Roland Jančo & Branislav Hučko Introduction to Mechanics of Materials Part I Download free eBooks at bookboon.com Introduction to Mechanics of Materials: Part I First Edition © 2013 Roland Jančo, Branislav Hučko & bookboon.com (Ventus Publishing ApS) ISBN 978-87-403-0364-3 Reviewers: Assoc prof Karel Frydrýšek, Ph.D ING-PAED IGIP, VŠB-Technical University of Ostrava, Czech Republic prof Milan Žmindák, PhD., University of Žilina, Slovak Republic Dr Michal Čekan, PhD., Canada Language corrector: Dr Michal Čekan, PhD., Canada Download free eBooks at bookboon.com Introduction to Mechanics of Materials: Part I Contents Contents List Of Symbols Preface 10 Introduction – Concept of stress 11 1.1 Introduction 11 1.2 A Short Review of the Methods of Statics 11 1.3 Deinition of the Stresses in the Member of a Structure 16 1.4 Basic Stresses (Axial, Normal, Shearing and Bearing stress) 19 1.5 Application to the Analysis and Design of Simple Structures 24 1.6 Method of Problem Solution and Numerical Accuracy 25 1.7 Components of Stress under General Loading Conditions 27 1.8 Design Considerations and Factor of Safety 30 Stress and Strain – Axial Loading 32 2.1 Introduction 32 2.2 Normal Stress and Strain under Axial Loading 32 e Graduate Programme for Engineers and Geoscientists I joined MITAS because I wanted real responsibili Maersk.com/Mitas Real work International Internationa al opportunities ree work wo or placements Month 16 I was a construction supervisor in the North Sea advising and helping foremen he ssolve problems Download free eBooks at bookboon.com Click on the ad to read more Introduction to Mechanics of Materials: Part I Contents 2.3 Stress-Strain Diagram, Hooke’s Law, and Modulus of Elasticity 35 2.4 Poisson’s Ratio 38 2.5 Generalised Hooke’s Law for Multiaxial Loading 40 2.6 Saint Venant’s Principle 44 2.7 Deformations of Axially Loaded Members 47 2.8 Problems Involving Temperature Changes 51 2.9 Trusses 54 2.10 Examples, Solved and Unsolved Problems 55 Torsion 86 3.1 Introduction 86 3.2 Deformation in a Circular Shat 88 3.3 Stress in the Elastic Region 94 3.4 Angle of Twist in the Elastic Region 97 3.5 Statically indeterminate Shats 98 3.6 Design of Transmission Shats 100 3.7 Torsion of Non-Circular Members 100 3.8 hin-Walled hollow Members 106 3.9 Examples, Solved and Unsolved Problems 110 www.job.oticon.dk Download free eBooks at bookboon.com Click on the ad to read more Introduction to Mechanics of Materials: Part I Contents Bending of Straight Beams Part II 4.1 Introduction Part II 4.2 Supports and Reactions Part II 4.3 Bending Moment and Shear Force Part II 4.4 Shear and Bending Moment Diagrams Part II 4.5 Relations among Load, Shear, and the Bending Moment Part II 4.6 Deinition of Normal and Shearing Stresses Part II 4.7 Design of Straight Prismatic Beams Part II 4.8 Examples, Solved and Unsolved Problems Part II Delection of Beams Part II 5.1 Introduction Part II 5.2 Integration method Part II 5.3 Using a Singularity Function to Determine the Slope and Delection of Beams Part II 5.4 Castigliano’s heorem Part II 5.5 Delections by Castigliano’s heorem Part II 5.6 Statically Indeterminate Beams Part II 5.7 Examples, solved and unsolved problems Part II Download free eBooks at bookboon.com Click on the ad to read more Introduction to Mechanics of Materials: Part I Contents Columns Part II 6.1 Introduction Part II 6.2 Stability of Structures Part II 6.3 Euler’s formulas for Columns Part II 6.4 Design of Columns under a Centric Load Part II 6.5 Design of Columns under an Eccentric Load Part II 6.6 Examples, solved and unsolved problems Part II Appendix 135 A.1 Centroid and irst moment of areas 135 A.2 Second moment, moment of areas 138 A.3 Parallel axis theorem 143 A.4 Product of Inertia, Principal Axes 151 A.5 Strain energy for simple loads 152 References 159 Download free eBooks at bookboon.com Click on the ad to read more Introduction to Mechanics of Materials: Part I List Of Symbols List Of Symbols A b B.C D E fS F F.S G h Iz, Iy Jo L DL M N Qz, Qy rz R Ri s T t ∆T u U V V w y(x) Area width buckling coeicient