Structural impact

603 Pages·2011·5.704 MB·English

by  Norman Jones

STRUCTURAL IMPACT
SecondEdition
Structural Impact is concerned with the behaviour of structures and com-
ponentssubjectedtolargedynamic,impactandexplosiveloadswhichpro-
duceinelasticdeformationsandisofinterestforsafetycalculations,hazard
assessments and energy-absorbing systems throughout industry. The first
fivechaptersofthisbookintroducetherigidplasticmethodsofanalysisfor
the static behaviour and the dynamic response of beams, plates and shells.
Thesechaptersdevelopthekeyfeaturesofthesubjectfromanengineering
viewpoint and are followed by several chapters on various phenomena of
importancetostructuralimpact.Theinfluenceoftransverseshear,rotatory
inertia,finitedisplacementsanddynamicmaterialpropertiesareintroduced
andstudiedinsomedetail.Dynamicprogressivebuckling,whichdevelopsin
severalenergy-absorbingsystems,isthenexamined,andthephenomenonof
dynamicplasticbucklingisintroducedinthepenultimatechapter.Thelast
chapter on the scaling laws is important for relating the response of small-
scaleexperimentalteststothedynamicbehaviouroffull-scaleprototypes.
This text is invaluable to undergraduates, graduates and professionals
whowanttolearnmoreaboutthebehaviourofstructuressubjectedtolarge
impact,dynamicandblastloadingsproducinganinelasticresponse.
DrNormanJonesisanEmeritusProfessorofEngineeringattheUniversity
ofLiverpool,UK.HewaspreviouslytheA.A.GriffithProfessorofEngineer-
ing,headedtheUniversity’sDepartmentofMechanicalEngineering(1982–
1990) and served as Director of the Impact Research Centre (1985–2005).
Priortothat,hewasaProfessorofOceanEngineeringatMITintheUnited
States.Hehaspublishedmorethan300papers,principallyonmanyaspects
oftheresponseofstructuressubjectedtodynamic,impactandblastloadings
which produce large inelastic strains. He is the honorary editor-in-chief of
theInternationalJournalofImpactEngineeringandwaseditor(1983–87)and
editor-in-chief(1988–2008),andheistheauthorofthefirsteditionofStruc-
turalImpact(CambridgeUniversityPress,1989).ProfessorJonesishonorary
professoratHuazhongandTaiyuanUniversitiesofScienceandTechnology
in China, a Fellow of the Royal Academy of Engineering (London) and a
ForeignFellowoftheIndianNationalAcademyofEngineering.

Structural Impact
Second Edition
Norman Jones
UniversityofLiverpool
cambridgeuniversitypress
Cambridge,NewYork,Melbourne,Madrid,CapeTown,
Singapore,Sa˜oPaulo,Delhi,Tokyo,MexicoCity
CambridgeUniversityPress
32AvenueoftheAmericas,NewYork,NY10013-2473,USA
www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107010963
(cid:2)C NormanJones1989,2012
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished1989
Firstpaperbackedition1997
Secondeditionpublished2012
PrintedintheUnitedStatesofAmerica
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloginginPublicationdata
Jones,Norman,1938–
Structuralimpact/NormanJones.–2nded.
p. cm.
Includesbibliographicalreferencesandindexes.
ISBN978-1-107-01096-3
1.Impact. 2.Structuraldynamics. 3.Girders. 4.Plates(Engineering).
5.Shells(Engineering). I.Title.
TA654.2.J66 2012
624.1′76–dc23
ISBN978-1-107-01096-3Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyof
URLsforexternalorthird-partyInternetWebsitesreferredtointhispublication
anddoesnotguaranteethatanycontentonsuchWebsitesis,orwillremain,
accurateorappropriate.
