Nonlinear buckling analysis of shallow arches with elastic horizontal supports

The stiffness of the supports has an influence on the buckling modes and buckling loads of the arch. This paper investigates the in-plane nonlinear behavior and stability of shallow circular arches with elastic horizontal supports that are uniformly subjected to a radial load by the principle of virtual work. The three limiting shallowness values and the critical flexibility of the elastic horizontal supports are derived to differentiate the buckling mode. As the flexibilities of the elastic horizontal supports of an arch increase, the buckling load of the arch decreases, and the central radial displacement increases. And the buckling mode of the arch would then be changed from asymmetric bifurcation buckling to asymmetric bifurcation buckling after the occurrence of snap-through buckling. Then, snap-through buckling occurs, and finally, there is no buckling. Then the parameters including rise-to-span ratio(f/L) and load type are further investigated. An experimental model is designed to verify the analytical results. Finally, a design method for a shallow circular arch with elastic horizontal supports is proposed with the requirement of the elastic-plastic buckling load carrying capacity and the maximum horizontal displacement of the supports for engineering reference.