Nonlinear elastic analysis and buckling of pinned–fixed arches

This paper presents a theoretical analysis of the linear and nonlinear elastic in-plane behaviour and buckling of pinned–fixed circular arches that are subjected to a radial load distributed uniformly around the arch axis. In contrast to most previously reported studies, the pinned support and fixed support of a pinned–fixed arch provide different boundary conditions at each of its ends. Because of this, the structural behaviour of a pinned–fixed arch is quite different from that of a pinned–pinned or a fixed–fixed arch. The linear and nonlinear analyses show that the uniform radial load produces both an unsymmetrical bending moment and an axial compressive force in pinned–fixed arches; particularly in shallow pinned–fixed arches, the unsymmetrical bending moments are significant prior to in-plane buckling. It is found that a pinned–fixed arch under a uniform radial load can buckle in a limit point mode, but cannot buckle in a bifurcation mode. This is quite different from pinned–pinned or fixed–fixed arches under a uniform radial load that may buckle in a bifurcation mode and in a limit point mode. Analytical solutions for the nonlinear equilibrium path and limit point buckling load of shallow pinned–fixed circular arches are derived. Comparisons with finite element results show that the analytical solutions can predict the nonlinear equilibrium path and the nonlinear buckling and postbuckling behaviour of shallow pinned–fixed arches accurately. Although these solutions are derived for shallow pinned–fixed arches, comparisons with finite element results have demonstrated that they can also provide reasonably good predictions for the nonlinear buckling load of deep pinned–fixed arches under a uniform radial load.