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أحضرت لكم كتاب
Mechanics of Materials, Volume 2
THIRD EDITION
An Introduction to the Mechanics of Elastic and Plastic Deformation of Solids and Structural Materials
E. J. HEARN
PhD; BSc(Eng) Hons; CEng; FIMechE; FIProdE; FIDiagE
University of Warwick
United Kingdom
و المحتوى كما يلي :
CONTENTS
Introduction xv
Notation xvii
1 Unsymmetrical Bending 1
Summary
Introduction
1.7 Momenta1 ellipse
1.8 Stress determination
1.9 Alternative procedurefor stress determination
1.10 Alternative procedure using the momenta1 ellipse
1.11 Dejections
Examples
Problems
Product second moment of area
Principal second moments of area
Mohr’s circle of second moments of area
Land’s circle of second moments of area
Rotation of axes: determination of moments of area in terms of the
principal values
The ellipse of second moments of area
2 Struts
Summary
Introduction
2.1 Euler’s theory
2.2 Equivalent strut length
2.3
2.4 Euler “validity limit”
2.5 Rankine or Rankine-Gordon formula
2.6 Perry- Robertsonformula
2.7
2.8 Struts with initial curvature
2.9 Struts with eccentric load
2.10 Laterally loaded struts
2.11
Comparison of Euler theory with experimental results
British Standard procedure (BS 449)
Alternative procedurefor any strut-loading condition
Vvi Contents
2.12 Struts with unsymmetrical cross-section
Examples
Problems
3 Strains Beyond the Elastic Limit
Summary
Introduction
Plastic bending of rectangular-sectioned beams
Shapefactor - symmetrical sections
Application to I-section beams
Partially plastic bending of unsymmetrical sections
Shapefactor - unsymmetrical sections
Dejections of partially plastic beams
Length of yielded area in beams
Collapse loads -plastic limit design
Residual stresses after yielding: elastic-perfectly plastic material
Torsion ofshafts beyond the elastic limit -plastic torsion
Angles of twist of shafts strained beyond the elastic limit
Plastic torsion of hollow tubes
Plastic torsion of case-hardened shafts
Residual stresses after yield in torsion
Plastic bending and torsion of strain-hardening materials
(a)Inelastic bending
(b)Inelastic torsion
Residual stresses- strain-hardening materials
Influence of residual stresses on bending and torsional strengths
Plastic yielding in the eccentric loadirzg of rectangular sections
Plastic yielding and residual stresses under axial loading with stress
concentrations
Plastic yielding of axially symmetric components
(a)Thick cylinders - collapse pressure
(b)Thick cylinders - “auto-frettage’’
(c)Rotating discs
Examples
Problems
4 Rings, Discs and Cylinders Subjected to Rotation
and Thermal Gradients
Summary
4.2 Rotating solid disc
Thin rotating ring or cylinder
Rotating disc with a central hole
Rotating thick cylinders or solid shafs
Rotating disc of uniform strength
125Contents
4.6 Combined rotational and thermal stresses in uniform discs and
thick cylinders
Examples
Problems
5 Torsion of Non-Circular and Thin-Walled Sections
Summary
Rectangular sections
Narrow rectangular sections
Thin-walled open sections
Thin-walled split tube
Other solid (non-tubular)shafts
Thin-walled closed tubes of non-circular section (Bredt-Batho theory)
Use of “equivalentJ ” for torsion of non-circular sections
Thin-walled cellular sections
Torsion of thin-walled stifSened sections
Membrane analogy
EfSect of warping of open sections
Examples
Problems
6 Experimental Stress Analysis
Introduction
Brittle lacquers
Strain gauges
Unbalanced bridge circuit
Null balance or balanced bridge circuit
Gauge construction
Gauge selection
Temperature compensation
Installation procedure
Basic measurement systems
D.C. and A.C. systems
Other types of strain gauge
Photoelasticity
Plane-polarised light - basic polariscope arrangements
Temporary birefringence
Production offringe patterns
Interpretation offringe patterns
Calibration
Fractional fringe order determination - compensation techniques
Isoclinics-circular polarisation
Stress separation procedures
Three-dimensional photoelasticity
VI11 Contents
6.22 Rejective coating technique
6.23 Other methods of strain measurement
Bibliography
7 Circular Plates and Diaphragms
Summary
A. CIRCULAR PLATES
Stresses
Bending moments
General equation for slope and dejection
General case of a circular plate or diaphragm subjected to
combined uniformly distributed load q (pressure)and central
concentrated load F
