The Shallow Arch—General Buckling, Postbuckling, and Imperfection Analysis∗

Abstract

Abstract A general discussion of the behavior of the shallow circular arch is presented. It is shown that, irrespective of specific loading or boundary conditions, it is possible to arrive at general conclusions regarding buckling, postbuckling, and imperfection sensitivity. General methods of analysis are established which lead to the determination of points of bifurcation and of postbuckling paths under symmetric loads. Modifications accounting for antisymmetric load components are introduced, with special emphasis on their asymptotic and limit load effect. A typical numerical example is carried through in detail. The solution is “exact” in the sense of shallow arch theory. Its asymptotic behavior conforms to the asymptotic theory of Koiter.