3. Modeling A#

3.1. Characteristics of modeling and meshing#

_images/10000201000002C100000269B2B922DFB5CA4F0C.png

The mesh of the model calculated with Code_Aster consists of 3357 nodes and 3387 meshes including 135 Timoshenko right beam elements (including 12 SEG2 per column, or 108 for the columns) and 3072 DKT plate elements (1024 per floor). In order to ensure the continuity of the degrees of freedom DRZ of natural rotation of the beams with the rotation around the normal of the plates (not automatically ensured by Code_Aster), beam elements are added locally at the edge of the plates DKT, at the level of the 27 column-floor connections (group of elements” JONCTIONS “in the command file), to ensure the transmission of rotations DRZ linked to the plane movement of the plate rotating in plane \((x,y)\).

The mesh of the model calculated with CASTEM 2000 consists of 3765 nodes and 7368 elements including 108 elements (right Timoshenko beam) and 6960 elements of shell DKT.

The model mesh calculated with SAMCEF consists of 3360 nodes and 3180 elements including 108 Mindlin straight beam elements and 3072 Mindlin shell elements.

3.2. Results of modeling A#

3.2.1. notes#

For a given \(i\) node, the generalized effort for element \(i-1\) and for element \(i\) is compared in the « low » element and « high » element arrays respectively.

The efforts are given in the local coordinate system of the beam elements (main inertia coordinate system).

3.2.2. Calculating the modal base#

Natural frequencies in \(\mathrm{Hz}\)

Mode

Code_Aster

CASTEM 2000

Difference in %

SAMCEF

Difference in %

Difference in %

1

1.512

1.512

1.512

0.036

1.495

1.11

2

2.052

2.050

2.050

0.125

2.014

1.93

3

2.365

2.343

2.343

0.916

2.291

3.24

4

4.848

4.859

4.859

0.237

4.823

0.522

5

7.488

7.521

0.421

0.448

7.415

0.99

6

8.388

8.426

8.426

0.456

8.355

0.392

7

8.547

8.543

8.543

0.037

8.438

1.30

8

15.185

15.405

15.405

1.428

15.186

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

Visualization: Mode No. 1;

Mode #3;

Fashion No. 7.

Effective modal masses in \(\mathrm{kg}\)

Fashion and direction

Aster_code

CASTEM 2000

Difference in %

SAMCEF

Difference in %

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

Cumulation

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%

Note:

The error norm for modes calculated by Code_Aster’s Sorensen method is always less than \({10}^{-9}\).

Note:

The total mass of the building is \(132552\mathrm{kg}\); the strong orientation along y of the modes is due to the relative lower inertia along y of the columns. The cumulative effective modal mass in the \(x\) direction of the earthquake obtained by Code_Aster represents \(\text{97.678 \%}\) of the total mass.

Note:

The differences between models and software are quite strong in the \(z\) direction, as it is not very popular in these modes.

3.2.3. Spectral response - method CQC#

**Displacements - column* \(B\) (in meters)

Reaction in \(N\) and Moment in \(\mathrm{N.m}\) when embedding the column \(B\) ( group*node* “PFE” )

Reaction or moment

Code_Aster

CASTEM 2000

Difference in %

SAMCEF

Code_Aster

Difference in %

Fx

3.445E+04

3.325E+04

3.325E+04

3.362E+04

2.460

Fy

1.644E+03

1.629E+03

1.629E+03

1.629E+03

—27.405

Fz

4.015E+03

3.761E+03

3.761E+03

3.761E+03

—19.694

Mx

2.986E+03

2.975E+03

2.975E+03

2.975E+03

—27.967

My

8.488E+04

8.135E+04

8.135E+04

8.225E+04

3.208

Mz

1.8460E—03

1.772E—01

—98.958

2.165E+01

-99.99

**Reaction in* \(N\) and Moment in \(\mathrm{N.m}\) to embedding the central column \(E\) (node group “ PFE “)

Reaction/Moment

Code_Aster

CASTEM 2000

Difference in %

SAMCEF

Code_Aster

Difference in %

Fx

5.799E+04

5341E+04

8.552

5.056E+04

14.686

Fy

2.080E+03

2.071E+03

2.071E+03

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

3.417E+03

3.417E+03

—27.691

My

1.202E+05

1.116E+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

Generalized efforts from the column \(B\) (as a local benchmark)

