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Conception; CRT; Guyon-Massonet; Lignes d'influence; Moment fléchissant; Effort tranchant; Al; Bc; Mc120; Mc80...
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Caractéristiques transversaleslargeur roulable Lr 8largeur de trottoir ltr 1.25
Caractéristiques longitudinales
Longueur de travée L 21Distance d'about d 0.5
Béton
45 25 39125.83
Caractéristiques du béton de l’hourdis
Béton
Ei
25 25 32164.20
Caractéristiques de la poutre
hp hd
Poutre seule 1 0
Poutre +hourdis(Caractéristique mécaniques) 1.20 0.2
Poutre +hourdis(Caractéristique géométriques) 1.20 0.2
ETUDE DU PONT A POUTRES
Caractéristiques du béton des poutres
Fc28 (Mpa) Poids volumique
(kN/m3)
Module d'élasticité instantanné Ei
Fc28 (Mpa)
Poids volumique
(kN/m3)
Poutre I
Conception de la section transversaleLt = Lr + 2 Ltr 10.5
Lc=L-2 d 20Hp=Lc/17 1.20
bt 0.44
largeur de l'âme au about 0.3
ba 0.18première estimation b0 1.5
Nombre des éspacements 6.707
1.437
Section equivalente 1.181
Inertie de la poutre 0.0789
Nombre des poutres Np 8
Hd=b0/16 0.2La largeur de la pré-dalle b0 – bt + 0.1 = 1.097
Diemsionnement de l'entretoiseLe = 10.06 mhe = 1 mepaisseur be = 0.2 m
Détermination des paramètres fondamentaux
Rigidité à la flexion 0.0548676345984901
Le moment d'inertie de torsion
Senction en I0.0016
2(hp-hd)/ba = 11.1111Γ2 0.0019 Formule EmpiriqueΓ2 0.0004 Formule Sâada(bta-ba)/hta = 1.4857Γ3 0.0003 Formule EmpiriqueΓ3 0.0003 Formule Sâada
Largeur total du pont
Longeur de calcul Lc Hauteur de la poutre Avec Hourdis
Largeur de la table de compression
btabout
Largeur de l’ame
(Lt – bt)/b0 =
b0corrigé
b0équivalente
IGx
Hauteur de l’hourdis
Γ1
(bta'-ba)/hta' = 2.6Γ3' 6.523E-05 Formule EmpiriqueΓ3' 6.576E-05 Formule Sâada
9.951E-04 x E (MN)
Rigidité à la torsion de la poutre et de l’entretoise
9.951E-04 x E (MN)
0.00066666667 x E (MN)0.00066666667 x E (MN)
Paramètre de torsion 0.13737972355
b= 5.25Paramètre d'entretoisement 0.791
Calcul des coefficients de répartition transversale CRT
0.05487
ρe= 0.000667
b= 5.25
b0= 1.437
Poutre de riveY = 5.03 5.03Y'= -5.03 -5.03e = -5.25 -3.9375e' = 5.25 3.9375
λ 0.335 0.335a' 2.000 2.000A -9.527 -14.798b' 0.147 0.147B1 -6.077 8.827B2 -6.077 -1.871E 8.452 1.273F -42.970 -29.092
γp
γp =
γe =ρe =
Paramètres fondamentaux
Traçage des courbes K = F(e)
ρp=
σ 2.484 2.484ψ 3.142 2.356Χ -3.010 -2.225β -3.010 -3.010C 114.094 62.600D 75.854 29.487Rβ -26.610 -26.610Rψ -33.441 -5.038Qβ -66.864 -66.864Qψ 70.856 47.972
K0 -0.261 -0.358K1 0.130 0.186K -0.116 -0.156
Poutre centrale 3Y = 3.593 3.593Y'= -3.593 -3.593e = -5.250 -3.938e'= 5.250 3.938
λ 0.335 0.335a' 1.969 1.969A -9.527 -14.798b' 1.105 1.105B1 -6.077 8.827B2 -6.077 -1.871E 0.381 0.057F -27.334 -18.506σ 2.484 2.484ψ 3.142 2.356Χ -2.150 -1.365β -2.150 -2.150C 59.228 34.362D 26.764 8.353Rβ -1.201 -1.201Rψ -33.441 -5.038Qβ -42.533 -42.533Qψ 70.856 47.972
K0 -0.403 -0.268K1 0.193 0.265K -0.182 -0.071
Poutre centrale 2Y = 2.156 2.156Y'= -2.156 -2.156
e = -5.250 -3.938e'= 5.250 3.938
λ 0.335 0.335a' 1.618 1.618A -9.527 -14.798b' 1.991 1.991B1 -6.077 8.827B2 -6.077 -1.871E -2.173 -0.327F -14.735 -9.976σ 2.484 2.484ψ 3.142 2.356Χ -1.290 -0.505β -1.290 -1.290C 32.815 22.633D 7.322 0.973Rβ 6.841 6.841Rψ -33.441 -5.038Qβ -22.929 -22.929Qψ 70.856 47.972
K0 -0.496 -0.126K1 0.301 0.398K -0.201 0.068
Poutre centrale 1Y = 0.719 0.719Y'= -0.719 -0.719e = -5.250 -3.938e'= 5.250 3.938
λ 0.335 0.335a' 0.262 0.262A -9.527 -14.798b' 2.502 2.502B1 -6.077 8.827B2 -6.077 -1.871E -2.816 -0.424F -4.614 -3.124σ 2.484 2.484ψ 3.142 2.356Χ -0.430 0.355β -0.430 -0.430C 22.166 21.776D 0.701 0.476Rβ 8.866 8.866Rψ -33.441 -5.038
Qβ -7.179 -7.179Qψ 70.856 47.972
K0 -0.412 0.169K1 0.492 0.622K -0.077 0.337
Détermination des CRT
Caractéristiques du pontNombre de dispositive de Retenue Dr 0Largeur chargeable Lch =Lr-0.5*Dr 8 mNombre de voies Nv =ENT(Lch/3) 2Largeur d'une voie V =Lch/Nv 4 m
Classe du pont 1Largeur d'une voie standard V0 3.5a2 =V0/V 0.875
Poutre de riveCharge AlNombre de voies chargées 1a1 = 1
x1=b-Ltr 4
x2=x1-V 0
#VALUE!Kal=Wal/V #VALUE!
#VALUE!a1 x ηAL x Lal = #VALUE!
Nombre de voies chargées 2a1= 1
x1=b-Ltr 4
x2=x1-V -4
#VALUE!Kal=Wal/(V*Nv) #VALUE!
#VALUE!a1 x ηAL x Lal = #VALUE!
RecapitulationCRT a1 x ηAL x Lal Nombre de voies chargées
#VALUE! #VALUE! #VALUE!
Charge qtr
F-1(x1)=
F-1(x2)=
Wal=F-1(x1)-F-1(x2)
CRT ηAL= Kal/Np
F-1(x1)=
F-1(x2)=
Wal=F-1(x1)-F-1(x2)
CRT ηAL=
Nombre de trottoires chargées 1
x1=b 5.25
x2=b-Ltr 4.000
#VALUE!Ktr=Wtr/(Ntr*Ltr) #VALUE!
