Engineering mechanics of deformable solids: a presentation with exercises
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford Univ. Press
2013
|
| Edition: | 1. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XIV, 334 S. Ill., zahlr. graph. Darst. 25 cm |
| ISBN: | 9780199651641 0199651647 |
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MARC
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| 020 | |a 9780199651641 |9 978-0-19-965164-1 | ||
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| 100 | 1 | |a Govindjee, Sanjay |d 1964- |e Verfasser |0 (DE-588)1048155714 |4 aut | |
| 245 | 1 | 0 | |a Engineering mechanics of deformable solids |b a presentation with exercises |c Sanjay Govindjee |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2013 | |
| 300 | |a XIV, 334 S. |b Ill., zahlr. graph. Darst. |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Deformations (Mechanics) | |
| 650 | 4 | |a Solids / Mechanical properties | |
| 650 | 4 | |a Mechanical engineering / Problems, exercises, etc | |
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Record in the Search Index
| _version_ | 1804149749085896704 |
|---|---|
| adam_text | This book covers the essential elements of engineering mechanics of deformable
bodies, including mechanical elements in tension-compression, torsion, and bending.
It emphasizes a fundamental bottom-up approach to the subject in a concise and
uncluttered presentation. Of special interest are chapters dealing with potential energy
as well as principle of virtual work methods for both exact and approximate solutions.
The book places an emphasis on the underlying assumptions of the theories in order
to encourage the
readerto
think more deeply about the subject matter. The book should
be of special interest to undergraduate students looking for a streamlined presentation
as well as those returning to the subject for a second time. Solutions to the end of
chapter exercises are available on request for instructors.
Contents
1
Introduction
1
1.1 Force
systems
2
1.1.1
Units
2
1.2
Characterization of force systems
3
1.2.1
Distributed forces
3
1.2.2
Equivalent forces systems
5
1.3
Work and power
6
1.3.1
Conservative forces
7
1.3.2
Conservative systems
8
1.4
Static equilibrium
8
1.4.1
Equilibrium of a body
8
1.4.2
Virtual work and virtual power
8
1.5
Equilibrium of subsets: Free-body diagrams
9
1.5.1
Internal force diagram
9
1.6
Dimensional homogeneity
11
Exercises
11
I Tension—Compression Bars: The One-Dimensional
Case
13
2.1
Displacement field and strain
13
2.1.1
Units
14
2.1.2
Strain at a point
15
2.2
Stress
17
2.2.1
Units
17
2.2.2
Pointwise equilibrium
17
2.3
Constitutive relations
18
2.3.1
One-dimensional Hooke s Law
18
2.3.2
Additional constitutive behaviors
19
2.4
A one-dimensional theory of mechanical response
19
2.4.1
Axial deformation of bars: Examples
19
2.4.2
Differential equation approach
26
2.5
Energy methods
31
2.6
Stress-based design
34
Chapter summary
35
Exercises
36
χ
Contents
Stress
41
3.1
Average
normal
and shear stress
41
3.1.1
Average stresses for a bar under axial load
42
3.1.2
Design with average stresses
43
3.2
Stress at a point
46
3.2.1
Nomenclature
47
3.2.2
Internal reactions in terms of stresses
48
3.2.3
Equilibrium in terms of stresses
50
3.3
Polar and spherical coordinates
53
3.3.1
Cylindrical/polar stresses
54
3.3.2
Spherical stresses
55
Chapter summary
56
Exercises
56
Strain
59
4.1
Shear strain
59
4.2
Pointwise strain
59
4.2.1
Normal strain at a point
60
4.2.2
Shear strain at a point
61
4.2.3
Two-dimensional strains
62
4.2.4
Three-dimensional strain
63
4.3
Polar/cylindrical and spherical strain
64
4.4
Number of unknowns and equations
64
Chapter summary
65
Exercises
65
Constitutive Response
67
5.1
Three-dimensional Hooke s Law
67
5.1.1
Pressure
69
5.1.2
Strain energy in three dimensions
70
5.2
Two-dimensional Hooke s Law
70
5.2.1
Two-dimensional plane stress
70
5.2.2
Two-dimensional plane strain
71
5.3
One-dimensional Hooke s Law:
Uniaxial
state
of stress
72
5.4
Polar/cylindrical and spherical coordinates
72
Chapter summary
72
Exercises
73
Basic Techniques of Strength of Materials
75
6.1
One-dimensional axially loaded rod revisited
75