Uniformly loaded circular plate with edges clamped
Uniformly loaded circular plate with edgesfreely supported
Circular plate with central concentrated load F and edges clamped
Circular plate with central concentrated load F and edges freely
supported
Circular plate subjected to a load F distributed round a circle
Application to the loading of annular rings
Summary of end conditions
Stress distributions in circular plates and diaphragms subjected to
lateral pressures
Discussion of results - limitations of theory
Other loading cases of practical importance
B. BENDING OF RECTANGULAR PLATES
7.15
7.16
Rectangular plates with simply supported edges carrying uniformly
distributed loads
Rectangular plates with clamped edges carrying uniformly distributed
loads
Examples
Problems
8 Introduction to Advanced Elasticity Theory
8.1 Types of stress
The Cartesian stress components: notation and sign convention
8.2.1 Sign conventions
The state of stress at a point
Direct, shear and resultant stresses on an oblique plane
8.4.1
8.4.2
Line of action of resultant stress
Line of action of normal stress
227Contents ix
Principal stresses and strains in three dimensions - Mohr 's circle
representation
Graphical determination of the direction of the shear stress r,, on an
inclined plane in a three-dimensional principal stress system
The combined Mohr diagram for three-dimensional stress and strain
systems
Application of the combined circle to two-dimensional stress systems
Graphical construction for the state of stress at a point
Constructionfor the state of strain on a general strain plane
State of stress-tensor notation
The stress equations of equilibrium
Principal stresses in a three-dimensional Cartesian stress system
8.13.1 Solution of cubic equations
Stress invariants - Eigen values and Eigen vectors
Stress invariants
Reduced stresses
Strain invariants
Alternative procedure for determination of principal stresses
8.18.1 Evaluation of direction cosines for principal stresses
Octahedral planes and stresses
Deviatoric stresses
Deviatoric strains
Plane stress and plane strain
8.22.1 Plane stress
8.22.2 Plane strain
The stress-strain relations
The strain-displacement relationships
The strain equations of transformation
Compatibility
The stress function concept
8.27.1 Forms of Airy stressfunction in Cartesian coordinates
8.27.2 Case 1 - Bending of a simply supported beam by a uniformly
8.27.3 The use of polar coordinates in two dimensions
8.27.4 Forms of stress function in polar coordinates
8.27.5 Case 2 - hi-symmetric case: solid shaft and thick cylinder
radially loaded with uniform pressure
8.27.6 Case 3 - The pure bending of a rectangular section
curved beam
8.27.7 Case 4 - Asymmetric case n = 1. Shear loading of a circular
arc cantilever beam
8.27.8 Case 5 - The asymmetric cases n >, 2 -stress concentration at
a circular hole in a tension$eld
Line of action of shear stress
Shear stress in any other direction on the plane
distributed loading
276X Contents
8.27.9 Other useful solutions of the biharmonic equation
Examples
Problems
9 Introduction to the Finite Element Method
Introduction
Basis of thefinite element method
Applicability of thefinite element method
Formulation of the Jinite element method
General procedure of the Jinite element method
9.4.1 Identification of the appropriateness of analysis by the jinite
element method
9.4.2 Identification of the type of analysis
9.4.3 Idealisation
9.4.4 Discretisation of the solution region
9.4.5 Creation of the material model
9.4.6 Node and element ordering
9.4.7 Application of boundary conditions
9.4.8 Creation of a data file
9.4.9 Computer, processing, steps
9.4.10 Interpretation and validation of results
9.4.11 Modification and re-run
Fundamental arguments
9.5.1 Equilibrium
9.5.2 Compatibility
9.5.3 Stress-strain law
9.5.4 Forceldisplacement relation
The principle of virtual work
A rod element
9.7.1 Formulation of a rod element using fundamental equations
9.7.2 Formulation of a rod element using the principle of virtual work
equation
A simple beam element
9.8.1 Formulation of a simple beam element using fundamental
equations
93.2 Formulation of a simple beam element using the principle of
virtual work equation
A simple triangular plane membrane element
9.9.1 Formulation of a simple triangular plane membrane element
using the principle of virtual work equation
Formation of assembled stcfiess matrix by use of a dof.
