Saint-Venant’s Principle for a Helical Spring

Abstract

We consider a linear elastic helical spring of arbitrary length and of uniform cross section loaded by a self-equilibrated force system at one end only. We show that the elastic energy, stored in the portion of the spring beyond a certain distance from the loaded end, decreases exponentially with the distance. We thus establish an analog of Toupin’s version of the Saint-Venant principle for a helical spring.