« Low » element array (see note [§ 4.1])

Altitude Z (m)

Component

Component

Code_Aster

CASTEM 2000

Difference in %

SAMCEF

Difference in %

PM1: 1.5

N (N)

4.015E+03

4.015E+03

3.7618E+03

6.728

5.000E+03

—19.702

PM1_BAS

Vy (N)

1.640E+03

1.627E+03

1.627E+03

2.260E+03

—27.445

Vz (N)

3.441E+04

3.441E+04

3.323E+04

3.320E+04

3.634

MT (N.m)

1.846E—03

1.846E—03

1.756E—01

—98.949

2.160E+01

—99.99

Mfy (N.m)

3.325E+04

3.325E+04

3.151E+04

5.522

3.320E+04

0.154

Mfz (N.m)

5.215E+02

5.215E+02

5.333E+02

—2.227

7.650E+02

—31.835

PM2: 3.0

N (N)

4.015E+03

4.015E+03

3.761E+03

6.727

4.999E+03

—19.689

1st floor

Vy (N)

1.618E+03

1.618E+03

1.610E+03

2.230E+03

—27.450

PM2_BAS

Vz (N)

3.420E+04

3.420E+04

3.308E+04

3.371

3.286E+04

4.073

MT (N.m)

1.846E—03

1.846E—03

1.645E—01

—98.879

2.160E+01

—99.99

Mfy (N.m)

1.830E+04

1.830E+04

1.824E+04

1.750E+04

4.603

Mfz (N.m)

1.925E+03

1.925E+03

1.891E+03

2.620E+03

—26.542

PM3: 4.5

N (N)

2.104E+03

2.104E+03

1.976E+03

6.448

2.636E+03

—20.176

PM3_BAS

Vy (N)

1.381E+03

1.381E+03

1.368E+03

0.952

1.930E+04

—28.439

Vz (N)

3.061E+04

3.061E+04

3.000E+04

2.6010

2.993E+04

2.265

MT (N.m)

1.594E—03

1.594E—03

1.402E—01

—98.863

2.570E+01

—99.99

Mfy (N.m)

1.434E+03

1.390E+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

2.104E+03

1.976E+03

6.450

2.636E+03

—20.187

2nd floor

Vy (N)

1.324E+03

1.324E+03

1.315E+03

0.618

1.850E+03

—28.458

PM4_BAS

Vz (N)

2.993E+04

2.993E+04

2.941E+04

1.751

2.931E+04

2.119

MT (N.m)

1.594E—03

1.594E—03

1.049E—01

—98.481

2.570E+01

—99.99

Mfy (N.m)

4.583E+04

4.583E+04

4.471E+04

2.480

4.430E+04

3.445

Mfz (N.m)

2.157E+03

2.157E+03

2.126E+03

2.990E+03

—27.858

PM5: 7.5

N (N)

5.956E+02

5.956E+02

5.629E+02

5.817

7.749E+02

—23.133

PM5_BAS

Vy (N)

7.279E+02

7.279E+02

7.312E+02

—0.453

1.040E+03

—30.006

Vz (N)

1.935E+04

1.935E+04

1.934E+04

1.934E+04

0.039

MT (N.m)

9.470E—04

9.470E—04

6.137E—02

-98.457

2.660E+01

—99.99

Mfy (N.m)

1.234E+04

1.234E+04

1.184E+04

1.210E+04

2.006

Mfz (N.m)

2.511E+02

2.511E+02

2.578E+02

—2.607

3.800E+02

—33.921

« Top » element array (see note [§ 4.1])

Altitude Z (m)

