book

Strength of Materials

by U. C. Jindal

April 2012

Intermediate to advanced

868 pages

22h 25m

English

Pearson India

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IntroductionTensile and Compressive StressesShear Stress and Shear StrainComplementary Shear StressesStresses on an Inclined PlaneBars of Varying Cross-sectionsLongitudinal Strain, Lateral Strain and Poisson’s RatioTapered BarTapered FlatBars Subjected to Various ForcesExtension in Bar Due to Self-weightBar of Uniform StrengthVolumetric Stress and Volumetric StrainStatically Indeterminate ProblemsStrain Energy and ResilienceSudden LoadImpact LoadTensile Test on Mild SteelStress ConcentrationFactor of SafetyKey Points to RememberReview QuestionsMultiple Choice QuestionsPractice ProblemsSpecial Problems
IntroductionStresses in a Composite BarComposite SystemBars of Different LengthsBolt and Tube AssemblyTemperature Stresses in a Single BarTemperature Stresses in a Composite BarKey Points to RememberReview QuestionsMultiple Choice QuestionsPractice ProblemsSpecial Problems
IntroductionStresses on an Inclined Plane (I)Stresses on Inclined Plane (II)Principal StressesPractical Cases of Principal PlanesGraphical SolutionEllipse of StressesStrain ComponentsStrain Components on an Inclined PlaneMohr’s Strain CircleThree-Dimensional StressesPrincipal Strains in Terms of Principal StressesStrain Gauge RosettesRosettesKey Points to RememberReview QuestionsMultiple Choice QuestionsPractice ProblemsSpecial Problems
IntroductionYoung’s Modulus and Poisson’s RatioDetermination of Modulus of RigidityRelation Between Young’s Modulus and Modulus of RigidityRelation Between Young’s Modulus and Bulk ModulusKey Points to RememberReview QuestionsMultiple Choice QuestionsPractice ProblemsSpecial Problems

