3. Modélisation A#

3.1. Caractéristiques de la modélisation et du maillage#

_images/10000201000002C100000269B2B922DFB5CA4F0C.png

Le maillage du modèle calculé avec code_aster est constitué de 3357 nœuds et de 3387 mailles dont 135 éléments de poutre droite de Timoshenko (dont 12 SEG2 par colonne, soit 108 pour les colonnes) et 3072 éléments plaque DKT (1024 par plancher). Afin d’assurer la continuité des degrés de liberté DRZ de rotation propre des poutres avec la rotation autour de la normale des plaques (non assurée automatiquement par code_aster ) des éléments de poutres sont ajoutés localement au bord des plaques DKT, au niveau des 27 raccords colonne-plancher (groupe de mailles “JONCTIONS” dans le fichier de commande), pour assurer la transmission des rotations DRZ liées au mouvement plan de la plaque en rotation dans le plan \((x,y)\) .

Le maillage du modèle calculé avec CASTEM 2000 est constitué de 3765 nœuds et de 7368 éléments dont 108 éléments poutre droite de Timoshenko et 6960 éléments de coque DKT.

Le maillage du modèle calculé avec SAMCEF est constitué de 3360 nœuds et de 3180 éléments dont 108 éléments poutre droite de Mindlin et 3072 éléments de coque de Mindlin.

3.2. Résultats de la modélisation A#

3.2.1. Remarques#

Pour un nœud \(i\) donné, l’effort généralisé pour l’élément \(i-1\) et pour l’élément \(i\) est comparé respectivement dans les tableaux élément “bas” et élément “haut”.

Les efforts sont donnés dans le repère local des éléments de poutre (repère principal d’inertie).

3.2.2. Calcul de la base modale#

Fréquences propres en \(\mathrm{Hz}\)

Mode

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

1

1.512

1.512

0.036

1.495

1.11

2

2.052

2.050

0.125

2.014

1.93

3

2.365

2.343

0.916

2.291

3.24

4

4.848

4.859

0.237

4.823

0.522

5

7.488

7.521

0.448

7.415

0.99

6

8.388

8.426

0.456

8.355

0.392

7

8.547

8.543

0.037

8.438

1.30

8

15.185

15.405

1.428

15.186

0.004
_images/100000000000025800000258A379CF693A6F8011.jpg _images/100000000000025800000258158DB3D8EC25370D.jpg _images/1000000000000258000002583F583A9E3ADE3EA7.jpg

Visualisation: Mode n° 1;

Mode n° 3;

Mode n° 7.

Masses modales effectives en \(\mathrm{kg}\)

Mode et direction

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

1

X

2,129E+01

2.300E+01

–7,451

2.070E+01

2,846

Y

1,115E+05

1.113E+05

0,127

1.102E+05

1,186

Z

5,203E–02

6.698E–02

–22,319

5.816E–02

–10,531

2

X

9,559E+04

9.365E+04

2,068

9.294E+04

2,847

Y

1,532E+02

1.817E+02

–15,689

1.683E+02

–8,967

Z

1,002E–02

1.440E–02

–30,405

1.500E–02

–33,186

3

X

1,063E+04

1.238E+04

–14,202

1.201E+04

–11,509

Y

4,954E+02

5.181E+02

–4,399

5.010E+02

–1,119

Z

6,074E–03

9.450E–03

–35,736

8.390E–03

–27,609

4

X

9,222E–01

9.3722E–01

–1,606

8.338E–01

10,599

Y

1,434E+04

1.438E+04

–0,296

1.438E+04

–0,247

Z

1,553E–01

2.066E–01

–24,850

1.791E–01

–13,286

5

X

1,606E+04

1.582E+04

1,514

1.594E+04

0,749

Y

1,537E+01

1.751E+01

–12,252

1.491E+01

3,096

Z

3,026E–02

4.386E–02

–31,012

4.668E–02

–35,178

6

X

1,829E+02

3.9466E+02

–53,662

1.901E+03

–90,380

Y

3,771E+03

3.622E+03

4,112

1.300E+03

190,089

Z

1,282E–01

1.809E–01

–29,145

1.336E–01

–4,028

7

X

2,064E+03

2.1461E+03

–3,842

5.331E+02

287,105

Y

9,264E+01

2.7942E+02

–66,846

2.627E+03

–96,474

Z

1,449E–02

1.222E–02

18,522

2.709E–02

–46,519

8

X

4,932E+03

4.948E+03

–0,346

4.974E+03

–0,851

Y

1,130E+00

1.121E+00

0,752

1.035E+00

9,143

Z

5,731E+01

1.5420E+02

–62,836

5.098E+01

12,411

Cumul

X

1,2948E+05

1,2936E+05

0,092%

1,2832E+05

0,905%

Y

1,3037E+05

1,3030E+05

0,053%

1,2919E+05

0,911%

Z

5,7706E+01

1,5473E+02

-62,706%

5,1448E+01

12.16%
Remarque

La norme d’erreur des modes calculés par la méthode de Sorensen de code_aster est toujours inférieure à \({10}^{-9}\) .

