Practical Stress Analysisin Engineering DesignThird EditionHuston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page i 8.11.2008 3:29pm Compositor Name: BManiMECHANICAL ENGINEERINGA Series of Textbooks and Reference BooksFounding EditorL. L. FaulknerColumbus Division, Battelle Memorial Instituteand Department of Mechanical EngineeringThe Ohio State UniversityColumbus, Ohio1. Spring Designers Handbook, Harold Carlson2. Computer-Aided Graphics and Design, Daniel L. Ryan3. Lubrication Fundamentals, J. George Wills4. Solar Engineering for Domestic Buildings, William A. Himmelman5. Applied Engineering Mechanics: Statics and Dynamics, G. Boothroyd and C. Poli6. Centrifugal Pump Clinic, Igor J. Karassik7. Computer-Aided Kinetics for Machine Design, Daniel L. Ryan8. Plastics Products Design Handbook, Part A: Materials and Components; Part B:Processes and Design for Processes, edited by Edward Miller9. Turbomachinery: Basic Theory and Applications, Earl Logan, Jr.10. 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Practical Stress Analysis in Engineering Design, Third Edition, Ronald Huston and Harold JosephsHuston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page vii 8.11.2008 3:29pm Compositor Name: BManiHuston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page viii 8.11.2008 3:29pm Compositor Name: BManiPractical Stress Analysisin Engineering DesignThird EditionRonald HustonHarold JosephsCRC Press is an imprint of theTaylor & Francis Group, an informa businessBoca Raton London New YorkHuston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page ix 8.11.2008 3:29pm Compositor Name: BManiCRC PressTaylor & Francis Group6000 Broken Sound Parkway NW, Suite 300Boca Raton, FL 33487-2742 2009 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa businessNo claim to original U.S. Government worksPrinted in the United States of America on acid-free paper10 9 8 7 6 5 4 3 2 1International Standard Book Number-13: 978-1-57444-713-2 (Hardcover)This book contains information obtained from authentic and highly regarded sources. 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For orga-nizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged.Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe.Library of Congress Cataloging-in-Publication DataHuston, Ronald L., 1937-Practical stress analysis in engineering design / Ronald Huston and Harold Josephs. -- 3rd ed.p. cm. -- (Dekker mechanical engineering)Prev. ed. authored by Alexander Blake.Includes bibliographical references and index.ISBN 978-1-57444-713-2 (alk. paper)1. Strains and stresses. 2. Engineering design. I. Josephs, Harold. II. Blake, Alexander. Practical stress analysis in engineering design. III. Title. TA648.3.B57 2009624.176--dc22 2008029335Visit the Taylor & Francis Web site athttp://www.taylorandfrancis.comand the CRC Press Web site athttp://www.crcpress.comHuston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page x 8.11.2008 3:29pm Compositor Name: BManiContentsPreface........................................................................................................................................... xxvAuthors........................................................................................................................................ xxviiPART I Fundamental Relations and ConceptsChapter 1 Forces and Force Systems........................................................................................... 31.1 Concept of a Force................................................................................................................. 31.2 Concept of a Moment ............................................................................................................ 31.3 Moment of a Force about a Line........................................................................................... 41.4 Force Systems ........................................................................................................................ 41.5 Special Force Systems ........................................................................................................... 71.5.1 Zero Force Systems .................................................................................................... 71.5.2 Couples ....................................................................................................................... 71.5.3 Equivalent Force Systems........................................................................................... 71.5.4 Equivalent Replacement by a Force and a Couple .................................................... 9Symbols........................................................................................................................................... 10References ....................................................................................................................................... 10Chapter 2 Simple Stress and Strain: Simple Shear Stress and Strain........................................ 112.1 Concept of Stress ................................................................................................................. 112.2 Concept of Strain ................................................................................................................. 132.3 Shear Stress.......................................................................................................................... 132.4 Shear Strain.......................................................................................................................... 14Symbols........................................................................................................................................... 16Chapter 3 Hookes Law and Material Strength ......................................................................... 173.1 Hookes Law in One Dimension ......................................................................................... 173.2 Limitations of Proportionality.............................................................................................. 183.3 Material Strength.................................................................................................................. 183.4 Hookes Law in Shear.......................................................................................................... 19Symbols........................................................................................................................................... 21References ....................................................................................................................................... 22Chapter 4 Stress in Two and Three Dimensions ....................................................................... 234.1 Stress Vectors....................................................................................................................... 234.2 Stresses within a Loaded Elastic BodyNotation and Sign Convention........................... 234.3 Equilibrium ConsiderationsIndex Notation ..................................................................... 274.4 Stress Matrix, Stress Dyadic................................................................................................ 324.5 Eigenvectors and Principal Stresses..................................................................................... 344.5.1 Illustrative Computation ........................................................................................... 364.5.2 Discussion................................................................................................................. 38Huston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page xi 8.11.2008 3:29pm Compositor Name: BManixi4.6 Eigenvalues and EigenvectorsTheoretical Considerations .............................................. 384.6.1 Maximum and Minimum Normal Stresses............................................................... 394.6.2 Real Solutions of the HamiltonCayley Equation.................................................... 394.6.3 Mutually Perpendicular Unit Eigenvectors............................................................... 404.6.4 Multiple (Repeated) Roots of the HamiltonCayley Equation ................................ 424.7 Stress Ellipsoid..................................................................................................................... 444.8 Maximum Shear Stress ........................................................................................................ 464.9 Two-Dimensional AnalysisMohrs Circle ....................................................................... 