{"text_format":"3","workbook":"xls","n_sheets":3,"sheets":["Table simple","Table double","Calculs manuels"],"not_rendered":{"charts":2,"images":3,"external_links":1,"defined_names":117},"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"Table simple","index":0,"n_rows":86,"n_cols":44,"rows_kept":86,"merged":[[1,1,2,11],[4,1,4,4],[4,6,4,11],[8,1,8,2],[8,6,8,9],[8,10,8,11],[10,70,10,75],[10,77,10,82],[11,15,11,26],[11,28,11,38],[11,40,11,43],[11,63,12,64],[11,65,12,66],[11,67,12,68],[11,70,12,71],[11,72,12,73],[11,74,12,75],[12,6,13,11],[12,15,12,16],[12,17,12,18],[12,19,12,20],[12,21,12,22],[12,23,12,24],[12,25,12,26],[12,28,12,29],[12,30,12,31],[12,33,12,35],[12,36,12,38],[14,6,15,11],[17,6,18,11],[37,10,37,14],[48,28,50,34],[49,1,51,3],[51,15,51,43],[52,15,52,16],[52,17,52,18],[52,19,52,20],[52,21,52,22],[52,23,52,24],[52,25,52,26],[52,28,52,29],[52,30,52,31],[52,33,52,35],[52,36,52,38],[59,10,59,14],[59,15,59,20],[61,15,61,23],[65,15,65,20],[66,15,67,23],[71,15,71,23],[75,15,75,23],[76,15,77,23],[78,15,78,23],[79,15,79,20],[80,15,80,20],[83,15,83,23],[85,15,92,23]],"flags":["formulas_cached_only"]}
[]
[null,"Entrez les valeurs uniquement dans les cellules jaunes. A noter que cette application ne vérifie pas les éventuelles impossibilités\nde fonctionnement mécanique pouvant survenir selon les valeurs saisies. Pour les valeurs dans des repères : attention au signe"]
[{"$nulls":13},"Solutions données par MAXIMA (après factorisation) - Seules les deux premières sont utilisées telles quelles ici ; les autres sont remplacées par des équations de départ utilisant ces deux solutions (calculs plus simples)"]
[]
[null,"Longueurs",{"$nulls":4},"Dans repère xAy",{"$nulls":6},"Ryc = -(Pb1*Xg1*Xh*Yj+Pb2*Xd*Xh*Yj+Fye*Xd*Xh*Yj+Fyb*Xb*Xh*Yj-Pb2*Xd*Xg2*Yj-Pb1*Xd*Xg1*Yj-Fye*Xd*Xe*Yj-Fyb*Xb*Xd*Yj-Pb1*Xg1*Xj*Yh-Pb2*Xd*Xj*Yh-Fye*Xd*Xj*Yh-Fyb*Xb*Xj*Yh+Pb2*Xd*Xg2*Yh+Pb1*Xd*Xg1*Yh+Fye*Xd*Xe*Yh+Fyb*Xb*Xd*Yh+Pb2*Xg2*Xj*Yd+Pb1*Xg1*Xj*Yd+Fye*X"]
[null,"AD (mm)","DE (mm)","EN (mm)","EM (mm)",null,"Charge (N)","Table Pt (N)","Bras Pb1 (N)","BrasPb2 (N)","Xj (mm)","Yj (mm)",null,"Fyv = -((Pb2*Xd*Xg2+Pb1*Xd*Xg1-Pb1*Xc*Xg1+Fye*Xd*Xe-Pb2*Xc*Xd-Fye*Xc*Xd+Fyb*Xb*Xd-Fyb*Xb*Xc)*(Yj-Yh))/(Xd*Xh*Yj-Xc*Xd*Yj-Xd*Xj*Yh+Xc*Xd*Yh+Xc*Xj*Yd-Xc*Xh*Yd)"]
[null,275,275,200,200,null,-200,-50,-40,-40,0,0,null,"Rxa = ((Pb2*Xd*Xg2+Pb1*Xd*Xg1-Pb1*Xc*Xg1+Fye*Xd*Xe-Pb2*Xc*Xd-Fye*Xc*Xd+Fyb*Xb*Xd-Fyb*Xb*Xc)*(Xj-Xh))/(Xd*Xh*Yj-Xc*Xd*Yj-Xd*Xj*Yh+Xc*Xd*Yh+Xc*Xj*Yd-Xc*Xh*Yd)"]
[{"$nulls":13},"Rya = (Pb1*Xg1*Xh*Yj-Pb1*Xd*Xh*Yj-Fyb*Xd*Xh*Yj+Fyb*Xb*Xh*Yj-Pb1*Xc*Xg1*Yj+Pb1*Xc*Xd*Yj+Fyb*Xc*Xd*Yj-Fyb*Xb*Xc*Yj-Pb1*Xg1*Xj*Yh+Pb1*Xd*Xj*Yh+Fyb*Xd*Xj*Yh-Fyb*Xb*Xj*Yh+Pb1*Xc*Xg1*Yh-Pb1*Xc*Xd*Yh-Fyb*Xc*Xd*Yh+Fyb*Xb*Xc*Yh+Pb2*Xg2*Xj*Yd+Pb1*Xg1*Xj*Yd+Fye*Xe*X"]