#VALUE!
Nombre de trottoires chargées 2
x1=b 5.25
x2=b-Ltr 4.000
x3=-b -5.25
x4=-b+Ltr -4.000
#VALUE!Ktr=Wtr/(Ntr*Ltr) #VALUE!
#VALUE!
RecapitulationCRT Ltr Nbr de trottoires chargées
#VALUE! #VALUE! #VALUE!
Charge BcNbr de file 1bc 1.2
x1 = 3.75 F(x1)=x2 = 1.75 F(x2)=
Kbc = #VALUE!ηbc = #VALUE!bc x ηbc = #VALUE!
Nbr de file 2bc 1.1
x1 = 3.75 F(x1)=x2 = 1.75 F(x2)=x3 = 1.25 F(x3)=x4 = -0.75 F(x4)=
Kbc =0.5*[F(x1)+F(x2)+F(x3)+F(x4)] #VALUE!ηbc =Kbc/Np #VALUE!bc x ηbc = #VALUE!
RecapitulationCRT bc Nbr de voies chargées
F-1(x1)=
F-1(x2)=
Wtr=F-1(x1)-F-1(x2)
CRT ηtr=Ktr/Np
F-1(x1)=
F-1(x2)=
F-1(x3)=
F-1(x4)=
Wtr=F-1(x1)+F-1(x4)-F-1(x2)-F-1(x3)
CRT ηtr=Ktr/Np
#VALUE! #VALUE! #VALUE!
Charge Mc80LMc80 = 0.85 m
x1 = 4 F(x1)=x2 = 3.15 F(x2)=x3 = 1.2 F(x3)=x4 = 0.35 F(x4)=KMc80 = #VALUE!ηMc80 = #VALUE!
RecapitulationCRT LMc80
#VALUE! 0.85
Charge Mc120LMc120 = 1 m
x1 =b-Ltr 4 F(x1)=x2 =x1-LMc120 3 F(x2)=x3 =x2-2.3 0.7 F(x3)=x4 =x3-1 -0.3 F(x4)=KMc120 =(1/4)*[F(x1)+F(x2)+F(x3)+F(x4)] #VALUE!ηMc120 =KMc120/Np #VALUE!
RecapitulationCRT LMc120
#VALUE! 1
Mc120 CRT LMc120#VALUE! 1
Mc80 CRT LMc80#VALUE! 0.85
Bc CRT bc#VALUE! #VALUE!
Trottoires CRT Ltr#VALUE! #VALUE!
AL CRT a1 x ηAL x Lal #VALUE! #VALUE!
Poutre centrale 3Mc120 CRT LMc120
#VALUE! 1Mc80 CRT LMc80
#VALUE! 0.85
Récap des « CRT » :
Poutre de rive
Bc CRT bc#VALUE! #VALUE!
Trottoires CRT Ltr#VALUE! #VALUE!
AL CRT a1 x ηAL x Lal #VALUE! #VALUE!
Poutre ModèleMc120 CRT LMc120
#VALUE! #VALUE!Mc80 CRT LMc80
#VALUE! #VALUE!Bc CRT bc
#VALUE! #VALUE!Trottoires CRT Ltr
#VALUE! #VALUE!AL CRT a1 x ηAL x Lal
#VALUE! #VALUE!
Charges permanentes 1Poids propre de la poutre Ba = 0.3385 m²Bc = 0.2515 m²Bmoyenne = 0.273 m²
Gpoutre = 6.817 KN/m
Gd = 7.186 KN/m
Gétanchéité 0.949 KN/mGcouche de roulement 2.213 KN/mGtrottoirs 10.000 KN/mGgarde corps 0.300 KN/mPoids de l'entretoise Ge = 3.989 KNGst = 15.052 KN/m
Gpermanent 29.054 KN/m
γ x ELU 1.35ELS 1
γ x
Calcul des sollicitations
Poids propre de l’hourdis
Poids de la super-structure
Moment fléchissant
Mperx (KN.m)
Effort tranchant
γ x ELU 1.35ELS 1
Charge Al 1
Al = 13.55 KN/m²Poutre de riveA2 = #VALUE!qAL = #VALUE! KN/m²
γ x ELU 1.6ELS 1.2
γ x ELU 1.6ELS 1.2
Poutre centrale 3A2 = #VALUE!qAL = #VALUE! KN/m²
γ x ELU 1.6ELS 1.2
γ x ELU 1.6ELS 1.2
Charge du trottoir 1
qtr = 1.5 kN/m²Qtr = 1.875 kN/mPoutre de rive
γ x ELU 1.6ELS 1
γ x
Effort tranchant
Tperx (KN.m)
Moment fléchissant
MALx (KN.m)
Effort tranchant
TAlx (KN)
Moment fléchissant
MALx (KN.m)
Effort tranchant
TALx (KN)
Moment fléchissant
MTrx (KN.m)
Effort tranchant
γ x ELU 1.6ELS 1
Poutre centrale 3
γ x ELU 1.6ELS 1
γ x ELU 1.6ELS 1
Charge Bc 1
Poids total G = 2676.46 KNSBc = #VALUE! KNSBt = #VALUE! KNSBr = 100.00 KNSb = #VALUE! KN
#VALUE!
