"If we consider a force F perpendicular to the axis of a beam (or lamina) so as to displace it from the position AC to AD, and \delta be the projection of D parallel to AC on a line through C perpendicular to AC, Euler finds by easy analysis D \delta = \frac{F\cdot a^3}{3\cdot Ek^2}, supposing the displacement to be small. This suggests to him a method of determining the 'moment of stiffness' Ek^2, and he makes various remarks on proposed experimental investigations. He then notes the curious distinction between forces acting parallel and perpendicular to a built-in rod at its free end; the latter, however small, produce a deflection, the former only when they exceed a certain magnitude. It is shewn that the force required to give curvature to a beam acting parallel to its axis would give it an immense deflection if acting perpendicularly."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
Imported from EN Wikiquote
https://en.wikiquote.org/wiki/A_History_of_the_Theory_of_Elasticity_and_of_the_Strength_of_Materials
Revision History
No revisions have been submitted for this quote.
Categories
A History of the Theory of Elasticity and of the Strength of Materials
A History of the Theory of Elasticity and of the Strength of Materials: from Galilei to the Present Time is a two volume set edited and completed by Karl Pearson from notes written by . It was published by Cambridge at the University Press posthumously in Todhunter's name. Volume I. Galilei to Saint-Venant 1639-1850 was first published in 1886. Volume II. Saint-Venant to Lord Kelvin was first published in 1893.
Related Quotes
"Euler takes the case in which forces act at every point of the elastic curve; and he obtains an equation like the fir…"
"It would be a great aid to science, if, at any rate, the innumerable mathematical journals could be to a great extent…"
"In the summer of 1884... the Syndics... placed in my hands the manuscript of the late Dr Todhunter's History of Elast…"
"[I]t was not till I had advanced... into the work that I felt convinced that... the... writer's terminology and notat…"
"[T]he notation and terminology will be found fully discussed in Notes B—D of the Appendix, which I would ask the read…"
"[C]onsistency in [notation and terminology] will be found after the middle of the chapter devoted to Poisson."
"The symbols and terms used in the manuscript are occasionally those of the original memoirs, occasionally those of La…"
"Dr Todhunter's manuscript consists of two distinct parts, the first contains a purely mathematical treatise on the th…"
"The changes I have made in that manuscript are of the following character; the introduction of a uniform terminology …"
"Keeping the twofold object of this work in view I have endeavoured to give it completeness (1) as a history of develo…"