[null,"Position table (distance P)",{"$nulls":4},"Dans repère vEw *",{"$nulls":3},"Dans repère tAu **",null,null,"Fxd = -((Pb2*Xd*Xg2+Pb1*Xd*Xg1-Pb1*Xc*Xg1+Fye*Xd*Xe-Pb2*Xc*Xd-Fye*Xc*Xd+Fyb*Xb*Xd-Fyb*Xb*Xc)*(Xj-Xh))/(Xd*Xh*Yj-Xc*Xd*Yj-Xd*Xj*Yh+Xc*Xd*Yh+Xc*Xj*Yd-Xc*Xh*Yd)"]
[null,"Mini (mm)","Maxi (mm)",{"$nulls":3},"a (mm)","b (mm)","d (mm)","e (mm)","f (mm)","g(mm)",null,"Fyd = -(Pb1*Xg1*Xh*Yj+Fyb*Xb*Xh*Yj-Pb1*Xc*Xg1*Yj-Fyb*Xb*Xc*Yj-Pb1*Xg1*Xj*Yh-Fyb*Xb*Xj*Yh+Pb1*Xc*Xg1*Yh+Fyb*Xb*Xc*Yh+Pb2*Xg2*Xj*Yd+Pb1*Xg1*Xj*Yd+Fye*Xe*Xj*Yd-Pb2*Xc*Xj*Yd-Fye*Xc*Xj*Yd+Fyb*Xb*Xj*Yd-Pb2*Xg2*Xh*Yd-Pb1*Xg1*Xh*Yd-Fye*Xe*Xh*Yd+Pb2*Xc*Xh*Yd+Fye*X"]
[null,20,500,{"$nulls":3},449.99999,0,500,20,275,0]
[{"$nulls":15},"Positions des points",{"$nulls":12},"Composantes des forces",{"$nulls":11},"Angles ( pour information )"]
[null,"Pos. table","Long. vérin","Effort  vérin",null,null,"La charge ne se déplace pas par rapport au point E et le point B est glissant ; la \ncharge se répartit donc selon Fe et Fb qui n'ont aucune composante horizontale.",{"$nulls":8},"Coord. point B",null,"Coord. point C",null,"Coord. point D",null,"Coord. point E",null,"Coord. point H",null,"Pos. en X des CdG bras",null,null,"Charge + Table",null,"Fv (vérin)",null,"Rc","Fd (action mutuelle en D)",null,null,"Ra",{"$nulls":3},"Angle de AB","Angle vérin","Angle de AB","Angle vérin"]
[null,"P (mm)","JH (mm)","Fv (N)",{"$nulls":11},"Xb (mm)","Yb (mm)","Xc (mm)","Yc (mm)","Xd (mm)","Yd (mm)","Xe (mm)","Ye (mm)","Xh (mm)","Yh (mm)","Xg1 (mm)","Xg2 (mm)",null,"Fyb (N)","Fye (N)","Fxv (N)","Fyv (N)","Ryc (N)","Fxd (N)","Fyd (N)","Module (N)","Rxa (N)","Rya (N)","Module (N)",null,"α (rad)","β (rad)","α (°)","β (°)"]
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[null,65,{"v":447.0026339855283,"d":"447.00"},{"v":2955.223732986241,"d":"2955.22"},null,null,"Les actions des poids propres des parties fixes et coulissantes du vérin ne sont pas prises en compte",{"$nulls":8},{"v":546.1455849862746,"d":"546.15"},65,{"v":546.1455849862746,"d":"546.15"},0,{"v":273.0727924931373,"d":"273.07"},{"v":32.5,"d":"32.50"},{"v":0,"d":"0.00"},65,{"v":446.8463777861231,"d":"446.85"},{"v":11.818182999999998,"d":"11.82"},{"v":273.0727924931373,"d":"273.07"},{"v":498.8596227147951,"d":"498.86"},null,{"v":-91.55068057770086,"d":"-91.55"},{"v":-158.44931942229914,"d":"-158.45"},{"v":-2954.1906920289853,"d":"-2954.19"},{"v":-78.13236931285115,"d":"-78.13"},{"v":148.0874309555205,"d":"148.09"},{"v":-2954.1906920289853,"d":"-2954.19"},{"v":-128.4942577796298,"d":"-128.49"},{"v":2956.9838381622976,"d":"2956.98"},{"v":2954.1906920289853,"d":"2954.19"},{"v":260.0449383573307,"d":"260.04"},{"v":2965.6139355681416,"d":"2965.61"},null,{"v":0.11845866820915658,"d":"0.1184587"},{"v":0.02644181346122977,"d":"0.0264418"},{"v":6.78718173512521,"d":"6.79"},{"v":1.515004314000673,"d":"1.52"}]