diameter modulus of elasticity, Young’s modulus shearing factor external force factor of safety modulus of rigidity height second moment, or moment of inertia, of the area A respect to the z or y axis polar moment of inertia of the area A length elongation of bar bending moment, couple normal or axial force irst moment of area with respect to the z or y axis radius of gyration of area A with respect to the z axis radius reaction at point i length of centreline torque thickness change of temperature strain energy density strain energy volume transversal force uniform load delection A α α γ ε ϕ Θi τ area bounded by the centerline of wall cross-section area coeicient of thermal expansion (in chapter 2) parameter of rectangular cross-section in torsion shearing strain strain angle of twist slope at point i shearing stress Download free eBooks at bookboon.com Introduction to Mechanics of Materials: Part I τall σ σall σmax σMises σN List Of Symbols allowable shearing stress stress or normal stress allowable normal stress maximum normal stress von Misses stress normal or axial stress Download free eBooks at bookboon.com Introduction to Mechanics of Materials: Part I Preface Preface his book presents a basic introductory course to the mechanics of materials for students of mechanical engineering It gives students a good background for developing their ability to analyse given problems using fundamental approaches he necessary prerequisites are the knowledge of mathematical analysis, physics of materials and statics since the subject is the synthesis of the above mentioned courses he book consists of six chapters and an appendix Each chapter contains the fundamental theory and illustrative examples At the end of each chapter the reader can ind unsolved problems to practice their understanding of the discussed subject he results of these problems are presented behind the unsolved problems Chapter discusses the most important concepts of the mechanics of materials, the concept of stress his concept is derived from the physics of materials he nature and the properties of basic stresses, i.e normal, shearing and bearing stresses; are presented too Chapter deals with the stress and strain analyses of axially loaded members he results are generalised into Hooke’s law Saint-Venant’s principle explains the limits of applying this theory In chapter we present the basic theory for members subjected to torsion Firstly we discuss the torsion of circular members and subsequently, the torsion of non-circular members is analysed In chapter 4, the largest chapter, presents the theory of beams he theory is limited to a member with at least one plane of symmetry and the applied loads are acting in this plane We analyse stresses and strains in these types of beams Chapter continues the theory of beams, focusing mainly on the delection analysis here are two principal methods presented in this chapter: the integration method and Castigliano’s theorem Chapter deals with the buckling of columns In this chapter we introduce students to Euler’s theory in order to be able to solve problems of stability in columns In closing, we greatly appreciate the fruitful discussions between our colleagues, namely prof Pavel Élesztős, Dr Michal Čekan And also we would like to thank our reviewers’ comments and suggestions Roland Jančo Branislav Hučko Download free eBooks at bookboon.com 10 [...]... bookboon.com 20 Introduction to Mechanics of Materials: Part I Introduction – Concept of stress Fig 1. 16 Fig 1. 17 軽 噺 鶏 ̊æœ 肯" " cpf"" " 撃 噺 鶏 œÆº 肯" (1. 11) Are you remarkable? Win one of the six full tuition scholarships for International MBA or MSc in Management Download free eBooks at bookboon.com 21 register now rode www.Nyen ge.com n le MasterChal Introduction to Mechanics of Materials: Part I Introduction. . .Introduction to Mechanics of Materials: Part I Introduction – Concept of stress 1 Introduction – Concept of stress 1. 