Nonlinear structural engineering : with unique theories and methods to solve effectively complex nonlinear problems

The practicing design engineer, who deals with the design of structures and structural and mechanical components in general, is often confronted with nonlinear problems and he/she needs to develop a design procedure that deals e?ectively with such types of problems. Flexible members, structures subjected to blast and earthquake, suspension bridges, aircraft structural elements, and so on, are only a few examples where understanding of their nonlinear behavior is extremely important for an adequate and safe design. Many of our nonlinear structures are composed of beam elements that can be taken apart from the structure, and their behavior can be studied by satisfying appropriate boundary conditions. Once we are in a position to understand completely the behavior of the nonlinear beam problem, we can then expand our knowledge e?ectively so that it includes a complete und- standing of the nonlinear behavior of two-dimensional and three-dimensional structures and structural components. In part, the purpose of this book is to concentrate its e?orts on the n- linear static and dynamic analysis of structural beam components that are widely used in everyday engineering applications. The analysis and design of the beam component can become very complicated when it is subjected to a large deformation, or when its material is permitted to be stressed well - yond its elastic limit and all the way to failure.

Author Notes

Demeter G. Fertis is professor of civil engineering at the University of Akron. He was previously an associate professor at the University of Iowa and at Wayne State University, and a research engineer in the Michigan State Department of Transportation. Dr. Fertis was also visiting professor at the National Technical University in Athens, Greece. During his teaching career, he taught more than twenty graduate courses on different subjects, in the Civil, Mechanical, and Engineering Mechanics Departments. He has received a BS degree (1952) in civil engineering and urban planning and an MS degree (1955) in civil engineering from Michigan State University, East Lansing, and a Doctor of Engineering degree (1964) from the National Technical University of Athens, Greece. Dr. Fertis has consulted for NASA, Ford Motor Company, the Atomic Power Development Associates, General Motors, Boeing Aircraft Company, Lockheed California Company, Goodyear Aerospace, and the Department of the Navy. He has developed patents, which received international attention and used by professional engineers. He is the author of many books, published by major publishers, and numerous articles in professional journals and proceedings. A member of ASCE, ASME, the American Academy of Mechanics, Who's Who in America, Who's Who in the World, and many other organizations, Professor Fertis has served as a professional journal editor and as a member of many national and international technical committees.

Dr. Fertis is now an Emeritus Professor at the University of Akron and devotes his time doing scholarly research, writing scholarly books, giving lectures, and advancing technology by developing new methodologies for the solution of complicated engineering problems.

Reviews 1

Choice Review

Fertis (emer., civil engineering, Univ. of Akron) effectively brings to this book many years of teaching, research, and industrial experience on nonlinear structural engineering. He successfully presents usually complex and difficult techniques of solving such problems in a manner that is concise, clear, and easily understood. He presents fundamental theoretical concepts effectively, using adequate illustrations and structures of practical importance, first presenting nonlinear solution methodologies in detail for uniform and variable stiffness beams under several loading conditions. Other structures and structural components treated include columns, plates, thick cylinders, suspension bridges, and buildings, as well as static and dynamic nonlinear problems. The last chapter, on nonlinear/inelastic analyses of suspension bridges, multistory buildings under earthquakes, eccentrically loaded columns, plates, and thick cylinders, will be significantly interesting to practicing engineers and researchers. Also provided is methodology for solving nonlinear problems using finite element techniques. Each chapter concludes with problems to solve. Extremely useful reference list; two appendixes, one with a computer program for the Acceleration Impulse Extrapolation Method for solving nonlinear problems. For libraries serving engineering and physical science programs. ^BSumming Up: Recommended. Upper-division undergraduates through professionals. R. B. Malla University of Connecticut

