Large displacement behavior of horizontally curved beams

The primary loads of a horizontally curved beam are those acting perpendicular to the plane of curvature, such as gravity forces, moments, torsional moments, and bimoments., In the case of arches, where only in-plane loads are considered, the only possible non-zero displacements are the radial and axial displacements. The vertical displacement and the rotation will not occur even in the large displacement analysis unless a lateral instability arises. On the contrary, neither the radial nor the axial displacement occurs in the linear analysis of a horizontally curved beam if the loading is applied only in the direction perpendicular to the plane of curvature. However, in the large displacement analysis of a horizontally curved beam, all of the four displacements become coupled as can be seen from the nonlinear differential equations. As a consequence, the radial and axial displacements as well as the vertical displacement and the rotation become important displacement components in the large displacement analysis even if the external loading does not include any in-plane component. Die to complex coupling, the large displacement analysis of a horizontally curved beam becomes much more complicated than that of a straight beam or of an arch. To investigate the large displacement behavior and the instability of a horizontally curved beam, numerical example studies are made again using the developed computer program.