47Symbols........................................................................................................................................... 53References ....................................................................................................................................... 54Chapter 5 Strain in Two and Three Dimensions ....................................................................... 555.1 Concept of Small Displacement .......................................................................................... 555.2 Two-Dimensional Analyses ................................................................................................. 555.3 Shear Strain.......................................................................................................................... 575.4 Displacement, Deformation, and Rotation........................................................................... 585.5 Generalization to Three Dimensions ................................................................................... 595.6 Strain and Rotation Dyadics ................................................................................................ 625.7 Strain and Rotation Identities .............................................................................................. 63Symbols........................................................................................................................................... 64References ....................................................................................................................................... 65Chapter 6 Curvilinear Coordinates ............................................................................................ 676.1 Use of Curvilinear Coordinates ........................................................................................... 676.2 Curvilinear Coordinate Systems: Cylindrical and Spherical Coordinates........................... 676.2.1 Cylindrical Coordinates ............................................................................................ 676.2.2 Spherical Coordinates ............................................................................................... 706.3 Other Coordinate Systems ................................................................................................... 716.4 Base Vectors ........................................................................................................................ 726.5 Metric Coefcients, Metric Tensors .................................................................................... 746.6 Reciprocal Base Vectors ...................................................................................................... 766.7 Differentiation of Base Vectors ........................................................................................... 786.8 Covariant Differentiation ..................................................................................................... 816.9 Equilibrium Equations and StrainDisplacement Relations in Curvilinear Coordinates...... 83Symbols........................................................................................................................................... 86References ....................................................................................................................................... 86Chapter 7 Hookes Law in Two and Three Dimensions ........................................................... 877.1 Introduction.......................................................................................................................... 877.2 Poissons Ratio..................................................................................................................... 877.3 Brittle and Compliant Materials........................................................................................... 917.4 Principle of Superposition of Loading................................................................................. 917.5 Hookes Law in Two and Three Dimensions...................................................................... 917.6 Relations between the Elastic Constants ............................................................................. 937.7 Other Forms of Hookes Law.............................................................................................. 977.8 Hydrostatic Pressure and Dilatation..................................................................................... 98Symbols........................................................................................................................................... 99Reference......................................................................................................................................... 99Huston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page xii 8.11.2008 3:29pm Compositor Name: BManixii ContentsPART II Straight and Long Structural Components:Beams, Rods, and BarsChapter 8 Beams: Bending Stresses (Flexure) ........................................................................ 1038.1 Beams............................................................................................................................... 1038.2 Loadings........................................................................................................................... 1038.3 Coordinate Systems and Sign Conventions..................................................................... 1038.4 Equilibrium and Governing Equations ............................................................................ 1068.5 Beam Deection due to Bending..................................................................................... 1078.6 Beam Stresses due to Bending ........................................................................................ 109Symbols......................................................................................................................................... 110Chapter 9 Beams: Displacement from Bending ...................................................................... 1119.1 Beam Displacement and Bending Moment ..................................................................... 1119.2 Beam Displacement in Terms of Transverse Shear and the Loading on the Beam.......... 1119.3 Beam Supports, Support Reactions, and Boundary Conditions...................................... 1129.3.1 Built-In (Clamped or Cantilever) Support ............................................................ 1129.3.2 Simple (Pin or Roller) Support ............................................................................. 1139.3.3 Free (Unconstrained) Support............................................................................... 1139.3.4 Elastic Support ...................................................................................................... 1149.4 Summary of Governing Equations .................................................................................. 1149.5 Illustrations....................................................................................................................... 1159.5.1 Uniformly Loaded Cantilever Beam..................................................................... 1159.5.2 Cantilever Beam with a Concentrated End Load................................................. 1179.5.3 Simply Supported Beam with a Uniform Load.................................................... 1199.5.4 Simply Supported Beams with a Concentrated Interior Load.............................. 1219.6 Comment .......................................................................................................................... 124Symbols......................................................................................................................................... 124Reference....................................................................................................................................... 125Chapter 10 Beam Analysis Using Singularity Functions ........................................................ 12710.1 Use of Singularity Functions ........................................................................................... 12710.1.1 Heavyside Unit Step Function............................................................................ 12710.1.2 Dirac Delta Function........................................................................................... 12710.2 Singularity Function Denition ....................................................................................... 