"Galileo does not attempt any theory to account for the flexure of the beam. This theory, supplied by , was applied by Mariotte, Leibnitz, De Lahire, and Varignon, but they neglect compression of the fibres, and so place the neutral in the lower face of Galileo's beam. The true position of the neutral plane was assigned by James Bernoulli 1695, who in his investigation of the simplest case of bent beam, was led to the consideration of the curve called the "elastica." This "elastica" curve speedily attracted the attention of the great Euler (1744), and must be considered to have directed his attention to the s. Probably the extraordinary divination which led Euler to the formula connecting the sum of two elliptic integrals, thus giving the fundamental theorem of the addition equation of s, was due to mechanical considerations concerning the "elastica" curve; a good illustration of the general principle that the pure mathematician will find the best materials for his work in the problems presented to him by natural and physical questions."
Quote Details
Added by wikiquote-import-bot
Unverified quote
0 likes
Original Language: English
Available Languages (1)
Sources
A. G. Greenhill, Nature (Feb. 3, 1887) Review of A History of the Theory of Elasticity, Volume 35, pp. 313-314.
https://en.wikiquote.org/wiki/Euler%E2%80%93Bernoulli_beam_theory
Revision History
No revisions have been submitted for this quote.
Categories
Euler–Bernoulli beam theory
(also known as engineer's beam theory or classical beam theory) is a simplification of the linear and provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case for small deflections of a beam that are subjected to lateral loads only, and is thus a special case of . It was first enunciated circa 1750, but was not generally applied until the development of the and the in the late 19th century. Following these successful demonstrations, it quickly
7 quotes on TrueQuotesView all quotes by Euler–Bernoulli beam theory →
Related Quotes
"We consider the case of a horizontal rod or beam slightly bent by vertical forces applied to it. The state of strain …"
"The assumption that the varies as the curvature is the basis of the 'Euler-Bernoulli' theory of flexure. This was dev…"
"[C]alculations... based on the simple theory of bending... are approximate only. While the simple (or Bernoulli-Euler…"
"The assumptions in the design of reinforced concrete beams are those of the ordinary beam theory, namely: the Bernoul…"
"The first investigation of any importance is that of the elastic line or elastica by James Bernoulli in 1705, in whic…"
"In Euler's work on the elastica the rod is thought of as a line of particles which resists bending. The theory of the…"
"Newton’s glory was to fulfil, in his Principia of 1687, Galileo's hope of geometrizing gravitation. The ingredients o…"
"Only around the end of the nineteenth century did scientists come across a few observations that did not fit well wit…"
"Lex I. Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus i…"
"If matter escapes us, as that of air and light, by its extreme tenuity, if bodies are placed far... in the immensity …"