This is the third and final book in a series of texts for Mechanics of Materials.Full description
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Intermediate Mechanics of Materials is designed for the second course in mechanics of materials. In the first course, the students are introduced to mechanics of materials variables, the rel…Full description
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Descripción: JAMES W. DALLY ROBERT J. BONENBERGER WILLIAM L. FOURNE
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Descripción: This book, framed in the processes of engineering analysis and design, presents concepts in mechanics of materials for students in two-year or four-year programs in engineering technology, architec...
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Mechanics of Materials SolutionsFull description
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SIXTH EDITION
ADVANCED
MECHANICS
OF MATERIALS
ARTHUR P. BORESI
Professor Emeritus Civil and Architectural Engineering The University ofWyoming at Laramie an Professor Emeritus Theoretical and Applied Mechanics University of Illinois at Urbana-Champaign
RICHARD J. SCHMIDT
Professor Civil and Architectural E ngineering The University ofWyoming at Laramie
JOHN WILEY WILEY & SONS , INC.
CONTENTS CHAPTER 1.1
1.2
1.3
1.4
2.4
2.5
2.6
2.7
Review of Elem entary Mech anics of Materials 1.1.1 Axially Loaded Mem bers 1.1.2 Torsionally Loaded Mem bers 1.1.3 Bending of Beam s Me thods of Ana lysis 1.2.1 Method of Mecha nics of Materials 1.2.2 Method of Continuum Mecha nics and the Theory of Elasticity 1.2.3 Deflections by Energ y Me thods Stress-Strain Relations 8 1.3.1 Elastic and Inelastic Response of a Solid 1.3.2 Ma terial Prop erties Failure and Lim its on Des ign 1.4.1 Mo des of Failure 19 Problems 22 References 24
CHAPTER
2.1 2.2 2.3
INTRODUCTION
THEORIES OF STRESS AND STRAIN
25
Definition of Stress at a Poin t 25 Stress Nota tion 26 Symm etry of the Stress Array and Stress on an Arbitrarily Oriented Plane 28 2.3.1 Symm etry of Stress Com ponents 28 2.3.2 Stresses Acting on Arbitrary Planes 29 2.3.3 Norma l Stress and Shear Stress on an Oblique Plane 30 Transformation of Stress, Principal Stresses, and Other Properties 31 2.4.1 Transformation of Stress 31 2.4.2 Principal Stresses 32 2.4.3 Principal Values and Directions 33 2.4.4 Octahedral Stress 36 2.4.5 Mean and Deviator Stresses 37 2.4.6 Plan e Stress 38 2.4.7 Mo hr's Circle in Two Dimen sions 40 2.4.8 Mohr's " Circles in Three Dimen sions 43 Differential Equations of Motion of a Deformable Body 50 2.5.1 Specialization of Equations 2.46 52 Deformation of a Deformable Body 54
2.8
2.9
Strain Theory, Transformation of Strain, and Principal Strains 55 2.7.1 Strain of a Line Elemen t 55 2.7.2 Final Direction of a Line Element 57 2.7.3 Rotation Between Two Line Elemen ts (Definition of Shear Strain) 58 2.7.4 Principal Strains 60 Small-Displacem ent Theory 61 2.8.1 Strain Com patibility Relations 62 2.8.2 Strain-D isplacem ent Relations for Orthogonal Curvilinear Coordinates 63 Strain Measurem ent and Strain Rosettes Problems 72 References 78
