DOI QR코드

DOI QR Code

Comparison of alternative algorithms for buckling analysis of slender steel structures

  • Dimopoulos, C.A. (Institute of Steel Structures, School of Civil Engineering, National Technical University of Athens) ;
  • Gantes, C.J. (Institute of Steel Structures, School of Civil Engineering, National Technical University of Athens)
  • Received : 2011.07.01
  • Accepted : 2012.09.28
  • Published : 2012.10.25

Abstract

Objective of this paper is to compare linear buckling analysis formulations, available in commercial finite element programs. Modern steel design codes, including Eurocode 3, make abundant use of linear buckling loads for calculation of slenderness, and of linear buckling modes, used as shapes of imperfections for nonlinear analyses. Experience has shown that the buckling mode shapes and the magnitude of buckling loads may differ, sometimes significantly, from one algorithm to another. Thus, three characteristic examples have been used in order to assess the linear buckling formulations available in the finite element programs ADINA and ABAQUS. Useful conclusions are drawn for selecting the appropriate algorithm and the proper reference load in order to obtain either the classical linear buckling load or a good approximation of the actual geometrically nonlinear buckling load.

Keywords

References

  1. ABAQUS/Standard and ABAQUS/Explicit - Version 6.8 (2008), Abaqus Theory Manual, Dassault Systems.
  2. ADINA R & D Inc. (2006), Theory and Modeling Guide Volume I: ADINA, Report ARD 06-7.
  3. Aguero, A. and Pallares, F.J. (2007), "Proposal to evaluate the ultimate limit state of slender structures. Part 1: Technical aspects", Eng. Struct., 29(4), 483-497. https://doi.org/10.1016/j.engstruct.2006.05.014
  4. Al-Bermani, F.G.A. and Kitipornchai, S. (1990), "Elastoplastic large deformation analysis of thin walled structures", Eng. Struct., 12(1), 28-36. https://doi.org/10.1016/0141-0296(90)90035-Q
  5. Al-Bermani, F.G.A. and Kitipornchai, S. (1992), "Nonlinear analysis of transmission towers", Eng. Struct., 14(3), 139-151. https://doi.org/10.1016/0141-0296(92)90025-L
  6. American Institute of Steel Construction (1999), Load and Resistance Factor Design for Structural Steel Buildings.
  7. Baldassino, N. and Bernuzzi, C. (2000), "Analysis and behaviour of steel storage pallet racks", Thin Wall. Struct., 37(4), 277-304. https://doi.org/10.1016/S0263-8231(00)00021-5
  8. Bathe, K.J. and Cimento, A.P. (1980), "Some practical procedures for the solution of nonlinear finite element equations", Comput. Meth. Appl. Mech. Eng., 22(1), 59-85. https://doi.org/10.1016/0045-7825(80)90051-1
  9. Bathe, K.J., Snyder, M.D., Cimento, A.P. and Rolph, W.D. (1980), "On some current procedures and difficulties in finite element analysis of elastic-plastic response", Comput. Struct., 12(4), 607-624. https://doi.org/10.1016/0045-7949(80)90135-2
  10. Bathe, K.J. and Dvorkin, E.N. (1983), "On the automatic solution of nonlinear finite element equations", Comput. Struct., 17, 871-879. https://doi.org/10.1016/0045-7949(83)90101-3
  11. Bathe, K.J. (1995), Finite Element Procedures, Prentice-Hall, Englewood Cliffs.
  12. Belytschko, T., Liu, W.K. and Moran, B. (2000), Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons Ltd.
  13. Berry, P.A., Rotter, J.M. and Bridge, R.Q. (2000), "Compression tests on cylinders with circumferential weld depressions", J. Eng. Mech., ASCE, 126(4), 405-413. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:4(405)
  14. Brendel, B. and Ramm, E. (1980), "Linear and nonlinear stability analysis of cylindrical shells", Comput. Struct., 12, 549-558. https://doi.org/10.1016/0045-7949(80)90130-3
  15. Chan, S.L. (1989), "Inelastic post-buckling analysis of tubular beam-columns and frames", Eng. Struct., 11(1), 23-30. https://doi.org/10.1016/0141-0296(89)90029-1
  16. Chan, S.L. and Chui, P.T. (2000), Non-linear Static and Cyclic Analysis of Semirigid Steel Frames, Elsevier Science, Amsterdam.
  17. Chang, S.C. and Chen, J.J. (1986), "Effectiveness of linear bifurcation analysis for predicting the nonlinear stability limits of structures", Int. J. Numer. Meth. Eng., 23, 831-846. https://doi.org/10.1002/nme.1620230506
  18. Chen, W.F. and Kim, S.E. (1997), LRFD Steel Design Using Advanced Analysis, CRC Press, Boca Raton, Florida.
  19. Crisfield, M.A. (1981), "A fast incremental/iterative solution procedure that handles snap-through", Comput. Struct., 13, 55-62. https://doi.org/10.1016/0045-7949(81)90108-5