Component

Component

Code_Aster

CASTEM 2000

Difference in %

SAMCEF

Difference in %

PM0: 0.0

N (N)

4.015E+03

4.015E+03

3.762E+03

6.729

PM0_HAUT

Vy (N)

1.644E+03

1.629E+03

1.629E+03

0.928

Vz (N)

3.444E+04

3.325E+04

3.593

MT (N.m)

1.846E—03

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

4.015E+03

3.762E+03

6.728

5.000E+03

—19.702

PM1_HAUT

Vy (N)

1.640E+03

1.640E+03

1.621E+03

2.250E+03

—27.123

Vz (N)

3.440E+04

3.440E+04

3.318E+04

3.683

3.300E+04

4.258

MT (N.m)

1.846E—03

1.846E—03

1.717E—01

—98.925

2.160E+01

—99.99

Mfy (N.m)

3.325E+04

3.325E+04

3.150E+04

5.529

3.260E+04

1.997

Mfz (N.m)

5.215E+02

5.215E+02

5.331E+02

—2.183

7.640E+02

—31.746

PM2: 3.0

N (N)

2.104E+03

2.104E+03

1.976E+03

6.454

2.640E+03

—20.289

1st floor

Vy (N)

1.419E+03

1.419E+03

1.386E+03

2.319

1.950E+03

—27.233

PM2_HAUT

Vz (N)

3.103E+04

3.103E+04

3.020E+04

2.733

3.010E+04

3.094

MT (N.m)

1.595E—03

1.595E—03

1.540E—01

—98.965

2.570E+01

—99.99

Mfy (N.m)

4.591E+04

4.591E+04

4.485E+04

4.500E+04

2.022

Mfz (N.m)

1.976E+03

1.976E+03

1.935E+03

2.730E+03

—27.610

PM3: 4.5

N (N)

2.104E+03

2.104E+03

1.976E+03

6.453

2.640E+03

—20.297

PM3_HAUT

Vy (N)

1.381E+03

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

1.594E—03

1.237E—01

—98.712

2.570E+01

—99.99

Mfy (N.m)

1.434E+03

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

2nd floor

Vy (N)

7.978E+02

7.978E+02

7.660E+02

4.147

1.080E+03

—26.130

PM4_HAUT

Vz (N)

2.023E+04

2.023E+04

1.976E+04

2.358

1.970E+04

2.696

MT (N.m)

9.477E—04

8.477E—04

8.407E—02

—98.873

2.670E+01

—99.99

Mfy (N.m)

1.751E+04

1.751E+04

1.762E+04

—0.636

1.790E+04

—2.179

Mfz (N.m)

8.967E+02

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

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

1.935E+04

1.886E+04

2.561

1.890E+04

2.360

MT (N.m)

9.470E—04

9.470E—04

3.736E—02

—97.466

2.660E+01

—99.99

Mfy (N.m)

1.234E+04

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. Spectral response - method SRSS#

Travel — column \(B\) (in \(m\))

Altitude Z (m)

