Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Generalized curved beam on elastic foundation solved by transfer matrix method

  • Received : 2011.01.26
  • Accepted : 2011.08.18
  • Published : 2011.10.25
⟨ Previous Next ⟩

Abstract

A solution of space curved bars with generalized Winkler soil found by means of Transfer Matrix Method is presented. Distributed, concentrated loads and imposed strains are applied to the beam as well as rigid or elastic boundaries are considered at the ends. The proposed approach gives the analytical and numerical exact solution for circular beams and rings, loaded in the plane or perpendicular to it. A well-approximated solution can be found for general space curved bars with complex geometry. Elastic foundation is characterized by six parameters of stiffness in different directions: three for rectilinear springs and three for rotational springs. The beam has axial, shear, bending and torsional stiffness. Numerical examples are given in order to solve practical cases of straight and curved foundations. The presented method can be applied to a wide range of problems, including the study of tanks, shells and complex foundation systems. The particular case of box girder distortion can also be studied through the beam on elastic foundation (BEF) analogy.

Keywords

References

  1. Akoz, A.Y. and Kadioglu, F. (1996), "The mixed finite element solution of circular beam on elastic foundation", Comput. Struct., 60(4), 643-651. https://doi.org/10.1016/0045-7949(95)00418-1
  2. Arici, M. (1985), "Analogy for beam-foundation elastic systems", J. Struct. Eng.-ASCE, 111(8), 1691-1702. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:8(1691)
  3. Arici, M. (1989), "Reciprocal conjugate method for space curved bars", J. Struct. Eng.-ASCE, 115(3), 560-575. https://doi.org/10.1061/(ASCE)0733-9445(1989)115:3(560)
  4. Arici, M. and Granata, M.F. (2005), "A general method for nonlinear analysis of bridge structures", Bridge Struct., 1(3), 223-244. https://doi.org/10.1080/15732480500278236
  5. Arici, M. and Granata, M.F. (2007), "Analysis of curved incrementally launched box concrete bridges using the Transfer Matrix Method", Bridge Struct., 3(3), 165-181. https://doi.org/10.1080/15732480701510445
  6. Arici, M., Granata, M.F. and Recupero, A. (2010), "BEF analogy for concrete box girder analysis of bridges", Proceedings of IABSE Symposium, Venice.
  7. Aydogan, M. (1995), "Stiffness-Matrix formulation of beams with shear effect on elastic foundation", J. Struct. Eng.-ASCE, 121(9), 1265-1270. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:9(1265)
  8. Banan, M.R., Karami, G. and Farshad, M. (1989), "Finite elment analysis of curved beams on elastic foundation", Comput. Struct., 32(1), 44-53.
  9. Chen, C.N. (1998), "Solution of beam on elastic foundation by DQEM", J. Eng. Mech.-ASCE, 124(12), 1381-1384. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:12(1381)
  10. Colajanni, P., Falsone, G. and Recupero, A. (2009), "Simplified Formulation of Solution for Beams on Winkler Foundation allowing Discontinuities due to Loads and Constraints", Int. J. Eng. Ed., 25(1), 75-83.
  11. Courbon, J. (1972), Calcul des Structures, Dunod, Paris.
  12. Dasgupta, S. and Sengupta, D. (1988), "Horizontally curved isoparametric beam element with or without elastic foundation including effect of shear deformation", Comput. Struct., 29(6), 967-973. https://doi.org/10.1016/0045-7949(88)90322-7
  13. Eisenberger, M. and Yankelevsky, D.Z. (1985), "Exact stiffness matrix for beam on elastic foundation", Comput. Struct., 21(6), 1355-1359. https://doi.org/10.1016/0045-7949(85)90189-0
  14. Erguven, M.E. and Gedikli, A. (2003), "A mixed finite element formulation for Timoshenko beam on Winkler foundation", Comput. Mech., 31, 229-237.
  15. Gelu, O. (2008), "Finite elements on generalized elastic foundation in Timoshenko beam theory", J. Eng. Mech.- ASCE, 134(9), 763-776. https://doi.org/10.1061/(ASCE)0733-9399(2008)134:9(763)
  16. Gery, P.M. and Calgaro, J.A. (1973), Les Matrices-Transfert dans le calcul des structures, Editions Eyrolles, Paris.
  17. Guo, Y.J. and Weitsman, Y.J. (2002), "Solution method for beams on nonuniform elastic foundations", J. Eng. Mech.-ASCE, 128(5), 592-594. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:5(592)
  18. Haktanir, V. and Kiral, E. (1993), "Statical analysis of elastically and continuously supported helicoidal structures by the Transfer and Stiffness Matrix Methods", Comput. Struct., 49(4), 663-677.
  19. Hetenyi, M. (1946), Beams on Elastic Foundation, Univ. of Michigan Press, Ann Arbor, Michigan.
  20. Kerr, A.D. (1964), "Elastic and viscoelastic foundation models", J. Appl. Mech.-ASME, 31, 491-498. https://doi.org/10.1115/1.3629667
  21. Kim, N.I., Jeon, S.S. and Kim, M.Y. (2005), "An improved numerical method evaluating exact static element stiffness matrices of thin-walled beam-columns on elastic foundations", Comput. Struct., 83(23-24), 2003- 2022. https://doi.org/10.1016/j.compstruc.2005.02.024
  22. Kim, N.I. and Shin, D.K. (2009), "A series solution for spatially coupled deflection analysis of thin-walled Timoshenko curved beam with and without elastic foundation", J. Mech. Sci. Technol., 23, 475-488. https://doi.org/10.1007/s12206-008-1112-3
  23. Kristek, V. (1979), Theory of Box Girders, John Wiley and Sons, NY.
  24. Lacroix, R. (1967), "La methode des matrices-transfert", Annales de l'Institut Technique du Batiment et des travaux publics, XX, 231-232.
  25. Pestel, E.C. and Leckie, F.A. (1963), Matrix Methods in Elastomechanics, Mc Graw-Hill, New York.
  26. Rodriguez, D.A. (1961), "Three-dimensional bending of a ring on an elastic foundation", J. Appl. Mech. ASME, 28, 461-463. https://doi.org/10.1115/1.3641732
  27. Selvadurai, A.P.S. (1979), Elastic Analysis of Soil-Foundation interaction, Elsevier, Amsterdam.
  28. Volterra, E. (1952), "Bending of a circular beam resting on an elastic foundation", J. Appl. Mech. ASME, 19, 1-4.
  29. Yavari, A., Sarkani, S. and Reddy, J.N. (2001), "Generalized solutions of beams with jump discontinuities on elastic foundations", Arch. Appl. Mech., 71, 625-639. https://doi.org/10.1007/s004190100169

