Formulas for Stress, Strain, and Structural Matrices,9780471032212

Formulas for Stress, Strain, and Structural Matrices

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Edition: 2nd
ISBN13: 9780471032212
ISBN10: 0471032212
Format: Hardcover
Pub. Date: 2004-11-11
Publisher(s): Wiley
List Price: $285.81

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Summary

The most comprehensive book in its field, Formulas for Stress, Strain, and Structural Matrices, Second Edition is a source of formulas for the analysis and design of structural members and mechanical elements. * Presents simple formulas, organized by type of member, to permit more complex members to be solved. * Includes formulas for dynamic response as well as nominal vibration formulas. * Contains background material on stress and strain, mechanical properties of materials, stress analysis, stress concentration, and fracture and fatigue mechanics.

Author Biography

WALTER D. PILKEY, PhD, is a Morse Professor of Mechanical Engineering in the School of Engineering and Applied Science at the University of Virginia, Charlottesville. He is recognized as an authority in the areas of stress and strain from both the mechanical and civil engineering points of view.

Table of Contents

Preface xxi
Acknowledgments xxiii
Introduction
1(16)
Notation
1(1)
Conversion Factors
2(1)
Sign Conventions and Consistent Units
2(1)
SI Units
2(1)
Typical Design Loads and Stresses
2(15)
Tables for Chapter 1
3(14)
Geometric Properties of Plane Areas
17(72)
Notation
17(1)
Centroids
18(1)
Moments of Inertia
19(2)
Section Moduli
20(1)
Polar Moment of Inertia
21(1)
Principal Moments of Inertia
22(2)
Mohr's Circle for Moments of Inertia
24(4)
First Moment of Areas Associated with Shear Stresses in Beams
28(1)
Shear Correction Factors
29(2)
Torsional Constant
31(5)
Thin-Walled Sections
31(5)
Sectorial Properties
36(2)
Sectorial Area
36(1)
First Sectorial Moment
37(1)
Sectorial Linear Moments
37(1)
Warping Constant (Sectorial Moment of Inertia)
37(1)
Shear Center for Thin-Walled Cross Sections
38(3)
Open Cross Sections
39(2)
Modulus-Weighted Properties for Composite Sections
41(48)
References
44(1)
Tables for Chapter 2
45(44)
Stress and Strain
89(60)
Notation
90(1)
Definitions and Types of Stress
91(1)
Stress Component Analysis
92(16)
Sign Convention
92(1)
Stress Tensor
93(1)
Plane Stress
93(1)
Variation of Normal and Shear Stress in Tension
94(1)
Stress at an Arbitrary Orientation for the Two-Dimensional Case
95(2)
Principal Stresses and Maximum Shear Stress for the Two-Dimensional Case
97(3)
Mohr's Circle for a Two-Dimensional State of Stress
100(1)
Construction of Mohr's Circle
100(1)
Use of Mohr's Circle
101(1)
Stress Acting on an Arbitrary Plane in Three-Dimensional Systems
102(1)
Normal and Shear Stress on an Oblique Plane
102(1)
Maximum Shear Stress in Three-Dimensional Systems
103(1)
Mohr's Circle for Three Dimensions
104(2)
Octahedral Stress
106(1)
Mean and Deviator Stress
107(1)
Relationship between Stress and Internal Forces
108(1)
Average Shear Stress
109(1)
Differential Equations of Equilibrium
109(1)
Allowable Stress
109(1)
Residual Stress
109(1)
Definition of Strain
110(2)
Relationship between Strain and Displacement
112(1)
Analysis of Strain
112(1)
Elastic Stress-Strain Relations
113(1)
Poisson's Ratio
113(1)
Hooke's Law
