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DOMES FOR CIRCULAR KILNS *
Author(s) -
Fellows J. A.
Publication year - 1932
Publication title -
journal of the american ceramic society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.9
H-Index - 196
eISSN - 1551-2916
pISSN - 0002-7820
DOI - 10.1111/j.1151-2916.1932.tb13967.x
Subject(s) - dome (geology) , surface (topology) , geometry , mathematics , base (topology) , mathematical analysis , limiting , point (geometry) , stress (linguistics) , ruled surface , section (typography) , stability (learning theory) , tangent , geology , engineering , mechanical engineering , paleontology , linguistics , philosophy , machine learning , advertising , computer science , business
The object of this study was to find the shape of a dome having no circumferential stresses. To find such a surface of revolution, the calculus of variations was employed, and a differential equation set up whose solution would be a curve which, when revolved about the vertical axis, would give this surface. This differential equation was found to be unsolvable except by graphical methods. A graphical solution was obtained using an integrating machine. The vertical cross‐section of this surface is compared with well‐known curves. It is found that spherical domes with small heights lie inside the surface in question, and are therefore stable, while spherical domes which approach a hemisphere lie outside this surface at certain points, and are unstable. These conclusions are in accordance with the physical facts. Tables containing all the data relative to this derived surface are given. The relation between the resultant stress at the base and the height is shown graphically. The radial component of stress is found to approach infinity for a very flat dome, and to approach zero for a high dome. The value of this dome lies in the fact that stability of any curve may be determined by comparison with it. Any curve which lies outside this limiting curve at any point will give an unstable dome. It also makes it possible to find the surface having a minimum resultant stress for any given base diameter or any given height.