Maxwell, Jenkin and Cotterill and the theory of statically-indeterminate structures

Abstract

The decade 1860-1870 witnessed some remarkable and enduring contributions to the theory of structures in Britain by Clerk Maxwell (F.R.S. 1861), Fleeming Jenkin (F.R.S. 1865) and J. H. Cotterill (F.R.S. 1878). Indeed it was in the course of his work in this field that Maxwell formulated the reciprocal theorem for linear systems. The general problem of calculating the forces within frame structures due to applied loads was widely believed to be unresolved when Jenkin addressed himself to it in 1861. The difficulty arose when the number of structural supports and elements exceeded the number of available independent equations of equilibrium, that is, when there were supports and elements supernumerary to the needs of statics. So-called staticallyindeterminate construction of that kind was encountered frequently as the technology of economical metal structures developed partly to fulfil the needs of railway construction. Now the problem had been solved in principle by L. M. H. Navier early in the nineteenth century and published in his celebrated book (1) in France in 1826. But though that work received some attention in France, notably from Lame, Saint Venant and Levy, there seems to be no record of wider appreciation except, perhaps, in the work of the German mathematician Clebsch; certainly Maxwell approached the problem de novo at Jenkin’s instigation. Indeed Maxwell is nowadays commonly regarded as the first to solve the general problem of the statically-indeterminate framework.