Abstract
According to the principles of mechanics, having acquired the concept of “quantity”, if we wish to define the sum of two homogeneous quantities it is necessary to introduce the concept of “magnitude” as the ratio between the quantity under consideration and another one, homogeneous to it, chosen as unity. We define a “dimensional system” as the whole set of derived quantities whose units can be obtained from certain predetermined “fundamental” units. Among the various dimensional systems we mention those of:
geometry, where all the quantities can be derived from one fundamental quantity represented by the length L;
kinematics, where all the quantities can be derived from those of length L and time T;
statics, where all the quantities can be derived from those of length L and force P, or (see 1.4) length L and specific force;
mechanics in general, in which all the quantities can be derived from the above three fundamental ones.
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References
Arountiounian, N.: Applications de la théorie du fluage. Paris: Eyrolles. 1957.
Beaujoint, N.: Similitude et théorie des modèles. Rilem, Bulletin Nr. 7, 14–39, Paris (June 1960).
Bertrand, J.: Note sur la similitude en mécanique. Journal de l’Ecole Polytechnique, t. XIX, Cahier XX XII, 1848.
Bonvalet, M.: La similitude des maquettes en élasticimétrie. Exemples d’application à deux ouvrages d’art. Mémoire du G. A. M. A. C. (February 1954).
Borges, J. F.: Statistical Theories of Structural Similitude. Rilem, Bulletin Nr. 7, 59–67, Paris (June 1960).
Borges, J. F., Arga, L. J.: Crack and Deformation Similitude in Reinforced Concrete. Rilem Bulletin Nr. 7, 79–90, Paris (June 1960).
Bridgman, P. W.: Dimensional Analysis. Yale University Press. 1952
Duncan, W. J.: Physical Similarity and Dimensional Analysis. London: Arnold 1953.
Esnault Pelterie, R.: L’analyse dimensionnelle. Paris: Gauthier-Villars; Lausanne: Ed. Rouge. 1946.
Fumagalli, E.: Model Simulation of Rock Mechanics Problems. Rock Mechanics in Engineering Practice (Stagg-Zienkiewicz, eds.). London: J. Wiley. 1968.
Fumagalli, E.: Caratteristiche di resistenza dei conglomerati cementizi per stati di compressione pluriassiale. Ismes, Bulletin Nr. 30 (October 1965).
Gabrielli, G.: Le esperienze su modelli e le leggi di similitudine. Ingegneria Meccanica IV, 1955, 2.
Ghaswala, S. K.: Model and Analogies in Structural Engineering. Civil Engineering and Public Works Review (January—June, 1952 ).
Jaeger, J. C., Cook, N. G. W.: Fundamentals of Rock Mechanics. London: Methuen. 1969.
Jasiewicz, J.: Applications of Dimensional Analysis Methods to Civil Engineering Problems. Civil Engineering and Public Works Review, London, Vol. 58, Nr. 686, 1125–1128 (September 1953); Nr. 687,1270–1280 (October 1963); Nr. 688,1409–1410 (November 1963); Nr. 689, 1547–1549 (December 1963).
Mattock, A. H.: Structural Model Testing — Theory and Applications. Journal, PCA Research and Development Laboratories, Vol. 4, Nr. 3, 12–13 (September 1962).
McHenry, D., Kami, J.: Strength of Concrete under Combined Tensile and Compressive Stress. ACI Journal, Proceedings, Vol. 54, Nr. 10, 829–840 (April 1958).
Murphy, G.: Similitude in Engineering. New York: Ronald Press. 1950.
Nowacki, W.: Théorie du fluage. Paris: Eyrolles. 1965.
Oberti, G.: Sulla valutazione del coefficiente globale di sicurezza di una struttura mediante esperienze su modelli. Ismes, Bulletin Nr. 2 (June 1954).
Oberti, G.: Large Scale Model Testing of Structures outside the Elastic Limit. Ismes, Bulletin Nr. 12 (April 1959).
Oberti, G., Lauletta, E.: Evaluation Criteria for Factors of Safety. Model Test Results. Ismes, Bulletin Nr. 25 (October 1964).
Pistolesi, E.: Omogeneità, similitudine, modelli. Questioni di matematica applicata, Collana CNR. Bologna: Zanichelli. 1940.
Pletta, D. H., Frederick, D.: Experimental Analysis. Proceedings ASCE, Vol. 79 (July 1953).
Somerville, G.: The Behaviour and Simulation of Concrete. Presented to the Joint British Committee for Stress Analysis at a Meeting entitled: The Behaviour and Simulation of Engineering Materials. University College, London (January 2, 1967 ).
Templin, R. L.: Tests of Engineering Structures and their Models. Transactions, ASCE, Vol. 102, 1211–1225 (1937).
Wilbur, J. B., Norris, C. H.: Structural Model Analysis. Handbook of Experimental Stress Analysis. New York: J. Wiley. 1950.
Wright, J.: Use of Models in Structural Analysis. Engineering (London), Vol. 175, Nr. 4558, 110–712 (June 5, 1953); Nr. 4559, 741–743 (June 12, 1953 ).
Zia, P., Van Horn, D. A., White, R. N.: Principles of Model Analysis. Models of Concrete Structures, Special Publication, Nr. 24. Detroit: American Concrete Institute. 1970.
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© 1973 Springer-Verlag Wien
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Fumagalli, E. (1973). Principles of Similitude. In: Statical and Geomechanical Models. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8317-5_1
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DOI: https://doi.org/10.1007/978-3-7091-8317-5_1
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