Flexural-Torsional Buckling of Steel Arches under a Localized Uniform Radial-Load Incorporating Shear Deformations
Publication: Journal of Structural Engineering
Volume 145, Issue 10
Abstract
This paper concentrates on the laterally flexural-torsional buckling analysis incorporating shear deformations for elastic steel circular arches having boundary rotational restraints under a localized uniform radial load, which has not been reported in the literature. The localized uniform radial load and elastic restrained boundaries produce complex nonuniform shear force, axial force, and bending moment in an arch, which need to be considered in the flexural-torsional buckling analysis of the arch. Therefore, the in-plane elastic analysis is carefully performed to derive exact prebuckling shear force, axial force, and bending moment based on which the analytical solutions of the critical value of localized uniform radial load for flexural-torsional buckling of elastic steel arches are derived. Comparisons show that analytical solutions agree extremely well with finite element results. The influences of various factors on the flexural-torsional buckling are studied. The localized loading segment length and/or the elastic stiffness of boundary rotational restraints are found to have significant influences on the flexural-torsional buckling load. The buckling load decreases with a decrease in the stiffness of the rotational restraints and with a decrease in the loading segment length. The influence of shear deformations on the flexural-torsional buckling load is also investigated, and the results show that shear deformations reduce the critical flexural-torsional buckling loads for arches with a medium and small slenderness ratio.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The research for this paper was financially supported by the National Natural Science Foundation of China (Grant No. 51878188), Technology Planning Project of Guangdong Province (Grant No. 2016B050501004), and Technology Planning Project of Guangzhou City (Grant No. 201807010021). The authors are grateful for this support.
References
Bažant, Z. P., and L. Cedolin. 2003. Stability of structures. Mineola, NY: Dove Publication.
Bradford, M. A., and Y. L. Pi. 2006. “Elastic flexural-torsional buckling of circular arches under uniform compression and effects of load height.” J. Mech. Mater. Struct. 1 (7): 1235–1255. https://doi.org/10.2140/jomms.2006.1.1235.
Bradford, M. A., and Y. L. Pi. 2012. “A new analytical solution for lateral-torsional buckling of arches under axial uniform compression.” Eng. Struct. 41 (Aug): 14–23. https://doi.org/10.1016/j.engstruct.2012.03.022.
Cai, J., and J. Feng. 2010. “Buckling of parabolic shallow arches when support stiffens under compression.” Mech. Res. Commun. 37 (5): 467–471. https://doi.org/10.1016/j.mechrescom.2010.05.004.
Cai, J., Y. Xu, J. Feng, and J. Zhang. 2012. “In-plane elastic buckling of shallow parabolic arches under an external load and temperature changes.” J. Struct. Eng. 138 (11): 1300–1309. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000570.
Dou, C., Y. L. Guo, Y. L. Pi, S. Y. Zhao, and M. A. Bradford. 2014. “Effects of shape functions on flexural-torsional buckling of fixed circular arches.” Eng. Struct. 59 (Feb): 238–247. https://doi.org/10.1016/j.engstruct.2013.10.028.
Dou, C., and Y. L. Pi. 2016. “Flexural-torsional buckling resistance design of circular arches with elastic end restraints.” J. Struct. Eng. 142 (2): 04015104. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001373.
Guo, Y. L., S. Y. Zhao, Y. L. Pi, M. A. Bradford, and C. Dou. 2015. “An experimental study on out-of-plane inelastic buckling strength of fixed steel arches.” Eng. Struct. 98 (Sep): 118–127. https://doi.org/10.1016/j.engstruct.2015.04.029.
Hu, C. F., Y. L. Pi, W. Gao, and L. Li. 2018. “In-plane nonlinear elastic stability of parabolic arches with different rise-to-span ratios.” Thin-Walled Struct. 129 (Aug): 74–84. https://doi.org/10.1016/j.tws.2018.03.019.
Huang, Y. H., A. R. Liu, C. J. Zhu, and H. W. Lu. 2019. “Experimental and numerical investigations on out-of-plane ultimate resistance of parallel twin-arch under uniform radial load.” Thin-Walled Struct. 135 (Feb): 147–159. https://doi.org/10.1016/j.tws.2018.10.042.
Kang, Y. J., and C. H. Yoo. 1994. “Thin-walled curved beams. II: Analytical solutions for instability of arches.” J. Eng. Mech. 120 (10): 2102–2125. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:10(2102).
Liu, A. R., Y. H. Huang, J. Y. Fu, Q. C. Yu, and R. Rao. 2015. “Experimental research on stable ultimate bearing capacity of leaning-type arch rib systems.” J. Constr. Steel Res. 114 (Nov): 281–292. https://doi.org/10.1016/j.jcsr.2015.08.011.
