Brzoska / Zyczkowski Strength of Structural Elements

1. Auflage 2013
ISBN: 978-1-4832-9169-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 26, 789 Seiten, Web PDF

Reihe: Studies in Applied Mechanics

This volume describes engineering applications of the mechanics of deformable bodies and the elasticity theory relevant to them. It is concerned mainly with one-dimensional problems, which arise because either one of the dimensions of a body is much greater than the remaining two or the functions of two or three variables may be reduced to one variable.Problems of this type are of twofold importance. Firstly, many engineering problems can be described with sufficient accuracy just in this way. Secondly, unidimensional problems with known analytical solutions may serve either for testing numerical methods or for the analysis of fundamental concepts and phenomena, whose physical nature in three-dimensional approach might be obscured by the analytical-numerical aspect. The authors have confined themselves for the most part to the analysis of elastic behaviour of structures; however some attention is also given to elastic problems. A deterministic approach has been applied throughout the book. It will serve as a springboard for further work with stochastic approaches which are being increasingly used in engineering practice today.

Autoren/Hrsg.

Brzoska, Zbigniew

Zyczkowski, M.

Inhaltsverzeichnis

1;Front Cover;1
2;Strength of Structural Elements;4
3;Copyright Page;5
4;Table of Contents;8
5;Preface;6
6;Part 1: Statics of Bars and Bar Structures;16
6.1;Chapter 1. Introduction;18
6.2;Chapter 2. Bars of Solid Cross-Section;25
6.2.1;2.1. Tension and Bending of a Straight Bar,;25
6.2.2;2.2. Torsion of a Straight Bar,;31
6.2.3;2.3. In-Plane Curved Bar,;34
6.3;Chapter 3. Fundamental Static-Kinematic Analysis of Bar Structures;41
6.3.1;3.1. Elements and Their Connections,;41
6.3.2;3.2. The Static-Kinematic Discriminant,;44
6.3.3;3.3. The Degree of Static Indeterminability and the Degree of Kinematic Variabilityof a Structure,;45
6.4;Chapter 4. The Principle of Virtual Work and the Reciprocity Theorems;50
6.4.1;4.1. The Principle of Virtual Work,;50
6.4.2;4.2. The Principle of Complementary Virtual Work;55
6.4.3;4.3. The Reciprocal Work Theorem,;58
6.4.4;4.4. The Reciprocal Displacement Theorem,;59
6.4.5;4.5. The Reciprocal Reaction Theorem,;62
6.4.6;4.6. The Reciprocal Displacement and Reaction Theorem,;64
6.4.7;4.7. The Reciprocal Displacement and Internal Force Theorem,;66
6.5;Chapter 5. Internal Forces and Displacements of the Axis of an Element;70
6.5.1;5.1. The Second Stage of Discretization of a Structure,;70
6.5.2;5.2. A Straight Element under Tension, Compression or Torsion,;71
6.5.3;5.3. Straight Element under Bending,;74
6.5.4;5.4. Element on an Elastic Foundation,;79
6.5.5;5.5. Element Subjected to Bending Moment and Large Axial Force,;83
6.5.6;5.6. Element in the Shape of in-Plane Curved Bar,;86
6.6;Chapter 6. Static Equations of Bar Structures and Fundamental Solution Methods;100
6.6.1;6.1. General Remarks,;100
6.6.2;6.2. Equations of Kinematics, Equilibrium and Elasticity for a Space Truss,;101
6.6.3;6.3. Equations of Kinematics, Equilibrium and Elasticity for a Plane Frame,;107
6.6.4;6.4. Analysis of a Complete Set of Equations,;116
6.6.5;6.5. Isostatic Structures,;117
6.6.6;6.6. The Direct Stiffness Method (Displacement Method),;118
6.6.7;6.7. The Direct Flexibility Method (Force Method),;119
6.6.8;6.8. Final Remarks,;122
6.7;Chapter 7. Isostatic Systems;123
6.7.1;7.1. Multi Span Hinged Beams,;123
6.7.2;7.2. Plane Trusses,;136
6.8;Chapter 8. The Direct Flexibility Method (Force Method);142
6.8.1;8.1. The Set of Canonical Equations of the Direct Flexibility Method,;142
6.8.2;8.2. Influence Lines,;149
