Elastic Buckling of Steel Columns Under Axial Compression
American Journal of Civil Engineering
Volume 2, Issue 3, May 2014, Pages: 102-108
Received: May 27, 2014; Accepted: Jun. 12, 2014; Published: Jun. 30, 2014
Views 4237      Downloads 718
Mehmet Avcar, Civil Engineering Department, Suleyman Demirel University, Isparta, Turkey
Article Tools
Follow on us
In the present study elastic buckling of steel columns with three different cross sections, i.e. square, rectangle and circle cross sections, and two different boundary conditions, i.e. fixed-free(F-F) and pinned-pinned (P-P) boundary conditions, under axial compression has been investigated. At first, the basic equations of the problem have been given. Then solutions are found and the effects of the boundary conditions, cross sections, slenderness ratios on the buckling loads of the steel columns have been discussed. For the solution of the problem not only numerical computations have been performed but also finite element modeling (FEM) has been employed. For the validation of the present study, the results of numerical computations have been compared with the results of FEM, and a very good agreement has been achieved.
Column, Elastic Buckling, Finite Element Modeling
To cite this article
Mehmet Avcar, Elastic Buckling of Steel Columns Under Axial Compression, American Journal of Civil Engineering. Vol. 2, No. 3, 2014, pp. 102-108. doi: 10.11648/j.ajce.20140203.17
Gardner, L. (2005), "The use of stainless steel in structures", Progress in Structural Engineering and Materials, Vol. 7, No. 2, pp. 45–55.
Elishakoff, I. (2001), "Columns", Encyclopedia of Vibration, pp. 236–243.
Musschenbroek P. Van. (1729), "Introductio da Cohaerentiam Corporum Firmorum", Lugdu-ni.
Euler, L. (1759), "On the strength of columns" , Academy Royal Society Belles Lettres Berlin Memoires 13 p. 252.
Bleich, F. (1952), Buckling Strength of Metal Struc-tures, Eng. Soc. Monograph, McGraw-Hill, New York.
Timoshenko, S.P. (1953), History of Strength of Materials, McGraw-Hill, New York
Timoshenko, S. P. and Gere, J. M. (1961), Theory of Elastic Stability, McGraw-Hill, New York.
Brush, D.O. and Almroth, B.O. (1975), Buck-ling of Bars, Plates, and Shells, McGraw-Hill, New York.
Shrivastava, S.C. (1980), "Elastic buckling of a column under varying axial force", Engineering Jour-nal-American Institute of Steel Construction, Vol. 17, No. 1, pp. 19-21.
Reissner, E., (1982), "Some remarks on the problem of column buckling", Ingenieur-Archiv, Vol. 52, No. 1-2, pp. 115-119.
Johnston, B.G., (1983), "Col-umn buckling theory - historic highlights", Journal of Structural Engineering-ASCE, Vol. 109, No. 9, pp. 2086-2096.
Simitses, G.J., (1986), An Introduction to the Elastic Stability of Structures, Krieger, Malabar, FL.
Ings, N.L. and Trahair, N.S., (1987), "Beam and column buckling under directed loading", Journal of Structural Engineering ASCE, Vol. 113, No.6, pp. 1251-1263.
Bert, C.W., (1990), "Effect of axial compressibility on buckling of columns", Journal of Engineering Mechanics-ASCE, Vol. 116, No. 3, 728-732.
Gjelsvik, A., (1991), "Stability of built-up columns", Journal of Engineering Mechanics- ASCE, Vol. 117, No. 6, pp. 1331–1345.
Vaziri, H.H. and Xie, J., (1992), "Buckling of columns under Variably Distributed Axial Loads", Computers & Structures, Vol. 45, No. 3, pp. 505-509.
Mukherjee, A., Deshpande, J.M. and Anmala, J (1996), "Prediction of buckling load of columns using artificial neural networks", Journal of Structural Engineering-ASCE, Vol. 122, No. 11, pp. 1385-1387
Xie, Y.J., Ning, Q.H. and Chen, M.L., (1998), "The approximate analytical solution for the buckling loads of a thin-walled box column with variable cross-section", Applied Mathematics And Mechanics-English, Vol. 19, No. 5, pp. 445-456.
Elishakoff, I. and Rollot, O., (1999), "New Closed-Form Solutions For Buckling Of A Variable Stiff-ness Column By Mathematica (R)", Journal of Sound And Vibra-tion, Vol. 224, No. 1, pp. 172-182.
Schafer, B.W., (2002), "Local, distortional, and Euler buckling of thin-walled columns", Journal Of Structural Engineering-ASCE, Vol. 128, No. 3, pp. 289-299.
Rasmussen, K.J.R. and Trahair, N.S., (2005), "Exact and approximate solutions for the flexural buckling of columns with oblique rotational end restraints", Thin-Walled Structures, Vol. 43, No. 3, pp. 411-426.
Jang, H.J., Seo, S.Y. and Yang, Y.S., (2006) "Buckling behavior of stainless steel square hollow columns under eccentric loadings", Structural Engineering and Mechanics, Vol. 23, No. 5, pp. 563-577.
Ellobody, E., (2007), "Buckling analysis of high strength stainless steel stiffened and unstiffened slender hollow section columns", Journal of Constructional Steel Research Vol. 63, No. 2, pp. 145-155.
Chan, T.M. and Gardner, L., (2009), "Flexural buckling of elliptical hollow section columns", Journal of Structural Engineering-ASCE, Vol. 135, No. 5, pp. 546-557.