Poutre de riveLc 20section choisit Lc/ 2
ELU 1.6ELS 1.2
section choisit 4Poids 1ER ESSIEU 60 POIDS 2EM ESSIEUx1 5x2 6.5x3 11x4 15.5
Effort tranchant
TTrx (KN.m)
Moment fléchissant
MTrx (KN.m)
Effort tranchant
TTrx (KN.m)
δB =
Moment fléchissant MBc
x (KN.m)
x5 17x6 21.5
i 1 2xi 5.00 6.50yi 3.75 3.38Pi 120.00 120.00Yi Pi 450.00 405.00
section choisit 6Poids 1ER ESSIEU 60 POIDS 2EM ESSIEUx1 3.33x2 4.83x3 9.33x4 13.83x5 15.33x6 19.83
i 1 2xi 3.33 4.83yi 2.78 2.53Pi 120.00 120.00Yi Pi 333.33 303.33
section choisit 8Poids 1ER ESSIEU 60 POIDS 2EM ESSIEUx1 2.5x2 4x3 8.5x4 13x5 14.5x6 19
i 1 2xi 2.50 4.00yi 2.19 2.00Pi 120.00 120.00Yi Pi 262.50 240.00
Poutre de rive
γ x ELU 1.6ELS 1.2
Poutre Centrale 3
γ x
Moment fléchissant
MBcx (KN.m)
Moment fléchissant
γ x ELU 1.6ELS 1.2
Effort tranchant
section choisit 0Poids 1ER ESSIEU 60 POIDS 2EM ESSIEUx1 0x2 1.5x3 6x4 10.5x5 12x6 16.5
i 1 2xi 0.00 1.50yi 1.00 0.93Pi 120.00 120.00Yi Pi 120.00 111.00
section choisit 2Poids 1ER ESSIEU 60 POIDS 2EM ESSIEUx1 10x2 11.5x3 16x4 20.5x5 22x6 26.5
i 1 2xi 10.00 11.50yi 0.50 0.43Pi 120.00 120.00Yi Pi 60.00 51.00
section choisit 4Poids 1ER ESSIEU 60 POIDS 2EM ESSIEUx1 5x2 6.5x3 11x4 15.5x5 17x6 21.5
i 1 2xi 5.00 6.50yi 0.75 0.68
Moment fléchissant
MBcx (KN.m)
Pi 120.00 120.00Yi Pi 90.00 81.00
section choisit 6Poids 1ER ESSIEU 60 POIDS 2EM ESSIEUx1 3.33x2 4.83x3 9.33x4 13.83x5 15.33x6 19.83
i 1 2xi 3.33 4.83yi 0.83 0.76Pi 120.00 120.00Yi Pi 100.00 91.00
section choisit 8Poids 1ER ESSIEU 60 POIDS 2EM ESSIEUx1 2.5x2 4x3 8.5x4 13x5 14.5x6 19
i 1 2xi 2.50 4.00yi 0.88 0.80Pi 120.00 120.00Yi Pi 105.00 96.00
Poutre de rive
Effort tranchant γ x ELU 1.6ELS 1.2
Poutre Centrale 3
Effort tranchant γ x ELU 1.6ELS 1.2
Charges militaires
TBcx (KN.m)
TBcx (KN.m)
G = 2676.46 KNPoids du charge S = 720 KNδMc = 1.11780899952
Charge Mc80 1
Valeyr de la charge répartie q = 147 kN/mLc80 4.9 m
t =x(Lc-4.9)/Lcy1 = x(Lc-x)/Lcy2 = Y1*t/xy3 = (Lc-t-4.9) Y1 /(Lc-x)w
Poutre de rive
γ x ELU 1.35ELS 1
Poutre Centrale 3
γ x ELU 1.35ELS 1
γ x y1y2w
Poutre de rive
γ x ELU 1.35ELS 1
Poutre Centrale 3
γ x ELU 1.35
Moment fléchissant
MMc80x (KN.m)
Moment fléchissant
MMc80x (KN.m)
Effort tranchant
TMc80x (KN.m)
Effort tranchant
TMc80x (KN.m)
ELS 1
Charge Mc120 1
Valeur de la charge répartie q = 180 kN/mLc120 = 6.1 mG = 2676.46 KNPoids du charge S = 1100 KNδMc = 1.13590448267
γ x t =x(Lc-4.9)/Lcy1 = x(Lc-x)/Lcy2 = Y1*t/xy3 = (Lc-t-4.9) Y1 /(Lc-x)w
Poutre de rive
γ x ELU 1.35ELS 1
Poutre Centrale 3
γ x ELU 1.35ELS 1
γ x y1y2w
Poutre de rive
γ x ELU 1.35ELS 1
Poutre Centrale 3
γ x ELU 1.35
TMc80x (KN.m)
Moment fléchissant
MMc120x (KN.m)
Moment fléchissant
MMc120x (KN.m)
Effort tranchant
TMc120x (KN.m)
Effort tranchant
TMc120x (KN.m)
ELS 1
Sollicitations de calcul
Poutre de rive
Mx (KN.m) ELUELS
Poutre Centrale 3
Mx (KN.m) ELUELS
Poutre de rive
Tx (KN) ELUELS
Poutre Centrale 3
Tx (KN) ELUELS
Poutre Modèle
Mx (KN.m) ELUELS
Tx (KN) ELUELS
Charge dominante #VALUE!
TMc120x (KN.m)
Moment fléchissant
Moment fléchissant
Effort tranchant
Effort tranchant
Moment fléchissant
Effort tranchant
Réalisé par ZARROUK Ghassen Ingénieur Genie Civil de l'ENITVeuillez demander un devis de prix par EMAIL: zarrouk.ghassen@gmail.com
Béton
13041.94
Ev
10721.40
ba bta(inférieur)
0 0.18 0.3 0.44
1.181 0.18 0.3 0.44
1.437 0.18 0.3 0.44
ETUDE DU PONT A POUTRES
Module d'élasticité différé Ev
b0équivalente babout
m
mm (Recommandation SETRA)
m
m
mm
7.000
m
m
m4
mm
x E (MN)
m
x E (MN)
x E (MN)
e= 5.35 L= 20
0.137 θ = 0.791
5.03 5.03 5.03 5.03-5.03 -5.03 -5.03 -5.03
-2.625 -1.3125 0 1.31252.625 1.3125 0 -1.3125
0.335 0.335 0.335 0.3352.000 2.000 2.000 2.000
-19.045 -19.189 -9.418 18.6870.147 0.147 0.147 0.147
26.061 44.168 57.791 55.1190.349 1.193 1.251 0.956
-1.320 -2.121 -2.285 -2.121-17.473 -8.104 0.000 8.104
α=
2.484 2.484 2.484 2.4841.571 0.785 0.000 -0.785
-1.439 -0.654 0.132 0.917-3.010 -3.010 -3.010 -3.01036.029 23.804 21.057 26.694
9.480 1.662 0.065 3.411-26.610 -26.610 -26.610 -26.610
5.225 8.394 9.039 8.394-66.864 -66.864 -66.864 -66.86428.813 13.364 0.000 -13.364
-0.428 -0.397 -0.127 0.5710.272 0.418 0.656 1.026
-0.169 -0.095 0.163 0.740
3.593 3.593 3.593 3.593-3.593 -3.593 -3.593 -3.593-2.625 -1.313 0.000 1.3132.625 1.313 0.000 -1.313
0.335 0.335 0.335 0.3351.969 1.969 1.969 1.969
-19.045 -19.189 -9.418 18.6871.105 1.105 1.105 1.105
26.061 44.168 57.791 55.1190.349 1.193 1.251 0.956
-0.060 -0.096 -0.103 -0.096-11.115 -5.155 0.000 5.155
2.484 2.484 2.484 2.4841.571 0.785 0.000 -0.785
-0.579 0.206 0.992 1.777-2.150 -2.150 -2.150 -2.15023.178 21.223 27.717 45.248
1.292 0.159 4.045 16.015-1.201 -1.201 -1.201 -1.2015.225 8.394 9.039 8.394
-42.533 -42.533 -42.533 -42.53328.813 13.364 0.000 -13.364
-0.104 0.155 0.585 1.2360.376 0.554 0.826 1.2020.074 0.303 0.674 1.224
2.156 2.156 2.156 2.156-2.156 -2.156 -2.156 -2.156
-2.625 -1.313 0.000 1.3132.625 1.313 0.000 -1.313
0.335 0.335 0.335 0.3351.618 1.618 1.618 1.618
-19.045 -19.189 -9.418 18.6871.991 1.991 1.991 1.991
26.061 44.168 57.791 55.1190.349 1.193 1.251 0.9560.339 0.545 0.587 0.545
-5.992 -2.779 0.000 2.7792.484 2.484 2.484 2.4841.571 0.785 0.000 -0.7850.281 1.066 1.852 2.637
-1.290 -1.290 -1.290 -1.29021.462 28.837 47.693 85.539
0.296 4.749 17.827 49.1426.841 6.841 6.841 6.8415.225 8.394 9.039 8.394
-22.929 -22.929 -22.929 -22.92928.813 13.364 0.000 -13.364
0.273 0.742 1.281 1.7760.544 0.766 1.068 1.3920.373 0.751 1.202 1.634
0.719 0.719 0.719 0.719-0.719 -0.719 -0.719 0.719-2.625 -1.313 0.000 1.3132.625 1.313 0.000 1.313
0.335 0.335 0.335 0.3350.262 0.262 0.262 -3.099
-19.045 -19.189 -9.418 -19.1892.502 2.502 2.502 1.922
26.061 44.168 57.791 44.1680.349 1.193 1.251 1.1930.440 0.707 0.761 0.707
-1.876 -0.870 0.000 0.8702.484 2.484 2.484 2.4841.571 0.785 0.000 0.7851.141 1.926 2.712 2.786
-0.430 -0.430 -0.430 0.43030.057 50.304 90.581 95.939
5.526 19.796 53.695 58.6148.866 8.866 8.866 8.8665.225 8.394 9.039 8.394
-7.179 -7.179 -7.179 7.17928.813 13.364 0.000 13.364
0.765 1.358 1.818 1.8360.810 1.064 1.320 1.3640.781 1.249 1.634 1.661
Poutre de rive Poutre centrale 3Charge AlNombre de voies chargées 1a1 = 1
#VALUE! x1= 4
#VALUE! x2= 0
Wal= #VALUE!Kal= #VALUE!
