Peterson's Stress Concentration Factors E-Book

Walter D. Pilkey

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 657

Veröffentlichungsjahr: 2020

Beschreibung

The bible of stress concentration factors--updated to reflect today's advances in stress analysis This book establishes and maintains a system of data classification for all the applications of stress and strain analysis, and expedites their synthesis into CAD applications. Filled with all of the latest developments in stress and strain analysis, this Fourth Edition presents stress concentration factors both graphically and with formulas, and the illustrated index allows readers to identify structures and shapes of interest based on the geometry and loading of the location of a stress concentration factor. Peterson's Stress Concentration Factors, Fourth Edition includes a thorough introduction of the theory and methods for static and fatigue design, quantification of stress and strain, research on stress concentration factors for weld joints and composite materials, and a new introduction to the systematic stress analysis approach using Finite Element Analysis (FEA). From notches and grooves to shoulder fillets and holes, readers will learn everything they need to know about stress concentration in one single volume. * Peterson's is the practitioner's go-to stress concentration factors reference * Includes completely revised introductory chapters on fundamentals of stress analysis; miscellaneous design elements; finite element analysis (FEA) for stress analysis * Features new research on stress concentration factors related to weld joints and composite materials * Takes a deep dive into the theory and methods for material characterization, quantification and analysis methods of stress and strain, and static and fatigue design Peterson's Stress Concentration Factors is an excellent book for all mechanical, civil, and structural engineers, and for all engineering students and researchers.

Leseprobe

Table of Contents

COVER

INDEX TO THE STRESS CONCENTRATION FACTORS

PREFACE FOR THE FOURTH EDITION

REFERENCES

PREFACE FOR THE THIRD EDITION

PREFACE FOR THE SECOND EDITION

NOTE

CHAPTER 1: FUNDAMENTALS OF STRESS ANALYSIS

1.1 STRESS ANALYSIS IN PRODUCT DESIGN

1.2 SOLID OBJECTS UNDER LOADS

1.3 TYPES OF MATERIALS

1.4 MATERIALS PROPERTIES AND TESTING

1.5 STATIC AND FATIGUE FAILURES

1.6 UNCERTAINTIES, SAFETY FACTORS, AND PROBABILITIES

1.7 STRESS ANALYSIS OF MECHANICAL STRUCTURES

1.8 FAILURE CRITERIA OF MATERIALS

1.9 STRESS CONCENTRATION

1.10 STRESS CONCENTRATION AS A TWO-DIMENSIONAL PROBLEM

1.11 STRESS CONCENTRATION AS A THREE-DIMENSIONAL PROBLEM

1.12 PLANE AND AXISYMMETRIC PROBLEMS

1.13 LOCAL AND NONLOCAL STRESS CONCENTRATION

1.14 MULTIPLE STRESS CONCENTRATION

1.15 PRINCIPLE OF SUPERPOSITION FOR COMBINED LOADS

1.16 NOTCH SENSITIVITY

1.17 DESIGN RELATIONS FOR STATIC STRESS

1.18 DESIGN RELATIONS FOR ALTERNATING STRESS

1.19 DESIGN RELATIONS FOR COMBINED ALTERNATING AND STATIC STRESSES

1.20 LIMITED NUMBER OF CYCLES OF ALTERNATING STRESS

1.21 STRESS CONCENTRATION FACTORS AND STRESS INTENSITY FACTORS

1.22 SELECTION OF SAFETY FACTORS

REFERENCES

NOTES

CHAPTER 2: NOTCHES AND GROOVES

2.1 NOTATION

2.2 STRESS CONCENTRATION FACTORS

2.3 NOTCHES IN TENSION

2.4 DEPRESSIONS IN TENSION

2.5 GROOVES IN TENSION

2.6 BENDING OF THIN BEAMS WITH NOTCHES

2.7 BENDING OF PLATES WITH NOTCHES

2.8 BENDING OF SOLIDS WITH GROOVES

2.9 DIRECT SHEAR AND TORSION

2.10 TEST SPECIMEN DESIGN FOR MAXIMUM KT FOR A GIVEN R/D OR R/H

REFERENCES

NOTES

CHAPTER 3: SHOULDER FILLETS

3.1 NOTATION

3.2 STRESS CONCENTRATION FACTORS

3.3 TENSION (AXIAL LOADING)

3.4 BENDING

3.5 TORSION

3.6 METHODS OF REDUCING STRESS CONCENTRATION AT A SHOULDER

REFERENCES

CHAPTER 4: HOLES

4.1 NOTATION

4.2 STRESS CONCENTRATION FACTORS

4.3 CIRCULAR HOLES WITH IN-PLANE STRESSES

4.4 ELLIPTICAL HOLES IN TENSION

4.5 VARIOUS CONFIGURATIONS WITH IN-PLANE STRESSES

4.6 HOLES IN THICK ELEMENTS

4.7 ORTHOTROPIC THIN MEMBERS

4.8 BENDING

4.9 SHEAR AND TORSION

REFERENCES

NOTE

CHAPTER 5: MISCELLANEOUS DESIGN ELEMENTS

5.1 NOTATION

5.2 SHAFT WITH KEYSEAT

5.3 SPLINED SHAFT IN TORSION

5.4 GEAR TEETH

5.5 PRESS- OR SHRINK-FITTED MEMBERS

5.6 BOLT AND NUT

5.7 BOLT HEAD, TURBINE-BLADE, OR COMPRESSOR-BLADE FASTENING (T-HEAD)

5.8 LUG JOINT

5.9 CURVED BAR

5.10 HELICAL SPRING

5.11 CRANKSHAFT

5.12 CRANE HOOK

5.13 U-SHAPED MEMBER

5.14 ANGLE AND BOX SECTIONS

5.15 CYLINDRICAL PRESSURE VESSEL WITH TORISPHERICAL ENDS

5.16 WELDS

5.17 PARTS WITH INHOMOGENEOUS MATERIALS OR COMPOSITES

5.18 PARTS WITH DEFECTS

5.19 PARTS WITH THREADS

5.20 FRAME STIFFENERS

5.21 DISCONTINUITIES WITH ADDITIONAL CONSIDERATIONS

5.22 PHARMACEUTICAL TABLETS WITH HOLES

5.23 PARTS WITH RESIDUAL STRESSES

5.24 SURFACE ROUGHNESS

5.25 NEW APPROACHES FOR PARAMETRIC STUDIES

REFERENCES

CHAPTER 6: FINITE ELEMENT ANALYSIS (FEA) FOR STRESS ANALYSIS

6.1 STRUCTURAL ANALYSIS PROBLEMS

6.2 TYPES OF ENGINEERING ANALYSIS METHODS

6.3 STRUCTURAL ANALYSIS THEORY

6.4 FINITE ELEMENT ANLAYSIS (FEA) FOR STRUCTURAL ANALYSIS

6.5 PLANNING V&V IN FEA MODELING

6.6 FINITE ELEMENT ANALYSIS FOR VERIFICATION OF STRUCTURAL ANALYSIS

6.7 FEA FOR STRESS ANALYSIS OF ASSEMBLY MODELS

6.8 PARAMETRIC STUDY FOR STRESS ANALYSIS

6.9 FEA ON STUDY OF STRESS CONCENTRATION FACTORS

REFERENCES

INDEX

END USER LICENSE AGREEMENT

List of Tables

Chapter 1

TABLE 1.1 Typical Material Properties and Standardized Testing Methods

TABLE 1.2 Common Failure Types, Mechanisms, and Characterization Methods of ...

