664
Practical Stress Analysisin Engineering Design
Third Edition
Huston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page i 8.11.2008 3:29pm Compositor Name: BMani
MECHANICAL ENGINEERINGA Series of Textbooks and Reference Books
Founding EditorL. L. Faulkner
Columbus Division, Battelle Memorial Instituteand Department of Mechanical Engineering
The Ohio State UniversityColumbus, Ohio
1. 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:
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33. CAD/CAM Systems: Justification, Implementation, Productivity Measurement, Edward J. Preston, George W. Crawford, and Mark E. Coticchia
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Lawrence E. Murr, Karl P. Staudhammer, and Marc A. Meyers53. Magnesium Products Design, Robert S. Busk54. How to Integrate CAD/CAM Systems: Management and Technology,
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113. Handbook of Materials Selection for Engineering Applications, edited by G. T. Murray114. Handbook of Thermoplastic Piping System Design, Thomas Sixsmith
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Andrei Makartchouk144. Handbook of Machine Tool Analysis, Ioan D. Marinescu, Constantin Ispas,
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Vijay Srinivasan164. Handbook of Mechanical Alloy Design, edited by George E. Totten, Lin Xie,
and Kiyoshi Funatani165. Structural Analysis of Polymeric Composite Materials, Mark E. Tuttle166. Modeling and Simulation for Material Selection and Mechanical Design, edited by
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Arun Shukla184. Practical Guide to Designed Experiments, Paul D. Funkenbusch185. Gigacycle Fatigue in Mechanical Practive, Claude Bathias and Paul C. Paris186. Selection of Engineering Materials and Adhesives, Lawrence W. Fisher187. Boundary Methods: Elements, Contours, and Nodes, Subrata Mukherjee
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191. Industrial Heating: Principles, Techniques, Materials, Applications, and Design,Yeshvant V. Deshmukh
192. Micro Electro Mechanical System Design, James J. Allen193. Probability Models in Engineering and Science, Haym Benaroya and Seon Han194. Damage Mechanics, George Z. Voyiadjis and Peter I. Kattan195. Standard Handbook of Chains: Chains for Power Transmission and Material Handling,
Second Edition, American Chain Association and John L. Wright, Technical Consultant196. Standards for Engineering Design and Manufacturing, Wasim Ahmed Khan
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Michael R. Gosz199. Microengineering, MEMS, and Interfacing: A Practical Guide, Danny Banks200. Fundamentals of Natural Gas Processing, Arthur J. Kidnay and William Parrish201. Optimal Control of Induction Heating Processes, Edgar Rapoport
and Yulia Pleshivtseva202. Practical Plant Failure Analysis: A Guide to Understanding Machinery Deterioration
and Improving Equipment Reliability, Neville W. Sachs, P.E.203. Shaft Alignment Handbook, Third Edition, John Piotrowski204. Advanced Vibration Analysis , S. Graham Kelly205. Principles of Composite Materials Mechanics, Second Edition, Ronald F. Gibson206. Applied Combustion, Second Edition, Eugene L. Keating207. Introduction to the Design and Behavior of Bolted Joints, Fourth Edition:
Non-Gasketed Joints, John H. Bickford208. Analytical and Approximate Methods in Transport Phenomena,
Marcio L. de Souza-Santos209. Design and Optimization of Thermal Systems, Second Edition, Yogesh Jaluria210. Friction Science and Technology: From Concepts to Applications, Second Edition,
Peter J. Blau211. Practical Guide to the Packaging of Electronics, Second Edition: Thermal
and Mechanical Design and Analysis, Ali Jamnia212. Practical Stress Analysis in Engineering Design, Third Edition, Ronald Huston
and Harold Josephs
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Practical Stress Analysisin Engineering Design
Third Edition
Ronald HustonHarold Josephs
CRC Press is an imprint of theTaylor & Francis Group, an informa business
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Huston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page ix 8.11.2008 3:29pm Compositor Name: BMani
CRC PressTaylor & Francis Group6000 Broken Sound Parkway NW, Suite 300Boca Raton, FL 33487-2742
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Library of Congress Cataloging-in-Publication Data
Huston, 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 2008029335
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Huston/Practical Stress Analysis in Engineering Design DK4291_C000 Final Proof page x 8.11.2008 3:29pm Compositor Name: BMani
ContentsPreface........................................................................................................................................... xxvAuthors........................................................................................................................................ xxvii
PART I Fundamental Relations and Concepts
Chapter 1 Forces and Force Systems........................................................................................... 3
1.1 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 ........................................................................................................... 7
1.5.1 Zero Force Systems .................................................................................................... 71.5.2 Couples ....................................................................................................................... 71.5.3 Equivalent Force Systems........................................................................................... 71.5.4 Equivalent Replacement by a Force and a Couple .................................................... 9
Symbols........................................................................................................................................... 10References ....................................................................................................................................... 10
Chapter 2 Simple Stress and Strain: Simple Shear Stress and Strain........................................ 11
2.1 Concept of Stress ................................................................................................................. 112.2 Concept of Strain ................................................................................................................. 132.3 Shear Stress .......................................................................................................................... 132.4 Shear Strain .......................................................................................................................... 14Symbols........................................................................................................................................... 16
Chapter 3 Hookes Law and Material Strength ......................................................................... 17
3.1 Hookes Law in One Dimension ......................................................................................... 173.2 Limitations of Proportionality.............................................................................................. 183.3 Material Strength.................................................................................................................. 183.4 Hookes Law in Shear.......................................................................................................... 19Symbols........................................................................................................................................... 21References ....................................................................................................................................... 22
Chapter 4 Stress in Two and Three Dimensions ....................................................................... 23
4.1 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..................................................................................... 34
