A History of the Theory of Elasticity and of the Strength of Materials Volume 1

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. 1886 ...of approximation in series involving the use of Maclaurin's and Ohm's Theorems are given (see pp. 55--178). The approximation to be adopted for any particular case depends largely on the character of the constant C, and the equation to the central axis is given not only in algebraic, but in trigonometrical and logarithmic forms. The approximations involve very long anatytical work and seem unnecessarily fine for any practical application. In fact the only case in which we can suppose the BernoulliEulerian hypothesis to approach the actual state of affairs is that wherein the length of the beam is very great as compared with the linear dimensions of its section; in this case the majority of terms involved in these approximations are insensible. 909. It is somewhat startling to find a practical man like Heim (he was colonel of Artillery) even asserting that the equation (i) is perfectly valid when the normal section varies from point to point of the central line (p. 179) and applying it to various surfaces of revolution, for example (p. 181) the frustrum of any right circular cone. This is much on a par with the formula he gives (p. 28) for the extension by a longitudinal load of any beam of varying section, extension = P where a is of course a function of x. 910. On p. 190 Heim gives an equation for the flexure when not only a terminal load, but in addition any distribution of load in the plane of flexure is added from point to point of the beam. He applies this to Euler's problem of columns bent by their own weight and considers also the case of the maximum height for a conical column (pp. 191--221). Heim's numerical result for a cylindrical column on p. 209 does not agree with Euler's (see our Art. 85), but he is treating a somewhat different probl...

314 pages, Paperback

First published March 31, 2010

About the author

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