The Theory of Plates and Shells (McGraw-Hill Classic Textbook Reissue Series)

Title......Page 1 Preface......Page 3 Notation......Page 4 Contents......Page 6 Introduction......Page 17 1.1 Differential Equation for Cylindrical Bending of Plates......Page 20 1.2 Cylindrical Bending of Uniformly Loaded Rectangular Plates with Simply Supported Edges......Page 22 1.3 Cylindrical Bending of Uniformly Loaded Rectangular Plates with Built-in Edges......Page 29 1.4 Cylindrical Bending of Uniformly Loaded Rectangular Plates with Elastically Built-in Edges......Page 33 1.5 The Effect on Stresses and Deflections of Small Displacements of Longitudinal Edges in the Plane of the Plate......Page 36 1.6 An Approximate Method of Calculating the Parameter u......Page 40 1.7 Long Uniformly Loaded Rectangular Plates Having a Small Initial Cylindrical Curvature......Page 43 1.8 Cylindrical Bending of a Plate on an Elastic Foundation......Page 46 2.9 Slope and Curvature of Slightly Bent Plates......Page 49 2.10 Relations between Bending Moments and Curvature in Pure Bending of Plates......Page 53 2.11 Particular Cases of Pure Bending......Page 58 2.12 Strain Energy in Pure Bending of Plates......Page 62 2.13 Limitations on the Application of the Derived Formulas......Page 63 2.14 Thermal Stresses in Plates with Clamped Edges......Page 65 3.15 Differential Equation for Symmetrical Bending of Laterally Loaded Circular Plates......Page 67 3.16 Uniformly Loaded Circular Plates......Page 70 3.17 Circular Plate with a Circular Hole at the Center......Page 74 3.18 Circular Plate Concentrically Loaded......Page 79 3.19 Circular Plate Loaded at the Center......Page 83 3.20 Corrections to the Elementary Theory of Symmetrical Bending of Circular Plates......Page 88 4.21 The Differential Equation of the Deflection Surface......Page 95 4.22 Boundary Conditions......Page 99 4.23 Alternative Method of Derivation of the Boundary Conditions......Page 104 4.24 Reduction of the Problem of Bending of a Plate to That of Deflection of a Membrane......Page 108 4.25 Effect of Elastic Constants on the Magnitude of Bending Moments......Page 113 4.26 Exact Theory of Plates......Page 114 5.27 Simply Supported Rectangular Plates under Sinusoidal Load......Page 121 5.28 Navier Solution for Simply Supported Rectangular Plates......Page 124 5.29 Further Applications of the Navier Solution......Page 127 5.30 Alternate Solution for Simply Supported and Uniformly Loaded Rectangular Plates......Page 129 5.31 Simply Supported Rectangular Plates under Hydrostatic Pressure......Page 140 5.32 Simply Supported Rectangular Plate under a Load in the Form of a Triangular Prism......Page 146 5.33 Partially Loaded Simply Supported Rectangular Plate......Page 151 5.34 Concentrated Load on a Simply Supported Rectangular Plate......Page 157 5.35 Bending Moments in a Simply Supported Rectangular Plate with a Concentrated Load......Page 159 5.36 Rectangular Plates of Infinite Length with Simply Supported Edges......Page 165 5.37 Bending Moments in Simply Supported Rectangular Plates under a Load Uniformly Distributed over the Area of a Rectangle......Page 174 5.38 Thermal Stresses in Simply Supported Rectangular Plates......Page 178 5.39 The Effect of Transverse Shear Deformation on the Bending of Thin Plates......Page 181 5.40 Rectangular Plates of Variable Thickness......Page 189 6.41 Bending of Rectangular Plates by Moments Distributed along the Edges......Page 196 6.42 Rectangular Plates with Two opposite Edges Simply Supported and the Other Two Edges Clamped......Page 201 6.43 Rectangular Plates with Three Edges Simply Supported and One Edge Built In......Page 208 6.44 Rectangular Plates with All Edges Built In......Page 213 6.45 Rectangular Plates with One Edge or Two Adjacent Edges Simply Supported and the Other Edges Built In......Page 221 6.46 Rectangular Plates with Two Opposite Edges Simply Supported, the Third Edge Free, and the Fourth Edge Built In or Simply Supported......Page 224 6.47 Rectangular Plates with Three Edges Built In and the Fourth Edge Free......Page 227 6.48 Rectangular Plates with Two Opposite Edges Simply Supported and the Other Two Edges Free or Supported Elastically......Page 230 6.49 Rectangular Plates Having Four Edges Supported Elastically or Resting on Corner Points with All Edges Free......Page 234 6.50 Semi-infinite Rectangular Plates under Uniform Pressure......Page 237 6.51 Semi-infinite Rectangular Plates under Concentrated Loads......Page 241 7.52 Simply Supported Continuous Plates......Page 245 7.53 Approximate Design of Continuous Plates with Equal Spans......Page 252 7.54 Bending of Plates Supported by Rows of Equidistant Columns (Flat Slabs)......Page 261 7.55 Flat Slab Having Nine Panels and Slab with Two Edges Free......Page 269 7.56 Effect of a Rigid Connection with Column on Moments of the Flat Slab......Page 273 8.57 Bending Symmetrical with Respect to a Center......Page 275 8.58 Application of Bessel Functions to the Problem of the Circular Plate......Page 281 8.59 Rectangular and Continuous Plates on Elastic Foundation......Page 285 8.60 Plate Carrying Rows of Equidistant Columns......Page 292 8.61 Bending of Plates Resting on a Semi-infinite Elastic Solid......Page 294 9.62 