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In-Plane Elastic Stability of Arches under a Radial Concentrated Load

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DOI: 10.4236/eng.2014.69058    2,411 Downloads   2,805 Views   Citations


This paper is concerned with the in-plane elastic stability of arches subjected to a radial concentrated load. The equilibrium equation for pin-ended circular arches is established by using energy method, and it is proved that the axial force is nearly a constant along the circumference of the circular arches. Based on force method, the equation for the primary eigen function is derived and solved, and the approximate analytical solution of critical instability load is obtained. Numerical examples are given and discussed.

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Xu, Y. , Gui, X. , Zhao, B. and Zhou, R. (2014) In-Plane Elastic Stability of Arches under a Radial Concentrated Load. Engineering, 6, 572-583. doi: 10.4236/eng.2014.69058.


[1] Timoshenko, S.P. and Gere, J.M. (1961) Theory of Elastic Stability. 2nd Edition, McGraw-Hill, New York.
[2] Vlasov, V.Z. (1961) Thin-Walled Elastic Beams. 2nd Edition, Israel Program for Scientific Translation, Israel.
[3] Simitses, G.J. (1976) An Introduction to the Elastic Stability of Structures. Prentice-Hall, Englewood Cliffs.
[4] Bradford, M.A., Uy, B. and Pi, Y.L. (2002) In-Plane Stability of Arches under a Central Concentrated Load. Journal of Engineering Mechanics, 128, 10-20.
[5] Gjelsvik, A. and Bodner, S.R. (1962) The Energy Criterion and Snap Buckling of Arches. Journal of the Engineering Mechanics, ASCE, 88, 87-134.
[6] Schreyer, H.L. and Masur, E.F. (1966) Buckling of Shallow Arches. Journal of the Engineering Mechanics, ASCE, 92, 1-20.
[7] Pi, Y.L. and Trahair, N.S. (1999) In-Plane Buckling and Design of Steel Arches. Journal of the Structural Engineering, ASCE, 125, 1291-1298.
[8] Pi, Y.L., Bradford, M.A. and Uy, B. (2002) In-Plane Stability of Arches. International Journal of Solids and Structures, 39, 105-125.
[9] ABAQUS Standard User’s Manual. Copyright 2009, Karlsson and Sorensen Inc.
[10] ANSYS User’s Manual 12.0. Copyright 2009 SAS IP, Inc.
[11] Rajasekaran, S. and Padmanabhan, S. (1989) Equations of Curved Beams. Journal of Engineering Mechanics, 115, 1094-1111.
[12] Kang, Y.J. and Chai, H.Y. (1994) Thin-Walled Curved Beams. II: Analytical Solutions for Buckling of Arches. Journal of Engineering Mechanics, 120, 2102-2125.
[13] Cheng, J. and Jiang, J.J. (2003) Ultimate Load-Carrying Capacity of Long-Span Steel Arch Bridges. Engineering Mechanics, 20, 7-10. (in Chinese)
[14] Pi, Y.L. and Trahair, N.S. (1996) In-Plane Inelastic Buckling and Strengths of Steel Arches. Journal of the Structural Engineering, ASCE, 122, 734-747.
[15] Pi, Y.L. and Trahair, N.S. (1998) Non-Linear Buckling and Postbuckling of Elastic Arches. Engineering Structures, 20, 571-579.
[16] Long, Y.Q. and Bao, S.H. (2000) Structure Mechanics. Higher Education Press, Beijing. (in Chinese)
[17] Ding, J.G. (2003) The Analysis of Stability on Cable-Arch Structure Acted by a Concentrated Load at the Middle Point of a Span. Journal of Nanjing University of Science and Technology, 27, 214-217.
[18] Xiang, H.F. and Liu, G.D. (1991) Stability and Vibration of arch Structure. China Communication Press, Beijing. (in Chinese)
[19] Gui, X.M., Xu, Y.J. and Zhao, B. (2011) Finite Element Analysis on Stability of u-Type Arch. Proceedings of the 20th National Conference on Structure Engineering, Ningbo, 5-7 November 2011, 182-186. (in Chinese)

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