TABLE 1.3 Some Fatigue Failures of Aircrafts (Wikipedia 2018)

TABLE 1.4 Stress Concentration Factor as a Function of Poisson's Ratio for a ...

TABLE 1.5 The Use of Stress State in Different Failure Criteria

TABLE 1.6 Stress Concentration Factors for the Configurations of Fig. 1.67

TABLE 1.7 Guides for Selection of Safety Factors of Machine Elements in Diff...

TABLE 1.8 A List of Commonly Used Design Factors in Determining Safety Factor

Chapter 3

TABLE 3.1 Proportions for a Streamline Fillet

a

Chapter 4

TABLE 4.1 Maximum for Circular Holes in Circular Element Loaded Externally with ...

TABLE 4.2 Maximum Kt for Circular Holes in Circular Element Loaded with Inte...

TABLE 4.3 Countersunk Stress Concentration Factors

Chapter 5

TABLE 5.1 Stress Concentration Factors for Press-Fit Shafts of 2-in. Diameter

TABLE 5.2 Stress Concentration Factors for Press-Fit Shafts of 0.66-in. Diam...

TABLE 5.3 Coefficients for SCFs of X-joints of cold-formed steel with square ...

TABLE 5.4 SCFs of Aluminum Cast with Due Spherical Cavities (Bidhar et al. 2...

Chapter 6

TABLE 6.1 Guides for Selection of Fatigue Analysis Methods (Bi 2018)

TABLE 6.2 The Common Formats of Computer Solid Models (Bi 2018)

TABLE 6.3 Common Analysis Types of Simulation in Solidworks (Bi 2018)

TABLE 6.4 Displacement Boundary Conditions for Structural Analysis (Bi 2018)

TABLE 6.5 Load Boundary Conditions for Structural Analysis (Bi 2018)

TABLE 6.6 Basic properties of materials.

List of Illustrations

Chapter 1

Figure 1.1 V-Model for product design and objectives of book (Bi 2018).

Figure 1.2 Examples of common machine elements for which stress analysis is es...

Figure 1.3 Relations in stress analysis of solids.

Figure 1.4 Inputs, relations, and outputs of stress analysis.

Figure 1.5 Classification of engineering materials.

Figure 1.6 Schematic of tensile testing.

Figure 1.7 Terminologies of stress-strain curve from tensile test.

Figure 1.8 Schematic of compression testing.

Figure 1.9 Terminologies of stress-strain curve from compression test.

Figure 1.10 Schematic of hardness testing.

Figure 1.11 Schematic of hardness testing.

Figure 1.12 Schematic of torsional test.

Figure 1.13 Schematic of fatigue testing.

Figure 1.14 Other fatigue tests subjected to different loading conditions.

Figure 1.15 Schematic of toughness testing.

Figure 1.16 Six main types of materials failures.

Figure 1.17 Examples of aircraft fatigue failures.

Figure 1.18 Appearances of impurities in composites.

Figure 1.19 Examples of aircraft fatigue failures.

Figure 1.20 Three fundamental methods for solid modeling.

Figure 1.21 Basic features of a solid object from material removal processes.

Figure 1.22 Common features of geometric discontinuities.

Figure 1.23 Classification of load types.

Figure 1.24 Stress types corresponding to different types of loads.

Figure 1.25 Stress equilibrium at an infinitesimal volume.

Figure 1.26 Mohr's circle for a three-dimensional stress state (Wikipedia 2018...

Figure 1.27 Two-dimensional stress equilibrium at an infinitesimal volume.

Figure 1.28 Mohr's circle for a two-dimensional stress state.

Figure 1.29 Commonly used failure theories for static loads.

Figure 1.30 Deformed energy U from stress

and

.

Figure 1.31 Decomposition of strain energy of three-dimensional stress state.

Figure 1.32 MSS and DET in three-dimensional space.

Figure 1.33 The maximum normal stress (MNS) theory.

Figure 1.34 The Coulomb-Mohr (CM) theory.

Figure 1.35 The Modified-Mohr (MM) theory.

Figure 1.36 Selection guide for static failure criterion.

Figure 1.37 Simple stress distribution in testing of material properties.

Figure 1.38 Stress concentration by a notch (Peterson 1974).

Figure 1.39 Stress concentration of tension bar by notches (Doz Dr-ing habil K...

Figure 1.40 Example of determining nominal stress.

Figure 1.41 Circular cylinder with an eccentric hole.

Figure 1.42 Circular cylinder with an eccentric hole.

Figure 1.43 Round bar with a circumferential groove and torsional loading.

Figure 1.44 Hyperbolic circumferential groove in a round bar.

Figure 1.45 Shaft with a circumferential groove and a plane element with the s...

Figure 1.46 Stress concentration in shallow groove and shoulder.

Figure 1.47 Rotating disk with a central hole and two symmetrically located ho...

Figure 1.48 Analysis of a hollow rotating disk with two holes.

Figure 1.49 Thin flat element with a shallow notch under a uniaxial load.

Figure 1.50 Thin flat element with a deep notch under a uniaxial load.

Figure 1.51 Multiple stress concentration.

Figure 1.52 Small radial hole through a groove.

Figure 1.53 Two stress raisers of almost equal magnitude in an infinite two-di...

Figure 1.54 Special cases of multiple stress concentration.

Figure 1.55 Equivalent ellipses.

Figure 1.56 Element under tension and bending loading.

Figure 1.57 Grooved shaft subject to tension, bending, and torsion.

Figure 1.58 (

a

) Infinite element subjected to internal pressure

p

on a circula...

Figure 1.59 Specimens for obtaining

.

Figure 1.60 Stress distribution near a notch for a ductile material.

Figure 1.61 Average fatigue notch sensitivity.

Figure 1.62 Limit safety factors for tubular members.

Figure 1.63 Combined alternating and steady stresses.

Figure 1.64 Limiting values of combined alternating and steady stresses for pl...

Figure 1.65 Elliptic hole model of a crack as

.

Figure 1.66 Coordinate system for stress at the tip of an ellipse.

Figure 1.67 Element with a circular hole with two opposing semicircular lobes.

Figure 1.68 Element with a circular hole and a pair of equal length cracks.

Figure 1.69 Infinite element with two identical ellipses that are not aligned ...

Chapter 2

Figure 2.1 Examples of grooved shafts.

Figure 2.2 Bar with opposite notches.

Figure 2.3 Notches: (

a

) deep hyperbolic; (

b

) shallow elliptical.

Figure 2.4 Equivalent notch from splitting a thin element with a hole: (

a

) thi...

Figure 2.5 Multiple notches.

Figure 2.6 Semi-infinite body with a hemispherical depression under equal biax...

Figure 2.7 Hyperbolical depression in the surface of a finite thickness panel ...

Figure 2.8 Bending of a flat beam with opposite U-shaped notches.

Figure 2.9 Grooved shaft.

Figure 2.10 Shaft, with circumferential U-shaped groove, subject to torsion a...

Chart 2.1 Stress concentration factors

for opposite deep hyperbolic notches ...

Chart 2.2 Stress concentration factors

for an elliptical or U-shaped notch i...

Chart 2.3 Stress concentration factors

and

for a tension strip ...

Chart 2.4 Stress concentration factors

for a flat tension bar with opposite ...

Chart 2.5 Stress concentration factors

for a flat tension bar with opposite ...

Chart 2.6 Stress concentration factors

for a flat test specimen with opposit...

