On the Evaluation of Critical Lateral-Torsional Buckling Loads of Monosymmetric Beam-Columns

Authors: T. Yilmaz, N. Kirac

Abstract:

Beam-column elements are defined as structural members subjected to a combination of axial and bending forces. Lateral torsional buckling is one of the major failure modes in which beam-columns that are bent about its strong axis may buckle out of the plane by deflecting laterally and twisting. This study presents a compact closed-form equation that it can be used for calculating critical lateral torsional-buckling load of beam-columns with monosymmetric sections in the presence of a known axial load. Lateral-torsional buckling behavior of beam-columns subjected to constant axial force and various transverse load cases are investigated by using Ritz method in order to establish proposed equation. Lateral-torsional buckling loads calculated by presented formula are compared to finite element model results. ABAQUS software is utilized to generate finite element models of beam-columns. It is found out that lateral-torsional buckling load of beam-columns with monosymmetric sections can be determined by proposed equation and can be safely used in design.

Keywords: Lateral-torsional buckling, stability, beam-column, monosymmetric section.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1125661

References:

[1] M.A.M. Torkamani, E.R. Roberts, “Energy Equations for Elastic Flexural-Torsional Buckling Analysis of Plane Structures”, Thin Walled Structures, vol. 47, no.4, pp. 463-473, 2009.
[2] A. Chajes, Principles of Structural Stability Theory, Englewood Cliffs NJ, Prentice-Hall, 1974.
[3] S. P. Timoshenko, J. M. Gere, Theory of Elastic Stability. 2nd ed., McGraw-Hill, New York, 1961.
[4] W. F. Chen, E. M Lui, Theory of Beam-Columns vol.2 Space Behavior and Design , McGraw-Hill, New York, 1977.
[5] W. F. Chen, E. M. Lui, Structural Stability: Theory and Implementation, Elsevier Science Publishing Co. Inc., New York, 1987.
[6] T.V. Galambos, A. E. Surovek, Structural Stability of Steel: Concepts and Application for Structural Engineers, John Wiley and Sons, 2008.
[7] C. H. Yoo, S. C. Lee, Stability of structures, principles and applications, Elsevier, Oxford, 2011.
[8] Z. P. Bazant, L. Cedolin, Stability of Structures Elastic, Inelastic Fracture and Damage Theories, Dover Publications, New York, 1991.
[9] N. S. Trahair, Flexural-Torsional Buckling of Structures, CRC Press, London, 1993.
[10] M. G. Salvadori, Lateral buckling of eccentrically loaded I columns, Transcations of the ASCE, vol. 121, pp. 1163–1178, 1956.
[11] H. N. Hill, J. W. Clark, Lateral buckling of eccentrically loaded I-section columns, Transcations of the ASCE , vol. 116,pp. 1179, 1951.
[12] F. Bleich, Buckling Strength of Metal Structures, McGraw Hill, New York, 1952.
[13] M. Assadi, C. W. Roeder, “Stability of Continuously Restrained Cantilevers”, Journal of Engineering Mechanics, vol. 111, no. 12, pp. 1440–1456, 1985.
[14] M. A. Serna, A. Lopez, I. Puente, D. J. Yong, “Equivalent Uniform Moment Factors for Lateral-Torsional Buckling of Steel Members”, Journal of Constructional Steel Research, vol. 62, no. 6, pp. 566-580, 2006.
[15] B. Suryoatmono, D. Ho, “The Moment-Gradient Factor in Lateral-Torsional Buckling on Wide Flange Steel Sections”, Journal of Constructional Steel Research, vol. 58, no. 9, pp. 1247-1264, 2002.
