Etude du pont à poutres

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!


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!


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


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


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!


#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


i 1 2xi 10.00 11.50yi 0.50 0.43Pi 120.00 120.00Yi Pi 60.00 51.00


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: [email protected]

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


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!


Nombre de voies chargées 2a1= 1

#VALUE! x1= 4

#VALUE! x2= -4

Wal= #VALUE!Kal= #VALUE!


RecapitulationLal a1 CRT a1 x ηAL x Lal

#VALUE! #VALUE! #VALUE! #VALUE!

Charge qtr

CRT ηAL=

CRT ηAL=


#VALUE! x1= 5.25

#VALUE! x2= 4

Wtr= #VALUE!Ktr= #VALUE!

#VALUE!


#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


Nbr de file 2bc 1.11ér disposition

#VALUE! x1 = 0.5#VALUE! x2 = 2.5#VALUE! x3 = 0#VALUE! x4 = -2


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!


#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!


#VALUE! 1

Nbr de voies chargées#VALUE!

Nbr de trottoires chargées#VALUE!

Nombre de voies chargées Lal a1#VALUE! #VALUE! #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


x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5


x = Lc/4 x=Lc/6 x=Lc/810.00 5.00 3.33 2.50


x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5



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


x = Lc/4 x=Lc/6 x=Lc/810.00 5.00 3.33 2.50


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



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


x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5


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


x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5


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


x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5


x=Lc /2

x=Lc /2

x=Lc /2

x=Lc /2

x=Lc /2

x=Lc /2


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


x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5


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


x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5


x=Lc /2

x=Lc /2

x=Lc /2

x=Lc /2

x=Lc /2

x=Lc /2


x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5


x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5


x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5


x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5


x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5


x = Lc/4 x=Lc/6 x=Lc/810 5 3.33 2.5


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: [email protected]

bta'(superieur) h1 h2

0.44 0.05 0.15

0.44 0.05 0.15

0.44 0.05 0.15


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!


F(x1)= #VALUE!

F(x2)= #VALUE!

F(x1)= #VALUE!

F(x2)= #VALUE!

F(x3)= #VALUE!

F(x4)= #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!


-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


-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

-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!


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!






























6.3 #VALUE!


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!


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!






























6.3 #VALUE!

Etude du pont à poutres

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Transcript of Etude du pont à poutres