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Preface | |

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Acknowledgments | |

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List of Symbols | |

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*Fundamentals | |

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Basic Concepts | |

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Introduction | |

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Methods of Analysis | |

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Conditions of Equilibrium | |

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Stress Defined | |

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Components of Stress | |

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Sign Convention | |

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Internal-Force Resultants | |

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Differential Equations of Equilibrium | |

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Transformation of Stress | |

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Mohr's Circle for Stress | |

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Strain Defined | |

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Components of Strain | |

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Conditions of Compatibility | |

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Large Strains | |

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Transformation of Strain | |

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Engineering Materials | |

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Stress-Strain Diagrams | |

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Hooke's Law, Poisson's Ratio | |

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Rational Design Procedure | |

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Factor of Safety | |

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Problem Formulation and Solutions | |

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Significant Digits | |

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Computational Tools | |

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References | |

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Problems | |

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Stresses in Simple Structural Members | |

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Introduction | |

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Types of Structures | |

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Axially Loaded Members | |

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Stress Concentration Factors | |

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Torsion of Circular Bars | |

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Shear Stress | |

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Angle of Twist | |

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Stresses in Beams | |

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Normal Stress | |

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Shear Stress | |

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Shear Flow | |

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Deflection of Beams by Integration | |

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Beam Deflections by Superposition | |

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Thin-Walled Pressure Vessels | |

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Yield and Fracture Criteria | |

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Maximum Principal Stress Theory | |

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Coulomb-Mohr Theory | |

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Maximum Shear Stress Theory | |

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Maximum Distortion Energy Theory | |

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A Typical Case of Combined Loadings | |

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Strain Energy | |

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CastigUano's Theorem | |

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Statically Indeterminate Structures | |

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References | |

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Problems | |

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Plates | |

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Elements of Plate-Bending Theory | |

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Introduction | |

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Historical Development of Plate and Shell Theory | |

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General Behavior of Plates | |

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Strain-Curvature Relations | |

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Mohrs Circle of Curjvature | |

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Stresses and Stress Resultants | |

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Equations for Transformation of Moment | |

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Variation of Stress within a Plate | |

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The Governing Equation for Deflection of Plates | |

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Reduction of Plate-Bending Problem to That of Deflection of a Membrane | |

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Boundary Conditions | |

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Exact Theory of Plates | |

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Methods for Solution of Plate Deflections | |

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Strain Energy of Plates | |

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Energy Methods in Theory of Plates | |

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The Principle of Virtual Work | |

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The Principle of Minimum Potential Energy | |

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The Ritz Method | |

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*Natural Frequencies of Plates by the Energy Method | |

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References | |

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Problems | |

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Circular Plates | |

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Introduction | |

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Basic Relations in Polar Coordinates | |

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The Axisymmetrical Bending | |

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Equations of Equilibrium for AxisymmetricallyLoaded Circular Plates | |

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Uniformly Loaded Circular Plates | |

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*Effect of Shear on the Plate Deflection | |

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Local Stresses at the Point of Application of a Concentrated Load | |

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Circular Plates under a Concentrated Load at the Center | |

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A Short Catalog of Solutions | |

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Annular Plates with Simply Supported Outer Edges | |

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Deflection and Stress by Superposition | |

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Design Tables for Annular Plates | |

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The Ritz Method Applied to Bending of Circular Plates | |

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Asymmetrical Bending of Circular Plates | |

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*Deflection by the Reciprocity Theorem | |

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References | |

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Problems | |

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Rectangular Plates | |

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Introduction | |

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Navier's Solution for Simply Supported Rectangular Plates | |

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Simply Supported Rectangular Plates under Various Loadings | |

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Lï¿½vy's Solution for Rectangular Plates | |

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Simply Supported Rectangular Plate underUniform Loading | |

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Lï¿½vy's Method Applied to Rectangular Plates under Nonuniform Loading | |