12810.3 Singularity Function Description and Additional Properties........................................... 12810.4 Illustration of Singularity Function Use .......................................................................... 13010.4.1 Uniformly Loaded Cantilever Beam................................................................... 13010.4.2 Cantilever Beam with a Concentrated End Load............................................... 13210.4.3 Simply Supported Beam with a Uniform Load.................................................. 13410.4.4 Simply Supported Beam with a Concentrated Interior Load ............................. 13610.5 Discussion and Recommended Procedure....................................................................... 13810.6 Comments on the Evaluation of Integration Constants................................................... 13910.7 Shear and Bending Moment Diagrams............................................................................ 14010.8 Additional Illustration: Cantilever Beam with Uniform Load over Half the Span........... 143Symbols......................................................................................................................................... 146References ..................................................................................................................................... 147Huston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page xiii 8.11.2008 3:29pm Compositor Name: BManiContents xiiiChapter 11 Beam Bending Formulas for Common Congurations ........................................ 14911.1 Prospectus ........................................................................................................................ 14911.2 Cantilever Beams ............................................................................................................. 14911.2.1 Left-End Supported Cantilever Beam................................................................. 14911.2.2 Cantilever Beam, Left-End Support, and Concentrated End Load.................... 14911.2.3 Cantilever Beam, Left-End Support, and Uniform Load ................................... 15011.2.4 Right-End Supported Cantilever Beam.............................................................. 15211.2.5 Cantilever Beam, Right-End Support, and Concentrated End Load.................. 15211.2.6 Cantilever Beam, Right-End Support, and Uniform Load................................. 15411.3 Simply Supported Beams................................................................................................. 15511.3.1 Positive Directions .............................................................................................. 15511.3.2 Simply Supported Beam and Concentrated Center Load................................... 15511.3.3 Simply Supported Beam and Concentrated Off-Center Load............................ 15711.3.4 Simply Supported Beam and Uniform Load...................................................... 15811.4 Double Built-In Beams .................................................................................................... 16011.4.1 Positive Directions .............................................................................................. 16011.4.2 Double Built-In Supported Beam and Concentrated Center Load..................... 16011.4.3 Double Built-In Supported Beam and Concentrated Off-Center Load.............. 16211.4.4 Double Built-In Supported Beam and Uniform Load........................................ 16311.5 Principle of Superposition................................................................................................ 16511.6 Summary and Formulas for Design................................................................................. 168Symbols......................................................................................................................................... 173References ..................................................................................................................................... 174Chapter 12 Torsion and Twisting of Rods .............................................................................. 17512.1 Introduction...................................................................................................................... 17512.2 Basic Assumptions in the Twisting of Rods or Round Bars .......................................... 17512.3 Stresses, Strains, and Deformation (Twisting) of Round Bars........................................ 17512.4 Torsion of Noncircular Cross-Sectional Bars.................................................................. 17812.5 Illustration: Twisting of a Rectangular Steel Bar ............................................................ 17912.6 Torsion of Noncircular, Nonrectangular Bars ................................................................. 18012.7 Torsion of Thin-Walled Ducts, Tubes, and Channels ..................................................... 181Symbols......................................................................................................................................... 185References ..................................................................................................................................... 185PART III Special Beam Geometries: Thick Beams,Curved Beams, Stability, and Shear CenterChapter 13 Thick Beams: Shear Stress in Beams ................................................................... 18913.1 Development of Shear Stress in a Beam......................................................................... 18913.2 Shear Loading Analysis ................................................................................................... 18913.3 Maximum Transverse Shear Stress.................................................................................. 19413.4 Nonrectangular Cross Sections ........................................................................................ 19513.5 Signicance of Beam Shear Stress .................................................................................. 195Symbols......................................................................................................................................... 198Reference....................................................................................................................................... 198Huston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page xiv 8.11.2008 3:29pm Compositor Name: BManixiv ContentsChapter 14 Curved Beams ....................................................................................................... 19914.1 Historical Perspective..................................................................................................... 19914.2 Neutral Axis Shift .......................................................................................................... 19914.3 Stresses in Curved Beams.............................................................................................. 20714.4 Approximation of Stress Concentration Factors............................................................ 20914.5 Application: Stresses in Hooks...................................................................................... 21014.6 Example of Curved Beam Computations ...................................................................... 21114.6.1 Flexure of a Curved Machine Bracket ............................................................. 21114.6.2 Expansion of a Machine Clamp ....................................................................... 21214.7 Further Comments on the Stresses in CurvedBeams and Hooks .......................................................................................................... 213Symbols......................................................................................................................................... 214References ..................................................................................................................................... 214Chapter 15 Stability: Buckling of Beams, Rods, Columns,and Panels.............................................................................................................. 21715.1 Introduction.................................................................................................................... 21715.2 Long Bars Subjected to Compression Loading............................................................. 21715.3 Buckling with Various End-Support Conditions........................................................... 