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Generalization of the equations for frame-type structures; a variational approach

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Summary

The differential equations for frame-type structures with elastically deformable joints, derived recently by A. D. Kerr and A. M. Zarembski [1], are genealized first by including the translational inertia terms. The corresponding variational principle is then derived formally, and the mechanical meaning of each term is established. The variational principle is then generalized by including a geometrical non-linearity, the effect of thermal and variable axial forces, and the variation of sectional properties. The corresponding differential equations are derived and the admissible boundary and matching conditions are discussed. As examples, formulations for two problems are presented.

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References

  1. Kerr, A. D., Zarembski, A. M.: The response equations for a cross-tie track. Acta Mechanica40, 253–276 (1981).

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  2. Mayer, M.: Eine Näherungsberechnung von Rahmennetzen mittels gleichmäßig verteilter Drehmomente. (In German.) (An approximate analysis for frame systems by means of uniformly distributed moments.) Beton und Eisen, 1928.

  3. Minelli, C.: Metodo di calcolo per travi Vierendeel con grande numero di traversi. (In Italian.) (Method for calculating Vierendeel girders with a large number of cross bars.) La Ricerca Scientifica, 1939.

  4. Hetényi, M.: An analytical study of Vierendeel girders. Proc. Fourth U. S. National Congress of Applied Mechanics, 1962.

  5. Hildebrand, F. B.: Methods of applied mathematics. Englewood Cliffs, N.J.: Prentice-Hall 1958.

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  6. Kerr, A. D.: On the derivation of well posed boundary value problems in structural mechanics. Int. J. Solids and Structures12, 1–11 (1976).

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  7. Kerr, A. D.: An improved analysis for thermal track buckling. Int. J. Non-Linear Mech.15, 99–114 (1980).

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Authors and Affiliations

  1. Department of Civil Engineering, University of Delaware, 19716, Newark, DE, USA

    A. D. Kerr

  2. Department of Civil Engineering, Northwestern University, 69201, Evanston, IL, USA

    M. L. Accorsi

Authors
  1. A. D. Kerr
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  2. M. L. Accorsi
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With 8 Figures

Research supported by the National Science Foundation, Washington, DC under grants CME 8001928 and CEE 8308919.

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Kerr, A.D., Accorsi, M.L. Generalization of the equations for frame-type structures; a variational approach. Acta Mechanica 56, 55–73 (1985). https://doi.org/10.1007/BF01306024

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  • DOI: https://doi.org/10.1007/BF01306024

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