Chart 2.7 Stress concentration factors

for a flat tension bar with opposite ...

Chart 2.8 Stress concentration factors

for tension loading of a semi-infinit...

Chart 2.9 Stress concentration factors

for a flat tension bar with a U-shape...

Chart 2.10 Stress concentration factors

for opposing notches with flat botto...

Chart 2.11 Stress concentration factors

for notches with flat bottoms in sem...

Chart 2.12 Stress concentration factors

for a tension bar with infinite rows...

Chart 2.13 Stress concentration factors

for a tension bar with infinite rows...

Chart 2.14 Stress concentration factors

for tension case of a flat bar with ...

Chart 2.15 Stress concentration factors

for tension case of a flat bar with ...

Chart 2.16 Stress concentration factors

for tension case of a flat bar with ...

Chart 2.17 Stress concentration factors

for a uniaxially stressed infinite t...

Chart 2.18 Stress concentration factors

for a deep hyperbolic groove in an i...

Chart 2.19 Stress concentration factors

for a tension bar of circular cross ...

Chart 2.20 Stress concentration factors

for a grooved shaft in tension with ...

Chart 2.21 Stress concentration factors

for a test specimen of circular cros...

Chart 2.22 Stress concentration factors

for flat-bottom grooves in tension (...

Chart 2.23 Stress concentration factors

for opposite deep hyperbolic notches...

Chart 2.24 Stress concentration factors

for bending of a flat beam with semi...

Chart 2.25 Stress concentration factors

for bending of a flat beam with oppo...

Chart 2.26 Stress concentration factors

for bending of flat beam with opposi...

Chart 2.27 Stress concentration factors

for bending of a flat beam with oppo...

Chart 2.28 Effect of notch angle on stress concentration factors for a thin be...

Chart 2.29 Stress concentration factors

for bending of a semi-infinite thin ...

Chart 2.30a Bending of a thin beam element with a notch on one side (Leven and...

Chart 2.30b Bending of a thin beam element with a notch on one side (Leven and...

Chart 2.31 Effect of span on stress concentration factors for various impact t...

Chart 2.32 Stress concentration factors

for bending of a thin beam having si...

Chart 2.33 Stress concentration factors

for thin beam in bending with opposi...

Chart 2.34 Stress concentration factors

for a shaft in bending and/or tensio...

Chart 2.35 Stress concentration factors

for a deep hyperbolic notch in an in...

Chart 2.36 Stress concentration factors

for rounded triangular or rectangula...

Chart 2.37 Stress concentration factors

for an elliptical notch in a semi-in...

Chart 2.38 Stress concentration factors

for infinite row of semicircular not...

Chart 2.39 Stress concentration factors

for a thin notched plate in transver...

Chart 2.40 Stress concentration factors

for a deep hyperbolic groove in an i...

Chart 2.41 Stress concentration factors

for bending of a bar of circular cro...

Chart 2.42 Stress concentration factors

for a U-shaped grooved shaft of circ...

Chart 2.43 Stress concentration factors

for bending of a bar of circular cro...

Chart 2.44 Stress concentration factors

for bending of a bar of circular cro...

Chart 2.45 Stress concentration factors

and

for opposite deep ...

Chart 2.46 Stress concentration factors

for a deep hyperbolic groove in an i...

Chart 2.47 Stress concentration factors

for torsion of a bar of circular cro...

Chart 2.48 Stress concentration factors

for torsion of a bar of circular cro...

Chart 2.49 Stress concentration factors

for a U-shaped grooved shaft of circ...

Chart 2.50 Stress concentration factors

for the torsion of a bar of circular...

Chart 2.51 Stress concentration factors

for torsion of a bar of circular cro...

Chart 2.52 Stress concentration factors

for a shaft in torsion with flat-bot...

Chart 2.53 Approximate geometric relations for maximum stress concentration fo...

Chapter 3

Figure 3.1 Examples of filleted members: (

a

) engine crankshaft; (

b

) turbine ro...

Figure 3.2 Fillets in a thin element and a circular bar.

Figure 3.3 Element of length

.

Figure 3.4 Effect of a narrow shoulder.

Figure 3.5 Compound fillet.

Figure 3.6 Ideal frictionless liquid flow from an opening in the bottom of a t...

Figure 3.7 Notation for Table 3.1

Figure 3.8 Construction of special fillet (Grodzinski 1941).

Figure 3.9 Tapered fillet suggested by Morgenbrod (1939).

Figure 3.10 Location of

maximum stress in the fillet.

Figure 3.11 Double radius fillet.

Figure 3.12 Techniques for reducing stress concentration in stepped shaft with...

Chart 3.1 Stress concentration factors

for a stepped flat tension bar with s...

Chart 3.2a Stress concentration factors

for a stepped flat tension bar with ...

Chart 3.2b Stress concentration factors

for a stepped flat tension bar with ...

Chart 3.2c Stress concentration factors

for a stepped flat tension bar with ...

Chart 3.2d Stress concentration factors

for a stepped flat tension bar with ...

Chart 3.3a Stress concentration factors

for a trapezoidal protuberance on a ...

Chart 3.3b Stress concentration factors

for a trapezoidal protuberance on a ...

Chart 3.4 Stress concentration factors

for a stepped tension bar of circular...

Chart 3.5 Stress concentration factors

for a tube in tension with fillet (Le...

Chart 3.6 Stress concentration factors

for a stepped pressure vessel wall wi...

Chart 3.7 Stress concentration factors

for bending of a stepped flat bar wit...

Chart 3.8a Effect of shoulder width

on stress concentration ...

Chart 3.8b Effect of shoulder width

on stress ...

Chart 3.8c Effect of shoulder width

on stress concentration ...

Chart 3.9 Stress concentration factors

for the bending case of a flat bar wi...

Chart 3.10 Stress concentration factors

for bending of a stepped bar of circ...

Chart 3.11 Stress concentration factors

for bending of a stepped bar of circ...

Chart 3.12 Stress concentration factors

for torsion of a shaft with a should...

Chart 3.13 Stress concentration factors

for torsion of a shaft with a should...

Chart 3.14 Effect of axial hole on stress concentration factors of a torsion s...

Chart 3.15a Stress concentration factors of a torsion tube with a shoulder fil...

Chart 3.15b Stress concentration factors of a torsion tube with a shoulder fil...

Chart 3.15c Stress concentration factors of a torsion tube with a shoulder fil...

Chart 3.16a Radius of compound fillet for shoulder shaft in torsion,

(Batten...

Chart 3.16b Radius of compound fillet for shoulder shaft in torsion,

(Batten...

Chart 3.17 Maximum possible reduction in stress concentration,

(Battenbo and...

Chapter 4

Figure 4.1 Examples of parts with transverse holes: (

a

) oil hole in crankshaft...

Figure 4.2 Thin infinite element with four holes.

Figure 4.3 Infinite thin element with hole under tensile load.

Figure 4.4 Circumferential stress distribution on the edge of a circular hole ...

Figure 4.5 Distribution of

on section

−

and

on section

−

.

Figure 4.6 Effect of length of an element (Troyani et al. 2002).

Figure 4.7 Infinite thin element under biaxial tensile in-plane loading.

Figure 4.8 Region of validity of shallow, thin shell theory (Van Dyke 1965).

Figure 4.9 Hole with

L

-section reinforcement.

Figure 4.10 Shape factor for a nonsymmetric reinforced circular hole.

Figure 4.11 Symmetrically reinforced circular hole in an infinite in-plane lo...

