A history of the theory of elasticity and of the strength of materials Volume 2, pt. 2; from Galilei to the present time

by Isaac Todhunter

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1893 ...= 0. No results of practical importance seem to flow from this assumption (pp. 145-6). 1603. (/) Case of da/dr = 0 in equations (lxv), or the least principal traction making the same angle with a radius-vector at every point of its length (pp. 145-56). Rp being a constant, we have in this a + j = C + ( da, J c--cos 2a where C, C, and c are arbitrary constants. Boussinesq applies results (lxx) to the consideration of the special case, where a cylindrical sector of material is placed between two intersecting rigid planes, sufficiently rough to stop all sliding of the particles of the material touching them. The application to the case where the rigid planes are hinged to a common axis and squeeze a wedge of plastic material placed between them might possibly have some practical interest. 1604. To the memoir is appended a Note Sur la methode de M. Macquorn-Rankine, pour le calcul des pressions exercees aux divers points d'un massif pesant (pp. 157-173). The method dealt with by Boussinesq is that discussed in B&nkine's memoir On the Stability of Loose Earth (see our Art. 453), but as it does not start from an elastic hypothesis, we have not considered it in our volume. Boussinesq explains and supplements Rankine's investigations, but remarks of the hypothesis by which Rankine solves his fundamental Peut-etre trouvera-t-on un jour quelque ordre de phenomenes auquel l'hypothese considered sera plus applicable, et qui realisera ainsi cette curieuse analogie d'une distribution de pressions avec le mouvement de la chaleur dans une barre (173). The memoir concludes with two notes, the first of which deduces Hopkins' theorem for the value and direction of the maximum shear (see our Art. 1368), while the second deduces Saint-Venant'...

200 pages, Paperback

First published June 2, 2011

About the author

English mathematician known for his writings on the history of mathematics.