21815.3.1 Clamped (Nonrotating) Ends ............................................................................ 21815.3.2 A Clamped (Nonrotating) and a Free End ....................................................... 21915.3.3 A Clamped (Nonrotating) and a Pinned End ................................................... 21915.4 Summary of Results for Long Bar Buckling with CommonlyOccurring End Conditions ............................................................................................. 22215.5 Intermediate Length Bars and ColumnsJohnson Formula ........................................ 22315.6 Intermediate Length Bars and ColumnsEccentric Loadingand the Secant Formula ................................................................................................. 22515.7 Buckling of Plates.......................................................................................................... 22815.8 Buckling due to Bending............................................................................................... 23015.9 Buckling of Columns Loaded by Their Own Weight ................................................... 23115.10 Other Buckling Problems: Rings and Arches................................................................ 23215.11 Summary Remarks......................................................................................................... 233Symbols......................................................................................................................................... 234References ..................................................................................................................................... 234Chapter 16 Shear Center .......................................................................................................... 23716.1 Introductory Comments ................................................................................................. 23716.2 Shear Flow..................................................................................................................... 23716.3 Application with Narrow Web Beam Cross Section..................................................... 24016.4 Twisting of Beams=Shear Center................................................................................... 24316.5 Example: Shear Center of a Channel Beam.................................................................. 24516.6 A Numerical Example ................................................................................................... 250Symbols......................................................................................................................................... 253References ..................................................................................................................................... 253Huston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page xv 8.11.2008 3:29pm Compositor Name: BManiContents xvPART IV Plates, Panels, Flanges, and BracketsChapter 17 Plates: Bending Theory......................................................................................... 25717.1 Historical Perspective and Introductory Remarks ......................................................... 25717.2 Modeling and Simplifying Assumptions ....................................................................... 25717.3 Stress Resultants ............................................................................................................ 25817.4 Bending and Twisting (Warping) Moments.................................................................. 26117.5 Equilibrium for a Plate Element .................................................................................... 26317.6 Summary of Terms and Equations ................................................................................ 26617.6.1 In-Plane Normal (Membrane) Forces ............................................................. 26717.6.2 In-Plane Shear Forces ..................................................................................... 26717.6.3 Vertical (Z-Direction) Shear Forces................................................................ 26717.6.4 Bending Moments........................................................................................... 26717.6.5 Twisting Moments .......................................................................................... 26717.6.6 Loading Conditions......................................................................................... 26717.6.7 Equilibrium Equations .................................................................................... 26817.6.8 Comment......................................................................................................... 26817.7 StressStrainDisplacement Relations........................................................................... 26817.8 Integration of StressStrainDisplacement Equations throughthe Thickness of the Plate.............................................................................................. 26917.9 Governing Differential Equations.................................................................................. 27217.9.1 Equilibrium Equations .................................................................................... 27217.9.2 Displacement=Shear Assumptions .................................................................. 27317.9.3 MomentCurvature and In-Plane Force Relations ......................................... 27317.9.4 Governing Equation........................................................................................ 27317.10 Boundary Conditions ..................................................................................................... 27517.10.1 Simple (Hinge) Support .................................................................................. 27517.10.2 Clamped (Fixed or Built-In) Support ............................................................. 27517.10.3 Free Edge ........................................................................................................ 27517.10.4 Elastic Edge Support....................................................................................... 27617.11 Internal Stresses ............................................................................................................. 27717.12 Comments ...................................................................................................................... 277Symbols......................................................................................................................................... 278References ..................................................................................................................................... 278Chapter 18 Plates: Fundamental Bending Congurations and Applications........................... 27918.1 Review ........................................................................................................................... 27918.2 Simple Bending of Rectangular Plates .......................................................................... 28118.3 Simply Supported Rectangular Plate ............................................................................. 28218.4 Simply Supported Rectangular Plate with a Uniform Load.......................................... 28418.5 Simply Supported Rectangular Plate with a Concentrated Load .................................. 28418.6 Comments ...................................................................................................................... 28518.7 Circular Plates ................................................................................................................ 28518.8 Solution of the Governing Equation for Circular Plates ............................................... 28718.8.1 Simply Supported, Uniformly Loaded, Circular Plate ................................... 28818.8.2 Clamped Uniformly Loaded Circular Plate.................................................... 28918.9 Circular Plate with Concentrated Center Load.............................................................. 290Huston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page xvi 8.11.2008 3:29pm Compositor Name: BManixvi Contents18.9.1 Simply Supported Circular Plate with a Concentrated Center Load................ 29018.9.2 Clamped Circular Plate with a Concentrated Center Load .............................. 29018.10 Example Design Problem .............................................................................................. 