CHAPTER LINEAR RELATIONS 79 3.1
3.2 3.3
3.4 3.5
First Law of Therm odynam ics, Internal-Energy Density, and Com plementary Internal-Energy Density 79 3.1.1 Elasticity and Internal-Energy Density 81 3.1.2 Elasticity and Com plementary Internal-Energy Density 82 Hook e's Law: Anisotropic Elasticity 84 Hook e's Law: Isotropic Elasticity 85 3.3.1 Isotropic and Hom ogeneous Materials 85 3.3.2 Strain-Energy Density of Isotropic Elastic Materials 85 Equations of Therm oelasticity for Isotropic Materials 91 Hook e's Law : Orthotropic Materials 93 Problems 101 References 103
CHAPTER 4.1
STRESS-STRAIN-TEMPERATURE
INELASTIC MATERIAL BEHAVIOR
104
Limitations on the Use of Uniaxial Stress-Stra in Data 104 4.1.1 Rate of Loading 10 4.1.2 Temperature Lower Than Room Temperature 105 4.1.3 Temperature Higher Than Room Temperature 105
CONTENTS
4.2 4.3
4.4
4.5
4.6
4.1.4 Unloa ding and Load Reversal 10 4.1.5 Multiaxia l States of Stress 10 Nonlinear Material Response 4.2.1 Models of Uniaxial Stress-Strain Curves 10 Yield Criteria: Gen eral Con cepts 11 4.3.1 Max imum Principa l Stress Criterion 11 4.3.2 Maximu m Principal Strain Criterion 4.3.3 Strain-Ene rgy Density Criterion 11 Yielding of Du ctile Me tals 11 4.4.1 Ma xim um Shear-Stress (Tresca) Criterion 11 4.4.2 Distortional Energy Density (von Mises) Criterion 120 4.4.3 Effect of Hyd rostatic Stress and the TT-Plane 122 Alternative Yield Criteria 26 4.5.1 Moh r-Coulo mb Yield Criterion 4.5.2 Drucke r-Prager Yield Criterion 12 4.5.3 Hi ll's Criterion for Ortho tropic Ma terials 12 Gene ral Yielding 4.6.1 Elastic-Plastic Bending 31 4.6.2 Fully Plastic Mom ent 13 4.6.3 Shear Effect on Inelastic Bend ing 13 4.6.4 Mod ulus of Ruptu re 13 4.6.5 Com parison of Failure Criteria 13 4.6.6 Interpretation of Failure Criteria for Gene ral Yielding 137 Problems 142 References 146
CHAPTER 5.1 5.2 5.3
5.4
5.5
6.2
147
Princip le of Stationary Poten tial Energy 14 Cas tiglian o's Theorem on Deflections 15 Castigliano's Theorem on Deflections for Linear Load-Deflection Relations 15 5.3.1 Strain Energy for Axial Load ing 15 5.3.2 Strain Energie an for Bea ms 15 5.3.3 Strain Energy for Torsio n 16 Deflections of Statically Determ inate Structures 16 5.4.1 Curved Beam s Treated as Straight Beam s 16 5.4.2 Dumm y Load Method and Dumm y Unit Load Method 170 Statically Indete rmin ate Structures 17 5.5.1 Deflections of Statically Indete rmin ate Structures 180 Problems 187 References 199
CHAPTER 6.1
APPLICATIONS OF ENERGY METHODS
TORSION
6.2.2
6.3
6.4 6.5
6.6 6.7
6.8
6.9 6.10
6.11
CHAPTER 7.1
7.2
200
Torsion of a Prisma tic Bar of Circular Cross Section 6.1.1 Design of Transm ission Shafts 20 Saint-Vena nt's Sem iinverse Method 20 6.2.1 Geom etry of Deform ation 20