Cited by

  1. Theoretical modelling of post - buckling contact interaction of a drill string with inclined bore-hole surface vol.49, pp.4, 2014, https://doi.org/10.12989/sem.2014.49.4.427
  2. A parametric study of curved incrementally launched bridges vol.49, 2013, https://doi.org/10.1016/j.engstruct.2012.11.007
  3. Influence of secondary torsion on curved steel girder bridges with box and I-girder cross-sections vol.19, pp.7, 2015, https://doi.org/10.1007/s12205-015-1373-1
  4. Hamiltonian structural analysis of curved beams with or without generalized two-parameter foundation vol.83, pp.12, 2013, https://doi.org/10.1007/s00419-013-0772-3
  5. Ring foundation on elastic subgrade: an analytical solution for computer modelling using the Lagrangian multiplier method vol.40, pp.14, 2016, https://doi.org/10.1002/nag.2521
  6. Effects of strength difference and intermediate principal stress on plane strain elastic–plastic bending of a curved beam vol.227, pp.12, 2016, https://doi.org/10.1007/s00707-016-1681-7
  7. Analysis of non-uniform torsion in curved incrementally launched bridges vol.75, 2014, https://doi.org/10.1016/j.engstruct.2014.05.047
  8. Accident Analysis in Relation to Main Roof Structure When Longwall Face Advances toward a Roadway: A Case Study vol.2018, pp.1687-8094, 2018, https://doi.org/10.1155/2018/3810315
  9. Curved beam through matrices associated with support conditions vol.76, pp.3, 2011, https://doi.org/10.12989/sem.2020.76.3.395