#VALUE!a1 x ηAL x Lal = #VALUE!
Nombre de voies chargées 2a1= 1
#VALUE! x1= 4
#VALUE! x2= -4
Wal= #VALUE!Kal= #VALUE!
#VALUE!a1 x ηAL x Lal = #VALUE!
RecapitulationLal a1 CRT a1 x ηAL x Lal
#VALUE! #VALUE! #VALUE! #VALUE!
Charge qtr
CRT ηAL=
CRT ηAL=
Nombre de trottoires chargées 1
#VALUE! x1= 5.25
#VALUE! x2= 4
Wtr= #VALUE!Ktr= #VALUE!
#VALUE!
Nombre de trottoires chargées 2
#VALUE! x1= 5.25
#VALUE! x2= 4.000
#VALUE! x3= -5.25
#VALUE! x4= -4.000
Wtr= #VALUE!Ktr= #VALUE!
#VALUE!
RecapitulationCRT Ltr
#VALUE! #VALUE!
Charge BcNbr de file 1bc 1.21ér disposition
#VALUE! x1 = 0.5#VALUE! x2 = 2.5
Kbc = #VALUE!ηbc = #VALUE!bc x ηbc = #VALUE!
Nbr de file 2bc 1.11ér disposition
#VALUE! x1 = 0.5#VALUE! x2 = 2.5#VALUE! x3 = 0#VALUE! x4 = -2
Kbc = #VALUE!ηbc = #VALUE!bc x ηbc = #VALUE!
RecapitulationCRT bc
CRT ηtr=
CRT ηtr=
#VALUE! #VALUE!
Charge Mc80LMc80 = 0.851ér disposition
#VALUE! x1 = 0#VALUE! x2 = 0.85#VALUE! x3 = 2.8#VALUE! x4 = 3.65
KMc80 = #VALUE!ηMc80 = #VALUE!
RecapitulationCRT LMc80
#VALUE! 0.85
Charge Mc120LMc120 = 11ér disposition
#VALUE! x1 = 2.5#VALUE! x2 = 1.5#VALUE! x3 = -0.8#VALUE! x4 = -1.8
KMc120 = #VALUE!ηMc120 = #VALUE!
RecapitulationCRT LMc120
#VALUE! 1
Nbr de voies chargées#VALUE!
Nbr de trottoires chargées#VALUE!
Nombre de voies chargées Lal a1#VALUE! #VALUE! #VALUE!
Nbr de voies chargées#VALUE!
Nbr de trottoires chargées#VALUE!
Nombre de voies chargées Lal a1#VALUE! #VALUE! #VALUE!
Nbr de voies chargées#VALUE!
Nbr de trottoires chargées#VALUE!
Nombre de voies chargées LAl a1#VALUE! #VALUE! #VALUE!
Lt 21Lc 20
Coefficients de majoration1.21.4
1.051.05
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
1961.15 1470.86 1089.53 858.001452.70 1089.53 807.06 635.56
x = Lc/4 x=Lc/6 x=Lc/8
x=Lc /2
x=Lc /2
10.00 5.00 3.33 2.500.00 196.12 261.49 294.170.00 145.27 193.69 217.91
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810.00 5.00 3.33 2.50
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810.00 5.00 3.33 2.50
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/8
x=Lc /2
x=Lc /2
x=Lc /2
x=Lc /2
x=Lc /2
x=Lc /2
10.00 5.00 3.33 2.50#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810.00 5.00 3.33 2.50
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
Poutre centrale
section choisit Lc/ 2
#VALUE! ELU#VALUE! ELS
120y1 3.75y2 3.375y3 2.250y4 1.125
x=Lc /2
x=Lc /2
Moment fléchissant MBc
x (KN.m)
y5 0.750y6 -0.375
3 4 5 611.00 15.50 17.00 21.50
2.25 1.13 0.75 0.0060.00 120.00 120.00 60.00
135.00 135.00 90.00 0.00MAX=
120y1 2.78y2 2.528y3 1.778y4 1.028y5 0.778y6 0.028
3 4 5 69.33 13.83 15.33 19.831.78 1.03 0.78 0.03
60.00 120.00 120.00 60.00106.67 123.33 93.33 1.67
MAX=
120y1 2.19y2 2.000y3 1.438y4 0.875y5 0.688y6 0.125
3 4 5 68.50 13.00 14.50 19.001.44 0.88 0.69 0.13
60.00 120.00 120.00 60.0086.25 105.00 82.50 7.50
MAX=
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/8
x=Lc /2
x=Lc /2
10 5 3.33 2.5#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
120y1 1.00y2 0.925y3 0.700y4 0.475y5 0.400y6 0.175
3 4 5 66.00 10.50 12.00 16.500.70 0.48 0.40 0.18
60.00 120.00 120.00 60.0042.00 57.00 48.00 10.50
120y1 0.50y2 0.425y3 0.200y4 -0.025y5 -0.100y6 -0.325
3 4 5 616.00 20.50 22.00 26.50
0.20 0.00 0.00 0.0060.00 120.00 120.00 60.0012.00 0.00 0.00 0.00
120y1 0.75y2 0.675y3 0.450y4 0.225y5 0.150y6 -0.075
3 4 5 611.00 15.50 17.00 21.50
0.45 0.23 0.15 0.00
60.00 120.00 120.00 60.0027.00 27.00 18.00 0.00
120y1 0.83y2 0.758y3 0.533y4 0.308y5 0.233y6 0.008
3 4 5 69.33 13.83 15.33 19.830.53 0.31 0.23 0.01
60.00 120.00 120.00 60.0032.00 37.00 28.00 0.50
120y1 0.88y2 0.800y3 0.575y4 0.350y5 0.275y6 0.050
3 4 5 68.50 13.00 14.50 19.000.58 0.35 0.28 0.05
60.00 120.00 120.00 60.0034.50 42.00 33.00 3.00
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x=Lc /2
x=Lc /2
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
7.55 3.78 2.52 1.895.00 3.75 2.78 2.193.78 2.83 2.10 1.653.78 2.83 2.10 1.65
21.50 16.12 11.94 9.41
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
0.50 0.75 0.83 0.880.26 0.51 0.59 0.631.85 3.07 3.48 3.69
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!