113(1)
Stress and Strain in Simple Configurations
114(12)
Direct Axial Loading (Extension and Compression)
114(2)
Direct Shear in Connections
116(1)
Torsion
116(4)
Normal and Shear Stress of Beams
120(2)
Deflection of Simple Beams
122(2)
Stress in Pressure Vessels
124(2)
Combined Stresses
126(3)
Unsymmetric Bending
129(5)
Normal Stress
129(2)
Shear Stress
131(3)
Theories of Failure
134(5)
Concept of Failure
134(4)
Validity of Theories
138(1)
Application of Failure Theories
139(10)
References
141(2)
Tables for Chapter 3
143(6)
Mechanical Properties and Testing of Engineering Materials
149(86)
Notation
151(1)
Material Laws: Stress-Strain Relations
152(2)
Tensile Test
154(5)
Impact Tests
159(3)
Notched-Bar Tests
159(1)
Drop-Weight Test for the Nil-Ductility Temperature
160(2)
Dynamic Tear Energy Test
162(1)
Hardness Tests
162(3)
Brinell Hardness Test
163(1)
Vickers Hardness Test
163(1)
Rockwell Hardness Test
163(1)
Microhardness Test
164(1)
Creep
165(4)
Cumulative Creep
167(2)
Simultaneous Creep and Fatigue
169(1)
Ferrous Metals
169(8)
Steel Classification and Specifications
172(1)
Carbon Steels
173(1)
Alloy Steels
174(1)
Stainless Steels
175(1)
Cast Irons
176(1)
High-Strength, Low-Alloy Steels
177(1)
Tool Steels
177(1)
Nonferrous Metals
177(1)
Aluminum
177(1)
Magnesium
178(1)
Other Nonferrous Metals
178(1)
Plastics
178(1)
Ceramics
179(1)
Composites
180(1)
Biomechanics
181(2)
Bone Tissue Mechanics
181(1)
Soft Tissue Mechanics
182(1)
Factors That Influence Properties
183(1)
Biomaterials
183(1)
Classes of Biomaterials
184(1)
Microelectromechanical Systems (MEMS)
184(1)
Material Selection
185(50)
References
189(2)
Tables for Chapter 4
191(44)
Experimental Stress Analysis
235(20)
Notation
235(1)
Introduction
236(1)
Electrical Resistance Strain Gage
237(7)
Brittle Coating
244(1)
Photoelasticity
245(10)
References
245(2)
Tables for Chapter 5
247(8)
Stress Concentration
255(52)
Notation
255(1)
Stress Concentration Factors
256(3)
Effective Stress Concentration Factors
259(6)
Neuber's Rule
261(4)
Designing to Minimize Stress Concentration
265(42)
References
271(2)
Tables for Chapter 6
273(34)
Fracture Mechanics and Fatigue
307(62)
Notation
308(1)
Linear Elastic Fracture Mechanics and Applications
309(17)
General Design by Linear Elastic Fracture Mechanics
315(11)
Energy Analysis of Fracture
326(1)
J Integral
327(2)
Fatigue Fracture
329(1)
Traditional S-N Curve Approach to Fatigue
330(10)
Stress Concentration
331(1)
Nonzero Mean Load
331(3)
Load with Varying Amplitude
334(2)
Effects of Load, Size, Surface, and Environment
336(2)
Stress Concentration with a Nonzero Mean Load
338(2)
Fracture Mechanics Approach to Fatigue
340(4)
Combined Approach
344(25)
References
345(4)
Tables for Chapter 7
349(20)
Joints
369(44)
Notation
369(2)
Riveted and Bolted Joints
371(8)
Joint Failure Mode under Shear Loading
373(4)
Boiler Joints
377(1)
Bolted Joints in Machine Design
377(2)
Load Analysis of Fastener Groups
379(3)
Design of Riveted and Bolted Connections
382(8)
Welded Joints and Connections
390(23)
Types of Welded Joints and Typical Drawing Symbols
390(2)
Analysis of Welded Joints
392(3)
References
395(2)
Tables for Chapter 8
397(16)
Contact Stresses
413(38)
Notation
414(1)
Hertzian Contact Stresses
415(17)
Two Bodies in Point Contact
415(14)
Two Bodies in Line Contact
429(1)
Contact Stress with Friction
