| Basic Theories and Principles of Nonlinear Beam Deformations | p. 1 |
| Introduction | p. 1 |
| Brief Historical Developments Regarding the Static and the Dynamic Analysis of Flexible members | p. 1 |
| The Euler-Bernoulli Law of Linear and Nonlinear Deformations for Structural Members | p. 8 |
| Integration of the Euler-Bernoulli Nonlinear Differential Equation | p. 10 |
| Simpson's One-Third Rule | p. 14 |
| The Elastica Theory | p. 16 |
| Moment and Stiffness Dependence on the Geometry of the Deformation of Flexible Members | p. 22 |
| General Theory of the Equivalent Systems for Linear and Nonlinear Deformations | p. 29 |
| Nonlinear Theory of the Equivalent Systems: Derivation of Pseudolinear Equivalent Systems | p. 30 |
| Nonlinear Theory of the Equivalent Systems: Derivation of Simplified Nonlinear Equivalent Systems | p. 40 |
| Linear Theory of the Equivalent Systems | p. 44 |
| Solution Methodologies for Uniform Flexible Beams | p. 63 |
| Introduction | p. 63 |
| Pseudolinear Analysis for Uniform Flexible Cantilever Beams Loaded with Uniformly Distributed Loading Throughout their Length | p. 64 |
| Pseudolinear Analysis for Uniform Simply Supported Beams Loaded with a Uniformly Distributed Loading Throughout their Length | p. 71 |
| Flexible Uniform Simply Supported Beam Loaded with a Vertical Concentrated Load | p. 76 |
| Uniform Statically indeterminate Single Span Flexible Beam Loaded with a Uniformly Distributed Load woon its Entire Span | p. 82 |
| Uniform Statically Indeterminate Single Span Flexible Beam Subjected to a Vertical Concentrated Load | p. 86 |
| Flexible Uniform Cantilever Beam Under Combined Loading Conditions | p. 90 |
| Flexible Uniform Cantilever Beam Under Complex Loading Conditions | p. 96 |
| Application of Equivalent Pseudolinear Systems | p. 96 |
| Deriving Simpler Nonlinear Equivalent Systems | p. 101 |
| Solution Methodologies for Variable Stiffness Flexible Beams | p. 105 |
| Introduction | p. 105 |
| Flexible Tapered Cantilever Beam with a Concentrated Vertical Load at its Free End | p. 105 |
| Doubly Tapered Flexible Cantilever Beam Subjected to a Uniformly Distributed Loading | p. 113 |
| Solution of the Problem in the Preceding Section by Using a Simplified Nonlinear Equivalent System | p. 119 |
| Flexible Tapered Simply Supported Beam with Uniform Load | p. 121 |
| Flexible Tapered Simply Supported Beam Carrying a Trapezoidal Load | p. 125 |
| Using an Alternate Approach to Derive a Simpler Equivalent Nonlinear System of Constant Stiffness | p. 128 |
| Application to Cantilever Flexible Beam Problems | p. 129 |
| Application to Flexible Simply Supported Beam Problems | p. 133 |
| Inelastic Analysis of Structural Components | p. 143 |
| Introduction | p. 143 |
| Theoretical Aspects of Inelastic Analysis | p. 144 |
| The Theory and Concept of the Reduced Modulus Er | p. 144 |
| Application of the Method of the Equivalent Systems for Inelastic Analysis | p. 155 |
| Inelastic Analysis of Simply Supported Beams | p. 165 |
| Ultimate Design Loads Using Inelastic Analysis | p. 172 |
| Vibration Analysis of Flexible Structural Components | p. 185 |
| Introduction | p. 185 |
| Nonlinear Differential Equations of Motion | p. 186 |
| The general Nonlinear Differential Equation of Motion | p. 186 |
| Small Amplitude Vibrations of Flexible Members | p. 189 |
| Application of the Theory and Method | p. 193 |
| Free Vibration of Uniform Flexible Cantilever Beams | p. 193 |
| Free Vibration of Flexible Simply supported Beams | p. 204 |
| The Effect of Mass Position Change During the Vibration of Flexible Members | p. 211 |
| Galerkin's Finite Element Method (GFEM) | p. 213 |
| Vibration of Tapered Flexible Simply Supported Beams Using Galerkin's FEM | p. 221 |
| Concluding Remarks | p. 224 |
| Suspension Bridges, Failures, Plates, and Other Types of Nonlinear Structural Problems | p. 229 |
| Introduction | p. 229 |
| Brief Discussion on Fundamental Aspects of Suspension Bridges | p. 229 |
| The Collapse of the Tacoma Narrows Suspension Bridge | p. 232 |
| Other Failures and What We Learn from Them | p. 235 |
| Eccentrically Loaded Columns | p. 237 |
| Inelastic Analysis of Members with Axial Restraints Using Equivalent Systems | p. 240 |
| The Longest Cable-Stayed Suspension Bridge in the World | p. 253 |
| Inelastic Analysis of Thin Rectangular Plates | p. 259 |
| Inelastic Earthquake Response of Multistory Buildings | p. 269 |
| Resistant R of a Structure | p. 270 |
| Multistory Buildings Subjected to Strong Earthquakes | p. 276 |
| Elastic and Inelastic Analysis of Thick-Walled Cylinders Subjected to Uniform External and Internal Pressures | p. 285 |
| Elastic Analysis of Thick Cylinders | p. 285 |
| Inelastic Analysis of Thick Cylinders | p. 290 |
| Inelastic Analysis of Members of Non-Rectangular Cross Sections | p. 294 |
| Torsion Beyond the Elastic Limit of the Material | p. 297 |
| Vibration Analysis of Inelastic Structural Members | p. 299 |
| Inelastic Analysis of Flexible Members | p. 307 |
| Acceleration Impulse Extrapolation Method (AIEM) | p. 323 |
| Computer Program Using the AIEM for the Elastoplastic Analysis in Example 6.5 | p. 327 |
| References | p. 329 |
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