Euler's Paper on Statically Indeterminate Analysis
Publication: Journal of Engineering Mechanics
Volume 113, Issue 2
Abstract
It is well known that Leonhard Euler contributed a great deal to structural analysis; an example is the column formula that goes by his name. However, his seminal contribution to statically indeterminate analysis has generally been overlooked. Euler published the first paper on statically indeterminate analysis in 1773, and an edited version of this paper was published in 1795. A translation of the edited version of this paper is presented here since it illustrates the concepts developed by Euler but is without the large number of examples of the longer paper. The problem analyzed by Euler is a rigid table resting on an elastic foundation. Forces are related to displacements in the foundation by a linear constitutive law. Euler recognizes that a statically in‐determinate problem such as this can be solved uniquely by considering deformations in addition to forces. Although Euler's paper is rarely cited in text‐books or in historical studies, it was the first to contain the fundamentals of today's method of compatible deformations.
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References
1.
D'Alembert, J., “Sur Quelques Questions de Mecanique,” Opuscules Mathematiques, Vol. 8, Paris, France, 1780.
2.
Euler, L., “Methodus Inveniendi Lineas Curves Maximi Minimive Proprietate Quadentes,” Additamentum I, “De curvis elasticis,” Bousquet, Lausanne and Geneva, Switzerland, 1744.
3.
Euler, L., “Sur la Force des Colonnes,” Mémories de L'Acádemie Royale des Sciences et Belles Lettres, Vol. 13, Berlin, 1759, pp. 252–282.
4.
Euler, L., “De Pressione Ponderis in Planum cui Incumbit,” Novi Commentarii, Academiae Scientarum Imperialis Petropolitaneae, Tomus XVIII, St. Petersburg, 1773, pp. 289–329.
5.
Oldfather, W. A., Ellis, C. A., and Brown, D. M., English translation of “Methodus Inveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes,” Additamentum I, “De Curvis Elasticis,” ISIS, Vol. 20, 1933, pp. 72–160.
6.
Van der Broek, J. A., “Euler's Classic Paper On the Strength of Columns,” American Journal of Physics, Vol. 15, No. 4, July–Aug., 1947, pp. 309–318.
7.
“Von dem Drucke eines mit Einem Gewichte Beschwerten Tisches auf eine Fläche. Aus den Papieren des sel. Leonhard Eulers Gezogen, von Jakob Bernoulli,” C. F. Hindenburg, Archiv der Reinen und angewandten Mathematik, Vol. 1, 1795, pp. 74–80.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 113 • Issue 2 • February 1987
Pages: 186 - 195
Copyright
Copyright © 1987 ASCE.
History
Published online: Feb 1, 1987
Published in print: Feb 1987
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