Advanced Steel Construction

Vol. 16, No. 1, pp. 55-64 (2020)




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




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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.



Circular arch, Buckling, Nonlinear analysis, Shear deformation, Linear analysis


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