Vol. 1, No. 1, pp. 47-66 (2005)
AN EQUILIBRIUM APPROACH FOR FLEXURAL-TORSIONAL BUCKLING OF ELASTIC STEEL ARCHES
Y.L. Pi1, M.A. Bradford and Y.Y. Chen
1The corresponding author, Senior Research Fellow, School of Civil and Environmental Engineering,
NSW, Sydney, NSW 2052, Australia.
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ABSTRACT
When an arch is subjected to in-plane loading, it may suddenly deflect laterally and twist out of the plane of loading and fail in a flexural-torsional buckling mode. This paper presents a static equilibrium approach for theelastic flexural-torsional buckling of circular arches under uniform bending, or under uniform compression. Solutionsfor the buckling moment and buckling load are obtained in closed form, and discrepancies among existing solutionsare clarified. It is found that it is reasonable to use material curvatures and twist, rather than spatial curvatures andtwist, for the flexural-torsional buckling analysis of arches. First order buckling deformations provide a sufficientbasis for the static equilibrium methods for the flexural-torsional buckling analysis of arches. Equilibrium of alengthwise differential element of an arch should be considered in the analysis, and so the couplings between thelateral bending and torsional actions and resistances can be included in the differential equations of equilibrium. If theequilibrium is considered only at the cross-section, this is equivalent to treating arches as analogous with straightmembers, and so the coupling terms in the differential equations of equilibrium are lost.
KEYWORDS
Arch, Bending, Buckling, Compression, Elastic, Equilibrium Approach, Flexural-Torsional
REFERENCES
[1] Pi YL, Trahair NS, Out-of-plane inelastic buckling and strength of steel arches. Journal of Structural Engineering, ASCE 1998;124(2):174-183.
[2] Timoshenko SP, Gere JM. Theory of elastic stability, 2nd Edition New York, USA: McGraw-Hill, 1961.
[3] Yoo CH. Flexural-torsional stability of curved beams. Journal of the Engineering Mechanics Division, ASCE 1982;108(EM6):1351-1369.
[4] Papangelis JP, Trahair NS. Flexural-torsional buckling of arches. Journal of Structural Engineering, ASCE 1987;113(4):889-906.
[5] Yang YB, Kuo SR. Effects of curvature on stability of curved beams. Journal of Structural Engineering, ASCE 1987;113(6):821-841.
[6] Rajasekaran S, Padmanabhan S. Equations of curved beams. Journal of Engineering Mechanics, ASCE 1989;115(5):1094-1111.
[7] Trahair NS. Flexural-torsional buckling of structures, London, UK: E & FN Spon, 1993.
[8] Kang YJ, Yoo CH. Thin-walled curved beams. II: Analytical solutions for buckling of arches. Journal of Engineering Mechanics, ASCE 1994;120(10):2102-2125.
[9] Pi YL, Bradford MA. Elastic flexural-torsional buckling of continuously restrained arches. International Journal of Solids and Structures 2002;128(6):719-727.
[10] Pi YL, Bradford MA. Effects of approximations in analysis of beams of open thin-walled cross-section: 1. Flexural-torsional stability. International Journal for Numerical Methods in Engineering 2001; 51(7):757-772.
[11] Vlasov VZ. Thin-walled elastic beams, 2nd Edition. Jerusalem, Israel: Israel Program for Scientific Translation, 1961.
[12] Pi YL, Trahair NS. Nonlinear inelastic analysis of steel beam-columns. I: Theory. Journal of Structural Engineering, ASCE 1994;120(7):2041-2061.
[13] Pi YL, Bradford MA, Uy B. Nonlinear analysis of members curved in space with warping and Wagner effects. International Journal of Solids and Structures 2005; 42(11-12): 3147-3169.
[14] Gibbs J. Vector analysis. New York, USA: Dover, 1961.
[15] Trahair NS, Bradford MA, Nethercot DA. The behaviour and design of steel structures to BS5950, Third Edition - British, London, UK: E & FN Spon, 2001.
[16] BHP. Hot rolled and structural steel products, 2000 Edition, Melbourne, Australia: BHP Co. Pty Ltd, 2000.
[17] Pi YL, Papangelis JP, Trahair NS. Prebuckling deformations and flexural-torsional buckling of arches. Journal of Structural Engineering, ASCE 1995;121(9):1313-1322.