3. Modeling A#

3.1. Characteristics of modeling#

The modeling is three-dimensional. The beam is broken down into 10 modeling elements POU_D_E.

3.2. Characteristics of the mesh#

Number of knots: 11

Number of meshes and types: 10 meshes of type SEG2 (POU_D_E)

Node group \(\mathit{encastre}\) contains node \(\mathit{N1}\) (\(\mathit{dx}\mathrm{=}\mathit{dy}\mathrm{=}\mathit{dz}\mathrm{=}\mathit{drx}\mathrm{=}\mathit{dry}\mathrm{=}\mathit{drz}\mathrm{=}0\)).

Node group \(\mathit{attache}\) contains nodes \(\mathit{N5}\) and \(\mathit{N9}\) (\(\mathit{dx}\mathrm{=}\mathit{dy}\mathrm{=}0\)).

3.3. Modeling parameters#

Calculation SISM_MO1: Single-press response on the first 10 modes, excitation according to \(x\), without static correction (combination of modal responses CQC)

Calculation SISM_MO2: Single-press response on the first 10 modes, excitation according to \(x\), with static correction (combination of modal responses CQC)

Calculation SISM_MU1: Multi-press response on the first 10 modes with identical excitation according to \(x\) at all supports, without static correction and without anchor movements (combination of modal responses CQC)

Calculation SISM_MU2: Multi-press response on the first 10 modes with excitations in \(x\) and \(y\) different and correlated to the supports, with static correction (combination of modal responses CQC), with differential movements at the supports. Quadratic combination of answers to DDS.

Calculation SISM_MU6: Multi-press response on the first 10 modes with identical excitation according to \(x\) at all supports, with static correction and without anchor movements (combination of modal responses CQC)

Quadratic combination of directional responses (QUAD)

3.4. Tested sizes and results#

3.4.1. Single-press excitation according to x#

3.4.1.2. Single-support seismic analysis#

Size: “depl” NOM_MODE: (“dir” “x”) NOM_CMP: “dx”

Horizontal excitation according to \(x\), combination “CQC” without static correction (calculation SISM_MO1)

Identification

Reference

Tolerance (%)

Travel according to \(x\)

CASTEM 2000

NODE N3

1.78952E-04

0.3

NODE N7

3.29499E-04

0.1

NODE N11

1.09032E-03

0.1

Absolute acceleration

NODE N1

0.0001

NODE N5

0.0001

NODE N9

0.0001

Nodal reaction

NODE N1

0.0001

NODE N5

0.0001

NODE N9

0.0001

Horizontal excitation according to \(x\), combination CQC with static correction (calculation SISM_MO2)

Identification

Reference

Tolerance (%)

Travel according to \(x\)

CASTEM 2000

NODE N3

1.78952E-04

0.3

NODE N7

3.29499E-04

0.1

NODE N11

1.09032E-03

0.1

Absolute acceleration

NODE N1

0.0001

NODE N5

0.0001

NODE N9

0.0001

Nodal reaction

NODE N1

0.0001

NODE N5

0.0001

NODE N9

0.0001

3.4.2. Multi-press excitation according to x#

3.4.2.1. Modal analysis#

— VALEURS FROM SPECTRE —

MODE FREQUENCE AMORTISSEMENT DIR SUPPORT SPECTRE

1-2 1.54569D+01 3.00000D-02 X N1 N5 N9 1.96200D+01

3-4 3.35823D+01 3.00000D-02 X N1 N5 N9 1.58128D+01

5-6 4.73076D+01 3.00000D-02 X N1 N5 N9 8.21089D+00

7 5.45850D+01 3.00000D-02 X N1 N5 N9 6.24517D+00

8 8.80156D+01 3.00000D-02 X N1 N5 N9 2.50454D+00

9-10 1.01614D+02 3.00000D-02 X N1 N5 N9 1.96200D+00

MASSE TOTALE FROM THE STRUCTURE: 4.60967D+02

MASSE MODALE EFFECTIVE CUMULEE:

DIRECTION: X, CUMUL: 3.09868D+02, SOIT 67.221%

Multi-support seismic analysis (with excitations identical to the supports, without static correction, without anchor movements) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Horizontal excitation according to \(x\), combination “CQC” without static correction (calculation SISM_MU1)

Identification

Reference

Tolerance (%)

Travel according to \(x\)

