5 - Theory of statically-indeterminate frameworks: the reciprocal theorem

Summary

The precise analysis of statically-indeterminate systems of bars, including trusses and pin-jointed frameworks generally, seems to be due to the famous French engineer, Navier. It was included in his lectures at l'Ecole des Ponts et Chaussées, which appeared in the form of his celebrated Leçons in 1826. According to Saint-Venant (Navier, 1864, p. 108) the method was part of the course as early as 1819. It was elaborated (1862) by the mathematician Clebsch in Germany; while, in Britain, Maxwell (1864b) who, it seems, was unaware of Navier's elegant and general method, published an original method of solving the problem. Levy, who was apparently aware of Navier's work, published a novel method in 1874 (Chapter 6). But it was not really until the German engineer, Mohr, published his analysis in the same year that the subject began to be appreciated by engineers (on the Continent at first and much later in Britain).

This chapter is concerned with those original contributions, in principle only: various sophistications and devices to increase their utility in engineering are considered in Chapters 8 and 10.

Navier, 1826

Navier's contribution to the analysis of statically-indeterminate pin-jointed systems is to be found essentially in the two articles of his Leçons (1826, art. 632, p. 296; 1833, art. 533, p. 345).