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[null,395,{"v":321.2652491478032,"d":"321.27"},{"v":347.8131239379142,"d":"347.81"},{"$nulls":8},"Mat. inv. de rotation α",null,null,{"v":382.7205246651922,"d":"382.72"},395,{"v":382.7205246651922,"d":"382.72"},0,{"v":191.3602623325961,"d":"191.36"},{"v":197.5,"d":"197.50"},{"v":0,"d":"0.00"},395,{"v":313.13496776751134,"d":"313.13"},{"v":71.81818899999996,"d":"71.82"},{"v":191.3602623325961,"d":"191.36"},{"v":362.2913860592657,"d":"362.29"},null,{"v":-130.6436336116034,"d":"-130.64"},{"v":-119.3563663883966,"d":"-119.36"},{"v":-339.01099369545966,"d":"-339.01"},{"v":-77.75291208094967,"d":"-77.75"},{"v":188.5084840923767,"d":"188.51"},{"v":-339.01099369545966,"d":"-339.01"},{"v":-48.60079437696956,"d":"-48.60"},{"v":342.47699347613917,"d":"342.48"},{"v":339.01099369545966,"d":"339.01"},{"v":219.24442798857297,"d":"219.24"},{"v":403.72834065794734,"d":"403.73"},null,{"v":0.8011859106621445,"d":"0.8011859"},{"v":0.22545303346090925,"d":"0.2254530"},{"v":45.904571286286306,"d":"45.90"},{"v":12.917507295731827,"d":"12.92"}]
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[null,515,{"v":183.6313023152646,"d":"183.63"},{"v":151.14923047236113,"d":"151.15"},{"$nulls":11},{"v":193.06734576307824,"d":"193.07"},515,{"v":193.06734576307824,"d":"193.07"},0,{"v":96.53367288153912,"d":"96.53"},{"v":257.5,"d":"257.50"},{"v":0,"d":"0.00"},515,{"v":157.96418847765773,"d":"157.96"},{"v":93.63637299999999,"d":"93.64"},{"v":96.53367288153912,"d":"96.53"},{"v":194.2430416027984,"d":"194.24"},null,{"v":-258.9769896218353,"d":"-258.98"},{"v":8.976989621835287,"d":"8.98"},{"v":-130.02230681562966,"d":"-130.02"},{"v":-77.07327424424892,"d":"-77.07"},{"v":319.2205721572606,"d":"319.22"},{"v":-130.02230681562966,"d":"-130.02"},{"v":211.12428753484699,"d":"211.12"},{"v":247.95012614788982,"d":"247.95"},{"v":130.02230681562966,"d":"130.02"},{"v":87.8527020869883,"d":"87.85"},{"v":156.920035475534,"d":"156.92"},null,{"v":1.2121238080594645,"d":"1.2121238"},{"v":0.5350860866575062,"d":"0.5350861"},{"v":69.4495784491328,"d":"69.45"},{"v":30.658174441646537,"d":"30.66"}]
[]
[null,"Mettre une valeur particulière de P dans la cellule jaune puis lire les résultats sur la même ligne (suite à droite → )"]
[]
[{"$nulls":15},"- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Mettre une valeur particulière de P dans la cellule jaune, à gauche dans la première colonne et lire les résultats du calcul sur la même ligne  - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -"]
