Vol. 16, No. 1, pp. 55-64 (2020)
IN-PLANE NONLINEAR ANALYSIS AND BUCKLING OF
SHEAR-DEFORMABLE CIRCULAR ARCHES
Gen-shu Tong1,*, Yong-lin Pi2 and Wei Gao2
1Department of Civil Engineering, Zhejiang University, Hangzhou 310058, China,
2Department of Civil & Environmental Engineering, The University of New South Wales, NSW 2052, Australia
*(Corresponding author: E-mail:This email address is being protected from spambots. You need JavaScript enabled to view it.)
Received: 22 February 2019; Revised: 15 January 2020; Accepted: 20 January 2020
DOI:10.18057/IJASC.2020.16.1.7
 View Article |
Export Citation: Plain Text | RIS | Endnote |
ABSTRACT
A new theory for nonlinear analysis of shear-deformable circular arches is derived, in which Timoshenko’s assumption on the deformation of cross-section and the Green strains are adopted. In the variational equation, the nonlinear energy of the shear and the transverse normal stresses is included. Substituting the internal forces from linear analysis, a set of linearized equations is derived for buckling analysis of shear deformable arches. These equations are then used to solve the buckling of circular arches and rings under three types of radial pressures to compare the various results appeared in the literature.
Linear analysis is carried out on hinged arches under uniform radial pressure to check the changes of displacements and internal forces after the shear deformation is considered. It is found that the axial force is more uniform along the arch length when shear deformation is considered, and the bending moment and shear force are smaller, but the displacements are always larger.
Buckling of arches under radial pressure under various boundary conditions are studied, buckling factors for symmetrical and anti-symmetrical buckling are tabulated, and approximate formulas for the critical loads are proposed.
KEYWORDS
Circular arch, Buckling, Nonlinear analysis, Shear deformation, Linear analysis
REFERENCES
[1] Timoshenko, S. P, Gere, J. M., Theory of elastic stability, McGrawHill Kogakusha Ltd, Tokyo, 109,1961.
[2] Pi Y.L., Bradford M.A. and Uy B., “In plane stability of arches”, International Journal of Solids and Structures, 39(1), 105 125, 2002.
[3] Simitses G.J., An introduction to the elastic stability of structures, Prentice Hall Inc, Englewood Cliffs, 1976.
[4] Tong G.S., Pi Y.L., Bradford M.A. and Tin Loi F., “In plane nonlinear buckling analysis of deep circular arches incorporating transverse stresses”, Journal of engineering mechanics, 134(5), 362 373, 2008.
[5] Friedman Z. and Kosmatka Z.B., “An Accurate two node finite element for shear deformable curved beams”, International Journal for Numerical Methods in Engineering, 41, 473 498, 1998.
[6] Huang C.S, Nieh K.Y. and Yang M.C., “In plane free vibration and stability of loaded and shear deformable circular arches”, International Journal of Solids and Structures, 40, 5865 5886, 2003
[7] Dinnik A.N., “Stability of arches”, OGIS, Gostechizdat (in Russian, Chinese translation in 1958),1946.
[8] Smith C.V. and Simitses G.J., “Effect of shear and load behavior on ring stability”, Journal of the Engineering Mechanics Division, 95(3), 559 570, 1969.
[9] Guo Y.L. and Huang L., “Design theory and method for in plane ultimate strength of arches with web openings”, Journal of Building Structures, 3, 003, 2007.
[10] Dou C., Guo Y.F., Jiang Z.Q., Gao W. and Pi Y.L., “In plane buckling and design of steel tubular truss arches”, Thin Walled Structures, 130, 613 621, 2018
[11] Guo Y.L., Guo Y.F. and Dou C., “In plane buckling and design of two hinged steel tube circular truss arches under pure compression”, Journal of Building Structures, 31(8), 45-53, 2010.
[12] Guo Y.L., Chen H., Pi Y.L. and Bradford M.A., “In plane strength of steel arches with a sinusoidal corrugated web under a full span uniform vertical load: Experimental and numerical investigations”, Engineering Structures, 110, 105 115, 2016.
[13] Attard M.M., Zhu J.B. and Kellermann D.C., “In plane buckling of circular arches and rings with shear deformations”, Archive of Applied Mechanics, 83(8), 1145 1169, 2013.
[14] Zhu J.B., Attard M.M. and Kellermann D.C., “In plane nonlinear buckling of circular arches including shear deformation”, Archive of Applied Mechanics, 84, 1841 1860, 2014.
[15] Attard M.M., Zhu J.B. and Kellermann D.C., “In plane buckling of prismatic funicular arches with shear deformations”, Archive of Applied Mechanics, 84, 693 713, 2014.
[16] Washizu K., Variational methods in elasticity and plasticity, Pergamon press, 1975.