Lateral Buckling of Parabolic Arches with Tilting Loads

Lateral buckling loads are presented for parabolic arches loaded uniformly by means of either hangers or columns. Buckling loads for arches with hangers have been previously obtained by Godden who used a mathematical model for his analysis which differs from the gravity loaded arches considered herein. It is found that the two representations of the arch yield almost identical results. The torsional stiffness and the flexural stiffness of the arch in the lateral direction as well as the height-to-span ratio influence the buckling load. Buckling loads are given for height-to-span ratios ranging from 0.1 to 0.6 and torsional to flexural stiffness ratios from 0.01 to 1.6. The range of stiffness ratios covers arch cross sections of closed and open profile, but for certain thin-walled open profile cross sections the buckling loads are conservative because warping torsion has been ignored. An optimum height to span ratio is found to exist for each torsional to lateral stiffness ratio.