Stresses at a Point and Equ ations of Equilibrium 210 6.2.3 Boun dary Cond itions 21 Linea r Elastic Solution 213 6.3.1 Elliptical Cross Section 21 6.3.2 Equilate ral Triangle Cross Section 215 6.3.3 Other Cross Sections 21 The Prandtl Elastic-Mem brane (Soap-Film) Analogy 21 6.4.1 Remark on Reentrant Corners 21 Narrow Recta ngula r Cross Section 21 6.5.1 Cross Sections Made Up of Long Narrow Rectangles 221 Torsion of Rectangular Cross Section Mem bers 22 Hollow Thin-Wall Torsion Mem bers and Multiply Connected Cross Sections 22 6.7.1 Hollow Thin-Wall Torsion Mem ber Having Several Com partments 23 Thin-Wall Torsion Mem bers with Restrained Ends 234 6.8.1 I-Section Torsion Mem ber Having One End Restrain ed from Warping 235 6.8.2 Various Loads and Suppo rts for Beam s in Torsion 239 Num erical Solution of the Torsion Problem 23 Inelastic Torsion: Circular Cross Section s 243 6.10.1 Mo dulus of Rup ture in Torsion 24 6.10.2 Elastic-Plastic and Fully Plastic Torsion 244 6.10.3 Residu al Shear Stress 24 Fully Plastic Torsion: Gen eral Cross Sections 25 Problems 254 References 262
200
7.3
BENDING OF STRAIGHT BEAMS
263
Fundam entals of Beam Bending 26 7.1.1 Centroid al Coord inate Axes 263 7.1.2 Shear Loading of a Beam and Shear Center Defined 264 7.1.3 Symm etrical Bending 26 7.1.4 Nonsymm etrical Bending 26 7.1.5 Plane of Loads: Symmetrical and Nonsymm etrical Loading 26 Bending Stresses in Beams Subjected to Nonsymmetrical Bending 272 7.2.1 Equa tions of Equilibrium 27 7.2.2 Geom etry of Deform ation 27 7.2.3 Stress-Strain Relations 273 7.2.4 Load -Stress Relation for Nonsym metrical Bending 273 7.2.5 Neutral Axis 27 7.2.6 More Convenient Form for the Flexure Stres 275 zz Deflections of Straight Beam s Subjected to Nonsymm etrical Bending 28
C O N T E N TS
7.4 7.5
Effect of Inclined Loads 284 Fully Plastic Load for Nonsym metrical Bending Problems 287 References 294
10.5 28 10.6 10.7
SHEAR CENTER FOR THIN-WALL BEAM CROSS SECTIONS 295 CHAPTER
8.1 8.2 8.3 8.4 8.5
CHAPTER
9.1 9.2 9.3
9.4
9.5 9.6 9.7
10.3
11.2
11.3
319
BEAMS ON ELASTIC FOUNDATIONS
PL'
371
10.3.3 L' ->°° 371 10.3.4 Interm ediate Values of/3L' 37 10.3.5 Triangu lar Load 37 Semiinfinite Beam Subjected to Loa ds at Its End
11.4
11.5 11.6
11.7
THE THICK-WALL CYLINDER
389
Basic Rela tions 38 11.1.1 Equa tion of Equilib rium 39 11.1.2 Strain-Displace men t Relations and Comp atibility Condition 39 11.1.3 Stress—Strain-Temperature Relations 39 11.1.4 Material Response Data 39 Stress Com ponents at Sections Far from Ends for Cylinder with Closed Ends 39 11.2.1 Open Cylin der 394 Stress Com ponents and Radial Displacement for Constant Temperature 39 11.3.1 Stress Com ponents 39 11.3.2 Radial Displacem ent for a Closed Cylinder 396 11.3.3 Radial Displacem ent for an Open Cylinder 396 Criteria of Failure 39 11.4.1 Failure of Brittle Ma terials 39 11.4.2 Failure of Duc tile Ma terials 40 11.4.3 Mate rial Resp onse Data for Design 40 11.4.4 Ideal Resid ual Stress Distribution s for Com posite Open Cylinders 40 Fully Plastic Pressu re and Autofrettag e 40 Cylinder Solution for Temperature Change Only 09 11.6.1 Steady-State Temperature Change (Distribution) 409 11.6.2 Stress Com pone nts 410 Rotating Disks of Constant Thickness 41 Problems 419 References 422
357"
Gene ral Theory 35 Infinite Beam Subjected to a Concentrated Load Boundary Conditions 36 10.2.1 Me thod of Supe rposition 363 10.2.2 Beam Supported on Equally Spaced Discrete Elastic Suppo rts 36 Infinite Beam Subjected to a Distributed Load Segment 369 10.3.1 Uniform ly Distribute d Load 36 10.3.2
