New Theory on Buckling of Curved Beams

Abstract

Vlasov and Yoo's curved‐beam theories have been criticized for not applying the principles of mechanics directly to the curved beam but deriving their equations as the analogies of straight‐beam equations. Although later researchers have worked directly on the curved beam, they have inevitably introduced ambiguities in maintaining consistent orders of magnitude for the terms involved in their formulations. The reality is that not all the theories are consistent with each other. This paper intends to demonstrate that by considering a curved beam in the limit as an infinite number of infinitesimal straight beams—the only kinematic assumption—the classic straight‐beam equations can be manipulated to derive a new set of curved‐beam equations. Because the ambiguities involved in previous formulations are totally circumvented, the presented method is believed to be most convincing. For the two cases of uniform bending and uniform compression, the presented results are compared with those obtained by couples of existing theories.