Overview

It was clear to Galileo that a beam resting on three supports could be subjected to forces not envisaged by the engineer. Two supports are sufficient to carry the beam and, for a known weight, the use of simple equations of statics (well understood by Galileo) enables the support forces to be found. This simple structure is, in fact, statically determinate; once the support forces are known, further straightforward equations enable the internal forces in the beam to be calculated, and the science of strength of materials, summarised in Chapter 4, may be used to assess the suitability of the dimensions of the beam.

By contrast, the introduction of a third support for the beam makes the structure statically indeterminate, or hyperstatic; there is no way that the simple equations of statics can be used on their own to find the propping forces at the three supports. Technically there are available only two relevant equations, and these do not suffice to determine three unknown quantities. Galileo did not himself explore this idea, nor did he give any general analysis of the hyperstatic structure. Instead, in his account of the broken column he pursued, very briefly, a different line of discussion, in which he considered displacements, rather than forces. The line proved, much later, to give an alternative and powerful method of attack on the problem of the analysis of structures. Galileo's explanation of the breakage of the column stored horizontally sprang from his understanding that no...