1 Basic Theories and Principles of Nonlinear Beam Deformations	p. 1
1.1 Introduction	p. 1
1.2 Brief Historical Developments Regarding the Static and the Dynamic Analysis of Flexible members	p. 1
1.3 The Euler-Bernoulli Law of Linear and Nonlinear Deformations for Structural Members	p. 8
1.4 Integration of the Euler-Bernoulli Nonlinear Differential Equation	p. 10
1.5 Simpson's One-Third Rule	p. 14
1.6 The Elastica Theory	p. 16
1.7 Moment and Stiffness Dependence on the Geometry of the Deformation of Flexible Members	p. 22
1.8 General Theory of the Equivalent Systems for Linear and Nonlinear Deformations	p. 29
1.8.1 Nonlinear Theory of the Equivalent Systems: Derivation of Pseudolinear Equivalent Systems	p. 30
1.8.2 Nonlinear Theory of the Equivalent Systems: Derivation of Simplified Nonlinear Equivalent Systems	p. 40
1.8.3 Linear Theory of the Equivalent Systems	p. 44
2 Solution Methodologies for Uniform Flexible Beams	p. 63
2.1 Introduction	p. 63
2.2 Pseudolinear Analysis for Uniform Flexible Cantilever Beams Loaded with Uniformly Distributed Loading Throughout their Length	p. 64
2.3 Pseudolinear Analysis for Uniform Simply Supported Beams Loaded with a Uniformly Distributed Loading Throughout their Length	p. 71
2.4 Flexible Uniform Simply Supported Beam Loaded with a Vertical Concentrated Load	p. 76
2.5 Uniform Statically indeterminate Single Span Flexible Beam Loaded with a Uniformly Distributed Load w o on its Entire Span	p. 82
2.6 Uniform Statically Indeterminate Single Span Flexible Beam Subjected to a Vertical Concentrated Load	p. 86
2.7 Flexible Uniform Cantilever Beam Under Combined Loading Conditions	p. 90
2.8 Flexible Uniform Cantilever Beam Under Complex Loading Conditions	p. 96
2.8.1 Application of Equivalent Pseudolinear Systems	p. 96
2.8.2 Deriving Simpler Nonlinear Equivalent Systems	p. 101
3 Solution Methodologies for Variable Stiffness Flexible Beams	p. 105
3.1 Introduction	p. 105
3.2 Flexible Tapered Cantilever Beam with a Concentrated Vertical Load at its Free End	p. 105
3.3 Doubly Tapered Flexible Cantilever Beam Subjected to a Uniformly Distributed Loading	p. 113
3.4 Solution of the Problem in the Preceding Section by Using a Simplified Nonlinear Equivalent System	p. 119
3.5 Flexible Tapered Simply Supported Beam with Uniform Load	p. 121
3.6 Flexible Tapered Simply Supported Beam Carrying a Trapezoidal Load	p. 125
3.7 Using an Alternate Approach to Derive a Simpler Equivalent Nonlinear System of Constant Stiffness	p. 128
3.7.1 Application to Cantilever Flexible Beam Problems	p. 129
3.7.2 Application to Flexible Simply Supported Beam Problems	p. 133
4 Inelastic Analysis of Structural Components	p. 143
4.1 Introduction	p. 143
4.2 Theoretical Aspects of Inelastic Analysis	p. 144
4.2.1 The Theory and Concept of the Reduced Modulus E r	p. 144
4.2.2 Application of the Method of the Equivalent Systems for Inelastic Analysis	p. 155
4.3 Inelastic Analysis of Simply Supported Beams	p. 165
4.4 Ultimate Design Loads Using Inelastic Analysis	p. 172
5 Vibration Analysis of Flexible Structural Components	p. 185
5.1 Introduction	p. 185
5.2 Nonlinear Differential Equations of Motion	p. 186
5.2.1 The general Nonlinear Differential Equation of Motion	p. 186
5.2.2 Small Amplitude Vibrations of Flexible Members	p. 189
5.3 Application of the Theory and Method	p. 193
5.3.1 Free Vibration of Uniform Flexible Cantilever Beams	p. 193
5.3.2 Free Vibration of Flexible Simply supported Beams	p. 204
5.4 The Effect of Mass Position Change During the Vibration of Flexible Members	p. 211
5.5 Galerkin's Finite Element Method (GFEM)	p. 213
5.6 Vibration of Tapered Flexible Simply Supported Beams Using Galerkin's FEM	p. 221
5.7 Concluding Remarks	p. 224
6 Suspension Bridges, Failures, Plates, and Other Types of Nonlinear Structural Problems	p. 229
6.1 Introduction	p. 229
6.2 Brief Discussion on Fundamental Aspects of Suspension Bridges	p. 229
6.3 The Collapse of the Tacoma Narrows Suspension Bridge	p. 232
6.4 Other Failures and What We Learn from Them	p. 235
6.5 Eccentrically Loaded Columns	p. 237
6.6 Inelastic Analysis of Members with Axial Restraints Using Equivalent Systems	p. 240
6.7 The Longest Cable-Stayed Suspension Bridge in the World	p. 253
6.8 Inelastic Analysis of Thin Rectangular Plates	p. 259
6.9 Inelastic Earthquake Response of Multistory Buildings	p. 269
6.9.1 Resistant R of a Structure	p. 270
6.9.2 Multistory Buildings Subjected to Strong Earthquakes	p. 276
6.10 Elastic and Inelastic Analysis of Thick-Walled Cylinders Subjected to Uniform External and Internal Pressures	p. 285
6.10.1 Elastic Analysis of Thick Cylinders	p. 285
6.10.2 Inelastic Analysis of Thick Cylinders	p. 290
6.11 Inelastic Analysis of Members of Non-Rectangular Cross Sections	p. 294
6.12 Torsion Beyond the Elastic Limit of the Material	p. 297
6.13 Vibration Analysis of Inelastic Structural Members	p. 299
6.14 Inelastic Analysis of Flexible Members	p. 307
Appendix A Acceleration Impulse Extrapolation Method (AIEM)	p. 323
Appendix B Computer Program Using the AIEM for the Elastoplastic Analysis in Example 6.5	p. 327
References	p. 329

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