Contents xiⅷ 9.69 Circular Plates with Linearly Varying Thickness........ 305 9.70 Nonlinear Problems in Bending of Circular Plates… 308 9.71 Elliptical Plates.......... 310 9.72 Triangular Plates.… 313 9.73 Skewed Plates........... 318 9.74 Stress Distribution around Holes ............... 319 10.Special and Approximate Methods in Theory of Plates ........ 325 10.75 Singularities in Bending of Plates 325 10.76 The Use of Influence Surfaces in the Design of Plates 328 10.77 Influence Functions and Characteristic Functions....... 334 10.78 The Use of Infinite Integrals and Transforms........ 336 10.79 Complex Variable Method ........... 340 10.80 Application of the Strain Energy Method in Calculating Deflections ........ 342 10.81 Alternative Procedure in Applying the Strain Energy Method...... 347 10.82 Various Approximate Methods ........ 348 10.83 Application of Finite Differences Equations to the Bending of Simply Supported Plates … 351 10.84 Experimental Methods 362 This page has been reformatted by Knovel to provide easier navigation
Contents xiii This page has been reformatted by Knovel to provide easier navigation. 9.69 Circular Plates with Linearly Varying Thickness ..................................................... 305 9.70 Nonlinear Problems in Bending of Circular Plates ........................................................... 308 9.71 Elliptical Plates ............................................. 310 9.72 Triangular Plates .......................................... 313 9.73 Skewed Plates ............................................. 318 9.74 Stress Distribution around Holes .................. 319 10. Special and Approximate Methods in Theory of Plates ............................................................ 325 10.75 Singularities in Bending of Plates ................. 325 10.76 The Use of Influence Surfaces in the Design of Plates ........................................... 328 10.77 Influence Functions and Characteristic Functions ...................................................... 334 10.78 The Use of Infinite Integrals and Transforms ................................................... 336 10.79 Complex Variable Method ............................ 340 10.80 Application of the Strain Energy Method in Calculating Deflections ................................. 342 10.81 Alternative Procedure in Applying the Strain Energy Method .................................. 347 10.82 Various Approximate Methods ..................... 348 10.83 Application of Finite Differences Equations to the Bending of Simply Supported Plates ........................................................... 351 10.84 Experimental Methods ................................. 362
xiv Contents 11.Bending of Anisotropic Plates ....................... 364 11.85 Differential Equation of the Bent Plate … 364 11.86 Determination of Rigidities in Various Specific Cases ........ 366 11.87 Application of the Theory to the Calculation of Gridworks .... 369 11.88 Bending of Rectangular Plates 371 11.89 Bending of Circular and Elliptic Plates 376 12.Bending of Plates under the Combined Action of Lateral Loads and Forces in the Middle Plane of the Plate ............ 378 12.90 Differential Equation of the Deflection Surface......... 378 12.91 Rectangular Plate with Simply Supported Edges under the Combined Action of Uniform Lateral Load and Uniform Tension ......... 380 12.92 Application of the Energy Method ............ 382 12.93 Simply Supported Rectangular Plates under the Combined Action of Lateral Loads and of Forces in the Middle Plane of the Plate .............. 387 12.94 Circular Plates under Combined Action of Lateral Load and Tension or Compression ......... 391 12.95 Bending of Plates with a Small Initial Curvature 393 This page has been reformatted by Knovel to provide easier navigation