  20. Crisfield, M.A., Jelenic, G., Mi, Y., Zhong, H.G. and Fan, Z. (1997), "Some aspects of the non-linear finite element method", Finite Elem. Anal. Des., 27(1), 19-40. https://doi.org/10.1016/S0168-874X(97)00004-8
  21. Dimopoulos, C.A. and Gantes, C.J. (2008a), "Design of circular steel arches with hollow circular cross-sections according to EC3", J. Constr. Steel Res., 64(10), 1077-1085. https://doi.org/10.1016/j.jcsr.2007.09.009
  22. Dimopoulos, C.A. and Gantes, C.J. (2008b), "Nonlinear in-plane behavior of circular steel arches with hollow circular cross-section", J. Constr. Steel Res., 64(12), 1436-1445. https://doi.org/10.1016/j.jcsr.2008.01.005
  23. Earls C.J. (2007), "Observations on eigenvalue buckling analysis within a finite element context", Proceedings of the Structural Stability Research Council, Annual Stability Conference, New Orleans, LA, USA.
  24. Elgaaly, M. (2000), "Post-buckling behaviour of thin steel plates using computational models", Adv. Eng. Softw., 31(8-9), 511-517. https://doi.org/10.1016/S0965-9978(00)00037-5
  25. European Committee for Standardization (2004a), Eurocode 3 - Design of Steel Structures - Part 1-1: General Rules and Rules for Buildings.
  26. European Committee for Standardization (2004b), Eurocode 3 - Design of Steel Structures - Part 1.5: Plated Structural Elements.
  27. European Committee for Standardization (2006), Eurocode 3 - Design of Steel Structures - Part 1.6: Strength and Stability of Shell Structures.
  28. Feng, M., Wang, Y.C. and Davies, J.M. (2004), "A numerical imperfection sensitivity study of cold-formed thinwalled tubular steel columns at uniform elevated temperatures", Thin Wall. Struct., 42, 533-555. https://doi.org/10.1016/j.tws.2003.12.005
  29. Gantes, C.J. and Fragkopoulos, K.A. (2010), "Strategy for numerical verification of steel structures at the ultimate limit state", Struct. Infrastr. Eng., 6(1-2).
  30. Gettel, M. and Schneider, W. (2007), "Buckling strength verification of cantilevered cylindrical shells subjected to transverse load using Eurocode 3", J. Constr. Steel Res., 63(11), 1467-1478. https://doi.org/10.1016/j.jcsr.2007.01.003
  31. Hawileh, R.A., Abed, F., Abu-Obeidah, A.S. and Abdalla, J.A. (2012), "Experimental investigation of inelastic buckling of built-up steel columns", Steel Compos. Struct., 13(3).
  32. Herynk, M.D., Kyriakides, S., Onoufriou, A. and Yun, H.D. (2007), "Effects of the UOE/UOC pipe manufacturing processes on pipe collapse pressure", Int. J. Mech. Sci., 49, 533-553. https://doi.org/10.1016/j.ijmecsci.2006.10.001
  33. Hsieh, S.H. and Deierlein, G.G. (1991), "Nonlinear analysis of three-dimensional steel frames with semi-rigid connections", Comput. Struct., 41(5), 995-1009. https://doi.org/10.1016/0045-7949(91)90293-U
  34. Johansson, B., Maquoi, R. and Sedlacek, G. (2001), "New design rules for plated structures in Eurocode 3", J. Constr. Steel Res., 57(3), 279-311. https://doi.org/10.1016/S0143-974X(00)00020-1
  35. Kaitila, O. (2002), "Imperfection sensitivity analysis of lipped channel columns at high temperatures", J. Constr. Steel Res., 58, 333-351. https://doi.org/10.1016/S0143-974X(01)00060-8
  36. Kato, S., Mutoh, I. and Shomura, M. (1998), "Collapse of semi-rigidly jointed reticulated domes with initial geometric imperfections", J. Constr. Steel Res., 48(2-3), 145-167. https://doi.org/10.1016/S0143-974X(98)00199-0
  37. Kim, S.E., Park, M.H. and Choi, S.H. (2001), "Direct design of three-dimensional frames using practical advanced analysis", Eng. Struct., 23(11), 1491-1502. https://doi.org/10.1016/S0141-0296(01)00041-4
  38. Kojic, M. and Bathe, K.J. (2004), Inelastic Analysis of Solids and Structures, Series in Computational Fluid and Solid Mechanics, Springer Verlag, Berlin.
  39. Liew, J.Y.R., White, D.W. and Chen, W.F. (1993), "Limit states design of semi-rigid frames using advanced analysis: part 2: analysis and design", J. Constr. Steel Res., 26(1), 29-57. https://doi.org/10.1016/0143-974X(93)90066-2
  40. Liew, J.Y.R., Chen, W.F. and Chen, H. (2000), "Advanced inelastic analysis of frame structures", J. Constr. Steel Res., 55(1-3), 245-265. https://doi.org/10.1016/S0143-974X(99)00088-7
  41. Lignos, D.G., Krawinkler, H. and Whittaker A.S. (2011), "Prediction and validation of sidesway collapse of two scale models of a 4-story steel moment frame", Earthq. Eng. Struct. D., 40, 807-825. https://doi.org/10.1002/eqe.1061
  42. Paik, J.K. and Thayamballi, A.K. (2003), Ultimate Limit State Design of Steel-plated Structures, Wiley, New Jersey.
