Sobotka Theory of Plasticity and Limit Design of Plates

1. Auflage 2013
ISBN: 978-1-4832-9179-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 18, 657 Seiten, Web PDF

Reihe: Studies in Applied Mechanics

An extensive review of the theory of plasticity, limit design and limit analysis of plates is contained in this volume. Detailed descriptions are given on the plastic behaviour of homogeneous, reinforced and sandwich plates, and on the rise of various yield-line patterns. The volume differs from other books on the plastic analysis of plates by its comprehensive treatment of: the theory of yield fans connected with yield-line planning; the plastic behaviour of plates under combined loadings characterized by the load factors; statical solutions; and continuous, rectangular and skew plates.Before discussing the upper-bound solutions for various types of ultimate loads acting on isotropic, orthotropic and anisotropic plates, the kinematic conditions of the plastic behaviour of plates and the principles and methods of the yield-line theory are examined in detail. Generalized yield conditions of the second degree for orthotropic and anisotropic plates are introduced. Special attention is paid to the rise of yield fans. The concept of yield line planning is also discussed, which may be of practical interest since it indicates the possibilities for preventing the rise of yield fans. Upper-bound and lower-bound solutions for the ultimate uniform load, concentrated loads, triangular and trapexoidal loads, are presented. Similar solutions are provided for continuous loads bounded by various plane and curved surfaces and for various combinations of loads acting on rectangular, polygonal, circular, elliptic and skew plates. Solutions are given for plates on hinged supports, on free supports with elevating corners, on point supports and also for plates with built-in edges. Numerical tables are provided for determining the ultimate loads, bearing moments needed for the given load systems and the parameters of yield-line patterns. The procedures detailed in the volume will prove an indispensable reference source in the practical design of roof, ceiling and bridge slabs.

Autoren/Hrsg.

Sobotka, Z.