6.8.3;8.3. Selection of the Primary System,;159
6.9;9. The Direct Stiffness Method (Displacement Method);173
6.9.1;9.1. Frames with Inextensible Bars,;173
6.9.2;9.2. Frames on Continuous Foundations,;178
6.9.3;9.3. Frames Loaded by Considerable Axial Forces,;181
6.10;References to Part;190
7;Part 2: Dynamics of Bars and Bar Structures;196
7.1;Chapter 1. Introduction;198
7.2;Chapter 2. Bars with Infinitely Many Dynamic Degrees of Freedom;202
7.2.1;2.1. General Relations,;202
7.2.2;2.2. Vibration of a Straight Bar,;204
7.2.3;2.3. Vibrations of a Curved Bar,;216
7.2.4;2.4. The Influence of Axial Forces and Elastic Foundation on Transverse Vibrationsof a Bar,;220
7.3;Chapter 3. Vibration of Composed Bar Structures;224
7.3.1;3.1. General Remarks;224
7.3.2;3.2. The Direct Flexibility Method (Force Method). Volterra's Integral Equations,;224
7.3.3;3.3. The Direct Stiffness Method (Displacement Method),;232
7.4;Chapter 4. Structures with a Finite Number of Dynamic Degrees of Freedom;246
7.4.1;4.1. Some Techniques of Reducing the Number of Degrees of Freedom,;246
7.4.2;4.2. Integration Techniques for Matrix Equations of Motion,;250
7.5;References to Part 2,;258
8;Part 3: Stability of Bars and Bar Structures;262
8.1;Introduction;264
8.2;Chapter 1. Fundamental Concepts and Stability Criteria;265
8.2.1;1.1. The Definition of Stability of Equilibrium of an Elastic Body,;265
8.2.2;1.2. The Kinetic Criterion of Stability,;266
8.2.3;1.3. The Static Criterion of Stability,;269
8.2.4;1.4. The Energy Form of the Static Criterion,;271
8.2.5;1.5. Stability Versus Buckling,;273
8.3;Chapter 2. Elastic Stability of Axially Compressed Prismatic Bars;274
8.3.1;2.1. The Euler Problem,;274
8.3.2;2.2. The Influence of the Behaviour of Loading on the Critical Value,;278
8.3.3;2.3. Postcritical Behaviour of Bars under Compression,;289
8.3.4;2.4. Stability of Bars under Distributed Loadings,;294
8.3.5;2.5. Stability of Bars in an Elastic Medium,;299
8.3.6;2.6. Multi-Span Bars. Elastic Supports,;302
8.4;Chapter 3. Approximate Calculation Methods for Critical Loadings;305
8.4.1;3.1. The Collocation Method,;305
8.4.2;3.2. The Iteration Method,;306
8.4.3;3.3. Energy (Variational) Methods,;307
8.4.4;3.4. Orthogonalization Methods,;310
8.4.5;3.5. The Trace of the Kemel of Integral Equation Method,;312
8.4.6;3.6. The Method of Assumption of an Exact Solution,;313
8.4.7;3.7. The Finite Diff'erence Method,;313
8.4.8;3.8. The Finite Element Method,;314
8.4.9;3.9. Approximate Formulae for Combined Loadings,;318
8.5;Chapter 4. Compressed Elastic Bars with Initial Imperfections;319
8.5.1;4.1. Classification of Theories,;319
8.5.2;4.2. Small Deflections of Eccentrically Compressed Bars,;319
8.5.3;4.3. Small Deflections of Compresssed Bars with Initial Curvature,;321
8.5.4;4.4. Finite Deflections of Eccentrically Compressed Bars with Initial Curvature,;323
8.6;Chapter 5. Elastic-Plastic Buckling;330
8.6.1;5.1. Bifurcation of the Equilibrium of Straight Bars,;330
8.6.2;5.2. Empirical Equations for Critical Stress;335
8.6.3;5.3. Small Deflections of Eccentrically Compressed Bars in the Case of Linear PlasticStrain Hardening,;336
8.6.4;5.4. Perfectly Elastic-Plastic Bars under Eccentric Compression,;340
8.6.5;5.5. Buckling Calculation after Polish Standard;341
8.7;Chapter 6. Creep Buckling;344
8.7.1;6.1. Buckling of Bars with Initial Imperfections Subject to Linear Creep,;344
8.7.2;6.2. Buckling of Bars with Initial Imperfections Subject to Non-Linear Creep;347
8.7.3;6.3. Stability of Straight Bars Axially Compressed in Creep Conditions;351
8.8;Chapter 7. Stability and Optimal Design of Compressed Non-Prismatic Bars;355
8.8.1;7.1. Stabihty of Elastic Bars,;355
8.8.2;7.2. Stability of Bars in Elastic-Plastic Range,;358