Hosseini H.B. and Jafari, M.A., (2009), "Expe-rimental evaluation of elastic critical load in batten columns", Journal of Constructional Steel Research, Vol. 65, No. 1, pp. 125-131.
Darbandi, S.M., Firouz-Abadi, R.D. and Had-dadpour, H., (2010), "Buckling of variable section columns under axial loading", Journal of Engineering Mechanics-ASCE, Vol. 136, No. 4, pp. 472-476.
Gross, D., Schröder, J., Bonet, J., Hauger, W. and Wall W.A., (2011), "Buckling of Bars", Engineering Mechanics Vol. 2, pp. 287-305.
Ziolkowski, A. and Imieowski, S., (2011), "Buckling and post-buckling behaviour of prismatic aluminium columns submitted to a series of compressive loads", Experimental Mechanics, Vol. 51, No. 8, pp. 1335-1345.
Huang, Y. and Li, X.-F., (2012), "An analytic approach for exactly determining critical loads of buckling of nonuniform columns", International Journal Of Structural Stability And Dynamics, Vol. 12, No. 4, id. 1250027
Adman, R. and Saidani, M., (2013), "Elastic buckling of columns with end restraint effects", Journal of Constructional Steel Research, Vol. 87, pp. 1-5.
Kumar, M. and Yadav, N., (2013), "Buck-ling analysis of a beam-column using multilayer perceptron neur-al network technique", Journal of the Franklin Insti-tute-Engineering and Applied Mathematics, Vol. 350, No. 10, pp. 3188-3204.
Longshithung, P.M. and Darunkumar, S.K., (2013), Buckling of fixed-ended lean duplex stainless steel hollow columns of square, L-, T-, and +-shaped sections under pure axial compression - A finite element study, Thin-Walled Structures, Vol. 63, pp.106-116.
Tekeli, H., Korkmaz, K.A., Demir, F. and Carhoglu, A.I., (2014) "Comparison of critical column buckling load in regression, fuzzy logic and ANN based estimations", Journal of Intelligent and Fuzzy Systems, Vol. 26, No. 3, pp. 1077-1087.
Yuan, W.B., Kim B. and Li L-Y., (2014), "Buckling of axially loaded castellated steel columns", Journal of Constructional Steel Research, Vol. 92, pp. 40-45.
Keller, J.B., (1960), "The shape of the strongest column", Archive for Rational Mechanics and Analysis, Vol. 5, No.1, pp. 275-285.
Yura, J.A., (1971), "Effective length of columns in unbraced frames", Engineering Journal-American Institute of Steel Construction, Vol. 8, No. 2, pp. 37-42.
Olhoff, N. and Rasmussen, S.H., (1977), "On single and bimodal optimum buckling loads of clamped columns", International Journal of Solids and Structures, Vol. 13, No. 7, pp. 605–614.
Szyszkowski, W. and Watson, L.G., (1988), "Optimization of the buckling load of columns and frames", Engineering Structures, Vol. 10, No. 4, pp. 249–256.
Egorov, Y.V. and Karaa, S., (1996), "On the optimal shape of a column against buckling", Comptes Rendus De L Academie Des Sciences Serie I-Mathematique, Vol. 322, No. 6, pp. 519-524.
Chase, J. and Yim, M. (1999), "Optimal Stabilization of Column Buckling", Journal of Engineering Me-chanics-ASCE, Vol. 125, No. 9, pp. 987–993.
Manickarajah, D., Xie, Y.M. and Steven, G.P., (2000), "Optimization of columns and frames against buckling", Computers & Structures, Vol. 75, No. 1, pp.45-54.
Maalawi, K.Y., (2002), "Buckling optimization of flexible columns", International Journal Of Solids And Struc-tures, Vol. 39, No. 23, pp. 5865-5876.
Kruzelecki, J and Smas, P., (2004), "Optimal design of simply supported columns for buckling under loading controlled by displacements", Engi-neering Optimization, Vol. 36, No. 6, pp. 645-658.
Ata-nackovic, T.M., (2007), "Optimal shape of a strongest inverted column", Journal of Computational and Applied Mathematics, Vol. 203, No. 1, pp. 209–218.
Jelicic, Z.D. and Atanackovic, T.M., (2007), "Optimal shape of a vertical rotating column", In-ternational Journal of Non-Linear Mechanics, Vol. 42, No. 1, pp. 172–179.
Atanackovic, T.M., Novakovic, B.N. and Basara, E., (2010), "On the optimal shape of a compressed column", Theoretical Applied Mechanics, Vol.37, No.1, pp. 37-48.
Krużelecki, J. and Ortwein, R., (2012), "Optimal design of clamped columns for stability under combined axial compression and torsion", Structural and Multidisciplinary Opti-mization, Vol.45, No. 5, pp. 729-737.
Lee, B.K., Lee, T.E. and Jung, Y.S., (2012), "Numerical methods for determining strongest cantilever beam with constant volume", KSCE Journal of Civil Engineering, Vol. 16, No. 1, pp. 169-178.
Kripka, M. and Martin, Z., (2013), "Cold-formed steel channel columns optimization with simulated annealing method", Structural Engineering and Mechanics, Vol. 48 No. 3, pp. 383-394.
Jatav, S.K. and Datta, P.K., (2014) "Shape optimization of damaged columns subjected to conservative and non-conservative forces",International Journal of Aeronautical and Space Sciences, Vol. 15 No. 1, pp. 20-31.
ANSYS® Academic Research, Release 15.0
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
Tel: (001)347-983-5186