4.5.1 Illustrative Computation ........................................................................................... 364.5.2 Discussion ................................................................................................................. 38
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xi
4.6 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 ................................ 42
4.7 Stress Ellipsoid..................................................................................................................... 444.8 Maximum Shear Stress ........................................................................................................ 464.9 Two-Dimensional AnalysisMohrs Circle ....................................................................... 47Symbols........................................................................................................................................... 53References ....................................................................................................................................... 54
Chapter 5 Strain in Two and Three Dimensions ....................................................................... 55
5.1 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 ....................................................................................................................................... 65
Chapter 6 Curvilinear Coordinates ............................................................................................ 67
6.1 Use of Curvilinear Coordinates ........................................................................................... 676.2 Curvilinear Coordinate Systems: Cylindrical and Spherical Coordinates........................... 67
6.2.1 Cylindrical Coordinates ............................................................................................ 676.2.2 Spherical Coordinates ............................................................................................... 70
6.3 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 ....................................................................................................................................... 86
Chapter 7 Hookes Law in Two and Three Dimensions ........................................................... 87
7.1 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......................................................................................................................................... 99
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xii Contents
PART II Straight and Long Structural Components:Beams, Rods, and Bars
Chapter 8 Beams: Bending Stresses (Flexure) ........................................................................ 103
8.1 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......................................................................................................................................... 110
Chapter 9 Beams: Displacement from Bending ...................................................................... 111
9.1 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...................................... 112
9.3.1 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 ...................................................................................................... 114
9.4 Summary of Governing Equations .................................................................................. 1149.5 Illustrations....................................................................................................................... 115
9.5.1 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.............................. 121
9.6 Comment.......................................................................................................................... 124Symbols......................................................................................................................................... 124Reference....................................................................................................................................... 125
Chapter 10 Beam Analysis Using Singularity Functions ........................................................ 127
10.1 Use of Singularity Functions ........................................................................................... 12710.1.1 Heavyside Unit Step Function............................................................................ 12710.1.2 Dirac Delta Function........................................................................................... 127
10.2 Singularity Function Denition ....................................................................................... 12810.3 Singularity Function Description and Additional Properties........................................... 12810.4 Illustration of Singularity Function Use .......................................................................... 130
10.4.1 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 ............................. 136
10.5 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 ..................................................................................................................................... 147
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Contents xiii
Chapter 11 Beam Bending Formulas for Common Congurations ........................................ 149
11.1 Prospectus ........................................................................................................................ 14911.2 Cantilever Beams ............................................................................................................. 149
11.2.1 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................................. 154
11.3 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...................................................... 158
11.4 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........................................ 163
11.5 Principle of Superposition................................................................................................ 16511.6 Summary and Formulas for Design................................................................................. 168Symbols......................................................................................................................................... 173References ..................................................................................................................................... 174
Chapter 12 Torsion and Twisting of Rods .............................................................................. 175
12.1 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 ..................................................................................................................................... 185
PART III Special Beam Geometries: Thick Beams,Curved Beams, Stability, and Shear Center
Chapter 13 Thick Beams: Shear Stress in Beams ................................................................... 189
13.1 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....................................................................................................................................... 198
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Chapter 14 Curved Beams ....................................................................................................... 199
14.1 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 ...................................................................... 211
14.6.1 Flexure of a Curved Machine Bracket ............................................................. 21114.6.2 Expansion of a Machine Clamp ....................................................................... 212
14.7 Further Comments on the Stresses in CurvedBeams and Hooks .......................................................................................................... 213
Symbols......................................................................................................................................... 214References ..................................................................................................................................... 214
