Structural Engineering and Mechanics

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Response of a finite beam on a tensionless Pasternak foundation under symmetric and asymmetric loading

  • Coskun, Irfan (Faculty of Civil Engineering, Yildiz Technical University) ;
  • Engin, Hasan (Faculty of Civil Engineering, lstanbul Technical University) ;
  • Ozmutlu, Aydin (Department of Civil Engineering, Trakya University)
  • Received : 2006.12.06
  • Accepted : 2008.06.25
  • Published : 2008.09.10
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Abstract

The static response of a finite beam resting on a tensionless Pasternak foundation and subjected to a concentrated vertical load is assessed in this study. The concentrated vertical load may be applied at the center of the beam, or it may be offset from the center. The tensionless character of the foundation results in the creation of lift-off regions between the beam and the foundation. An analytical/ numerical solution is obtained from the governing equations of the contact and lift-off regions to determine the extent of the contact region. Although there is no nonlinear term in the equations, the problem shows a nonlinear character since the contact region is not known in advance. Due to that nonlinearity, the essentials of the problem (the coordinates of the lift-off points) are calculated numerically using the Newton-Raphson technique. The numerical results are presented in figures to illustrate the behaviours of the free-free and pinned-pinned beams under symmetric or asymmetric loading. The figures illustrate the effects of the shear foundation parameter and the symmetric and asymmetric loading options on the variation of the contact lengths and the displacement of the beam.