10.4
11.1
Introductio n 31 Circumferential Stresses in a Curved Beam 32 9.2.1 Location of Neutral Axis of Cross Section 32 Radial Stresses in Curved Beam s 33 9.3.1 Curved Beam s Mad e from Anisotropic Materials 334 Correction of Circumferential Stresses in Curved Beam Having I, T, or Sim ilar Cross Section s 33 9.4.1 Bleich 's Correction Factors 34 Deflections of Curved Bea ms 343 9.5.1 Cross Sections in the Form of an I, T, etc. 34 Statically Indeterminate Curved Beam s: Closed Ring Subjected to a Concentrated Load 34 Fully Plastic Loads for Curved Beam s 35 9.7.1 Fully Plastic Versus Maxim um Elastic Loads for Curved Beam s 35 Problems 352 References 356
CHAPTER 1 10.1 10.2
CURVED BEAMS
Semiinfinite Beam with Concentrated Load Near Its End 376 Short Beam s 377 Thin-W all Circula r Cylin ders 378 Problems 384 References 388
CHAPTER
Approximations for Shear in Thin-Wall Beam Cross Sections 295 Shear Flow in Thin-Wall Beam Cross Sections 29 Shear Cente r for a Chan nel Section 298 Shear Center of Com posite Beam s Formed from Stringers and Thin Webs 303 Shear Cente r of Box Beam s 30 Problems 312 References 318
X
37
CHAPTER 12 COLUMNS 12.1 12.2
12.3
ELASTIC AND INELASTIC STAB ILITY OF 423
Introduction to the Concept of Column Buckling 42 Deflection Response of Colum ns to Compressive Loads 425 12.2.1 Elastic Buckling of an Ideal Slender Column 425 12.2.2 Imperfect Slender Colum ns 42 The Euler Formula for Column s with Pinned Ends 42 12.3.1 The Equilibrium Method 42 12.3.2 Higher Buckling Loads; 1 431 12.3.3 The Imperfection Method 43 12.3.4 The Energy Method 43
I
12.4 12.5 12.6
CONTENT
Euler Buckling of Columns with Linearly Elastic End Constraints 436 Local Buck ling of Colum ns 44 Inelastic Buckling of Colum ns 44 12.6.1 Inelastic Buc kling 44 12.6.2 Two Formulas for Inelastic Buckling of an Ideal Column 44 12.6.3 Tangent-Modulus Formula for an Inelastic Buckling Load 44 12.6.4 Direct Tangent-Modulus Method 44 Problems 450 References 455
13.9.9
Significant Stress When Edge s Are Clamped 495 13.9.10 Load on a Plate When Edges Are Clamped 496 13.9.11 Summ ary for Large Elastic Deflections of Circular Plates: Simply Supported Edg e and Uniform ly Distributed Load 49 13.9.12 Rectangu lar or Other Shaped Plates with Larg e Deflections 498 Problems 500 References 501 CHAPTER 1
CHAPTER 13.1 13.2 13.3
13.4 13.5
13.6 13.7 13.8
13.9
FLAT PLATES
457
Introduc tion 45 Stress Resu ltants in a Flat Plate 458 Kinem atics: Strain-Displace men t Relations for Plates 461 13.3.1 Rota tion of a Plate Surface Elem ent 46 Equilibrium Equations for Small-Di splacement Theory of Flat Plates 46 Stress-Strain-T em perature Relations for Isotropic Elastic Plates 46 13.5.1 Stress Com ponents in Terms of Tractions and Mom ents 47 13.5.2 Pure Ben ding of Plates 47 Strain Energy of a Plate 47 Bou ndary Con ditions for Plates 473 Solution of Rectangular Plate Problems 47 13.8.1 Solution of w = £ for a Rectangular Plate 477 13.8.2 Westergaard Approx imate Solution for Rectangular Plates: Uniform