Code_Aster ®
Version
7.1
Titrate:
SDLL130 - Seismic Réponse of a beam BA to linear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key: V2.02.130-A Page:
1/8
Organization (S): EDF-R & D/AMA, LMT Cachan
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
Document: V2.02.130
SDLL130 - Seismic Réponse of a beam in
reinforced concrete (rectangular section) with behavior
linear
Summary:
The problem consists in analyzing the seismic response of a concrete beam reinforced via one
modeling beam multifibre (POU_D_EM, modeling B).
The calculation of reference (modeling A) is made using Code_Aster with “traditional” elements of
beam Euler Bernoulli (POU_D_E).
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
Code_Aster ®
Version
7.1
Titrate:
SDLL130 - Seismic Réponse of a beam BA to linear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key: V2.02.130-A Page:
2/8
1 Characteristics
general
1.1 Geometry
It is about a beam simply supported on its two supports [Figure 1.1-a].
y
X
5.400 mm
500 mm
Frameworks HA8 separated by 100 mm
5.000 mm
20 mm
44 mm
20 mm
32 mm
28
y
500 mm
Z
Tally HA8 spaced 100 mm
232
200 mm
44 mm
Appear 1.1-a: geometry of the structure
1.2
Material properties
·
concrete: E = 37.272 MPa, = 0.2, = 2400 kg/m3
·
steel: E = 200.000 MPa, = 0.33, = 7800 kg/m3
·
damping: of type Rayleigh (K+M), with 5% on modes 1 and 2
1.3
Boundary conditions and loadings
Simple support in b: Dy = 0
Support “doubles” in a: dx = Dy = 0
To avoid the clean modes except plan, one blocks the following degrees of freedom on all the beam:
X-ray = ry = dz = 0
Loading: seism ac_s2_c_1 [Figure 1.3-a], in axis OY applied to the two supports (factor
of amplification of the signal = 137).
NB: the transverse reinforcements are not taken into account in calculations
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
Code_Aster ®
Version
7.1
Titrate:
SDLL130 - Seismic Réponse of a beam BA to linear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key: V2.02.130-A Page:
3/8
3
2
1
0
- 1
- 2
- 3
0
2
4
6
8
10
12
14
16
Time (S)
Appear 1.3-a: Accélérogramme ac_s2_c_1 imposed on the structure
2
Reference solution Modélisation A
The reference is obtained by a Code_Aster calculation with traditional elements of beam of Euler
(POU_D_E). The characteristics for this calculation of reference are obtained while homogenizing
steel-concrete section:
Ea
200000
Section:
2
S
= S +
S = 1
,
0 +
×,
0 0017 = 109
,
0
m
eq
B
E
has
37272
B
Ea
-
200000
Quadratic moment:
3
- 5
- 3
4
I
= I +
I =,
2 078.10
+
× 122
,
8
.10
= 514
,
2
.10
m
eq
B
E
has
37272
B
The density selected is that of the concrete (the weight of steel is neglected).
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
Code_Aster ®
Version
7.1
Titrate:
SDLL130 - Seismic Réponse of a beam BA to linear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key: V2.02.130-A Page:
4/8
3
Modeling B (POU_D_EM)
3.1
Characteristics of modeling
Longitudinal grid of the beam:
It is composed of 17 nodes and 16 pairs of elements POU_D_EM (16 elements for the concrete and 16 for
steel).
Cross section of the beam:
The concrete is modelled by a grid (AFFE_SECT) composed of 2 X 20 quadrilaterals (40 fibers)
Appear 3.1-a: Discrétisation of the section
Steel is modelled by 4 specific fibers (AFFE_FIBER)
The coefficients and for damping are calculated using the following formula
1 2
1
1 1
=
2
2
2
-
2
1
2
1
2
-
2
1
where
1
and 2 are the first two own pulsations (F =
2
) and 1 and 2 is them
depreciation wished on the first two modes.
With F
37 8
, Hz
1 =
and F
,
149 2 Hz
2 =
(see paragraph [§4]), for modal depreciation of
5%, we find:
5
5
,
8..10-
=
and =
985
,
18
.
For the calculation of the temporal answer, the step of selected time is 1/100ème of second.