[null,"Pos. table","Long. vérin","Effort  vérin",{"$nulls":11},"Coord. point B",null,"Coord. point C",null,"Coord. point D",null,"Coord. point E",null,"Coord. point H",null,"Pos. en X des CdG bras",null,null,"Décomposition charge",null,"Composantes F vérin",null,"Réac. en C","Compos. F en D sur AB",null,null,"Compos. réaction en A",{"$nulls":3},"Angle de AB","Angle vérin","Angle de AB","Angle vérin"]
[null,"P (mm)","JH (mm)","Fv (N)",{"$nulls":11},"Xb (mm)","Yb (mm)","Xc (mm)","Yc (mm)","Xd (mm)","Yd (mm)","Xe (mm)","Ye (mm)","Xh (mm)","Yh (mm)","Xg1 (mm)","Xg2 (mm)",null,"Fyb (N)","Fye (N)","Fxv (N)","Fyv (N)","Ryc (N)","Fxd (N)","Fyd (N)","Module (N)","Rxa (N)","Rya (N)","Module (N)",null,"α (rad)","β (rad)","α (°)","β (°)"]
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[]
[]
[]
[]
[{"$nulls":10},"Coordonnées de G1 dans xAy",{"$nulls":4},"Pour effectuer un calcul de RdM sur les barres, il faut :"]
[]
[{"$nulls":12},"Mat. inv. de rotation α",null,null,"1 - Avoir les projections des efforts sur la barre pour calculer la traction / compression appliquée sur les différentes parties"]
[]
[{"$nulls":15},"Pour cela, pour chaque force :"]
[]
[{"$nulls":15},"- on calcule le produit scalaire des vecteurs \"Force\" et \"Barre\""]
[{"$nulls":15},"- puisque ce produit est égal au produit de leurs modules par le cos. de leur angle, on divise ce produit par le module\n  du vecteur \"Barre\""]
[]
[{"$nulls":15},"- on obtient la projection sur l'axe de la barre. La barre étant en équilibre, la somme de ces projections est nulle"]
[]
[]
[{"$nulls":15},"2 - Avoir les projections des efforts sur la normale à la barre, pour calculer la fleXjon"]
[]
[{"$nulls":15},"Pour cela, pour chaque force :"]
[]
[{"$nulls":15},"- on calcule le produit vectoriel des vecteurs \"Force\" et \"Barre\""]
[{"$nulls":15},"- puisque ce produit est égal au produit de leurs modules par le sin. de leur angle, on divise ce  produit par le module\n  du vecteur \"Barre\""]
[]
[{"$nulls":15},"- on obtient la projection sur la normale à l'axe de la barre. La barre étant en équilibre, la somme de ces projections est nulle"]
[]
[{"$nulls":15},"Des exemples sont donnés dans la feuille : Exemples calcul projections"]
[]
[]
[{"$nulls":15},"3 - Prendre en compte du poids propre des barres, pour en calculer la compression et la flexion"]
[]
[{"$nulls":15},"Dans le calcul des efforts, le poids propre de chaque barre est considéré comme une charge ponctuelle, appliquée à son CdG. Pour le calcul de RdM de ces barres, si l'on considère le poids propre appliqué au CdG, le calcul sera plutôt défavorable. Si l'on veut en tenir compte, on peut procéder comme indiqué plus bas à droite, mais cela ne fonctionne que pour une charge également répartie le long de la barre ; si le CdG n'est pas au milieu de la barre (comme ce peut être le cas dans les tableaux plus haut), ce sera faux quand même. Il faudrait connaître la répartition exacte du poids, mais la résolution risque d'être compliquée pour le peu d'avantage qu'elle apporte alors, le calcul défavorable cité plus haut (charge ponctuelle) devrait suffire. "]

