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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