Remarque

La masse totale du bâtiment est de \(132552\mathrm{kg}\) ; la forte orientation selon y des modes est due à la relative moindre inertie selon y des colonnes. La masse modale effective cumulée dans la direction \(x\) du séisme obtenue par code_aster représente \(\text{97.678 \%}\) de la masse totale.

Remarque

Les différences entre modélisations et logiciels sont assez fortes dans la direction \(z\) , car elle est peu sollicitée dans ces modes.

3.2.3. Réponse spectrale - méthode CQC#

Déplacements - colonne \(B\) (en mètre)

Altitude Z (m)

Composante

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

PM1: 1.5

X

1.829E–03

1.717E–03

6.466

1.641E–03

11.439

Y

2.303E–04

2.276E–04

1.190

1.730E–03

–86.686

Z

1.882E–06

1.763E–06

6.728

2.112E–05

–91.087

PM2: 3.0

X

5.411E–03

5.108E–03

5.935

5.255E–03

2.968

1erplancher

Y

5.709E–04

5.679E–04

0.526

3.304E–03

–82.722

Z

3.764E–06

3.526E–06

6.729

4.223E–05

–91.087

PM3: 4.5

X

9.762E–03

9.243E–03

5.608

9.551E–03

2.209

Y

9.277E–04

9.246E–04

0.331

8.594E–03

–89.205

Z

4.750E–06

4.452E–06

6.671

5.540E–05

–91.426

PM4: 6.0

X

1.409E–02

1.336E–02

5.462

1.381E–02

2.047

2èmeplancher

Y

1.259E–03

1.255E–03

0.296

1.229E–02

–89.756

Z

5.736E–06

5.379E–06

6.633

6.857E–05

–91.634

PM5: 7.5

X

1.780E–02

1.689E–02

5.352

1.747E–02

1.890

Y

1.486E–03

1.482E–03

0.224

1.539E–02

–90.347

Z

6.014E–06

5.642E–06

6.598

7.376E–05

–91.846

PM6: 9.0

X

2.085E–02

1.980E–02

5.319

2.057E–02

1.383

3èmeplancher

Y

1.661E–03

1.657E–03

0.223

1.789E–02

–90.713

Z

6.293E–06

5.905E–06

6.567

7.896E–05

–92.029

Réaction en \(N\) et Moment en \(\mathrm{N.m}\) à l’encastrement de la colonne \(B\) (groupe nœud “PFE”)

Réaction ou moment

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

Fx

3.445E+04

3.325E+04

3.590

3.362E+04

2.460

Fy

1.644E+03

1.629E+03

0.916

2.265E+03

–27.405

Fz

4.015E+03

3.761E+03

6.729

5.000E+03

–19.694

Mx

2.986E+03

2.975E+03

0.348

4.145E+03

–27.967

My

8.488E+04

8.135E+04

4.336

8.225E+04

3.208

Mz

1.8460E–03

1.772E–01

–98.958

2.165E+01

-99.99

Réaction en \(N\) et Moment en \(\mathrm{N.m}\) à l’encastrement de la colonne centrale \(E\) (groupe nœud “PFE”)

Réaction/Moment

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

Fx

5.799E+04

5341E+04

8.552

5.056E+04

14.686

Fy

2.080E+03

2.071E+03

0.428

2.849E+03

–26.994

Fz

2.471E+02

4.067E+02

–39.247

1.978E+03

–87.504

Mx

3.419E+03

3.417E+03

0.044

4.728E+03

–27.691

My

1.202E+05

1.116E+05

7.705

1.074E+05

11.913

Mz

1.842E–03

1.770E–01

–98.959

2.591E+01

-99.99

Efforts généralisés de la colonne \(B\) (en repère local)

Tableau élément «bas» (voir remarque Section 4.1)

Altitude Z (m)

Composante

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

PM1: 1.5

N (N)

4.015E+03

3.7618E+03

6.728

5.000E+03

–19.702

PM1_BAS

Vy (N)

1.640E+03

1.627E+03

0.770

2.260E+03

–27.445

Vz (N)