6.2
Thinness
79
6.2.1
Cylindrical thin-walled pressure vessels
79
6.2.2
Spherical thin-walled pressure vessels
81
6.3
Saint-Venant s principle
82
Chapter summary
85
Exercises
86
Contents xi
Circular
and Thin-Wall Torsion
89
7.1
Circular bars: Kinematic assumption
89
7.2
Circular bars: Equilibrium
92
7.2.1
Internal torque-stress relation
93
7.3
Circular bars: Elastic response
94
7.3.1
Elastic examples
94
7.3.2
Differential equation approach
103
7.4
Energy methods
107
7.5
Torsionai
failure: Brittle materials
108
7.6
Torsionai
failure: Ductile materials
110
7.6.1
Twist-rate at and beyond yield
110
7.6.2
Stresses beyond yield 111
7.6.3
Torque beyond yield
112
7.6.4
Unloading after yield
113
7.7
Thin-walled tubes
116
7.7.1
Equilibrium
117
7.7.2
Shear flow
117
7.7.3
Internal torque-stress relation
118
7.7.4
Kinematics of thin-walled tubes
119
Chapter summary
121
Exercises
122
Bending of Beams
128
8.1
Symmetric bending: Kinematics
128
8.2
Symmetric bending: Equilibrium
131
8.2.1
Internal resultant definitions
132
8.3
Symmetric bending: Elastic response
136
8.3.1
Neutral axis
136
8.3.2
Elastic examples: Symmetric bending stresses
138
8.4
Symmetric bending: Elastic deflections by differential
equations
144
8.5
Symmetric multi-axis bending
148
8.5.1
Symmetric multi-axis bending: Kinematics
149
8.5.2
Symmetric multi-axis bending: Equilibrium
149
8.5.3
Symmetric multi-axis bending: Elastic
150
8.6
Shear stresses
152
8.6.1
Equilibrium construction for shear stresses
153
8.6.2
Energy methods: Shear deformation of beams
158
8.7
Plastic bending
158
8.7.1
Limit cases
159
8.7.2
Bending at and beyond yield: Rectangular
cross-section
161
8.7.3
Stresses beyond yield: Rectangular cross-section
163
8.7.4
Moment beyond yield: Rectangular cross-section
163
8.7.5
Unloading after yield: Rectangular cross-section
164
Chapter summary
167
Exercises
168
χϋ
Contents
9
Analysis of
Multi-
Axial Stress and Strain
179
9.1
Transformation of vectors
179
9.2
Transformation of stress
180
9.2.1
Traction vector method
181
9.2.2
Maximum normal and shear stresses
184
9.2.3
Eigenvalues and eigenvectors
185
9.2.4
Mohr s circle of stress
187
9.2.5
Three-dimensional Mohr s circles of stress
190
9.3
Transformation of strains
192
9.3.1
Maximum normal and shear strains
193
9.4
Multi-axial failure criteria
197
9.4.1
Tresca s yield condition
198
9.4.2
Henky-von
Mises
condition
200
Chapter summary
204
Exercises
205
10
Virtual Work Methods: Virtual Forces
209
10.1
The virtual work theorem: Virtual force version
209
10.2
Virtual work expressions
211
10.2.1
Determination of displacements
211
10.2.2
Determination of rotations
211
10.2.3
Axial rods
212
10.2.4
Torsion rods
213
10.2.5
Bending of beams
214
10.2.6
Direct shear in beams (elastic only)
215
10.3
Principle of virtual forces: Proof
217
10.3.1
Axial bar: Proof
217
10.3.2
Beam bending: Proof
218
10.4
Applications: Method of virtual forces
220
Chapter summary
225
Exercises
226
11
Potential-Energy Methods
230
11.1
Potential energy: Spring-mass system
230
11.2
Stored elastic energy: Continuous systems
232
11.3
Castigliano s first theorem
235
11.4
Stationary complementary potential energy
236
11.5
Stored complementary energy: Continuous systems
237
11.6
Castigliano s second theorem
240
11.7
Stationary potential energy: Approximate methods
246
11.8
Ritzs method
250
11.9
Approximation errors
254
11.9.1
Types of error
254
11.9.2
Estimating error in Ritz s method
255
11.9.3
Selecting functions for Ritz s method
257
Chapter summary
258
Exercises
259
Contents xiii
12 Geometrie
Instability
263
12.1
Point-mass pendulum: Stability
263
12.2
Instability: Rigid links
264
12.2.1
Potential energy: Stability
265
12.2.2
Small deformation assumption
267
12.3
Euler
buckling of beam-columns
270
12.3.1
Equilibrium
270
12.3.2
Applications
271
12.3.3
Limitations to the buckling formulae
274
12.4
Eccentric loads
275
12.4.1
Rigid links
275
12.4.2
Euler
columns
277
12.5
Approximate solutions
278
12.5.1
Buckling with distributed loads
282
12.5.2
Deflection behavior for beam-columns with
combined axial and transverse loads
285
Chapter summary
286
Exercises
287
13
Virtual Work Methods: Virtual Displacements
291
13.1
The virtual work theorem: Virtual displacement