430(2)
Contact Fatigue
432(1)
Rolling Contact
432(1)
Non-Hertzian Contact Stress
432(1)
Nanotechnology: Scanning Probe Microscopy
433(18)
Hertz Model
433(1)
Sneddon's Model
434(1)
Derjaguin-Muller-Toporov Theory (DMT)
434(1)
Johnson-Kendall-Roberts Theory (JKR)
434(1)
Maugis-Dugdale Model
434(1)
References
434(3)
Tables for Chapter 9
437(14)
Dynamic Loading
451(68)
Notation
452(1)
Classification and Source of Dynamic Loadings
453(1)
Vibration Fundamentals
453(12)
Simple Kinematics
453(1)
Harmonic Motion
454(2)
Single-Degree-of-Freedom System
456(8)
Damping in Structures
464(1)
Natural Frequencies
465(6)
Approximate Formulas
467(4)
Viscoelastic Elements
471(1)
Human Body Vibrations
471(1)
Impact Formulas
472(2)
Energy-Absorbing Characteristics of Structures
474(5)
Dynamic Behavior of Materials
479(2)
Increasing the Dynamic Strength of Structures and Minimizing Dynamic Effects
481(38)
Geometric Configuration
481(1)
Material Properties
481(1)
Loading
481(1)
References
482(1)
Tables for Chapter 10
483(36)
Beams and Columns
519(100)
Notation
520(1)
Sign Convention
521(1)
Stresses
522(1)
Normal Stress
522(1)
Shear Stress
523(1)
Simple Beams
523(5)
Tabulated Formulas
524(2)
Formulas for Beams with Arbitrary Loading
526(2)
Beams with Axial Forces on Elastic Foundations
528(3)
Plastic Design
531(1)
Buckling Loads and Columns
531(4)
Columns
534(1)
Short Bars with Eccentric Loading
535(1)
Natural Frequencies and Mode Shapes
535(1)
General Beams
536(3)
Transfer Matrices
536(3)
Stiffness and Mass Matrices
539(80)
Stiffness Matrix
539(3)
Geometric Stiffness Matrix
542(1)
Mass Matrix
542(1)
References
542(2)
Tables for Chapter 11
544(75)
Torsion and Extension of Bars
619(42)
Notation
619(2)
Torsion
620(1)
Extension
621(1)
Sign Conventions
621(1)
Stresses
622(3)
Torsional Stresses
622(1)
Hollow Thin-Walled Cross Sections
622(2)
Thin-Walled Open Sections
624(1)
Specific Stress Formulas
624(1)
Extensional Stress
625(1)
Simple Bars
625(1)
Torsion
625(1)
Extension
626(1)
Tabulated Formulas
626(1)
Natural Frequencies
626(1)
General Bars
627(34)
References
631(2)
Tables for Chapter 12
633(28)
Frames
661(72)
Notation
662(1)
Notation for Gridworks
662(1)
Frames
663(4)
Formulas
663(3)
Buckling Loads
666(1)
Natural Frequencies
666(1)
Plastic Design
666(1)
Gridworks
667(5)
Static Loading
668(2)
Buckling Loads
670(1)
Natural Frequencies
671(1)
General Grillages
672(1)
Matrix Methods
672(61)
Transfer Matrix Method
673(1)
Stiffness and Mass Matrices
673(1)
Stability Analysis
673(1)
References
674(1)
Tables for Chapter 13
675(58)
Torsion of Thin-Walled Beams
733(30)
Notation
733(2)
Sign Convention and Definitions
735(1)
Stresses
736(2)
Normal Warping Stress
736(1)
Shear Warping Stress
737(1)
Twisting of Thin-Walled Beams
738(3)
Formulas for Beams with Arbitrary Loading
738(3)
Buckling Loads
741(1)
Natural Frequencies
741(1)
General Beams
742(21)
References
745(2)
Tables for Chapter 14
747(16)
Cross-Sectional Stresses: Combined Stresses
763(38)
Notation
764(1)
Sign Convention
764(1)
Warping Properties
765(12)
Integration Method
766(1)
Piecewise Integration Method
767(10)
Normal Stresses
777(5)
Neutral Axis
777(5)
Shear Stresses
782(6)
Shear Center
783(5)
Combined Normal and Shear Stresses
788(6)
Internal Moments
791(2)
Combined Results
793(1)
Finite Element Analysis
794(7)
References
795(2)