CASTEM 2000

NODE N3

1.78952E-04

0.3

NODE N7

3.29499E-04

0.1

NODE N11

1.09032E-03

0.1

Absolute acceleration

AUTRE_ASTER Aster 13.2.2 mono-support §3.4.1.2 SISM_MO1

NODE N1

1.96200E+00

0.0001

NODE N5

1.96200E+00

0.0001

NODE N9

1.96200E+00

0.0001

Nodal reaction

AUTRE_ASTER Aster 13.2.2 mono-support §3.4.1.2 SISM_MO1

NODE N1

6.696036E+02

0.0001

NODE N5

1.164223E+03

0.0001

NODE N9

9.281995E+02

0.0001

Multi-support seismic analysis (with excitations identical to the supports, with static correction, without anchor movements) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Horizontal excitation according to \(x\), combination CQC with static correction (calculation SISM_MU6)

Identification

Reference

Tolerance (%)

Travel according to \(x\)

CASTEM 2000

NODE N3

1.78952E-04

0.3

NODE N7

3.29499E-04

0.1

NODE N11

1.09032E-03

0.1

Absolute acceleration

AUTRE_ASTER Aster 13.2.2 mono-support §3.4.1.2

NODE N1

1.96200E+00

0.0001

NODE N5

1.96200E+00

0.0001

NODE N9

1.96200E+00

0.0001

Nodal reaction

AUTRE_ASTER Aster 13.2.2 mono-support §3.4.1.2 SISM_MO1

NODE N1

6.716683E+02

0.2

NODE N5

1.169727E+03

0.4

NODE N9

9.373269E+02

0.9

3.4.3. Multi-press excitation according to x and y#

3.4.3.1. Modal analysis#

— VALEURS FROM SPECTRE —

MODE FREQUENCE AMORTISSEMENT DIR SUPPORT SPECTRE

1-2 1.54569D+01 3.00000D-02 X Y N1 1.96200D+01

N5 2.94300D+01

N9 3.92400D+01

3-4 3.35823D+01 3.00000D-02 X Y N1 1.58128D+01

N5 2.37192D+01

N9 3.16256D+01

5 4.73076D+01 3.00000D-02 X Y N1 8.21089D+00

N5 1.23163D+01

N9 1.64218D+01

6 4.73076D+01 3.00000D-02 X Y N1 8.21089D+00

N5 1.23163D+01

N9 1.64218D+01

7 5.45850D+01 3.00000D-02 X Y N1 6.24517D+00

N5 9.36775D+00

N9 1.24903D+01

8 8.80156D+01 3.00000D-02 X Y N1 2.50454D+00

N5 3.75681D+00

N9 5.00908D+00

9-10 1.01614D+02 3.00000D-02 X Y N1 1.96200D+00

N5 2.94300D+00

N9 3.92400D+00

MASSE TOTALE FROM THE STRUCTURE: 4.60967D+02

MASSE MODALE EFFECTIVE CUMULEE:

DIRECTION: X, CUMUL: 3.09868D+02, SOIT 67.221%

DIRECTION: Y, CUMUL: 3.09868D+02, SOIT 67.221%

Multi-support seismic analysis (with different correlated excitations, with static correction, with anchor movements) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

Excitations identical in both directions \(x\) and \(y\)

Combining “CQC” modes

Load case combination: “LIN”

Combination of directions” QUAD “

(Calculation SISM_MU2)

Identification

Tolerance (%)
\[\]

: label: EQ-None

textrm {Travel by}

X

NODE N3 | 0.0001 |

NODE N5

0.0001

NODE N7

0.0001

NODE N9

0.0001

NODE N11

Absolute acceleration

NODE N 1

0.0001

NODE N5

0.0001

NODE N9

0.0001

Nodal reaction

NODE N 1

0.0001

NODE N5

0.0001
\[\]

: label: EQ-None

textrm {Directional response based on}

Y

Moves according to: math: y | |

NODE N3

0.0001

NODE N5

0.0001

NODE N7

0.0001

NODE N9

0.0001

NODE N11

0.0001

Absolute acceleration

NODE N 1

0.0001

NODE N5

0.0001

NODE N9

0.0001
\[\]

: label: EQ-None

textrm {Component according to}

X

NODE N3 | 0.0001 |

NODE N5

0.0001

NODE N7

0.0001

NODE N9

0.0001
\[\]

: label: EQ-None

textrm {Component according to}

Y

NODE N3 | 0.0001 |

NODE N5

0.0001

NODE N7

0.0001

NODE N9

0.0001

NODE N11

0.0001

3.5. notes#

The displacement results are in good agreement with those obtained by CASTEM 2000, relative to the combination of CQC modes (error < 0.3%), for single-press cases without and with static correction, and multi-support without static correction, and multi-support without static correction.

The results in movements, accelerations and nodal reactions, with excitations equal to the supports, are strictly identical via the two correlated single-support and multi-support models, in the case without static correction. In the case with static correction via the pseudo-mode, a difference of 0.9% maximum is observed in the nodal reactions.