A history of the theory of elasticity and of the strength of materials Volume 2, no. 1 ; 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 ...however, to have known that Young and Tredgold had long previously reached this result. It led him to consider how the work of au elastic body could be expressed. In a memoir of 1833 Lamd and he had noted that on the uniconstant hypothesis if W be the work and E the 2W= i JU' +1? + C-i (AB + BC+ GA) dxdydz, where A, B, C are the principal tractions and the integration is 1 A long series of memoirs on continuous beams will be found discussed in Section III. of this Chapter. over the volume of the elastic solid. I hold that this result of the memoir of 1833 was due entirely to Clapeyron, for Lame" in his Lemons, of 1852, giving the formula in the form 2W=jjfAa+B,+ C-2v(AB + BG+GA)dxdi/dz, due to bi-constant isotropy (77 being the stretch-squeeze ratio), terms it Clapeyron's Theorem, and Clapeyron here speaks of it as he would do only if it were entirely due to himself. 609. Clapeyron proceeds after stating this formula in its modified form to suppose only one principal traction T, when we He then applies this to the calculation of Wfor various simple cases of rods under traction or flexure etc. and also for railway springs. He remarks that if a framework be constructed in such a manner that the cross-sections of the various members are proportional to their total stresses, and these stresses are merely longitudinal tractions, then 2W=vr, where V is the volume of the whole framework. Hence if T be the safe tractional stress, and the load P be applied at one point with a resulting deflection /: pf=±vr. Thus the same volume V of material distributed in different ways will give a maximum P for a minimum f; the resilience, however, will be quite independent of the particular distribution. Un prisme pose de champ sur deux appuis por...

266 pages, Paperback

First published January 28, 2010

About the author

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