Analysis ofEngineering Structures and Material Behavior Analysis of Engineering Structures and Material Behavior Josip Brnić University of Rijeka – Faculty of Engineering, Department of Engineering Mechanics, Rijeka, Croatia Thiseditionfirstpublished2018 ©2018JohnWiley&SonsLtd Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted, inanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptas permittedbylaw.Adviceonhowtoobtainpermissiontoreusematerialfromthistitleisavailableat http://www.wiley.com/go/permissions. TherightofJosipBrnićtobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewithlaw. 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LibraryofCongressCataloging-in-PublicationData Names:Brnić,Josip,1951–author. Title:Analysisofengineeringstructuresandmaterialbehavior/byJosip BrnićUniversityofRijeka. Description:Firstedition.|Hoboken,NJ:Wiley,2018.|Includes bibliographicalreferencesandindex.| Identifiers:LCCN2017042809(print)|LCCN2017048581(ebook)| ISBN9781119329107(pdf)|ISBN9781119329060(epub)| ISBN9781119329077(cloth) Subjects: LCSH:Structuralanalysis(Engineering) Classification:LCCTA645(ebook)|LCCTA645.B6592018(print)| DDC624.1/7–dc23 LCrecordavailableathttps://lccn.loc.gov/2017042809 CoverDesign:Wiley CoverImage:©Photoephemera/Gettyimages Setin10/12ptWarnockbySPiGlobal,Pondicherry,India PrintedandboundbyCPIGroup(UK)Ltd,Croydon,CR04YY 10 9 8 7 6 5 4 3 2 1 “Theory and the real process are referred toeach other; theory teaches understanding of the processand the process testifies to the real event.” Let this book be dedicated to the memory ofmy parents, who instilledin me respect towards people. vii Contents FrequentlyUsedSymbolsandtheMeaningofSymbols xv PrincipalSIUnitsandtheUSEquivalents xxiii SIPrefixes,BasicUnits,PhysicalConstants,theGreekAlphabet xxv ImportantNoticeBeforeReadingtheBook xxvii Preface xxix AbouttheAuthor xxxi Acknowledgements xxxiii 1 Introduction 1 1.1 The Task of Design and Manufacture 1 1.2 Factors that Influence the Design of EngineeringStructures 1 1.3 TheImportanceofOptimizationintheProcessofDesignandtheSelectionof Structural Materials 3 1.4 Commonly Observed Failure Modes inEngineeringPractice 4 1.5 Structures and the Analysis of Structures 5 References 5 2 Stress 7 2.1 Definition of Average Stress and Stress at a Point 7 2.2 Stress Components and Equilibrium Equations 8 2.2.1 Stress Components 8 2.2.2 Equilibrium Equations 9 2.3 Stress Tensor 10 2.3.1 Mean and Deviatoric Stress Tensors 10 2.4 States of Stress 12 2.4.1 Uniaxial State of Stress 12 2.4.2 Two-dimensional State of Stress 14 2.4.3 Three-dimensional State of Stress 18 2.4.3.1 Stress on an Arbitrary Plane 20 2.4.3.2 Stress on an Octahedral Plane 21 2.4.3.3 PrincipalStresses and Stress Invariants 22 2.5 Transformation of Stress Components 24 References 28 viii Contents 3 Strain 29 3.1 Definition of Strain 29 3.1.1 Some Properties of Materials Associated with Strain 30 3.1.1.1 Poisson’s Ratio 30 3.1.1.2 Volumetric Strain 30 3.1.1.3 Bulk Modulus 31 3.1.1.4 Modulus of Elasticity 32 3.1.1.5 Shear Modulus (Modulus of Rigidity) 32 3.2 Strain–Displacement Equations 33 3.3 Strain Tensors 35 3.3.1 Small Strain Tensor 35 3.3.2 Finite Strain Tensor 38 3.3.3 Mean and Deviatoric Strain Tensors 40 3.3.4 Principal Strains and Strain Invariants 41 3.3.4.1 Strain Tensor 41 3.3.4.2 Deviatoric Strain Tensor 42 3.4 Transformation of Strain Components 43 3.4.1 Mohr’s Circle 44 3.5 Strain Measurement 44 References 48 4 MechanicalTestingofMaterials 51 4.1 Material Properties 51 4.2 Types of Material Testing 52 4.3 Test Methods Related to Mechanical Properties 52 4.4 Testing Machines and Specimens 52 4.4.1 Static Tensile Testing Machine and Specimens 52 4.4.2 Impact Testing Machine and Specimens 54 4.4.3 Hardness TestingMachine 54 4.4.4 Fatigue Testing Machines 56 4.5 Test Results 56 4.5.1 Static Tensile Test Results 56 4.5.1.1 Engineering Stress–Strain Diagram 56 4.5.1.2 Creep Diagram/Curve 62 4.5.1.3 Relaxation Diagram/Curve 62 4.5.2 Dynamic Test Results 63 4.5.2.1 Tensile, Flexural and TorsionalTest Results 63 4.5.2.2 Toughness Test Results 64 4.5.2.3 Fracture Toughness Test Results 64 References 64 5 MaterialBehaviorandYieldCriteria 67 5.1 Elastic and Inelastic Responses of a Solid 67 5.2 Yield Criteria 67 5.2.1 Ductile Materials 71 5.2.1.1 Maximum Shear Stress Criterion (Tresca Criterion) 71