Load 47 13.8.3 Deflection of a Rec tangu lar Plate Uniform ly Distributed Loa d 48 Solution of Circu lar Plate Proble ms 48 13.9.1 Solution of w = £ for a Circular Plate 486 13.9.2 Circular Plates with Simply Supported Edges 488 13.9.3 Circula r Plates with Fixed Edg es 488 13.9.4 Circular Plate with a Circular Hole at the Center 489 13.9.5 Summ ary for Circular Plates with Simply Suppo rted Edg es 49 13.9.6 Summ ary for Circular Plates with Fixed Edges 491 13.9.7 Sum mary for Stresses and Deflections in Flat Circular Plates with Central Holes 49 13.9.8 Sum mary for Larg e Elastic Deflections of Circular Plates: Clamped Edge and Uniformly Distributed Load 49
14.1 14.2
14.3
*" 14.4
14.5
STRESS CONCENTRATIONS
502
Nature of a Stress Concentration Problem and the Stress Concentration Factor 50 Stress Concentration Factors: Theory of Elasticity 50 14.2.1 Circula r Hole in an Infinite Plate Und er Unia xial Tension 50 14.2.2 Elliptic Hole in an Infinite Plate Stressed in Direction Perpendicular to the Major Axis of the Ho le 50 14.2.3 Elliptica l Hole in an Infinite Plate Stressed in the Direction Perpendicular to the Mino r Axis of the Hole 51 14.2.4 Crack in a Plate 51 14.2.5 Ellipso idal Cavity 51 14.2.6 Groove s and Hole s 513 Stress Concentration Factors: Combined Loads 51 14.3.1 Infinite Plate with a Circu lar Hole 51 14.3.2 Elliptic al Hole in an Infinite Plate Uniform ly Stressed in Directions of Major an d Minor Axes of the Hole 51 14.3.3 Pure Shear Parallel to Major and Minor Axes of the Elliptica l Hole 516 14.3.4 Elliptica l Hole in an Infinite Plate with Different Loads in Two Perpendicular Directions 517 14.3.5 Stress Concentration at Groove in a C ircular Shaft 520 Stress Concentration Factors: Experimental Techniques 522 14.4.1 Photoelastic Method 52 14.4.2 Strain-Gage Method 52 14.4.3 Elastic Torsional Stress Concentration at Fillet in a Shaft 52 14.4.4 Elastic Mem brane Method: Torsional Stress Concentration 525 14.4.5 Beam s with Rectangular Cross Sections 52 Effective Stress Con centra tion Factors 53 14.5.1 Definition of Effective Stress Conc entration Factor 530 14.5.2 Static Load s 532 14.5.3 Repe ated Loads 53
CONTENTS
16.4.2
Fatigue-Life Curve and the eRelation 581 Problems 585 References 588
14.5.4 14.5.5
14.6
Resid ual Stresses 534 Very Abrupt Changes in Section: Stress Gradient 534 14.5.6 Significance of Stress Grad ient 535 14.5.7 Impact or Energy Loading 53 Effective Stress Conce ntration Factors: Inelastic Strains 536 14.6.1 Neu ber's Theorem 53 Problems 539 References 541
CHAPTER 15 15.1
15.2
15.3
15.4
16.2 16.3
16.4
CHAPTER 17 17.1 17.2 17.3
543
Failure Criteria and Fracture 54 15.1.1 Brittle Fracture of Mem bers Free of Cracks and Flaws 54 15.1.2 Brittle Fracture of Cracked or Flawed Members 545 The Stationary Crack 55 15.2.1 Blunt Crack 553 15.2.2 Sharp Crack 554 Crack Propag ation and the Stress Intensity Factor 55 15.3.1 Elastic Stress at the Tip of a Sharp Crack 555 15.3.2 Stress Intens ity Facto r: Definition and Derivation 556 15.3.3 Derivation of Crack Extension Force 556 15.3.4 Critical Value of Crack Extension Force 55 Fractu re: Other Facto rs 561 15.4.1 Elastic—Plastic Frac ture Me chan ics 562 15.4.2 Crack-Growth Analysis 56 15.4.3 Load Spectra and Stress History 56 15.4.4 Testing and Experimen tal Data Interpretation 563 Problems 564 References 565