Figure 4.12 Effect of narrow reinforcement.

Figure 4.13 Effects of different

ratios: (

a

)

; (

b

)

.

Figure 4.14 Reinforcement shape optimal design based on weight.

Figure 4.15 Infinite element with a hole with internal pressure.

Figure 4.16 Two circular holes of equal diameter, aligned on a line perpendicu...

Figure 4.17 Two circular holes of equal diameter, aligned along

.

Figure 4.18 Two holes in an infinite panel subject to combined stresses.

Figure 4.19 Two holes lying at an angle, subject to combined stresses.

Figure 4.20 Thin element with two circular holes of unequal diameters.

Figure 4.21 Elliptical hole in uniaxial tension: (

a

) notation; (

b

) elliptical ...

Figure 4.22 Elliptical hole in biaxial tension. (

a

) notation. (

b

) decay patter...

Figure 4.23 Biaxial tension of an obliquely oriented elliptical hole.

Figure 4.24 Single elliptical hole in an infinite thin element subject to arbi...

Figure 4.25 Elliptical hole in pure shear.

Figure 4.26 Maximum stress location for uniaxial stress.

Figure 4.27 Equivalent ellipses: (

a

) ovaloid; (

b

) two holes connected by a sli...

Figure 4.28 Half section of “balanced” design of nozzle in spherical vessel (L...

Figure 4.29 Element with a transverse hole.

Figure 4.30 Notation for a countersunk hole.

Figure 4.31 Intersecting holes in cylinder: (

a

) cross hole; (

b

) T hole; (

c

) ro...

Figure 4.32 Pressurized thick cylinder with a circular crosshole.

Figure 4.33 Pressurized hollow thick square block with a circular hole in the ...

Figure 4.34 Finite-width panel subjected to tension with a central elliptical ...

Figure 4.35 Transverse bending of beam and plate: (

a

) beam; (

b

) plate.

Figure 4.36 Elliptical hole subject to shear force.

Chart 4.1 Stress concentration factors

and

for the tension...

Chart 4.2 Stress concentration factors for the tension of a thin semi-infinite...

Chart 4.3 Stress concentration factors for the tension of a finite-width eleme...

Chart 4.4 Stress concentration factors for a circular hole in a cylindrical sh...

Chart 4.5 Stress concentration factors for a circular hole in a cylindrical sh...

Chart 4.6 Stress concentration factors for a pressurized spherical shell with ...

Chart 4.7 Stress concentration factors for various shaped reinforcements of a ...

Chart 4.8a Stress concentration factors

for a reinforced circular hole in a ...

Chart 4.8b Stress concentration factors

for a reinforced circular hole in a ...

Chart 4.8c Stress concentration factors

for a reinforced circular hole in a ...

Chart 4.9 Stress concentration factors

for a reinforced circular hole in a t...

Chart 4.10 Stress concentration factors

for a reinforced circular hole in a ...

Chart 4.11 Stress concentration factors for a uniaxially stressed thin element...

Chart 4.12 Extrapolation of

and

values of Chart 4.11 to an ...

Chart 4.13a Analytical stress concentration factors for a symmetrically reinfo...

Chart 4.13b Analytical stress concentration factors for a symmetrically reinfo...

Chart 4.13c Analytical stress concentration factors for a symmetrically reinfo...

Chart 4.13d Analytical stress concentration factors for a symmetrically reinfo...

Chart 4.13e Analytical stress concentration factors for a symmetrically reinfo...

Chart 4.14 Area ratios and experimental stress concentration factors

for a s...

Chart 4.15 Volume ratios and experimental stress concentration factors

for a...

Chart 4.16 Area ratios and experimental stress concentration factors

for a s...

Chart 4.17 Volume ratios and experimental stress concentration factors

for a...

Chart 4.18 Approximate minimum values of

versus area ratios for a symmetrica...

Chart 4.19 Approximate minimum values of

versus volume ratios for a symmetri...

Chart 4.20 Stress concentration factors

for a square panel with a pressurize...

Chart 4.21a Stress concentration factors for the tension of a finite-width p...

Chart 4.21b Stress concentration factors

and

for tension ...

Chart 4.22 Stress concentration factors

for uniaxial tension case of an infi...

Chart 4.23 Stress concentration factors

for tension case of an infinite pane...

Chart 4.24 Stress concentration factors

and

for equal biaxial ...

Chart 4.25a Stress concentration factors

for a panel with two holes under bi...

Chart 4.25b Stress concentration factors

for a panel with two holes under bi...

Chart 4.25c Stress concentration factors

for a panel with two holes under bi...

Chart 4.25d Stress concentration factors

for a panel with two holes under bi...

Chart 4.25e Stress concentration factors

for a panel with two holes under bi...

Chart 4.25f Stress concentration factors

for a panel with two holes under bi...

Chart 4.25g Stress concentration factors

for a panel with two holes under bi...

Chart 4.26 Stress concentration factors

and

for tension in an ...

Chart 4.27 Stress concentration factors

for tension in an infinite thin elem...

Chart 4.28 Stress concentration factors

for biaxial tension in infinite thin...

Chart 4.29 Stress concentration factors

for tension in infinite thin element...

Chart 4.30 Stress concentration factors

for tension in infinite thin element...

Chart 4.31 Stress concentration factors

for tension in infinite thin element...

Chart 4.32 Stress concentration factors

and

for uniaxial tension ...

Chart 4.33 Stress concentration factors

for uniaxial tension of a finite-wid...

Chart 4.34 Stress concentration factors

and

for a biaxially ...

Chart 4.35 Stress concentration factors

for a double row of holes in a thin ...

Chart 4.36 Stress concentration factors

for a double row of holes in a thin ...

Chart 4.37 Stress concentration factors

and

for a triangular ...

Chart 4.38 Stress concentration factors

for the triangular pattern of holes ...

Chart 4.39a,b Stress concentration factors

for particular locations on the h...

Chart 4.39c Stress concentration factors

for particular locations on the hol...

Chart 4.39d Stress concentration factors

for particular locations on the hol...

Chart 4.40 Stress concentration factors

and

for a square pattern ...

Chart 4.41 Stress concentration factors

for patterns of holes in a thin elem...

Chart 4.42 Stress concentration factors

versus

for a square ...

Chart 4.43 Stress concentration factors

for a rectangular pattern of holes i...

Chart 4.44 Stress concentration factors

for a diamond pattern of holes in a ...

Chart 4.45 Stress concentration factors

for a diamond pattern of holes in a ...

Chart 4.46 Stress concentration factors

for a radially stressed circular ele...

Chart 4.47 Stress concentration factors

for a perforated flange with interna...

Chart 4.48 Stress concentration factors

for a circular thin element with an ...

Chart 4.49 Stress concentration factors

for a circular thin element with a c...

Chart 4.50 Stress concentration factors

for an elliptical hole in an infinit...

Chart 4.51 Stress concentration factors

and

of an elliptical ...

Chart 4.52 Stress concentration factors

for a semi-infinite tension panel wi...

Chart 4.53 Finite-width correction factor

for a tension strip with a central...

Chart 4.54 Stress concentration factors

and

for an elliptical ...

Chart 4.55 Stress concentration factors

for an elliptical hole in a biaxiall...

Chart 4.56 Effect of spacing on the stress concentration factor of an infinite...

Chart 4.57 Effect of spacing on the stress concentration factor of an infinite...

Chart 4.58a Stress concentration factors

of elliptical holes with bead reinf...