3.441E+04

3.323E+04

3.528

3.320E+04

3.634

MT (N.m)

1.846E–03

1.756E–01

–98.949

2.160E+01

–99.99

Mfy (N.m)

3.325E+04

3.151E+04

5.522

3.320E+04

0.154

Mfz (N.m)

5.215E+02

5.333E+02

–2.227

7.650E+02

–31.835

PM2: 3.0

N (N)

4.015E+03

3.761E+03

6.727

4.999E+03

–19.689

1erplancher

Vy (N)

1.618E+03

1.610E+03

0.482

2.230E+03

–27.450

PM2_BAS

Vz (N)

3.420E+04

3.308E+04

3.371

3.286E+04

4.073

MT (N.m)

1.846E–03

1.645E–01

–98.879

2.160E+01

–99.99

Mfy (N.m)

1.830E+04

1.824E+04

0.228

1.750E+04

4.603

Mfz (N.m)

1.925E+03

1.891E+03

1.771

2.620E+03

–26.542

PM3: 4.5

N (N)

2.104E+03

1.976E+03

6.448

2.636E+03

–20.176

PM3_BAS

Vy (N)

1.381E+03

1.368E+03

0.952

1.930E+04

–28.439

Vz (N)

3.061E+04

3.000E+04

2.010

2.993E+04

2.265

MT (N.m)

1.594E–03

1.402E–01

–98.863

2.570E+01

–99.99

Mfy (N.m)

1.434E+03

1.390E+03

3.161

1.440E+03

–0.385

Mfz (N.m)

1.295E+02

1.342E+02

–3.554

1.890E+02

–31.483

PM4: 6.0

N (N)

2.104E+03

1.976E+03

6.450

2.636E+03

–20.187

2èmeplancher

Vy (N)

1.324E+03

1.315E+03

0.618

1.850E+03

–28.458

PM4_BAS

Vz (N)

2.993E+04

2.941E+04

1.751

2.931E+04

2.119

MT (N.m)

1.594E–03

1.049E–01

–98.481

2.570E+01

–99.99

Mfy (N.m)

4.583E+04

4.471E+04

2.480

4.430E+04

3.445

Mfz (N.m)

2.157E+03

2.126E+03

1.456

2.990E+03

–27.858

PM5: 7.5

N (N)

5.956E+02

5.629E+02

5.817

7.749E+02

–23.133

PM5_BAS

Vy (N)

7.279E+02

7.312E+02

–0.453

1.040E+03

–30.006

Vz (N)

1.935E+04

1.934E+04

0.039

1.934E+04

0.039

MT (N.m)

9.470E–04

6.137E–02

-98.457

2.660E+01

–99.99

Mfy (N.m)

1.234E+04

1.184E+04

4.184

1.210E+04

2.006

Mfz (N.m)

2.511E+02

2.578E+02

–2.607

3.800E+02

–33.921

Tableau élément «haut» (voir remarque Section 4.1)

Altitude Z (m)

Composante

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

PM0: 0.0

N (N)

4.015E+03

3.762E+03

6.729

PM0_HAUT

Vy (N)

1.644E+03

1.629E+03

0.928

Vz (N)

3.444E+04

3.325E+04

3.593

MT (N.m)

1.846E–03

1.770E–01

–98.957

Mfy (N.m)

8.488E+04

8.135E+04

4.336

Mfz (N.m)

2.986E+02

2.975E+02

0.348

PM1: 1.5

N (N)

4.015E+03

3.762E+03

6.728

5.000E+03

–19.702

PM1_HAUT

Vy (N)

1.640E+03

1.621E+03

1.149

2.250E+03

–27.123

Vz (N)

3.440E+04

3.318E+04

3.683

3.300E+04

4.258

MT (N.m)

1.846E–03

1.717E–01

–98.925

2.160E+01

–99.99

Mfy (N.m)

3.325E+04

3.150E+04

5.529

3.260E+04

1.997

Mfz (N.m)

5.215E+02

5.331E+02

–2.183

7.640E+02

–31.746

PM2: 3.0

N (N)

2.104E+03

1.976E+03

6.454

2.640E+03

–20.289

1erplancher

Vy (N)

1.419E+03

1.386E+03

2.319

1.950E+03

–27.233

PM2_HAUT

Vz (N)

3.103E+04

3.020E+04

2.733

3.010E+04

3.094

MT (N.m)

1.595E–03

1.540E–01

–98.965

2.570E+01

–99.99

Mfy (N.m)

4.591E+04

4.485E+04

2.354

4.500E+04

2.022

Mfz (N.m)