ToJenny,AlisonandCatherine,
WilliamandGeorgina
Contents
PrefacetotheSecondEdition pagexi
PrefacetotheFirstEdition xiii
1 StaticPlasticBehaviourofBeams . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
1.1 Introduction 1
1.2 BasicEquationsforBeams 2
1.3 PlasticCollapseTheoremsforBeams 5
1.4 StaticPlasticCollapseofaCantilever 8
1.5 StaticPlasticCollapseofaSimplySupportedBeam 10
1.6 StaticPlasticCollapseofaFullyClampedBeam 12
1.7 StaticPlasticCollapseofaBeamSubjected
toaConcentratedLoad 13
1.8 StaticPlasticCollapseofaPartiallyLoadedBeam 14
1.9 ExperimentsonBeams 17
1.10FinalRemarks 19
problems
19
2 StaticPlasticBehaviourofPlatesandShells . . . . . . . . . . . . . . . . . . . .21
2.1 Introduction 21
2.2 GeneralisedStressesandStrains 21
2.3 BasicConcepts 23
2.4 PlasticCollapseTheorems 26
2.5 BasicEquationsforCircularPlates 27
2.6 StaticPlasticCollapsePressureofCircularPlates 30
2.7 BasicEquationsforRectangularPlates 33
2.8 StaticPlasticCollapsePressureofRectangularPlates 34
2.9 BasicEquationsforCylindricalShells 41
2.10StaticCollapsePressureofaLongReinforcedCylindricalShell 45
2.11StaticPlasticCollapseofaRing-LoadedCylindricalShell 48
2.12ExperimentsonPlatesandShells 51
2.13FinalRemarks 55
problems
57
vii
viii Contents
3 DynamicPlasticBehaviourofBeams . . . . . . . . . . . . . . . . . . . . . . . . 59
3.1 Introduction 59
3.2 GoverningEquationsforBeams 61
3.3 SimplySupportedBeam,p ≤p ≤3p 62
c 0 c
3.4 SimplySupportedBeam,p >3p 66
0 c
3.5 SimplySupportedBeamLoadedImpulsively 78
3.6 FullyClampedBeam, p¯ ≤ p ≤3p¯ 83
c 0 c
3.7 FullyClampedBeam, p >3p¯ 85
0 c
3.8 ImpactofaMassonaFullyClampedBeam 86
3.9 ImpactofaCantileverBeam 94
3.10FinalRemarks 99
problems
103
4 DynamicPlasticBehaviourofPlates . . . . . . . . . . . . . . . . . . . . . . . . 105
4.1 Introduction 105
4.2 GoverningEquationsforCircularPlates 107
4.3 AnnularPlateLoadedDynamically 107
4.4 SimplySupportedCircularPlateLoadedDynamically,
p ≤p ≤2p 115
c 0 c
4.5 SimplySupportedCircularPlateLoadedDynamically,
p >2p 120
0 c
4.6 FullyClampedCircularPlateLoadedImpulsively 131
4.7 GoverningEquationsforRectangularPlates 133
4.8 SimplySupportedSquarePlateLoadedDynamically,
p ≤p ≤2p 135
c 0 c
4.9 SimplySupportedSquarePlateLoadedDynamically,p >2p 140
0 c
4.10FinalRemarks 146
problems
149
5 DynamicPlasticBehaviourofShells . . . . . . . . . . . . . . . . . . . . . . . . 151
5.1 Introduction 151
5.2 GoverningEquationsforCylindricalShells 152
5.3 LongCylindricalShell 153
5.4 LongReinforcedCylindricalShell 158
5.5 FullyClampedShortCylindricalShell 162
5.6 Elastic,PerfectlyPlasticSphericalShellSubjectedtoa
SphericallySymmetricDynamicPressure 170
5.7 ShallowShells 190
5.8 SomeCommentsonSphericalShells 196
5.9 InfluenceofPressurePulseCharacteristics 197
5.10FinalRemarks 203
problems
205
6 InfluenceofTransverseShearandRotatoryInertia . . . . . . . . . . . . . .206
6.1 Introduction 206
6.2 GoverningEquationsforBeams 208
Contents ix
6.3 TransverseShearEffectsinaSimplySupportedBeam
LoadedImpulsively 209
6.4 ImpactofaMassonaLongBeam 225
6.5 TransverseShearEffectsinaSimplySupportedCircularPlate 231
6.6 TransverseShearEffectsinCylindricalShells 243
6.7 FinalRemarks 251
problems
265
7 InfluenceofFiniteDisplacements . . . . . . . . . . . . . . . . . . . . . . . . . . 267
7.1 Introduction 267
7.2 StaticPlasticBehaviourofaBeamSubjected
toaConcentratedLoad 269
7.3 StaticPlasticBehaviourofCircularPlates 281
7.4 StaticPlasticBehaviourofRectangularPlates 283
7.5 DynamicPlasticBehaviourofRectangularPlates 291
7.6 DynamicPlasticBehaviourofBeams 302
7.7 DynamicPlasticBehaviourofCircularPlates 304
7.8 DynamicPlasticBehaviourofaCircularMembrane 309
7.9 MassImpactLoadingofPlates 311
7.10FinalRemarks 316
problems
326
8 Strain-Rate-SensitiveBehaviourofMaterials . . . . . . . . . . . . . . . . . . 327
8.1 Introduction 327
8.2 MaterialCharacteristics 329
8.3 ConstitutiveEquations 340
8.4 TheoreticalSolutionsofIdealisedModels 347
8.5 TheoreticalBehaviourofStrain-Rate-Sensitive
Structures 363
8.6 FinalRemarks 374
problems
375
9 DynamicProgressiveBuckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
9.1 Introduction 377
9.2 StaticAxialCrushingofaCircularTube 381
9.3 DynamicAxialCrushingofaCircularTube 385
9.4 StaticAxialCrushingofaSquareTube 392
9.5 DynamicAxialCrushingofaSquareTube 396