x=Lc /2
x=Lc /2
x=Lc /2
x=Lc /2
x=Lc /2
x=Lc /2
#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
6.95 3.475 2.32 1.745 3.75 2.78 2.19
3.48 2.61 1.93 1.523.48 2.61 1.93 1.52
25.85 19.39 14.36 11.31
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
0.50 0.75 0.83 0.880.20 0.45 0.53 0.572.12 3.64 4.15 4.41
x = Lc/4 x=Lc/6 x=Lc/810 5 3.333 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!
x=Lc /2
x=Lc /2
x=Lc /2
x=Lc /2
x=Lc /2
x=Lc /2
#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5
#VALUE! #VALUE! #VALUE! #VALUE!#VALUE! #VALUE! #VALUE! #VALUE!
x=Lc /2
x=Lc /2
x=Lc /2
x=Lc /2
x=Lc /2
x=Lc /2
Réalisé par ZARROUK Ghassen Ingénieur Genie Civil de l'ENITVeuillez demander un devis de prix par EMAIL: zarrouk.ghassen@gmail.com
bta'(superieur) h1 h2
0.44 0.05 0.15
0.44 0.05 0.15
0.44 0.05 0.15
ETUDE DU PONT A POUTRES
bta'
h'2
h'1
ba
h1
h2
bta
babout
5.03 5.03 5.03-5.03 -5.03 5.032.625 3.9375 5.25
-2.625 -3.9375 5.25
0.335 0.335 0.3352.000 2.000 -29.822
74.493 163.899 -9.5270.147 0.147 -19.453
16.146 -86.430 -6.0770.564 0.191 -6.077
-1.320 1.273 8.45217.473 29.092 42.970
2.484 2.484 2.484-1.571 -2.356 3.1421.702 2.488 3.010
-3.010 -3.010 3.01042.960 76.330 114.09414.349 41.032 75.854
-26.610 -26.610 -26.6105.225 -5.038 -33.441
-66.864 -66.864 66.864-28.813 -47.972 70.856
1.896 3.945 6.5161.569 2.302 3.1431.775 3.336 5.266
3.593 3.593 3.593-3.593 3.593 3.5932.625 3.938 5.250
-2.625 3.938 5.250
0.335 0.335 0.3351.969 -18.995 -18.995
74.493 -14.798 -9.5271.105 -7.686 -7.686
16.146 8.827 -6.0770.564 -1.871 -6.077
-0.060 0.057 0.38111.115 18.506 27.334
2.484 2.484 2.484-1.571 2.356 3.1422.562 2.935 2.150
-2.150 2.150 2.15080.794 107.675 59.22844.929 69.663 26.764-1.201 -1.201 -1.2015.225 -5.038 -33.441
-42.533 42.533 42.533-28.813 47.972 70.856
2.067 2.849 3.4351.645 1.983 2.1101.910 2.528 2.944
2.156 2.156 2.1562.156 2.156 2.156
2.625 3.938 5.2502.625 3.938 5.250
0.335 0.335 0.335-9.447 -9.447 -9.447
-19.045 -14.798 -9.527-0.961 -0.961 -0.96126.061 8.827 -6.077
0.349 -1.871 -6.0770.339 -0.327 -2.1735.992 9.976 14.7352.484 2.484 2.4841.571 2.356 3.1422.861 2.075 1.2901.290 1.290 1.290
101.630 56.062 32.81563.927 24.251 7.322
6.841 6.841 6.8415.225 -5.038 -33.441
22.929 22.929 22.92928.813 47.972 70.856
1.935 1.666 1.2731.544 1.453 1.3341.790 1.587 1.296
0.719 0.719 0.7190.719 0.719 0.7192.625 3.938 5.2502.625 3.938 5.250
0.335 0.335 0.335-3.099 -3.099 -3.099
-19.045 -14.798 -9.5271.922 1.922 1.922
26.061 8.827 -6.0770.349 -1.871 -6.0770.440 -0.424 -2.8161.876 3.124 4.6142.484 2.484 2.4841.571 2.356 3.1422.001 1.215 0.4300.430 0.430 0.430
53.091 31.381 22.16621.932 6.382 0.701
8.866 8.866 8.8665.225 -5.038 -33.441
7.179 7.179 7.17928.813 47.972 70.856
1.374 0.742 0.0771.173 0.971 0.8151.300 0.827 0.351
Poutre centrale 3
F(x1)= #VALUE!
F(x2)= #VALUE!
F(x1)= #VALUE!
F(x2)= #VALUE!
Nombre de voies chargées Lal a1#VALUE! #VALUE! #VALUE!
F(x1)= #VALUE!
F(x2)= #VALUE!
F(x1)= #VALUE!
F(x2)= #VALUE!
F(x3)= #VALUE!
F(x4)= #VALUE!
Nbr de trottoires chargées#VALUE!
2éme dispositionF(x1)= #VALUE! x'1=F(x2)= #VALUE! x'2=Total #VALUE!
2éme dispositionF(x1)= #VALUE! x'1 =F(x2)= #VALUE! x'2 =F(x3)= #VALUE! x'3 =F(x4)= #VALUE! x'4 =Total #VALUE!
Nbr de voies chargées
#VALUE!
m2éme disposition
F(x1)= #VALUE! x1 =F(x2)= #VALUE! x2 =F(x3)= #VALUE! x3 =F(x4)= #VALUE! x4 =
#VALUE!
m2éme disposition
F(x1)= #VALUE! x1 =F(x2)= #VALUE! x2 =F(x3)= #VALUE! x3 =F(x4)= #VALUE! x4 =
#VALUE!
00
0.000.00
0.00
0.00397.61294.53
00
#VALUE!#VALUE!
0.000.00
#VALUE!#VALUE!
00
#VALUE!#VALUE!
0.000.00
#VALUE!#VALUE!
00
#VALUE!#VALUE!
