Representative Curves of the Laws of Longitudinal and Transverse Impact on a Prismatic Bar

摘要

The object of the present work was to publish the curves set up about 25 years ago, by Saint-Venant, for representing graphically the laws of longitudinal and transverse impact on a prismatic bar struck at its end or its center by a body having a mass comparable to its own. These curves were drawn in 1873, but the author, distracted by other work, had never completed them by adding the letters, marks and legends necessary for their understanding. Moreover, he had been most scrupulous in regard to their accuracy: the ordinates of these curves are expressed, as will be seen, by means of convergent series of which he had only taken the first terms, and he was most concerned lest the neglected terms, even though very small, should in their ensemble modify the form of the curves which he had deduced from the first terms. This scruple was especially accentuated since the publication in Comptes rendus of the representative curves of longitudinal impact according to the solution in finite terms given by Boussinesg. These curves, which are exact, seemed to differ considerably from those deduced from the first terms of the series, although the difference was, basically, more apparent than real.