Inhaltsverzeichnis

1;Front Cover;1
2;Theory of Plasticity and Limit Design of Plates;4
3;Copyright Page;5
4;Table of Contents;6
5;STUDIES IN APPLIED MECHANICS;3
6;PREFACE;20
7;CHAPTER 1. PLASTIC BEHAVIOUR AND LIMIT ANALYSIS OF PLATES;22
7.1;1-1 Plastic Deformation of Plates;22
7.2;1-2 Plastic Bearing Moments per Unit Length of Plates;25
7.3;1-3 Fundamental Relations and Principles of Limit Analysis of Plates;31
7.4;1-4 Equations of Equilibrium of Plates;36
7.5;1-5 Various Yield Criteria for Plates;39
7.6;1-6 Some Topics of Statical and Kinematic Solutions;59
8;CHAPTER 2. RECTANGULAR PLATES WITH HINGED SUPPORTS;68
8.1;2-1 Uniformly Loaded, Orthotropic, Rectangular Plates with Edges Supported by Hinges;68
8.2;2-2 Uniformly Loaded, Rectangular Plates with Hinged Supportsalong Three Edges;86
8.3;2-3 Uniformly Loaded Rectangular Plates Supported on Two Opposite Edges;106
8.4;2-4 Rectangular Plates with a Triangular Load Distribution;106
8.5;2-5 Rectangular Plates with a Trapezoidal Load and Hinged Supports along the Periphery;111
8.6;2-6 Uniformly Loaded Rectangular Plates with the Point Load in the Centre;115
8.7;2-7 Uniformly Loaded, Long, Rectangular Plates with a Point Load and Supported along the Opposite Short Edges;132
8.8;2-8 Uniformly Loaded, Wide, Rectangular Plates Supported along Two Opposite Edges and with a Point Load;139
8.9;2-9 Static Solutions for the Ultimate Loads on Rectangular Plates;152
9;CHAPTER 3. YIELD-LINE PLANNING FOR RECTANGULAR PLATES WITH A CONCENTRATED LOAD;187
9.1;3-1 Ultimate Concentrated Load Applied in the Centre;187
9.2;3-2 Ultimate Point Load Eccentrically Applied to Rectangular Plates on Hinged Supports;208
9.3;3-3 Concluding Remarks;245
10;CHAPTER 4. POLYGONAL, CIRCULAR AND ELLIPTICAL PLATES; PLATES OF SPECIAL FORMS;250
10.1;4-1 Isotropic Polygonal Plates with Straight Yield Lines;250
10.2;4-2 Isotropic Polygonal Plates with Yield Fans;258
10.3;4-3 Uniformly Loaded, Polygonal Plates with Yield Fans;264
10.4;4-4 Singular Yield-Line Patterns of Polygonal Plates;278
10.5;4-5 Orthotropic Polygonal Plates;284
10.6;4-6 Regular Polygonal, Orthotropic Plates with Yield Fans;290
10.7;4-7 Plates with Curvilinear Boundaries;296
10.8;4-8 Circular Plates with Hinged Supports;305
10.9;4-9 Elliptical Plates with Hinged Supports;309
10.10;4-10 Polygonal Plates with Rounded Corners;313
10.11;4-11 Uniformly Loaded, Polygonal Plates Supported at the Cornersby Columns and with a Point Load in the Centre;323
10.12;4-12 Uniformly Loaded Circular Plates Supported on the Peripheral Columns, with a Point Load in the Centre;327
10.13;4-13 Plates with Overhanging Boundaries;330
10.14;4-14 The Statical Solution for the Bearing Capacity of Polygonal Plates;342
11;CHAPTER 5. BUILT-IN PLATES;345
11.1;5-1 Uniformly Loaded, Rectangular, Built-in Plates;345
11.2;5-2 Uniformly Loaded, Orthotropic, Rectangular Plates Built-inalong Three Edges;358
11.3;5-3 Uniformly Loaded, Orthotropic, Rectangular Plates with Built-in and Hinged Edges;367
11.4;5-4 Built-in Plates with Uniform and Concentrated Loads;377
11.5;5-5 Rectangular Plates, Built-in along Three Edges, with Uniformand Concentrated Loads;386
11.6;5-6 Statical Solutions for the Bearing Capacity of Rectangular,Built-in Plates;395
11.7;5-7 Built-in, Polygonal Plates;405
12;CHAPTER 6. SKEW PLATES;407
12.1;6-1 Elementary Solutions for Skew Plates on Hinged Supports;407
12.2;6-2 Hinge-Supported, Skew Plates with Yield Fans;414
12.3;6-3 Ultimate Uniform Load of Skew Plates with Hinged Supportsalong Three Edges;425
12.4;6-4 Skew Plates with Hinged Supports along Three Edges andwith Yield Fans;439
12.5;6-5 Skew Plates Supported on Two Opposite Edges;450
12.6;6-6 Uniformly Loaded, Skew Plates with Hinged Supports alongthe Periphery and a Point Load in the Centre;462
12.7;6-7 Built-in Skew Plates;475
12.8;6-8 Experimental Investigation of the Skew Reinforced-ConcretePlates;489
13;CHAPTER 7. PLATES WITH FREE SUPPORTS;497
13.1;7-1 Regular Polygonal Plates;497
13.2;7-2 Uniformly Loaded, Rectangular Plates with Free Supports;500
14;CHAPTER 8. THE BEARING CAPACITY OF PLATES WITH SHEAR EFFECTS;511
14.1;8-1 Shear Effects Determined by the Kinematic Method;511
14.2;8-2 Shear Effects in the Statical Method;520
15;CHAPTER 9. CONTINUOUS RECTANGULAR PLATES;522
15.1;9-1 Uniformly Loaded, Continuous, Rectangular Plates with Peripheral Hinged Supports;522
15.2;9-2 Inner Fields of Orthotropic, Continuous Rectangular Plates with Yield Fans;542
15.3;9-3 Continuous Rectangular Plates with Free Edges;553
15.4;9-4 The Boundary Fields with Yield Fans;564
15.5;9-5 Continuous Rectangular Plates with Uniform and Concentrated Loads;574
15.6;9-6 The Static Method for the Limit Analysis of Continuous Rectangular Plates;581
15.7;9-7 MUSHROOM PLATES;588
16;CHAPTER 10. CONTINUOUS SKEW PLATES;590
16.1;10-1 Uniformly Loaded, Continuous Skew Plates with Peripheral Hinged Supports;590
16.2;10-2 Inner Fields of Continuous Skew Plates with Yield Fans;602
16.3;10-3 Continuous Skew Plates with Free Edges;612
16.4;10-4 The Boundary Fields of Continuous Skew Plates with Yield Fans;629
17;BIBLIOGRAPHY;643
18;INDEX;649