Component

Component

Code_Aster

CASTEM 2000

Difference in %

SAMCEF

Difference in %

PM1: 1.5

X

1.593E—03

1.593E—03

1.4749E—03

1.40E—03

13.779

N982

Y

2.767E—04

2.767E—04

2.795E—04

—1.050

1.47E—03

—81.179

Z

2.253E+06

2.156E—06

2.156E—06

4.469

1.95E—05

—88.447

PM2: 3.0

X

4.714E—03

4.714E—03

4.386E—03

7.475

4.46E—03

5.707

1st floor

Y

6.854E—04

6.854E—04

6.969E—04

—1.653

4.12E—03

—83.364

N1245

Z

4.506E—06

4.506E—06

4.312E—06

4.469

3.90E—05

—88.447

PM3: 4.5

X

8.508E—03

8.508E—03

7.939E—03

8.13E—03

4.655

N1530

Y

1.113E—03

1.113E—03

1.133E—03

—1.797

7.32E—03

—84.798

Z

5.684E—06

5.443E—06

5.443E—06

4.412

5.12E—05

—88.898

PM4: 6.0

X

1.229E—02

1.229E—02

1.148E—02

7.043

1.18E—02

4.153

2nd floor

Y

1.510E—03

1.510E—03

1.538E—03

—1.842

1.05E—02

—85.621

N1815

Z

6.862E—06

6.862E—06

6.574E—06

4.374

6.33E—05

—89.159

PM5: 7.5

X

1.552E—02

1.552E—02

1.451E—02

1.49E—02

4.187

N2106

Y

1.780E—03

1.815E—03

1.815E—03

—1.902

1.31e—02

—86.410

Z

7.195E—06

6.896E—06

6.896E—06

6.80E—06

—89.419

PM6: 9.0

X

1.820E—02

1.701E—02

6.944

1.75E—02

3.981

3rd floor

Y

1.990E—03

2.028E—03

2.028E—03

—1.902

1.52E—02

—86.908

N2355

Z

7.528E—06

7.528E—06

7.217E—06

7.27E—06

—89.646

Reaction in \(N\) and Moment in \(\mathrm{N.m}\) to the embedding of column \(B\) (node \(\mathrm{N758}\)).

Reaction/Moment

Code_Aster

CASTEM 2000

Difference in %

SAMCEF

Code_Aster

Difference in %

Fx

2.999E+04

2.854E+04

2.854E+04

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

4.600E+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

6.985E+04

6.985E+04

6.985E+04

5.448

Mz

2.240E—03

1.772E—01

—98.736

1.989E+01

-99.99

Reaction in \(N\) and Moment in \(\mathrm{N.m}\) to the embedding of the central column \(E\) (node \(\mathrm{N885}\)).

Reaction/Moment

Code_Aster

CASTEM 2000

Difference in %

SAMCEF

Code_Aster

Difference in %

Fx

5.591E+04

5.094E+04

5.094E+04

5.094E+04

16.558

Fy

2.499E+03

2.545E+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

4.196E+03

—2.161

4.008E+03

2.454

My

1.159E+05

1.064E+05

1.064E+05

1.064E+05

1.064E+05

1.064E+05

1.064E+05

8.897

Mz

2.236E—03

1.770E—01

—98.737

2.288E+01

—99.99

Generalized efforts from column \(B\)

« Low » element array (see note [§4.1])

Altitude Z (m)

Component

Component

Code_Aster

CASTEM 2000

Difference in %

SAMCEF

Difference in %

PM1: 1.5

N (N)

4.806E+03

4.600E+03

4.469

4.250E+03

4.250E+03

13.082

M3158, N982

Vy (N)

1.972E+03

2.003E+03

—1.580

1.910E+03

1.910E+03

3.233

Vz (N)

2.995E+04

2.995E+04

2.853E+04

2.830E+04

5.832

MT (N.m)

2.240E—03

2.240E—03

1.756E—01

—98.725

1.990E+01

—99.99

Mfy (N.m)

2.898E+04

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

4.250E+03

13.078

1st floor

Vy (N)

1.944E+03

1.944E+03

1.980E+03

1.890E+03

2.867

M3160, N1245

Vz (N)

2.977E+04

2.840E+04

4.825

2.800E+04

2.800E+04

6.326

MT (N.m)

2.240E—03

2.240E—03

1.646E—01

—98.639

1.990E+01

—99.99

Mfy (N.m)

1.590E+04

1.590E+04

1.566E+04

1.510E+04

5.284

Mfz (N.m)

2.317E+03

2.317E+03

2.334E+03

—0.746

2.200E+03

5.327

PM3: 4.5

N (N)

2.515E+03

2.515E+03

2.414E+03

4.184

2.240E+03

12.268

M3162

Vy (N)

1.664E+03

1.664E+03

1.694E+03

—1.789

1.620E+03

2.703

Vz (N)

2.670E+04

2.670E+04

2.578E+04

2.560E+04

4.291

MT (N.m)