Liu, A. R., H. W. Lu, J. Y. Fu, and Y. L. Pi. 2017a. “Lateral-torsional buckling of circular steel arches under arbitrary radial concentrated load.” J. Struct. Eng. 143 (9): 04017129. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001858.
Liu, A. R., H. W. Lu, J. Y. Fu, and Y. L. Pi. 2017b. “Lateral-torsional buckling of fixed circular arches having a thin-walled section under a central concentrated load.” Thin-Walled Struct. 118 (Sep): 46–55. https://doi.org/10.1016/j.tws.2017.05.002.
Lu, H. W., A. R. Liu, Y. L. Pi, M. A. Bradford, and J. Y. Fu. 2019. “Lateral-torsional buckling of arches under an arbitrary radial point load in a thermal environment incorporating shear deformations.” Eng. Struct. 179 (Jan): 189–203. https://doi.org/10.1016/j.engstruct.2018.10.071.
Lu, H. W., A. R. Liu, Y. L. Pi, M. A. Bradford, J. Y. Fu, and Y. H. Huang. 2018. “Localized loading and nonlinear instability and post-instability of fixed arches.” Thin-Walled Struct. 131 (Oct): 165–178. https://doi.org/10.1016/j.tws.2018.06.019.
Papangelis, J. P., and N. S. Trahair. 1987. “Flexural-torsional buckling of arches.” J. Struct. Eng. 113 (4): 889–906. https://doi.org/10.1061/(ASCE)0733-9445(1987)113:4(889).
Papangelis, J. P., and N. S. Trahair. 1988. “Buckling of monosymmetric arches under point loads.” Eng. Struct. 10 (4): 257–264. https://doi.org/10.1016/0141-0296(88)90047-8.
Pi, Y. L., and M. A. Bradford. 2013. “Lateral-torsional elastic buckling of rotationally restrained arches with a thin-walled section under a central concentrated load.” Thin-Walled Struct. 73 (Dec): 18–26. https://doi.org/10.1016/j.tws.2013.07.006.
Pi, Y. L., M. A. Bradford, and F. Tin-Loi. 2007. “Flexural-torsional buckling of shallow arches with open thin-walled section under uniform radial loads.” Thin-Walled Struct. 45 (3): 352–362. https://doi.org/10.1016/j.tws.2007.02.002.
Pi, Y. L., M. A. Bradford, and G. S. Tong. 2010. “Elastic lateral-torsional buckling of circular arches subjected to a central concentrated load.” Int. J. Mech. Sci. 52 (6): 847–862. https://doi.org/10.1016/j.ijmecsci.2010.02.003.
Pi, Y. L., M. A. Bradford, N. S. Trahair, and Y. Y. Chen. 2005. “A further study of flexural-torsional buckling of elastic arches.” Int. J. Struct. Stab. 5 (2): 163–183. https://doi.org/10.1142/S0219455405001568.
Rajasekaran, S., and S. J. E. M. Padmanabhan. 1989. “Equations of curved beams.” J. Eng. Mech. 115 (5): 1094–1111. https://doi.org/10.1061/(ASCE)0733-9399(1989)115:5(1094).
Timoshenko, S. P., and J. M. Gere. 1961. Theory of elastic stability. 2nd ed. New York: McGraw-Hill.
Trahair, N. S. 1993. Flexural-torsional buckling of structures. London: CRC Press.
Vlasov, V. Z. 1984. Thin-walled elastic beams. 2nd ed. Jerusalem: Israel Program for Scientific Translation.
Yang, Y. B., and S. R. Kuo. 1987. “Effect of curvature on stability of curved beams.” J. Struct. Eng. 113 (6): 1185–1202. https://doi.org/10.1061/(ASCE)0733-9445(1987)113:6(1185).
Yang, Y. B., S. R. Kuo, and J. D. Yau. 1991. “Use of straight-beam approach to study buckling of curved beams.” J. Struct. Eng. 117 (7): 1963–1978. https://doi.org/10.1061/(ASCE)0733-9445(1991)117:7(1963).
Yoo, C. H. 1982. “Flexural-torsional stability of curved beams.” J. Eng. Mech. Div. 108 (6): 1351–1369.
Ziemian R. D., ed. 2010. Guide to stability design criteria for metal structures. New York: Wiley.
Information & Authors
Information
Published In
Copyright
©2019 American Society of Civil Engineers.
History
Received: Nov 20, 2018
Accepted: Mar 7, 2019
Published online: Aug 15, 2019
Published in print: Oct 1, 2019
Discussion open until: Jan 15, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.