4. B modeling#

4.1. Characteristics of modeling#

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

4.2. Characteristics of the mesh#

Number of knots: 11

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

Problem plan: for all nodes: \(\mathit{dy}\mathrm{=}0\); \(\mathit{drx}\mathrm{=}\mathit{drz}\mathrm{=}0\)

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

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

4.3. Modeling parameters#

Single-press response on the first 5 modes, excitation according to \(x\), without static correction (combination of modal responses CQC)

Single-press response on the first 5 modes, excitation according to \(x\), with static correction (combination of modal responses CQC)

Multi-press response on the first 5 modes with identical excitation according to \(x\) at all supports, without static correction and without anchor movements (combination of modal responses CQC)

Multi-press response on the first 5 modes with identical excitation according to \(x\) at all supports, with static correction and without anchor movements (combination of modal responses CQC)

Multi-press response on the first 5 modes with different \(x\) excitations and correlated to the supports, with static correction (combination of CQC modal responses)

Linear combination of load cases.

4.4. Tested sizes and results#

4.4.1. Single-press excitation according to x#

4.4.1.2. Single-support seismic analysis#

NOM_CHAMP: “depl” NOEUD_CMP: (“dir” “x”) NOM_CMP: “dx”

NOM_CHAMP: “acce_absolute” NOEUD_CMP: (“dir” “x”) NOM_CMP: “dx”

NOM_CHAMP: “reac_noda” NOEUD_CMP: (“dir” “x”) NOM_CMP: “dx”

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

Identification

Tolerance (%)

Travel according to \(x\)

NODE N3

0.0001

NODE N7

0.0001

NODE N11

0.0001

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

Tolerance (%)

Travel according to \(x\)

NODE N3

0.0001

NODE N7

0.0001

NODE N11

0.0001

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

4.4.2. Multi-press excitation according to x#

4.4.2.1. Modal analysis#

— VALEURS FROM SPECTRE —

MODE FREQUENCE AMORTISSEMENT DIR SUPPORT SPECTRE

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

2 3.35823D+01 3.00000D-02 X N1 N5 N9 1.58128D+01

3 4.73076D+01 3.00000D-02 X N1 N5 N9 8.21089D+00

4 8.80156D+01 3.00000D-02 X N1 N5 N9 2.50454D+00

5 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:

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

NOM_CHAMP: “depl” NOEUD_CMP: (“dir” “x”) NOM_CMP: “dx”

NOM_CHAMP: “acce_absolute” NOEUD_CMP: (“dir” “x”) NOM_CMP: “dx”

NOM_CHAMP: “reac_noda” NOEUD_CMP: (“dir” “x”) NOM_CMP: “dx”

Combination “CQC” without static correction (calculation SISM_MU1)

Identification

AUTRE_ASTER Aster 13.2.2 single-support §4.4.1.2 SISM_MO1

Tolerance (%)

Travel according to \(x\)

NODE N3

0.000178493287046

0.0001

NODE N7

0.00032927087105

0.0001

NODE N11

0.00108971744115

0.0001

Absolute acceleration

NODE N1

1.962

0.0001

NODE N5

1.962

0.0001

NODE N9

1.962

0.0001

Nodal reaction

NODE N1

669.603610534

0.0001

NODE N5

1164.22268299

0.0001

NODE N9

928.199473667

0.0001

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

NOM_CHAMP: “depl” NOEUD_CMP: (“dir” “x”) NOM_CMP: “dx”

NOM_CHAMP: “acce_absolute” NOEUD_CMP: (“dir” “x”) NOM_CMP: “dx”

NOM_CHAMP: “reac_noda” NOEUD_CMP: (“dir” “x”) NOM_CMP: “dx”

Combination “CQC” with static correction (calculation SISM_MU6)

Identification

AUTRE_ASTER Aster 13.2.2 single-support §4.4.1.2 SISM_MO2

Tolerance (%)

Travel according to \(x\)

NODE N3

0.000178493681539

0.0001

NODE N7

0.000329270911406

0.0001

NODE N11

0.00108971827966

0.00108971827966

0.0001

Absolute acceleration

NODE N1

1.962

0.0001

NODE N5

1.962

0.0001

NODE N9

1.962

0.0001

Nodal reaction

NODE N1

671.668298435

0.2

NODE N5

1169.72688401

0.4

NODE N9

937.326875436

0.9

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

NOM_CHAMP: “depl” NOEUD_CMP: (“dir” “x”) NOM_CMP: “dx”

NOM_CHAMP: “depl” NOEUD_CMP: (“dir” “y”) NOM_CMP: “dy”

NOM_CHAMP: “acce_absolute” NOEUD_CMP: (“dir” “x”) NOM_CMP: “dx”

NOM_CHAMP: “reac_noda” NOEUD_CMP: (“dir” “x”) NOM_CMP: “dx”

NOM_CHAMP: “depl” NOEUD_CMP: (“dir” “x”) NOM_CMP: “combi” “” quad “

NOM_CHAMP: “depl” NOEUD_CMP: (“dir” “” y “) NOM_CMP:” combi “” “quad”

Combining “CQC” modes

Load case combination: “LIN”

(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

0.0001

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

NODE N9

0.0001

4.5. 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 rigorously 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.