1.935E—03

1.935E—03

1.402E—01

—98.621

2.570E+01

—99.99

Mfy (N.m)

1.246E+03

1.246E+03

1.152E+03

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

2.514E+03

2.413E+03

4.183

2.240E+03

12.253

2nd floor

Vy (N)

1.592E+03

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

2.500E+04

4.461

MT (N.m)

1.934E—03

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

6.590E+02

8.197

M3166, N2106

Vy (N)

8.779E+02

9.099E+02

—3.521

8.730E+02

8.730E+02

0.564

Vz (N)

1.693E+04

1.693E+04

1.663E+04

1.650E+04

2.635

MT (N.m)

1.150E—03

1.150E—03

6.137E—02

—98.128

2.500E+01

—99.99

Mfy (N.m)

1.075E+04

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

« Top » element array (see note [§ 4.1])

Altitude Z (m)

Component

Component

Code_Aster

CASTEM 2000

Difference in %

SAMCEF

Difference in %

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

2.998E+04

2.854E+04

MT (N.m)

2.240E—03

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

4.250E+03

13.082

M3159, N982

Vy (N)

1.972E+03

1.995E+03

—1.176

1.900E+03

1.900E+03

3.776

Vz (N)

2.995E+04

2.848E+04

5.140

2.810E+04

2.810E+04

6.580

MT (N.m)

2.240E—03

2.240E—03

1.717E—01

—98.696

1.990E+01

—99.99

Mfy (N.m)

2.898E+04

2.898E+04

2.706E+04

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

2.515E+03

2.414E+03

4.191

2.240E+03

12.280

1st floor

Vy (N)

1.709E+03

1.709E+03

1.716E+03

1.640E+03

1.709E+03

4.231

M3161, N1245

Vz (N)

2.706E+04

2.595E+04

4.269

2.570E+04

2.570E+04

5.304

MT (N.m)

1.935E—03

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

2.380E+03

2.397E+03

2.300E+03

3.481

PM3: 4.5

N (N)

2.515E+03

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

1.600E+03

3.987

Vz (N)

2.670E+04

2.670E+04

2.555E+04

2.670E+04

2.670E+04

5.534

MT (N.m)

1.935E—03

1.935E—03

1.237E—01

-98.437

2.570E+01

—99.99

Mfy (N.m)

1.246E+03

1.246E+03

1.153E+03

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

2nd floor

Vy (N)

9.610E+02

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

1.680E+04

5.325

MT (N.m)

1.150E—03

1.150E—03

8.407E—02

—98.632

2.500E+01

—99.99

Mfy (N.m)

1.537E+04

1.537E+04

1.516E+04

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

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

8.310E+02

5.647

Vz (N)

1.693E+04

1.622E+04

4.345

1.610E+04

1.693E+04

5.174

MT (N.m)

1.149E—03

1.149E—03

3.736E—02

—96.925

2.490E+01

—99.99

Mfy (N.m)

1.075E+04

1.075E+04

1.017E+04

1.030E+04

4.382

Mfz (N.m)

3.034E+02

3.202E+02

—5.282

3.210E+02

—5.494

3.2.5. Spectral response - method ROSENBLUETH DSC#

For this method, we used a simulation time of 30 seconds.

Travel - column \(B\) (in \(m\))

Altitude Z (m)

