Deflections of Elastic Structures

Chapter

Abstract

This chapter describes some effective methods for computing different types of deflections of deformable structures. The structure may be subjected to different actions, such as variety of external loads, change of temperature, settlements of supports, and errors of fabrication. Advantages and disadvantages of each method and field of their effective application are discussed. Much attention is given to a graph multiplication method which is a most effective method for bending structures. Fundamental properties of deformable structures are described by reciprocal theorems.

Keywords

Shrinkage Betti 

References

  1. [Bir68].
    Birger, I.A., Panovko, J.G.: (Биpгep ИA, Пaнoвкo ЯГ, Peд. Пpoчнocть, уcтoйчивocть, кoлeбaния. Cпpaвoчник в тpex тoмax. M.: Maшинocтpoeниe, 1968) (1968)Google Scholar
  2. [Cra00].
    Craig, R.R.: Mechanics of Materials. Wiley, New York (2000)Google Scholar
  3. [Dar89].
    Darkov, A.V. (ed.): Structural Mechanics, 6th edn. Mir Publishers, Moscow (1989)Google Scholar
  4. [Kar10].
    Karnovsky, I.A., Lebed, O.: Advanced Methods of Structural Analysis. Springer, New York (2010)CrossRefGoogle Scholar
  5. [Kir76].
    Kirchhoff, G.R.: Vorlesungen über mathematische Physic. Mechanik, Bd.1, Leipzig (1876)Google Scholar
  6. [Lam1888].
    Lamb, H.: (1888) Proc. Math. Soc., v.XIX, LondonGoogle Scholar
  7. [Lov20].
    Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity, 3rd edn. The University Press, Cambridge (4th edn. 1927) (1920)Google Scholar
  8. [Rab60].
    Rabinovich, I.M.: (Paбинoвич ИM. Ocнoвы cтpoитeльнoй мexaники cтepжнeвыx cиcтeм, 3 изд. M.: Гoccтpoйиздaт, 1960) (1960)Google Scholar
  9. [Rek73].
    Rekach, V.G.: (Peкaч BГ. Pукoвoдcтвo к peшeнию зaдaч пpиклaднoй тeopии упpугocти, M.: Bыcшaя шкoлa, 1973) (1973)Google Scholar
  10. [Roa75].
    Roark, R.J.: Formulas for Stress and Strain, 5th edn. McGraw-Hill, New York (1975)Google Scholar
  11. [Rzh55].
    Rzhanitsun, A.R.: (Pжaницын AP. Уcтoйчивocть paвнoвecия упpугиx cиcтeм. M.: ГOCИЗДAT, 1955) (1955)Google Scholar
  12. [Rzh82].
    Rzhanitsun, A.R.: (Pжaницын AP. Cтpoитeльнaя мexaникa, M.: Bыcшaя шкoлa, 1982) (1982)Google Scholar
  13. [Sni66].
    Snitko, N.K.: (Cниткo HК. Cтpoитeльнaя мexaникa, M.: Bыcшaя шкoлa, 1966) (1966)Google Scholar
  14. [Tim72].
    Timoshenko, S.P.: (Tимoшeнкo CП. Куpc тeopии упpугocти. Киeв: Haукoвa думкa, 1972) (1972)Google Scholar
  15. [Tim53].
    Timoshenko, S.P.: History of Strength of Materials. McGraw-Hill, New York (1953)Google Scholar
  16. [Tod60].
    Todhunter, I., Pearson, K.: A History of the Theory of Elasticity and of the Strength of Materials, vol. I –II. Dover, New York (originally published by the Cambridge University Press in 1886 and 1893) (1960)Google Scholar
  17. [Uma72-73].
    Umansky, A.A.: (Умaнcкий AA. Peд. Cпpaвoчник пpoeктиpoвщикa, изд.2. M.: Cтpoйиздaт, т. 1–1972, т.2-1973) (1972–1973)Google Scholar
  18. [You89].
    Young, W.C.: Roark’s Formulas for Stress and Strain, 6th edn. McGraw-Hill, New York (1989)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.CoquitlamCanada

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