IntroductionThin Cylinder Subjected to Internal PressureThin Spherical ShellCylindrical Shell with Hemispherical EndsWire Winding of Thin Cylindrical ShellsPressure Vessel with a Double Curved WallConical Water TankKey Points to RememberReview QuestionsMultiple Choice QuestionsPractice ProblemsSpecial Problems
IntroductionLame’s EquationsThick Cylindrical Shell Subjected to External PressureCompound CylinderShrinkage AllowanceHub and Shaft AssemblyThick Spherical ShellKey Points to RememberReview QuestionsMultiple Choice QuestionsPractice ProblemsSpecial Problems
IntroductionDifferent Types of BeamsShear Force (Positive and Negative)Bending Moments (Positive and Negative)SF Diagrams of Beams/Cantilevers Carrying Point LoadsSF Diagrams of Cantilevers and Beams with UDLSF Diagrams of Beam/Cantilevers with Applied MomentBM Diagrams of Cantilevers/Beams with Point LoadsBM Diagrams of Cantilevers/Beams with UDLSF and BM Diagrams of Beam/Cantilever with Load Through a CrankVariable Loading on a BeamRelation Between Rate of Loading, SF and BM in a BeamKey Points to RememberReview QuestionsMultiple Choice QuestionsPractice ProblemsSpecial Problems
IntroductionAssumptions in Theory of Simple BendingTheory of Simple BendingNeutral AxisMoment of ResistancePerpendicular Axes and Parallel Axes TheoremsSymmetrical I-SectionT-SectionChannel SectionUnequal I-SectionModulus of RuptureBuilt Up SectionsBeams of Uniform StrengthComposite BeamsReinforced Cement Concrete BeamRCC Beams (Rectangular Section)Stress Concentration in BendingKey Points to RememberReview QuestionsMultiple Choice QuestionsPractice ProblemsSpecial Problems
IntroductionShear Stress DistributionShear Stress Distribution in a Rectangular Section of a BeamShear Stress Distribution in a Circular Section of a BeamCurves of Principal Stresses in a BeamDirectional Distribution of Shear StressesKey Points to RememberReview QuestionsMultiple Choice QuestionsPractice ProblemsSpecial Problems
IntroductionEccentric Axial Thrust on a ColumnLoad Eccentric to Both Axes (Rectangular Section)Core of Rectangular SectionCore of Circular SectionCore of Any SectionWind Pressure on WallsWind Pressure on Chimney ShaftsKey Points to RememberReview QuestionsMultiple Choice QuestionsPractice ProblemsSpecial Problems
IntroductionRelation Between Bending Moment and CurvatureSign ConventionsSimply Supported Beam with a Central Point LoadA Beam Carrying UDL with Simply Supported EndsA Cantilever with the Point Load at Free EndA Cantilever with a UDLMacaulay’s MethodEccentric Load on a BeamImpact Loading of a BeamPropped CantileversStepped BeamSlope and Deflection by Area Moment MethodConjugate Beam MethodDeflectionSlope and Deflection of Stepped BeamsKey Points to RememberReview QuestionsMultiple Choice QuestionsPractice ProblemsSpecial Problems
IntroductionDevelopment of Shear Stress and Angular Twist in a Shaft Due to Twisting MomentModulus of RuptureHorse-Power Transmitted by a ShaftShafts of Varying DiametersCompound ShaftStresses in a Shaft Subjected to Twisting MomentShafts Subjected to T and MTorsional Resilience of a ShaftStresses Developed in a KeyStress Concentration in Torsional LoadingKey Points to RememberReview QuestionsMultiple Choice QuestionsPractice ProblemsSpecial Problems
IntroductionHelical SpringsWahl’s FactorClose-coiled Helical Spring Subjected to an Axial LoadClosed-coiled Helical Spring Subjected to an Axial MomentOpen-coiled Helical SpringOpen-coiled Helical Spring Subjected to Axial MomentOpen-coiled Helical Spring—Stresses Developed in Spring WirePlane Spiral SpringConical SpringLeaf SpringCantilever Leaf Spring (Quarter Elliptic Spring)Key Points to RememberReview QuestionsMultiple Choice QuestionsPractice ProblemsSpecial Problems
IntroductionEuler’s Theory of BucklingEquivalent LengthLimitations of Euler’s Theory of BucklingHigher-order Differential EquationRankine Gordon FormulaJohnson’s Parabolic FormulaEccentric Loading of ColumnsProfessor Perry’s Approximate FormulaLong Columns with Eccentricity in GeometryProfessor Perry Robertson FormulaLateral Loading of Strut with Point LoadStrut with an Uniformly Distributed Lateral LoadEnergy ApproachKey Points to RememberReview QuestionsMultiple Choice QuestionsPractice Problems
IntroductionMaximum Principal Stress Theory (Rankine’s Theory)Maximum Shear Stress Theory (Tresca Theory)Maximum Principal Strain Theory (St. Venant’s Theory)Strain Energy Theory (Beltrami, Haigh Theory)Shear Strain Energy or Distortional Strain Energy Theory (Von Mises Theory)Mohr’s Theory of FailureKey Points to RememberReview QuestionsMultiple Choice QuestionsPractice ProblemsSpecial Problems
IntroductionCastigliano’s First TheoremStrain Energy Due to Axial ForceStrain Energy Due to Shear StressStrain Energy Due to BendingStrain Energy Due to Twisting MomentMaxwell’s Reciprocal TheoremPrinciple of Virtual Forces Applied to TrussesMultiple Choice QuestionsPractice Problems
IntroductionStresses in a Curved BarAh2 for a Rectangular SectionValue of h2 for Sections Made Up of Rectangular StripsAh2 for a Trapezoidal SectionAh2 for a Circular SectionRing Subjected to a Diametral LoadChain Link Subjected to a Tensile LoadDeflection of Curved BarDeflection of a Chain LinkMultiple Choice QuestionsPractice Problems
IntroductionPrincipal AxesParallel Axes Theorem for Product of InertiaDetermination of Principal AxesStresses Due to Unsymmetrical BendingDeflection of Beams Due to Unsymmetrical BendingShear CentreKey Points to RememberMultiple Choice QuestionsPractice Problems
IntroductionStress TensorStress at a PointPlane Stress ConditionStrain TensorDeformationsGeneralized Hooke’s LawElastic Constants K and GEquilibrium EquationsSecond-degree PolynomialA Beam Subjected to Pure BendingMultiple Choice QuestionsPractice Problems
IntroductionMaterials Behaviour Under Static TensionBehaviour of Materials Under Static CompressionBehaviour of Materials Under BendingBehaviour of Materials Under TorsionBehaviour of Materials Under ImpactHardnessFatigueCreepReview QuestionsMultiple Choice Questions
Tensile Test on a Specimen Using a TensometerShear Punching Test on Sheet SampleTensile Test on a Sample Using UTMDouble Shear Test on a Specimen Using UTMCompression Test on a Cast Iron Specimen Using UTMDeflection Test on a Bar Using UTMCompression Test on BrickCompression Test on a Wooden SampleHardness Test—Brinell Hardness NumberHardness Test—Rockwell Hardness NumberHardness Test—Vickers Pyramid NumberIzod Impact TestCharpy Impact TestTorsion TestStiffness of a Helical SpringStiffness of a Leaf Spring
IntroductionCarbon SteelsAlloy SteelsCast IronAluminium, Magnesium, Titanium and Their AlloysCopper and its AlloysNickel, Cobalt and Their AlloysBabbitsPlasticsRubberCeramic MaterialsGlassesPolymorph of CarbonReview QuestionsMultiple Choice Questions

Content preview from Strength of Materials

3 Principal Stresses and Strains

CHAPTER OBJECTIVES

We will learn about principal stresses, planes of principal stresses and strains on principal planes. Practical examples of principal planes in actual components will also be discussed. In this chapter we will learn about principal stresses/strains.

Determination of the normal and shear stresses on a plane inclined on two planes on which stresses are given.
Determination of the angle of the plane on which shear stress is zero.
Determination of the maximum and minimum principal stresses and the planes of such stresses.
Graphical method to determine principal stresses at a point. In many typical cases students are confused to locate the centre of Mohr’s stress circle. This concept is clearly ...