  43. Pi, Y.L. and Trahair, N.S. (1994a), "Nonlinear inelastic analysis of steel beam columns-theory", J. Struct. Eng., ASCE, 120(7), 2041-2061. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:7(2041)
  44. Pi, Y.L. and Trahair, N.S. (1994b), "Nonlinear inelastic analysis of steel beam columns-applications", J. Struct. Eng., ASCE, 120(7), 2062-2085. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:7(2062)
  45. Pi, Y.L. and Trahair, N.S. (1998), "Out-of-plane inelastic buckling and strength of steel arches", J. Struct. Eng., ASCE, 124(2), 174-183. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:2(174)
  46. Pi, Y.L., Put, B.M. and Trahair, N.S. (1999), "Lateral buckling strengths of cold-formed Z-section beams", Thin Wall. Struct., 34(1), 65-93. https://doi.org/10.1016/S0263-8231(99)00004-X
  47. Pi, Y.L. and Bradford, M.A. (2004), "In-plane strength and design of fixed steel I-section arches", Eng. Struct., 26(3), 291-301. https://doi.org/10.1016/j.engstruct.2003.09.011
  48. Ramm, E. (1981), "Strategies for tracing nonlinear responses near limit points", Nonlinear Finite Element Analysis in Structural Mechanics (Eds. W. Wunderlich, E. Stein and K.J. Bathe), Springer-Verlag, New York.
  49. Riks, E. (1979), "An incremental approach to the solution of snapping and buckling problems", Int. J. Solids Struct., 15, 529-551. https://doi.org/10.1016/0020-7683(79)90081-7
  50. Rodrigues, P.F.N. and Jacob, B.P. (2005), "Collapse analysis of steel jacket structures for offshore oil exploitation", J. Constr. Steel Res., 61(8), 1147-1171. https://doi.org/10.1016/j.jcsr.2005.02.005
  51. Schneider, W. and Brede, A. (2005), "Consistent equivalent geometric imperfections for the numerical buckling strength verification of cylindrical shells under uniform external pressure", Thin Wall. Struct., 43(2), 175-188. https://doi.org/10.1016/j.tws.2004.08.006
  52. Schneider, W., Timmel, I. and Hohn, K. (2005), "The conception of quasi-collapse-affine imperfections: A new approach to unfavourable imperfections of thin-walled shell structures", Thin Wall. Struct., 43(8), 1202-1224. https://doi.org/10.1016/j.tws.2005.03.003
  53. Sedlacek, G. and Müller, C. (2006), "The European standard family and its basis", J. Constr. Steel Res., 62(11), 1047-1059. https://doi.org/10.1016/j.jcsr.2006.06.027
  54. Shanmugam, N.E., Liew, J.Y.R. and Lee, S.L. (1993), "Ultimate strength design of biaxially loaded steel box beam-columns", J. Constr. Steel Res., 26(2-3), 99-123. https://doi.org/10.1016/0143-974X(93)90031-M
  55. Shi, G., Liu, Z., Ban, H.Y., Zhang, Y., Shi, Y.J. and Wang, Y.Q. (2012), "Tests and finite element analysis on the local buckling of 420 MPa steel equal angle columns under axial compression", Steel Compos. Struct., 12(1), 31-51. https://doi.org/10.12989/scs.2012.12.1.031
  56. Trahair, N.S. and Chan, S.L. (2003), "Out-of-plane advanced analysis of steel structures", Eng. Struct., 25(13), 1627-1637. https://doi.org/10.1016/S0141-0296(03)00134-2
  57. Tschope, H., Onate, E. and Wriggers, P. (2001), Direct Computation of Instability Points with Inequality Constraints Using the Finite Element Method, International Centre for Numerical Methods in Engineering, Barcelona.
  58. Vila Real, P.M.M., Cazeli, R., Simões da Silva, L., Santiago, A. and Piloto, P. (2004), The effect of residual stresses in the lateral-torsional buckling of steel I-beams at elevated temperature, J. Constr. Steel Res., 60, 783-793. https://doi.org/10.1016/S0143-974X(03)00143-3
  59. White, D.W. (1993), "Plastic-hinge methods for advanced analysis of steel frames", J. Constr. Steel Res., 24(2), 121-152. https://doi.org/10.1016/0143-974X(93)90059-2
  60. White, D.W. and Hajjar, J.F. (2000), "Stability of steel frames: the cases for simple elastic and rigorous inelastic analysis/design procedures", Eng. Struct., 22(5), 155-167. https://doi.org/10.1016/S0141-0296(98)00105-9
  61. Wriggers, P., Wagner, W. and Miehe, C. (1987), "A quadratically convergent procedure for the calculation of stability points in finite element analysis", Comput. Meth. Appl. Mech. Eng., 70, 329-347.
  62. Wriggers, P. and Simo, J.C. (1990), "A general procedure for the direct computation of turning and bifurcation points", Int. J. Numer. Meth. Eng., 30, 155-176. https://doi.org/10.1002/nme.1620300110
  63. Yang, Y.B., Yang, C.T., Chang, T.P. and Chang, P.K. (1997), "Effects of member buckling and yielding on ultimate strengths of space trusses", Eng. Struct., 19(2), 179-191. https://doi.org/10.1016/S0141-0296(96)00032-6

