The problem of the breaking strength of a beam continued to be visualized in the form stated by Galileo, namely that of a cantilever beam encastred at its left-hand end and loaded by a single weight at the free end. From this formulation was abstracted the ‘cleaner’ problem of the calculation of the breaking resistance of the cross-section adjacent to the support, since clearly this was the critical section of the beam.

In calculating the moment of resistance of the beam, Galileo considered only one of the three statical equations (or four, since Persy's contribution of 1834 must be included), namely that the moment of the forces acting at the cross-section must equal the moment of the applied load. He did not write the equation of longitudinal equilibrium (Parent (1713)) which helps to determine the location of the neutral axis of bending, nor did he resolve forces vertically, which leads to the idea of a shearing action on the critical section.

As has been seen, Coulomb (1773) did realise that the forces acting on the critical section must have vertical components in order to balance the load applied to the tip of the cantilever. Indeed two of Coulomb's four problems (the strength of columns, the thrust of soil) are concerned with shear fractures, and he tried to test his (stone) cantilever beam in pure shear by applying the load as close as he could to the encastred end. The experimental technique was not good, but Coulomb measured to his own reasonable satisfaction the strength of stone in pure tension and in pure shear, and related these two strengths by ‘Coulomb's equation’, involving two physical parameters, cohesion and friction.