Dym / Williams Analytical Estimates of Structural Behavior

Erscheinungsjahr 2012
ISBN: 978-1-4398-7091-4
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 223 Seiten

Explicitly reintroducing the idea of modeling to the analysis of structures, Analytical Estimates of Structural Behavior presents an integrated approach to modeling and estimating the behavior of structures. With the increasing reliance on computer-based approaches in structural analysis, it is becoming even more important for structural engineers to recognize that they are dealing with models of structures, not with the actual structures. As tempting as it is to run innumerable simulations, closed-form estimates can be effectively used to guide and check numerical results, and to confirm physical insights and intuitions.

Spend Less Time Generating Numbers, and More Time Understanding What They Mean

This book encourages readers to think about structures and their models in a way that is rooted in classic elementary elasticity—depending less on advanced mathematical techniques and more on the dimensions and magnitudes of the underlying physics. The authors stretch the mold, emphasizing and more explicitly describing the modeling process. The focus is on learning which calculations to perform and how to validate and interpret the results—skills that will be increasingly useful for professional engineers.

Chapters cover:

- Key principles and techniques of mathematical modeling, including dimensional analysis, scaling, linearity, and balance and conservation laws

- Basic structural models

- How to develop and express physical intuition

- How to track the behavior of arches under lateral load

- Two methods of analyzing coupled discrete systems—Castigliano’s theorems and Rayleigh’s quotient—to lay a foundation for their application to continuous systems

- How to derive simple, accurate estimates of the transverse displacements of structures modeled in terms of coupled Timoshenko beams

- How to analyze the dimensional behavior and calculate numerical values of fundamental frequencies of structures modeled in terms of Euler-Bernoulli, Timoshenko, and coupled-beam systems

Taking a unique approach, Analytical Estimates of Structural Behavior is suitable for advanced undergraduates, as well as graduate students and practitioners, who want to spend less time and effort generating numbers, and more time understanding what those numbers mean.

Zielgruppe

Practicing structural engineers; graduate students in structural engineering and applied mechanics; and practicing civil, mechanical, and aerospace engineers.

Autoren/Hrsg.

Dym, Clive L.

Williams, Harry E.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Technische Wissenschaften Bauingenieurwesen Technische Dynamik (Modalanalyse), Erdbebensicherheit

Inhaltsverzeichnis

Mathematical Modeling for Structural Analysis
Summary
Principles of Mathematical Modeling
Abstraction and Scale (I)
Dimensional Consistency and Dimensional Analysis
Abstraction and Scale (II)
Notes on Approximating: Dimensions and Numbers
The Assumption of Linear Behavior
Conservation and Balance Principles
Conclusions
Bibliography

Structural Models and Structural Modeling
Summary
Bars, Beams, Arches, Frames, and Shells
One-Dimensional Structural Elements
Two-Dimensional Structural Elements
Modeling Structural Supports
Indeterminacy, Redundancy, Load Paths, and Stability
Modeling Structural Loading
Modeling Structural Materials
Idealization and Discretization in Structural Modeling
Bibliography

Exploring Intuition: Beams, Trusses, and Cylinders
Summary
Introduction
Engineering Beams: The Two-Dimensional Model
Reasoning Intuitively about Engineering Beams
Trusses as Beams
Pressurized Circular Cylinders: A Two-Dimensional Model
Conclusions
Bibliography

Estimating Stresses and Displacements in Arches
Summary
Introduction
Normal and Bending Stresses in Transversely Loaded Arches
Arches under Centrally Applied, "Dead" Loading
Shallow Arches under Centrally Directed, "Dead" Loading
Arches under Gravitational Loading
Interpreting Arch Behavior
Shallow Curved Beams under End Loading
Interpreting Curved Beam Behavior
Conclusions
Bibliography

Estimating the Behavior of Coupled Discrete Systems
Summary
Introduction
Extending the Castigliano Theorems to Discrete Systems
Formally Proving the Castigliano Theorem Extensions
Rayleigh Quotients for Discrete Systems
Conclusions
Bibliography

Buildings Modeling as Coupled Beams: Static Response Estimates
Summary
Introduction
Coupled Timoshenko Beams: Exact Solutions
Coupled Timoshenko Beams: Castigliano Estimates (I)
Validating Castigliano-Based Deflection Estimates
Coupled Timoshenko Beams: Castigliano Estimates (II)
Remarks on Modeling Buildings as Coupled-Beam Systems
Conclusions
Appendix A: Exact Solution for Coupled Timoshenko Beams
Appendix B: The Coupled Euler–Shear System as a Limit
Appendix C: Special Cases for Two Timoshenko Cantilevers
Bibliography

Buildings Modeled as Coupled Beams: Natural Frequency Estimates
Summary
Introduction
Rayleigh Quotients for Elementary Beams
Beams and Models of Buildings
Frequency–Height Dependence in Coupled Two-Beam Models
Frequency-Height Dependence in Timoshenko Beams
Comparing Frequencies for Coupled Two-Beam Models
Conclusions
Bibliography

Index

Über Autor(innen)

Clive L. Dym is Fletcher Jones Professor of Engineering Design and director of the Center for Design Education at Harvey Mudd College. After receiving his PhD from Stanford University, Dr. Dym held appointments at the University of Buffalo; the Institute for Defense Analyses; Carnegie Mellon University; Bolt, Beranek and Newman; and the University of Massachusetts at Amherst. He has held visiting appointments at the TECHNION-Israel Institute of Technology, the Institute for Sound and Vibration Research at Southampton, Stanford, Xerox PARC, Carnegie Mellon, Northwestern, USC, and the Singapore University of Technology and Design. Dr. Dym has authored or coauthored more than a dozen books and 90 refereed journal articles, was founding editor of the journal Artificial Intelligence for Engineering Design, Analysis, and Manufacturing, and has served on the editorial boards of several other journals, including the ASME’s Journal of Mechanical Design. Dr. Dym is also a co-winner of the NAE’s 2012 Bernard M. Gordon Prize "for creating and disseminating innovations in undergraduate engineering design education to develop engineering leaders" (NAE).

Harry E. Williams is Professor Emeritus of Engineering at Harvey Mudd College. After receiving his PhD from the California Institute of Technology, Dr. Williams joined the research staff of the Jet Propulsion Laboratory and then joined Harvey Mudd College as one of the founding faculty of its engineering program, serving there for 40 years. He has also been a Fulbright fellow at the University of Manchester, a liaison scientist for the Office of Naval Research, and a consultant to General Dynamics, Teledyne Microelectronics, the Naval Weapons Center, Aerojet-General, and the Boeing Company. He has published widely over the years, reflecting his interests in fluid mechanics, thermoelasticity, and the mechanics of solids and structures.