Statics of loose triangular embankment under Nadai's sand hill analogy
| Autor: | Pipatpongsa, Thirapong, Heng, Sokbil, Iizuka, Atsushi, Ohta, Hideki |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Journal of the Mechanics and Physics of Solids, 2010 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jmps.2010.07.013 |
| Popis: | In structural mechanics, Nadai's sand hill analogy is the interpretation of an ultimate torque applied to a given structural member with a magnitude that is analogously twice the volume of stable sand heap which can be accommodated on a transverse cross-section basis. Nadai's analogy is accompanied by his observation of a loose triangular embankment, based on the fact that gravitating loose earth is stable if inclined just under the angle of repose. However, Nadai's analysis of stress distribution in a planar sand heap was found to be inaccurate because the total pressure obtained from Nadai's solution is greater than the self-weight calculated from the heap geometry. This raises a question about the validity of his observation in relation to the analogy. To confirm his criterion, this article presents and corrects the error found in Nadai's solution by analyzing a radially symmetric stress field for a wedge-shaped sand heap with the purpose of satisfying both force balance and Nadai's closure. The fundamental equation was obtained by letting the friction state vary as a function of angular position and deduce it under the constraint that the principal stress orientation obeys Nadai's closure. The theoretical solution sufficiently agreed with the past experimental measurements. Comment: text 29 pages, 16 figures, 1 table |
| Databáze: | arXiv |
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