Peterson's Stress Concentration Factors

, by Pilkey, Walter D.; Peterson, Rudolph Earl

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ISBN: 9780471538493 | 0471538493
Cover: Hardcover
Copyright: 1/1/1997

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A complete revision of the definitive work on the subject of stress concentration. This new edition updates all of the graphics with computer-generated art which incorporates both a visual representation of the product/structure under consideration along with the graph of the stress concentration factors. Contains extensive material on how to perform computer analyses for stress concentrations and how to design to reduce them. A "quick-finder" feature has been provided for locating frequently used charts.

INDEX TO THE STRESS CONCENTRATION FACTORS

(16)

PREFACE

xxxi

1 DEFINITIONS AND DESIGN RELATIONS

(58)

1.1 Notation

(2)

1.2 Stress Concentration

(7)

1.2.1 Selection of Nominal Stresses

(3)

1.2.2 Accuracy of Stress Concentration Factors

(1)

1.3 Stress Concentration as a Two-Dimensional Problem

(1)

1.4 Stress Concentration as a Three-Dimensional Problem

(2)

1.5 Plane and Axisymmetric Problems

(2)

1.6 Local and Nonlocal Stress Concentration

(6)

1.6.1 Examples of "Reasonable" Approximations

(2)

1.7 Multiple Stress Concentration

(3)

1.8 Theories of Strength and Failure

(12)

1.8.1 Maximum Stress Criterion

(1)

1.8.2 Mohr's Theory

(2)

1.8.3 Maximum Shear Theory

(1)

1.8.4 von Mises Criterion

(2)

1.8.5 Observations on the Use of the Theories of Failure

(2)

1.8.6 Stress Concentration Factors under Combined Loads, Principle of Superposition

(4)

1.9 Notch Sensitivity

(5)

1.10 Design Relations For Static Stress

(3)

1.10.1 Ductile Materials

(2)

1.10.2 Brittle Materials

(1)

1.11 Design Relations for Alternating Stress

(1)

1.11.1 Ductile Materials

(1)

1.11.2 Brittle Materials

(1)

1.12 Design Relations for Combined Alternating and Static Stresses

(4)

1.12.1 Ductile Materials

(3)

1.12.2 Brittle Materials

(1)

1.13 Limited Number of Cycles of Alternating Stress

(1)

1.14 Stress Concentration Factors and Stress Intensity Factors

(5)

References

(4)

2 NOTCHES AND GROOVES

(76)

2.1 Notation

(1)

2.2 Stress Concentration Factors

(2)

2.3 Notches in Tension

(5)

2.3.1 Opposite Deep Hyperbolic Notches in an Infinite Thin Element; Shallow Elliptical, Semicircular, U-Shaped or Keyhole-Shaped Notches in Semi-Infinite Thin Elements; Equivalent Elliptical Notch

(1)

2.3.2 Opposite Single Semicircular Notches in a Finite-Width Thin Element

(1)

2.3.3 Opposite Single U-Shaped Notches in a Finite-Width Thin Element

(1)

2.3.4 "Finite-Width Correction Factors" for Opposite Narrow Single Elliptical Notches in a Finite-Width Thin Element

(1)

2.3.5 Opposite Single V-Shaped Notches in a Finite-Width Thin Element

(1)

2.3.6 Single Notch on One Side of a Thin Element

(1)

2.3.7 Notches with Flat Bottoms

(1)

2.3.8 Multiple Notches in a Thin Element

(1)

2.4 Depressions in Tension

(2)

2.4.1 Hemispherical Depression (Pit) in the Surface of a Semi-infinite Body

(1)

2.4.2 Hyperboloid Depression (Pit) in the Surface of a Finite-Thickness Element

(2)

2.4.3 Opposite Shallow Spherical Depressions (Dimples) in a Thin Element

(1)

2.5 Grooves in Tension

(1)

2.5.1 Deep Hyperbolic Groove in an Infinite Member (Circular Net Section)

(1)

2.5.2 U-Shaped Circumferential Grooves in a Bar of Circular Cross Section

(1)

2.5.3 Flat-Bottom Grooves

(1)

2.6 Bending of Thin Beams with Notches

(2)

2.6.1 Opposite Deep Hyperbolic Notches in an Infinite Thin Element

(1)

2.6.2 Opposite Semicircular Notches in a Flat Beam

(1)

