Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Buckling analysis of semi-rigid connected and partially embedded pile in elastic soil using differential transform method

  • Catal, Seval (Civil Engineering Department, Engineering Faculty, Dokuz Eylul University)
  • Received : 2013.01.30
  • Accepted : 2014.08.04
  • Published : 2014.12.10
⟨ Previous Next ⟩

Abstract

The parts of semi-rigid connected and partially embedded piles in elastic soil, above the soil and embedded in the soil are called the first region and second region, respectively. The upper end of the pile in the first region is supported by linear-elastic rotational spring. The forth order differential equations of both region for critical buckling load of partially embedded and semi-rigid connected pile with shear deformation are established using small-displacement theory and Winkler hypothesis. These differential equations are solved by differential transform method (DTM) and analytical method and critical buckling loads of semirigid connected and partially embedded pile are obtained, results are given in tables and graphs are presented for investigating the effects of relative stiffness of the pile and flexibility of rotational spring.

Keywords

References

  1. Aydogan, M. (1995), "Stiffness-matrix formulation of beams with shear effect on elastic foundation", J. Struct. Eng., ASCE, 121, 1265-1270. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:9(1265)
  2. Banarje, J.R. and Williams, F.W. (1994), "The effect of shear deformation on the critical buckling of columns", J. Sound Vib., 174, 607-616. https://doi.org/10.1006/jsvi.1994.1297
  3. Catal, H.H. and Alku, S. (1996a), "Calculation of the second order stiffness matrix of the beam on elastic foundation", Turkish J. Eng. Envir. Sci., TUBITAK, 20, 145-201.
  4. Catal, H.H. and Alku, S. (1996b), "Comparison solutions of the continuoud footing subjected to bending moment, shear and axial force using finite difference equations and matrix-displacement methods", Proc. of 2nd National Computational Mechanic Congress, Trabzon, Turkey.
  5. Catal, H.H. (2002), "Free vibration of partially supported piles with the effects of bending moment, axial and shear force", Eng. Struct., 24, 1615-1622. https://doi.org/10.1016/S0141-0296(02)00113-X
  6. Catal, H.H. (2006), "Free vibration of semi-rigid connected and partially embedded piles with the effects of the bending moment, axial and shear forces", Eng. Struct., 28(14), 1911-1918. https://doi.org/10.1016/j.engstruct.2006.03.018
  7. Catal, S. and Catal, H.H. (2006), "Buckling analysis of partially embedded pile in elastic soil using differential transform method", Struct. Eng. Mech., 24(2), 247-268. https://doi.org/10.12989/sem.2006.24.2.247
  8. Catal, S. (2006), "Analysis of free vibration of beam on elastic soil using differential transform method", Struct. Eng. Mech., 24(1), 51-62. https://doi.org/10.12989/sem.2006.24.1.051
  9. Chen, C.N. (1998), "Solution of beam on elastic foundation by DQEM", J. Eng. Mech., 124, 1381-1384. https://doi.org/10.1061/(ASCE)0733-9399(1998)124:12(1381)
  10. Chen, C.K. and Ho, S.H. (1996), "Application of differential transformation to eigenvalue problem", J. Appl. Math. Comput., 79, 173-178. https://doi.org/10.1016/0096-3003(95)00253-7
  11. Chen, Y. (1997), "Assessment on pile effective lengths and their effects on design I and II", Comput. Struct., 62, 265-286. https://doi.org/10.1016/S0045-7949(96)00201-5
  12. Heelis, M.E., Pavlovic, M.N. and West, R.P. (1999), "The stability of uniform-friction piles in homogeneous and non-homogeneous elastic foundations", Int. J. Solid. Struct., 36, 3277-3292. https://doi.org/10.1016/S0020-7683(98)00150-4
  13. Heelis, M.E., Pavlovic, M.N. and West, R.P. (2004), "The analytical prediction of the buckling loads of fully and partially embedded piles", Geotechnique, 54, 363-373. https://doi.org/10.1680/geot.2004.54.6.363
  14. Hetenyi, M. (1995), Beams on Elastic Foundations, The University of Michigan Press, Michigan.
  15. Jang, M.J. and Chen, C.L. (1997), "Analysis of response of strongly non-linear damped system using a differential transformation technique", Appl. Math. Comput., 88, 137-151. https://doi.org/10.1016/S0096-3003(96)00308-6
  16. Kumar, P.S., Karuppaiah, K.B. and Parameswaran, P. (2007), "Buckling behavior of partially embedded reinforced concrete piles in sands", ARPN J. Eng. Appl. Sci., 2, 22-26.
  17. Li, Q.S. (2001a), "Buckling of multi-step cracked columns with shear deformation", Eng. Struct., 23, 356-364. https://doi.org/10.1016/S0141-0296(00)00047-X
  18. Li, Q.S. (2001b), "Buckling of multi-step non-uniform beams with elastically restrained boundary conditions", J. Construct. Steel Res., 57, 753-777. https://doi.org/10.1016/S0143-974X(01)00010-4
