Tapered steel members: Flexural and lateral‐torsional buckling

Liliana Marques

Publications

Publication Details

Title

Tapered steel members: Flexural and lateral‐torsional buckling

Authors

Liliana Marques

Abstract

Tapered steel members are usually adopted in order to optimize the load capacity at each cross section taking into account the respective distribution of stresses.
Eurocode 3 – part 1-1 (CEN, 2005) provides several methodologies for the stability verification of members and frames. However, regarding non-uniform members in general, with tapered cross section, irregular distribution of restraints, non-linear axis, castellated, etc., several difficulties are noted. There are yet no guidelines to overcome any of these issues and, as a result, safety verification is conservative, not accounting for the advantages non-uniform members provide. This research deals with the stability design of tapered members.
The designer has nowadays sophisticated numerical tools which allow him to study any of the above-mentioned structures. However, there is not yet enough guidance to safely perform fully non-linear numerical verification.
Therefore, approaches based on structural analysis followed by design checks are usually preferred. EC3-1-1 provides a set of design formulae for member design, covering column and/or lateral-torsional buckling. However, these formulae are related to standard conditions of structural members, such as simply supported members, with double-symmetric and constant sections and with intermediate regular lateral restraints.
As a consequence, EC3-1-1 includes a general method for lateral and lateral-torsional buckling of structural components, specifically developed to verify the structures that lie outside the validation range of the interaction formulae, namely tapered members. However, considering the coded buckling curves for application of this method is not only inconsistent from a mechanical point of view but also may lead to an over-conservative or even unconservative level of resistance.
For all of the referred reasons, and because tapered steel members lead to competitive structural solutions, this dissertation focus on developing new stability rules for lateral and lateral-torsional buckling of web-tapered members in which the buckling phenomena is accounted for by a proper buckling coefficient related to realistic imperfections. The objective is to have a straight forward procedure, nevertheless with mechanical consistency. The outcomes of this research are consistent with existing rules for prismatic members and aim at contributing to the harmonization of stability member verification procedures of Eurocode 3.