correspondence table
Amlieation of boundarv conditions and uartitioninn
349Contents xi
9.12 Solutionfor displacements and reactims
Bibliography
Examples
Problems
10 Contact Stress, Residual Stress and Stress Concentrations
Summary
10.1 Contact stresses
Introduction
10.1.1 General case of contact between two curved surfaces
10.1.2 Special case I - Contact of parallel cylinders
10.1.3 Combined normal and tangential loading
10.1.4 Special case 2 - Contacting spheres
10.1.5 Design considerations
10.1.6 Contact loading of gear teeth
10.1.7 Contact stresses in spur and helical gearing
10.1.8 Bearing failures
Introduction
10.2.1 Reasom for residual stresses
(a)Mechanical processes
(b)Chemical treatment
(c)Heat treatment
(d)Welds
(e)Castings
10.2 Residual stresses
10.2.2 The injuence of residual stress onfailure
10.2.3 Measurement of residual stresses
The hole-drilling technique
X-ray difiaction
10.2.4 Summary of the principal effects of residual stress
Introduction
10.3.1 Evaluation of stress concentrationfactors
10.3.2 St. Venant'sprinciple
10.3.3 Theoretical considerations of stress concentrations due to
10.3 Stress concentrations
concentrated loads
(a)Concentrated load on the edge of an infiniteplate
(b)Concentrated load on the edge of a beam in bending
10.3.4 Fatigue stress concentrationfactor
10.3.5 Notch sensitivity
10.3.6 Strain concentration-Neuber's rule
10.3.7 Designing to reduce stress concentrations
(a)Fillet radius
(b)Keyways or splines
427xii Contents
(e)Grooves and notches
( d )Gear teeth
(e)Holes
cf) Oil holes
(g) Screw threads
(h)Press or shrink Jit members
10.3.8 Use of stress concentration factors with yield criteria
10.3.9 Design procedure
References
Examples
Problems
11 Fatigue, Creep and Fracture
Summary
11.1 Fatigue
Introduction
11.1.1 The SIN curve
11.1.2 PISIN curves
11.1.3 Effect of mean stress
1 1.1.4 Effect of stress concentration
11.1.5 Cumulative damage
1 1.1.6 Cyclic stress-strain
11.1.7 Combating fatigue
11.1.8 Slip bands and fatigue
Introduction
1 1.2.1 The creep test
11.2.2 Presentation of creep data
11.2.3 The stress-rupture test
11.2.4 Parameter methods
11.2.5 Stress relaxation
11.2.6 Creep-resistant alloys
11.3 Fracture mechanics
Introduction
11.3.1 Energy variation in cracked bodies
(a) Constant displacement
(b)Constant loading
(a)Grifith'scriterion for fiacture
(b)Stress intensity factor
11.2 Creep
11.3.2 Linear elastic fracture mechanics (L.E.F.M.)
11.3.3 Elastic-plastic fracture mechanics (E.P.F.M.)
11.3.4 Fracture toughness
11.3.5 Plane strain and plane stress fracture modes
11.3.6 General yielding fracture mechanics
11.3.7 Fatigue crack growth
11.3.8 Crack tip plasticity under fatigue loading
488Contents X l l l ...
11.3.9 Measurement of fatigue crack growth
References
Examples
Problems
12 Miscellaneous topics 509
12.1 Bending of beams with initial curvature
12.2 Bending of wide beams
12.3 General expression for stresses in thin-walled
pressure or selj-weight
12.4 Bending stresses at discontinuities in thin shells
12.5 Viscoelasticity
References
Examples
Problems
shells subjected to
Appendix 1. npical mechanical and physical properties for
engineering metals
Appendix 2. Typical mechanical properties of non-metals
Appendix 3. Other properties of non-metals
Index 537
INDEX
AC system 179
Acoustic gauge 180
Acoustoelasticity 192
Active gauge 172, 176, 178-9
Airy stress function 263, 265
Allowable working load 73
Alternating stress amplitude 447
Annular rings 208
Area, principal moments of 4
Area, product moment of 3
Area, second moment of 3- 10
Auto frettage 89
Ayrton and Perry 42
Balanced circuit 173
Banded method 313
Basquin’s law 457
Beams, curved 509
Bending, of beams 509-16
Bending, unsymmetrical 1
Birefringence 183
Body force stress 220
Boundary condition, application 316, 349
Boundary stress 185
Bredt-Batho theory 147, 150
Brittle lacquers 167
Buckling of struts 30
Built-up girders 52
Calibration 69, 169, 186
Capacitance gauge 180
Carrier frequency system 180
Cartesian stress 220
Case-hardened shafts 79
Circular plates 193
Circular polarisation 188
Clarke 168
Coffin-Manson Law 457
Collapse 64
Columns 30
Combined circle (Mohr) 228
Combined diagram 229
Compatibility 261, 321
Compensation 187
Conjugate diameters 13
Contact stress 382
Corkscrew rule 12
Correspondence table 347
Crack detection 169
Crack tip plasticity 482, 488
Creep 169,462
Crinkling of struts 50
Crossed set-up 182
Cross-sensitivity 173
Crushing stress 37
Cyclic stress-strain 455
Cylinders, residual stresses in 87
Cylindrical components 239
Dark field 182
DC system 179
De Forrest 168
Deflections, unsymmetrical members 15
Deviatoric stress 251
