Engineering Transactions, 8, 4, pp. 699-724, 1960

Powloka Katenoidalna

Z. Pelka
Politechnika Warszawska

By moving one catenary along another both curves lying in mutually perpendicular vertical planes, a translational shell is obtained called here the catenoidal shell. The equation of this shell is given and the method of calculating the membrane forces under vertical load, the shell being supported along the contour on diaphragms rigid in their planes only. The differential equation of the stress function for a shell covering a square is solved by means of the method of funicular polygon. Two cases are considered: a shell acted on by a uniform load and a constant thickness shell loaded by its own weight. Normal and tangential forces are determined, the inverse matrix being also obtained thus enabling the passage from the values of the stress function F to those of the second derivatives F1’ the segment being divided into ten parts.
Next, the problem of distribution of the forces in a corner is considered and the way of appraising the influence on these forces of the transversal rigidity of the diaphragms. Also the possibility of generalizing the results obtained for the shell, of which the projection has the half-side length a = 1, to a geo- metrically similar shell is considered. It is found that the values of the stress function in the nodes of the net are proportional to the third power of a and the normal and tangential forces depend linearly on a.

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