{"title":"一根重的水平杆在刚性基座上的纵向弯曲。","authors":"Y. I. Dorogov","doi":"10.37538/0039-2383.2023.2.38.45","DOIUrl":null,"url":null,"abstract":"The loss of stability of a heavy horizontal rod on a rigid base is investigated. The differential equation of the angle of inclination of the curved axis of the rod is obtained using the exact expression of curvature. Various cases of conditions for fixing the ends of the rod are considered. From the possible forms of equilibrium of the rod, those are selected that satisfy the condition of equality of the compressive force work and the sum of elastic and gravitational energies accumulated by the rod. The curved shape of the equilibrium is determined by the maximum angle of deviation of the axis of the rod, which increases with increasing weight of the rod and does not depend on the geometric characteristics of its cross-section.","PeriodicalId":273885,"journal":{"name":"STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS","volume":"18 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"LONGITUDINAL BENDING OF A WEIGHTY HORIZONTAL ROD ON A RIGID BASE.\",\"authors\":\"Y. I. Dorogov\",\"doi\":\"10.37538/0039-2383.2023.2.38.45\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The loss of stability of a heavy horizontal rod on a rigid base is investigated. The differential equation of the angle of inclination of the curved axis of the rod is obtained using the exact expression of curvature. Various cases of conditions for fixing the ends of the rod are considered. From the possible forms of equilibrium of the rod, those are selected that satisfy the condition of equality of the compressive force work and the sum of elastic and gravitational energies accumulated by the rod. The curved shape of the equilibrium is determined by the maximum angle of deviation of the axis of the rod, which increases with increasing weight of the rod and does not depend on the geometric characteristics of its cross-section.\",\"PeriodicalId\":273885,\"journal\":{\"name\":\"STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS\",\"volume\":\"18 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-04-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37538/0039-2383.2023.2.38.45\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"STRUCTURAL MECHANICS AND ANALYSIS OF CONSTRUCTIONS","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37538/0039-2383.2023.2.38.45","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
LONGITUDINAL BENDING OF A WEIGHTY HORIZONTAL ROD ON A RIGID BASE.
The loss of stability of a heavy horizontal rod on a rigid base is investigated. The differential equation of the angle of inclination of the curved axis of the rod is obtained using the exact expression of curvature. Various cases of conditions for fixing the ends of the rod are considered. From the possible forms of equilibrium of the rod, those are selected that satisfy the condition of equality of the compressive force work and the sum of elastic and gravitational energies accumulated by the rod. The curved shape of the equilibrium is determined by the maximum angle of deviation of the axis of the rod, which increases with increasing weight of the rod and does not depend on the geometric characteristics of its cross-section.
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