Cited by

  1. Numerical methods for the design of cylindrical steel shells with unreinforced or reinforced cutouts vol.96, 2015, https://doi.org/10.1016/j.tws.2015.07.024
  2. Buckling and Post-buckling Behavior of Beams With Internal Flexible Joints Resting on Elastic Foundation Modeling Buried Pipelines vol.7, 2016, https://doi.org/10.1016/j.istruc.2016.06.007
  3. Optimum topology design of multi-material structures with non-spurious buckling constraints vol.114, 2017, https://doi.org/10.1016/j.advengsoft.2017.06.002
  4. Experimental and numerical investigation of eccentrically loaded laced built-up steel columns vol.101, 2014, https://doi.org/10.1016/j.jcsr.2014.04.032
  5. Thermal and Mechanical Computational Study of Load-Bearing Cold-Formed Steel Drywall Systems Exposed to Fire vol.52, pp.6, 2016, https://doi.org/10.1007/s10694-016-0604-4
  6. Optimal Formation Assessment of Multi-layered Ground Retrofit with Arch-Grid Units Considering Buckling Load Factor pp.2093-6311, 2018, https://doi.org/10.1007/s13296-018-0115-x
  7. A branch-switching procedure for analysing instability of steel structures subjected to fire vol.67, pp.6, 2012, https://doi.org/10.12989/sem.2018.67.6.629