Large deflections of heavy cantilever beams and columns
Large deflections of the heavy horizontal cantilever of uniform cross section have been investigated by Hummel and Morton [1], Bickley [2], and Rohde [3]. No exact analysis of the postbuckling deflections of the heavy column could be found in technical and mathematical publications. The purpose of this note is to extend and improve Rohde's results for the horizontal cantilever as well as to present an exact analysis of large postbuckling deflections of the heavy column. For notations refer to Fig. 1. According to the Bernoulli-Euler hypothesis for slender beams and columns, the bending couple M is proportional to the curvature dip/ds of the deflected inextensional elastica. Hence, m where EI = const, is the flexural stiffness of the column and dM/ds = ws sin by the conditions of equilibrium. Thus, d2\p ws . . ,0. -5 + -sin* = 0, (2) in which w is the weight per unit length of the column. Let