2.6.3 Opposite U-Shaped Notches in a Flat Beam

(1)

2.6.4 V-Shaped Notches in a Flat Beam Element

(1)

2.6.5 Notch on One Side of a Thin Beam

(1)

2.6.6 Single or Multiple Notches with Semicircular or Semielliptical Notch Bottoms

(1)

2.6.7 Notches with Flat Bottoms

(1)

2.7 Bending of Plates with Notches

(1)

2.7.1 Various Edge Notches in an Infinite Plate in Transverse Bending

(1)

2.7.2 Notches in Finite-Width Plate in Transverse Bending

(1)

2.8 Bending of Solids with Grooves

(2)

2.8.1 Deep Hyperbolic Groove in an Infinite Member

(1)

2.8.2 U-Shaped Circumferential Groove in a Bar of Circular Cross Section

(1)

2.8.3 Flat-Bottom Grooves in Bars of Circular Cross Section

(1)

2.9 Direct Shear and Torsion

(2)

2.9.1 Deep Hyperbolic Notches in an Infinite Thin Element in Direct Shear

(1)

2.9.2 Deep Hyperbolic Groove in an Infinite Member

(1)

2.9.3 U-Shaped Circumferential Groove in a Bar of Circular Cross Section

(2)

2.9.4 V-Shaped Circumferential Groove in a Bar of Circular Cross Section

(1)

2.9.5 Shaft in Torsion with Grooves with Flat Bottoms

(1)

2.10 Test Specimen Design for Maximum K(t) for a Given r/D or r/H

(2)

References

(2)

Charts

(54)

3 SHOULDER FILLETS

135

(40)

3.1 Notation

135

(2)

3.2 Stress Concentration Factors

137

(1)

3.3 Tension (Axial Loading)

137

(6)

3.3.1 Opposite Shoulder Fillets in a Flat Bar

137

(1)

3.3.2 Effect of Shoulder Geometry in a Flat Member

138

(1)

3.3.3 Effect of a Trapezoidal Protuberance on the Edge of a Flat Bar

139

(1)

3.3.4 Fillet of Noncircular Contour in a Flat Stepped Bar

139

(3)

3.3.5 Stepped Bar of Circular Cross Section with a Circumferential Shoulder Fillet

142

(1)

3.3.6 Tubes

142

(1)

3.3.7 Stepped Pressure Vessel Wall with Shoulder Fillets

143

(1)

3.4 Bending

143

(1)

3.4.1 Opposite Shoulder Fillets in a Flat Bar

143

(1)

3.4.2 Effect of Shoulder Geometry in a Flat Thin Member

143

(1)

3.4.3 Elliptical Shoulder Fillet in a Flat Member

143

(1)

3.4.4 Stepped Bar of Circular Cross Section with a Circumferential Shoulder Fillet

143

(1)

3.5 Torsion

144

(3)

3.5.1 Stepped Bar of Circular Cross Section with a Circumferential Shoulder Fillet

144

(1)

3.5.2 Stepped Bar of Circular Cross Section with a Circumferential Shoulder Fillet and a Central Axial Hole

144

(1)

3.5.3 Compound Fillet

145

(2)

3.6 Methods of Reducing Stress Concentration at a Shoulder

147

(1)

References

148

(2)

Charts

150

(25)

4 HOLES

175

(202)

4.1 Notation

175

(2)

4.2 Stress Concentration Factors

177

(3)

4.3 Circular Holes with In-Plane Stresses

180

(31)

4.3.1 Single Circular Hole in an Infinite Thin Element in Uniaxial Tension

180

(4)

4.3.2 Single Circular Hole in an Infinite Thin Element under Biaxial In-plane Stresses

184

(2)

4.3.3 Single Circular Hole in a Cylindrical Shell with Tension or Internal Pressure

186

(2)

4.3.4 Circular or Elliptical Hole in a Spherical Shell with Internal Pressure

188

(1)

4.3.5 Reinforced Hole Near the Edge of a Semi-infinite Element in Uniaxial Tension

188

(2)

4.3.6 Symmetrically Reinforced Hole in Finite-Width Element in Uniaxial Tension

190

(1)

4.3.7 Nonsymmetrically Reinforced Hole in Finite-Width Element in Uniaxial Tension

191

(1)

