Formulas for Stress, Strain, and Structural Matrices

by Pilkey, Walter D.

• ISBN13: 9780471032212
• ISBN10: 0471032212
• Edition: 2nd
• Format: Hardcover
• Copyright: 2004-11-11
• Publisher: Wiley

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