viii Contents 1.7 Long Uniformly Loaded Rectangular Plates Having a Small Initial Cylindrical Curvature...... 27 1.8 Cylindrical Bending of a Plate on an Elastic Foundation.… 30 2. Pure Bending of Plates .............. 33 2.9 Slope and Curvature of Slightly Bent Plates....… 33 2.10 Relations between Bending Moments and Curvature in Pure Bending of Plates ........... 37 2.11 Particular Cases of Pure Bending 42 2.12 Strain Energy in Pure Bending of Plates...... 46 2.13 Limitations on the application of the Derived Formulas 47 2.14 Thermal Stresses in Plates with Clamped Edges. 49 3. Symmetrical Bending of Circular Plates 51 3.15 Differential Equation for Symmetrical Bending of Laterally Loaded Circular Plates ........ 51 3.16 Uniformly Loaded Circular Plates ............ 54 3.17 Circular Plate with a Circular Hole at the Center ............ 58 3.18 Circular Plate Concentrically Loaded … 63 3.19 Circular Plate Loaded at the Center 67 3.20 Corrections to the Elementary Theory of Symmetrical Bending of Circular Plates ...... 72 This page has been reformatted by Knovel to provide easier navigation.viii Contents This page has been reformatted by Knovel to provide easier navigation. 1.7 Long Uniformly Loaded Rectangular Plates Having a Small Initial Cylindrical Curvature ..................................................... 27 1.8 Cylindrical Bending of a Plate on an Elastic Foundation ........................................ 30 2. Pure Bending of Plates ................................... 33 2.9 Slope and Curvature of Slightly Bent Plates ........................................................... 33 2.10 Relations between Bending Moments and Curvature in Pure Bending of Plates ............ 37 2.11 Particular Cases of Pure Bending ................ 42 2.12 Strain Energy in Pure Bending of Plates ...... 46 2.13 Limitations on the Application of the Derived Formulas ......................................... 47 2.14 Thermal Stresses in Plates with Clamped Edges ........................................................... 49 3. Symmetrical Bending of Circular Plates ........ 51 3.15 Differential Equation for Symmetrical Bending of Laterally Loaded Circular Plates ........................................................... 51 3.16 Uniformly Loaded Circular Plates ................. 54 3.17 Circular Plate with a Circular Hole at the Center .......................................................... 58 3.18 Circular Plate Concentrically Loaded ........... 63 3.19 Circular Plate Loaded at the Center ............. 67 3.20 Corrections to the Elementary Theory of Symmetrical Bending of Circular Plates ....... 72