xiv Contents This page has been reformatted by Knovel to provide easier navigation. 11. Bending of Anisotropic Plates ........................ 364 11.85 Differential Equation of the Bent Plate ......... 364 11.86 Determination of Rigidities in Various Specific Cases ............................................. 366 11.87 Application of the Theory to the Calculation of Gridworks .............................. 369 11.88 Bending of Rectangular Plates ..................... 371 11.89 Bending of Circular and Elliptic Plates ......... 376 12. Bending of Plates under the Combined Action of Lateral Loads and Forces in the Middle Plane of the Plate ................................ 378 12.90 Differential Equation of the Deflection Surface ......................................................... 378 12.91 Rectangular Plate with Simply Supported Edges under the Combined Action of Uniform Lateral Load and Uniform Tension ........................................................ 380 12.92 Application of the Energy Method ................ 382 12.93 Simply Supported Rectangular Plates under the Combined Action of Lateral Loads and of Forces in the Middle Plane of the Plate ................................................... 387 12.94 Circular Plates under Combined Action of Lateral Load and Tension or Compression ................................................ 391 12.95 Bending of Plates with a Small Initial Curvature ..................................................... 393
Contents XV 13.Large Deflections of Plates ............ 396 13.96 Bending of Circular Plates by Moments Uniformly Distributed along the Edge 396 13.97 Approximate Formulas for Uniformly Loaded Circular Plates with Large Deflections ........ 400 13.98 Exact Solution for a Uniformly Loaded Circular Plate with a Clamped Edge ........... 404 13.99 A Simply Supported Circular Plate under Uniform Load ........ 408 13.100 Circular Plates Loaded at the Center .......... 412 13.101 General Equations for Large Deflections of Plates........ 415 13.102 Large Deflections of Uniformly Loaded Rectangular Plates ....... 421 13.103 Large Deflections of Rectangular Plates with Simply Supported Edges ......... 425 14.Deformation of Shells without Bending 429 14.104 Definitions and Notation ....... 429 14.105 Shells in the Form of a Surface of Revolution and Loaded Symmetrically with Respect to Their Axis.......... 433 14.106 Particular Cases of Shells in the Form of Surfaces of Revolution ........ 436 14.107 Shells of Constant Strength ........................ 442 14.108 Displacements in Symmetrically Loaded Shells Having the Form of a Surface of Revolution ...... 445 This page has been reformatted by Knovel to provide easier navigation
Contents xv This page has been reformatted by Knovel to provide easier navigation. 13. Large Deflections of Plates ............................. 396 13.96 Bending of Circular Plates by Moments Uniformly Distributed along the Edge ........... 396 13.97 Approximate Formulas for Uniformly Loaded Circular Plates with Large Deflections ......... 400 13.98 Exact Solution for a Uniformly Loaded Circular Plate with a Clamped Edge ............ 404 13.99 A Simply Supported Circular Plate under Uniform Load ................................................ 408 13.100 Circular Plates Loaded at the Center ........... 412 13.101 General Equations for Large Deflections of Plates ....................................................... 415 13.102 Large Deflections of Uniformly Loaded Rectangular Plates ....................................... 421 13.103 Large Deflections of Rectangular Plates with Simply Supported Edges ...................... 425 14. Deformation of Shells without Bending ......... 429 14.104 Definitions and Notation ............................... 429 14.105 Shells in the Form of a Surface of Revolution and Loaded Symmetrically with Respect to Their Axis ............................ 433 14.106 Particular Cases of Shells in the Form of Surfaces of Revolution ................................. 436 14.107 Shells of Constant Strength ......................... 442 14.108 Displacements in Symmetrically Loaded Shells Having the Form of a Surface of Revolution .................................................... 445
xvi Contents 14.109 Shells in the Form of a Surface of Revolution under Unsymmetrical Loading.… 447 14.110 Stresses Produced by Wind Pressure 449 14.111 Spherical Shell Supported at Isolated Points 453 14.112 Membrane Theory of Cylindrical Shells 457 14.113 The Use of a Stress Function in Calculating Membrane Forces of Shells 461 15.General Theory of Cylindrical Shells ............ 466 15.114 A Circular Cylindrical Shell Loaded Symmetrically with Respect to Its Axis ........ 466 15.115 Particular Cases of Symmetrical Deformation of Circular Cylindrical Shells ... 471 15.116 Pressure Vessels ....... 481 15.117 Cylindrical Tanks with Uniform Wall Thickness........ 485 15.118 Cylindrical Tanks with Nonuniform Wall Thickness......... 488 15.119 Thermal Stresses in Cylindrical Shells 497 15.120 Inextensional Deformation of a Circular Cylindrical Shell 501 15.121 General Case of Deformation of a Cylindrical Shell 507 15.122 Cylindrical Shells with Supported Edges 514 15.123 Deflection of a Portion of a Cylindrical Shell 516 This page has been reformatted by Knovel to provide easier navigation
