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A new approach to the calculation of cross-section deformation modes in the framework of generalized beam theory

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Abstract

This paper presents a new and general approach for the calculation of cross-section deformation modes in thin-walled beams, to be used in the framework of generalized beam theory (GBT). The proposed approach subdivides and hierarchizes the cross-section deformation modes by employing several kinematic hypotheses. This makes it possible to discard a priori specific types of deformation modes and consequently reduce the number of cross-section degrees-of-freedom. The approach is applicable to arbitrary (with open and closed parts) polygonal cross-sections with external and internal constraints and allows for the a posteriori inclusion of particular deformation modes (e.g., shear deformation modes in a part of the cross-section). Although only GBT applications are dealt with, the deformation modes obtained may be straightforwardly incorporated in other thin-walled beam formulations that include cross-section deformation.

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References

  1. Vlasov V (1959) Tonkostenye sterjni, 2nd edn. Fizmatgiz, Moscow, Russia (French translation: “Piéces Longues en Voiles Minces”, Éditions Eyrolles, Paris, France, 1962)

  2. Dabrowski R (1970) Curved thin-walled girders: theory and analysis. Cement and Concrete Association, London

    Google Scholar 

  3. Schardt R (1966) Eine Erweiterung der Technische Biegetheorie zur Berechnung prismatischer Faltwerke. Stahlbau 35: 161–171

    Google Scholar 

  4. Sedlacek G (1968) Systematische Darstellung des Biege- und Verdrehvorganges für Stäbe mit dünnwandigem, prismatischem Querschnitt unter Berücksichtigung der Profilverformung. Dissertation, TU Berlin, Germany

  5. Schardt R (1989) Verallgemeinerte Technische Biegetheorie. Springer, Berlin

    Google Scholar 

  6. Altenbach J, Zwicke M (1986) Theoretische Ableitung und Bewertung unterschiedlicher quasieindimensionaler Modelle für die statische Strukturanalyse dünnwandiger komplexer Konstructionen. Technische Mechanik 7(3): 52–64

    Google Scholar 

  7. Altenbach J, Altenbach H, Matzdorf V (1994) A generalized Vlasov theory for thin-walled composite beam structures. Mech Compos Mater 30(1): 43–54

    Article  Google Scholar 

  8. Davies JM, Leach P (1994) First order generalized beam theory. J Constr Steel Res 31(2–3): 187–220

    Article  Google Scholar 

  9. Davies JM (1998) Generalised beam theory (GBT) for coupled instability problems. In: Rondal J (eds) Coupled instability in metal structures: theoretical and design aspects (CISM Course n. 379). Springer, Vienna, pp 151–223

    Google Scholar 

  10. Silvestre N, Camotim D (2002) First order generalised beam theory for arbitrary orthotropic materials. Thin Walled Struct 40(9): 755–789

    Article  Google Scholar 

  11. Silvestre N, Camotim D (2003) Non-linear generalised beam theory for cold-formed steel members. Int J Struct Stab Dyn 3(4): 461–490

    Article  Google Scholar 

  12. Camotim D, Silvestre N, Gonçalves R, Dinis PB (2004) GBT analysis of thin-walled members: new formulation and applications. In: Loughlan J (eds) Thin-walled structures: recent advances and future trends in thin-walled structures technology. Canopus Publishing, Bath, pp 137–168

    Google Scholar 

  13. Camotim D, Silvestre N, Gonçalves R, Dinis PB (2006) GBT-based structural analysis of thin-walled members: overview, recent progress and future developments. In: Pandey M, Xie WC, Chu L (eds) Advances in engineering structures, mechanics and construction. Springer, Dorderecht, pp 187–204

    Chapter  Google Scholar 

  14. Gonçalves R, Camotim D (2007) Thin-walled member plastic bifurcation analysis using generalised beam theory. Adv Eng Softw 38: 637–646

    Article  Google Scholar 

  15. Silva N, Camotim D, Silvestre N (2008) GBT cross-section analysis of thin-walled members with arbitrary cross-sections: a novel approach. In: Mahendran M (ed) Proceedings of the 5th international conference on thin-walled structures, Brisbane, pp 1161–1171

  16. Camotim D, Basaglia C, Silvestre N (2010) GBT buckling analysis of thin-walled steel frames: a state-of-the-art report. Thin Walled Struct (in press)

