Flexibility Influence Functions for Curved Beams

The curve representing the elastic axis may consist of straight sections, curved sections, or both, and may have a locus of points lying in a plane or in three-space. Each differential element of the elastic axis is given six degrees of freedom, namely, three translations and three rotations. Three shears and three moments are assumed to act at each point of the elastic axis. In passing to the limit as all segment lengths simultaneously approach zero, the general element becomes a flexibility influence function. The results of the method are illustrated through the derivation of the flexibility influence functions associated with a circular beam with uniform stiffness. Mention is also made of how the procedure presented may be applied to special beam problems.