{"id":182,"date":"2018-04-29T17:56:59","date_gmt":"2018-04-29T15:56:59","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=182"},"modified":"2018-06-09T09:46:49","modified_gmt":"2018-06-09T07:46:49","slug":"forme-de-tour-eiffel","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/04\/29\/forme-de-tour-eiffel\/","title":{"rendered":"La forme de la tour Eiffel"},"content":{"rendered":"

Selon les \u00e9crits de Gustave Eiffel, la forme de sa tour ne doit rien au hasard, m\u00eame si le r\u00e9sultat pourrait plaider pour un simple souci d\u2019esth\u00e9tique. Selon lui, tout a \u00e9t\u00e9 \u00e9tudi\u00e9 math\u00e9matiquement pour r\u00e9sister au vent. Plus pr\u00e9cis\u00e9ment, il affirme que le moment des forces appliqu\u00e9es par le vent en chaque point est \u00e9gal et oppos\u00e9 au moment du poids de la structure en ce point. Les calculs math\u00e9matiques d\u2019Eiffel n\u2019ayant pas \u00e9t\u00e9 publi\u00e9s, on a longtemps soup\u00e7onn\u00e9 les ing\u00e9nieurs d\u2019Eiffel d\u2019avoir op\u00e9r\u00e9 empiriquement pour obtenir la forme de type exponentiel qu\u2019on conna\u00eet.<\/p>\n

\"\"
La tour Eiffel vue du champ de Mars @Herv\u00e9 Lehning<\/figcaption><\/figure>\n

Reconstitution des calculs<\/h2>\n

Les calculs ont \u00e9t\u00e9 repris en 2005 par deux math\u00e9maticiens am\u00e9ricains, Patrick Weidman et Iosif Pinelis. En suivant les indications d\u2019Eiffel, ils ont d\u00e9bouch\u00e9 sur une \u00e9quation int\u00e9gro-diff\u00e9rentielle relativement simple … pour les sp\u00e9cialistes \u2026 dont la solution est bien une exponentielle.<\/p>\n

\"\"
Axes choisis par Weidman et Pinelis, f (x0) = 5 m, l\u2019\u00e9quation \u00e0 r\u00e9soudre est \u00e9crite en dessous.<\/figcaption><\/figure>\n

Mais, en r\u00e9alit\u00e9, la tour Eiffel est compos\u00e9e de deux exponentielles pour tenir compte de la diff\u00e9rence de forces du vent \u00e0 la base et au sommet.<\/p>\n","protected":false},"excerpt":{"rendered":"

Selon les \u00e9crits de Gustave Eiffel, la forme de sa tour ne doit rien au hasard, m\u00eame si le r\u00e9sultat pourrait plaider pour un simple souci d\u2019esth\u00e9tique. Selon lui, tout a \u00e9t\u00e9 \u00e9tudi\u00e9 math\u00e9matiquement pour r\u00e9sister au vent. Plus pr\u00e9cis\u00e9ment, il affirme que le moment des forces appliqu\u00e9es par le vent en chaque point est … Continuer la lecture de La forme de la tour Eiffel<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":12,"featured_media":184,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[5,29],"tags":[89,35,86,88,85,87],"class_list":["post-182","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-arts","category-maths-2","tag-architecture","tag-esthetique","tag-exponentielle","tag-pinelis","tag-tour-eiffel","tag-weidman"],"yoast_head":"\nLa forme de la tour Eiffel, par Herv\u00e9 Lehning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/04\/29\/forme-de-tour-eiffel\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"La forme de la tour Eiffel, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"Selon les \u00e9crits de Gustave Eiffel, la forme de sa tour ne doit rien au hasard, m\u00eame si le r\u00e9sultat pourrait plaider pour un simple souci d\u2019esth\u00e9tique. 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