4.3.8 Symmetrically Reinforced Circular Hole in a Biaxially Stressed Wide, Thin Element

192

(7)

4.3.9 Circular Hole with Internal Pressure

199

(1)

4.3.10 Two Circular Holes of Equal Diameter in a Thin Element in Uniaxial Tension or Biaxial In-plane Stresses

200

(5)

4.3.11 Two Circular Holes of Unequal Diameter in a Thin Element in Uniaxial Tension or Biaxial In-plane Stresses

205

(2)

4.3.12 Single Row of Equally Distributed Circular Holes in an Element in Tension

207

(1)

4.3.13 Double Row of Circular Holes in a Thin Element in Uniaxial Tension

208

(1)

4.3.14 Symmetrical Pattern of Circular Holes in a Thin Element in Uniaxial Tension or Biaxial In-plane Stresses

208

(1)

4.3.15 Radially Stressed Circular Element with a Ring of Circular Holes, with or without a Central Circular Hole

209

(1)

4.3.16 Thin Element with Circular Holes with Internal Pressure

210

(1)

4.4 Elliptical Holes in Tension

211

(14)

4.4.1 Single Elliptical Hole in Infinite-and Finite-Width Thin Elements in Uniaxial Tension

213

(2)

4.4.2 Width Correction Factor for a Cracklike Central Slit in a Tension Panel

215

(1)

4.4.3 Single Elliptical Hole in an Infinite, Thin Element Biaxially Stressed

215

(9)

4.4.4 Infinite Row of Elliptical Holes in Infinite-and Finite-Width Thin Elements in Uniaxial Tension

224

(1)

4.4.5 Elliptical Hole with Internal Pressure

224

(1)

4.4.6 Elliptical Holes with Bead Reinforcement in an Infinite Thin Element under Uniaxial and Biaxial Stresses

225

(1)

4.5 Various Configurations with In-Plane Stresses

225

(13)

4.5.1 Thin Element with an Ovaloid; Two Holes Connected by a Slit under Tension; Equivalent Ellipse

225

(1)

4.5.2 Circular Hole with Opposite Semicircular Lobes in a Thin Element in Tension

226

(1)

4.5.3 Infinite Thin Element with a Rectangular Hole with Rounded Corners Subject to Uniaxial or Biaxial Stress

227

(1)

4.5.4 Finite-Width Tension Thin Element with Round-Cornered Square Hole

228

(1)

4.5.5 Square Holes with Rounded Corners and Bead Reinforcement in an Infinite Panel under Uniaxial and Biaxial Stresses

228

(1)

4.5.6 Round-Cornered Equilateral Triangular Hole in an Infinite Thin Element under Various States of Tension

228

(1)

4.5.7 Uniaxially Stressed Tube or Bar of Circular Cross Section with a Transverse Circular Hole

229

(1)

4.5.8 Round Pin Joint in Tension

229

(2)

4.5.9 Inclined Round Hole in an Infinite Panel Subjected to Various States of Tension

231

(1)

4.5.10 Pressure Vessel Nozzle (Reinforced Cylindrical Opening)

232

(1)

4.5.11 Spherical or Ellipsoidal Cavities

232

(2)

4.5.12 Spherical or Ellipsoidal Inclusions

234

(2)

4.5.13 Cylindrical Tunnel

236

(1)

4.5.14 Intersecting Cylindrical Holes

236

(2)

4.5.15 Other Configurations

238

(1)

4.6 Bending

238

(5)

4.6.1 Bending of a Beam with a Central Hole

239

(1)

4.6.2 Bending of a Beam with a Circular Hole Displaced from the Center Line

240

(1)

4.6.3 Bending of a Beam with an Elliptical Hole; Slot with Semicircular Ends (Ovaloid); or Round-Cornered Square Hole

240

(1)

4.6.4 Bending of an Infinite- and of a Finite-Width Plate with a Single Circular Hole

240

(1)

4.6.5 Bending of an Infinite Plate with a Row of Circular Holes

241

(1)

4.6.6 Bending of an Infinite Plate with a Single Elliptical Hole

241

(1)

4.6.7 Bending of an Infinite Plate with a Row of Elliptical Holes

242

(1)

4.6.8 Tube or Bar of Circular Cross Section with a Transverse Hole

242

(1)

4.7 Shear, Torsion

243

(4)

