Bilan des actions une liaison encastrement en a r 1 m

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– bilan des actions : une liaison encastrement en A ~ R 1 ˘ M 1 A ; un torseur de chargement F ~ j ˘ 0 B – calcul du torseur des efforts int´ erieurs : on oriente la poutre de A vers B. Le torseur des efforts int´ erieurs en H ( s ) tel que ~ AH = s ~ i , se calcule en fonction de la partie aval : { τ H } = F ~ j ˘ 0 B = F ~ j F ( l - s ) ˘ k H = F~y F ( l - s z H (2.67) avec ( H, ~x, ~ y, ~ z ) le rep` ere local en H . – d´ etermination des ´ evolutions de ses composantes le long de la poutre (avec l’abscisse s ) : – effort normal : N ( s ) = 0 – effort tranchant dans la direction ~ y : T y ( s ) = F – effort tranchant dans la direction ~ z : T z ( s ) = 0 – moment de torsion : M x ( s ) = 0 – moment de flexion autour de l’axe H ˘ y : M fy ( s ) = 0 – moment de flexion autour de l’axe H ˘ z : M fz ( s ) = F ( l - s ) – recherche du point le plus sollicit´ e : La poutre est soumise `a de la flexion M fz de l’effort tranchant T y , la contrainte en un point P de la section droite tel que ~ HP = ˆ y~y + ˆ z~ z est donn´ ee par : σ xx ( s, ˆ y ) = - F ( l - s y πr 4 / 4 . (2.68) Il faut rechercher le maximum et le minimum de σ xx . On consid´ erera donc les demie-´ epaisseurs de la poutre ˆ y maxi = r ou ˆ y maxi = - r . On obtient donc : σ xx (0 , - r ) = Flr πr 4 / 4 = 4 Fl πr 3 , (2.69) d’o`u, F < 24010 6 πr 3 4 l . (2.70) Soit pour une poutre de rayon r = 0 . 005 m et une longueur de l = 0 . 2 m , une force maximale admissible de F = 118 N . 53 cel-00611692, version 1 - 27 Jul 2011
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2.8 Non lin´ earit´ es g´ eom´ etriques (grands d´ eplacements) 2.8.1 Exemple 2.8.2 ´ equation 2.8.3 ethode incr´ ementale 2.8.4 flambement 2.9 Formulation variationnelle 2.9.1 Principe des travaux virtuels W* = 2.9.2 Equation d’´ equilibre W* = 2.9.3 Mod` ele variationnel en d´ eplacement W* = 2.9.4 Mod` ele variationnel mixte W* = 54 cel-00611692, version 1 - 27 Jul 2011
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