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Rectangular Plates under ^Distributed Edge Moments | |

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Method of Superposition Applied to Bending ofRectangular Plates | |

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*The Strip Method | |

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*Simply Supported Continuous Rectangular Plates | |

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*Rectangular Plates Supported by Intermediate Columns | |

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Rectangular Plates on Elastric Foundation | |

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Simply Supported Plates | |

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Plates with Arbitrary Boundary Conditions | |

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The Ritz Method Applied to Bending of Rectangular Plates | |

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References | |

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Problems | |

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Plates of Various Geometrical Fprms | |

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Introduction | |

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*Method of Images | |

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Equilateral Triangular Plate with Simply Supported Edges | |

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Equilateral Triangtllar Plate under Uniform Moment M<sub>0</sub> along its Boundary | |

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Equilateral Triangular Plate under Uniform Load p<sub>0</sub> | |

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Elliptical Plates | |

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Uniformly Loaded Elliptic Plate with Clamped Edge | |

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Uniformly Loaded Elliptic Plate with SimplySupporred Edge | |

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Sector-Shaped Plates | |

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*Stress Concentration around Holes in a Plate | |

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References | |

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Problems | |

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Numerical Methods | |

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Introduction | |

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Finite Differences | |

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Solution of the Finite Difference Equations | |

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Load Representation | |

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*Plates with Curved Boundaries | |

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*The Polar Mesh | |

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*The Triangular Mesh | |

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The Finite Element Method | |

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Properties of a Finite Element | |

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Displacement Matrix | |

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Strain, Stress, and Elasticity Matrices | |

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Formulation of the Finite Element Method | |

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Beam Element | |

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Methods of Assemblage of the [k]e's | |

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Triangular Finite Element | |

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Displacement Function | |

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The Stiffness Matrix | |

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External Nodal Forces | |

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Rectangular Finite Element | |

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Displacement Function | |

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The Stiffness Matrix | |

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External Nodal Forces | |

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References | |

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Problems | |

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Anisotropic Plates | |

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Introduction | |

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Basic Relationships | |

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Determination of Rigidities | |

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Application of Navier's Method | |

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Application of Lï¿½vy's Method | |

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Application of the Finite Difference Method | |

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Elliptic and Circular Orthotropic Plates | |

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Deflection by the Energy Method | |

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*Plates of Isotropic Multilayers | |

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The Finite Element Solution | |

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A Typical Layered Orthotropic Plate | |

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Laminated Composite Plates | |

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References | |

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Problems | |

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Plates under Combined Lateral and In-Plane Loads | |

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Introduction | |

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Governing Equation for the Deflection Surface | |

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Buckling of Plates | |

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Application of the Energy Method | |

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*The Finite Difference Solution | |

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Plates with Small Initial Curvature | |

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*Bending to a Cylindrical Surface | |

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References | |

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Problems | |

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Large Deflections of Plates | |

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Introduction | |

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Plate Behavior When Deflections Are Large | |

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Comparison of Small- and Large-Deflection Theories | |

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An Approximate Method for the Circular Plate | |

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Exact Solution for the Circular Plate Problem | |

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General Equations for Large Deflections of Plates | |

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Deflections by the Energy Method | |

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The Finite Element Solution | |

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Rectangular Finite Element373 | |

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References | |

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Problems | |

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Thermal Stresses in Plates | |

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Introduction | |

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Stress, Strain, and Displacement Relations | |

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Stress Resultants | |

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The Governing Differential Equations | |

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Simply Supported Rectangular Plate Subject to an Arbitrary Temperature Distribution | |

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Simply Supported Rectangular Plate with Temperature Distribution Varying over the Thickness | |

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Analogy between Thermal and Isothermal PlateProblems | |

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Plates with Clamped Edges | |

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Plates with Simply Supported or Free Edges | |

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Axisymmetrically Heated Circular Plates | |