1.976E+03

1.935E+03

2.095

2.730E+03

–27.610

PM3: 4.5

N (N)

2.104E+03

1.976E+03

6.453

2.640E+03

–20.297

PM3_HAUT

Vy (N)

1.381E+03

1.344E+03

2.739

1.900E+03

–-27.309

Vz (N)

3.061E+04

2.974E+04

2.917

2.970E+04

3.062

MT (N.m)

1.594E–03

1.237E–01

–98.712

2.570E+01

–99.99

Mfy (N.m)

1.434E+03

1.391E+03

3.109

1.440E+03

–0.385

Mfz (N.m)

1.295E+02

1.345E+02

–3.741

1.900E+02

–31.843

PM4: 6.0

N (N)

5.960E+02

5.630E+02

5.847

7.750E+02

–23.103

2èmeplancher

Vy (N)

7.978E+02

7.660E+02

4.147

1.080E+03

–26.130

PM4_HAUT

Vz (N)

2.023E+04

1.976E+04

2.358

1.970E+04

2.696

MT (N.m)

9.477E–04

8.407E–02

–98.873

2.670E+01

–99.99

Mfy (N.m)

1.751E+04

1.762E+04

–0.636

1.790E+04

–2.179

Mfz (N.m)

8.967E+02

8.675E+02

3.363

1.280E+03

–29.945

PM5: 7.5

N (N)

5.956E+02

5.627E+02

5.842

7.750E+02

–23.143

PM5_HAUT

Vy (N)

7.279E+02

6.933E+02

4.987

9.930E+02

–26.693

Vz (N)

1.935E+04

1.886E+04

2.561

1.890E+04

2.360

MT (N.m)

9.470E–04

3.736E–02

–97.466

2.660E+01

–99.99

Mfy (N.m)

1.234E+04

1.184E+04

4.167

1.210E+04

2.006

Mfz (N.m)

2.511E+02

2.579E+02

–2.664

3.810E+02

–34.095

3.2.4. Réponse spectrale - méthode SRSS#

Déplacements – colonne \(B\) (en \(m\) )

Altitude Z (m)

Composante

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

PM1: 1.5

X

1.593E–03

1.4749E–03

7.998

1.40E–03

13.779

N982

Y

2.767E–04

2.795E–04

–1.050

1.47E–03

–81.179

Z

2.253E+06

2.156E–06

4.469

1.95E–05

–88.447

PM2: 3.0

X

4.714E–03

4.386E–03

7.475

4.46E–03

5.707

1erplancher

Y

6.854E–04

6.969E–04

–1.653

4.12E–03

–83.364

N1245

Z

4.506E–06

4.312E–06

4.469

3.90E–05

–88.447

PM3: 4.5

X

8.508E–03

7.939E–03

7.169

8.13E–03

4.655

N1530

Y

1.113E–03

1.133E–03

–1.797

7.32E–03

–84.798

Z

5.684E–06

5.443E–06

4.412

5.12E–05

–88.898

PM4: 6.0

X

1.229E–02

1.148E–02

7.043

1.18E–02

4.153

2èmeplancher

Y

1.510E–03

1.538E–03

–1.842

1.05E–02

–85.621

N1815

Z

6.862E–06

6.574E–06

4.374

6.33E–05

–89.159

PM5: 7.5

X

1.552E–02

1.451E–02

6.956

1.49E–02

4.187

N2106

Y

1.780E–03

1.815E–03

–1.902

1.31e–02

–86.410

Z

7.195E–06

6.896E–06

4.338

6.80E–06

–89.419

PM6: 9.0

X

1.820E–02

1.701E–02

6.944

1.75E–02

3.981

3èmeplancher

Y

1.990E–03

2.028E–03

–1.902

1.52E–02

–86.908

N2355

Z

7.528E–06

7.217E–06

4.303

7.27E–06

–89.646

Réaction en \(N\) et Moment en \(\mathrm{N.m}\) à l’encastrement de la colonne \(B\) (nœud \(\mathrm{N758}\) )

Réaction/Moment

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

Fx

2.999E+04

2.854E+04

5.040

2.883E+04

4.006

Fy

1.977E+03

2.006E+03

–1.434

1.914E+03

3.336

Fz

4.806E+03

4.600E+03

4.468

4.254E+03

12.973

Mx

3.587E+03

3.657E+03

–1.902

3.510E+03

2.203

My

7.393E+04

6.985E+04

5.830

7.011E+04

5.448

Mz

2.240E–03

1.772E–01

–98.736

1.989E+01

-99.99

Réaction en \(N\) et Moment en \(\mathrm{N.m}\) à l’encastrement de la colonne centrale \(E\) (nœud \(\mathrm{N885}\) )

