Out-of-plane buckling of arches with varying curvature

A number of theoretical solutions have been reported for the elastic out-of-plane buckling of arches with open thin-walled sections. However, most of theses studies are limited to arches with constant curvatures such as circular arches. This paper investigates the out-of-plane buckling of arches with varying curvature. Buckling equations for arches with varying curvature are derived and verified by comparing with those proposed earlier by different researchers. For this, the out-of-plane buckling of circular arches under pure axial compression and pure bending is studied. For an application of the derived buckling equations to arches with varying curvature, buckling loads of parabolic arches are determined. The solutions for parabolic arches are successfully verified by comparing with results of previous researcher and finite element analyses. Finally, comparative studies of circular and parabolic arches are conducted. The results show that the difference in buckling loads of circular and parabolic arches increases as the rise to span ratio increases.