0.00
0.00#VALUE!#VALUE!
00
#VALUE!#VALUE!
0.000.00
#VALUE!#VALUE!
202
1.6 #VALUE!1.2 #VALUE!
section choisit 4Poids 1ER ESSIEU 60x1 3.5x2 5x3 9.5x4 14
Moment fléchissant
x5 15.5x6 20
i 1xi 3.5yi 2.625
somme Pi 1201215.00 Yi Pi 3151237.50
section choisit 6Poids 1ER ESSIEU 60x1 1.83x2 3.33x3 7.83x4 12.33x5 13.83x6 18.33
i 1xi 1.83yi 1.53
somme Pi 120.00961.67 Yi Pi 183.33961.67
section choisit 8Poids 1ER ESSIEU 60x1 1x2 2.5x3 7x4 11.5x5 13x6 17.5
i 1xi 1yi 0.875
somme Pi 120783.75 Yi Pi 105783.75
00
0.000.00
0
00.000.00
somme388.50
somme123.00
somme243.00
somme288.50
somme313.50
00
#VALUE!#VALUE!
00
#VALUE!#VALUE!
00
0.000.000.000.000.00
00
#VALUE!#VALUE!
00
#VALUE!#VALUE!
00
1.000.764.30
00
#VALUE!#VALUE!
00
#VALUE!
#VALUE!
00
00
0.000.000.00
00
#VALUE!#VALUE!
00
#VALUE!#VALUE!
00
1.000.705.17
00
#VALUE!#VALUE!
00
#VALUE!
#VALUE!
00
#VALUE!#VALUE!
00
#VALUE!#VALUE!
00
#VALUE!#VALUE!
00
#VALUE!#VALUE!
00
#VALUE!#VALUE!
00
#VALUE!#VALUE!
hta(inférieur) h'1 h'2 hta'(superieur)
0.175 0.04 0.08 0.1
0.175 0.04 0.08 0.1
0.175 0.04 0.08 0.1
-6 -4 -2 0 2 4 6-1.000
0.000
1.000
2.000
3.000
4.000
5.000
6.000
POUTRE DE RIVE
FONCTION Polynomiale de LEGENDREx6 x5
y= #VALUE! #VALUE!x= 0y(x)= #VALUE!PRIMITIVE
x7 x6Y-1= #VALUE! #VALUE!x= 0y-1(x)= #VALUE!
-6 -4 -2 0 2 4 6-1.000
0.000
1.000
2.000
3.000
4.000
5.000
6.000
POUTRE DE RIVE
-6.000 -4.000 -2.000 0.000 2.000 4.000 6.000-0.500
0.000
0.500
1.000
1.500
2.000
2.500
3.000
3.500
POUTRE CENTRALE 3
POUTRE CENTRALE 3
-6.000 -4.000 -2.000 0.000 2.000 4.000 6.000
-0.500
0.000
0.500
1.000
1.500
2.000
POUTRE CENTRALE 2
POUTRE CENTRALE 2
FONCTION Polynomiale de LEGENDREx8 x7
y= #VALUE! #VALUE!x= 0y(x)= #VALUE!
-6.000 -4.000 -2.000 0.000 2.000 4.000 6.000
-0.500
0.000
0.500
1.000
1.500
2.000
POUTRE CENTRALE 2
POUTRE CENTRALE 2
-6.000 -4.000 -2.000 0.000 2.000 4.000 6.000-0.200
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
1.600
1.800
POUTRE CENTRAL 1
POUTRE CENTRAL 1
PRIMITIVEx9 x8
Y-1= #VALUE! #VALUE!x=y-1(x)= #VALUE!
1 F(x'1)= #VALUE!3 F(x'2)= #VALUE!
Total #VALUE!
0.8 F(x'1)= #VALUE!2.8 F(x'2)= #VALUE!0.3 F(x'3)= #VALUE!
-1.7 F(x'4)= #VALUE!Total #VALUE!
3éme disposition0.5 F(x1)= #VALUE! x1 =
1.35 F(x2)= #VALUE! x2 =3.3 F(x3)= #VALUE! x3 =
4.15 F(x4)= #VALUE! x4 =#VALUE!
3éme disposition2 F(x1)= #VALUE! x1 =1 F(x2)= #VALUE! x2 =
-1.3 F(x3)= #VALUE! x3 =-2.3 F(x4)= #VALUE! x4 =
#VALUE!
POIDS 2EM ESSIEU 120y1 2.625y2 3.75y3 2.625y4 1.5
y5 1.125y6 0
2 3 4 55 9.5 14 15.5
3.75 2.625 1.50 1.13120 60 120 120450 157.5 180 135
POIDS 2EM ESSIEU 120y1 1.53y2 2.78y3 2.03y4 1.28y5 1.03y6 0.28
2 3 4 53.33 7.83 12.33 13.832.78 2.03 1.28 1.03120 60 120 120
333.33 121.67 153.33 123.33
POIDS 2EM ESSIEU 120y1 0.875y2 2.1875y3 1.625y4 1.0625y5 0.875y6 0.3125
2 3 4 52.5 7 11.5 13
2.1875 1.625 1.06 0.88120 60 120 120
262.5 97.5 127.5 105
y2 y1 Ip(médiane)
0.5281 0.4719 0.01800.4238 0.7762 0.07890.3931 0.8069 0.0836
-6 -4 -2 0 2 4 6-1.000
0.000
1.000
2.000
3.000
4.000
5.000
6.000
POUTRE DE RIVE
x4 x3 x2#VALUE! #VALUE! #VALUE!
x5 x4 x3#VALUE! #VALUE! #VALUE!
-6 -4 -2 0 2 4 6-1.000
0.000
1.000
2.000
3.000
4.000
5.000
6.000
POUTRE DE RIVE
-6.000 -4.000 -2.000 0.000 2.000 4.000 6.000-0.500
0.000
0.500
1.000
1.500
2.000
2.500
3.000
3.500
POUTRE CENTRALE 3
POUTRE CENTRALE 3
-6.000 -4.000 -2.000 0.000 2.000 4.000 6.000
-0.500
0.000
0.500
1.000
1.500
2.000
POUTRE CENTRALE 2
POUTRE CENTRALE 2
x6 x5 x4#VALUE! #VALUE! #VALUE!
-6.000 -4.000 -2.000 0.000 2.000 4.000 6.000
-0.500
0.000
0.500
1.000
1.500
2.000
POUTRE CENTRALE 2
POUTRE CENTRALE 2
-6.000 -4.000 -2.000 0.000 2.000 4.000 6.000-0.200
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
1.600
1.800
POUTRE CENTRAL 1
POUTRE CENTRAL 1
x7 x6 x5#VALUE! #VALUE! #VALUE!
-0.5 F(x1)= #VALUE!0.35 F(x2)= #VALUE!
2.3 F(x3)= #VALUE!3.15 F(x4)= #VALUE!
#VALUE!