Chart 4.58b Stress concentration factors

of elliptical holes with bead reinf...

Chart 4.58c Stress concentration factors

of elliptical holes with bead reinf...

Chart 4.59 Optimization of slot end,

(Durelli et al. 1968).

Chart 4.60 Stress concentration factor

for an infinitely wide tension elemen...

Chart 4.61 Stress concentration factors

for a finite-width tension thin el...

Chart 4.62a Stress concentration factors

for a rectangular hole with rounded...

Chart 4.62b Stress concentration factors

for a rectangular hole with rounded...

Chart 4.62c Stress concentration factors

for a rectangular hole with rounded...

Chart 4.62d Stress concentration factors

for a rectangular hole with rounded...

Chart 4.63 Comparison of stress concentration factors of various-shaped holes.

Chart 4.64a,b Stress concentration factors of round-cornered square holes with...

Chart 4.64c Stress concentration factors of round-cornered square holes with b...

Chart 4.65a Stress concentration factors

for an equilateral triangular hole ...

Chart 4.65b Stress concentration factors

for an equilateral triangular hole ...

Chart 4.66 Stress concentration factors

and

for tension of a bar ...

Chart 4.67 Stress concentration factors

for a pin joint with a closely fitti...

Chart 4.68 Stress concentration factors

for a pinned or riveted joint with m...

Chart 4.69 Stress concentration factors

for a circular hole ...

Chart 4.70 Stress concentration factors

for a circular hole ...

Chart 4.71 Stress concentration factors

for a circular cavity of elliptical ...

Chart 4.72 Stress concentration factors

for an ellipsoidal cavity of circula...

Chart 4.73 Stress concentration factors

and

for spherical ...

Chart 4.74 Effect of spacing on the stress concentration factor of an infinite...

Chart 4.75 Stress concentration factors

for an infinite member in tension ha...

Chart 4.76 Effect of spacing on the stress concentration factor of an infinite...

Chart 4.77 Maximum peripheral stress in a cylindrical tunnel subjected to hydr...

Chart 4.78 Stress concentration factors

for a cylindrical tunnel subjected t...

Chart 4.79 Stress concentration factors

for a rotating disk with a central h...

Chart 4.80 Stress concentration factors

for a rotating disk with a noncentra...

Chart 4.81 Stress concentration factors

for a ring or hollow roller subjecte...

Chart 4.82 Stress concentration factors

for a ring or hollow roller compress...

Chart 4.83 Stress concentration factors

for a cylinder subject to internal p...

Chart 4.84 Hoop stress concentration factors

for a pressurized thick cylinde...

Chart 4.85 Shear stress concentration factors

for a pressurized thick cylind...

Chart 4.86 Hoop stress concentration factors

for a pressurized block with a ...

Chart 4.87 Shear stress concentration factors

for a pressurized block with a...

Chart 4.88 Stress concentration factors

for in-plane bending of a thin beam ...

Chart 4.89 Stress concentration factors

for bending of a thin beam with a ci...

Chart 4.90 Stress concentration factors

and

for bending of a ...

Chart 4.91 Stress concentration factors

for bending of an infinite plate wit...

Chart 4.92 Stress concentration factors

and

for bending of a ...

Chart 4.93 Stress concentration factors for an infinite row of circular holes ...

Chart 4.94 Stress concentration factors

for bending of an infinite plate hav...

Chart 4.95 Effects of spacing on the stress concentration factors of an infini...

Chart 4.96 Stress concentration factors

and

for bending of a bar ...

Chart 4.97 Stress concentration factors for an elliptical hole in an infinite ...

Chart 4.98 Stress concentration factors

for elliptical holes with symmetrica...

Chart 4.99 Stress concentration factors

for a rectangular hole with rounded ...

Chart 4.100 Stress concentration factor

for square holes with symmetrical re...

Chart 4.101a Stress concentration factors

for pure shear in an infinite thin...

Chart 4.101b Stress concentration factors

for pure shear in an infinite thin...

Chart 4.102 Stress concentration factors

for single row of circular holes in...

Chart 4.103 Stress concentration factors

for an infinite pattern of holes in...

Chart 4.104 Stress concentration factors

for an infinite rectangular pattern...

Chart 4.105 Stress concentration factors

for an infinite diamond pattern of ...

Chart 4.106 Stress concentration factors

for a twisted plate with a circular...

Chart 4.107 Stress concentration factors for a circular hole in a cylindrical ...

Chart 4.108 Stress concentration factors

and

for torsion of a ...

Chapter 5

Figure 5.1 Keyseat.

Figure 5.2 Types of keyseat ends: (a) end-milled keyseat (also, referred to as...

Figure 5.3 Location of end of keyseat with respect to shaft shoulder: (a) keys...

Figure 5.4 Gear notation.

Figure 5.5 Press-fit models, with dimensions in inches: (a) plain member; (b) ...

Figure 5.6 Shoulder design for fitted member, with schematic stress “flow line...

Figure 5.7 Nut designs tested photoelastically, with dimensions in inches (Het...

Figure 5.8 Nut designs fatigue tested (Wiegand 1933).

Figure 5.9 Transmittal of load (schematic): (a) stepped tension bar; (b) T-hea...

Figure 5.10 Lugs with pins: (a) square-ended lug; (b) round-ended lug; (c) sec...

Figure 5.11 Clearance of a lug-pin fit.

Figure 5.12 Lug of Example 5.1.

Figure 5.13 Stress concentration in curved bar subjected to bending.

Figure 5.14 Factor

for a torsion bar of rectangular cross section.

Figure 5.15 Classification of joint types by Saini et al (2016).

Figure 5.16 Stress concentration factors of T-joints. (Mashiri and Zhao 2006; ...

Figure 5.17 Geometry and SCFs of weld subjected to a combined load. (N'Diaye e...

Figure 5.18 Stiffened KT-joint subjected to balanced axial loading. (Ahmadia e...

Figure 5.19 Different K-joints consisting of circular chord and square braces....

Figure 5.20 Square bird-beak T-joints with square hollow section. Cheng et al....

Figure 5.21 Description of X-joint and hot stress spots (Feng and Young 2013)

Figure 5.22 SCFs of circular vessel with a radial U notch (de Carvalho 2005).

Figure 5.23 A pipe with local wall thinning, subject to internal pressure

p

an...

Figure 5.24 Layout of a pair of identical spherical cavities in an infinite co...

Figure 5.25 Configuration of countersunk hole (Darwish et al. 2012).

Figure 5.26 SCF of countersunk hole (Darwish et al. 2012).

Figure 5.27 Details of stiffen supports in ship structures (Parunov et al. 201...

Figure 5.28 SCFs of the block with cross-bores subjected to uniform internatio...

Figure 5.29 SCFs of bended plate affected lengths (Troyani et al. 2004).

Figure 5.30 SCF of tablet subjected to diametric compression (Croquelois et al...

Figure 5.31 Surface topography viewed as geometric discontinuities (Cheng et a...

Chart 5.1 Stress concentration factors

for bending of a shaft of circular cr...

Chart 5.2 Stress concentration factors

,

for a torsion shaft ...

Chart 5.3 Stress concentration factors

and

for combined bending ...

Chart 5.4 Stress concentration factors

for torsion of a splined shaft withou...

Chart 5.5 Stress concentration factors

for the tension side of a gear tooth ...

Chart 5.6 Stress concentration factors

for the tension side of a gear tooth ...

