Structural Engineering and Mechanics

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Analysis of partially embedded beams in two-parameter foundation

  • Akoz, A.Yalcin (Engineering Faculty, Civil Engineering Department, T.C. Maltepe University) ;
  • Ergun, Hale (Civil Engineering Faculty, Civil Engineering Department, ITU)
  • Received : 2011.06.18
  • Accepted : 2012.02.21
  • Published : 2012.04.10
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Abstract

In this study, Pasternak foundation model, which is a two parameter foundation model, is used to analyze the behavior of laterally loaded beams embedded in semi-infinite media. Total potential energy variation of the system is written to formulate the problem that yielded the required field equations and the boundary conditions. Shear force discontinuities are exposed within the boundary conditions by variational method and are validated by photo elastic experiments. Exact solution of the deflection of the beam is obtained. Both foundation parameters are obtained by self calibration for this particular problem and loading type in this study. It is shown that, like the first parameter k, the second foundation parameter G also depends not only on the material type but also on the geometry and the loading type of the system. On the other hand, surface deflection of the semi infinite media under singular loading is obtained and another method is proposed to determine the foundation parameters using the solution of this problem.

Keywords

References

  1. Akoz, A.Y. and Ergun, H. (2009), "Implants and Pasternak foundation", Proceeding of the 16th National Mechanics Congress, Erciyes University, Kayseri, Turkey, June. (in Turkish)
  2. American Society of Testing and Materials (1998), "Standard test method for repetitive static plate load tests of soils and flexible pavement components, for use in evaluation and design of airport and highway pavements" (D1195-93), 04.08, 110-113.
  3. Bowles, J.E. (1974), Analytical and Computer Methods in Foundation Eng, Mc Graw-Hill.
  4. Civalek, O. (2007), "Nonlinear analysis of thin rectangular plates on Winkler-Pasternak elastic foundations by DSC-HDQ methods", Appl. Math. Model., 31(3), 606-624. https://doi.org/10.1016/j.apm.2005.11.023
  5. Dinçer, . (2011), "Models to predict the deformation modulus and the coefficient of subgrade reaction for earth filling structures", Adv. Eng. Softw., 42, 160-171. https://doi.org/10.1016/j.advengsoft.2011.02.001
  6. 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
  7. Frocht, M.M. (1941), Photoelasticity, Vol.I, John Wiley & Sons Inc.
  8. Gelfand, I.M. and Fomin, S.V. (1963), Calculus of Variations, Prentice-Hall Inc.
  9. Gulkan, P. and Alemdar, B.N. (1999), "An exact finite element for a beam on a two-parameter elastic foundation: a revisit", Struct. Eng. Mech., 7(3), 259-276. https://doi.org/10.12989/sem.1999.7.3.259
  10. Hetenyi, M. (1946), Beams on Elastic Foundation, University of Michigan, Ann Arbor.
  11. Kerr, A.D. (1976), "On the derivation of well posed boundary value problems in structural mechanics", Int. J. Solids Struct., 12, 1-11. https://doi.org/10.1016/0020-7683(76)90069-X
  12. Kim, Y. and Jeong, S. (2011), "Analysis of soil resistance on laterally loaded piles based on 3D soil-pile interaction", Comput. Geotech., 38, 248-257. https://doi.org/10.1016/j.compgeo.2010.12.001
  13. Kobayashi, N., Shibata, T., Kikuchi, Y. and Murakami, A. (2008), "Estimation of horizontal subgrade reaction coefficient by inverse analysis", Comput. Geotech., 35(4), 616-626. https://doi.org/10.1016/j.compgeo.2007.11.002
  14. Setiadji, B.H., Fwa, T.F. (2009), "Examining k-E relationship of pavement subgrade based on load-deflection consideration", J. Transp. Eng.-ASCE, 135(3), 140-148. https://doi.org/10.1061/(ASCE)0733-947X(2009)135:3(140)
  15. Zhaohua, F. and Cook, R.D. (1983), "Beam elements on two-parameter elastic foundations", J. Eng. Mech.-ASCE, 109(6), 1390-1402. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:6(1390)

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