Réaction/Moment

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

Fx

5.591E+04

5.094E+04

9.754

4.797E+04

16.558

Fy

2.499E+03

2.545E+03

–1.818

2.413E+03

3.571

Fz

2.472E+02

4.068E+02

–39.240

1.972E+03

–87.462

Mx

4.106E+03

4.196E+03

–2.161

4.008E+03

2.454

My

1.159E+05

1.064E+05

8.897

1.019E+05

13.769

Mz

2.236E–03

1.770E–01

–98.737

2.288E+01

–99.99

Efforts généralisés de la colonne \(B\)

Tableau élément «bas» (voir remarque Section 4.1)

Altitude Z (m)

Composante

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

PM1: 1.5

N (N)

4.806E+03

4.600E+03

4.469

4.250E+03

13.082

M3158, N982

Vy (N)

1.972E+03

2.003E+03

–1.580

1.910E+03

3.233

Vz (N)

2.995E+04

2.853E+04

4.979

2.830E+04

5.832

MT (N.m)

2.240E–03

1.756E–01

–98.725

1.990E+01

–99.99

Mfy (N.m)

2.898E+04

2.706E+04

7.088

2.780E+04

4.261

Mfz (N.m)

6.254E+02

6.536E+02

–4.319

6.500E+02

–3.781

PM2: 3.0

N (N)

4.806E+03

4.600E+03

4.467

4.250E+03

13.078

1erplancher

Vy (N)

1.944E+03

1.980E+03

–1.839

1.890E+03

2.867

M3160, N1245

Vz (N)

2.977E+04

2.840E+04

4.825

2.800E+04

6.326

MT (N.m)

2.240E–03

1.646E–01

–98.639

1.990E+01

–99.99

Mfy (N.m)

1.590E+04

1.566E+04

1.513

1.510E+04

5.284

Mfz (N.m)

2.317E+03

2.334E+03

–0.746

2.200E+03

5.327

PM3: 4.5

N (N)

2.515E+03

2.414E+03

4.184

2.240E+03

12.268

M3162

Vy (N)

1.664E+03

1.694E+03

–1.789

1.620E+03

2.703

Vz (N)

2.670E+04

2.578E+04

3.551

2.560E+04

4.291

MT (N.m)

1.935E–03

1.402E–01

–98.621

2.570E+01

–99.99

Mfy (N.m)

1.246E+03

1.152E+03

8.141

1.120E+03

11.269

Mfz (N.m)

1.564E+02

1.656E+02

–5.535

1.600E+02

–2.217

PM4: 6.0

N (N)

2.514E+03

2.413E+03

4.183

2.240E+03

12.253

2èmeplancher

Vy (N)

1.592E+03

1.626E+03

–2.151

1.560E+03

2.033

M3164, N1815

Vz (N)

2.611E+04

2.528E+04

3.308

2.500E+04

4.461

MT (N.m)

1.934E–03

1.049E–01

–98.156

2.570E+01

–99.99

Mfy (N.m)

3.993E+04

3.840E+04

3.962

3.780E+04

5.635

Mfz (N.m)

2.598E+03

2.630E+03

–1.242

2.520E+03

3.085

PM5: 7.5

N (N)

7.130E+02

6.904E+02

3.270

6.590E+02

8.197

M3166, N2106

Vy (N)

8.779E+02

9.099E+02

–3.521

8.730E+02

0.564

Vz (N)

1.693E+04

1.663E+04

1.802

1.650E+04

2.635

MT (N.m)

1.150E–03

6.137E–02

–98.128

2.500E+01

–99.99

Mfy (N.m)

1.075E+04

1.017E+04

5.675

1.030E+04

4.382

Mfz (N.m)

3.034E+02

3.201E+02

–5.243

3.200E+02

–5.199

Tableau élément «haut» (voir remarque Section 4.1)

Altitude Z (m)

Composante

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

PM0: 0.0

N (N)

4.806E+03

4.600E+03

4.468

M3157, N758

Vy (N)

1.977E+03

2.006E+03

–1.429

Vz (N)

2.998E+04

2.854E+04

5.043

MT (N.m)

2.240E–03

1.770E–01

–98.735

Mfy (N.m)

7.393E+04

6.986E+04

5.830

Mfz (N.m)

3.587E+03

3.657E+03

–1.902

PM1: 1.5

N (N)

4.806E+03

4.600E+03

4.469

4.250E+03

13.082

M3159, N982

Vy (N)