Chapter 15 Stability: Buckling of Beams, Rods, Columns,and Panels.............................................................................................................. 217
15.1 Introduction .................................................................................................................... 21715.2 Long Bars Subjected to Compression Loading ............................................................. 21715.3 Buckling with Various End-Support Conditions........................................................... 218
15.3.1 Clamped (Nonrotating) Ends ............................................................................ 21815.3.2 A Clamped (Nonrotating) and a Free End ....................................................... 21915.3.3 A Clamped (Nonrotating) and a Pinned End ................................................... 219
15.4 Summary of Results for Long Bar Buckling with CommonlyOccurring End Conditions ............................................................................................. 222
15.5 Intermediate Length Bars and ColumnsJohnson Formula ........................................ 22315.6 Intermediate Length Bars and ColumnsEccentric Loading
and 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 ..................................................................................................................................... 234
Chapter 16 Shear Center .......................................................................................................... 237
16.1 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 ..................................................................................................................................... 253
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PART IV Plates, Panels, Flanges, and Brackets
Chapter 17 Plates: Bending Theory ......................................................................................... 257
17.1 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 ................................................................................ 266
17.6.1 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......................................................................................................... 268
17.7 StressStrainDisplacement Relations........................................................................... 26817.8 Integration of StressStrainDisplacement Equations through
the Thickness of the Plate.............................................................................................. 26917.9 Governing Differential Equations .................................................................................. 272
17.9.1 Equilibrium Equations .................................................................................... 27217.9.2 Displacement=Shear Assumptions .................................................................. 27317.9.3 MomentCurvature and In-Plane Force Relations ......................................... 27317.9.4 Governing Equation........................................................................................ 273
17.10 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....................................................................................... 276
17.11 Internal Stresses ............................................................................................................. 27717.12 Comments ...................................................................................................................... 277Symbols......................................................................................................................................... 278References ..................................................................................................................................... 278
Chapter 18 Plates: Fundamental Bending Congurations and Applications........................... 279
18.1 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 ............................................... 287
18.8.1 Simply Supported, Uniformly Loaded, Circular Plate ................................... 28818.8.2 Clamped Uniformly Loaded Circular Plate .................................................... 289
18.9 Circular Plate with Concentrated Center Load.............................................................. 290
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18.9.1 Simply Supported Circular Plate with a Concentrated Center Load................ 29018.9.2 Clamped Circular Plate with a Concentrated Center Load .............................. 290
18.10 Example Design Problem .............................................................................................. 29018.11 A Few Useful Results for Axisymmetrically Loaded Circular Plates........................... 29218.12 Comments ...................................................................................................................... 293Symbols......................................................................................................................................... 294References ..................................................................................................................................... 294
Chapter 19 Panels and Annular Plate Closures ....................................................................... 295
19.1 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......................................................................................................................................... 306
Chapter 20 Flanges .................................................................................................................. 309
20.1 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 ..................................................................................................................................... 334
Chapter 21 Brackets ................................................................................................................. 337
21.1 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 ..................................................................................................................................... 354
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Chapter 22 Special Plate Problems and Applications.............................................................. 355
22.1 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 ..................................................................................................................................... 369
PART V Dynamic Loadings, Fatigue, and Fracture
Chapter 23 Dynamic Behavior of Structures: A Conceptual Review ..................................... 373
23.1 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................................................................... 384
23.9.1 Cantilever Subjected to Free-End-Sudden Loading ......................................... 38423.9.2 VehicleBarrier Impact ..................................................................................... 385
23.10 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 ..................................................................................................................................... 401
Chapter 24 Elements of Seismic Design ................................................................................. 403
24.1 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 ..................................................................................................................................... 411
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Chapter 25 Impact Stress Propagation..................................................................................... 413
25.1 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............................................................................................. 420