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[]
[null,"Entrez les valeurs uniquement dans les cellules jaunes. A noter que cette application ne vérifie pas les éventuelles impossibilités\nde fonctionnement mécanique pouvant survenir selon les valeurs saisies. Pour les valeurs dans des repères : attention au signe !",{"$nulls":14},"Solutions données par MAXIMA (après factorisation) - Seules les deux premières, pour chaque étage, sont utilisées telles quelles ici ; les autres sont remplacées par des équations de départ utilisant ces deux solutions (calculs plus simples)"]
[{"$nulls":16},"Rxr = -(Fxe*Xs*Yt-Fxe*Xr*Yt-Fxe*Xt*Ys-Fxb*Xt*Ys+Fxe*Xr*Ys+Fxb*Xr*Ys+Fxe*Xt*Ye-Fxe*Xs*Ye+Fxb*Xt*Yb-Fxb*Xr*Yb+Pb1*Xs*Xt+Fyb*Xs*Xt+Pb2*Xr*Xt+Fye*Xr*Xt-Pb2*Xg2*Xt-Pb1*Xg1*Xt-Fye*Xe*Xt-Fyb*Xb*Xt-Pb2*Xr*Xs-Pb1*Xr*Xs-Fye*Xr*Xs-Fyb*Xr*Xs+Pb2*Xg2*Xs+Fye*Xe*Xs+Pb1*Xg1*Xr+Fyb*Xb*Xr)/(Xs*Yt-Xr*Yt-Xt*Ys+Xr*Ys+Xt*Yr-Xs*Yr)"]
[{"$nulls":16},"Ryr = (Fxb*Ys*Yt+Fxe*Yr*Yt-Fxe*Ye*Yt-Fxb*Yb*Yt-Pb2*Xs*Yt-Pb1*Xs*Yt-Fye*Xs*Yt-Fyb*Xs*Yt+Pb2*Xg2*Yt+Pb1*Xg1*Yt+Fye*Xe*Yt+Fyb*Xb*Yt-Fxe*Yr*Ys-Fxb*Yr*Ys+Fxe*Ye*Ys+Pb2*Xt*Ys+Fye*Xt*Ys-Pb2*Xg2*Ys-Fye*Xe*Ys+Fxb*Yb*Yr-Pb2*Xt*Yr-Fye*Xt*Yr+Pb2*Xs*Yr+Pb1*Xs*Yr+Fye*Xs*Yr+Fyb*Xs*Yr-Pb1*Xg1*Yr-Fyb*Xb*Yr)/(Xs*Yt-Xr*Yt-Xt*Ys+Xr*Ys+Xt*Yr-Xs*Yr)"]
[null,"Longueurs (Nota : DC=AB,  ST=RT=RD=SD  et  TB=TE)",{"$nulls":4},"Position table (distance P)",{"$nulls":9},"Rxs = -(Fxb*Xs*Yt-Fxb*Xr*Yt+Fxe*Xt*Yr+Fxb*Xt*Yr-Fxe*Xs*Yr-Fxb*Xs*Yr-Fxe*Xt*Ye+Fxe*Xs*Ye-Fxb*Xt*Yb+Fxb*Xr*Yb-Pb1*Xs*Xt-Fyb*Xs*Xt-Pb2*Xr*Xt-Fye*Xr*Xt+Pb2*Xg2*Xt+Pb1*Xg1*Xt+Fye*Xe*Xt+Fyb*Xb*Xt+Pb2*Xr*Xs+Pb1*Xr*Xs+Fye*Xr*Xs+Fyb*Xr*Xs-Pb2*Xg2*Xs-Fye*Xe*Xs-Pb1*Xg1*Xr-Fyb*Xb*Xr)/(Xs*Yt-Xr*Yt-Xt*Ys+Xr*Ys+Xt*Yr-Xs*Yr)"]
[null,"AD (mm)","DS (mm)","TE (mm)","EN (mm)","EM (mm)","Mini (mm)","Maxi (mm)",{"$nulls":8},"Rys = -(Fxb*Ys*Yt+Fxe*Yr*Yt-Fxe*Ye*Yt-Fxb*Yb*Yt-Pb2*Xr*Yt-Pb1*Xr*Yt-Fye*Xr*Yt-Fyb*Xr*Yt+Pb2*Xg2*Yt+Pb1*Xg1*Yt+Fye*Xe*Yt+Fyb*Xb*Yt-Fxe*Yr*Ys-Fxb*Yr*Ys+Fxe*Ye*Ys-Pb1*Xt*Ys-Fyb*Xt*Ys+Pb2*Xr*Ys+Pb1*Xr*Ys+Fye*Xr*Ys+Fyb*Xr*Ys-Pb2*Xg2*Ys-Fye*Xe*Ys+Fxb*Yb*Yr+Pb1*Xt*Yr+Fyb*Xt*Yr-Pb1*Xg1*Yr-Fyb*Xb*Yr)/(Xs*Yt-Xr*Yt-Xt*Ys+Xr*Ys+Xt*Yr-Xs*Yr)"]
[null,350,350,350,100,350,90,852,{"$nulls":8},"Fxt = (Fxb*Xt*Ys-Fxb*Xr*Ys+Fxe*Xt*Yr-Fxe*Xs*Yr-Fxe*Xt*Ye+Fxe*Xs*Ye-Fxb*Xt*Yb+Fxb*Xr*Yb-Pb1*Xs*Xt-Fyb*Xs*Xt-Pb2*Xr*Xt-Fye*Xr*Xt+Pb2*Xg2*Xt+Pb1*Xg1*Xt+Fye*Xe*Xt+Fyb*Xb*Xt+Pb2*Xr*Xs+Pb1*Xr*Xs+Fye*Xr*Xs+Fyb*Xr*Xs-Pb2*Xg2*Xs-Fye*Xe*Xs-Pb1*Xg1*Xr-Fyb*Xb*Xr)/(Xs*Yt-Xr*Yt-Xt*Ys+Xr*Ys+Xt*Yr-Xs*Yr)"]
