Abstract
The tangent stiffness equation for a planar straight beam to reflect the displacement dependency of loading is derived. The load stiffness matrices for water pressure and the center directed uniform distributive loading for circular members are obtained explicitly. Using the stiffness equation derived, planar buckling and post-buckling of elastic rings and arches subject to a variety of loading patterns have been examined. It is found from the computations that the displacement dependency of loadings significantly affects not only the buckling strength, but also, even more, the post buckling finite displacement behavior of the structures.