Chart 5.7 Minimum fillet radius

of gear tooth generated by a basic rack (for...

Chart 5.8 Stress concentration factors

for the tension side of a gear tooth ...

Chart 5.9 Stress concentration factors

for bending of a short beam with a sh...

Chart 5.10a Stress concentration factors for a

T

-head (photoelastic tests of H...

Chart 5.10b Stress concentration factors for a

T

-head (photoelastic tests of H...

Chart 5.10c,d Stress concentration factors for a

T

-head (photoelastic tests of...

Chart 5.10e Stress concentration factors for a

T

-head (photoelastic tests of H...

Chart 5.10f Stress concentration factors for a

T

-Head (photoelastic tests of H...

Chart 5.11 Stress concentration factors

for square-ended lugs,

...

Chart 5.12 Stress concentration factors

for round-ended lugs,

...

Chart 5.13 Stress concentration factors

for thick lugs. Square or round ende...

Chart 5.14 Stress concentration factors

for a curved bar in bending.

Chart 5.15 Stress factors

and

for helical compression or ...

Chart 5.16 Stress concentration factors

for a helical compression or tension...

Chart 5.17 Stress concentration factors

for a helical torsion spring (Wahl 1...

Chart 5.18 Stress concentration factors

for a crankshaft in bending (from st...

Chart 5.19 Stress concentration factors

for a crankshaft in bending (strain ...

Chart 5.20 Stress concentration factors

for a U-shaped member (based on phot...

Chart 5.21 Stress concentration factors

for a U-shaped member (based on phot...

Chart 5.22 Stress concentration factors

for angle or box sections in torsion...

Chart 5.23 Stress concentration factors

for a cylindrical pressure vessel wi...

Chapter 6

Figure 6.1 Classification of structural analysis problems (Bi 2018).

Figure 6.2 Types of design analysis methods for engineering solutions.

Figure 6.3 Description of structural analysis.

Figure 6.4 Stress equilibrium at an infinitesimal volume.

Figure 6.5 Truss-structure examples with distributed loads in large space (Bi ...

Figure 6.6 A one-dimensional truss element in LCS and GCS.

Figure 6.7 Types of boundary conditions for truss structure.

Figure 6.8 Various joints in truss, beam, and frame structures (Bi 2018).

Figure 6.9 Description of three-dimensional frame element.

Figure 6.10 Examples of plane-stress applications (Bi 2018).

Figure 6.11 Triangular element with plane stress.

Figure 6.12 Rectangle element with plane stress.

Figure 6.13 Examples of plane strain parts.

Figure 6.14 Stress state in a plane-strain model (Bi 2018).

Figure 6.15 Examples of products where modal analyses are needed (Bi 2018).

Figure 6.16 Two-dimensional truss member in LCS for modal analysis.

Figure 6.17 Two-dimensional beam element in LCS for modal analysis.

Figure 6.18 Two-dimensional frame member in LCS for modal analysis.

Figure 6.19 Examples of products where modal analysis needed (Bi 2018).

Figure 6.20 Linear elastic fracture mechanics method.

Figure 6.21 Stress-life method for fatigue analysis

Figure 6.22 Discretization of a continual domain into nodes and elements.

Figure 6.23 Preprocessing, processing, and postprocessing in an FEA model.

Figure 6.24 Solidworks simulation for FEA (Bi 2018).

Figure 6.25 A list of file formats compatible to Solidworks 2017 (Bi 2018). (B...

Figure 6.26 Typical structure of materials library in FEA package (Bi 2018).

Figure 6.27 Interface to create custom material model (Bi 2018).

Figure 6.28 Generate S-N curve for fatigue analysis (Bi 2018).

Figure 6.29 Exemplified element types for different shapes (Bi 2018).

Figure 6.30 Detecting and fixing interferences in an assembled object (Bi 2018...

Figure 6.31 Comparison of compatible and incompatible meshes (Bi 2018).

Figure 6.32 Classification of structural analysis problems (Bi 2018).

Figure 6.33 Verification and validation in FEA modeling (Bi 2018).

Figure 6.34 Example of strain discontinuity due to discretization (Bi 2018).

Figure 6.35 Errors caused by a model with basic elements (Bi 2018).

Figure 6.36 Example of mathematical model (Bi 2018).

Figure 6.37 Verification at different modeling stages (Bi 2018).

Figure 6.38 Verification subjects in an FEA model (Bi 2018).

Figure 6.39 Code verification in software life cycle (Adopted from Wall and Ko...

Figure 6.40 Example of code verification (Bi 2018).

Figure 6.41 Calculation verification based on force equilibrium of free body d...

Figure 6.42 Parametric study on cantilever beam (Fig. 6.40) for mesh verificat...

Figure 6.43 Example of using symmetric relation in computing reduction (Bi 201...

Figure 6.44 Estimating gradient distribution to justify mesh control (Bi 2018)...

Figure 6.45 Impact of aspect ratio on mesh quality (Bi 2018).

Figure 6.46 A finite-width thin element with semicircular notches subject to t...

Figure 6.47 A finite thin element with semicircular notches subject to tensile...

Figure 6.48 A two-dimensional FEA model of finite thin element.

Figure 6.49 An two-dimensional FEA model of finite thin element.

Figure 6.50 Comparison of stress concentration from the simulation and the emp...

Figure 6.51 Assembly model of fastening.

Figure 6.52 Simulation model of bolt-nut assembly.

Figure 6.53 Meshing and stress distribution of bolt-nut assembly.

Figure 6.54 Parametric study of preload for bolt-nut assembly.

Figure 6.55 Parametric model of a wheel design.

Figure 6.56 Wheel model with support and simplification.

Figure 6.57 FEA model and simulation for wheel design.

Figure 6.58 The maximum von Mises stress in rim with respect to the number of ...

Figure 6.59 The total weight of the rim with respect to the number of spoke gr...

Guide

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PETERSON'S STRESS CONCENTRATION FACTORS

Fourth Edition

WALTER D. PILKEY, DEBORAH F. PILKEY, ZHUMING BI

This edition first published 2020

© 2020 John Wiley & Sons, Inc.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Zhuming Bi to be identified as the author of this work has been asserted in accordance with law.

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Limit of Liability/Disclaimer of WarrantyWhile the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

Library of Congress Cataloging-in-Publication Data is Available:

ISBN 9781119532514 (Hardback)ISBN 9781119532538 (ePDF)ISBN 9781119532521 (ePub)

Cover Design: WileyCover Images: Car lights on highway © BABAROGA/Shutterstock, Structure of verification Courtesy of Zhuming Bi, Parametric study Courtesy of Zhuming Bi

INDEX TO THE STRESS CONCENTRATION FACTORS

CHAPTER 2: NOTCHES AND GROOVES

Form of Stress Raiser

Load Case

Shape of Stress Raiser

Section and Equation Number

Chart Number

Page Number of Chart

Single notch insemi-infinitethin element

Tension

U-shaped

2.3.1

2.2

82

Hyperbolic

2.3.6

2.8

88

Elliptical

2.3.1

2.2

82

Flat bottom

2.3.7

2.11

91

Bending(in-plane)

Hyperbolic

2.6.5

2.29

109

Bending(out-of-plane)

V-shaped

2.7.1

2.36

117

Flat bottom

2.7.1

2.36

117

Elliptical

2.7.1

2.37

118

Multiple notchesin semi-infinitethin element

Bending(out-of-plane)

