Collapse of Heavy Cantilevered Elastica With Frictional Internal Support

Abstract

Equilibrium states are investigated for a heavy flexible strip that is fixed at one end and rests on an internal frictional support. Large vertical deflections are admitted. In the analytical portion of the study, the strip is modeled as an inextensible elastica. Experiments are conducted on strips of transparency film. For a sufficiently large gap between the fixed end and the internal support, the strip slips through the gap and collapses downward. For moderate gaps, two continuous ranges of equilibrium shapes exist, one with relatively small deflections within the gap and one with large deflections within the gap. The results for a given gap size depend on the length, weight per unit length, and bending stiffness of the strip, and the coefficient of friction between the strip and the internal support. The case of a frictionless support is also analyzed. The experimental results agree well with those from the analysis for cases with small deflections within the gap, but exhibit a larger range of stable large-deflection equilibrium states before collapse occurs.