Abstract
This paper revisits the nonlinear in-plane analysis of a shallow pin-ended circular arch under a central concentrated load. It is found that the arch may have multiple equilibrium branches and limit points, and a modified slenderness of the arch defined in the paper plays an important role in the number of the limit points and equilibrium branches. The analytical solution for the specific modified slendernesses that switch the number of equilibrium branches and limit points is derived. The analytical solutions for the load, axial force, and radial displacements corresponding to the specific modified slendernesses are also derived. This paper deepens the understanding for the geometric nonlinear analysis of circular arches and their geometric softening and stiffening behavior and provides useful benchmarks for the analyses of shallow arches. In addition, this paper extends the current solutions of nonlinear equilibrium of arches associated with axial compression to those associated with axial tension caused by large deformations.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work has been supported by the Australian Research Council through Discovery Projects (DP140101887 and DP150100446) awarded to the first two authors, an Australian Laureate Fellowship (FL100100063) awarded to the second author, and a Linkage Project (LP150101196) awarded to the second and third authors.
References
Abaqus [Computer software]. Dassault Systèmes, Waltham, MA.
Bažant, Z. P., and Cedolin, L. (2003). Stability of structures, Dover, New York.
Bradford, M. A., Uy, B., and Pi, Y.-L. (2002). “In-plane stability of arches under a central concentrated load.” J. Eng. Mech., 710–719.
Cardoso, E. L., and Fonseca, J. S. O. (2007). “The GDC method as an orthogonal arc-length method.” Commun. Numer. Methods Eng., 23(4), 263–271.
Dickie, J. F., and Broughton, P. (1971). “Stability criteria for shallow arches.” J. Eng. Mech. Div., 97(EM3), 951–965.
Gjelsvik, A., and Bodner, S. R. (1962). “Energy criterion and snap buckling of arches.” J. Eng. Mech. Div., 88(EM5), 87–134.
Harrison, H. B. (1982). “In-plane stability of parabolic arches.” J. Struct. Div., 108(ST1), 195–205.
Kuo, S. R., and Yang, Y. B. (1995). “Tracing postbuckling paths of structures containing multi loops.” Int. J. for Numer. Methods Eng., 38(23), 4053–4075.
Moona, J., Yoon, K.-Y., Lee, T.-H., and Lee, H.-E. (2007). “In-plane elastic buckling of pin-ended shallow parabolic arches.” Eng. Struct., 29(10), 2611–2617.
Oran, C., and Reagan, R. S. (1969). “Buckling of uniformly compressed circular arches.” J. Eng. Mech. Div., 95(EM4), 879–895.
Pi, Y.-L., and Bradford, M. A. (2009). “Non-linear in-plane postbuckling of arches with rotational end restraints under uniform radial loading.” Int. J. Non-Linear Mech., 44(9), 975–989.
Pi, Y.-L., and Bradford, M. A. (2012). “Non-linear buckling and postbuckling analysis of arches with unequal rotational end restraints under a central concentrated load.” Int. J. Solids Struct., 49(26), 3762–3773.
Pi, Y.-L., and Bradford, M. A. (2014). “Multiple unstable equilibrium branches and non-linear dynamic buckling of shallow arches.” Int. J. Non-Linear Mech., 60, 33–45.
Pi, Y.-L., Bradford, M. A., and Uy, B. (2002). “In-plane stability of shallow arches.” Int. J. Solids Struct., 39(1), 105–125.
Qaqish, S., and Haddadin, A. (1991). “Buckling behavior of elastic circular arches.” J. Eng. Mech., 117(11), 2659–2680.
Riks, E. (1979). “An incremental approach to the solution of snapping and buckling problems.” Int. J. Solids Struct., 15(7), 529–551.
Simitses, G. J. (1973). “Snapping of low pinned arches on an elastic foundation.” J. Appl. Mech., 40(3), 741–744.
Virgin, L. N., Wiebea, R., Spottswood, S. M., and Eason, T. G. (2014). “Sensitivity in the structural behavior of shallow arches.” Int. J. Non-Linear Mech., 58, 212–221.
Yang, Y. B., and Shieh, M. A. (1990). “Solution method for nonlinear problems with multiple critical points.” AIAA J., 28(12), 2110–2116.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 142 • Issue 8 • August 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Aug 30, 2015
Accepted: Jan 29, 2016
Published online: Mar 29, 2016
Published in print: Aug 1, 2016
Discussion open until: Aug 29, 2016
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.