The elastic arch and its modes of instability

Abstract

An arch of highly tempered steel strip, with both ends fixed at an adjustable angle, and loaded at its crown, may become unstable either by a symmetrical plunging of the crown or by skewing sideways. A simple demonstration model is described which allows the conditions for these catastrophes, and for their simultaneous occurrence, to be studied in detail. The various modes of behaviour are analysed by elementary means, including curve drawing and series expansion to illustrate how such discontinuities may be understood without the formal procedures of catastrophe theory. Excellent agreement between theory and experiment is obtained, and the arrangement is recommended as an introduction to the physics of instability.