Peterson's Stress Concentration Factors

by Pilkey, Walter D.; Peterson, Rudolph Earl

• ISBN13: 9780471538493
• ISBN10: 0471538493
• Edition: 2nd
• Format: Hardcover
• Copyright: 1997-01-01
• Publisher: Wiley-Interscience

Summary

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.

Author Biography

WALTER D. PILKEY is the Frederick Morse Professor in the Department of Mechanical, Aerospace, and Nuclear Engineering at the University of Virginia and a leading authority in the areas of stress and strain in mechanical and civil engineering. He is the author of Formulas for Stress, Strain, and Structural Matrices, also available from Wiley.

Table of Contents

INDEX TO THE STRESS CONCENTRATION FACTORS	xv	(16)
PREFACE	xxxi
1 DEFINITIONS AND DESIGN RELATIONS	1	(58)
1.1 Notation	1	(2)
1.2 Stress Concentration	3	(7)
1.2.1 Selection of Nominal Stresses	6	(3)
1.2.2 Accuracy of Stress Concentration Factors	9	(1)
1.3 Stress Concentration as a Two-Dimensional Problem	10	(1)
1.4 Stress Concentration as a Three-Dimensional Problem	11	(2)
1.5 Plane and Axisymmetric Problems	13	(2)
1.6 Local and Nonlocal Stress Concentration	15	(6)
1.6.1 Examples of "Reasonable" Approximations	19	(2)
1.7 Multiple Stress Concentration	21	(3)
1.8 Theories of Strength and Failure	24	(12)
1.8.1 Maximum Stress Criterion	25	(1)
1.8.2 Mohr's Theory	26	(2)
1.8.3 Maximum Shear Theory	28	(1)
1.8.4 von Mises Criterion	28	(2)
1.8.5 Observations on the Use of the Theories of Failure	30	(2)
1.8.6 Stress Concentration Factors under Combined Loads, Principle of Superposition	32	(4)
1.9 Notch Sensitivity	36	(5)
1.10 Design Relations For Static Stress	41	(3)
1.10.1 Ductile Materials	41	(2)
1.10.2 Brittle Materials	43	(1)
1.11 Design Relations for Alternating Stress	44	(1)
1.11.1 Ductile Materials	44	(1)
1.11.2 Brittle Materials	45	(1)
1.12 Design Relations for Combined Alternating and Static Stresses	45	(4)
1.12.1 Ductile Materials	46	(3)
1.12.2 Brittle Materials	49	(1)
1.13 Limited Number of Cycles of Alternating Stress	49	(1)
1.14 Stress Concentration Factors and Stress Intensity Factors	50	(5)
References	55	(4)
2 NOTCHES AND GROOVES	59	(76)
2.1 Notation	59	(1)
2.2 Stress Concentration Factors	60	(2)
2.3 Notches in Tension	62	(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	62	(1)
2.3.2 Opposite Single Semicircular Notches in a Finite-Width Thin Element	63	(1)
2.3.3 Opposite Single U-Shaped Notches in a Finite-Width Thin Element	63	(1)
2.3.4 "Finite-Width Correction Factors" for Opposite Narrow Single Elliptical Notches in a Finite-Width Thin Element	64	(1)
2.3.5 Opposite Single V-Shaped Notches in a Finite-Width Thin Element	65	(1)
2.3.6 Single Notch on One Side of a Thin Element	65	(1)
2.3.7 Notches with Flat Bottoms	65	(1)
2.3.8 Multiple Notches in a Thin Element	66	(1)
2.4 Depressions in Tension	67	(2)
2.4.1 Hemispherical Depression (Pit) in the Surface of a Semi-infinite Body	67	(1)
2.4.2 Hyperboloid Depression (Pit) in the Surface of a Finite-Thickness Element	67	(2)
2.4.3 Opposite Shallow Spherical Depressions (Dimples) in a Thin Element	69	(1)
2.5 Grooves in Tension	69	(1)
2.5.1 Deep Hyperbolic Groove in an Infinite Member (Circular Net Section)	69	(1)
2.5.2 U-Shaped Circumferential Grooves in a Bar of Circular Cross Section	69	(1)
2.5.3 Flat-Bottom Grooves	70	(1)
2.6 Bending of Thin Beams with Notches	70	(2)
2.6.1 Opposite Deep Hyperbolic Notches in an Infinite Thin Element	70	(1)
2.6.2 Opposite Semicircular Notches in a Flat Beam	70	(1)
2.6.3 Opposite U-Shaped Notches in a Flat Beam	70	(1)
2.6.4 V-Shaped Notches in a Flat Beam Element	70	(1)
2.6.5 Notch on One Side of a Thin Beam	70	(1)
2.6.6 Single or Multiple Notches with Semicircular or Semielliptical Notch Bottoms	71	(1)
2.6.7 Notches with Flat Bottoms	71	(1)
2.7 Bending of Plates with Notches	72	(1)
2.7.1 Various Edge Notches in an Infinite Plate in Transverse Bending	72	(1)
2.7.2 Notches in Finite-Width Plate in Transverse Bending	72	(1)
2.8 Bending of Solids with Grooves	72	(2)
2.8.1 Deep Hyperbolic Groove in an Infinite Member	72	(1)
2.8.2 U-Shaped Circumferential Groove in a Bar of Circular Cross Section	72	(1)
2.8.3 Flat-Bottom Grooves in Bars of Circular Cross Section	73	(1)
2.9 Direct Shear and Torsion	74	(2)
2.9.1 Deep Hyperbolic Notches in an Infinite Thin Element in Direct Shear	74	(1)
2.9.2 Deep Hyperbolic Groove in an Infinite Member	74	(1)
2.9.3 U-Shaped Circumferential Groove in a Bar of Circular Cross Section	74	(2)
2.9.4 V-Shaped Circumferential Groove in a Bar of Circular Cross Section	76	(1)
2.9.5 Shaft in Torsion with Grooves with Flat Bottoms	76	(1)
2.10 Test Specimen Design for Maximum K(t) for a Given r/D or r/H	76	(2)
References	78	(2)
Charts	81	(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