On the analysis of experimental observations in problems of elastic stability

Abstract

1. In the concluding section of a paper published in 1913 I endeavoured to assess the practical value of a theory of elastic instability. Two factors operate to impair agreement with experimental results: (1) the finite strength of actual materials, and (2) unavoidable imperfections of workmanship, which prohibit the realisation of its concept of a “critical load.” I showed how in one problem (the centrally loaded strut) theory can be extended to take account of plastic distortion; and by reference to a mechanical example I indicated what kind of result is to be expected when inaccuracies in the specimen or in the experimental apparatus introduce displacements which increase continuously with the load. Thus (to take the simplest example as an illustration) the well-known theory of Euler indicates that an initially straight and centrally loaded strut will remain straight while the end thrust is increased from zero up to a certain value P c , but that when this “critical load” is attained the strut may bend into the form of a single bow, since this form can be maintained by end thrust acting alone . There is an “exchange of stabilities”, whereby for end thrusts exceeding the critical value the equilibrium of the straight form becomes unstable and that of the bent form stable. If on the other hand the strut is initially bowed, so that the central deflection has a small but finite value when the end thrust P is zero, this central deflection will increase with P, and experiment may be expected to yield some curve of the type shown by full lines in fig. 1, where l denotes the length and EI the (uniform) “flexural rigidity” of the strut. The smaller the initial deflection, the more closely will the experimental curve approach the limiting form OAB, which is the curve given by Euler’s analysis.