29018.11 A Few Useful Results for Axisymmetrically Loaded Circular Plates........................... 29218.12 Comments ...................................................................................................................... 293Symbols......................................................................................................................................... 294References ..................................................................................................................................... 294Chapter 19 Panels and Annular Plate Closures ....................................................................... 29519.1 Problem Denition......................................................................................................... 29519.2 Design Charts for Panels ............................................................................................... 29519.3 Similarities of Rectangular and Elliptical Panels .......................................................... 29619.4 Example Design Problem .............................................................................................. 29819.5 Annular Members .......................................................................................................... 29919.6 Selected Formulas for Annular Plates ........................................................................... 302Symbols......................................................................................................................................... 306Chapter 20 Flanges .................................................................................................................. 30920.1 Introductory Remarks .................................................................................................... 30920.2 Stress Criteria................................................................................................................. 30920.3 Early Design Methods ................................................................................................... 31020.4 Thin Hub Theory ........................................................................................................... 31020.5 Flanges with Thick Hubs............................................................................................... 31120.6 Criterion of Flange Rotation.......................................................................................... 31220.7 Use of Plate Theory with Flanges ................................................................................. 31320.8 Formula for Hub Stress.................................................................................................. 31520.9 German and American Flange Design Practice............................................................. 31620.10 Circumferential Stress.................................................................................................... 31720.11 Apparent Stress CriteriaA Discussion ....................................................................... 31820.12 Plastic Correction........................................................................................................... 31920.13 Heavy-Duty Flanges ...................................................................................................... 32120.14 Equivalent Depth Formula............................................................................................. 32220.15 Load Sharing in Ribbed Flanges ................................................................................... 32420.16 Strength of Flange Ribs ................................................................................................. 32720.17 Local Bending of Flange Rings..................................................................................... 32920.18 Correction for Tapered Gussets ..................................................................................... 331Symbols......................................................................................................................................... 332References ..................................................................................................................................... 334Chapter 21 Brackets ................................................................................................................. 33721.1 Introduction.................................................................................................................... 33721.2 Types of Common Bracket Design ............................................................................... 33721.3 Weld Stresses ................................................................................................................. 33921.4 Stress Formulas for Various Simple Bracket Designs................................................... 34421.5 Stress and Stability Analyses for Web-Bracket Designs............................................... 347Symbols......................................................................................................................................... 351References ..................................................................................................................................... 354Huston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page xvii 8.11.2008 3:29pm Compositor Name: BManiContents xviiChapter 22 Special Plate Problems and Applications.............................................................. 35522.1 Introduction.................................................................................................................... 35522.2 Large Displacement of Axisymmetrically Loaded and Supported Circular Plates ........ 35522.3 Design Charts for Large Deection of Circular Plates.................................................. 35622.4 Design Example for a Large Displacement of Circular Plate ....................................... 35822.5 Large Displacement of Rectangular Plates.................................................................... 35922.6 Perforated Plates ............................................................................................................ 35922.7 Reinforced Circular Plates ............................................................................................. 36122.8 Pin-Loaded Plates .......................................................................................................... 36222.9 Belleville Washers ......................................................................................................... 364Symbols......................................................................................................................................... 368References ..................................................................................................................................... 369PART V Dynamic Loadings, Fatigue, and FractureChapter 23 Dynamic Behavior of Structures: A Conceptual Review..................................... 37323.1 Introduction.................................................................................................................... 37323.2 Vibration and Natural Frequency .................................................................................. 37323.3 Dynamic Structural ResponseIntuitive Design Criteria............................................. 37523.4 Dynamic Strength .......................................................................................................... 37523.5 Suddenly Applied Weight Loading ............................................................................... 37523.6 Strain EnergyAn Elementary Review........................................................................ 37923.7 Loading from a Falling Weight ..................................................................................... 38023.8 Impact from a Horizontally Moving Mass .................................................................... 38323.9 Illustrative Design Problems and Solutions................................................................... 38423.9.1 Cantilever Subjected to Free-End-Sudden Loading ......................................... 38423.9.2 VehicleBarrier Impact ..................................................................................... 38523.10 Energy Loss during Impact............................................................................................ 38623.11 Impact of Falling Structural Components...................................................................... 