1.972E+03

1.995E+03

–1.176

1.900E+03

3.776

Vz (N)

2.995E+04

2.848E+04

5.140

2.810E+04

6.580

MT (N.m)

2.240E–03

1.717E–01

–98.696

1.990E+01

–99.99

Mfy (N.m)

2.898E+04

2.706E+04

7.096

2.780E+04

4.261

Mfz (N.m)

6.254E+02

6.533E+02

–4.276

6.500E+02

–3.781

PM2: 3.0

N (N)

2.515E+03

2.414E+03

4.191

2.240E+03

12.280

1erplancher

Vy (N)

1.709E+03

1.716E+03

–0.403

1.640E+03

4.231

M3161, N1245

Vz (N)

2.706E+04

2.595E+04

4.269

2.570E+04

5.304

MT (N.m)

1.935E–03

1.540E–01

–98.744

2.570E+01

–99.99

Mfy (N.m)

4.009E+04

3.856E+04

3.969

3.850E+04

4.131

Mfz (N.m)

2.380E+03

2.397E+03

–0.703

2.300E+03

3.481

PM3: 4.5

N (N)

2.515E+03

2.413E+03

4.193

2.240E+03

12.268

M3163, N1530

Vy (N)

1.664E+03

1.664E+03

–0.025

1.600E+03

3.987

Vz (N)

2.670E+04

2.555E+04

4.469

2.530E+04

5.534

MT (N.m)

1.935E–03

1.237E–01

-98.437

2.570E+01

–99.99

Mfy (N.m)

1.246E+03

1.153E+03

8.084

1.120E+03

11.269

Mfz (N.m)

1.564E+02

1.659E+02

–5.734

1.610E+02

–2.824

PM4: 6.0

N (N)

7.134E+02

6.906E+02

3.299

6.590E+02

8.255

2èmeplancher

Vy (N)

9.610E+02

9.506E+02

1.087

9.100E+02

5.607

M3165, N1815

Vz (N)

1.769E+04

1.700E+04

4.099

1.680E+04

5.325

MT (N.m)

1.150E–03

8.407E–02

–98.632

2.500E+01

–99.99

Mfy (N.m)

1.537E+04

1.516E+04

1.330

1.540E+04

–0.197

Mfz (N.m)

1.092E+03

1.1021E+03

–0.959

1.060E+03

2.974

PM5: 7.5

N (N)

7.130E+02

6.902E+02

3.297

6.580E+02

8.362

M3167, N2106

Vy (N)

8.779E+02

8.644E+02

1.561

8.310E+02

5.647

Vz (N)

1.693E+04

1.622E+04

4.345

1.610E+04

5.174

MT (N.m)

1.149E–03

3.736E–02

–96.925

2.490E+01

–99.99

Mfy (N.m)

1.075E+04

1.017E+04

5.654

1.030E+04

4.382

Mfz (N.m)

3.034E+02

3.202E+02

–5.282

3.210E+02

–5.494

3.2.5. Réponse spectrale - méthode ROSENBLUETH DSC#

Pour cette méthode, nous avons utilisé un temps de simulation de 30 secondes.

Déplacements - colonne \(B\) (en \(m\) )

Altitude Z (m)

Composante

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

PM1: 1.5

X

1.858E–03

1.746E–03

6.396

1.643E–3

13.110

N982

Y

2.230E–04

2.197E–04

1.493

1.732E–3

–87.124

Z

1.823E–06

1.703E–06

7.048

2.113E–5

–91.372

PM2: 3.0

X

5.499E–03

5.194E–03

5.864

5.241E–3

4.917

1 erplancher

Y

5.528E–04

5.4825E–04

0.827

4.845E–3

–88.590

N1245

Z

3.646E–06

3.406E–06

7.048

4.225E–5

–91.370

PM3: 4.5

X

9.919E–03

9.398E–03

5.534

9.560E–3

3.751

N1530

Y

8.983E–04

8.927E–04

0.631

8.603E–3

–89.558

Z

4.601E–06

4.300E–06

6.991

5.453E–5

–91.699

PM4: 6.0

X

1.432E–02

1.359E–02

5.386

1.383E–2

3.548

2èmeplancher

Y

1.219E–03

1.212E–03

0.596

1.23E–2

–90.087

N1815

Z

5.557E–06

5.195E–06

6.953

6.861E–5

–91.901

PM5: 7.5

X

1.808E–02

1.717E–02

5.273

1.748E–2

3.434

N2106

Y

1.439E–03

1.431E–03

0.525

1.54E–2

–90.657

Z

5.827E–06

5.450E–06

6.918

7.381E–5

–92.105

PM6: 9.0

X

2.119E–02

2.013E–02

5.239

2.059E–2

2.892

3ème plancher

Y

1.609E–03

1.600E–03

0.524

1.79E–2

–91.015

N2355

Z

6.097E–06

5.704E–06

6.886

7.901E–5

–92.283

Réaction en \(N\) et Moment en \(\mathrm{N.m}\) à l’encastrement de la colonne \(B\) (nœud \(\mathrm{N758}\))