References

Abaqus (2010). v.6.10, Dassault Systems/Simulia, Providence, RI, USA.
Andrade A., Dinis P.B., Providência P. and Camotim D. (2007b). “Vigas em I com Alma Linearmente Variável: Cálculo de Momentos Críticos Elásticos e Verificação da Segurança”, Métodos Numéricos e Computacionais em Engenharia (CMNE 2007 + XXVIII CILAMCE), J.C. Sá et al. (Eds.), 214, Porto, June 13-15.
Andrade A., Providência P., Dinis P.B. Camotim D. (2010b) “European Provisions for the Design of Web-Tapered I-Beams - An Appraisal of the EC3 'General Method' ”, Proceedings of 4th International Conference on Steel & Composite Structures (ICSCS’10), B. Uy et al. (Eds.), University of Western Sydney, Sydney, pp. 241-243, July 21-23.
Andrade A., Camotim D. and Dinis P.B. (2007a). “Lateral-torsional buckling of singly symmetric web-tapered thin-walled I-beams: 1D model vs. shell FEA”, Computers and Structures 85(17-18) 1343-1359.
Andrade A., Dinis P.B., Providência P. and Camotim D. (2007c). "On the design of web- tapered I-section beams; Proceedings of 5th International Conference on Advances in Steel Structures (ICASS 2007), Singapore, 2007, Vol. III, 316-321.
Andrade A., Providência P. and Camotim D. (2006). “Buckling formulae for doubly symmetric web-tapered I-section cantilevers acted by a tip load”, Proceedings of International Colloquium on Stability and Ductility of Steel Structures (SDSS 06 − Lisboa, 6-8/9), D. Camotim, N. Silvestre e P.B. Dinis (eds.), IST Press, 323-330 (Vol. 1), 2006.
Andrade A., Providência P. and Camotim D. (2010a). “Elastic Lateral-Torsional Buckling of Restrained Web-Tapered I-Beams”, Computers & Structures, Vol. 88, no 21-22, 1179-1196.
Andradre A., Camotim D., Providência P. (2005). “Critical moment formulae for doubly symmetric web-tapered I-section steel beams acted by end moments”, Proceedings of the 4th European Conference on Steel and Composite Structures, Eurosteel 2005, pp. 1.2-135-1.2- 143, Maastricht, The Netherlands.
Ayrton W.E. and Perry J. (1886). "On Struts", The Engineer, 62, pp. 464-465, 513-515.
Baptista A.M., Muzeau J.P. (1998). “Design of Tapered Compression Members According to Eurocode 3”, Journal of Constructional Steel Research 46 (1-3), pp. 146-148.
Beer H. and Schulz G. (1970). “Bases théoriques des courbes européenes de flambement”, Construction Métallique 3, pp. 5-12.
Beer H. and Schulz G. (1969). “Die Traglast des planmӓβig mittig gedrückten Stabes mit Imperfektionen”, VDI-Zeitschrift, 21, pp. 1537-1541, 1683-1687, 1767-1772.
Bleich F. (1932). Stahlhochbauten ihre theory, berechnung und bauliche gestaltung”, Berlin, Verlag von Julius Springer.
Boissonnade N., Greiner R., Jaspart J. P., and Lindner J. (2006). “Rules for member stability in DIN EN 1993-1-1, Background documentation and design guidelines”, ECCS (European Convention for Constructional Steelwork) / Publication no. 119, Brussels.
Boissonnade N., Jaspart J. P., Muzeau J. P., and Villette M. (2003). “New Interaction Formulae for Beam-Columns in Eurocode 3: The French- Belgian Approach”, Journal of Constructional Steel Research 60 (3-5), pp. 421-431.
Boissonnade N. (2002). “Mise au point d’un élément fini de type poutre à section variable et autres applications à la construction métallique”, PhD Thesis, Blaise Pascal University, Clermont-Ferrand, France.
Bradford M.A. (1988). "Stability of tapered I-beams". Journal of Constructional Steel Research, 9, pp. 195-216.
Braham M. (1997) "Elastic lateral torsional buckling of web lapered I-beams subjected to end moments". Proceedings of the Steel Structures and Bridges Conference, Brno, May.
Braham M. and Hanikenne D. (1993). “Lateral buckling of web tapered beams: An original design method confronted with a computer simulation”, Journal of Constructional Steel Research, 27(1-3), 23-36.
British Standard Institution (1985). "Structural Use of Steelwork in Building. BS 5950 – Part I", London, BSI.
Butler D.J. and Anderson G.B. (1963). “The elastic buckling of tapered beam-columns” Welding Research Supplement, January 1963, pp. 29-36.
CBCA (no date). Centro Brasileiro de Construção em Aço, Revista Arquitectura & Aço #13. http://www.cbca-acobrasil.org.br, accessed June 16th, 2010.
CEN (2002). “Eurocode, EN-1990, Eurocode: Basis of Structural Design”, European Committee for Standardization, Brussels, Belgium.
CEN (2005). “Eurocode 3, EN-1993-1-1:2005, Eurocode 3: Design of steel structures – Part 1-1: General Rules and Rules for Buildings”, European Committee for Standardization, Brussels, Belgium.