Diaphragms 193
Directions cosine 223
Disc
circular, solid 119
plastic yielding of 94
rotating 117
uniform strength 125
with central hole 122
Discretisation 305
Distortion 311
Dummy gauge 172, 175-6
Dye-etchant 169
Dynamic strain 171
Eccentric loading
of struts 42
to collapse 85
momenta1 11
of second moments of area 9
Ellipse
Ellis 168
Endurance limit 423
Equilibrium 319
Equilibrium
Cartesian coordinates 236
cylindrical coordinates 239
Equivalent length 35
Equivalent length (of Struts) 35
Euler theory 31
Extensometers 180
Factor, load 41,65, 166
Fatigue 446
Fatigue crack growth 486,489
Finite element analysis 302
537538 Index
Finite element mesh 308
Finite element method 300
Fixed-ended struts 33
Flexural stiffness 193. 197
Foil gauge 171, 173
Fracture mechanics 47
Fringe order 185-6
Fringe pattern 181-2,
Fringe value 185-6
Frontal method 315
Frozen stress technique
Full bridge circuit 173
84- 192,420,481
190
Gauge
acoustic 180
electrical resistance
strain 171-80
factor 172
17 1-180
Girder, built-up 50, 52
Graphical pmedure, stress 228-9
Grid technique 192
Griffith’s criterion 475
Half-bridge 172-3
Het6nyi 84
Holography 192
Hydrostatic stress 249, 251
Idealisation 305
Inductance gauge 180
Initial curvature 41
Interference 181, 184
Isochromatic 185
Isoclinic 188
Johnson parabolic formula 36
Land’s circle of moments of area 7
Larson-Miller parameter 468
Laterally loaded struts 46
Light field 182
Load factor 41, 73
Manson-Haferd parameter 469
Material fringe value 185-6
Maximum compressive stress 381, 385,387
Mean stress 252.45 1
Membrane 152
Modulus. reduced 82
Mohr’s circle of second moments of area
Mohr’s strain circle 228
Mohr’s stress circle 228
Moir6 192
Momenta1ellipse 1 I , 13
Monochromatic light 185
6
Neuber’s rule 425
Notch sensitivity 424
Null balance 173
Oblique plane, stress on 224
Octahedral planes 249
Octahedral shear stress 250
Octahedral stress 249
Overspeeding 95
Parallel set-up 183
Partitioning 349
Perry-Robertson 29.39
Photoelastic coating 190
Photoelasticity
reflection 190
transmission 181
Piezo-resistive gauge 180
Plane polarisation 182
Plane strain 254
Plane stress 254
Plastic bending 64
Plastic deformation
discs 94
thick cylinder 87
Plastic hinge 71
Plastic limit design 71
Plastic torsion 75, 79
Pneumatic gauge 180
Polariscope 182
Polariser 182
Principal axes 2
Principal second moments of area 4
Principal strain 228
Principal stress 228, 247
Product second moment of area 3
Quarter-bridge 173
Quarter-wave plates 187
Radial stress 117-23, 125-8, 193-9
Radius of gyration 28
Rankine-Gordon theory 38
Rectangular plates 213
Reduced modulus 82
Reflection polariscope 190
Reflective coating 190
Refraction 183
Replica technique 192
Residual stresses 73.79.84.86.95-6.394
Resistivity 172
Rotating cylinders 124
Rotating discs
and rings 117
collapse 94
Rotating hollow discs 122
Rotating uniform strength discs 125
Ruge and Simmons 171Index 539
Safety factor 41, 65, 166
Saint-Venant 420
Sand heap analogy 78
Second moment of area 2- 10
ellipse of 9
principle 4
product 3
Semi-conductor gauges 180
Senarment 187
Shape factor 65
Shear flow 147
Shear stress 224
Sherby-Dom parameter 469
Skew loading 2
Slenderness ration 28
Smith-Southwell theory 42
Southwell 42
Specific resistance 172
Stem 168
Straight line formula 36
Strain
deviatoric 251, 253
invariants 247
threshold 167
Strain circle 228
Strain gauge 171
Strain hardening 63-4, 80
Stress
unsymmetrical sections 67,69
body force 220
boundary 185
Cartesian 220
concentration 86
concentration factor 408
concentration factor (evaluation) 413
crushing 37
deviatoric 246, 251
direct 224
equations of equilibrium 236
freezing technique 190
hydrostatic 249-51
invariants 243-4
mean 252,447,451
radial 193, 199
range 447
relaxation 470
separation 190
shear 224
tangential 193, 199
three-dimensional 220
trajectory 189
yield 61
Stress concentration, effects 453
Stress intensity factor 477
stresscoat 168
Struts 28
Tangential stress 193, 199
Tardy compensation 187
Temperature stresses 126
Temporary birefringence 183
Tensor notation 235
Thermal stresses 126
Thin membranes 194
Thin shells 517-18
Threshold strain 167
Timoshenko 142, 144, 146,212,214
Torsion of cellular sections 150
Torsion of non-circular sections 141
Torsion of open sections
Torsion of rectangular sections 142
Torsion of square closed of closed section
Torsion of thin-walled closed sections
Torsion of thin-walled stiffened sections
Torsion section modulus 144
Torsional rigidity 150
Toughness 473
Transformation 259, 326
Transverse sensitivity 173
Triangular plane membrane element 343
Twist, angle of 141-7, 149-52
143, 150
141
147
151
Unbalanced bridge 173
