Engineering Transactions, 43, 4, pp. 571-590, 1995

Interactive Elastic Buckling of Thin-Walled Closed Orthotropic Beam-Columns

Z. Kołakowski
Department of Strength of Materials and Structures, Łódź University of Technology, Łódź

M. Królak
Department of Strength of Materials and Structures, Łódź University of Technology, Łódź

The present paper deals with an analysis of global and local stabilities and with the investigation of equilibrium paths in the initial post-buckling behaviour of elastic thin-walled beam-columns consisting of orthotropic rectangular walls. Closed or open cross-section beam-columns, simply supported at the ends, are subject to axial compression, eccentric compression or pure ben ding. The problem is solved by means of a variational method using the asymptotic nonlinear theory of stability of the conservative systems [7, 8]. Numerical calculations employ Byskov's and Hutchinson's asymptotic expansion [3] in the form of the transition matrix method. The calculation is restricted to the first order nonlinear approximation. The analysis is carried out in order to study the influence of the wall orthotropy factor of dosed cross-section beam-columns (square or trapezoid-shaped) subject to axial and eccentric compression influences the critical state and the initial post-buckling behaviour.

Full Text: PDF


M.A. ALI and S. SRIDHARAN, A versatile model for interactive buckling of columns and beam-columns, Int. J. Solids Struct., 24, 5, pp. 481-486, 1988.

B.L. BIDERMAN, Mechanics of thin-walled structures. Statics [in Russian], Mashinostroenie, pp. 488, Moscow 1977.

E. BYSKOV and J .W. HUTCHINSON, Mode interaction in axially stiffened cylindrical shells, AIAA J., 15, 7, pp. 941-948, 1977.

E. BYSKOV, An asymptotic expansion applied to van der Neut's column. Collapse: The buckling of structures in theory and practice, J.M.T. THOMPSON and G.W. HUNT [Ed.], Cambridge University Press, pp. 269-282, Cambridge 1983.

R. CHANDRA, and B.B. RAJU, Postbuckling analysis of rectangular orthotropic plates1 Int. J. Mech. Sci., 16, pp. 81-97, 1973.

K. KLOPPEL and W. BILSTEIN, Ein Verfahren zur Ermittlung der Beullasten be­liebiger rechtwinkling abgekanteter offener und geschlossener Profile nach der linearen Beultheorie unter Venoendung eines abgewandelten Reduktionsverfahrens, Veröffentlichungen des lnstitutes für Statik und Stahlbau der Technischen Hochschule, Darmstadt, Heft 16, 1971.

W.T. KOITER, Elastic stability and post-buckling behaviour, [in:] Proceedings of the Symposium on Nonlinear Problems, Univ. of Wisconsin Press, Wisconsin, 1963, pp. 257-275.

W.T. KOITER, General theory of mode interacction in shell and structures, WTHD Report 590, Delft, p. 41, 1976.

W.T. KOITER and A. VAN DER NEUT, Interaction between local and overall buckling of stiffened compression panels, [in:] Thin-Walled Structures, J. RHODES and A.G. WALKER [Eds.], Granada, St.Albans, part I, pp. 51-56, part Il, pp. 66-86, 1980.

Z. KOŁAKOWSKI, Mode interaction in thin-walled trapezoidal column under uniform compression, Thin-Walled Structures, 5, pp. 329-342, 1987.

Z. KOŁAKOWSKI, Interactive buckling of thin-walled beam8 with open and closed cross-section, Engng. Trans., 37, 2, pp. 375-397, 1989.

Z. KOŁAKOWSKI, Some thougths on mode interaction in thin-walled columns under uniform compression, Thin-Walled Structures, 7, pp. 23-35, 1989.

Z. KOŁAKOWSKI, Influence of modification of boundary conditions on load carrying capacity in thin-walled columns in the second order approximation, Int. J. Solids Struct., 30, 19, pp. 2597-2609, 1993.

Z. KOŁAKOWSKI, Interactive buckling of thin-walled beams with open and closed cross.section8, Thin-Walled Struct., 15, pp.159-183, 1993.

Z. KOŁAKOWSKI and A. TETER, Interactive buckling of thin-walled closed elastic beam-columns with intermediate stiffeners, Int. J. Solids Struct., 32, Il, 1501-15161 1995.

M. KRÓLAK [Ed.], Post buckling behaviour and load carrying capacity of thin-walled plate girders [in Polish], PWN, Warszawa-Łódź, 1990, pp. 553.

A.I. MANEVICH, Interaction of buckling modes of stiffened plate under compression [in Russian], Stroitel'naya Mekhanika i Raschet Sooruzhenii, 5, pp. 24-29, 1981.

A.I. MANEVICH, Theory of interactive buckling of stiffened thin-walled structures [in Russian], Prikl'adnaya Matematika i Mekhanika, 46, 2, pp. 337-345, 1982.

A.I. MANEVICH, Stability of shells and plates with T-section stiffeners [in Russian], Stroitel'naya Mekhanika i Raschet Sooruzhenii, 2, pp. 34-38, 1985.

A.I. MANEVICH, Interactive buckling of stiffened plate under compression [in Russian], Mekhanika Tverdogo Tela., 5, pp.152-159, 1988.

H. MOELLMANN and P. GOLTERMANN, Interactive buckling in thin-walled beams. Part 1. Theory; Part 2. Applications, Int. J. Solids Struct., 25, 7, pp. 715-728 and pp.729-749, 1989.

M. PIGNATARO and A. LUONGO, Asymmetric interactive buckling of thin-walled columns with initial imperfection, Thin-Walled Struct., 3, pp. 365-386, 1987.

M. PIGNATARO and A. LUONGO, Multiple interactive buckling of thin-walled members in compression, Proc. Int. Colloq. on Stability of Plate and Shell Structures, Ghent, University Ghent, pp. 235-240, 1987.

J. ROORDA, Buckling behaviour of thin-walled columns, Can. J. Civ. Engng., 15, pp.107-116, 1988.

S. SRIDHARAN and T.R. GRAVES-SMITH, Postbuckling analyses with finite strips, J. Engng. Mech. Div. ASCE., 107, EM5, pp. 869-888, 1981.

S. SRIDHARAN and M.A. ALI, Interactive buckling in thin-walled beam-columns, J. Engng. Mech. ASCE, 111, 12, pp.1470-1486, 1985.

S. SRIDHARAN and M.A. ALI, An improved interactive buckling analysis of thin­walled columns having doubly symmetric sections, Int. J. Solids Struct., 22, 4, pp. 429-443, 1986.

S. SRIDHARAN and M.H. PENG, Performance of axially compressed stiffened panels, Int. J. Solids and Struct., 25, 8, pp. 879-899, 1989.

V. TVERGAARD, lmperfections sensitivity of a wide integrally stiffened panel under compression, Int. J. Solids and Struct., 9, 1, pp. 177-192, 1973.

B. UNGER, Elastisches Kippen von beliebig gelagerten und aufgehängten Durch­laufträgern mit einfachsymmetrischen, in Trägerachse veränderlichem Querschnitt und einer Abwandlung des Reduktionsverfahrens als Läsungsmethode, Dissertation D17, Darmstadt 1969.

Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland