Ressant car il ne nécessite le calcul que de 4

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ressant car il ne nécessite le calcul que de 4 efforts puisque N 5 est nul à priori (voir §6) et que N 3 = N 9 : La résolution de ce treillis ne soulève pas de problème particulier. On obtient : n 1 = 2 [kN]; n 2 = 0 [kN]; n 3 = 1 [kN]; n 4 = 1,414 [kN]; n 5 = 0 [kN]; n 6 = 0 [kN]; n 7 = 1,414 [kN]; n 8 = 0 [kN]; n 9 = 1 [kN]; n 10 = n 11 = n 12 = 0; de la barre Longueur de la barre i L Effort normal dans la struc- ture hypersta- tique de base ) 2 ( F N Effort normal dans la struc- ture soumise à effort unitaire 0 1 n i L n N F 0 ) 2 ( 1 1 L 2,5061 Q 2 5,0122 QL 2 2 L 0,6985 Q 0 0 3 L 2,4939 Q 1 2,4939 QL 4 2 L 0,7157 Q 1,4142 1,4314 QL 5 L 0,0464 Q 0 0 6 L 1,4476 Q 0 0 7 2 L 0,7812 Q 1,4142 1,5624 QL 8 2 L 0,6330 Q 0 0 9 L 1,5524 Q 1 1,5524 QL 10 L 0,4476 Q 0 0 11 L Q 0 0 12 2 L 1,4142 Q 0 0 La somme des termes de la dernière colonne vaut 12,0523 QL et la flèche en F vaut donc : EA QL F 0523 , 12 = δ 1 [kN] 1 4 3 7 9 5 F
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Chapitre 8. Les treillis _____________________________________________________________________________________________________________ 213 La figure ci-dessous indique la déformée, la valeur des efforts normaux, ainsi que la flèche verticale en F, obtenus à partir du logiciel ISSD, avec les données suivan- tes : L = 2 [m], Q = 50 [kN], sections tubulaires (diamètre 50 [mm], épaisseur 5 [mm] : aire 706,86 [mm 2 ]), E = 210.000 [MPa]. Passerelle composée de deux treillis métalliques parallèles sur le Rhône en France : les noeuds sont rigides et très ramassés. ( Photo de l'auteur)
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