Uniform strength discs 125
Unsymmetrical bending 1
Unsymmetrical, section struts 49
Validity limit (Euler) 37
Virtual work 323
Viscoelasticity 521
Voight-Kelvin 522
Warping 153,310
Webb’s approximation 44
Wheatstonebridge 172
Wilson-Stokes equation 423
Wire gauge 171
X-rays 192
Yield stress 61
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Admin
مدير المنتدى
عدد المساهمات : 18992
تاريخ التسجيل : 01/07/2009
| | موضوع: كتاب Mechanics of Materials, Volume 2 السبت 29 يونيو 2013, 3:20 pm | |
|
أخواني في الله
أحضرت لكم كتاب
Mechanics of Materials, Volume 2
THIRD EDITION
An Introduction to the Mechanics of Elastic and Plastic Deformation of Solids and Structural Materials
E. J. HEARN
PhD; BSc(Eng) Hons; CEng; FIMechE; FIProdE; FIDiagE
University of Warwick
United Kingdom
و المحتوى كما يلي :
CONTENTS
Introduction xv
Notation xvii
1 Unsymmetrical Bending 1
Summary
Introduction
1.7 Momenta1 ellipse
1.8 Stress determination
1.9 Alternative procedurefor stress determination
1.10 Alternative procedure using the momenta1 ellipse
1.11 Dejections
Examples
Problems
Product second moment of area
Principal second moments of area
Mohr’s circle of second moments of area
Land’s circle of second moments of area
Rotation of axes: determination of moments of area in terms of the
principal values
The ellipse of second moments of area
2 Struts
Summary
Introduction
2.1 Euler’s theory
2.2 Equivalent strut length
2.3
2.4 Euler “validity limit”
2.5 Rankine or Rankine-Gordon formula
2.6 Perry- Robertsonformula
2.7
2.8 Struts with initial curvature
2.9 Struts with eccentric load
2.10 Laterally loaded struts
2.11
Comparison of Euler theory with experimental results
British Standard procedure (BS 449)
Alternative procedurefor any strut-loading condition
Vvi Contents
2.12 Struts with unsymmetrical cross-section
Examples
Problems
3 Strains Beyond the Elastic Limit
Summary
Introduction
Plastic bending of rectangular-sectioned beams
Shapefactor - symmetrical sections
Application to I-section beams
Partially plastic bending of unsymmetrical sections
Shapefactor - unsymmetrical sections
Dejections of partially plastic beams
Length of yielded area in beams
Collapse loads -plastic limit design
Residual stresses after yielding: elastic-perfectly plastic material
Torsion ofshafts beyond the elastic limit -plastic torsion
Angles of twist of shafts strained beyond the elastic limit
Plastic torsion of hollow tubes
Plastic torsion of case-hardened shafts
Residual stresses after yield in torsion
Plastic bending and torsion of strain-hardening materials
(a)Inelastic bending
(b)Inelastic torsion
Residual stresses- strain-hardening materials
Influence of residual stresses on bending and torsional strengths
Plastic yielding in the eccentric loadirzg of rectangular sections
Plastic yielding and residual stresses under axial loading with stress
concentrations
Plastic yielding of axially symmetric components
(a)Thick cylinders - collapse pressure
(b)Thick cylinders - “auto-frettage’’
(c)Rotating discs
Examples
Problems
4 Rings, Discs and Cylinders Subjected to Rotation
and Thermal Gradients
Summary
4.2 Rotating solid disc
Thin rotating ring or cylinder
Rotating disc with a central hole
Rotating thick cylinders or solid shafs
Rotating disc of uniform strength
125Contents
4.6 Combined rotational and thermal stresses in uniform discs and
thick cylinders
Examples
Problems
5 Torsion of Non-Circular and Thin-Walled Sections
Summary
Rectangular sections
Narrow rectangular sections
Thin-walled open sections
Thin-walled split tube
Other solid (non-tubular)shafts
Thin-walled closed tubes of non-circular section (Bredt-Batho theory)
Use of “equivalentJ ” for torsion of non-circular sections
Thin-walled cellular sections
Torsion of thin-walled stifSened sections
Membrane analogy
EfSect of warping of open sections
Examples
Problems
6 Experimental Stress Analysis
Introduction
Brittle lacquers
Strain gauges
Unbalanced bridge circuit
Null balance or balanced bridge circuit
Gauge construction
Gauge selection
Temperature compensation
Installation procedure
Basic measurement systems
D.C. and A.C. systems
Other types of strain gauge
Photoelasticity
Plane-polarised light - basic polariscope arrangements
Temporary birefringence
Production offringe patterns
Interpretation offringe patterns
Calibration
Fractional fringe order determination - compensation techniques
Isoclinics-circular polarisation
Stress separation procedures
Three-dimensional photoelasticity
VI11 Contents
6.22 Rejective coating technique
6.23 Other methods of strain measurement
Bibliography
7 Circular Plates and Diaphragms
Summary
A. CIRCULAR PLATES