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References | |

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Problems | |

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Shells | |

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Membrane Stresses in Shells | |

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Introduction | |

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Theories and General Behavior of Shells | |

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Load Resistance Action of a Shell | |

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Geometry of Shells of Revolution | |

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Symmetrically Loaded Shells of Revolution | |

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Some Typical Cases of Shells: of Revolution | |

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Spherical Shell | |

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Conical Shell | |

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Circular Cylindrical Shell | |

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Axially Symmetric Deformation | |

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Asymmetrically Loaded Shells of Revolution | |

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*Shells of Revolution under Wind Loading | |

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Cylindrical Shells of General'shape | |

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*Folded Structures | |

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*Shells of General Form | |

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*Breakdown of Elastic Action in Shells | |

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References | |

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Problems | |

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Bending Stresses in Shells | |

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Introduction | |

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Shell Stress Resultants | |

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Force, Moment, and Displacement Relations | |

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Compound Stresses in a Shell | |

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Strain Energy in the Bending and Stretching of Shells | |

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Axisym metrically Loaded Circular Cylindrical Shells | |

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A Typical Case of the Axisym metricallyLoaded Cylindrical Shell | |

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Shells of Revolution under Axisym metrical Loads | |

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Conical Shells | |

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Spherical Shells | |

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Cylindrical Shells | |

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Governing Equations for Axisym metrical Displacements | |

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Spherical Shells under Axisym metrical Load | |

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Comparison of Bending and Membrane Stresses | |

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*Simplified Theory of Spherical Shells underAxisymmetrical Load | |

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The Finite Element Representations of Shells of General Shape | |

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The Finite Element Solution of Axisym metrically Loaded Shells | |

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References | |

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Problems | |

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Applications to Pipes, Tanks, and Pressure Vessels | |

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Introduction | |

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Pipes Subjected to Edge Forces and Moments | |

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Long Pipes | |

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Short Pipes | |

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Reinforced Cylinders | |

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Cylinders with Collars That Prohibit Deflection | |

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Cylinders with Collars That Resist Deflection | |

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Cylinders with Closed Ends | |

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Cylindrical Tanks | |

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Thermal Stresses in Cylinders | |

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Uniform Temperature Distribution | |

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Radial Temperature Gradient | |

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Thermal Stresses in Compound Cylinders | |

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Discontinuity Stresses in Pressure Vessels | |

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Cylindrical Vessel with Hemispherical Heads | |

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Cylindrical Vessel with Ellipsoidal Heads | |

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Cylindrical Vessel with Flat Heads | |

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*Design Formulas for Conventional Pressure Vessels | |

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References | |

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Problems | |

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Cylindrical Shells under General Loads | |

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Introduction | |

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Differential Equations of Equilibrium | |

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Kinematic Relationships | |

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The Governing Equations for Deflections | |

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*Approximate Relations | |

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A Typical Case of Asymmetrical Loading | |

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Curved Circular Panels | |

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*A Simple Theory of Bending of Curved Circular Panels | |

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*Curved Circular Panels with Ends Simply Supported and Straight Edges Free | |

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Inextensional Deformations | |

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A Typical Layered Orthotropic Cylindrical Shell | |

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Laminated Composite Cylindrical Shells | |

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*Symmetrical Buckling under Uniform Axial Pressure | |

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Nonsymmetrical Buckling under Uniform Axial Compression | |

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References | |

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Problems | |

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Appendices | |

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Fourier Series Expansions | |

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Single Fourier Series | |

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Half-Range Expansions | |

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Double Fourier Series | |

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Reference | |

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Tables | |

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Conversion Factors: SI Units to U.S. Customary Units | |

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SI Unit Prefixes | |

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Typical Properties for Some Common Materials | |

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Properties of Common Areas | |

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Beam Deflection and Slopes | |

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Restrained Beam Reactions and Deflections | |

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Answers to Selected Problems | |

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Index | |