Abstract
The problem of the post-buckling response of a simply supported thin-walled beam subjected to an axial compressive load and supported by the Winkler–Pasternak foundation is studied in this paper. The strains are assumed to be small and elastic. The shear deformations and the in-plane cross-sectional deformations are assumed to be negligible. The post-buckling paths of the simply supported beam are determined for different values of the Winkler and Pasternak stiffness parameters. Bifurcation points are found.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability (McGraw-Hill, New York, 1961), pp. 212–229.
V. Z. Vlasov, Thin-Walled Elastic Beams (Nat. Sci. Foundation, Washington, 1961).
S. P. Timoshenko, Strength of Materials, Part 1 (D. VanNostarnd, Washington, 1961).
J. C. Buckley, “The Bifilar Property of Twisted Strips,” Philos. Mag. 28, 778–787 (1914).
M. S. G. Cullimore, “The Shortening Effect—A Non-Linear Feature of Pure Torsion,” in Engineering Structures (Butterworths, London, 1949), pp. 153–164.
W. K. Tso and A. A. Ghobarah, “Non-Linear Non-Uniform Torsion of Thin-Walled Beams,” Int. J. Mech. Sci. 13, 1039–1047 (1971).
A. A. Ghobarah and W. K. Tso, “A Non-Linear Thin-Walled Beam Theory,” Int. J. Mech. Sci. 13, 1025–1038 (1971).
Z. P. Bazant and M. El Nimeiri, “Large Deflections Spatial Buckling of Thin-Walled Beams and Frames,” J. Eng. Mech. Div. Proc. ASCE 99, 1259–1281 (1973).
M. Epstein and D. W. Murray, “Three-Dimensional Large Deformation Analysis of Thin-Walled Beams,” Int. J. Solids Structures 12, 867–876 (1976).
C. Szymzak, “Buckling and Initial Post-Buckling Behaviour of Thin-Walled I-Columns,” Comput. Structures 11, 481–487 (1980).
T. M. Roberts and Z. G. Azizian, “Instability of Thin-Walled Bars,” Proc. ASCE, J. Eng. Mech. 109, 781–794 (1983).
J. W. Wekezer, “Instability of Thin Walled Bars,” Proc. ASCE, J. Eng. Mech. 111, 923–935 (1985).
J. W. Wekezer, “Non-Linear of Torsion of Thin-Walled Bars of Variable Cross-Sections,” Int. J. Mech. Sci. 27, 631–641 (1985).
A. Grimaldi and M. Pignataro, “Postbuckling Behavior of Thin-Walled Open Cross-Section Compression Members,” J. Struct. Mech. 7 (2), 143–159 (1979).
C. Kameswara Rao, B. V. R. Gupta, and D. L. N. Rao, “Torsional Vibrations of Thin-Walled Beams on Continuous Elastic Foundations using Finite Element Method,” in Proc. of the Int. Conf. on Finite Element Methods in Engineering (Coimbatore Inst. of Technol., Coimbatore, 1974), pp. 231–248.
C. Kameswara Rao and A. Appala Satyam, “Torsional Vibrations and Stability of Thin-Walled Beams on Continuous Elastic Foundation,” AIAA J. 13, 232–234 (1975).
M. Hatenyi, Beams on Elastic Foundation (Univ. Michigan Press, Ann Arbor, 1946), pp. 151–155.
A. P. S. Selvadurai, Elastic Analysis of Soil-Foundation Interaction (Elsevier, New York, 1979).
C. Kameswara Rao and S. Mirzam, “Torsional Post-Buckling of Thin-Walled Open Section Beams Resting on a Continuous Elastic Foundation,” Thin-Walled Struct. 8, 55–62 (1989).
P. D. Sim˜ao, “Post-Buckling Bifurcational Analysis of Thin-Walled Prismatic Members in the Context of the Generalized Beam Theory,” Ph.D. Thesis (Univ. Coimbra, Coimbra, 2007).
M. Pignatoro, N. Rizzi, G. Puta, and V. Varano, “The Effects of Warping Constraints on the Buckling of Thin-Walled Structures,” J. Mech. Mater. Struct. 4 (10), 1711–1727 (2009).
D. Camotim, C. Basaglia, and N. Silvestre, “GBT Buckling Analysis of Thin-Walled Steel Frames: A State-ofthe-Art Report,” Thin-Walled Struct. 48, 726–743 (2010).
M. Kujawa, “Torsion of Restrained Thin-Walled Bars of Open Constant Bi-Symmetric Cross-Section,” Task Quart. 16 (1), 5–15 (2011).
N. L. Rizzi and V. Varano, “The Effects ofWarping on the Post-Buckling Behaviour of Thin-Walled Structures,” Thin-Walled Struct. 49, 1091–1097 (2011).
M. Kujava and C. Szymczak, “Elastic Distortional Buckling of Thin-Walled Bars of Closed Quadratic Cross Section,” Mech. Mech. Eng. 17 (2), 119–126 (2013).
P. L. Pasternak, Fundamentals of a New Method for Calculating Elastic Two-Parameter Foundations (Gos. Izd. Lit. Stroit. Arkhit., Moscow, 1954) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © Ch.K. Rao, L.B. Rao.
Rights and permissions
About this article
Cite this article
Rao, C.K., Rao, L.B. Torsional Post-Buckling of a Simply Supported Thin-Walled Open-Section Beam Resting on a Two-Parameter Foundation. J Appl Mech Tech Phy 59, 176–184 (2018). https://doi.org/10.1134/S0021894418010224
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894418010224