Stresses
Bending moments
General equation for slope and dejection
General case of a circular plate or diaphragm subjected to
combined uniformly distributed load q (pressure)and central
concentrated load F
Uniformly loaded circular plate with edges clamped
Uniformly loaded circular plate with edgesfreely supported
Circular plate with central concentrated load F and edges clamped
Circular plate with central concentrated load F and edges freely
supported
Circular plate subjected to a load F distributed round a circle
Application to the loading of annular rings
Summary of end conditions
Stress distributions in circular plates and diaphragms subjected to
lateral pressures
Discussion of results - limitations of theory
Other loading cases of practical importance
B. BENDING OF RECTANGULAR PLATES
7.15
7.16
Rectangular plates with simply supported edges carrying uniformly
distributed loads
Rectangular plates with clamped edges carrying uniformly distributed
loads
Examples
Problems
8 Introduction to Advanced Elasticity Theory
8.1 Types of stress
The Cartesian stress components: notation and sign convention
8.2.1 Sign conventions
The state of stress at a point
Direct, shear and resultant stresses on an oblique plane
8.4.1
8.4.2
Line of action of resultant stress
Line of action of normal stress
227Contents ix
Principal stresses and strains in three dimensions - Mohr 's circle
representation
Graphical determination of the direction of the shear stress r,, on an
inclined plane in a three-dimensional principal stress system
The combined Mohr diagram for three-dimensional stress and strain
systems
Application of the combined circle to two-dimensional stress systems
Graphical construction for the state of stress at a point
Constructionfor the state of strain on a general strain plane
State of stress-tensor notation
The stress equations of equilibrium
Principal stresses in a three-dimensional Cartesian stress system
8.13.1 Solution of cubic equations
Stress invariants - Eigen values and Eigen vectors
Stress invariants
Reduced stresses
Strain invariants
Alternative procedure for determination of principal stresses
8.18.1 Evaluation of direction cosines for principal stresses
Octahedral planes and stresses
Deviatoric stresses
Deviatoric strains
Plane stress and plane strain
8.22.1 Plane stress
8.22.2 Plane strain
The stress-strain relations
The strain-displacement relationships
The strain equations of transformation
Compatibility
The stress function concept
8.27.1 Forms of Airy stressfunction in Cartesian coordinates
8.27.2 Case 1 - Bending of a simply supported beam by a uniformly
8.27.3 The use of polar coordinates in two dimensions
8.27.4 Forms of stress function in polar coordinates
8.27.5 Case 2 - hi-symmetric case: solid shaft and thick cylinder
radially loaded with uniform pressure
8.27.6 Case 3 - The pure bending of a rectangular section
curved beam
8.27.7 Case 4 - Asymmetric case n = 1. Shear loading of a circular
arc cantilever beam
8.27.8 Case 5 - The asymmetric cases n >, 2 -stress concentration at
a circular hole in a tension$eld
Line of action of shear stress
Shear stress in any other direction on the plane
distributed loading
276X Contents
8.27.9 Other useful solutions of the biharmonic equation
Examples
Problems
9 Introduction to the Finite Element Method
Introduction
Basis of thefinite element method
Applicability of thefinite element method
Formulation of the Jinite element method
General procedure of the Jinite element method
9.4.1 Identification of the appropriateness of analysis by the jinite
element method
9.4.2 Identification of the type of analysis
9.4.3 Idealisation
9.4.4 Discretisation of the solution region
9.4.5 Creation of the material model
9.4.6 Node and element ordering
9.4.7 Application of boundary conditions
9.4.8 Creation of a data file
9.4.9 Computer, processing, steps
9.4.10 Interpretation and validation of results
9.4.11 Modification and re-run
Fundamental arguments
9.5.1 Equilibrium
9.5.2 Compatibility
9.5.3 Stress-strain law
9.5.4 Forceldisplacement relation
The principle of virtual work
A rod element
9.7.1 Formulation of a rod element using fundamental equations
9.7.2 Formulation of a rod element using the principle of virtual work
equation
A simple beam element
9.8.1 Formulation of a simple beam element using fundamental
equations
93.2 Formulation of a simple beam element using the principle of
virtual work equation
A simple triangular plane membrane element
9.9.1 Formulation of a simple triangular plane membrane element
using the principle of virtual work equation
Formation of assembled stcfiess matrix by use of a dof.