8.8.3;7.3. Optimal Design of Elastic Bars,;359
8.8.4;7.4. Optimal Design in Elastic-Plastic Range,;364
8.8.5;7.5. Optimal Design in Creep Conditions,;366
8.9;Chapter 8. Spatial Problems of Loss of Stability of Bars;368
8.9.1;8.1. Fundamental Equations,;368
8.9.2;8.2. Stability of Straight Bars under Simultaneous Compression and Torsion,;370
8.9.3;8.3. Stability of Initially Twisted Bars under Compression,;372
8.9.4;8.4. Stability of Helical Springs under Compression,;373
8.9.5;8,5. Lateral Buckling of Beams,;375
8.10;Chapter 9. Problems of Dynamic Buckling;379
8.10.1;9.L Fundamental Equations,;379
8.10.2;9.2. Dynamic Stability under Periodic Axial Forces,;380
8.10.3;9.3. Buckling under Impact Loadings,;384
8.11;Chapter 10. Stability of Bar Structures;386
8.11.1;10.1. Stability of Trusses,;386
8.11.2;10.2. Stability of Frames,;391
8.11.3;10.3. Stability of Arches,;394
8.12;Chapter 11. Some Recent Results;398
8.13;References to Part 3;400
9;Part 4: Mechanics of Thin-Walled Bars;418
9.1;Chapter 1. The Strength Scheme of a Thin-Walled Bar;420
9.1.1;1.1. The Thin-Walled Bar Structure,;420
9.1.2;1.2. Strains and Stresses in the Bar Skin,;421
9.2;Chapter 2. Statics of Bars of Open Cross-Section;425
9.2.1;2.1. Simple Bending of Bar. The Shear Centre,;425
9.2.2;2.2. Torsion of an Open Prismatic Bar,;431
9.2.3;2.3. Determination of Quantities 8.\;436
9.2.4;2.4. Examples of Torsion of an Open Bar,;440
9.2.5;2.5. Simplified Torsion Analysis of a Straight Bar,;447
9.2.6;2.6. Limitations in Application of Theory,;448
9.3;Chapter 3. Statics of Bars of Tubular Cross-Section;451
9.3.1;3.1. Pure Torsion of Thin-Walled Tubes;451
9.3.2;3.2. Simple Bending of a Tubular Bar;455
9.3.3;3.3. Restrained Torsion of a Tubular Bar,;460
9.3.4;3.4. Simplified Determination of Flows q in Tubular Bars;468
9.4;Chapter 4. Statics of Bars of Deformable Cross-Section;470
9.4.1;4.1. The Physical Image of Phenomena. A Partitioning of the Problem,;470
9.4.2;4.2. Analysis of Local Loading in Membrane Approach,;472
9.4.3;4.3. Analysis of Local Loading in Bending Approach,;479
9.4.4;4.4. Analysis of Global Loadings. A Segmental Model of Bar;487
9.5;Chapter 5. Statics of Curved Bars;496
9.5.1;5.1. Plane Bending of a Curved Bar. Special Case,;496
9.5.2;5.2. General Case of Plane Bending of a Bar,;504
9.5.3;5.3. Three-Dimensional Loading of a Plane Curved Bar;509
9.6;Chapter 6. Stability of Thin-Walled Bars;514
9.6.1;6.1. Torsional-FIexural Buckling of a Centrally Compressed Bar,;515
9.6.2;6.2. Torsional-FIexural Buckling of a Bar on Elastic Foundation,;521
9.6.3;6.3. Torsional-FIexural Buckling in an Elastic Medium,;524
9.6.4;6.4. Lateral Buckling of Beams Subjected to Bending,;527
9.7;Chapter 7. Some Recent Results;534
9.8;References to Part 4;536
10;Part 5: Stress Concentration, Contact Stresses;540
10.1;Chapter 1. Introduction;542
10.2;Chapter 2. Stresses Around Cavities and Notches;547
10.2.1;2.1. Stress Concentration, Neuber's Problem,;547
10.2.2;2.2. Stress Concentration in Two-Dimensional Problems,;549
10.2.3;2.3. Plastic Zone Due to Stress Concentration,;559
10.2.4;2.4. Notches in the Two-Dimensional State of Strain or Stress;562
10.2.5;2.5. Stress Concentration in the Vicinity of the Notches for Axially Symmetric Cases;570
10.3;Chapter 3. Stress Concentration in Plates and Shells;575
10.3.1;3.1. Stress in Plates Around Holes;575
10.3.2;3.2. Effect of Reinforcements on the Stress Concentration Around Holes;586
10.3.3;3.3. Stress Concentration Around the Holes in Thin Shells;589
10.4;Chapter 4. Theory of Fracture of Structural Components;591
10.4.1;4.1. Traditional Strength Criteria;591
10.4.2;4.2. Theoretical Strength, Calculations Based on the Strength Theories;593
10.4.3;4.3. Griffith's Theory, Fracture of Brittle Materials,;595
