Theory of Arched Structures: Strength, Stability, Vibration

458 Pages·2012·3.21 MB·English

by  Igor A Karnovsky (auth.)

Theory of Arched Structures

Igor A. Karnovsky
Theory of Arched Structures
Strength, Stability, Vibration
IgorA.Karnovsky
NorthviewPl811
V3J3R4Coquitlam
Canada
[email protected]
ISBN978-1-4614-0468-2 e-ISBN978-1-4614-0469-9
DOI10.1007/978-1-4614-0469-9
SpringerNewYorkDordrechtHeidelbergLondon
LibraryofCongressControlNumber:2011937582
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Inmemory ofProf. Anatoly B.Morgaevsky

Preface
In modern engineering, as a basis of construction, arches have a diverse range of
applications.Todaythetheoryofarcheshasreachedalevelthatissuitableformost
engineeringapplications.Manymethodspertainingtoarchanalysiscanbefoundin
scientific literature. However, most of this material is published in highly
specialized journals, obscure manuals, and inaccessible books. This is not
surprising, as the intensive development of arch theory, particularly stability and
vibrationhavemostlyoccurredinthe1940stothe1960s.Therefore,mostengineers
lacktheopportunitytoutilizethesedevelopmentsintheirpractice.
Theauthorhascommittedtothegoalofpresentingabookwhichencompasses
essentialandtestedmethodsonfundamentalmethodsofarchanalysisandequally
importantproblems.
TheobjectiveoftheBookistoprovidetoreaderswithdetailedproceduresforanalysisof
the strength, stability, and vibration of various types of arched structures, using exact
analyticalmethodsofclassicalStructuralAnalysis.
In2004,professorL.A.Godoypublishedthearticle“Arches:ANeglectedTopic
in Structural Analysis Courses.” This in-depth investigation highlights a deep rift
betweenthemodernlevelofdevelopmentofarchtheoryandthelevelofpresenta-
tionofthistheoryinexistingmaterialonstructuralanalysis.
In2009,theauthorofthisbook,withco-authorO.Lebedpublishedthetextbook
“Advanced Methods of Structural Analysis” (Springer), in which arch theory is
presentedinamuchgreaterdepthandvolumethaninexistingtextbooks.However,
the issue of producing a single book which covers both general and specialized
problems of arches remained unsolved. The book presented here sheds light on
issues of strength, stability, and vibrations, as well as special problems of arches
andarchedstructures.
In this book special attention is directed toward the discussion of fundamental
properties of structures. An engineer who is armed with fundamental knowledge
andmeansofcomputationisessentiallysettosucceedinmoderndayengineering.
Solutionsofproblemsofstrength,stability,andvibrationsofarchesinmostcases
vii
viii Preface
are broken down to basic formulas which can be easily applied to engineering
practice.
This book is based on the author’s experience as a teacher and consultant in
structuralmechanics. It is intendedfor seniorundergraduate students instructural
engineering and for postgraduate students who are concerned with different pro-
blemsofarchesstructures.Thebookwillbeausefulreferenceforengineersinthe
structuralindustry.
Vancouver,Canada IgorA.Karnovsky
Distribution of Material in the Book
Thisbookcontainsanintroduction,fourparts(ninechapters),andanappendix.
The first part “Strength” contains three chapters. Chapter 1 is devoted to
fundamental methods of determining displacement of elastic structures in general
accompaniedbyexamplesspecificallyforarches.
Chapter2coverstheanalysisofthree-hingedarches,whileanalysisofredundant
archesisconsideredinChap.3;inthesechaptersaspecialattentionisdedicatedto
theanalysisofarchedstructuresusinginfluencelines.
Second part “Stability” contains two chapters. Chapter 4 provides analytical
methods of the stability of arches. These methods are based on the integration of
differentialequations.
Chapter5presentsSmirnov’smatrixmethodandapproximatemethod.Approx-
imatemethodisbasedontheapproximationofthearchbystraightmemberswith
subsequentapplicationoftheprecisedisplacementmethodincanonicalform.
Thethirdpart,“Vibration”containstwochapters.Chapter6dealswithcompu-
tation of eigenvalues and eigenfunctions for arches. For analysis of the circular
uniform arch, Lamb’s differential equation is used; for analysis of parabolic
uniform arch the Rabinovich’s model is applied. The frequency of vibration for
archeswithdifferentratio“rise/span”ofanarcharepresentedonthebasisofthis
model.
Chapter7presentsforcedvibrationsofarches.
The fourth part of the book, “Special Topics” holds the goal of presenting
introductory information regarding problems which until now have only been
discussedinspecializedliterature.Chapter8containsthestaticnonlinearproblems.
They are plastic analysis of the arches and arched structures with one-sided con-
straints. Chapter 9 is devoted to dynamical stability of arches, and dynamics of
archedstructuressubjectedtomovinginertialload.
Finally, the appendix contains the fundamental tabulated data essential for
engineeringpracticeinvolvingarches.
Sections2.1,2.2,2.4,and2.6werewrittenbyOlgaLebed.
ix