Tables for Chapter 15
797(4)
Curved Bars
801(90)
Notation
802(2)
All Curved Bars
802(1)
In-Plane Stress and Deformation
802(1)
Out-of-Plane Stress and Deformation
803(1)
In-Plane Stress and Deformation
804(14)
Sign Convention
804(1)
Stresses
805(12)
Simple Curved Bars
817(1)
Buckling Loads
817(1)
Natural Frequencies
818(1)
Out-of-Plane Stress and Deformation
818(1)
Sign Convention
818(1)
Stresses
818(1)
Simple Curved Bars
818(1)
Buckling Loads
819(1)
Natural Frequencies
819(1)
General Bars
819(72)
Rings
820(2)
References
822(1)
Tables for Chapter 16
823(68)
Rotors
891(86)
Notation
892(2)
Sign Convention
894(1)
Bending Vibration
894(26)
Whirling of a Single-Mass Rotor
894(5)
Single-Mass Rotor on Elastic Supports
899(5)
Uniform Rotating Shaft
904(3)
Transfer Matrices
907(4)
Stiffness and Mass Matrices
911(9)
Torsional Vibration
920(1)
Vibration of a Radial Beam
921(56)
Bending Vibration
922(1)
Axial Vibration
923(2)
References
925(2)
Tables for Chapter 17
927(50)
Plates
977(154)
Notation
978(2)
All Plates
978(1)
Circular Plates
979(1)
Rectangular Plates
979(1)
Circular Plates
980(11)
Stresses
980(1)
Simple Circular Plates
980(2)
Complex Circular Plates
982(1)
Tabulated Formulas
983(1)
Formulas for Plates with Arbitrary Loading
984(1)
Buckling Loads
985(1)
Natural Frequencies
986(2)
General Circular Plates
988(2)
Large Deflections of Circular Plates
990(1)
Rectangular Plates
991(11)
Stresses
991(1)
Governing Differential Equations
991(2)
Tabulated Formulas
993(2)
Formulas for Plates with Arbitrary Loading
995(1)
Buckling Loads
996(1)
Natural Frequencies
997(1)
General Rectangular Plates
998(2)
Large Deflections of Rectangular Plates
1000(2)
Other Plates
1002(129)
References
1002(3)
Tables for Chapter 18
1005(126)
Thick Shells and Disks
1131(54)
Definitions and Notation
1131(2)
Thick Cylinders
1132(1)
Thick Spherical Shells
1133(1)
Disks
1133(1)
Stresses
1133(4)
Thick Cylinders
1134(1)
Thick Spherical Shells
1134(1)
Nonpressurized Rotating Disk of Constant Thickness
1135(2)
Design of Cylinders with Internal Pressure
1137(4)
Simple Shells and Disks
1141(5)
Thick Cylinders
1141(3)
Thick Spherical Shells
1144(1)
Disks
1145(1)
Natural Frequencies
1146(1)
General Shells and Disks
1146(39)
References
1150(1)
Tables for Chapter 19
1151(34)
Thin Shells
1185(134)
Definitions
1185(3)
Notation
1186(2)
Membrane Shells of Revolution
1188(3)
Shells of Revolution with Bending
1191(6)
Multiple-Segment Shells of Revolution
1197(7)
Other Shells
1204(1)
Stability
1205(3)
Natural Frequencies
1208(111)
Circular Cylindrical Shells
1208(6)
Conical Shells
1214(2)
Spherical Shells
1216(1)
References
1216(3)
Tables for Chapter 20
1219(100)
APPENDIX I FUNDAMENTAL MATHEMATICS
1319(50)
I.1 Algebraic Operations
1321(2)
Algebraic Laws
1321(1)
Exponents
1321(1)
Roots
1321(1)
Logarithms
1321(1)
Series
1322(1)
Binomial Theorem
1323(1)
I.2 Complex Numbers
1323(1)
Rules for Calculations
1324(1)
I.3 Plane Trigonometry
1324(6)
Definitions
1324(1)
Laws of Sines, Cosines, and Tangents
1325(1)
Identities
1326(2)
Equilateral Triangle
1328(1)
Right Triangle
1328(1)
Inverse Trigonometric Functions
1328(2)
Exponential Relations: Euler's Equation
1330(1)
I.4 Hyperbolic Functions
1330(1)
Definitions
1330(1)
Identities
1330(1)
I.5 Coordinate Systems
1331(7)
Rectangular Coordinate System
1331(2)
Direction Cosines
1333(1)
