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Version
7.1

Titrate:
SDNL130 - Seismic Réponse 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

Organization (S): EDF-R & D/AMA, LMT Cachan

Handbook of Validation
V5.02 booklet: Nonlinear dynamics of the linear systems
Document: V5.02.130

SDNL130 - Seismic Réponse 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
modelled with the law of behavior of Borderie in its version 1D [R7.01.07].

Handbook of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A

Code_Aster ®
Version
7.1

Titrate:
SDNL130 - Seismic Réponse 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

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
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: Géométrie 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,
1
ft = 3.9 MPa, FC = 38.3 Mpa, FC = 2.0.10-3, Gf = 110 J/m,
= 2400 kg/m3

· steel: E = 200.000 MPa, = 0.33, E = 400 MPa, AND = 3.280 MPa, = 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 = 45).
Handbook of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A

Code_Aster ®
Version
7.1

Titrate:
SDNL130 - Seismic Réponse 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

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
(constraints 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 principal source of the differences noted in
paragraph [§4].

Handbook of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A

Code_Aster ®
Version
7.1

Titrate:
SDNL130 - Seismic Réponse 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

3 Modeling


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: discretization 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
9
,
39
Hz
1 =
and F
157,6 Hz
2 =
(calculated with ASTER), for modal depreciation
from 5%, we find:
5

10
.
8
-
=
and = 20.

For the calculation of the temporal answer, the step of selected time is 1/100ème of second.

Handbook of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A

Code_Aster ®
Version
7.1

Titrate:
SDNL130 - Seismic Réponse 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

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”

“LABORD_1D'
“ECRO_LINE”
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
“SURFACE”
CARA
VALE
MODEL AFFE_CHAR_MECA


DDL_IMPO
GROUP_NO
VECT_ASSE
CALC_MATR_ELEM OPTION
“RIGI_MECA”


“MASS_MECA”

“AMOR_MECA”
NUME_DDL MATR_RIGI


METHODE
“LDLT”
RENUM
“SANS”
ASSE_MATRICE MATR_ELEM

NUME_DDL
CALC_CHAR_SEISME MONO_APPUI
“OUI”
DIRECTION
MODEL DYNA_NON_LINE


CHAM_MATER


CARA_ELEM


INCREMENT


NEWMARK


NEWTON
MATRICE
“TANGENTE”

PREDICTION
“ELASTIQUE”
EXCIT
CHARGE


FONC_MULT

COMP_INCR
RELATION
“LABORD_1D'


`VMIS_CINE_LINE


'
CONVERGENCE
RESI_GLOB_RELA


ITER_GLOB_MAXI

ARCHIVAGE
CHAM_EXCLU
“VITE”

“ACCE”
LIST_INST

CALC_NO OPTION

“REAC_NODA”


Handbook of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A

Code_Aster ®
Version
7.1

Titrate:
SDNL130 - Seismic Réponse 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

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
ASTER
EFICOS
Time (S)

Appear 4-a: Réaction in the first supports according to time

50
30
10
- 10
- 30
- 50
- 70
1,6
1,8
2
2,2
2,4
2,6
2,8
3
Time (S)
ASTER
EFICOS

Appear 4-b: Détail of the reaction between 1,6 and 3 seconds
Handbook of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A

Code_Aster ®
Version
7.1

Titrate:
SDNL130 - Seismic Réponse 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

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

6
5
4
3
2
1
0
- 1
- 2
- 3
- 4
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
Handbook of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A

Code_Aster ®
Version
7.1

Titrate:
SDNL130 - Seismic Réponse 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

Note:

Solution EFICOS is more oscillating because the step of time chosen with this code was
1/1000ème of second.

60
2,87s
2,04s
40
20
0
- 20
- 40
- 60
1,75s
- 80
2,68s
- 4
- 2
0
2
4
6
Time (S)
ASTER
EFICOS

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.

Handbook of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A

Code_Aster ®
Version
7.1

Titrate:
SDNL130 - Seismic Réponse 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

FLECHE
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
­ 3,7.104
­ 4,2.104
14,3




2,00 S
3,5.104
3,5.104
0,3




2,69 S
­ 6,8.105
­ 6,7.105
1,7




2,87 S
4,8.105
4,8.105
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.
Handbook of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A

Code_Aster ®
Version
7.1

Titrate:
SDNL130 - Seismic Réponse 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

6
Summary of the results

The results obtained with Code_Aster are in rather good agreement with those of code EFICOS.
Handbook of Validation
Booklet: V5.02: Nonlinear dynamics of the linear systems
HT-66/03/008/A

Outline document