Bridging a gap: A heavy elastica between point supports

TL;DR

This paper analyzes the deformation and load capacity of a heavy elastic beam between point supports, revealing a critical separation allowing infinite load support without slip, influenced by friction and tension effects.

Contribution

It introduces a combined asymptotic and numerical analysis of a heavy elastic beam, uncovering a critical support separation for infinite load capacity without friction.

Findings

Existence of a critical support separation below which the beam can support unlimited force

The maximum supported force depends on the separation between supports

Frictional forces influence deformation and load capacity

Abstract

We study the deformation and slip-through of a heavy elastic beam suspended above two point supports and subject to an increasing body force -- an idealized model of a fibre trapped in the pores of a filter as flow strength increases, for example. Using both asymptotic and numerical techniques, we investigate the behaviour of the beam under increasing body force and the maximum force that can be supported before it must slip between the supports. We quantify this maximum body force as a function of the separation between the two supports. Surprisingly, we show the existence of a critical separation below which the beam can withstand an arbitrarily large body force, even in the absence of friction. This is understood as the limit of a catenary between the supports that is connected to (and supported by the tension in) a vertically hanging portion outside the supports. We explore how frictional forces impact the deformation and load-bearing capacity of the beam and show that our results are consistent with laboratory experiments.