Engineering Transactions, 16, 2, pp. 178-207, 1968

Badania naprężeni w konstrukcjach niejednorodnych obciążonych ciężarem własnym

R.S. Doroszkiewicz
Zakład Mechaniki Ośrodków Ciągłych Instytutu Podstawowych Problemów Techniki
Poland

This is a discussion of the author's method of photoelastic analysis of a plane state of stress in a body of jump-like nonhomogeneity loaded by its own weight. The model rotates in a beam of polarized light. It is made of a number of photoelastic materials produced for this purpose and having different, low values of Young's modulus E. This method enables us to avoid the usual method of representing a jump-like variation of Young's modulus by a jump of thickness of the model. The latter method of modelling nonhomogeneity of an object gives a relatively correct stress distribution only at points at sufficient distance from the line of change of Young's modulus and the points of application of the forces representing the weight of the object.
In order that the directions of the centrifugal forces may be parallel (thus imitating the gravity forces) the centrifugal machine has been designed in such a manner that the model rotates about an axis lying in its middle plane. The apparatus used for this method enables visual observation of the photoelastic image of the stress (the isochromatic fringes and isoclines) produced by rotation and also photographing of those images. The example used to describe the method is that of an isosceles triangle resting on a foundation the coefficient (E») of which is different from that of the triangle (E). On the basis of the results of photoelastic analysis diagrams of stresses are plotted for models for the ratio Eb/Ep ≈ 0,001; 0,05; 1; 3; 26.
The method described can be used to determine the influence of the elastic properties of the foundation on the state of stress in heavy structures for which the action of the own weight should be taken into account. Two examples of isochromatic fringe patterns are given for a model of a dam loaded by its weight only and subject to simulateneous action of the own weight and the hydraulic pressure. The ratio of moduli of the dam and the foundation was Eg/Ep ≈ 5.
The paper contains also a survey the present state of knowledge in the domain of the problem discussed.

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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

E. BRIGHT WILSON, Jr, An Introduction to Scientific Research, McGraw-Hill, New York-Toronto-London 1952.

E. G. COKER, L. N. G. FIOLN, A Treatise on Photoelasticity, Cambridge University Press, 1931 i 1957.

[in Russian]

[in Russian]

M. HETENYI, Handbook of Experimental Stress Analysis, John Wiley and Sons, New York 1959.

M. T. HUBER, Teoria sprężystości, tom IV, cz. I, wyd. 2, PWN, Warszawa 1954.

A. U. HÜGGENBERGER, Talsperren, Messtechnik, Wilhelm Ernst u. Sohn, Berlin 1951, 101-103.

H. T. JESSOP, Photoelasticity Principles and Methods, Cleaver-Huma Press, London 1949.

M. MILBAUER, Fotoelasticimetrie a jeji pouzity y praxi, SNTL, Praha 1953.

M. PIGEAUD, Résistance des matériaux et élasticité, tome II, édit, Gauthier-Villars, Paris 1950.

, S. TIMOSHENKO, J. N. GOODIER, Teoria sprężystości, Arkady, Warszawa 1961.

F. TÖLKE, Wasserkraft Anlagen, Springer Verlag, Berlin 1951.

/20 H. WOLF, Spannungsoptik, Springer-Verlag, Berlin-Goettingen-Heidelberg 1961.

J. H. BRAHTZ, The stress function and photoelasticity applied to dams, Trans. A.S.C.E., 102 (1936), 1232.

P. B. BUCKY, A. G. SOLAKIAN, L.S. BALDIN, Centrifugal method of testing models, Civil Engineering, 5, 5 (1935).

[in Russian]

P. DIETRICH, Untersuchung des Spannungszustandes vor einer Drehstahlschneide i polarisierten Light, Diss. T.H. Hannover 1938.

R. S. DOROSZKIEWICZ, Elastooptyczne badania przekroju poprzecznego zapory filarowej, Mech. Teoret. Stos., 2, 2 (1964), 3-14.

R.S. DOROSZKIEWICZ, J. LIETZ, B. MICHALSKI, Badanie zapory grawitacyjnej posadowionej na podłożu o innych własnościach sprężystych, w opracowaniu.

R. S. DOROSZKIEWICZ, New photoelastic method for determining the state of stress in dams, Symp. Concrete Dam Models, October 14-19, 1963. Paper No 9, pages 9.1-9.25, Lisboa 1963.

R.S. DOROSZKIEWICZ, Some methods for determining the state of stress in bodies subjected to simultaneous own weight and hydrostatic pressure, Bull. Acad. Polon. Sci., Série Sci. Techn., 12, 10 (1962), 23-28.

