A History of the Theory of Elasticity and of the Strength of Materials Volume 2 - PT.1; From Galilei to the Present Time (Paperback)

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 Excerpt: ... 0, 28/2 = 0, 2 (bSP-aSQ) = 0, 2 (aSR-cSP) = 0, 2 (c8Q-bSR) = 0 Multiplying (v) by the indeterminate multipliers A, B, C, D, E, F respectively we have on adding to (iv): /=--' A+Db-Ec 2 =-e" B + Fc-Da (vi)' R =-t'"C + Ea-Fb J Substitute these values of P, Q, R in (iii), and we have six equations from which to find the multipliers and so can determine P, Q, R. Menabrea remarks that if we take f' = e" = t," and choose our origin and direction of axes so that 2e-s = 0, 2c6 = 0, 2-c = 0, 2-6c=0, 2--c = 0, 2-iA = 0, we obtain the elegant forms for P, Q, R first given by Dorna in a memoir of 1857; see our Art. 599. Here t for any link equals the Ejilm) of our notation. For earlier researches in this same direction Menabrea refers to Vene, Pagani and Mossotti besides Dorna. The memoirs of Vene and Pagani are those probably which we have cited in the footnote to our p. 411, while the reference to Mossotti is possibly to his Meccanica rationale. Menabrea concludes by referring to a memoir he is about to publish, dealing more fully with the whole subject. I do not think he published this, or returned to the matter till a memoir of 1869. 607. J. M. Heppei: On a method of computing the Strains and Deflections of Continuous Beams, nndei' various Conditions of Load. Proceedings of the Institution of Civil Engineers. Vol. xix., pp. 625-643, London, 1859-60. This paper deduces, apparently as a novelty, Clapeyron's theorem connecting the bending-moments at three successive T. E. II. 27 points of support of a continuous beam, when the load system consists for each span of a uniformly distributed load and an isolated central load. The consideration of the latter load is the author's addition to Clapeyron's work. Let i, Z...