"Determinatio onerum quae columnae gestare valent. Examen insignis paradoxi in theoria columnarum occurrentis. De altitudine columnarum sub proprio pondere corruentium. [all in] Acta Academiae Petropolitanae [1778, 1780]. The first memoir... points out that vertical columns do not break under vertical pressure by mere crushing, but that flexure of the column will be found to precede rupture. ...[Euler] proposes to deduce a result which is now commonly in use... to find an expression connecting Ek^2 with the dimensions of the transverse section of the column. Euler finds Ek^2 = h \cdot \int x^2 ydx, where x and y... Euler appears however to treat the unaltered fibre or 'neutral line' without remark as the extreme fibre on the concave side of the section of the column made by the central plane of flexure. Thus for a column of rectangular section of dimensions b [with]in, and c perpendicular to the plane of flexure, he finds...Ek^2 = \frac{1}{3} b^3 ch, and the like method is used in the case of a circular section."
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Pearson's note: In the case of a beam or column bent by a longitudinal force it may be shewn theoretically that the neutral line does not necessarily lie in the material of the beam, its position and form vary with the amount of the deflecting force; in other words Ek^2 is not a constant, but a function of the force and of the flexure. The assumption that the 'moment of stiffness' is constant seems to me to vitiate the results not only of Euler and Lagrange but of many later writers on the subje
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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.
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