Semicircular

2.7.1

2.38

119

Opposite notchesin infinite thinelement

Tension

Hyperbolic

2.3.1

2.1

81

Bending(in-plane)

Hyperbolic

2.6.1

2.23

103

Bending(out-of-plane)

Hyperbolic

2.7.1

2.35

116

Shear

Hyperbolic

2.9.1

2.45

126

Single notch infinite-width thinelement

Tension

U-shaped

2.3.6

2.9

89

Flat bottom

2.3.8

2.14

94

Bending(in-plane)

U-shaped

2.6.5

2.30

110

V-shaped

2.6.4

2.28

108

Various shapednotches inimpact test

2.6.5

2.31

112

Semi-elliptical

2.6.6

2.32

113

Multiple notches onone side of finite-width thin element

Tension

Semicircular

2.3.8

2.14

2.15

2.16

94

95

96

Bending(in-plane)

Semi-elliptical

2.6.6

2.32

113

Bending(out-of-plane)

Semicircular

2.7.1

2.38

119

Opposite singlenotches in finite-width thin element

Tension

U-shaped

2.3.3

Eq. (2.1)

2.4

2.5

2.6

2.53

84

85

86

134

Semicircular

2.3.2

2.3

83

V-shaped

2.3.5

2.7

87

Flat bottom

2.3.7

2.10

90

Bending(in-plane)

Semicircular

2.6.2

2.24

104

U-shaped

2.6.3

2.25

2.26

2.27

2.53

105

106

107

134

Flat bottom

2.6.7

2.33

114

Bending(out-of-plane)

Arbitrarilyshaped

2.7.2

2.39

120

Opposite multiplenotches in finite-width thin element

Tension

Semicircular

2.3.8

2.12

2.13

92

93

Depressions inopposite sides ofa thin element

Uniaxialtension

Spherical

2.4.3

2.17

97

Cylindricalgroove

Depression inthe surface of asemi-infinite body

Uniaxialtension

Hemispherical

2.4.1

Hyperboloid

2.4.2

Groove ininfinite medium

Tension

Hyperbolic

2.5.1

2.18

98

Bending

Hyperbolic

2.8.1

2.40

121

Torsion

Hyperbolic

2.9.2

2.46

127

Circumferentialgroove in shaft ofcircular cross section

Tension

U-shaped

2.5.2

2.19

2.20

2.21

2.53

99

100

101

134

Flat bottom

2.5.3

2.22

2.34

102

115

Bending

U-shaped

2.8.2

2.41

2.42

2.43

2.53

122

123

124

134

Flat bottom

2.6.7

2.8.3

2.34

2.44

115

125

Tension andbending

Flat bottom

2.6.7

2.34

115

Torsion

U-shaped

2.9.3

2.47

2.48

2.49

2.50

2.53

128

129

130

131

134

V-shaped

2.5.4

2.9.4

2.51

132

Flat bottom

2.9.5

2.52

133

CHAPTER 3: SHOULDER FILLETS

Form of Stress Raiser

Load Case

Shape of Stress Raiser

Section and Equation Number

Chart Number

Page Number of Chart

Shoulder fillets inthin element

Tension

Singleradius

3.3.1

Eq. (3.1)

3.1

151

Tapered

3.3.5

Bending

Single radius

3.4.1

3.7

160

Elliptical

3.4.3

3.9

164

Tapered

3.3.5

Torsion

Tapered

3.3.5

Shoulder filletsin thin element

Tension

Single radius

3.3.3

3.2

152

Trapezoidalprotuberance

3.3.4

3.3

155

Bending

Single radius

3.4.2

3.8

161

Shoulder filletin bar of circularcross section

Tension

Single radius

3.3.6

3.4

157

Bending

Single radius

3.4.4

3.10

3.11

165

166

Torsion

Single radius

3.5.1

3.12

3.13

167

168

Compoundradius

3.5.3

3.16

3.17

173

175

Shoulder filletin bar of circularcross section withaxial hole

Tension

Single radius

3.3.7

3.5

158

Torsion

Single radius

3.5.2

3.14

3.15

169

170

Stepped pressurevessel

Internalpressure

Steppedring

3.3.8

3.6

159

CHAPTER 4: HOLES

Form of Stress Raiser

Load Case

Shape of Stress Raiser

Section and Equation Number

Chart Number

Page Number of Chart

Hole in infinitethin element

Uniaxialtension

Circular

4.3.1

Eqs. (4.9)

–

(4.10)

Elliptical

4.4.1

Eqs. (4.57)

and

(4.58)

4.50

334

Elliptical holewith inclusion

4.5.12

4.50

4.75

334

366

Circular holewith oppositesemicircularlobes

4.5.2

4.60

346

Rectangular

4.5.3

4.5.4

4.62a

348

Equilateraltriangular

4.5.6

4.65

355

Inclined

4.5.9

4.70

361

Internalpressure

Circular,elliptical, andother shapes

4.3.12

,

4.3.19

,

4.4.5

Eqs. (4.41)

and

(4.77)

Biaxial stress(in-plane)

Circular

4.3.5

Eqs. (4.17)

and

(4.18)

Rectangular

4.5.3

4.62

348

Variousshapes

4.5.1

4.5.3

4.63

352

Equilateraltriangular

4.5.6

4.65

355

Elliptical

4.4.3

Eqs. (4.68)

–

(4.71)

4.54

4.55

338

339

Inclined

4.5.9

4.69

360

Bending(out-of-plane)

Circular

4.8.4

Eqs. (4.129)

and

(4.130)

4.91

382

Elliptical

4.8.7

Eqs. (4.132)

and

(4.133)

4.94

385

Shear

Circular orelliptical

4.9.1

4.97

388

Rectangular

4.9.2

4.99

390

Twist

Circular

4.9.6

Eq. (4.138)

4.106

398

Hole in finite-width thin element

Uniaxialtension

Circular

4.3.1

Eq. (4.9)

4.1

256

Crack

4.7.3

Circularorthotropicmaterial

4.7.2

Eccentricallylocated circular

4.3.3

Eq. (4.14)

4.3

272

Elliptical

4.4.1

,

4.4.2

4.53

337

Ellipticalorthotropicmaterial

4.7.1

Circular hole withopposite semi-circular lobes

4.5.2

Eqs. (4.78)

and

(4.79)

4.61

347

Slot withsemicircular orsemielliptical end

4.5.1

4.59

345

Internalpressure

Various shapes

4.3.19

4.4.5

Bending(in-plane)

Circular incurved beam

4.8.3

Circular

4.8.1

,

4.8.2

Eqs. (4.124)

–

(4.127)

4.88

4.89

379

380

Elliptical

4.8.4

4.90

381

Ovaloids,square

4.8.4

Eq. (4.128)

Bending(out-of-plane)

Circular

4.8.5

Eq. (4.129)

4.92

383

Hole in semi-infinitethin element

Uniaxialtension

Circular

4.3.2

Eq. (4.12)

4.2

271

Elliptical

4.4.1

4.52

336

Internalpressure

Various shapes

4.3.19

,

4.4.5

Hole in cylindricalshell, pipe, or bar

Tension

Circular

4.3.6

4.4

273

Internalpressure

Circular

4.3.6

Eqs. (4.19)

–

(4.21)

4.5

274

Torsion

Circular

4.9.7

4.107

399

Transverse holethrough rod ortube

Tension

Circular

4.5.7

4.66

357

Bending

Circular

4.8.9

4.96

388

Torsion

Circular

4.9.8

4.108

400

Row of holes ininfinite thin element

Uniaxialtension

Circular

4.3.15

4.32

314

Elliptical

4.4.4

4.56

340

Ellipticalholes withinclusions

4.5.12

4.76

367

Biaxial stresses(in-plane)

