Skip to main content
Springer Nature Link
Log in

On inner shearing constraints for a direct beam model coarsely describing warping

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

We investigate inner shearing constraints for a direct one-dimensional beam model coarsely describing warping. In particular, we study how they affect the field equations for the elastic buckling of open thin-walled beams. We show that the distinction between the axes of the shear centres and of the centroids is crucial for the kinematics of the beam, and to derive expression of reactive actions, hence of buckling critical conditions. We also show how a suitable definition of the warping inertial action and properly introduced inner shearing constraints yield the field equations of the literature for the beam in a general dynamic setting.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Vlasov VZ (1961) Thin-walled elastic beams, Israel Program for Scientific Translations, Monson, Jerusalem

    Google Scholar 

  2. Timoshenko SP, Gere JM (1961) Theory of elastic stability, 2nd edn. McGraw-Hill, New York

    Google Scholar 

  3. Simo JC, Vu-Quoc L (1991) A geometrically exact rod model incorporating shear and torsion-warping deformation. Int J Solids Struct 27(3):371–393

    Article  MathSciNet  MATH  Google Scholar 

  4. Grimaldi A, Pignataro M (1979) Postbuckling behavior of thin-walled open cross-section compression members. J Struct Mech 7(2):143–159

    Article  Google Scholar 

  5. Kim SB, Kim MY (2000) Improved formulation for spatial stability, and free vibration of thin-walled tapered beams, and space frames. Eng Struct 22(5):446–458

    Article  Google Scholar 

  6. Kim MY, Chang SP, Park HG (2001) Spatial postbuckling analysis of nonsymmetric thin-walled frames. I: Theoretical considerations based on semitangential property. J Eng Mech 127(8):769–778

    Article  Google Scholar 

  7. Garcea G, Trunfio GA, Casciaro R (2002) Path-following analysis of thin-walled structures, and comparison with asymptotic post-critical solutions. Int J Numer Methods Eng 55(1):73–100

    Article  MATH  Google Scholar 

  8. Mhori F, Damil N, Potier-Ferry M (2010) Linear and nonlinear stability analyses of thin-walled beams with monosymmetric I sections. Thin-Walled Struct 48(4–5):299–315

    Article  Google Scholar 

  9. Camotim D, Basaglia C, Silvestre N (2010) GBT buckling analysis of thin-walled steel frames: a state-of-the-art report. Thin-Walled Struct 48(10–11):726–743

    Article  Google Scholar 

  10. Ruta GC, Pignataro M, Rizzi N (2006) A direct one-dimensional beam model for the flexural-torsional buckling of thin-walled beams. J Mech Mater Struct 1(8):1479–1496

    Article  Google Scholar 

  11. Pignataro M, Rizzi N, Ruta G, Varano V (2009) The effects of warping constraints on the buckling of thin-walled structures. J Mech Mater Struct 4(10):1711–1727

    Article  Google Scholar 

  12. Rizzi N, Varano V (2011) The effects of warping on the postbuckling behavior of thin-walled structures. Thin-Walled Struct 49(9):1091–1097

    Article  Google Scholar 

  13. Lofrano E, Paolone A, Ruta G (2013) A numerical approach for the stability analysis of open thin-walled beams. Mech Res Commun 48:76–86

    Article  Google Scholar 

  14. Lofrano E, Paolone A, Ruta G (2012) Stability of non-trivial equilibrium paths of beams on partial visco-elastic foundation. Acta Mech 223:2183–2195

    Article  MathSciNet  MATH  Google Scholar 

  15. Andreaus UA, Ruta GC (1998) A review of the problem of the shear center(s). Contin Mech Thermodyn 10(6):369–380

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. Møllmann H (1986) Theory of thin-walled beams with finite displacements. In: Proceedings of the Euromech colloquium 197, Jablonna, Poland. Lecture notes in engineering, vol 19: pp 195–209

    Google Scholar 

  17. Budiansky B (1974) Theory of buckling and postbuckling behavior of elastic structures. In: Yih CS (ed) Advances in applied mechanics, vol 14. Academic Press, New York

    Google Scholar 

  18. Truesdell C, Noll W (1965) The non-linear field theories of mechanics. In: Handbuch der Physik, vol. III, Part 3. Springer, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento d’Ingegneria Strutturale e Geotecnica, “Sapienza” Università di Roma, Rome, Italy

    Matteo Brunetti, Achille Paolone & Giuseppe Ruta

Authors
  1. Matteo Brunetti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Achille Paolone
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Giuseppe Ruta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Giuseppe Ruta.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brunetti, M., Paolone, A. & Ruta, G. On inner shearing constraints for a direct beam model coarsely describing warping. Meccanica 48, 2439–2451 (2013). https://doi.org/10.1007/s11012-013-9759-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-013-9759-y

Keywords

Search

Navigation