CEN (2006). “Eurocode 3, EN-1993-1-5:2006, Eurocode 3: Plated structural elements”, European Committee for Standardization, Brussels, Belgium.
CEN (2007). “Eurocode 3, EN-1993-1-6:2007, Eurocode 3: Strength and stability of shell structures”, European Committee for Standardization, Brussels, Belgium.
Chen W.F. and Lui E.M. (1987). “Structural stability – Theory and implementation”, Elsevier Science Publishing Co., New York.
ECCS (1978). “European Recommendations for Steel Construction”, Brussels.
ECCS TC8 (2006).“Resolution of ECCS/TC8 with respect to the general method in EN 1993- 1-1”, Technical Committee 8 – Structural Stability.
ENV 1993-1-1:1992 (1992). “Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings”, Brussels.
Ermopoulos J. (1997). “Equivalent buckling length of non-uniform members”, Journal of Constructional Steel Research, 42 (2), pp. 141-158.
Galambos T.V. (1998) (editor). “Guide to Stability Design Criteria for Metal Structures, Fifth Edition”, John Wiley & Sons Inc.
Galéa Y. (1986). “Deversement des barres à section en I bissymétriques et hauteur d ́âme bilinéairement variable”, Construction Métallique 23(2), pp. 50-54.
Gere J.M., Timoshenko S.P. (1991). “Mechanics of Materials”, 3rd edition, Chapman & Hall.
Greiner R. (2003). “Concepts for the numerically-based buckling check of steel structures”, Conference Paper, ISBN 80-01-02747-3, Prague.
Greiner R. and Lechner A. (2007). “Comparison of General Method with traditional methods – Part 2 – Example of a sway frame with the free unrestrained corners”, ECCS TC8 Stability, TC8-2007-013.
Greiner R. and Lindner J. (2006). Interaction formulae for members subjected to bending and axial Compression in EUROCODE 3 – the Method 2 Approach”, Journal of Constructional Steel Research 62 (8), pp. 757-770.
Greiner R. and Ofner R. (2005). “Buckling design of steel structures based on overall load cases according to Eurocode 3”, Eurosteel Conference, Maastricht 2005, pp. 1.4-1 – 1.4-8.
Greiner R. and Ofner R. (2007). “Comparison of General Method with traditional methods – Example of a sway frame with lateral restraints”, ECCS TC8 Stability, TC8-2007-006.
Greiner R., Kettler M., Lechner A., Jaspart J.P. Weynand K. Ziller, C. and Örder, R. (2011). “SEMI-COMP+: Valorisation Action of Plastic Member Capacity of Semi-Compact Steel Sections – a more Economic Design”, RFS2-CT-2010-00023, Background Documentation, Research Programme of the Research Fund for Coal and Steel – RTD.
Greiner R., Salzgeber G. and Ofner R. (2000). “New lateral-torsional buckling curves – numerical simulations and design formulae”, ECCS TC8 Stability, TC8-2000-014.
Hirt M.A. and Crisinel. M (2001). “Charpentes Métaliques – Conception et Dimensionnement des Halles et Bâtiments”, Traité de Génie Civil, vol. 11, Press Polytechniques et Universitaires Romandes, Lausanne.
Horne M.R., Shakir-Khalil H. and Akhtar S. (1979). “The stability of tapered and haunched beams”. Proceedings of the Institution of Civil Engineers, Vol. 67, N° 2, September 1979, pp. 677-694.
Ibañez J.R. and Serna M.A. (2010) “Equivalent moment approach for elastic lateral-torsional buckling of tapered beams”, International Journal of Structural Stability and Dynamics, Vol. 10, No. 3, 387-409.
Kaehler R.C., White D.W. and Kim Y.D. (2010) "Frame Design Using Web-Tapered Members", Design Guide 25,Metal Building Manufacturers Association and AISC, Chicago, IL.
Kaim P. (2004). “Spatial buckling behavior of steel members under bending and compression”, PhD Thesis, Fakultät für Bauingenieurwesen der Technischen Universität Graz, Graz, Austria.
Kim Y.D. (2010), “Behavior and Design of Metal Building Frames with General Prismatic and Web-Tapered Steel I-Section Members,” PhD Thesis, School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, USA.
Kitipornchai S. and Trahair, N.S. (1972). “Elastic Stability of Tapered I-Beams”, Journal of the Structural Division – Proceedings of the American Society of Civil Engineers ST3, pp. 713-729.
Lee G. C., Morrell M. L., and Ketter R. L. (1972). “Design of Tapered Members”, Weld Res. Counc. Bull. No. 173, June, pp. 1-32.
Lindner J. (2004). “Comments on paper TC8-2004-021: Second draft of the background documentation”. ECCS TC8 Stability, TC8-2004-021.
MIMOA (no date). Mi modern architecture, http://www.mimoa.eu/, accessed March 31th, 2012.
Müller C. (2003). “Zum Nachweis ebener Tragwerke aus Stahl gegen seitliches Ausweichen”, PhD Thesis, RWTH Aachen, Germany.