9.6 ComparisonoftheAxialCrushingCharacteristicsofCircular
andSquareTubes 397
9.7 SomeCommentsonEnergyAbsorptionSystems 399
9.8 StructuralCrashworthiness 406
9.9 StructuralProtection 417
9.10FinalRemarks 419
problems
423
x Contents
10 DynamicPlasticBuckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
10.1Introduction 425
10.2DynamicElasticBucklingofaBar 427
10.3DynamicPlasticBucklingofaBar 437
10.4DynamicPlasticBucklingofaCircularRingSubjected
toanExternalImpulse 442
10.5DynamicAxialPlasticBucklingofaLongCylindricalShell 457
10.6CriticalImpulsiveRadialVelocityforCollapseofaCylindrical
ShellwithoutBuckling 472
10.7FinalComments 473
problems
478
11 ScalingLaws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479
11.1Introduction 479
11.2IntroductiontoGeometricallySimilarScaling 479
11.3PhenomenaWhichDoNotScaleGeometrically 484
11.4DimensionalAnalysis 486
11.5CrackPropagationinElasticStructures 492
11.6Ductile–BrittleFractureTransitions 495
11.7ExperimentalResultsontheScalingofStructures
LoadedDynamically 499
11.8FinalComments 508
problems
510
APPENDIX1: PrincipleofVirtualWork . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
APPENDIX2: Path-DependenceofanInelasticMaterial . . . . . . . . . . . . . . . 514
APPENDIX3: PrincipleofVirtualVelocities . . . . . . . . . . . . . . . . . . . . . . . . 516
APPENDIX4: ConsistentSetsofEquilibriumEquations
andGeometricalRelations . . . . . . . . . . . . . . . . . . . . . . . . . . 517
APPENDIX5: BuckinghamΠ-Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 528
APPENDIX6: Quasi-StaticBehaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . .532
APPENDIX7: Martin’sUpperBoundDisplacementTheorem . . . . . . . . . . . .538
References 541
AnswerstoSelectedProblems 571
AuthorIndex 575
SubjectIndex 580
Preface to the Second Edition
Thegeneralfieldofstructuralimpacthasexpandedsignificantlysincetheprepara-
tionofthefirsteditionofthisbookmorethan20yearsago.Thisexpansionisdriven
partlybythequestforthedesignofefficientstructureswhichrequiremoreaccur-
ate safety factors against various types of dynamic loadings causing large plastic
strains. The enhancement of safety in many industries, including transportation,
has become more prominent in recent years, as well as the protection of struc-
turesandsystemsagainstterroristattacks.Intandemwiththesedevelopmentsand
enhancedrequirements,rapidadvanceshaveoccurredinnumericalanalyses,which
haveoutpaced,inmanyways,ourunderstandingofstructuralimpact.Nevertheless,
numerical schemes are used throughout design offices. This book emphasises the
basicmechanicsofstructuralimpactinordertogainsomeinsightintoitsbroadfield.
Itisimportantthatanengineeringdesignerhasagoodgraspofthemechanicswhich
underpinthishighlynonlinearandcomplexengineeringfield.
The book attempts to achieve this aim through an analysis of simple models
whichexposethebasicaspectsoftheresponse,anunderstandingofwhichwillpay
dividends when interpreting the results emanating from both experimental studies
and numerical calculations. For example, the issues raised in Chapters 8 and 11,
on material strain rate sensitivity and scaling, respectively, are certainly important
forbothnumericalcalculationsaswellasexperimentalprogrammes.Insomecases,
the equations presented in this book are suitable for preliminary design purposes,
particularly when bearing in mind frequent uncertainties in the input data. For
example,thevaluesofcoefficientsandformofdynamicconstitutiveequationsare
oftenapproximate,andtherearedifficultiesinspecifyingthecorrectdetailsforthe
boundaryconditionsatjoints,etc.,andinobtainingthecharacteristicsoftheexternal
dynamicloadingswhicharisefromimpact,explosiveandlargedynamicloadings.
The first five basic chapters of this book remain largely unchanged, except
for some slight improvements here and there to aid clarity and the addition of
two appendices, one on quasi-static behaviour and the other giving the proof of
a displacement bound theorem. Recent developments on these topics have been
confined largely to solutions for special cases and numerical studies. Considerable
researchefforthasbeenexpended,overthelastfewdecades,onthetopicsstudied
in the last six chapters. Therefore, these chapters of the book have been updated
xi