R. S. DOROSZKIEWICZ, Wyznaczanie stanu naprężenia ciał znajdujących się pod jedno-czesnym działaniem ciężaru własnego parcia hydrostatycznego, Praca doktorska IPPT PAN, Warszawa 1962. Maszynopis niepublikowany.

R. S. DOROSZKIEWICZ, Zastosowanie elastooptycznych badan » budownictwie wodnym, Gospodarka wodna, 8, 21 (1961), 320-331.

R.S. DOROSZKIEWICZ, Z badań fotosprężystych stanu naprężenia wywołanego ciężarem własnym z uwzględnieniem wpływu podłoża, Mech. Teoret. Stos., 2, 2 (1964).

R. S. DOROSZKIEWICZ, A. LITEWKA, Doraźne badania własności mechanicznych i elastooptycznych materiałów używanych w elastooptyce, Mech. Teoret. Stos., 1, 1 (1964), 45-59.

R. S. DOROSZKIEWICZ, B. MICHALSKI, Pewne propozycje odnośnie polskiej terminologii z zakresu fotosprężystości, w przygotowaniu.

[in Russian]

H. G. EDMUNDS, Stress concentrations at holes in rotating disces, Engineering, London, 198 (1954), 618.

G. GRANDORI, Ancora sulla ricerca fotoelastica degli sforzi al peso proprio nelle strutture piane, Atti del Collegio degli ingegneri di Milano, N 5-6, Maggio-Ciugno 1957.

S. G. GUTMAN, Méthodes d'études en laboratoire de l'état des contraintes des ouvrage hydrauliques et de leurs éléments, Commission Internationale des Grands Barrages de la Conférence Mondiale de l'Energie, Cinquiéme Congrés des Grands Barrages, Paris 1955.

R. HILTSCHER, Gütebeurteilung spannungsoptischer Modellwerkstoffe, Forschung, 3, 20 (1954).

B. T. JACOBSEN, Stresses in gravity dams by principles of least work, Trans. A.S.C.E., 489, 96 (1932).

M. LEVY, Comptes Rendus, 1235, 126 (1898).

LOCATELLI, GRANDORI, MORAVIA, Sulla ricerca per via fotoelastica degli sforzi dovuti al peso proprio nelle strutture piane, La Ricerca Scientifica, Roma 1, 25 (1955).

S. MACKIEWICZ, Wpływ sprężystości podłoża na stan naprężenia w zaporze cienkiej, praca doktorska, Gdańsk 1964.

M. MILBAUER, M. PERLA, Fotoelasticimetricke Metody ve Vyzkumu Konstrukci, Zpravy 16, Ustavu Teoreticke a Aplikovane Mechaniky, Ceskoslovenska Akademia VED, Praha 1958.

M. PERLA, Napjatost rotuhiciho kotouée odlehcenoho Sesti excentrickymi otvoru, Dysertacja, Praha 1953.

J. PINDERA, Badania pewnych reologicznych własności elastooptycznych kilku żywic poliestrowych, Rozpr. Inzyn., 3 i 4, 7 (1959), 361-411 i 481-540.

A.J. S. PIPPARD, Unwin Memorial Lecture, J. Institute G.I., 33, (1949-50), 265.

L. F. RICHARDSON, The approximate arithmetical solutions by finite differences of physical problems involving differential equations with an application to the stresses in masonry dams, Phil. Trans. Roy. Soc., 210 (1909).

J. R. RYDZEWSKI, Experimental method of investigating stresses in buttres dams, British J. Appl. Phis., 11, 10 (1959). 49. J.R. RYDZEWSKI, Stress distribution in gravity dams, Water Power, June 1960.

J. K. SILVERMAN, Approximate stress functions for triangular wedges, J. Appl. Mech., 22 (1958), 123.

United States Bureau of Reclamation, Bulletin 2 of Part 5, Boulder Canyon Projekt Final Report, Denver, Colorado 1938. 52. J. S. WILSON and W. GORE, Stresses in dams. An Experimental investigation by means of indiarubber models, Min. Proc. Inst. C.E., 172 (1908), 107.

K. WOLF, Zur Integrationder Gleichung F = 0 durch Polynome in Falle des Straumauern- Problems, Sitz, Kai. Akad. Wissen., Wien, 123 (1914).

O. C. ZIENKIEWICZ, The stress distribution in gravity dams, J. Inst. C.E., 27 (1947), 244.