Component

Component

Code_Aster

CASTEM 2000

Difference in %

SAMCEF

Difference in %

PM1: 1.5

X

1.858E—03

1.858E—03

1.746E—03

6.396

1.643E—3

13.110

N982

Y

2.230E—04

2.230E—04

2.197E—04

1.493

1.732E—3

—87.124

Z

1.823E—06

1.703E—06

1.703E—06

7.048

2.113E—5

—91.372

PM2: 3.0

X

5.499E—03

5.499E—03

5.194E—03

5.864

5.241E—3

4.917

1st floor

Y

5.528E—04

5.528E—04

5.4825E—04

0.827

4.845E—3

—88.590

N1245

Z

3.646E—06

3.646E—06

3.406E—06

7.048

4.225E—5

—91.370

PM3: 4.5

X

9.919E—03

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

4.300E—06

6.991

5.453E—5

—91.699

PM4: 6.0

X

1.432E—02

1.432E—02

1.359E—02

5.386

1.383E—2

3.548

2nd floor

Y

1.219E—03

1.219E—03

1.212E—03

0.596

1.23E—2

—90.087

N1815

Z

5.557E—06

5.557E—06

5.195E—06

6.953

6.861E—5

—91.901

PM5: 7.5

X

1.808E—02

1.808E—02

1.717E—02

5.273

1.748E—2

3.434

N2106

Y

1.439E—03

1.439E—03

1.431E—03

0.525

1.54E—2

—90.657

Z

5.827E—06

5.450E—06

5.450E—06

6.918

7.381E—5

—92.105

PM6: 9.0

X

2.119E—02

2.119E—02

2.013E—02

5.239

2.059E—2

2.892

3rd floor

Y

1.609E—03

1.609E—03

1.600E—03

0.524

1.79E—2

—91.015

N2355

Z

6.097E—06

6.097E—06

5.704E—06

6.886

7.901E—5

—92.283

Reaction in \(N\) and Moment in \(\mathrm{N.m}\) to the embedding of column \(B\) (node \(\mathrm{N758}\)).

Reaction/Moment

Code_Aster

CASTEM 2000

Difference in %

SAMCEF

Code_Aster

Difference in %

Fx

3.501E+04

3.381E+04

3.381E+04

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

3.633E+03

3.633E+03

—22.330

Mx

2.891E+03

2.872E+03

2.872E+03

2.872E+03

—30.410

My

8.626E+04

8.273E+04

8.273E+04

8.236E+04

4.738

Mz

1.787E—03

1.772E—01

-98.992

2.170E+01

—99.99

—99.99

Reaction in \(N\) and Moment in \(\mathrm{N.m}\) to the embedding of the central column \(E\) (node \(\mathrm{N885}\)).

Reaction/Moment

Code_Aster

CASTEM 2000

Difference in %

SAMCEF

Code_Aster

Difference in %

Fx

5.827E+04

5.374E+04

5.374E+04

5.061E+04

15.148

Fy

2.014E+03

1.999E+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

3.298E+03

3.298E+03

—30.136

My

1.208E+05

1.122E+05

1.122E+05

7.586

1.075E+05

12.386

Mz

1.783E—03

1.770E—01

1.770E—01

-98.993

2.601E+01

—99.99

Generalized efforts from column \(B\)

« Low » element array (see note paragraph [§4.1])

Altitude Z (m)

Component

Component

Code_Aster

CASTEM 2000

Difference in %

SAMCEF

Difference in %

PM1: 1.5

N (N)

3.889E+03

3.889E+03

3.633E+03

7.048

5.007E+03

—22.327

Vy (N)

1.588E+03

1.588E+03

1.570E+03

2.266E+03

—29.938

Vz (N)

3.497E+04

3.497E+04

3.380E+04

3.325E+04

5.172

MT (N.m)

1.786E—03

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

5.050E+02

5.149E+02

—1.933

7.659E+02

—34.067

PM2: 3.0

N (N)

3.889E+03

3.889E+03

3.632E+03

7.047

5.007E+03

—22.330

1st floor

Vy (N)

1.566E+03

1.566E+03

1.554E+03

2.235E+03

—29.911

M3160, N1245

Vz (N)

3.476E+04

3.364E+04

3.304

3.290E+04

3.290E+04

5.646

MT (N.m)

1.786E—03

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

1.863E+03

1.825E+03

2.623E+03

—28.960

PM3: 4.5

N (N)

2.039E+03

2.039E+03

1.910E+03

6.770

2.641E+03

—22.799

M3162, N1530

Vy (N)

1.338E+03

1.338E+03

1.255

1.934E+03

1.934E+03

—30.834

Vz (N)