Equations of Bending of Plates in Polar Coordinates......Page 298 9.63 Circular Plates under a Linearly Varying Load......Page 301 9.64 Circular Plates under a Concentrated Load......Page 306 9.65 Circular Plates Supported at Several Points along the Boundary......Page 309 9.66 Plates in the Form of a Sector......Page 311 9.67 Circular Plates of Nonuniform Thickness......Page 314 9.68 Annular Plates with Linearly Varying Thickness......Page 319 9.69 Circular Plates with Linearly Varying Thickness......Page 321 9.70 Nonlinear Problems in Bending of Circular Plates......Page 324 9.71 Elliptical Plates......Page 326 9.72 Triangular Plates......Page 329 9.73 Skewed Plates......Page 334 9.74 Stress Distribution around Holes......Page 335 10.75 Singularities in Bending of Plates......Page 341 10.76 The Use of Influence Surfaces in the Design of Plates......Page 344 10.77 Influence Functions and Characteristic Functions......Page 350 10.78 The Use of Infinite Integrals and Transforms......Page 352 10.79 Complex Variable Method......Page 356 10.80 Application of the Strain Energy Method in Calculating Deflections......Page 358 10.81 Alternative Procedure in Applying the Strain Energy Method......Page 363 10.82 Various Approximate Methods......Page 364 10.83 Application of Finite Differences Equations to the Bending of Simply Supported Plates......Page 367 10.84 Experimental Methods......Page 378 11.85 Differential Equation of the Bent Plate......Page 380 11.86 Determination of Rigidities in Various Specific Cases......Page 382 11.87 Application of the Theory to the Calculation of Gridworks......Page 385 11.88 Bending of Rectangular Plates......Page 387 11.89 Bending of Circular and Elliptic Plates......Page 392 12.90 Differential Equation of the Deflection Surface......Page 394 12.91 Rectangular Plate with Simply Supported Edges under the Combined Action of Uniform Lateral Load and Uniform Tension......Page 396 12.92 Application of the Energy Method......Page 398 12.93 Simply Supported Rectangular Plates under the Combined Action of Lateral Loads and of Forces in the Middle Plane of the Plate......Page 403 12.94 Circular Plates under Combined Action of Lateral Load and Tension or Compression......Page 407 12.95 Bending of Plates with a Small Initial Curvature......Page 409 13.96 Bending of Circular Plates by Moments Uniformly Distributed along the Edge......Page 412 13.97 Approximate Formulas for Uniformly Loaded Circular Plates with Large Deflections......Page 416 13.98 Exact Solution for a Uniformly Loaded Circular Plate with a Clamped Edge......Page 420 13.99 A Simply Supported Circular Plate under Uniform Load......Page 424 13.100 Circular Plates Loaded at the Center......Page 428 13.101 General Equations for Large Deflections of Plates......Page 431 13.102 Large Deflections of Uniformly Loaded Rectangular Plates......Page 437 13.103 Large Deflections of Rectangular Plates with Simply Supported Edges......Page 441 14.104 Definitions and Notation......Page 445 14.105 Shells in the Form of a Surface of Revolution and Loaded Symmetrically with Respect to Their Axis......Page 449 14.106 Particular Cases of Shells in the Form of Surfaces of Revolution......Page 452 14.107 Shells of Constant Strength......Page 458 14.108 Displacements in Symmetrically Loaded Shells Having the Form of a Surface of Revolution......Page 461 14.109 Shells in the Form of a Surface of Revolution under Unsymmetrical Loading......Page 463 14.110 Stresses Produced by Wind Pressure......Page 465 14.111 Spherical Shell Supported at Isolated Points......Page 469 14.112 Membrane Theory of Cylindrical Shells......Page 473 14.113 The Use of a Stress Function in Calculating Membrane Forces of Shells......Page 477 15.114 A Circular Cylindrical Shell Loaded Symmetrically with Respect to Its Axis......Page 482 15.115 Particular Cases of Symmetrical Deformation of Circular Cylindrical Shells......Page 487 15.116 Pressure Vessels......Page 497 15.117 Cylindrical Tanks with Uniform Wall Thickness......Page 501 15.118 Cylindrical Tanks with Nonuniform Wall Thickness......Page 504 15.119 Thermal Stresses in Cylindrical Shells......Page 513 15.120 Inextensional Deformation of a Circular Cylindrical Shell......Page 517 15.121 General Case of Deformation of a Cylindrical Shell......Page 523 15.122 Cylindrical Shells with Supported Edges......Page 530 15.123 Deflection of a Portion of a Cylindrical Shell......Page 532 15.124 An Approximate Investigation of the Bending of Cylindrical Shells......Page 535 15.125 The Use of a Strain and Stress Function......Page 538 15.126 Stress Analysis of Cylindrical Roof Shells......Page 540 16.127 Equations of Equilibrium......Page 549 16.128 Reduction of the Equations of Equilibrium to Two Differential Equations of the Second Order......Page 553 16.129 Spherical Shell of Constant Thickness......Page 556 16.130 Approximate Methods of Analyzing Stresses in Spherical Shells......Page 563 16.131 Spherical Shells with an Edge Ring......Page 571 16.132 Symmetrical Bending of Shallow Spherical Shells......Page 574 16.133 Conical Shells......Page 578 16.134 General Case of Shells Having the Form of a Surface of Revolution......Page 582 Name Index......Page 585 Index......Page 590