[16] S. Kitipornchai, N. J. Richter, “Elastic Lateral Buckling of I-Beams with Discrete Intermediate Restraints”, Civil Eng.Trans.,vol. 20, no. 2, pp. 105-111, 1978.
[17] S. Kitipornchai, P. F. Dux, N. J. Richter, “Buckling and Bracing of Cantilevers”, Journal of the Structural Division, ASCE, vol. 110, no. 9, pp. 2250-2262, 1984.
[18] S. Kitipornchai, C. M. Wang, N. S. Trhair, “Buckling of Monosymmetric I Beams under Moment Gradient”, Journal of Structural Engineering, ASCE, vol. 112, no. 4,pp. 781-799, 1986.
[19] S. Kitipornchai, N. S. Trahair, “Buckling of Inelastic I-Beams under Moment Gradient”, Journal of the Structural Division, ASCE, vol 101, no. ST5, pp. 991-1004, 1975.
[20] R.S. Barsoum, R.H. Gallagher, “Finite Element Analysis of Torsional and Torsional–Flexural Stability Problems”, International Journal of Numerical Methods in Engineering, vol. 2, no. 3,pp. 335-352, 1970.
[21] G. Powell, R. Klingner, “Elastic Lateral Buckling of Steel Beams”, ASCE Journal of Structural Division, vol. 96, no. 9,pp. 1919–32, 1970.
[22] G.J. Hancock, N.S. Trahair, “Finite Element Analysis of Lateral Buckling of Continuously Restrained Beam-Columns”, Civil Eng. Trans. Institution of Engineering, Australia, vol. CE20, no. 2, pp. 120–127, 1978.
[23] M.A. Bradford, H.R. Ronagh, “Generalized Elastic Buckling of Restrained I-Beams by FEM”, ASCE Journal of Structural Engineering, vol. 123, no. 12 , pp. 1631–1637, 1997.
[24] J.P Papangelis, N.S. Trahair, G.L. Hancock, “Elastic Flexural–Torsional Buckling of Structures by Computer”, Computers and Structures, vol. 68, no. 13, pp. 125–37, 1998
[25] H. Lee, D.W. Jung, J. H. Jeong, S. Im, “Finite Element Analysis of Lateral Buckling for Beam Structures”, Computers and Structures, 53(6), 1357-1371, 1994.
[26] F. Mohri, A. Eddinari, N. Damil, M. Potier-Ferry, “A Beam Finite Element for Non-linear Analyses of Thin-Walled Elements”, Thin Walled Structures, vol. 46. ,no.7-9, pp. 981-990, 2008.
[27] J.S. Park, J.M. Stallings, Y.J. Kang, “Lateral-Torsional Buckling of Prismatic Beams with Continuous Top-Flange Bracing”, Journal of Constructional Steel Research, vol. 60, no.2, pp. 147-160, 2004.
[28] N.H. Lim, N.H. Park, Y.J. Kang, I.H. Sung, “Elastic Buckling of I-Beams under Linear Moment Gradient”, International Journal of Solids and Structures, vol. 40, no. 21, pp. 5635–5647, 2003.
[29] J.X. Gu, S.L Chan, “A Refined Finite Element Formulation for Flexural and Torsional Buckling of Beam-Columns with Finite Rotations”, Engineering Structures,vol. 27, pp. 749-759, 2005.
[30] H.R. Naderian, H.R. Ronagh, “Buckling Analysis of Thin-Walled Cold-Formed Steel Structural Members Using Complex Finite Strip Method”, Thin-Walled Structures, vol. 90, pp. 74-83, 2015.
[31] S. Adany, B.W .Schafer, “Generalized Constrained Finite Strip Method for Thin-Walled Members with Arbitrary Cross Section: Primary Modes”, Thin-Walled Structures, vol. 84, pp. 150-159, 2014.
[32] H.C. Bui, “Semi-Analytical Finite Strip Method Based on The Shallow Shell Theory in Buckling Analysis of Cold-Formed Sections”, Thin-Walled Structures, vol. 50, pp. 141-146, 2012.
[33] H.C. Bui, “Buckling Analysis of Thin-Walled Sections under General Loading Conditions”, Thin-Walled Structures, vol. 47, pp. 730-739, 2009.