3.109E+04

3.109E+04

3.050E+04

1.931

2.997E+04

3.751

MT (N.m)

1.543E—03

1.543E—03

1.402E—01

—98.900

2.573E+01

—99.99

Mfy (N.m)

1.441E+03

1.441E+03

1.397E+03

3.154

1.447E+03

—0.374

Mfz (N.m)

1.253E+02

1.253E+02

1.295E+02

—3.277

1.900E+02

—34.035

PM4: 6.0

N (N)

2.039E+03

2.039E+03

1.910E+03

6.767

2.640E+03

—22.780

2nd floor

Vy (N)

1.282E+03

1.282E+03

1.270E+03

1.282E+03

—31.030

M3164, N1815

Vz (N)

3.040E+04

2.990E+04

1.675

2.935E+04

2.935E+04

3.594

MT (N.m)

1.542E—03

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

4.436E+04

4.969

Mfz (N.m)

2.089E+03

2.089E+03

2.053E+03

2.999E+03

—30.340

PM5: 7.5

N (N)

5.775E+02

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

1.045E+03

—32.457

Vz (N)

1.964E+04

1.964E+04

1.964E+04

1.937E+04

1.389

MT (N.m)

9.165E—04

6.137E—04

6.137E—02

—98.51

2.669E+01

—100.00

Mfy (N.m)

1.254E+04

1.254E+04

1.205E+04

1.210E+04

3.652

Mfz (N.m)

2.431E+02

2.488E+02

—2.314

3.815E+02

—36.283

« Top » element array (see note paragraph [§4.1])

Altitude \(Z(m)\)

Component

Code_Aster

CASTEM 2000

Difference in %

SAMCEF

Difference in %

\(\mathrm{PM0}:0.0\)

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

3.501E+04

3.382E+04

—

—

MT (N.m)

1.787E—03

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

3.889E+03

3.633E+03

7.048

5.007E+03

—22.327

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

Vy (N)

1.587E+03

1.587E+03

1.451

2.255E+03

—29.596

Vz (N)

3.497E+04

3.497E+04

3.375E+04

3.306E+04

5.773

MT (N.m)

1.786E—03

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

3.263E+04

3.539

Mfz (N.m)

5.050E+02

5.050E+02

5.147E+02

—1.891

7.655E+02

—34.033

\(\mathrm{PM2}:3.0\)

N (N)

2.039E+03

2.039E+03

1.910E+03

7.358

2.641E+03

—22.791

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

Vy (N)

1.374E+03

1.374E+03

1.339E+03

2.625

1.374E+03

—-29.711

Vz (N)

3.153E+04

3.153E+04

3.071E+04

3.153E+04

4.493

MT (N.m)

1.543E—03

1.543E—03

1.540E—01

—98.99

2.572E+01

—99.99

Mfy (N.m)

4.663E+04

4.663E+04

4.559E+04

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

2.039E+03

1.909E+03

2.641E+03

—22.799

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

Vy (N)

1.338E+03

1.338E+03

1.298E+03

3.049

1.902E+03

—29.670

Vz (N)

3.110E+04

3.110E+04

3.023E+04

2.969E+04

4.734

MT (N.m)

1.543E—03

1.543E—03

1.237E—01

—97.75

2.573E+01

—99.99

Mfy (N.m)

1.442E+03

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

2nd floor

Vy (N)

7.731E+03

7.731E+03

7.402E+02

4.444

1.087E+03

—28.875

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

Vz (N)

2.054E+04

2.054E+04

2.267

1.977E+04

1.977E+04

3.887

MT (N.m)

9.172E—04

9.172E—04

8.407E—02

—98.909

2.670E+01

—100.00

Mfy (N.m)

1.776E+04

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

5.775E+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

1.964E+04

1.916E+04

2.466

1.891E+04

3.848

MT (N.m)

9.165E—04

9.165E—04

3.736E—02

—97.547

2.669E+01

—100.00

Mfy (N.m)

1.254E+04

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