correspondence table
Amlieation of boundarv conditions and uartitioninn
349Contents xi
9.12 Solutionfor displacements and reactims
Bibliography
Examples
Problems
10 Contact Stress, Residual Stress and Stress Concentrations
Summary
10.1 Contact stresses
Introduction
10.1.1 General case of contact between two curved surfaces
10.1.2 Special case I - Contact of parallel cylinders
10.1.3 Combined normal and tangential loading
10.1.4 Special case 2 - Contacting spheres
10.1.5 Design considerations
10.1.6 Contact loading of gear teeth
10.1.7 Contact stresses in spur and helical gearing
10.1.8 Bearing failures
Introduction
10.2.1 Reasom for residual stresses
(a)Mechanical processes
(b)Chemical treatment
(c)Heat treatment
(d)Welds
(e)Castings
10.2 Residual stresses
10.2.2 The injuence of residual stress onfailure
10.2.3 Measurement of residual stresses
The hole-drilling technique
X-ray difiaction
10.2.4 Summary of the principal effects of residual stress
Introduction
10.3.1 Evaluation of stress concentrationfactors
10.3.2 St. Venant'sprinciple
10.3.3 Theoretical considerations of stress concentrations due to
10.3 Stress concentrations
concentrated loads
(a)Concentrated load on the edge of an infiniteplate
(b)Concentrated load on the edge of a beam in bending
10.3.4 Fatigue stress concentrationfactor
10.3.5 Notch sensitivity
10.3.6 Strain concentration-Neuber's rule
10.3.7 Designing to reduce stress concentrations
(a)Fillet radius
(b)Keyways or splines
427xii Contents
(e)Grooves and notches
( d )Gear teeth
(e)Holes
cf) Oil holes
(g) Screw threads
(h)Press or shrink Jit members
10.3.8 Use of stress concentration factors with yield criteria
10.3.9 Design procedure
References
Examples
Problems
11 Fatigue, Creep and Fracture
Summary
11.1 Fatigue
Introduction
11.1.1 The SIN curve
11.1.2 PISIN curves
11.1.3 Effect of mean stress
1 1.1.4 Effect of stress concentration
11.1.5 Cumulative damage
1 1.1.6 Cyclic stress-strain
11.1.7 Combating fatigue
11.1.8 Slip bands and fatigue
Introduction
1 1.2.1 The creep test
11.2.2 Presentation of creep data
11.2.3 The stress-rupture test
11.2.4 Parameter methods
11.2.5 Stress relaxation
11.2.6 Creep-resistant alloys
11.3 Fracture mechanics
Introduction
11.3.1 Energy variation in cracked bodies
(a) Constant displacement
(b)Constant loading
(a)Grifith'scriterion for fiacture
(b)Stress intensity factor
11.2 Creep
11.3.2 Linear elastic fracture mechanics (L.E.F.M.)
11.3.3 Elastic-plastic fracture mechanics (E.P.F.M.)
11.3.4 Fracture toughness
11.3.5 Plane strain and plane stress fracture modes
11.3.6 General yielding fracture mechanics
11.3.7 Fatigue crack growth
11.3.8 Crack tip plasticity under fatigue loading
488Contents X l l l ...
11.3.9 Measurement of fatigue crack growth
References
Examples
Problems
12 Miscellaneous topics 509
12.1 Bending of beams with initial curvature
12.2 Bending of wide beams
12.3 General expression for stresses in thin-walled
pressure or selj-weight
12.4 Bending stresses at discontinuities in thin shells
12.5 Viscoelasticity
References
Examples
Problems
shells subjected to
Appendix 1. npical mechanical and physical properties for
engineering metals
Appendix 2. Typical mechanical properties of non-metals
Appendix 3. Other properties of non-metals
Index 537
INDEX
AC system 179
Acoustic gauge 180
Acoustoelasticity 192
Active gauge 172, 176, 178-9
Airy stress function 263, 265
Allowable working load 73
Alternating stress amplitude 447
Annular rings 208
Area, principal moments of 4
Area, product moment of 3
Area, second moment of 3- 10
Auto frettage 89
Ayrton and Perry 42
Balanced circuit 173
Banded method 313
Basquin’s law 457
Beams, curved 509
Bending, of beams 509-16
Bending, unsymmetrical 1
Birefringence 183
Body force stress 220
Boundary condition, application 316, 349
Boundary stress 185
Bredt-Batho theory 147, 150
Brittle lacquers 167
Buckling of struts 30
Built-up girders 52
Calibration 69, 169, 186
Capacitance gauge 180
Carrier frequency system 180
Cartesian stress 220
Case-hardened shafts 79
Circular plates 193
Circular polarisation 188
Clarke 168
Coffin-Manson Law 457
Collapse 64
Columns 30
Combined circle (Mohr) 228
Combined diagram 229
Compatibility 261, 321
Compensation 187
Conjugate diameters 13
Contact stress 382
Corkscrew rule 12
Correspondence table 347
Crack detection 169
Crack tip plasticity 482, 488
Creep 169,462
Crinkling of struts 50
Crossed set-up 182
Cross-sensitivity 173
Crushing stress 37
Cyclic stress-strain 455
Cylinders, residual stresses in 87
Cylindrical components 239
Dark field 182
DC system 179
De Forrest 168
Deflections, unsymmetrical members 15
Deviatoric stress 251
Diaphragms 193
Directions cosine 223
Disc
circular, solid 119
plastic yielding of 94
rotating 117
uniform strength 125
with central hole 122
Discretisation 305
Distortion 311