10.4.4;4.4. The Modes of Cracks, Stress Intensity Factors;597
10.4.5;4.5. Irwin's Criterion,;603
10.4.6;4.6. Other Concepts and Hypotheses;605
10.5;Chapter 5. Contact Problems;608
10.5.1;5.1. Attempt of Classification of the Contact Problems;608
10.5.2;5.2. Problems of Punches on Elastic Semi-Space;610
10.5.3;5.3. Compression of Balls and Shafts;617
10.6;References to Part 5,;623
11;Part 6: Axially Symmetrical Problems of Structural Mechanics ;628
11.1;Introduction;630
11.2;Chapter 1. Axially Synmietrical Thick-Walled Elements;632
11.2.1;1.1. The State of Stresses and Strain in a Thick-Walled Cylinder under Pressure, Heatedand Rotating,;633
11.2.2;1.2. Loading of Thick-Walled Cylinders;638
11.2.3;1.3. Thick-Walled Cylinder with Heads;643
11.2.4;1.4. Two- and Multilayer Thick-Walled Cylinder,;644
11.2.5;1.5. Thick-Walled Cylinder in Rotary Motion,;647
11.2.6;1.6. Stresses in a Heated Thick-Walled Cylinder,;649
11.2.7;1.7. Thick-Walled Sphere under Pressure and Temperature,;651
11.2.8;1.8. Combined Axially Symmetrical Problems of Thick-Walled Cylinders;653
11.3;Chapter 2. Circular Plates;657
11.3.1;2.1. The State of Stress in Circularly Symmetrical Plates,;658
11.3.2;2.2. The Differential Equation for Mid-Layer of Circularly Symmetrical Plate. BoundaryConditions,;661
11.3.3;2.3. Particular Case of Circularly Symmetrical Plates;663
11.3.4;2.4. Circular Ring Subjected to Bending by Moments Uniformly Distributed on theCircumference,;672
11.3.5;2.5. Circular Plates Reinforced by Circumferential Ribs,;674
11.3.6;2.6. Circular Plates of Variable Thickness;677
11.3.7;2.7. Axially Symmetrical Heated Plates. Non-Linear Problems;680
11.3.8;2.8. The Case of a Plate Heated to a Moderate Temperature T(r, z),;683
11.3.9;2.9. Thin Axially Symmetrical Circular Plates under Conditions of Large Deflections,;686
11.3.10;2.10. Other Non-Linear Problems of Axially Symmetrical Plates,;688
11.4;Chapter 3. Axially Symmetrical Disks;690
11.4.1;3.1. Heated Rotating Disk of Variable Thickness,;692
11.4.2;3.2. Cases of Unheated Disks of Constant Thickness,;693
11.4.3;3.3. Unheated Rotating Disk of Uniform Strength,;700
11.4.4;3.4. Unheated Disk of Trapezoid Profile,;703
11.4.5;3.5. Heated Disks of Constant Thickness,;704
11.4.6;3.6. Disks of Variable Thickness According to the Equation of Hyperbola Unevenly Heated and at Rest,;708
11.4.7;3.7. The General Differential Equation for Rotating Disks of Arbitrarily VariableThickness, Strongly Heated,;709
11.4.8;3.8. Torque-Induced Shear Stresses in Disks;721
11.4.9;3.9. Heated Rotating Disks under Pressure,;721
11.4.10;3.10. Axially Symmetrical Orthotropic Disks,;722
11.5;Chapter 4. Axially Symmetrical Shells;723
11.5.1;4.1. General Equations of Equilibrium of Shell Element;723
11.5.2;4.2. Axially Symmetrical Shells in Membrane State,;726
11.5.3;4.3. Particular Cases of Shells of Revolution in Membrane State,;727
11.5.4;4.4. Axially Synmietrical Shells in Bending State. Spherical and Conical Shells;730
11.5.5;4.5. Some Important Cases of Shells in Bending State,;734
11.5.6;4.6. Axially Symmetrical Shells Loaded on the Edges;736
11.5.7;4.7. Axially Symmetrical Cylindrical Shells in Bending State;741
11.5.8;4.8. Types of Cylindrical Shells. Loading Cases,;747
11.5.9;4.9. The Second Form of Function w(x) of Cylindrical Shells,;749
11.5.10;4.10. Cylindrical Shells Thermally Loaded,;751
11.5.11;4.11. Cylindrical Shells of Complete Axial Symmetry and Variable Wall Thickness;755
11.5.12;4.12. More General Problems of Cylindrical Shells of Complete Axial Symmetry,;756
11.5.13;4.13. General Remarks on Shell Solving Methods,;757
11.6;Chapter 5. Analysis of Axially Symmetrical Structures;758
11.7;Comments on Some Works Concerning Part 6;771
11.8;References to Part 6;774
12;Additional References;779
13;Subject Index;782