Réaction/Moment

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

Fx

3.501E+04

3.381E+04

3.524

3.368E+04

3.938

Fy

1.592E+03

1.572E+03

1.223

2.270E+03

–29.885

Fz

3.889E+03

3.633E+03

7.050

5.007E+03

–22.330

Mx

2.891E+03

2.872E+03

0.647

4.154E+03

–30.410

My

8.626E+04

8.273E+04

4.267

8.236E+04

4.738

Mz

1.787E–03

1.772E–01

-98.992

2.170E+01

–99.99

Réaction en \(N\) et Moment en \(\mathrm{N.m}\) à l’encastrement de la colonne centrale \(E\) (nœud \(\mathrm{N885}\))

Réaction/Moment

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

Fx

5.827E+04

5.374E+04

8.432

5.061E+04

15.148

Fy

2.014E+03

1.999E+03

0.724

2.855E+03

–29.471

Fz

2.471E+02

4.067E+02

–39.252

1.979E+03

–87.515

Mx

3.310E+03

3.298E+03

0.343

4.738E+03

–30.136

My

1.208E+05

1.122E+05

7.586

1.075E+05

12.386

Mz

1.783E–03

1.770E–01

-98.993

2.601E+01

–99.99

Efforts généralisés de la colonne \(B\)

Tableau élément «bas» (voir remarque Section 4.1)

Altitude Z (m)

Composante

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

PM1: 1.5

N (N)

3.889E+03

3.633E+03

7.048

5.007E+03

–22.327

Vy (N)

1.588E+03

1.570E+03

1.070

2.266E+03

–29.938

Vz (N)

3.497E+04

3.380E+04

3.461

3.325E+04

5.172

MT (N.m)

1.786E–03

1.756E–01

–98.983

2.169E+01

–99.99

Mfy (N.m)

3.378E+04

3.204E+04

5.445

3.264E+04

3.507

Mfz (N.m)

5.050E+02

5.149E+02

–1.933

7.659E+02

–34.067

PM2: 3.0

N (N)

3.889E+03

3.632E+03

7.047

5.007E+03

–22.330

1erplancher

Vy (N)

1.566E+03

1.554E+03

0.785

2.235E+03

–29.911

M3160, N1245

Vz (N)

3.476E+04

3.364E+04

3.304

3.290E+04

5.646

MT (N.m)

1.786E–03

1.646E–01

–98.915

2.167E+01

–99.99

Mfy (N.m)

1.861E+04

1.858E+04

0.181

1.752E+04

6.243

Mfz (N.m)

1.863E+03

1.825E+03

2.075

2.623E+03

–28.960

PM3: 4.5

N (N)

2.039E+03

1.910E+03

6.770

2.641E+03

–22.799

M3162, N1530

Vy (N)

1.338E+03

1.321E+03

1.255

1.934E+03

–30.834

Vz (N)

3.109E+04

3.050E+04

1.931

2.997E+04

3.751

MT (N.m)

1.543E–03

1.402E–01

–98.900

2.573E+01

–99.99

Mfy (N.m)

1.441E+03

1.397E+03

3.154

1.447E+03

–0.374

Mfz (N.m)

1.253E+02

1.295E+02

–3.277

1.900E+02

–34.035

PM4: 6.0

N (N)

2.039E+03

1.910E+03

6.767

2.640E+03

–22.780

2èmeplancher

Vy (N)

1.282E+03

1.270E+03

0.924

1.859E+03

–31.030

M3164, N1815

Vz (N)

3.040E+04

2.990E+04

1.675

2.935E+04

3.594

MT (N.m)

1.542E–03

1.049E–01

–98.53

2.573E+01

–99.99

Mfy (N.m)

4.656E+04

4.546E+04

2.413

4.436E+04

4.969

Mfz (N.m)

2.089E+03

2.053E+03

1.759

2.999E+03

–30.340

PM5: 7.5

N (N)

5.775E+02

5.441E+02

6.129

7.773E+02

–25.708

M3166, N2106

Vy (N)

7.058E+02

7.068E+02

–0.143

1.045E+03

–32.457

Vz (N)