38623.12 ExampleVehicleBarrier Impact ................................................................................ 38923.13 Impact Mitigation........................................................................................................... 39023.14 Design Problem Example .............................................................................................. 39123.15 Natural Frequency of Selected Structural Components................................................. 39223.16 Estimating Natural Frequency ....................................................................................... 394Symbols......................................................................................................................................... 400References ..................................................................................................................................... 401Chapter 24 Elements of Seismic Design ................................................................................. 40324.1 Introduction.................................................................................................................... 40324.2 Earthquake Design Philosophies.................................................................................... 40324.3 Building Code Method .................................................................................................. 40324.4 Spectral Velocity Method .............................................................................................. 40424.5 Richter Scale .................................................................................................................. 40524.6 IllustrationSpectral Velocity Method......................................................................... 40524.7 Structural Damping........................................................................................................ 410Symbols......................................................................................................................................... 410References ..................................................................................................................................... 411Huston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page xviii 8.11.2008 3:29pm Compositor Name: BManixviii ContentsChapter 25 Impact Stress Propagation..................................................................................... 41325.1 Introduction.................................................................................................................... 41325.2 A Simple Conceptual Illustration .................................................................................. 41325.3 Stress Propagation Theory............................................................................................. 41425.4 Elastic Impact................................................................................................................. 41525.5 Acoustic (Sonic) Speed and Critical Speed................................................................... 41625.6 Illustration ...................................................................................................................... 41825.7 Axial Impact on a Straight Bar...................................................................................... 41825.8 Conditions of Spall ........................................................................................................ 41925.9 Example Design Problems............................................................................................. 42025.9.1 Object Falling onto a Column .......................................................................... 42025.9.2 Object Impacting a Long Cylinder ................................................................... 42025.10 Axial and Radial Modes of Elementary Structures ....................................................... 42225.11 Response of Buried Structures....................................................................................... 42325.12 Stress Propagation in Granular Media........................................................................... 42425.13 Applications in Machine Design ................................................................................... 424Symbols......................................................................................................................................... 424References ..................................................................................................................................... 425Chapter 26 Fatigue................................................................................................................... 42726.1 Introduction.................................................................................................................... 42726.2 Cumulative Damage Criteria ......................................................................................... 42726.3 Neuber Effect ................................................................................................................. 42926.4 Elements of Design for Fatigue ..................................................................................... 42926.5 Effect of Surface Finish ................................................................................................. 42926.6 Effect of Creep............................................................................................................... 43126.7 Effect of Corrosion ........................................................................................................ 43126.8 Effect of Size ................................................................................................................. 43126.9 Low-Cycle Fatigue......................................................................................................... 43226.10 Low-Cycle Fatigue Example ......................................................................................... 433Symbols......................................................................................................................................... 434References ..................................................................................................................................... 434Chapter 27 Fracture Mechanics: Design Considerations......................................................... 43727.1 Introduction.................................................................................................................... 43727.2 Practical Aspects of Fracture Mechanics....................................................................... 43727.3 Design Implications of the Crack Size Parameters ....................................................... 43927.4 Illustrative Design Problems and Solutions................................................................... 44027.4.1 Example Problem 1........................................................................................... 44027.4.2 Example Problem 2........................................................................................... 44127.4.3 Example Problem 3........................................................................................... 44227.5 Comment ........................................................................................................................ 44327.5.1 Example Problem.............................................................................................. 44327.6 Implications of Fracture Toughness............................................................................... 44427.7 Plane Stress Parameter ................................................................................................... 44527.8 Plane Stress Criterion for Pressure Vessel Design ........................................................ 44627.9 Remarks ......................................................................................................................... 447Symbols......................................................................................................................................... 448References ..................................................................................................................................... 448Huston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page xix 8.11.2008 3:29pm Compositor Name: BManiContents xixChapter 28 Fracture Control .................................................................................................... 