25.9.1 Object Falling onto a Column .......................................................................... 42025.9.2 Object Impacting a Long Cylinder ................................................................... 420
25.10 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 ..................................................................................................................................... 425
Chapter 26 Fatigue ................................................................................................................... 427
26.1 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 ..................................................................................................................................... 434
Chapter 27 Fracture Mechanics: Design Considerations......................................................... 437
27.1 Introduction .................................................................................................................... 43727.2 Practical Aspects of Fracture Mechanics....................................................................... 43727.3 Design Implications of the Crack Size Parameters ....................................................... 43927.4 Illustrative Design Problems and Solutions................................................................... 440
27.4.1 Example Problem 1........................................................................................... 44027.4.2 Example Problem 2........................................................................................... 44127.4.3 Example Problem 3........................................................................................... 442
27.5 Comment........................................................................................................................ 44327.5.1 Example Problem.............................................................................................. 443
27.6 Implications of Fracture Toughness............................................................................... 44427.7 Plane Stress Parameter ................................................................................................... 44527.8 Plane Stress Criterion for Pressure Vessel Design ........................................................ 44627.9 Remarks ......................................................................................................................... 447Symbols......................................................................................................................................... 448References ..................................................................................................................................... 448
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Chapter 28 Fracture Control .................................................................................................... 449
28.1 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 ..................................................................................................................................... 456
PART VI Piping and Pressure Vessels
Chapter 29 Vessels with Internal Pressure .............................................................................. 459
29.1 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 ..................................................................................................................................... 476
Chapter 30 Externally Pressured Cylindrical Vessels and Structures ..................................... 477
30.1 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........................................................................ 495
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30.18 Design Criterion for Thick Cylinders ............................................................................ 496Symbols......................................................................................................................................... 497References ..................................................................................................................................... 498
Chapter 31 Buckling of Spherical Shells................................................................................. 499
31.1 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 ..................................................................................................................................... 506
Chapter 32 Axial and Bending Response ................................................................................ 509
32.1 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 ..................................................................................................................................... 526
PART VII Advanced and Specialized Problems
Chapter 33 Special Cylinder Problems .................................................................................... 529
33.1 Introduction .................................................................................................................... 52933.2 Dilation of Closed Cylinders ......................................................................................... 52933.3 Nested Cylinders ............................................................................................................ 52933.4 Design of Ring Stiffeners .............................................................................................. 532Symbols......................................................................................................................................... 534References ..................................................................................................................................... 534
Chapter 34 Stress Concentration.............................................................................................. 535
34.1 Introduction .................................................................................................................... 53534.2 Elastic Stress Factors ..................................................................................................... 53534.3 Common Types of Stress Raisers.................................................................................. 53534.4 Stress Distribution.......................................................................................................... 538
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34.5 Plastic Reduction of Stress Factors................................................................................ 539Symbols......................................................................................................................................... 540References ..................................................................................................................................... 541
Chapter 35 Thermal Considerations ........................................................................................ 543
35.1 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 ..................................................................................................................................... 550
Chapter 36 Axial Response of Straight and Tapered Bars...................................................... 551
36.1 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 ..................................................................................................................................... 563
Chapter 37 Thin Rings and Arches ......................................................................................... 565
37.1 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 ..................................................................................................................................... 586
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Chapter 38 Links and Eyebars ................................................................................................. 587
38.1 Introduction ..............................................................................................................
