3

3 1
2

2 1
6

3kL kL x kx .

The resulting shear and moment diagrams are as shown in Figure 5.28.

kL2/2

–kL3/3

L

kx

x

Figure 5.28

Page 490

Index 471

T
Tangential deviation, 263
Tangential stress, 28
Temperature
effects of, 35, 98, 121n.4
fluid viscosity, 313, 314f
Tensile forces, 21, 27
Tensile load, 102
Tensile specimen, 20f
Tensile strain, 49
Tensile strength, 141
problem, 71, 72f
Tensile testing, 99, 99f
Thermal strains definition, 48–49
Thermal stresses
steel railroad track example, 66–67
strain energy, 52f, 52–53
thin-walled pressure vessels, 143
Thermoplastics, 104
Thick-walled pressure vessels, 141
Thin-walled pressure vessels, 141
Thin-walled structures, 107
Thin-walled tubes, 138f, 138–140, 140f
Third-dimensional state of stress,

156–157
Three-dimensional equilibrium, 5
Three-dimensional stress state, 105–107,

106f
Three-dimensions
Hooke’s law, 96
strain-displacement, 92
Thrust, 418
Timber properties, 450t, 451t
Titanium, 103
Torque
examples, 163–164
indeterminacy, 131–133
and stress, assumptions, 125
twisting moment, 123, 124, 124f
Torsion
circular shafts formula, 128, 133
examples, 162f, 162–163
noncircular solids, 135–138
twisting moment, 123, 124f
term, 124
testing, 129
Torsional load,
Mohr’s circle, 153, 154f
term, 124

Torsional shear stress, 125–130, 126f,
127f, 129f

Torsional stiffness example, 170, 170f
Torsional stress-concentration, circular

shafts, 130f
Toughness definition, 102
Traction vector, 92
Transverse contraction, 85
Tresca criterion
cylindrical pressure vessel problem,

187
ductile material failure, 161
Trigonometric identities, 296
True strain, 21
Truss
example, 64–66
problem, 70, 71f
shear stress, 29, 29f, 31
Tubes
thin-walled in torsion, 138f, 138–140,

140f
torsion formula, 128
Tubular cross sections, 125
Tubular steel shaft problems, 185, 187
Turbulent flow
airplane flight, 418–419
curveballs, 420, 423f
Reynolds number, 412, 413t
Twisting moment, 123
Two shafts shear stresses and angle of

twist example, 166-169, 168f,
169f

Two-dimensional elasticity
applied loads, 113
compatibility, 111-112, 113
displacements, 110–111, 112
equation formulation, 109–114
examples, 114–116, 115f, 116f
problems, 116–120, 118f, 119f, 120f
Two-dimensional equilibrium, 5–6
Two-dimensional plane strain, 107, 108f,

108–109
Two-dimensions
extensional strain, 88f
Hooke’s law, 96

U
Ultimate material strength, 98, 100t
Ultimate torque, 134

Page 491

472 Index

Underwater rig
bolts, 30
mud-slide type platform, 2f
remodeling, 2–3, 3f
structures, 20f
truss, 29, 29f, 31
Ut tensio, sic vis, Hooke’s law, 32, 33

V
Vector(s)
and area, 92
components, 9–10
decomposition, 10f
equations, 455
example, 13–14
as first-order tensor, 89
and force, 92
internal forces as, 26
and Newton’s second law, 5
notation, 9, 11
problem, 17
Velocity, pipe flow average, 416–417
Velocity field, 316, 317
Velocity gradient, 316–317
Vertical surfaces, 349, 349f
Viscoelastic materials
deformation, 336
hysteresis, 336f, 336–337
mechanical models, 337f, 337
problems, 338
Viscosity
airplane flight, 417, 418f
dominant flow effect, 411–412
fluids, 311f, 311–314, 313f, 314f
pipe flows, 413, 417
Vise grip, 123
Voigt, Woldemar, 338
Volume
change/change rate, 455t
fluid motion equations, 379
Volumetric strain rate, 317

Von Mises criterion
cylindrical pressure vessel problem,

187
ductile material failure, 161–162
Vortices, 420, 421f
Vorticity, 319–320
Vorticity vector, 320

W
Wakes, 419, 421f
Water, typical properties, 453t, 454t
Water jet stream example, 396f, 396–398
Water siphon example, 402f, 402–404,

403f
Water tanks problem, 370, 370f
Watt unit, 131
Watt, James, 131
Weber number, 412, 413t
Weight, force analysis, 418
Weight and mass example, 15–17
Withstanding load, 19
Wood. See also Timber
grain, 35
nonmetals, 104
shear stress problem, 74
yield properties, 100t
Wood I beam example, 234–236
Wood post/concrete bases problem, 73
Wooden plank problem, 370, 370f
Work definition, 131
Wrought iron, 103

Y
Yield criteria, 160
Yield point, 98
Yield properties, 100t
Yield stress, 98
Young, Thomas, 27, 33, 83n.7
Young, W. C., 136
Young’s modulus, 33, 35, 99

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