1.5 F(x1)= #VALUE!0.5 F(x2)= #VALUE!
-1.8 F(x3)= #VALUE!-2.8 F(x4)= #VALUE!
#VALUE!
620
0.0060 somme
0 1237.5
618.33
0.2860 somme
16.67 931.67
617.50.31
60 somme18.75 716.25
Ip(about) Surface au mediane (m²)0.0222 0.25150.0876 0.48780.0937 0.5389
x 1#VALUE! #VALUE!
x2 x#VALUE! #VALUE!
x3 x2#VALUE! #VALUE!
x4 x3#VALUE! #VALUE!
Surface au about (m²)0.33850.57480.6259
x 1#VALUE! #VALUE!
x2 x#VALUE! #VALUE!
Interpolation polynomiale de Legendre
Points de passage Le polynome a pour équationx y
-5.250 -0.116 #VALUE!
-3.938 -0.156 #VALUE! #VALUE!
-2.625 -0.169 #VALUE! #VALUE!
-1.313 -0.095 #VALUE! #VALUE!
0.000 0.163 #VALUE! #VALUE!
1.313 0.740 #VALUE! #VALUE!
2.625 1.775 #VALUE! #VALUE!
3.938 3.336 #VALUE! #VALUE!
5.250 5.266 #VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
Le polynome de degré 8 passe par le point
x0 5.250
y #REF!-5 #VALUE!-4 #VALUE!-3 #VALUE!-2 #VALUE!-1 #VALUE!0 #VALUE!1 #VALUE!2 #VALUE!3 #VALUE!4 #VALUE!5 #VALUE!
x0 y1.312 #VALUE!
Interpolation polynomiale de Legendre
e=k=
-6 -4 -2 0 2 4 6
-1
0
1
2
3
4
5
6
ConcordenceOriginal
#REF! 1 -1.00 1.00 -1.00#REF! 1 -0.75 0.56 -0.42#REF! 1 -0.50 0.25 -0.13#REF! 1 -0.25 0.06 -0.02#REF! 1 0.00 0.00 0.00#REF! 1 0.25 0.06 0.02#REF! 1 0.50 0.25 0.13#REF! 1 0.75 0.56 0.42#REF! 1 1.00 1.00 1.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00
8
5.250 #REF!
-5.25 -3.9375 -2.625 -1.3125 0 1.3125 2.625-0.11584786 -0.15632145 -0.16869974678358 -0.09492686 0.16314383 0.73975349 1.7747948
-6 -4 -2 0 2 4 6
-1
0
1
2
3
4
5
6
ConcordenceOriginal
1.00 -1.00 1.00 -1.00 1.00 0.00 0.00 0.000.32 -0.24 0.18 -0.13 0.10 0.00 0.00 0.000.06 -0.03 0.02 -0.01 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.06 0.03 0.02 0.01 0.00 0.00 0.00 0.000.32 0.24 0.18 0.13 0.10 0.00 0.00 0.001.00 1.00 1.00 1.00 1.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 1.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 1.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 1.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
3.9375 5.253.33573974 5.26594393
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.001.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 1.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 1.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 1.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 1.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 1.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 1.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00
-0.12 #VALUE! #VALUE! 5.250 -6.3 #VALUE!-0.16 #VALUE! #VALUE! -5.250 -6.195 #VALUE!-0.17 #VALUE! #VALUE! 10.500 -6.09 #VALUE!-0.09 #VALUE! #VALUE! nm 5.250 -5.985 #VALUE!0.16 #VALUE! #VALUE! -5.88 #VALUE!0.74 #VALUE! #VALUE! -5.775 #VALUE!1.77 #VALUE! #VALUE! -5.67 #VALUE!3.34 #VALUE! #VALUE! -5.565 #VALUE!5.27 #VALUE! #VALUE! -5.46 #VALUE!0.00 #VALUE! #VALUE! -5.355 #VALUE!0.00 #VALUE! #VALUE! -5.25 #VALUE!0.00 #VALUE! #VALUE! -5.145 #VALUE!0.00 #VALUE! #VALUE! -5.04 #VALUE!0.00 #VALUE! #VALUE! -4.935 #VALUE!0.00 #VALUE! #VALUE! -4.83 #VALUE!0.00 #VALUE! #VALUE! -4.725 #VALUE!0.00 #VALUE! #VALUE! -4.62 #VALUE!0.00 #VALUE! #VALUE! -4.515 #VALUE!0.00 #VALUE! #VALUE! -4.41 #VALUE!0.00 #VALUE! #VALUE! -4.305 #VALUE!
-4.2 #VALUE!-4.095 #VALUE!
-3.99 #VALUE!-3.885 #VALUE!
-3.78 #VALUE!-3.675 #VALUE!
-3.57 #VALUE!-3.465 #VALUE!
-3.36 #VALUE!-3.255 #VALUE!
-3.15 #VALUE!-3.045 #VALUE!
-2.94 #VALUE!-2.835 #VALUE!
-2.73 #VALUE!-2.625 #VALUE!
-2.52 #VALUE!-2.415 #VALUE!
-2.31 #VALUE!-2.205 #VALUE!
-2.1 #VALUE!-1.995 #VALUE!
-1.89 #VALUE!-1.785 #VALUE!
-1.68 #VALUE!-1.575 #VALUE!
-1.47 #VALUE!-1.365 #VALUE!
-1.26 #VALUE!-1.155 #VALUE!
-1.05 #VALUE!-0.945 #VALUE!
-0.84 #VALUE!-0.735 #VALUE!
-0.63 #VALUE!-0.525 #VALUE!
-0.42 #VALUE!-0.315 #VALUE!
-0.21 #VALUE!-0.105 #VALUE!
8.46545E-15 #VALUE!0.105 #VALUE!
0.21 #VALUE!0.315 #VALUE!
0.42 #VALUE!0.525 #VALUE!
0.63 #VALUE!0.735 #VALUE!
0.84 #VALUE!0.945 #VALUE!
1.05 #VALUE!1.155 #VALUE!
1.26 #VALUE!1.365 #VALUE!
1.47 #VALUE!1.575 #VALUE!
1.68 #VALUE!1.785 #VALUE!
1.89 #VALUE!1.995 #VALUE!
2.1 #VALUE!2.205 #VALUE!
2.31 #VALUE!2.415 #VALUE!
2.52 #VALUE!2.625 #VALUE!
2.73 #VALUE!2.835 #VALUE!
2.94 #VALUE!3.045 #VALUE!
3.15 #VALUE!3.255 #VALUE!
3.36 #VALUE!3.465 #VALUE!
3.57 #VALUE!3.675 #VALUE!
3.78 #VALUE!3.885 #VALUE!
3.99 #VALUE!4.095 #VALUE!
4.2 #VALUE!4.305 #VALUE!
4.41 #VALUE!4.515 #VALUE!
4.62 #VALUE!4.725 #VALUE!
4.83 #VALUE!4.935 #VALUE!
5.04 #VALUE!5.145 #VALUE!
5.25 #VALUE!5.355 #VALUE!
5.46 #VALUE!5.565 #VALUE!