1 Introduction he main objective of the mechanics of materials is to provide engineers with the tools, methods and technologies for • analysing existing load-bearing structures; • designing new structures Both of the above mentioned tasks require the analyses of stresses... bookboon.com 18 Introduction to Mechanics of Materials: Part I Fig 1. 11 Hki0"3033" Introduction – Concept of stress " " Fig 1. 12 Hki0"3034" 1. 4 Basic Stresses (Axial, Normal, Shearing and Bearing stress) Fig 1. 13 In the previous Section we discussed the case when the resultant of internal forces and the resulting stress normal to the cross-section are considered Now let us consider the cutting process of material... value of shearing stress: Download free eBooks at bookboon.com 19 Introduction to Mechanics of Materials: Part I Introduction – Concept of stress Fig 1. 14 酵 噺 ØÆŒ 撃 撃 畦蝦ど 畦 酵欠懸結 噺 " 噺 穴撃 穴畦 "" qt"" 撃 噺 完 酵穴畦" 畦 (1. 8) (1. 9) he presented case of cutting is known as the shear he cutaway efect can be commonly found in bolts, screws, pins and rivets used to connect various structural components, see Fig 1. 15(a).Two... safety of the rod BC depends mainly on the material used and its geometry herefore we need to make observations of processes inside of the material during loading Fig 1. 3 Download free eBooks at bookboon.com 12 Introduction to Mechanics of Materials: Part I Introduction – Concept of stress Fig 1. 4 Fig 1. 5 Join the Vestas Graduate Programme Experience the Forces of Wind and kick-start your career As one of. .. bookboon.com 11 Introduction to Mechanics of Materials: Part I Introduction – Concept of stress Fig 1. 2 ね デ 繋捲 噺 ど"""""""繋稽系 伐 繋系経 噺 ど" の ぬ デ 繋検 噺 ど"""""""繋系経 伐 なの"倦軽 噺 ど" (1. 1) の Solving the equations (1. 1) we obtain the forces in each member: FBC = 20 kN ,FCD = 25 kN he force FBC is compressive and the force FCD is tensile At this moment we are not able to make the decision about the safety design of rod... right side of the body considered, see Fig 1. 26 Fig 1. 25 Fig .1. 26 Download free eBooks at bookboon.com 28 Introduction to Mechanics of Materials: Part I Introduction – Concept of stress Secondly we now pass a section parallel to the principal plane of xz, where we will get the stress components: 購検 , 酵検捲 and 酵検権 in a similar way hirdly, passing a section parallel to the principal plane of xy, we can... deinition of the axial stress is the same as previously deined stress types, i.e 喧 噺 ØÆŒ 鶏 畦蝦ど 畦 穴鶏 噺 穴畦 "" (1. 15) Download free eBooks at bookboon.com 22 Introduction to Mechanics of Materials: Part I Introduction – Concept of stress Fig 1. 19 Fig 1. 20 Do you have drive, initiative and ambition? Engage in extra-curricular activities such as case competitions, sports, etc – make new friends among cbs’ 19 ,000... 結捲建結堅券欠健"欠喧喧健件結穴"血剣堅潔結" Fig 1. 6 Download free eBooks at bookboon.com 14 (1. 3) Introduction to Mechanics of Materials: Part I Introduction – Concept of stress he resultant can be determined by applying the method of section Passing the section at some arbitrary point Q we get two portions of the rod: CQ and DQ, see Fig 1. 6 Since force FCD = 25 kN must be applied at point Q for both portions to keep them in equilibrium,... the ad to read more Introduction to Mechanics of Materials: Part I Introduction – Concept of stress Fittings, bolts, or screws have a lateral contact within the connected member, see Fig 1. 19 hey create the stress in the connected member along the bearing surface or the contact surface For example let us consider the bolt JK connecting two plates B and C, which are subjected to shear, see Fig 1. 19 he ... Introduction – Concept of stress 11 1. 1 Introduction 11 1. 2 A Short Review of the Methods of Statics 11 1. 3 Deinition of the Stresses in the Member of a Structure 16 1. 4 Basic Stresses (Axial, Normal,... Introduction to Mechanics of Materials: Part I Introduction – Concept of stress Introduction – Concept of stress 1. 1 Introduction he main objective of the mechanics of materials is to provide engineers... the method of section Download free eBooks at bookboon.com 18 Introduction to Mechanics of Materials: Part I Fig 1. 11 Hki0"3033" Introduction – Concept of stress " " Fig 1. 12 Hki0"3034" 1. 4 Basic