Code_Aster
®
Version
7.1
Titrate:
SDLL130 -
Seismic response 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
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA, LMT Cachan
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
Document: V2.02.130
SDLL130 - Seismic response 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 “conventional” elements of
beam Euler Bernoulli (
POU_D_E
).
Code_Aster
®
Version
7.1
Titrate:
SDLL130 -
Seismic response 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
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
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
5.000 mm
500 mm
20 mm
200 mm
Tally HA8 spaced 100 mm
2
8
2
32
20 mm
44 mm
44 mm
32 mm
y
Z
500 mm
Frameworks HA8 separated by 100 mm
Appear 1.1-a: geometry of the structure
1.2
Material properties
·
concrete: E = 37.272 MPa,
= 0.2, = 2400 kg/m
3
·
steel: E = 200.000 MPa,
= 0.33, = 7800 kg/m
3
·
damping: of Rayleigh type (
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 locks 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
Code_Aster
®
Version
7.1
Titrate:
SDLL130 -
Seismic response 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
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
- 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 conventional elements of beam of Euler
(
POU_D_E
). The characteristics for this calculation of reference are obtained while homogenizing
steel-concrete section:
Section:
2
109
,
0
0017
,
0
37272
200000
1
,
0
m
S
E
E
S
S
has
B
has
B
eq
=
×
+
=
+
=
Quadratic moment:
4
3
5
3
10
.
514
,
2
10
.
122
,
8
37272
200000
10
.
078
,
2
m
I
E
E
I
I
has
B
has
B
eq
-
-
-
=
×
+
=
+
=
The density selected is that of the concrete (the weight of steel is neglected).
Code_Aster
®
Version
7.1
Titrate:
SDLL130 -
Seismic response 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
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
3
Modeling B (
POU_D_EM
)
3.1
Characteristics of modeling
Longitudinal mesh 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 modelized by a mesh (
AFFE_SECT
) composed of 2 X 20 quadrilaterals (40 fibers)
Appear 3.1-a: Discretization of the section
Steel is modelized by 4 specific fibers (
AFFE_FIBER
)
Coefficients
and
for damping are calculated using the following formula
-
-
=
2
1
1
1
2
2
2
1
2
2
2
1
1
1
2
where
1
and
2
are the first two own pulsations
(
)
2
=
F
and
1
and
2
are them
depreciation wished on the first two modes.
With
Hz
F
8
,
37
1
=
and
Hz
F
2
,
149
2
=
(see paragraph [§4]), for modal depreciation of
5%, we find:
5
10
.
5
,
8
-
=
and
985
,
18
=
.
For the calculation of the temporal answer, the pitch of selected time is 1/100
ème
from second.
Code_Aster
®
Version
7.1
Titrate:
SDLL130 -
Seismic response 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
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
3.2 Functionalities
tested
Controls
CREA_
MESH
CREA_GROUP_MA
AFFE_MODELE MESH
AFFE
ALL
PHENOMENON
MODELING
“YES”
“MECHANICAL”
“POU_D_EM”
DEFI_MATERIAU
“ELAS”
AFFE_MATERIAU
GROUP_MA
MATER
AFFE_CARA_ELEM BEAM
ORIENTATION
AFFE_SECT
AFFE_PONCT
GROUP_MA
SECTION
GROUP_MA
CARA
GROUP_MA
MAILLAGE_SECT
TOUT_SECT
GROUP_MA
CARA
VALE
“ANGL_VRIL”
“YES”
“DIAMETER”
MODEL AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
CALC_MATR_ELEM OPTION
RIGI_MECA
MASS_MECA
AMOR_MECA
NUME_DDL MATR_RIGI
METHOD
RENUM
“LDLT”
“WITHOUT”
ASSE_MATRICE MATR_ELEM
NUME_DDL
MODE_ITER_SIMULT MATR_A
MATR_B
CALC_FREQ
OPTION
NMAX_FREQ
“PLUS_PETITE”
CALC_CHAR_SEISME MONO_APPUI
DIRECTION
“YES”
DYNA_LINE_TRAN MATR_MASS
MATR_RIGI
NEWMARK
EXCIT
INCREMENT
VECT_ASSE
FONC_MULT
CALC_ELEM OPTION
`SIEF_ELGA_DEPL
'
CALC_NO OPTION
“REAC_NODA”
Code_Aster
®
Version
7.1
Titrate:
SDLL130 -
Seismic response 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
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
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
300
0
2
4
6
8
10
12
14
16
Time (S)
Aster ref.
ASTER
Appear 4-a: Reaction in the first supports according to time
- 250
- 200
- 150
- 100
- 50
0
50
100
150
2
2,2
2,4
2,6
2,8
3
ASTER ref.
ASTER
Appear 4-b: Detail of the reaction between 2 and 3 seconds
Code_Aster
®
Version
7.1
Titrate:
SDLL130 -
Seismic response 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
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
- 10
- 8
- 6
- 4
- 2
0
2
4
6
8
10
0
5
10
15
Time (S)
ASTER ref.
ASTER
Appear 4-c: Arrow in the center according to time
- 3
- 1
1
3
5
7
9
2,5
2,55
2,6
2,65
2,7
2,75
2,8
ASTER ref.
ASTER
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).
Code_Aster
®
Version
7.1
Titrate:
SDLL130 -
Seismic response 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
Manual of Validation
V2.02 booklet: Linear dynamics of the beams
HT-66/03/008/A
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
1,8878.10
4
1,8479.10
4
2,1
2,00 S
6,3393.10
4
6,2184.10
4
1,9
2,68 S
2,3222.10
5
2,2443.10
5
3,4
4,68 S
2,4692.10
5
2,3979.10
5
2,9
ARROW ASTER
Ref.
ASTER
Relative error %
1,00 S
6,0694.10
4
5,9846.10
4
1,4
2,00 S
2,3507.10
3
2,3362.10
3
0,6
2,68 S
8,5790.10
3
8,3929.10
3
2,2
4,68 S
9,1084.10
3
8,9530.10
3
1,7
5
Summary of the results
Results obtained using modeling beam multifibre (
POU_D_EM)
are in concord
with the conventional modeling of right beam of Euler (
POU_D_E
) of Code_Aster.