5.67 #VALUE!5.775 #VALUE!
5.88 #VALUE!5.985 #VALUE!
6.09 #VALUE!6.195 #VALUE!
6.3 #VALUE!
Interpolation polynomiale de Legendre
Points de passage Le polynome a pour équationx y
-5.250 -0.077 #VALUE!
-3.938 0.337 #VALUE! #VALUE!
-2.625 0.781 #VALUE! #VALUE!
-1.313 1.249 #VALUE! #VALUE!
0.000 1.634 #VALUE! #VALUE!
1.313 1.661 #VALUE! #VALUE!
2.625 1.300 #VALUE! #VALUE!
3.938 0.827 #VALUE! #VALUE!
5.250 0.351 #VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
#VALUE! #VALUE!
Le polynome de degré 8 passe par le point
x0 5.250
y #REF! -5.25 #VALUE!-5 #VALUE!-4 #VALUE!-3 #VALUE!-2 #VALUE!-1 #VALUE!0 #VALUE!1 #VALUE!2 #VALUE!3 #VALUE!4 #VALUE!5 #VALUE!
5.25 #VALUE!
x0 y1.312 #VALUE!
Interpolation polynomiale de Legendre
Le polynome a pour équation
e=k=
-6 -4 -2 0 2 4 6-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
OriginalConcordence
#REF! 1 -1.00 1.00 -1.00#REF! 1 -0.75 0.56 -0.42#REF! 1 -0.50 0.25 -0.13#REF! 1 -0.25 0.06 -0.02#REF! 1 0.00 0.00 0.00#REF! 1 0.25 0.06 0.02#REF! 1 0.50 0.25 0.13#REF! 1 0.75 0.56 0.42#REF! 1 1.00 1.00 1.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00#REF! 0 0.00 0.00 0.00
8
5.250 #REF!
-5.25 -3.9375 -2.625 -1.3125 0 1.3125 2.625-0.07683749 0.33728028 0.78141572894016 1.24886527 1.63355541 1.66083463 1.29988208
-6 -4 -2 0 2 4 6-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
OriginalConcordence
1.00 -1.00 1.00 -1.00 1.00 0.00 0.00 0.000.32 -0.24 0.18 -0.13 0.10 0.00 0.00 0.000.06 -0.03 0.02 -0.01 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.06 0.03 0.02 0.01 0.00 0.00 0.00 0.000.32 0.24 0.18 0.13 0.10 0.00 0.00 0.001.00 1.00 1.00 1.00 1.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 1.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 1.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 1.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
3.9375 5.250.82655681 0.35087393
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 0.001.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000.00 1.00 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 1.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 1.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 1.00 0.00 0.00 0.000.00 0.00 0.00 0.00 0.00 1.00 0.00 0.000.00 0.00 0.00 0.00 0.00 0.00 1.00 0.000.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00
-0.08 #VALUE! #VALUE! 5.250 -6.3 #VALUE!0.34 #VALUE! #VALUE! -5.250 -6.195 #VALUE!0.78 #VALUE! #VALUE! 10.500 -6.09 #VALUE!1.25 #VALUE! #VALUE! nm 5.250 -5.985 #VALUE!1.63 #VALUE! #VALUE! -5.88 #VALUE!1.66 #VALUE! #VALUE! -5.775 #VALUE!1.30 #VALUE! #VALUE! -5.67 #VALUE!0.83 #VALUE! #VALUE! -5.565 #VALUE!0.35 #VALUE! #VALUE! -5.46 #VALUE!0.00 #VALUE! #VALUE! -5.355 #VALUE!0.00 #VALUE! #VALUE! -5.25 #VALUE!0.00 #VALUE! #VALUE! -5.145 #VALUE!0.00 #VALUE! #VALUE! -5.04 #VALUE!0.00 #VALUE! #VALUE! -4.935 #VALUE!0.00 #VALUE! #VALUE! -4.83 #VALUE!0.00 #VALUE! #VALUE! -4.725 #VALUE!0.00 #VALUE! #VALUE! -4.62 #VALUE!0.00 #VALUE! #VALUE! -4.515 #VALUE!0.00 #VALUE! #VALUE! -4.41 #VALUE!0.00 #VALUE! #VALUE! -4.305 #VALUE!
-4.2 #VALUE!-4.095 #VALUE!
-3.99 #VALUE!-3.885 #VALUE!
-3.78 #VALUE!-3.675 #VALUE!
-3.57 #VALUE!-3.465 #VALUE!
-3.36 #VALUE!-3.255 #VALUE!
-3.15 #VALUE!-3.045 #VALUE!
-2.94 #VALUE!-2.835 #VALUE!
-2.73 #VALUE!-2.625 #VALUE!
-2.52 #VALUE!-2.415 #VALUE!
-2.31 #VALUE!-2.205 #VALUE!
-2.1 #VALUE!-1.995 #VALUE!
-1.89 #VALUE!-1.785 #VALUE!
-1.68 #VALUE!-1.575 #VALUE!
-1.47 #VALUE!-1.365 #VALUE!
-1.26 #VALUE!-1.155 #VALUE!
-1.05 #VALUE!-0.945 #VALUE!
-0.84 #VALUE!-0.735 #VALUE!
-0.63 #VALUE!-0.525 #VALUE!
-0.42 #VALUE!-0.315 #VALUE!
-0.21 #VALUE!-0.105 #VALUE!
8.46545E-15 #VALUE!0.105 #VALUE!
0.21 #VALUE!0.315 #VALUE!
0.42 #VALUE!0.525 #VALUE!
0.63 #VALUE!0.735 #VALUE!
0.84 #VALUE!0.945 #VALUE!
1.05 #VALUE!1.155 #VALUE!
1.26 #VALUE!1.365 #VALUE!
1.47 #VALUE!1.575 #VALUE!
1.68 #VALUE!1.785 #VALUE!
1.89 #VALUE!1.995 #VALUE!
2.1 #VALUE!2.205 #VALUE!
2.31 #VALUE!2.415 #VALUE!
2.52 #VALUE!2.625 #VALUE!
2.73 #VALUE!2.835 #VALUE!
2.94 #VALUE!3.045 #VALUE!
3.15 #VALUE!3.255 #VALUE!
3.36 #VALUE!3.465 #VALUE!
3.57 #VALUE!3.675 #VALUE!
3.78 #VALUE!3.885 #VALUE!
3.99 #VALUE!4.095 #VALUE!
4.2 #VALUE!4.305 #VALUE!
4.41 #VALUE!4.515 #VALUE!
4.62 #VALUE!4.725 #VALUE!
4.83 #VALUE!4.935 #VALUE!
5.04 #VALUE!5.145 #VALUE!
5.25 #VALUE!5.355 #VALUE!
5.46 #VALUE!5.565 #VALUE!
5.67 #VALUE!5.775 #VALUE!
5.88 #VALUE!5.985 #VALUE!
6.09 #VALUE!6.195 #VALUE!
6.3 #VALUE!
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