  19. Malik, M. and Dang, H.H. (1998), "Vibration analysis of continuous systems by differential transformation", Appl. Math. Comput., 97, 17-26. https://doi.org/10.1016/S0096-3003(97)10153-9
  20. Monforton, G.R. and Wu, T.S. (1963), "Matrix analysis of semi-rigidly connected frames", J. Struct. Div., ASCE, 89(ST6), 13-42.
  21. Pochl, Th. (1930), Lehrbuch der Technischen Mekanik, Springer, Berlin.
  22. Pusjuso, S. and Thongmoon, M. (2010), "The numerical solutions of differential transform method and the Laplace transform method for a system of differential equations", Nonlin. Anal., Hybr. Syst., 4, 425 - 431. https://doi.org/10.1016/j.nahs.2009.10.006
  23. Reddy, A.S. and Vasangkar, A.J. (1970), "Buckling of fully and partially embedded piles", J. Soil Mech. Found. Div., 96, 1951-1965.
  24. Ross, S.L. (1984), Differential Equations, Third Edition, John Wiley & Sons, New York.
  25. Sapountzakis, E.J. and Kampitsis, A.E., (2010), "Nonlinear dynamic analysis of Timoshenko beam-columns partially supported on tensionless Winkler foundation", Comput. Struct., 88, 1206-1219. https://doi.org/10.1016/j.compstruc.2010.06.010
  26. Smith, I.M. (1979), "Discrete element analysis of pile instability", Int. J. Numer. Anal. Meth. Geomech., 3, 205-211. https://doi.org/10.1002/nag.1610030208
  27. Valsangkar, A.J. and Pradhanang, R.B. (1987), "Vibration of partially supported piles", J. Eng. Mech., 113, 1244-1247. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:8(1244)
  28. Vogt, N.,Vogt, S. and Kellner, C. (2009), "Buckling of selender piles in soft soils", Bautechnik, 86, 98-112. https://doi.org/10.1002/bate.200910046
  29. Wang, C.M., Ng, K.H. and Kitipornchai, S. (2002), "Stability criteria for Timoshenko columns with intermediate and end concentrated axial loads", J. Construct. Steel Res., 58, 1177-1193. https://doi.org/10.1016/S0143-974X(01)00071-2
  30. West, H.H. and Mafiu, M. (1984), "Eigenvalues for beam-columns on elastic supports", J. Struct. Eng., 110, 1305-1319. https://doi.org/10.1061/(ASCE)0733-9445(1984)110:6(1305)
  31. West, R.P., Heelis, M.E., Pavlovic, M.N. and Wylie, G.B. (1997), "Stability of end-bearing piles in a nonhomogeneous elastic foundation", Int. J. Numer. Anal. Meth. Geomech., 21, 845-861. https://doi.org/10.1002/(SICI)1096-9853(199712)21:12<845::AID-NAG905>3.0.CO;2-7
  32. Yang, J. and Ye, J.Q. (2002), "Dynamic elastic local buckling of piles under impact loads", Struct. Eng. Mech., 13, 543-556. https://doi.org/10.12989/sem.2002.13.5.543
  33. Yan, W. and Chen, W.Q. (2012), "Dynamic analysis of semi-rigidly connected and partially embedded piles via the method of reverberation-ray matrix", Struct. Eng. Mech., 42, 269-289. https://doi.org/10.12989/sem.2012.42.2.269
  34. Yesilce, Y. and Catal, H.H. (2008), "Free vibration of semi-rigid connected Reddy-Bickford piles embedded in elastic soil", Sadhana, 33(6), 781-801. https://doi.org/10.1007/s12046-008-0034-1
  35. Yesilce, Y. and Catal, H.H. (2006), "Free vibration of piles embedded in soil having different modulus of subgrade reactions", Appl. Math. Model., 32(5), 889-900.
  36. Yesilce, Y. and Catal, H.H. (2011), "Solution of free vibration equations of semi-rigid connected Reddy-Bickford beams resting on elastic soil using the differential transform method", Arch. Appl. Mech., 81(2), 199-213. https://doi.org/10.1007/s00419-010-0405-z
  37. Zhou, J.K. (1986), Differential transformation and its applications for electrical circuits, Huazhong University Press, Wuhan, China.
  38. Zhu, Y., Hu, Y. and Cheng, C. (2011), "Analysis of nonlinear stability and post-buckling for Euler-type beam-column structures", Appl. Math. Mech., 32, 719-728. https://doi.org/10.1007/s10483-011-1451-x
  39. Zou, L., Zong, Z., Wang, Z. and Tian, S. (2010), "Differential transform method for solving solitary wave discontinuity", Phys. Lett. A, 374, 3451-3454. https://doi.org/10.1016/j.physleta.2010.06.066

Cited by

  1. Dynamic stiffness approach and differential transformation for free vibration analysis of a moving Reddy-Bickford beam vol.58, pp.5, 2016, https://doi.org/10.12989/sem.2016.58.5.847
  2. A unified model for analyzing free vibration and buckling of end-bearing piles vol.152, 2018, https://doi.org/10.1016/j.oceaneng.2018.01.045
  3. Research on non-destructive testing technology for existing bridge pile foundations vol.7, pp.1, 2014, https://doi.org/10.12989/smm.2020.7.1.043
  4. Study on large tonnage pile foundation load test system and field test of long rock-socketed pile vol.21, pp.6, 2020, https://doi.org/10.12989/gae.2020.21.6.565
  5. Dynamic behavior of axially functionally graded simply supported beams vol.25, pp.6, 2014, https://doi.org/10.12989/sss.2020.25.6.669