Large Deflections and Stability of Hingeless Circular Arches Under Interacting Loads

Abstract

The buckling behavior subsequent to large prebuckling deflections of hingeless circular arches subjected to a downward point load at the crown as well as their own dead weight is investigated on the basis of Euler’s nonlinear theory of the inextensible curved elastica. The theory used is exact in the sense that no restrictions are imposed on the magnitudes of deflections. Among others, interaction curves of the critical values of the two loads (i.e., stability boundaries) are plotted and examined. With the aid of these interaction curves, simple approximate formulas relating the two critical loads are established. It is found that nonshallow hingeless arches may buckle by either asymmetrical sidesway or symmetrical snap-through, depending on the relative magnitudes of the point load and the weight of the arch. The results of this study are essential if arches are to be tested near buckling loads, since it is difficult to eliminate the effect of own dead weight in experimental work.