[{"$nulls":16},"Fyt = (Fxb*Ys*Yt+Fxe*Yr*Yt-Fxe*Ye*Yt-Fxb*Yb*Yt-Pb1*Xs*Yt-Fyb*Xs*Yt-Pb2*Xr*Yt-Fye*Xr*Yt+Pb2*Xg2*Yt+Pb1*Xg1*Yt+Fye*Xe*Yt+Fyb*Xb*Yt-Fxe*Yr*Ys-Fxb*Yr*Ys+Fxe*Ye*Ys+Pb2*Xr*Ys+Fye*Xr*Ys-Pb2*Xg2*Ys-Fye*Xe*Ys+Fxb*Yb*Yr+Pb1*Xs*Yr+Fyb*Xs*Yr-Pb1*Xg1*Yr-Fyb*Xb*Yr)/(Xs*Yt-Xr*Yt-Xt*Ys+Xr*Ys+Xt*Yr-Xs*Yr)"]
[null,"Poids dans repère xAy",{"$nulls":5},"H dans repère vSw *",null," J dans repère xAy",{"$nulls":6},"Fyv = -((Yj-Yh)*(Rxs*Xd*Ys+Rxr*Xd*Yr-Rxr*Xc*Yr-Rxs*Xc*Yd-Rys*Xd*Xs-Ryr*Xd*Xr+Ryr*Xc*Xr+Pb4*Xd*Xg4+Pb3*Xd*Xg3-Pb3*Xc*Xg3+Rys*Xc*Xd-Pb4*Xc*Xd))/(Xd*Xh*Yj-Xc*Xd*Yj-Xd*Xj*Yh+Xc*Xd*Yh+Xc*Xj*Yd-Xc*Xh*Yd)"]
[null,"Charge (N)","Table Pt (N)","Bras Pb1 (N)","BrasPb2 (N)","Bras Pb3 (N)","BrasPb4(N)","a (mm)","b (mm)","Xj (mm)","Yj (mm)",{"$nulls":5},"Ryc = (Rxs*Xd*Yj*Ys-Rxs*Xd*Yh*Ys-Rxs*Xj*Yd*Ys+Rxs*Xh*Yd*Ys-Rxr*Xh*Yj*Yr+Rxr*Xd*Yj*Yr+Rxr*Xj*Yh*Yr-Rxr*Xd*Yh*Yr-Rxr*Xj*Yd*Yr+Rxr*Xh*Yd*Yr-Rxs*Xh*Yd*Yj-Rys*Xd*Xs*Yj+Ryr*Xh*Xr*Yj-Ryr*Xd*Xr*Yj-Pb3*Xg3*Xh*Yj+Rys*Xd*Xh*Yj-Pb4*Xd*Xh*Yj+Pb4*Xd*Xg4*Yj+Pb3*Xd*Xg3*Yj+Rxs*Xj*Yd*Yh+Rys*Xd*Xs*Yh-Ryr*Xj*Xr*Yh+Ryr*Xd*Xr*Yh+Pb3*Xg3*Xj*Yh-Rys*Xd*Xj*Yh+Pb4*Xd*Xj*Yh-Pb4*Xd*Xg4*Yh-Pb3*Xd*Xg3*Yh+Rys*Xj*Xs*Yd-Rys*Xh*Xs*Yd+Ryr*Xj*Xr*Yd-Ryr*Xh*Xr*Yd-Pb4*Xg4*Xj*Yd-Pb3*Xg3*Xj*Yd+Pb4*Xg4*Xh*Yd+Pb3*Xg3*Xh*Yd)/(Xd*Xh*Yj-Xc*Xd*Yj-Xd*Xj*Yh+Xc*Xd*Yh+Xc*Xj*Yd-Xc*Xh*Yd)"]
[null,-1000,-150,-100,-100,-100,-100,699.999999,0,0,0,{"$nulls":5},"Rxa = (Rxs*Xd*Xj*Ys-Rxs*Xd*Xh*Ys+Rxr*Xd*Xj*Yr-Rxr*Xc*Xj*Yr-Rxr*Xd*Xh*Yr+Rxr*Xc*Xh*Yr+Rxs*Xd*Xh*Yj+Rxr*Xd*Xh*Yj-Rxs*Xc*Xd*Yj-Rxr*Xc*Xd*Yj-Rxs*Xd*Xj*Yh-Rxr*Xd*Xj*Yh+Rxs*Xc*Xd*Yh+Rxr*Xc*Xd*Yh+Rxr*Xc*Xj*Yd-Rxr*Xc*Xh*Yd-Rys*Xd*Xj*Xs+Rys*Xd*Xh*Xs-Ryr*Xd*Xj*Xr+Ryr*Xc*Xj*Xr+Ryr*Xd*Xh*Xr-Ryr*Xc*Xh*Xr+Pb4*Xd*Xg4*Xj+Pb3*Xd*Xg3*Xj-Pb3*Xc*Xg3*Xj+Rys*Xc*Xd*Xj-Pb4*Xc*Xd*Xj-Pb4*Xd*Xg4*Xh-Pb3*Xd*Xg3*Xh+Pb3*Xc*Xg3*Xh-Rys*Xc*Xd*Xh+Pb4*Xc*Xd*Xh)/(Xd*Xh*Yj-Xc*Xd*Yj-Xd*Xj*Yh+Xc*Xd*Yh+Xc*Xj*Yd-Xc*Xh*Yd)"]
[{"$nulls":16},"Rya = (Rxs*Xj*Yd*Ys-Rxs*Xh*Yd*Ys+Rxr*Xh*Yj*Yr-Rxr*Xc*Yj*Yr-Rxr*Xj*Yh*Yr+Rxr*Xc*Yh*Yr+Rxr*Xj*Yd*Yr-Rxr*Xh*Yd*Yr+Rxs*Xh*Yd*Yj-Rxs*Xc*Yd*Yj-Ryr*Xh*Xr*Yj+Ryr*Xc*Xr*Yj+Pb3*Xg3*Xh*Yj+Ryr*Xd*Xh*Yj-Pb3*Xd*Xh*Yj-Pb3*Xc*Xg3*Yj-Ryr*Xc*Xd*Yj+Pb3*Xc*Xd*Yj-Rxs*Xj*Yd*Yh+Rxs*Xc*Yd*Yh+Ryr*Xj*Xr*Yh-Ryr*Xc*Xr*Yh-Pb3*Xg3*Xj*Yh-Ryr*Xd*Xj*Yh+Pb3*Xd*Xj*Yh+Pb3*Xc*Xg3*Yh+Ryr*Xc*Xd*Yh-Pb3*Xc*Xd*Yh-Rys*Xj*Xs*Yd+Rys*Xh*Xs*Yd-Ryr*Xj*Xr*Yd+Ryr*Xh*Xr*Yd+Pb4*Xg4*Xj*Yd+Pb3*Xg3*Xj*Yd+Rys*Xc*Xj*Yd+Ryr*Xc*Xj*Yd-Pb4*Xc*Xj*Yd-Pb3*Xc*Xj*Yd-Pb4*Xg4*Xh*Yd-Pb3*Xg3*Xh*Yd-Rys*Xc*Xh*Yd-Ryr*Xc*Xh*Yd+Pb4*Xc*Xh*Yd+Pb3*Xc*Xh*Yd)/(Xd*Xh*Yj-Xc*Xd*Yj-Xd*Xj*Yh+Xc*Xd*Yh+Xc*Xj*Yd-Xc*Xh*Yd)"]