xvi Contents This page has been reformatted by Knovel to provide easier navigation. 14.109 Shells in the Form of a Surface of Revolution under Unsymmetrical Loading ........................................................ 447 14.110 Stresses Produced by Wind Pressure ......... 449 14.111 Spherical Shell Supported at Isolated Points ........................................................... 453 14.112 Membrane Theory of Cylindrical Shells ....... 457 14.113 The Use of a Stress Function in Calculating Membrane Forces of Shells ...... 461 15. General Theory of Cylindrical Shells ............. 466 15.114 A Circular Cylindrical Shell Loaded Symmetrically with Respect to Its Axis ......... 466 15.115 Particular Cases of Symmetrical Deformation of Circular Cylindrical Shells .... 471 15.116 Pressure Vessels ......................................... 481 15.117 Cylindrical Tanks with Uniform Wall Thickness ..................................................... 485 15.118 Cylindrical Tanks with Nonuniform Wall Thickness ..................................................... 488 15.119 Thermal Stresses in Cylindrical Shells ......... 497 15.120 Inextensional Deformation of a Circular Cylindrical Shell ............................................ 501 15.121 General Case of Deformation of a Cylindrical Shell ............................................ 507 15.122 Cylindrical Shells with Supported Edges ...... 514 15.123 Deflection of a Portion of a Cylindrical Shell ............................................................. 516
Contents xvii 15.124 An Approximate Investigation of the Bending of Cylindrical Shells ........... 519 15.125 The Use of a Strain and Stress Function..... 522 15.126 Stress Analysis of Cylindrical Roof Shells ... 524 16.Shells Having the Form of a Surface of Revolution and Loaded Symmetrically with Respect to Their Axis....... 533 16.127 Equations of Equilibrium .......... 533 16.128 Reduction of the Equations of Equilibrium to Two Differential Equations of the Second Order ........ 537 16.129 Spherical Shell of Constant Thickness 540 16.130 Approximate Methods of Analyzing Stresses in Spherical Shells ........... 547 16.131 Spherical Shells with an Edge Ring 555 16.132 Symmetrical Bending of Shallow Spherical Shells........... 558 16.133 Conical Shells ...... 562 16.134 General Case of Shells Having the Form of a Surface of Revolution ........ 566 Name Index 569 Index 575 This page has been reformatted by Knovel to provide easier navigation
Contents xvii This page has been reformatted by Knovel to provide easier navigation. 15.124 An Approximate Investigation of the Bending of Cylindrical Shells ........................ 519 15.125 The Use of a Strain and Stress Function ..... 522 15.126 Stress Analysis of Cylindrical Roof Shells .... 524 16. Shells Having the Form of a Surface of Revolution and Loaded Symmetrically with Respect to Their Axis ...................................... 533 16.127 Equations of Equilibrium .............................. 533 16.128 Reduction of the Equations of Equilibrium to Two Differential Equations of the Second Order ............................................... 537 16.129 Spherical Shell of Constant Thickness ......... 540 16.130 Approximate Methods of Analyzing Stresses in Spherical Shells ......................... 547 16.131 Spherical Shells with an Edge Ring ............. 555 16.132 Symmetrical Bending of Shallow Spherical Shells ........................................................... 558 16.133 Conical Shells .............................................. 562 16.134 General Case of Shells Having the Form of a Surface of Revolution ............................ 566 Name Index ............................................................. 569 Index ........................................................................ 575