44928.1 Introduction.................................................................................................................... 44928.2 Basic Concepts and Denitions ..................................................................................... 44928.3 Correlation of Fracture Properties.................................................................................. 45028.4 Practical Use of Crack Arrest Diagrams........................................................................ 45128.5 Thickness Criteria .......................................................................................................... 45328.6 Signicance of Stress and Strength ............................................................................... 45428.7 Concluding Remarks...................................................................................................... 455Symbols......................................................................................................................................... 456References ..................................................................................................................................... 456PART VI Piping and Pressure VesselsChapter 29 Vessels with Internal Pressure .............................................................................. 45929.1 Introduction.................................................................................................................... 45929.2 Thin Cylinders ............................................................................................................... 45929.3 Radial Growth (Dilation) ............................................................................................... 46129.4 Ellipsoidal Shells............................................................................................................ 46229.5 Toroidal Vessels............................................................................................................. 46229.6 Thick Cylinder Theory................................................................................................... 46429.7 Thick-Walled Sphere ..................................................................................................... 46829.8 Design Charts for Thick Cylinders................................................................................ 47029.9 Ultimate Strength Criteria.............................................................................................. 47129.10 Burst Pressure of Cylinders and Spheres....................................................................... 47229.11 Shrink-Fit Design........................................................................................................... 473Symbols......................................................................................................................................... 475References ..................................................................................................................................... 476Chapter 30 Externally Pressured Cylindrical Vessels and Structures ..................................... 47730.1 Introduction.................................................................................................................... 47730.2 Thinness Factor .............................................................................................................. 47730.3 Stress Response.............................................................................................................. 47830.4 Stability Response.......................................................................................................... 47830.5 Illustrative Design Problem ........................................................................................... 47930.6 Mixed Mode Response .................................................................................................. 48030.7 Classical Formula for Short Cylinders .......................................................................... 48030.8 Modied Formula for Short Cylinders .......................................................................... 48130.9 Simplied Criterion for Out-of-Roundness ................................................................... 48230.10 Long Cylinder with Out-of-Roundness ......................................................................... 48230.11 Effective Out-of-Roundness........................................................................................... 48330.12 Illustrative Design Example........................................................................................... 48430.13 Empirical Developments................................................................................................ 48630.14 Effect of Axial Stresses on Collapse ............................................................................. 48930.15 Strength of Thick Cylinders........................................................................................... 49230.16 Illustrative Design Problem ........................................................................................... 49430.17 Out-of-Roundness Correction for Stress........................................................................ 495Huston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page xx 8.11.2008 3:29pm Compositor Name: BManixx Contents30.18 Design Criterion for Thick Cylinders ............................................................................ 496Symbols......................................................................................................................................... 497References ..................................................................................................................................... 498Chapter 31 Buckling of Spherical Shells................................................................................. 49931.1 Introduction.................................................................................................................... 49931.2 ZoellyVan der Neut Formula....................................................................................... 49931.3 Corrected Formula for Spherical Shells......................................................................... 49931.4 Plastic Strength of Spherical Shells............................................................................... 50031.5 Effect of Initial Imperfections........................................................................................ 50131.6 Experiments with Hemispherical Vessels...................................................................... 50231.7 Response of Shallow Spherical Caps ............................................................................ 50331.8 Strength of Thick Spheres ............................................................................................. 505Symbols......................................................................................................................................... 506References ..................................................................................................................................... 506Chapter 32 Axial and Bending Response................................................................................ 50932.1 Introduction.................................................................................................................... 50932.2 Approximation of Cross-Section Properties .................................................................. 50932.3 Column Behavior of Pipe .............................................................................................. 51032.4 Pipe on an Elastic Foundation ....................................................................................... 51232.5 One-Way Buckling ........................................................................................................ 51332.6 Axial Response of Cylinders ......................................................................................... 51632.7 Plastic Buckling in an Axial Mode................................................................................ 51732.8 Analysis of Bellows-Type Buckle ................................................................................. 51832.9 Example of Load Eccentricity ....................................................................................... 51932.10 Theory of a Rolling Diaphragm .................................................................................... 520Symbols......................................................................................................................................... 