  17. Baláz I (1999) Dünnwandige Stäbe mit offenem oder geschlossenem deformierbaren Querschnitt. Stahlbau 68: 70–77

    Google Scholar 

  18. Bogensperger T (2000) Erweiterte Stabtheorie und der gevoutete Träger im Brückenbau. Ph.D. Dissertation, Institut für Stahlbau, Holzbau und Flächentragwerke, TU Graz, Austria

  19. Rendek S, Balaz I (2004) Distortion of thin-walled beams. Thin Walled Struct 42(2): 255–277

    Article  Google Scholar 

  20. Blümel S, Fontana M (2004) Load-bearing and deformation behaviour of truss joints using thin-walled pentagon cross-sections. Thin Walled Struct 42(2): 295–307

    Article  Google Scholar 

  21. Simão P, Simões da Silva L (2004) A unified energy formulation for the stability analysis of open and closed thin-walled members in the framework of the generalized beam theory. Thin Walled Struct 42(10): 1495–1517

    Article  Google Scholar 

  22. Casafont M, Marimon F, Pastor M (2009) Calculation of pure distortional elastic buckling loads of members subjected to compression via the finite element method. Thin Walled Struct 47(6–7): 701–729

    Article  Google Scholar 

  23. Gonçalves R, Dinis PB, Camotim D (2009) GBT formulation to analyze the first-order and buckling behaviour of thin-walled members with arbitrary cross-sections. Thin Walled Struct 47(5): 583–600

    Article  Google Scholar 

  24. Schardt R (1994) Lateral torsional and distortional buckling of channel and hat-sections. J Constr Steel Res 31(2–3): 243–265

    Article  Google Scholar 

  25. Silvestre N, Camotim D (2004) Distortional buckling formulae for cold-formed steel C and Z section members: part I–derivation. Thin Walled Struct 42(11): 1567–1597

    Article  Google Scholar 

  26. Gonçalves R, Le Grognec P, Camotim D (2010) GBT-based semi-analytical solutions for the plastic bifurcation of thin-walled members. Int J Solids Struct 47(1): 34–50

    Article  Google Scholar 

  27. Miosga G (1976) Vorwiegend längsbeanspruchte dünnwandige prismatische Stäbe und Platten mit endlichen elastischen Verformungen. Dissertation, Technische Hochschule Darmstadt, Germany

  28. Gonçalves R, Ritto-Corrêa M, Camotim D (2010) A large displacement and finite rotation thin-walled beam formulation including cross-section deformation. Comput Methods Appl Mech Eng 199(23–24): 1627–1643

    Article  Google Scholar 

  29. Haakh U (2004) Die Erweiterung der VTB für allgemeine dünnwandige Querschnitte sowie die Lösung des Differentialgleichungssystems mit Potenzreihen. Dissertation, TU Darmstadt, Germany

  30. Maxwell JC (1864) On the calculation of the equilibrium and stiffness of frames. Philos Mag 27: 294–299

    Google Scholar 

  31. Calladine CR (1978) Buckminster Fuller’s ‘Tensegrity’ structures and Clerk Maxwell’s rules for the construction of stiff frames. Int J Solids Struct 14: 161–172

    Article  MATH  Google Scholar 

  32. Möller R (1982) Zur Berechnung prismatischer Strukturen mit beliebigem nicht formtreuem Querschnitt. Institut für Statik, Technische Hochschule Darmstadt, Germany

  33. Schardt R (1994) Generalized beam theory—an adequate method for coupled stability problems. Thin Walled Struct 19(2–4): 161–180

    Article  Google Scholar 

  34. Bathe KJ (2004) ADINA system. ADINA R&D Inc, MA, USA

    Google Scholar 

  35. Murray NW (1986) Introduction to the theory of thin-walled structures. Clarendon Press, Oxford

    Google Scholar 

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Authors and Affiliations

  1. UNIC, Departamento de Engenharia Civil, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    Rodrigo Gonçalves

  2. ICIST/IST, Departamento de Engenharia Civil e Arquitectura, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001, Lisbon, Portugal

    Manuel Ritto-Corrêa & Dinar Camotim

Authors
  1. Rodrigo Gonçalves
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  2. Manuel Ritto-Corrêa
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  3. Dinar Camotim
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Correspondence to Rodrigo Gonçalves.

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Gonçalves, R., Ritto-Corrêa, M. & Camotim, D. A new approach to the calculation of cross-section deformation modes in the framework of generalized beam theory. Comput Mech 46, 759–781 (2010). https://doi.org/10.1007/s00466-010-0512-2

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