Circular

4.3.15

4.34

316

Bending(out-of-plane)

Circular

4.8.6

4.93

384

Elliptical

4.8.8

4.95

386

Shear

Circular

4.9.4

4.102

394

Row of holes in finite-width thin element

Uniaxialtension

Elliptical

4.4.4

4.33

,

4.57

315

,

341

Double row of holes ininfinite thin element

Uniaxialtension

Circular

4.3.16

Eqs. (4.46)

and

(4.47)

4.35

4.36

317

318

Triangular pattern of holesin infinite thin element

Uniaxialtension

Circular

4.3.17

4.37

,

4.38

,

4.39

319

,

320

,

321

Biaxial stresses(in-plane)

Circular

4.3.17

4.37

,

4.38

,

4.39

,

4.41

319

,

320

,

321

,

325

Shear

Circular

4.9.5

4.103

395

Square pattern of holes ininfinite thin element

Uniaxialtension

Circular

4.3.17

4.40

4.43

324

327

Biaxial stresses(in-plane)

Circular

4.3.17

4.40

,

4.41

,

4.42

324

,

325

,

326

Shear

Circular

4.9.5

4.103

4.104

395

396

Diamond pattern of holesin infinite thin element

Uniaxialtension

Circular

4.3.17

4.44

4.45

328

329

Shear

Circular

4.9.5

4.105

397

Hole in wall of thinspherical shell

Internalpressure

Circular orelliptical

4.3.7

4.6

275

Thick elementwith hole

Tensionandshear

Circular

4.6

Countersunk hole

Tensionandbending

Circular

4.6.1

Pressurized hollowthick cylinderwith hole

Circular

4.6.7

Eq. (4.110)

4.84

,

4.85

375

,

376

Pressurized hollowthick blockwith hole

Circular

4.6.8

4.86

,

4.87

377

,

378

Reinforced hole ininfinite thin element

Biaxialstress(in-plane)

Circular

4.3.11

4.13

,

4.14

,

4.15

,

4.16

,

4.17

,

4.18

,

4.19

284

,

289

,

290

,

291

,

292

,

293

,

294

Elliptical

4.4.6

4.58

342

Square

4.5.5

4.64

353

Shear

Elliptical

4.9.1

4.98

389

Square

4.9.2

4.100

391

Reinforced hole in semi-infinite thin element

Uniaxialtension

Circular

4.3.8

4.7

276

Square

4.5.5

4.64a

353

Reinforced hole in finite-width thin element

Uniaxialtension

Circular

4.3.9

4.3.10

Eq. (4.26)

4.8

4.9

4.10

4.11

277

280

281

282

Hole in panel

Internalpressure

Circular

4.3.12

4.20

295

Two holes in afinite thin element

Tension

Circular

4.3.13

4.21

296

Two holes in infinitethin element

Uniaxialtension

Circular

4.3.13

4.3.14

Eqs. (4.42)

,

(4.44)

, and

(4.45)

4.22

,

4.23

,

4.24

,

4.26

,

4.27

,

4.29

,

4.30

,

4.31

298

,

299

,

300

,

308

,

309

,

311

,

312

,

313

Biaxialstresses(in-plane)

Circular

4.3.13

4.3.14

Eqs.(4.43)

–

(4.45)

4.25

4.26

4.28

301

308

310

Shear

Circular

4.9.3

,

4.9.4

4.101

392

Ring of holes incircular thin element

Radialin-planestresses

Circular

4.3.18

Table 4.1

4.46

330

Internalpressure

Circular

4.3.19

Table 4.2

4.47

331

Hole in circularthin element

Internalpressure

Circular

4.3.19

Table 4.2

4.48

332

Circular pattern of holesin circular thin element

Internalpressure

Circular

4.3.19

Table 4.2

4.49

333

Pin joint with closelyfitting pin

Tension

Circular

4.5.8

Eqs. (4.83)

and

(4.84)

4.67

358

Pinned or riveted jointwith multiple holes

Tension

Circular

4.5.8

4.68

359

Cavity in infinite body

Tension

Circular cavityof ellipticalcross section

4.5.11

4.71

362

Ellipsoidal cavityof circularcross section

4.5.11

4.72

363

Cavities in infinitepanel and cylinder

Uniaxialtension orbiaxialstresses

Sphericalcavity

4.5.11

Eqs.(4.86)

–

(4.88)

4.73

364

Row of cavitiesin infinite element

Tension

Ellipsoidalcavity

4.5.11

4.74

365

Crack in thintension element

Uniaxialtension

Narrowcrack

4.4.2

Eqs. (4.62)

–

(4.64)

4.53

337

Tunnel

Hydraulicpressure

Circular

4.6.2

Eqs. (4.99)

4.77

4.78

368

369

Disk

Rotatingcentrifugalinertialforce

Central hole

4.6.4

4.79

370

Noncentralhole

4.6.4

4.80

371

Ring

Diametricallyopposite internalconcentratedloads

4.6.5

Eq. (4.105)

4.81

372

Diametricallyopposite externalconcentratedloads

4.6.5

Eq. (4.106)

4.82

373

Thick cylinder

Internalpressure

No hole incylinder wall

4.6.6

Eqs. (4.108)

and

(4.109)

4.83

374

Hole incylinder wall

4.6.7

Eq. (4.110)

4.84

375

CHAPTER 5: MISCELLANEOUS DESIGN ELEMENTS

Form of Stress Raiser

Load Case

Shape of Stress Raiser

Section and Equation Number

Chart Number

Page Number of Chart

Keyseat

Bending

Semicircularend

5.2.1

5.1

430

Sled runner

5.2.1

Torsion

Semicircularend

5.2.2

5.2.3

5.2

431

Combinedbending andtorsion

Semicircularend

5.2.4

5.3

432

Splined shaft

Torsion

5.3

5.4

433

Gear tooth

Bending

5.4

Eqs. (5.3)

and

(5.4)

5.5

5.6

5.7

5.8

434

435

436

437

Short beam

Bending

Shoulderfillets

5.4

Eq. (5.5)

5.9

438

Press-fitted member

Bending

5.5

Tables 5.1

and

5.2

Bolt and nut

Tension

5.6

T-head

Tension andbending

Shoulderfillets

5.7

Eqs. (5.7)

and

(5.8)

5.10

439

Lug joint

Tension

Squareended

5.8

5.11

5.13

444

446

Roundended

5.8

5.12

5.13

445

446

Curved bar

Bending

Uniformbar

5.9

Eq. (5.11)

5.14

447

Nonuniform:crane hook

5.12

Helical spring

Tension orcompression

Round orsquare wire

5.10.1

Eqs. (5.17)

and

(5.19)

5.15

448

Rectangularwire

5.10.2

Eq. (5.23)

5.16

449

Torsional

Round orrectangularwire

5.10.3

5.17

450

Crankshaft

Bending

5.11

Eq. (5.26)

5.18

5.19

451

452

U-shaped member

Tension andbending

5.13

Eqs. (5.27)

and

(5.28)

5.20

5.21

453

454

Angle or box sections

Torsion

5.14

5.22

455

Cylindricalpressure vessel

Internalpressure

Torisphericalends

5.15

5.23

456

Tubular joint

Variable

K and Tjoints withand withoutreinforcement

5.16