[34] H. Ozbasaran, “A Parametric Study on Lateral Torsional Buckling of European IPN and IPE cantilevers”, International Journal of Civil, Architectural, Structural and Construction Engineering, World Academy of Science, Engineering and Technology, vol. 8, no. 7, 2014.
[35] C. M. Wang, S. Kitipornchai, “On Stability of Monosymmetric Cantilevers”, Engineering Structures, vol. 8, pp. 168-180, 1986.
[36] R. Aydin, A. Gunaydin, N. Kirac, H. Ozabasaran, “On the Evaluation of Critical Lateral Buckling Loads of Prismatic Steel Beams”, Proceedings of the Fourteenth International Conference on Civil, Structural and Enviromental Engineering Computing, Civil-Comp Press, Stirlingshire, Scotland, 2013.
[37] EC3, EN 1993-1-1, “Eurocode 3: Design of Steel Structures-Part 1-1: General Rules and Rules for Buildings”, European Committee for Standardization, Brussels, 2005.
[38] AISC, “Specification for Structural Steel Buildings, American Institute of Steel Construction”, Chicago, 2005
[39] F. Mohri, A. Brouki, J.C. Roth, “Theoretical and Numerical Stability Analyses of Unrestrained, Mono-Symmetric Thin-Walled Beams”, Journal of Constructional Steel Research, vol. 59, no. 1, pp. 63-90, 2003.
[40] N. Kirac, T. Yilmaz, “ A Parametric Study on the Evaluation of Lateral Torsional Buckling of European IPE and IPN Beams”, Proceedings of the Fifteenth International Conference on Civil, Structural and Enviromental Engineering Computing, Stirlingshire, Scotland, 2015.
[41] A. Andrade, D. Camotim, and P. Providência e Costa, “On the evaluation of elastic critical moments in doubly and singly symmetric Isection cantilevers,” Journal of Constructional Steel Research, vol. 63, pp. 894-908, 2007.
[42] H. Ozbasaran, R. Aydın, M. Dogan, “An Alternative Design Procedure for Lateral-Torsional Buckling of Cantilever I-Beams”, Thin-Walled Structures, vol. 90, pp. 235-242, 2015.
[43] W. Yuan, B. Kim, C. Chen, “Lateral-torsional buckling of steel web tapered tee-section cantilevers”, Journal of Constructional Steel Research, vol. 87, pp. 31–37, 2013.
[44] B. Kim, L. Li, A. Edmonds, “Analytical Solutions of Lateral-Torsional Buckling of Castellated Beams”, International Journal of Structural Stability and Dynamics, vol. 16, pp. 155044, 2016.
[45] L. Zhang, G. Tong, “Lateral buckling of simply supported C- and Z-section purlins with top flange horizontally restrained” , Thin-Walled Structures, vol. 99, pp. 155-167, 2016.
[46] B. Asgarian, M.Soltani, F. Mohri, “Lateral-torsional buckling of tapered thin-walled beams with arbitrary cross-sections”, Thin-Walled Structures, vol. 62, pp. 96-108, 2013.
[47] C. M. Wang, S. Kitipornchai, “New set of buckling parameters for monosymmetric beam-columns/tie-beams”, Journal of Structural Engineering, vol. 115, no. 6, pp. 1497-1513, 1989.
[48] E. Magnucka-Blandzi, “Critical State of a Thin walled beam under combined load”, Applied Mathematical Modelling, vol. 33, pp. 3093-3098, 2009.
[49] S. Cheng, B. Kim, L. Li, “Lateral–torsional buckling of cold-formed channel sections subject to combined compression and bending”, Journal of Constructional Steel Research, vol. 80, pp. 174-180, 2013.
[50] M. Kucukler, L. Gardner, L. Macorini, “Flexural–torsional buckling assessment of steel beam–columns through a stiffness reduction method”, Engineering Structures, vol. 101, pp. 662-676, 2015.
[51] ABAQUS, “ABAQUS Theory Guide”, Version 6.13.1, 2013.