Engineering Transactions, 16, 3, pp. 319-344, 1968

Układ tarczowo-prętowy poddany działaniu sił masowych

R. Świtka
Katedra Mechaniki Budowli Politechniki Poznańskiej
Poland

The problem under consideration is that of a sheet strip of considerable height H. The lower edge is attached along a segment length 2a to a bar clamped at both ends and on the remaining part of the edge to an undeformable foundation. The system is acted on by body-forces: the weight of the sheet and that of the bar. The function p (x1) expressing the interaction between the sheet and the bar is assumed in the form of a Fourier cosine series. To construct the solution for the sheet the Neuber and Papkovich functions are used. Making use of the Fourier cosine transformation, the problem can be reduced to dual integral equations. The function u2 (x1, 0) |x1| < a determined in this way is expanded in Fourier cosine series. The deflection function V (x1) of the bar loaded by the weight p (x1) + g (where g is the weight of the bar per unit length) is determined by means of the finite cosine
Fourier transformation. The compatibility condition of displacement for the sheet and the bar u2(x1, 0) = V (x1) leads to an infinite set of algebraic equations with the Fourier coefficients pn (n = 0, 1, 2, ...) of the function p (x1) as unknown. In further considerations are derived equations expressing the stresses in the sheet. The problem is illustrated by a numerical example. The results obtained may find application for the analysis of the load with which a lintel is acted on by the wall.

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References

S. S. DAWYDOW, Obliczanie i projektowanie konstrukcji podziemnych, MON, Warszawa 1954.

M. NIEMINC, G. SZEFER, Koncepcja sklepienia ciśnień w świetle teorii sprężystości, Czasopismo Techniczne, nr 5, Kraków 1966.

[in Russian]

[in Russian]

I. N. SNEDDON, Fourier Transforms, Mc Graw-Hill Book Comp., New York-Toronto-London 1951.

[in Russian]

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I. N. SNEDDON, Zagadnienia szczelin w matematycznej teorii sprężystości, PAN, Warszawa 1962.