Dummy gauge 172, 175-6
Dye-etchant 169
Dynamic strain 171
Eccentric loading
of struts 42
to collapse 85
momenta1 11
of second moments of area 9
Ellipse
Ellis 168
Endurance limit 423
Equilibrium 319
Equilibrium
Cartesian coordinates 236
cylindrical coordinates 239
Equivalent length 35
Equivalent length (of Struts) 35
Euler theory 31
Extensometers 180
Factor, load 41,65, 166
Fatigue 446
Fatigue crack growth 486,489
Finite element analysis 302
537538 Index
Finite element mesh 308
Finite element method 300
Fixed-ended struts 33
Flexural stiffness 193. 197
Foil gauge 171, 173
Fracture mechanics 47
Fringe order 185-6
Fringe pattern 181-2,
Fringe value 185-6
Frontal method 315
Frozen stress technique
Full bridge circuit 173
84- 192,420,481
190
Gauge
acoustic 180
electrical resistance
strain 171-80
factor 172
17 1-180
Girder, built-up 50, 52
Graphical pmedure, stress 228-9
Grid technique 192
Griffith’s criterion 475
Half-bridge 172-3
Het6nyi 84
Holography 192
Hydrostatic stress 249, 251
Idealisation 305
Inductance gauge 180
Initial curvature 41
Interference 181, 184
Isochromatic 185
Isoclinic 188
Johnson parabolic formula 36
Land’s circle of moments of area 7
Larson-Miller parameter 468
Laterally loaded struts 46
Light field 182
Load factor 41, 73
Manson-Haferd parameter 469
Material fringe value 185-6
Maximum compressive stress 381, 385,387
Mean stress 252.45 1
Membrane 152
Modulus. reduced 82
Mohr’s circle of second moments of area
Mohr’s strain circle 228
Mohr’s stress circle 228
Moir6 192
Momenta1ellipse 1 I , 13
Monochromatic light 185
6
Neuber’s rule 425
Notch sensitivity 424
Null balance 173
Oblique plane, stress on 224
Octahedral planes 249
Octahedral shear stress 250
Octahedral stress 249
Overspeeding 95
Parallel set-up 183
Partitioning 349
Perry-Robertson 29.39
Photoelastic coating 190
Photoelasticity
reflection 190
transmission 181
Piezo-resistive gauge 180
Plane polarisation 182
Plane strain 254
Plane stress 254
Plastic bending 64
Plastic deformation
discs 94
thick cylinder 87
Plastic hinge 71
Plastic limit design 71
Plastic torsion 75, 79
Pneumatic gauge 180
Polariscope 182
Polariser 182
Principal axes 2
Principal second moments of area 4
Principal strain 228
Principal stress 228, 247
Product second moment of area 3
Quarter-bridge 173
Quarter-wave plates 187
Radial stress 117-23, 125-8, 193-9
Radius of gyration 28
Rankine-Gordon theory 38
Rectangular plates 213
Reduced modulus 82
Reflection polariscope 190
Reflective coating 190
Refraction 183
Replica technique 192
Residual stresses 73.79.84.86.95-6.394
Resistivity 172
Rotating cylinders 124
Rotating discs
and rings 117
collapse 94
Rotating hollow discs 122
Rotating uniform strength discs 125
Ruge and Simmons 171Index 539
Safety factor 41, 65, 166
Saint-Venant 420
Sand heap analogy 78
Second moment of area 2- 10
ellipse of 9
principle 4
product 3
Semi-conductor gauges 180
Senarment 187
Shape factor 65
Shear flow 147
Shear stress 224
Sherby-Dom parameter 469
Skew loading 2
Slenderness ration 28
Smith-Southwell theory 42
Southwell 42
Specific resistance 172
Stem 168
Straight line formula 36
Strain
deviatoric 251, 253
invariants 247
threshold 167
Strain circle 228
Strain gauge 171
Strain hardening 63-4, 80
Stress
unsymmetrical sections 67,69
body force 220
boundary 185
Cartesian 220
concentration 86
concentration factor 408
concentration factor (evaluation) 413
crushing 37
deviatoric 246, 251
direct 224
equations of equilibrium 236
freezing technique 190
hydrostatic 249-51
invariants 243-4
mean 252,447,451
radial 193, 199
range 447
relaxation 470
separation 190
shear 224
tangential 193, 199
three-dimensional 220
trajectory 189
yield 61
Stress concentration, effects 453
Stress intensity factor 477
stresscoat 168
Struts 28
Tangential stress 193, 199
Tardy compensation 187
Temperature stresses 126
Temporary birefringence 183
Tensor notation 235
Thermal stresses 126
Thin membranes 194
Thin shells 517-18
Threshold strain 167
Timoshenko 142, 144, 146,212,214
Torsion of cellular sections 150
Torsion of non-circular sections 141
Torsion of open sections
Torsion of rectangular sections 142
Torsion of square closed of closed section
Torsion of thin-walled closed sections
Torsion of thin-walled stiffened sections
Torsion section modulus 144
Torsional rigidity 150
Toughness 473
Transformation 259, 326
Transverse sensitivity 173
Triangular plane membrane element 343
Twist, angle of 141-7, 149-52
143, 150
141
147
151
Unbalanced bridge 173
Uniform strength discs 125
Unsymmetrical bending 1
Unsymmetrical, section struts 49
Validity limit (Euler) 37
Virtual work 323
Viscoelasticity 521
Voight-Kelvin 522
Warping 153,310
Webb’s approximation 44
Wheatstonebridge 172
Wilson-Stokes equation 423
Wire gauge 171
X-rays 192
Yield stress 61
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