CHAPTER 16.1
FRACTURE MECHANICS
FATIGUE:
PROGRESSIVE FRACTURE
XI
17.4 17.5 17.6
17.7 17.8
17.9
567
Fracture Resulting from Cyclic Loading 568 16.1.1 Stress Conc entrations 573 Effective Stress Co ncen tration Facto'rs: Rep eated Loads 575 Effective Stress Concen tration Factors: Other Influences 575 16.3.1 Corrosion Fatigue 575 16.3.2 Effect of Ran ge of Stress 577 16.3.3 Metho ds of Redu cing Harmful Effects of Stress Conc entrations 57 Low Cycle Fatigue and the e- Relation 580 16.4.1 Hysteresis Loop 58
CONTACT STRESSES
589
Introduction 58 The Problem of Determ ining Contact Stresses 59 Geom etry of the Contact Surface 59 17.3.1 Fundam ental Assump tions 591 17.3.2 Co ntact Surface Shap e After Load ing 59 17.3.3 Justification of Eq . 17.1 592 17.3.4 Brief Discussion of the Solution 595 Notation and Meaning of Terms 59 Expressions for Principal Stresses 59 Method of Com puting Contact Stresses 59 17.6.1 Principal Stresses 598 17.6.2 Max imum Shear Stress 59 17.6.3 Max imum Octahedral Shear Stress 59 17.6.4 Max imum Orthogo nal Shear Stress 59 17.6.5 Curves for Com puting Stresses for Any Valu of B/ 605 Deflection of Bod ies in Point Con tact 60 17.7.1 Significance of Stresses 611 Stress for Two Bodies in Line Con tact: Loads Normal to Contact Area 61 17.8.1 Max imum Principal Stresses: 0 613 17.8.2 Max imum Shear Stress: 0 613 17.8.3 Max imum Octahedral Shear Stress: 613 Stresses for Two Bod ies in Line Contact: Loads Normal and Tangent to Contact Area 61 17.9.1 Roller on Plane 61 17.9.2 Principal Stresses 61 17.9.3 Max imum Shear Stress 61 17.9.4 Max imum Octahedral Shear Stress 61 17.9.5 Effect of Mag nitude of Friction Coefficient 618 17.9.6 Range of Shear Stress for One Load Cycle 619 Problems 622 References 623
Definition of Creep and the Creep Curve 62 The Tension Creep Test for Metals 62 One-D imensional Creep Formulas for Metals Subjected to Constant Stress and Elevated Temperature 62
IV
18.4
18.5 18.6
18.7 18.8
CONTENTS
One-Dimensional Creep of Metals Subjected to Variable Stress and Temperature . 631 18.4.1 Preliminary Concep ts 63 18.4.2 , Similarity of Cree p Curv es 633 18.4.3 Temperature Dependen cy 63 18.4.4 Variable Stress and Tem perature 635 Creep Und er Multiaxial States of Stress 640 18.5.1 General Discussion 64 Flow Rule for Creep of Metals Subjected to Mu ltiaxial States of Stress 643 18.6.1 Steady-State Creep 64 18.6.2 Non steady Creep 64 An App lication of Creep of Metals 64 18.7.1 Summ ary 65 Creep of Non metals 65 18.8.1 Asp halt 65 18.8.2 Co ncrete 65 18.8.3 Woo d 65 References 654
AVERAGE MECHANICAL
APPENDIX
SELECTED M ATERIALS
PROPERTIES OF
657
APPENDIX SECOND MOMENT (MOMENT OF INERTIA) OF A PLANE AREA 660 .I .2 .3
oments of Inertia of a Plane Area 66 Parallel Axis Theorem 66 Transformation Equations for Moments and Products of Inertia 664 B.3.1 Principal Axes of Inertia 665 Problems 666