version
291
13.2
The virtual work expressions
293
13.2.1
External work expressions
293
13.2.2
Axial rods
294
13.2.3
Torsion rods
296
13.2.4
Bending of beams
297
13.3
Principle of virtual displacements: Proof
298
13.3.1
Axial bar: Proof
299
13.3.2
Beam bending: Proof
300
13.4
Approximate methods
301
Chapter summary
307
Exercises
308
Appendix A: Additional Reading
310
Appendix B: Units, Constants, and Symbols
311
Appendix C: Representative Material Properties
315
Appendix D: Parallel-Axis Theorem
317
Appendix E: Integration Facts
318
E.I Integration is addition in the limit
318
E.2 Additivity
320
E.3 Fundamental theorem of calculus
321
E.4 Mean value
321
E.5 The product rule and integration by parts
322
E.6 Integral theorems
323
xiv Contents
E.
6.1
Mean value theorem
323
E.6.2 Localization theorem
324
E.6.3 Divergence theorem
324
Appendix F: Bending without Twisting: Shear Center
325
F.I Shear center
325
Index
331
|
| any_adam_object | 1 |
| author | Govindjee, Sanjay 1964- |
| author_GND | (DE-588)1048155714 |
| author_facet | Govindjee, Sanjay 1964- |
| author_role | aut |
| author_sort | Govindjee, Sanjay 1964- |
| author_variant | s g sg |
| building | Verbundindex |
| bvnumber | BV040636087 |
| classification_rvk | UF 3000 |
| ctrlnum | (OCoLC)823257477 (DE-599)BVBBV040636087 |
| discipline | Physik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV040636087 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:27:58Z |
| institution | BVB |
| isbn | 9780199651641 0199651647 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025463239 |
| oclc_num | 823257477 |
| open_access_boolean | |
| owner | DE-29T DE-703 |
| owner_facet | DE-29T DE-703 |
| physical | XIV, 334 S. Ill., zahlr. graph. Darst. 25 cm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Govindjee, Sanjay 1964- Verfasser (DE-588)1048155714 aut Engineering mechanics of deformable solids a presentation with exercises Sanjay Govindjee 1. ed. Oxford Oxford Univ. Press 2013 XIV, 334 S. Ill., zahlr. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier Deformations (Mechanics) Solids / Mechanical properties Mechanical engineering / Problems, exercises, etc Elastizität (DE-588)4014159-7 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 s Elastizität (DE-588)4014159-7 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025463239&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025463239&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Govindjee, Sanjay 1964- Engineering mechanics of deformable solids a presentation with exercises Deformations (Mechanics) Solids / Mechanical properties Mechanical engineering / Problems, exercises, etc Elastizität (DE-588)4014159-7 gnd Festkörpermechanik (DE-588)4129367-8 gnd |
| subject_GND | (DE-588)4014159-7 (DE-588)4129367-8 |
| title | Engineering mechanics of deformable solids a presentation with exercises |
| title_auth | Engineering mechanics of deformable solids a presentation with exercises |
| title_exact_search | Engineering mechanics of deformable solids a presentation with exercises |
| title_full | Engineering mechanics of deformable solids a presentation with exercises Sanjay Govindjee |
| title_fullStr | Engineering mechanics of deformable solids a presentation with exercises Sanjay Govindjee |
| title_full_unstemmed | Engineering mechanics of deformable solids a presentation with exercises Sanjay Govindjee |
| title_short | Engineering mechanics of deformable solids |
| title_sort | engineering mechanics of deformable solids a presentation with exercises |
| title_sub | a presentation with exercises |
| topic | Deformations (Mechanics) Solids / Mechanical properties Mechanical engineering / Problems, exercises, etc Elastizität (DE-588)4014159-7 gnd Festkörpermechanik (DE-588)4129367-8 gnd |
| topic_facet | Deformations (Mechanics) Solids / Mechanical properties Mechanical engineering / Problems, exercises, etc Elastizität Festkörpermechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025463239&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025463239&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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