Unit Vectors on a Boundary Curve
1333(2)
Curvature Formulas
1335(1)
Basic Formulas in Plane Analytic Geometry
1336(2)
I.6 Quadratic Equations
1338(1)
I.7 System of Linear Equations
1338(2)
Determinants
1338(1)
Cramer's Rule
1339(1)
I.8 Differential and Integral Calculus
1340(3)
Basic Operations
1340(1)
Differentiation of Functions with Multiple Variables
1341(1)
Integral Formulas
1341(1)
Integral Theorems
1341(2)
I.9 Laplace Transform
1343(1)
I.10 Representation of Functions by Series
1343(3)
Taylor's Series for Single Variable
1343(1)
Maclaurin's Series
1343(1)
Taylor's Series for Two Variables
1344(1)
Fourier Series
1344(1)
Series Expansions of Some Common Functions
1345(1)
I.11 Matrix Algebra
1346(5)
Definitions
1346(1)
Laws
1347(1)
Basic Operations
1347(2)
Determinants
1349(1)
Eigenvalues and Eigenvectors
1349(2)
I.12 Numerical Methods
1351(18)
Linear Interpolation Method to Solve f(x) = 0
1351(1)
Newton's Method
1351(1)
Zeros of a Polynomial
1352(1)
Gauss Algorithm
1353(1)
Numerical Integration
1354(3)
Tables for Appendix I
1357(12)
APPENDIX II STRUCTURAL MEMBERS
1369(36)
II.1 Engineering Beam Theory: Differential Form of Governing Equations
1370(8)
Geometric Relationships
1370(2)
Material Laws
1372(1)
Equations of Equilibrium
1373(1)
Displacement Form of Governing Differential Equations
1374(2)
Mixed Form of Governing Differential Equations
1376(2)
Stress Formulas
1378(1)
II.2 Sign Convention for Beams
1378(2)
II.3 Solution of Governing Equations for a Beam Element
1380(9)
First-Order Form of Governing Equations
1381(6)
Effect of Applied Loading
1387(2)
II.4 Principle of Virtual Work: Integral Form of Governing Equations
1389(2)
Virtual Work
1389(1)
Statement of the Principle of Virtual Work
1390(1)
II.5 Stiffness Matrix
1391(9)
Definition of Stiffness Matrices
1391(2)
Determination of Stiffness Matrices
1393(6)
Properties of Stiffness Matrices
1399(1)
II.6 Mass Matrices
1400(2)
II.7 Dynamic Stiffness Matrices
1402(1)
II.8 Geometric Stiffness Matrices
1402(3)
References
1403(2)
APPENDIX III STRUCTURAL SYSTEMS
1405(86)
III.1 Transfer Matrix Method
1406(34)
Loading and In-Span Conditions
1408(2)
Introduction of Boundary Conditions
1410(7)
Stability
1417(5)
Free Vibrations
1422(12)
Steady-State Motion
1434(1)
Indeterminate In-Span Conditions
1435(3)
Numerical Difficulties
1438(2)
III.2 General Structural Systems
1440(6)
Coordinate Systems, Definitions, and Degrees of Freedom
1441(3)
Coordinate Transformations
1444(2)
III.3 Displacement Method
1446(20)
Displacement Method Based on the Principle of Virtual Work
1446(4)
Direct Derivation of Global Displacement Equations
1450(1)
System Stiffness Matrix Assembled by Summation
1451(1)
Characteristics of Stiffness Matrices
1451(1)
Incorporation of Boundary Conditions
1452(1)
Reactions and Internal Forces, Stress Resultants, and Stresses
1452(1)
Frames
1453(7)
Structures with Distributed Loads
1460(6)
Special Intermediate Conditions
1466(1)
III.4 Force Method
1466(1)
III.5 Stability Based on the Displacement Method
1467(3)
III.6 Free Vibrations Based on the Displacement Method
1470(13)
Mass Matrix
1471(1)
Eigenvalue Problem
1471(6)
Frequency-Dependent Stiffness and Mass Matrices
1477(6)
III.7 Transient Responses
1483(8)
References
1485(2)
Tables for Appendix III
1487(4)
Index 1491

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