Nahverkehrsdrehscheibe Graz-Hauptbahnhof (02-02-2012). www.nvd-graz-hbf.info/, accessed March 31st, 2012.
Naumes J. (2009). “Biegeknicken und Biegedrillknicken von Stäben und Stabsystemen auf einheitlicher Grundlage”, PhD thesis, RWTH Aachen, Germany.
Ofner R. (1997). “Traglasten von Stäben aus Stahl bei Druck and Biegung”, PhD thesis, Fakultät für Bauingenieurwesen der Technischen Universität Graz, Graz, Austria.
Ofner R. and Greiner R. (2005). “Buckling check of steel members based on numerical simulations of overall load cases”, Eurosteel Conference, Maastricht 2005, pp. 1.4-25 – 1.4- 32.
Optima Cube (no date). www.optimacube.com, accessed March 31st, 2012.
Petersen C. (1993). “Stahlbau”, Vieweg Verlag, Wiesbaden.
Prawell S.P., Morell M.L. and Lee G.C. (1974). “Bending and buckling strength of tapered structural members” Welding Research Supplement, 1974, pp. 75-84.
Raftoyiannis I. and Ermopoulos J. (2005). “Stability of tapered and stepped steel columns with initial imperfections”, Engineering Structures 27(2005), pp. 1248-1257.
Rebelo C., Simões da Silva L. and Simões R. (2006). “Statistical evaluation of the reliability of beam-column stability checks in EC3”, Proceedings of SDSS’06, Lisboa, Portugal, 6-8 September.
Rebelo C., Lopes N., Simões da Silva L., Nethercot D. and Vila Real P. (2009). “Statistical evaluation of the lateral-torsional buckling resistance of steel I-beams - Part 1: Variability of the Eurocode 3 design model", Journal of Constructional Steel Research 65 (4), pp. 818-831.
Rondal J. and Maquoi R. (1979). "Formulation d’Ayrton-Perry pour le flambement des barres métaliques", Construction Métallique, 4, pp. 41-53, 1979.
Rotter J.M. and Schmidt, H. (2008). “Buckling of Steel Shells European Design Recommendations”, 5th Edition, ECCS Press – P125, Brussels.
Salter J.B., Anderson D. and May I.M. (1980). “Tests on tapered steel columns”. The Structural Engineer, Vol. 58A, N°6, June 1980, pp. 189-193.
Salzgeber G. (2000a) “Lateral Torsional Buckling of Beam-Columns under N+My+Mz - Derivation of an elastic second order solution with mode-related imperfections”, March 2000 (not published).
Salzgeber G. (2000b) “LT-Buckling effect on the strong axis buckling mode”, Report 2000- 005 ECCS TC8.
Simões da Silva L. and Gervásio H. (2007). “Manual de Dimensionamento de Estruturas Metálicas: Métodos Avançados”, cmm Press, Coimbra, Portugal.
Simões da Silva L., Gervásio H. and Simões R. (2010b). “Design of Steel Structures – , Part 1-1: General Rules and Rules for Buildings”, ECCS.
Simões da Silva L., Marques L. and Rebelo C., (2010a). “Numerical validation of the General Method in EC3-1-1 for prismatic members”, Journal of Constructional Steel Research 66 (4), pp. 575-590.
Simões da Silva L., Rebelo C., Nethercot D., Marques L., Simões R., and Vila Real P. (2009). “Statistical evaluation of the lateral-torsional buckling resistance of steel I-beams - Part 1: Variability of steel properties", Journal of Constructional Steel Research 65 (4), pp. 832- 849.
Simões da Silva L., Marques L. and Martins, J.P., (2011). “Stability and Design of Thin- Walled Steel Shells”. International Conference on Thin-Walled Structures, Timisoara, Romania, 5 – 7 September, pp. 87-98.
Snijder B., Greiner R. and Jaspart J. P. (2006). “Fields and limits of the application of the General Method”, ECCS TC8 Stability, TC8-2006-015.
Standards Australia (1998) “AS4100-1998, Steel Structures”, 1998.
Steel Construct (no date). www.steelconstruct.com, accessed June 16th, 2010.
Tal Projecto (no date). http://www.talprojecto.pt, accessed March 31th, 2012.
Taras A. and Greiner R. (2006). “On the variety of buckling curves”, Proceedings of SDSS’06, Lisboa, Portugal, 6-8 September, pp. 1101–1108.
Taras A. (2010). “Contribution to the development of consistent stability design rules for steel members”, PhD Thesis, Technical University of Graz, Graz,Austria.
Timoshenko S.P. and Gere J.M. (1961). “Theory of Elastic Stability”, McGraw-Hill Book Company Inc., New York/Toronto/London.
Trahair N.S. (1993) “Flexural-Torsional Buckling of Structures”, E & FN SPON, London.
Vandermeulen T. (2007). “Le déversement des poutres métalliques en I à hauteur d’âme linéairement variable sous moments d’extrémité”, Diploma Work, ArGEnCo Department, University of Liège, Belgium.
Veer (no date). www.veer.com, accessed June 16th, 2010.
Ziemian R.D. (editor) (2010). “Guide to stability design criteria for metal structures – sixth edition”, John Wiley & Sons Ltd.

Files

2012_phd_Marques_Liliana.pdf

<< back