4.7.1 Shear Stressing of Infinite Thin Element with Circular or Elliptical Hole, Unreinforced and Reinforced

243

(1)

4.7.2 Shear Stressing of an Infinite Thin Element with a Round-Cornered Rectangular Hole, Unreinforced and Reinforced

244

(1)

4.7.3 Two Circular Holes of Unequal Diameter in a Thin Element in Pure Shear

244

(1)

4.7.4 Shear Stressing of an Infinite Thin Element with Two Circular Holes or a Row of Circular Holes

244

(1)

4.7.5 Shear Stressing of an Infinite Thin Element with an Infinite Pattern of Circular Holes

244

(1)

4.7.6 Twisted Infinite Plate with a Circular Hole

244

(1)

4.7.7 Torsion of a Cylindrical Shell with a Circular Hole

245

(1)

4.7.8 Torsion of a Tube or Bar of Circular Cross Section with a Transverse Circular Hole

245

(2)

References

247

(9)

Charts

256

(121)

5 MISCELLANEOUS DESIGN ELEMENTS

377

(64)

5.1 Notation

377

(1)

5.2 Shaft with Keyseat

378

(5)

5.2.1 Bending

379

(1)

5.2.2 Torsion

380

(1)

5.2.3 Torque Transmitted through a Key

380

(1)

5.2.4 Combined Bending and Torsion

381

(1)

5.2.5 Effect of Proximitiy of Keyseat to Shaft Shoulder Fillet

381

(1)

5.2.6 Fatigue Failures

381

(2)

5.3 Splined Shaft in Torsion

383

(1)

5.4 Gear Teeth

383

(2)

5.5 Press-Fitted or Shrink-Fitted Members

385

(2)

5.6 Bolt and Nut

387

(2)

5.7 Bolt Head, Turbine-Blade, or Compressor-Blade Fastening (T-Head)

389

(2)

5.8 Lug Joint

391

(3)

5.8.1 Lugs with h/d 0.5

392

(1)

5.8.2 Lugs with h/d > 0.5

393

(1)

5.9 Curved Bar

394

(1)

5.10 Helical Spring

395

(3)

5.10.1 Round or Square Wire Compression or Tension Spring

395

(2)

5.10.2 Rectangular Wire Compression or Tension Spring

397

(1)

5.10.3 Helical Torsion Spring

398

(1)

5.11 Crankshaft

398

(1)

5.12 Crane Hook

399

(1)

5.13 U-Shaped Member

399

(1)

5.14 Angle and Box Sections

400

(1)

5.15 Rotating Disk with Hole

400

(2)

5.16 Ring or Hollow Roller

402

(1)

5.17 Pressurized Cylinder

402

(1)

5.18 Cylindrical Pressure Vessel with Torispherical Ends

403

(1)

5.19 Pressurized Thick Cylinder with a Circular Hole in the Cylinder Wall

403

(1)

References

404

(4)

Charts

408

(33)

6 STRESS CONCENTRATION ANALYSIS AND DESIGN

441

(60)

6.1 Computational Methods

441

(4)

6.2 Finite Element Analysis

445

(22)

6.2.1 Principle of Virtual Work

445

(3)

6.2.2 Element Equations

448

(2)

6.2.3 Shape Functions

450

(4)

6.2.4 Mapping Functions

454

(2)

6.2.5 Numerical Integration

455

(2)

6.2.6 System Equations

457

(3)

6.2.7 Stress Computation

460

(7)

6.3 Design Sensitivity Analysis

467

(17)

6.3.1 Finite Differences

468

(1)

6.3.2 Discrete Systems

468

(3)

6.3.3 Continuum Systems

471

(3)

6.3.4 Stresses

474

(1)

6.3.5 Structural Volume

474

(1)

6.3.6 Design Velocity Field

475

(9)

6.4 Design Modification

484

(13)

6.4.1 Sequential Linear Programming

487

(1)

6.4.2 Sequential Quadratic Programming

488

(1)

6.4.3 Conservative Approximation

489

(1)

6.4.4 Equality Constraints

490

(1)

6.4.5 Minimum Weight Design

491

(1)

6.4.6 Minimum Stress Design

492

(5)

References

497

(4)

INDEX

501

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Peterson's Stress Concentration Factors

Summary

Author Biography

Table of Contents

Supplemental Materials