Keywords

References

  1. Celep, Z., Malaika, A. and Abu-Hussein, M. (1989), "Forced vibrations of a beam on a tensionless foundation", J. Sound Vib., 128, 235-246 https://doi.org/10.1016/0022-460X(89)90768-2
  2. Celep, Z. and Demir, F. (2005), "Circular rigid beam on a tensionless two-parameter elastic foundation", ZAMMZ. Angew. Math. Mech., 85(6), 431-439 https://doi.org/10.1002/zamm.200310183
  3. Celep, Z. and Demir, F. (2007), "Symmetrically loaded beam on a two-parameter tensionless foundation", Struct. Eng. Mech., 27(5), 555-574 https://doi.org/10.12989/sem.2007.27.5.555
  4. Celep, Z. and Guler, K. (2007), "Axisymmetric forced vibrations of an elastic free circular plate on a tensionless two parameter foundation", J. Sound Vib., 301, 495-509 https://doi.org/10.1016/j.jsv.2006.09.029
  5. Chen, W.Q., Lu, C.F. and Bian, Z.G. (2004), "A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation", Appl. Math. Model., 28, 877-890 https://doi.org/10.1016/j.apm.2004.04.001
  6. Choros, J. and Adams, G.G. (1979), "A steadily moving load on an elastic beam resting on a tensionless Winkler foundation", J. Appl. Mech., ASME, 46(1), 175-180 https://doi.org/10.1115/1.3424492
  7. Coskun, . and Engin, H. (1999), "Non-linear vibrations of a beam on an elastic foundation", J. Sound Vib., 223(3), 335-354 https://doi.org/10.1006/jsvi.1998.1973
  8. Coskun, . (2000), "Non-linear vibrations of a beam resting on a tensionless Winkler fundation", J. Sound Vib. 236(3), 401-411 https://doi.org/10.1006/jsvi.2000.2982
  9. Coskun, . (2003), "The response of a finite beam on a tensionless Pasternak foundation subjected to a harmonic load", Eur. J. Mech. A-Solid, 22, 151-161 https://doi.org/10.1016/S0997-7538(03)00011-1
  10. De Rosa, M.A. and Maurizi, M.J. (1998), "The influence of concentrated masses and Pasternak soil on the free vibrations of Euler beams-exact solution", J. Sound Vib., 212(4), 573-581 https://doi.org/10.1006/jsvi.1997.1424
  11. Dutta, S.C. and Roy, R. (2002), "A critical review on idealization and modeling for interaction among soilfoundation-structure system", Comput. Struct., 80, 1579-1594 https://doi.org/10.1016/S0045-7949(02)00115-3
  12. Filipich, C.P. and Rosales, M.B. (2002), "A further study about the behaviour of foundation piles and beams in a Winkler-Pasternak soil", Int. J. Mech. Sci., 44, 21-36 https://doi.org/10.1016/S0020-7403(01)00087-X
  13. Filonenko-Borodich, M.M. (1940), "Some approximate theories of the elastic foundation", Uchenyei Zapiski Moskovoskogo Gosudarstuennogo Universiteta Mechanika, U.S.S.R., No. 46, 3-18 (in Russian)
  14. Guler, K. (2004), "Circular elastic plate resting on tensionless Pasternak foundation", J. Eng. Mech., ASCE, 130(10), 1251-1254 https://doi.org/10.1061/(ASCE)0733-9399(2004)130:10(1251)
  15. Hetenyi, M. (1946), Beams on Elastic Foundation, The University of Michigan Press, Ann Arbor, MI
  16. Horibe, T. and Asano, N. (2001), "Large deflection analysis of beams on two-parameter elastic foundation using the boundary integral equation method", JSME Int. J. A-Mech. M., 44(2), 231-236 https://doi.org/10.1299/jsmea.44.231
  17. Ioakimidis, N.I. (1996), "Beams on tensionless elastic foundation: Approximate quantifier elimination with Chebyshev series", Int. J. Numer. Meth. Eng., 39(4), 663-686 https://doi.org/10.1002/(SICI)1097-0207(19960229)39:4<663::AID-NME875>3.0.CO;2-8
  18. Kargarnovin, D. and Younesian, D. (2004), "Dynamics of Timoshenko beams on Pasternak foundation under moving load", Mech. Res. Commun., 31, 713-723 https://doi.org/10.1016/j.mechrescom.2004.05.002
  19. Kerr, A.D. (1964), "Elastic and viscoelastic foundation models", J. Appl. Mech., ASME, 31, 491-498 https://doi.org/10.1115/1.3629667
  20. Kerr, A.D. and Coffin, D.W. (1991), "Beams on a two-dimensional Pasternak base subjected to loads that cause lift-off", Int. J. Solids Struct., 28(4), 413-422 https://doi.org/10.1016/0020-7683(91)90057-M
  21. Lancioni, G. and Lenci, S. (2007), "Forced nonlinear oscillations of a semi-infinite beam resting on a unilateral elastic soil: Analytical and numerical solutions", J. Comput. Nonlinear Dynam., ASME, 2(2), 155-166 https://doi.org/10.1115/1.2447406
  22. Lin, L. and Adams, G.G. (1987), "Beam on tensionless elastic foundation", J. Eng. Mech., ASCE, 113(4), 542-553 https://doi.org/10.1061/(ASCE)0733-9399(1987)113:4(542)
  23. Maheshwari, P., Chandra, S. and Basudhar, P.K. (2004), "Response of beams on a tensionless extensible geosynthetic-reinforced earth bed subjected to moving loads", Comput. Geotech., 31, 537-548 https://doi.org/10.1016/j.compgeo.2004.07.005
  24. Pasternak, P.L. (1954), On a New Method of Analysis of an Elastic Foundation by Means of Two Foundation Constants (in Russian), Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, Moscow, USSR
  25. Rao, N.V.S.K. (1974), "Onset of separation betwen a beam and tensionless elastic foundation due to moving loads", J. Appl. Mech., ASME, 41, 303-305 https://doi.org/10.1115/1.3423257
  26. Rao, G.V. (2003), "Large-amplitude free vibrations of uniform beams on Pasternak foundation", J. Sound Vib., 263, 954-960 https://doi.org/10.1016/S0022-460X(02)01486-4
  27. Scott, R.F. (1981), Foundation Analysis. Prentice-Hall, Englewood Cliffs, NJ
  28. Shen, H.-S. and Yu, L. (2004), "Nonlinear bending behavior of Reissner-Mindlin plates with free edges resting on tensionless elastic foundations", Int. J. Solids Struct., 41, 4809-4825 https://doi.org/10.1016/j.ijsolstr.2004.02.013
  29. Tsai, N.C. and Westmann, R.E. (1967), "Beams on tensionless foundation", J. Eng. Mech. Div., ASCE, 93, 1-12
  30. Vlasov, V.Z. and Leont'ev, U.N. (1966), Beams, Plates and Shells on Elastic Foundations (Translated from Russian), Israel Program for Scientific Translation, Jerusalem, Israel
  31. Weitsman, Y. (1970), "On foundations that react in compression only", J. Appl. Mech., ASME, 37(4), 1019-1030 https://doi.org/10.1115/1.3408653
  32. Weitsman, Y. (1971), "Onset of separation between a beam and tensionless elastic foundation under a moving load", Int. J. Mech. Sci., 13, 707-711 https://doi.org/10.1016/0020-7403(71)90070-1
  33. Weitsman, Y. (1972), "A tensionless contact between a beam and an elastic half-space", Int. J. Eng. Sci., 10, 73-81 https://doi.org/10.1016/0020-7225(72)90075-4
  34. Yu, L., Shen, H.S. and Huo, X.P. (2007), "Dynamic responses of Reissner-Mindlin plates with free edges resting on tensionless elastic foundations", J. Sound Vib., 299, 212-228 https://doi.org/10.1016/j.jsv.2006.07.015
  35. Zhang, Y. and Murphy, D.K. (2004), "Response of a finite beam in contact with a tensionless foundation under symmetric and asymmetric loading", Int. J. Solids Struct., 41, 6745-6758 https://doi.org/10.1016/j.ijsolstr.2004.05.028
  36. Zhaohua, F. and Cook, R.D. (1983), "Beam elements on two-parameter elastic foundations", J. Eng. Mech., ASCE, 109, 1390-1402 https://doi.org/10.1061/(ASCE)0733-9399(1983)109:6(1390)

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