Out-of-Plane Elastic Buckling of Circular Arches with Elastic End Restraints
Publication: Journal of Structural Engineering
Volume 140, Issue 10
Abstract
Circular arches subjected to in-plane loading are restrained with discrete lateral bracings to improve their out-of-plane stabilities in many cases. The arch segment between two adjacent bracings may buckle out of plane if the effective length of the arch segment is sufficiently large. During out-of-plane buckling, adjacent arch segments may provide elastic restraints which increase the out-of-plane stability of the arch segment significantly. This paper is concerned with out-of-plane elastic buckling of circular arch segments with elastic end restraints. The analytical method for deriving the out-of-plane buckling loads of circular arches with equal rotational restraints or equal warping restraints at both ends is formulated. For the convenience of structural designers, simple approximate formulas for predicting the out-of-plane buckling loads of these arches are developed by the curve-fitting method. As for circular arches with unequal rotational restraints, the approximate formula for the buckling load of the arch with equal rotational restraints is modified with a reduction factor. Comparisons with the finite-element results and the analytical solutions show that the predictions by approximate formulas are sufficiently accurate.
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Acknowledgments
This study has been supported by research grants from the National Natural Science Foundation of China (No. 51278273), 2012 College Doctoral Research Foundation of China (No. 20120002110001), 2013 Natural Science Foundation of Beijing (No. 8132036), and China Postdoctoral Science Foundation (No. 2012M510457) awarded to the third author.
References
ANSYS Multiphysics 12.1 (2010). [Computer software]. Ansys, Canonsber, PA.
Bradford, M. A., and Pi, Y.-L. (2002). “Elastic flexural-torsional buckling of discretely restrained arches.” J. Struct. Eng., 719–727.
Bradford, M. A., and Pi, Y. L. (2012). “A new analytical solution for lateral-torsional buckling of arches under axial uniform compression.” Eng. Struct., 41, 14–23.
Dou, C. (2011). “Out-of-plane stability and design of steel arches.” Ph.D. thesis, Tsinghua Univ., Beijing (in Chinese).
Guo, Y.-L., and Dou, C. (2012). “Out-of-plane elastic buckling of I-section steel arches braced laterally and design of bracing stiffness.” J. Build. Struct., 33(7), 37–45 (in Chinese).
Papangelis, J. P., and Trahair, N. S. (1987). “Flexural-torsional buckling of arches.” J. Struct. Eng., 1433–1443.
Pi, Y.-L., and Bradford, M. A. (2002). “Elastic flexural-torsional buckling of continuously restrained arches.” Int. J. Solids Struct., 39(8), 2299–2322.
Pi, Y.-L., and Bradford, M. A. (2004). “Elastic flexural-torsional buckling of fixed arches.” Q. J. Mech. Appl. Math., 57(4), 551–569.
Pi, Y.-L., and Bradford, M. A. (2005). “Out-of-plane strength design of fixed steel I-section arches.” J. Struct. Eng., 560–568.
Pi, Y.-L., Bradford, M. A., Trahair, N. S., and Chen, Y.-Y. (2005). “A further study of flexural-torsional buckling of elastic arches.” Int. J. Struct. Stabil. Dynam., 5(2), 163–183.
Pi, Y.-L., and Trahair, N. S. (1996). “Three-dimensional analysis of elastic arches.” Eng. Struct., 18(1), 49–63.
Rajasekaran, S., and Padmanabhan, S. (1989). “Equations of curved beams.” J. Eng. Mech., 1094–1111.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability, 2nd Ed., McGraw-Hill, New York.
Tokarz, F. J., and Sandhu, R. S. (1972). “Flexural-torsional buckling of parabolic arches.” J. Struct. Div., 1223–1238.
Trahair, N. S., and Bradford, M. A. (1998). The behavior and design of steel structures to AS4100, 3rd Australian Ed., E and FN Spon, London.
Vlasov, V. Z. (1961). Thin-walled elastic beams, 2nd Ed., Israel Program for Scientific Translation, Jerusalem.
Yang, Y. B., and Kuo, S. R. (1987). “Effect of curvature on stability of curved beams.” J. Eng. Mech., 113(6), 1185–1202.
Yang, Y. B., and McGuire, W. (1984). “A procedure for analysing space frames with partial warping restraint.” Int. J. Numer. Methods Eng., 20(8), 1377–1398.
Yoo, C. H. (1982). “Flexural-torsional stability of curved beams.” J. Eng. Mech., 108(6), 1351–1369.
Yoo, C. H., and Pfeiffer, P. A. (1984). “Buckling of curved beams with in-plane deformation.” J. Struct. Eng., 291–300.
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Published In
Journal of Structural Engineering
Volume 140 • Issue 10 • October 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Aug 1, 2013
Accepted: Oct 28, 2013
Published online: May 13, 2014
Published in print: Oct 1, 2014
Discussion open until: Oct 13, 2014
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