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
Code_Aster ®
Version
7.1
Titrate:
SDLL130 - Seismic Réponse of a beam BA to linear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key: V2.02.130-A Page:
5/8
3.2 Functionalities
tested
Commands
CREA_MAILLAGE
CREA_GROUP_MA
AFFE_MODELE GRID
AFFE
TOUT
“OUI”
PHENOMENE
“MECANIQUE”
MODELISATION
“POU_D_EM”
DEFI_MATERIAU
“ELAS”
AFFE_MATERIAU
GROUP_MA
MATER
AFFE_CARA_ELEM BEAM
GROUP_MA
SECTION
ORIENTATION
GROUP_MA
CARA
“ANGL_VRIL”
AFFE_SECT
GROUP_MA
MAILLAGE_SECT
“OUI”
TOUT_SECT
AFFE_PONCT
GROUP_MA
“DIAMETRE”
CARA
VALE
MODEL AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
CALC_MATR_ELEM OPTION
RIGI_MECA
MASS_MECA
AMOR_MECA
NUME_DDL MATR_RIGI
METHODE
“LDLT”
RENUM
“SANS”
ASSE_MATRICE MATR_ELEM
NUME_DDL
MODE_ITER_SIMULT MATR_A
MATR_B
CALC_FREQ
OPTION
“PLUS_PETITE”
NMAX_FREQ
CALC_CHAR_SEISME MONO_APPUI
“OUI”
DIRECTION
DYNA_LINE_TRAN MATR_MASS
MATR_RIGI
NEWMARK
EXCIT
VECT_ASSE
FONC_MULT
INCREMENT
CALC_ELEM OPTION
`SIEF_ELGA_DEPL
'
CALC_NO OPTION
“REAC_NODA”
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
Code_Aster ®
Version
7.1
Titrate:
SDLL130 - Seismic Réponse of a beam BA to linear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key: V2.02.130-A Page:
6/8
4 Results
The curves of reaction according to time and arrow in the center according to time are
presented on the figures [Figure 4-a] with [Figure 4-d].
300
200
100
0
- 100
- 200
Aster ref.
ASTER
- 300
0
2
4
6
8
10
12
14
16
Time (S)
Appear 4-a: Réaction in the first supports according to time
150
100
50
0
- 50
- 100
- 150
- 200
ASTER ref.
ASTER
- 250
2
2,2
2,4
2,6
2,8
3
Appear 4-b: Détail of the reaction between 2 and 3 seconds
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
Code_Aster ®
Version
7.1
Titrate:
SDLL130 - Seismic Réponse of a beam BA to linear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key: V2.02.130-A Page:
7/8
10
8
6
4
2
0
- 2
- 4
- 6
- 8
ASTER ref.
ASTER
- 10
0
5
10
15
Time (S)
Appear 4-c: Arrow in the center according to time
9
7
5
3
1
ASTER ref.
ASTER
- 1
- 3
2,5
2,55
2,6
2,65
2,7
2,75
2,8
Appear 4-d: Detail of the arrow between 2,5 and 2,8 seconds
Tests of results (TEST_RESU) are carried out for the first three Eigen frequencies. One
also test the reaction on the first support and the arrow in the center is tested at the moments 1s (not
100) and 2s (not 200), then for the 2 first extremums of the curves, at the moments 2,68s (not 268) and
4,68s (not 468).
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
Code_Aster ®
Version
7.1
Titrate:
SDLL130 - Seismic Réponse of a beam BA to linear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key: V2.02.130-A Page:
8/8
Eigen frequency
ASTER ref.
ASTER
Relative error %
1
37,80
37,83
0,07
2
149,20
149,28
0,05
3
200,30
200,39
0,04
REACTION
ASTER ref.
ASTER
Relative error %
1,00 S
1,8878.104
1,8479.104
2,1
2,00 S
6,3393.104
6,2184.104
1,9
2,68 S
2,3222.105
2,2443.105
3,4
4,68 S
2,4692.105
2,3979.105
2,9
ARROW ASTER
Ref.
ASTER
Relative error %
1,00 S
6,0694.104
5,9846.104
1,4
2,00 S
2,3507.103
2,3362.103
0,6
2,68 S
8,5790.103
8,3929.103
2,2
4,68 S
9,1084.103
8,9530.103
1,7
5
Summary of the results
The results obtained using modeling beam multifibre (POU_D_EM) are in concord
with the traditional modeling of right beam of Euler (POU_D_E) of Code_Aster.
Handbook of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
Outline document