[null,"G1 dans repère pSq **",null,"G2 dans repère rEs *",null,"G3 dans repère tAu **",null,"G4 dans repère vSw *",{"$nulls":8},"Fxd = -(Rxs*Xd*Xj*Ys-Rxs*Xd*Xh*Ys+Rxr*Xd*Xj*Yr-Rxr*Xc*Xj*Yr-Rxr*Xd*Xh*Yr+Rxr*Xc*Xh*Yr+Rxs*Xd*Xh*Yj-Rxs*Xc*Xd*Yj-Rxs*Xd*Xj*Yh+Rxs*Xc*Xd*Yh-Rys*Xd*Xj*Xs+Rys*Xd*Xh*Xs-Ryr*Xd*Xj*Xr+Ryr*Xc*Xj*Xr+Ryr*Xd*Xh*Xr-Ryr*Xc*Xh*Xr+Pb4*Xd*Xg4*Xj+Pb3*Xd*Xg3*Xj-Pb3*Xc*Xg3*Xj+Rys*Xc*Xd*Xj-Pb4*Xc*Xd*Xj-Pb4*Xd*Xg4*Xh-Pb3*Xd*Xg3*Xh+Pb3*Xc*Xg3*Xh-Rys*Xc*Xd*Xh+Pb4*Xc*Xd*Xh)/(Xd*Xh*Yj-Xc*Xd*Yj-Xd*Xj*Yh+Xc*Xd*Yh+Xc*Xj*Yd-Xc*Xh*Yd)"]
[null,"j (mm)","k (mm)","h (mm)","i (mm)","f (mm)","g (mm)","d (mm)","e (mm)",{"$nulls":7},"Fyd = -(Rxs*Xj*Yd*Ys-Rxs*Xh*Yd*Ys+Rxr*Xh*Yj*Yr-Rxr*Xc*Yj*Yr-Rxr*Xj*Yh*Yr+Rxr*Xc*Yh*Yr+Rxr*Xj*Yd*Yr-Rxr*Xh*Yd*Yr+Rxs*Xh*Yd*Yj-Rxs*Xc*Yd*Yj-Ryr*Xh*Xr*Yj+Ryr*Xc*Xr*Yj+Pb3*Xg3*Xh*Yj-Pb3*Xc*Xg3*Yj-Rxs*Xj*Yd*Yh+Rxs*Xc*Yd*Yh+Ryr*Xj*Xr*Yh-Ryr*Xc*Xr*Yh-Pb3*Xg3*Xj*Yh+Pb3*Xc*Xg3*Yh-Rys*Xj*Xs*Yd+Rys*Xh*Xs*Yd-Ryr*Xj*Xr*Yd+Ryr*Xh*Xr*Yd+Pb4*Xg4*Xj*Yd+Pb3*Xg3*Xj*Yd+Rys*Xc*Xj*Yd-Pb4*Xc*Xj*Yd-Pb4*Xg4*Xh*Yd-Pb3*Xg3*Xh*Yd-Rys*Xc*Xh*Yd+Pb4*Xc*Xh*Yd)/(Xd*Xh*Yj-Xc*Xd*Yj-Xd*Xj*Yh+Xc*Xd*Yh+Xc*Xj*Yd-Xc*Xh*Yd)"]
[null,350,0,350,0,350,0,350,0]
[{"$nulls":16},"Positions des points",{"$nulls":20},"Composantes des forces",{"$nulls":17},"Angles ( pour information )"]
[null,"Pos. table","Long. vérin","Effort  vérin",null,"Si la charge ne se déplace pas par rapport au point E et que le point B est glissant ; la charge se répartit donc selon Fye et Fyb et les composantes horizontales Fxe et Fxb sont nulles (mais prises en compte dans les calculs pour une éventuelle autre application avec un ciseau supplémentaire par ex.). Les colonnes Fxe et Fxb sont donc conservées et des formules y font référence, mais ici elles restent vides (=0)",{"$nulls":10},"Coord. point B",null,"Coord. point C",null,"Coord. point D",null,"Coord. point E",null,"Coord. point H",null,"Coord. point R",null,"Coord. point S",null,"Coord. point T",null,"Pos. en X des CdG bras",{"$nulls":4},"Charge + Table",{"$nulls":3},"Rr",null,"Rs",null,"Ft (action mutuelle en T)",null,"Rc","Fv (vérin)",null,"Fd (action mutuelle en D)",null,"Ra",null,null,"Angle de AB","Angle vérin","Angle de AB","Angle vérin"]
[null,"P (mm)","JH (mm)","Fv (N)",{"$nulls":12},"Xb (mm)","Yb (mm)","Xc (mm)","Yc (mm)","Xd (mm)","Yd (mm)","Xe (mm)","Ye (mm)","Xh (mm)","Yh (mm)","Xr (mm)","Yr (mm)","Xs (mm)","Ys (mm)","Xt (mm)","Yt (mm)","Xg1 (mm)","Xg2 (mm)","Xg3 (mm)","Xg4(mm)",null,"Fxb (N)","Fyb (N)","Fxe (N)","Fye (N)","Rxr (N)","Ryr (N)","Rxs (N)","Rys (N)","Fxt (N)","Fyt (N)","Ryc (N)","Fxv (N)","Fyv (N)","Fxd (N)","Fyd (N)","Rxa (N)","Rya (N)",null,"α (rad)","β (rad)","α (°)","β (°)"]
