Code_Aster
®
Version
7.1
Titrate:
SDNL130 -
Seismic response of a beam BA to nonlinear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key:
V5.02.130-A
Page:
1/10
Manual of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA, LMT Cachan
Manual of Validation
V5.02 booklet: Nonlinear dynamics of the linear systems
Document: V5.02.130
SDNL130 - Seismic response of a beam in
reinforced concrete (rectangular section) with behavior
nonlinear
Summary:
The problem consists in analyzing the seismic response of a concrete beam reinforced via one
modeling beam multifibre [R3.08.08]. The behavior of the beam BA is nonlinear. The concrete is
modelized with the law of behavior of Borderie in its version 1D [R7.01.07].
Code_Aster
®
Version
7.1
Titrate:
SDNL130 -
Seismic response of a beam BA to nonlinear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key:
V5.02.130-A
Page:
2/10
Manual of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A
1 Characteristics
general
1.1 Geometry
The geometry is identical to that of the cases test SSNL119 and safe SDLL130 for the reinforcements
longitudinal which is identical: 4 HA32
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
NB: the transverse reinforcements are not taken into account in calculations
1.2
Material properties
·
concrete: E = 37.272 MPa,
= 0.2,
ft
= 3.9 MPa,
FC
= 38.3 Mpa,
FC
= 2.0.10
- 3
,
G
f1
= 110 J/m,
= 2400 kg/m
3
·
steel: E = 200.000 MPa,
= 0.33,
E =
400 MPa, E
T
= 3.280 MPa,
= 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 = 45).
Code_Aster
®
Version
7.1
Titrate:
SDNL130 -
Seismic response of a beam BA to nonlinear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key:
V5.02.130-A
Page:
3/10
Manual of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
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
The reference solution is a calculation carried out using the computer code EFICOS [bib1]. It is about one
calculation multi-layer (2D) with the same models for materials. The elements do not comprise
that a point of Gauss according to their axis and the total resolution is made by an algorithm with matrix
secant.
To have comparable results in terms of localization and terms of local results
(stresses and deformations at the point of Gauss nearest to the medium of the beam), calculation with
EFICOS (1 point by element) is carried out with 10 elements per half bay whereas calculation with
Code_Aster (2 points per element) is carried out with 8 elements per half bay.
This difference in integration is the main source of the differences noted in
paragraph [§4].
Code_Aster
®
Version
7.1
Titrate:
SDNL130 -
Seismic response of a beam BA to nonlinear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key:
V5.02.130-A
Page:
4/10
Manual of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A
3 Modeling
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
9
,
39
1
=
and
Hz
F
6
,
157
2
=
(calculated with ASTER), for modal depreciation
from 5%, we find:
5
10
.
8
-
=
and
20
=
.
For the calculation of the temporal answer, the pitch of selected time is 1/100
ème
from second.
Code_Aster
®
Version
7.1
Titrate:
SDNL130 -
Seismic response of a beam BA to nonlinear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key:
V5.02.130-A
Page:
5/10
Manual of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
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”
“LABORD_1D'
“ECRO_LINE”
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”
“SURFACE”
MODEL AFFE_CHAR_MECA
DDL_IMPO
VECT_ASSE
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
CALC_CHAR_SEISME MONO_APPUI
DIRECTION
“YES”
MODEL DYNA_NON_LINE
CHAM_MATER
CARA_ELEM
INCREMENT
NEWMARK
NEWTON
EXCIT
COMP_INCR
CONVERGENCE
FILING
STAMP
PREDICTION
CHARGE
FONC_MULT
RELATION
RESI_GLOB_RELA
ITER_GLOB_MAXI
CHAM_EXCLU
LIST_INST
“TANGENT”
“ELASTIC”
“LABORD_1D'
`VMIS_CINE_LINE
'
“QUICKLY”
“ACCE”
CALC_NO OPTION
“REAC_NODA”
Code_Aster
®
Version
7.1
Titrate:
SDNL130 -
Seismic response of a beam BA to nonlinear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key:
V5.02.130-A
Page:
6/10
Manual of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
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].
- 80
- 60
- 40
- 20
0
20
40
60
80
0
5
10
15
Time (S)
ASTER
EFICOS
Appear 4-a: Reaction in the first supports according to time
- 70
- 50
- 30
- 10
10
30
50
1,6
1,8
2
2,2
2,4
2,6
2,8
3
Time (S)
ASTER
EFICOS
Appear 4-b: Detail of the reaction between 1,6 and 3 seconds
Code_Aster
®
Version
7.1
Titrate:
SDNL130 -
Seismic response of a beam BA to nonlinear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key:
V5.02.130-A
Page:
7/10
Manual of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A
- 7
- 5
- 3
- 1
1
3
5
7
0
5
10
15
Time (S)
ASTER
EFICOS
Appear 4-c: Arrow in the center according to time
- 4
- 3
- 2
- 1
0
1
2
3
4
5
6
1,6
1,8
2
2,2
2,4
2,6
2,8
3
Time (S)
ASTER
EFICOS
Appear 4-d: Detail of the arrow between 2,5 and 2,8 seconds
Code_Aster
®
Version
7.1
Titrate:
SDNL130 -
Seismic response of a beam BA to nonlinear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key:
V5.02.130-A
Page:
8/10
Manual of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A
Note:
Solution EFICOS is more oscillating because the pitch of time chosen with this code was
1/1000ème of second.
- 80
- 60
- 40
- 20
0
20
40
60
- 4
- 2
0
2
4
6
Time (S)
ASTER
EFICOS
1,75s
2,04s
2,68s
2,87s
Appear 4th: Curve reaction-arrow for the 3 first second
One carries out tests of results (
TEST_RESU
) for the reaction on the first support and the arrow with
center. One tests these values for some extremums in the 3 first second of seism,
i.e. in the neighborhoods of times 1,75s (any beginning of the nonlinear field), then 2,04s, 2,68s and
2,87s when the structure is already strongly damaged.
Note:
To have a case test not consuming unnecessarily time CPU, only the 3 first
seconds of seism are tested.
Code_Aster
®
Version
7.1
Titrate:
SDNL130 -
Seismic response of a beam BA to nonlinear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key:
V5.02.130-A
Page:
9/10
Manual of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A
ARROW
EFICOS
ASTER
Relative error %
1,75 S
1,5.10
- 3
1,7.10
- 3
13,3
2,04 S
1,3.10
- 3
1,1.10
- 3
13,1
2,68 S
5,2.10
- 3
4,7.10
- 3
9,6
2,87 S
3,4.10
- 3
3,1.10
- 3
7,9
REACTION
EFICOS
ASTER
Relative error %
1,75 S
3,7.10
4
4,2.10
4
14,3
2,00 S
3,5.10
4
3,5.10
4
0,3
2,69 S
6,8.10
5
6,7.10
5
1,7
2,87 S
4,8.10
5
4,8.10
5
0,2
It is noted that the differences in effort in the nonlinear field are very weak, whereas there is
an unquestionable difference for displacements. This difference is doubtless due to the effects
damping which exploits a great part displacements.
5 Bibliography
[1]
GHAVAMIAN HS., MAZARS J.
: Strategy of calculations simplified for the analysis of
behavior of the reinforced concrete structures: code EFICOS. French review of civil engineering
1998; 2: 61-90.
Code_Aster
®
Version
7.1
Titrate:
SDNL130 -
Seismic response of a beam BA to nonlinear behavior
Date:
15/10/03
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key:
V5.02.130-A
Page:
10/10
Manual of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A
6
Summary of the results
The results obtained with Code_Aster are in rather good agreement with those of code EFICOS.