525References ..................................................................................................................................... 526PART VII Advanced and Specialized ProblemsChapter 33 Special Cylinder Problems .................................................................................... 52933.1 Introduction.................................................................................................................... 52933.2 Dilation of Closed Cylinders ......................................................................................... 52933.3 Nested Cylinders............................................................................................................ 52933.4 Design of Ring Stiffeners .............................................................................................. 532Symbols......................................................................................................................................... 534References ..................................................................................................................................... 534Chapter 34 Stress Concentration.............................................................................................. 53534.1 Introduction.................................................................................................................... 53534.2 Elastic Stress Factors ..................................................................................................... 53534.3 Common Types of Stress Raisers.................................................................................. 53534.4 Stress Distribution.......................................................................................................... 538Huston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page xxi 8.11.2008 3:29pm Compositor Name: BManiContents xxi34.5 Plastic Reduction of Stress Factors................................................................................ 539Symbols......................................................................................................................................... 540References ..................................................................................................................................... 541Chapter 35 Thermal Considerations ........................................................................................ 54335.1 Introduction.................................................................................................................... 54335.2 Basic Stress Formula ..................................................................................................... 54335.3 Thermal Effect on Strength............................................................................................ 54435.4 Materials for Special Applications................................................................................. 54535.5 Thermal Stress Index ..................................................................................................... 54635.6 Thermal Shock............................................................................................................... 54735.7 Thermal Conditions in Piping........................................................................................ 54735.8 Thermal Stress Fatigue .................................................................................................. 54835.9 Preliminary Thermal Design.......................................................................................... 548Symbols......................................................................................................................................... 549References ..................................................................................................................................... 550Chapter 36 Axial Response of Straight and Tapered Bars...................................................... 55136.1 Introduction.................................................................................................................... 55136.2 Tapered and Stepped Bars ............................................................................................. 55136.3 Example Problem for a Stepped Bar ............................................................................. 55336.4 Tapered Bar under Its Own Weight .............................................................................. 55436.5 Discussion about the Tapered Bar Formula .................................................................. 55536.6 Example Problem for a Long Hanging Cable ............................................................... 55536.7 Heavy Hanging Cable with Uniform Stress along the Length...................................... 55736.8 Example Problem of an Axially Compressed Tube ...................................................... 55936.9 Kern Limit...................................................................................................................... 559Symbols......................................................................................................................................... 562References ..................................................................................................................................... 563Chapter 37 Thin Rings and Arches ......................................................................................... 56537.1 Introduction.................................................................................................................... 56537.2 Review of Strain Energy and Castiglianos Theorem ................................................... 56537.3 Diametrically Loaded Elastic Ring................................................................................ 56837.4 More Exact Results for the Diametrically Loaded Elastic Ring ................................... 57137.5 Design Charts for Circular Rings .................................................................................. 57137.6 Estimates via Superposition........................................................................................... 57237.7 Ring with Constraint ...................................................................................................... 57437.8 A Rotating Ring............................................................................................................. 57637.9 Simply Supported Arch ................................................................................................. 57837.10 Pin-Supported Arch ....................................................................................................... 58037.11 Built-In Arch.................................................................................................................. 58237.12 Pinned Arch under a Uniform Load.............................................................................. 584Symbols......................................................................................................................................... 585References ..................................................................................................................................... 586Huston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page xxii 8.11.2008 3:29pm Compositor Name: BManixxii ContentsChapter 38 Links and Eyebars................................................................................................. 58738.1 Introduction.................................................................................................................... 58738.2 Thick-Ring Theory......................................................................................................... 58738.3 Theory of Chain Links................................................................................................... 58838.4 Link Reinforcement ....................................................................................................... 59038.5 Proof Ring Formulas...................................................................................................... 59138.6 Knuckle Joint ................................................................................................................. 59138.7 Eyebar with Zero Clearance .......................................................................................... 59338.8 Thick-Ring Method of Eyebar Design ..........................................................................