[null,90,{"v":698.5520729378633,"d":"698.55"},{"v":41913.12449602358,"d":"41913.12"},{"$nulls":12},{"v":698.5520739357947,"d":"698.55"},90,{"v":698.5520739357947,"d":"698.55"},0,{"v":349.27603696789737,"d":"349.28"},{"v":22.5,"d":"22.50"},{"v":0,"d":"0.00"},90,{"v":698.5520729378633,"d":"698.55"},{"v":6.428571452943288e-08,"d":"0.00"},{"v":698.5520739357947,"d":"698.55"},{"v":45,"d":"45.00"},{"v":0,"d":"0.00"},{"v":45,"d":"45.00"},{"v":349.27603696789737,"d":"349.28"},{"v":67.5,"d":"67.50"},{"v":349.27603696789737,"d":"349.28"},{"v":349.27603696789737,"d":"349.28"},{"v":349.27603696789737,"d":"349.28"},{"v":349.27603696789737,"d":"349.28"},null,null,{"v":-218.30870695262809,"d":"-218.31"},null,{"v":-931.6912930473719,"d":"-931.69"},{"v":-19404.2242759943,"d":"-19404.22"},{"v":318.3087069526279,"d":"318.31"},{"v":19404.2242759943,"d":"19404.22"},{"v":1031.6912930473723,"d":"1031.69"},{"v":-19404.2242759943,"d":"-19404.22"},{"v":-713.382586094744,"d":"-713.38"},{"v":418.3087069526279,"d":"418.31"},{"v":-41913.12449602358,"d":"-41913.12"},{"v":-3.8571428827863805e-06,"d":"-0.00"},{"v":-61317.34877201788,"d":"-61317.35"},{"v":-713.3825899518872,"d":"-713.38"},{"v":41913.12449602358,"d":"41913.12"},{"v":1131.6912969045152,"d":"1131.69"},null,{"v":0.0643300752588186,"d":"0.0643301"},{"v":9.202709006226246e-11,"d":"0.0000000"},{"v":3.685841808089263,"d":"3.69"},{"v":5.272763861437959e-09,"d":"0.00"}]
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[null,"Mettre une valeur particulière de P dans\nla cellule jaune, ci-dessous, puis lire les\nrésultats sur la même ligne\n(suite à droite → )"]
[]
[{"$nulls":10},"Coordonnées de H, et de G4 dans xAy"]
[{"$nulls":11},"Mat. inv. de rotation α",{"$nulls":4},"- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Mettre une valeur particulière de P dans la cellule jaune, à gauche dans la première colonne et lire les résultats du calcul sur la même ligne  - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -"]
[null,"Pos. table","Long. vérin","Effort  vérin",{"$nulls":12},"Coord. point B",null,"Coord. point C",null,"Coord. point D",null,"Coord. point E",null,"Coord. point H",null,"Coord. point R",null,"Coord. point S",null,"Coord. point T",null,"Pos. en X des CdG bras",{"$nulls":4},"Charge + Table",{"$nulls":3},"Rr",null,"Rs",null,"Ft",null,"Rc","Composantes F vérin",null,"Compos. F en D sur AB",null,"Compos. réaction en A",null,null,"Angle de AB","Angle vérin","Angle de AB","Angle vérin"]
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{"$rows_empty":7}
[{"$nulls":10},"Coordonnées de G2 dans xAy"]
[{"$nulls":11},"Mat. inv. de rotation α"]
[]
[]
[]
[]
[]
[]
[{"$nulls":10},"Coordonnées de G3 dans xAy"]
[{"$nulls":11},"Mat. inv. de rotation α"]
[]
[]
[]
[]
[]
[]
[{"$nulls":10},"Coordonnées de G1 dans xAy"]
[{"$nulls":11},"Mat. inv. de rotation α"]

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[]
["Calcul des efforts en prenant en compte le poids propre des barres"]