1.964E+04

1.965E+04

–0.056

1.937E+04

1.389

MT (N.m)

9.165E–04

6.137E–02

–98.51

2.669E+01

–100.00

Mfy (N.m)

1.254E+04

1.205E+04

4.116

1.210E+04

3.652

Mfz (N.m)

2.431E+02

2.488E+02

–2.314

3.815E+02

–36.283

Tableau élément «haut» (voir remarque Section 4.1)

Altitude \(Z(m)\)

Composante

code_aster

CASTEM 2000

Écart en %

SAMCEF

Écart en %

\(\mathrm{PM0}:0.0\)

N (N)

3.889E+03

3.633E+03

7.050

–

–

\(\mathrm{M3157}\) , \(\mathrm{N758}\)

Vy (N)

1.592E+03

1.573E+03

1.229

–

–

Vz (N)

3.501E+04

3.382E+04

3.527

–

–

MT (N.m)

1.787E–03

1.770E–01

–98.991

–

–

Mfy (N.m)

8.626E+04

8.273E+04

4.267

–

–

Mfz (N.m)

2.891E+03

2.872E+03

0.647

–

–

\(\mathrm{PM1}:1.5\)

N (N)

3.889E+03

3.633E+03

7.048

5.007E+03

–22.327

\(\mathrm{M3159}\) , \(\mathrm{N982}\)

Vy (N)

1.587E+03

1.564E+03

1.451

2.255E+03

–29.596

Vz (N)

3.497E+04

3.375E+04

3.620

3.306E+04

5.773

MT (N.m)

1.786E–03

1.718E–01

–98.96

2.168E+01

–99.99

Mfy (N.m)

3.378E+04

3.204E+04

5.452

3.263E+04

3.539

Mfz (N.m)

5.050E+02

5.147E+02

–1.891

7.655E+02

–34.033

\(\mathrm{PM2}:3.0\)

N (N)

2.039E+03

1.910E+03

7.358

2.641E+03

–22.791

\(\mathrm{M3161}\) , \(\mathrm{N1245}\)

Vy (N)

1.374E+03

1.339E+03

2.625

1.374E+03

–-29.711

Vz (N)

3.153E+04

3.071E+04

2.659

3.017E+04

4.493

MT (N.m)

1.543E–03

1.540E–01

–98.99

2.572E+01

–99.99

Mfy (N.m)

4.663E+04

4.559E+04

2.271

4.51E+04

3.363

Mfz (N.m)

1.914E+03

1.869E+02

2.396

2.742E+03

–30.190

\(\mathrm{PM3}:4.5\)

N (N)

2.039E+03

1.909E+03

6.775

2.641E+03

–22.799

\(\mathrm{M3163}\) , \(\mathrm{N1530}\)

Vy (N)

1.338E+03

1.298E+03

3.049

1.902E+03

–29.670

Vz (N)

3.110E+04

3.023E+04

2.843

2.969E+04

4.734

MT (N.m)

1.543E–03

1.237E–01

–97.75

2.573E+01

–99.99

Mfy (N.m)

1.442E+03

1.398E+03

3.095

4.440E+04

0.110

Mfz (N.m)

1.253E+02

1.298E+02

–3.464

1.904E+02

–34.174

PM4: 6.0

N (N)

5.778E+03

5.442E+02

6.158

7.775E+02

–25.689

2èmeplancher

Vy (N)

7.731E+03

7.402E+02

4.444

1.087E+03

–28.875

\(\mathrm{M3165}\) , \(\mathrm{N1815}\)

Vz (N)

2.054E+04

2.008E+04

2.267

1.977E+04

3.887

MT (N.m)

9.172E–04

8.407E–02

–98.909

2.670E+01

–100.00

Mfy (N.m)

1.776E+04

1.789E+04

–0.745

1.797E+04

–1.176

Mfz (N.m)

8.696E+02

8.388E+02

3.663

1.284E+03

–32.273

\(\mathrm{PM5}:7.5\)

N (N)

5.775E+02

5.440E+02

6.153

7.771E+02

–25.689

\(\mathrm{M3167}\) , \(\mathrm{N2106}\)

Vy (N)

7.058E+02

6.704E+02

5.279

9.968E+02

–29.191

Vz (N)

1.964E+04

1.916E+04

2.466

1.891E+04

3.848

MT (N.m)

9.165E–04

3.736E–02

–97.547

2.669E+01

–100.00

Mfy (N.m)

1.254E+04

1.204E+04

4.099

1.211E+04

3.566

Mfz (N.m)

2.431E+02

2.490E+02

–2.369

3.816E+02

–36.299