Code_Aster ®
Version
6.0
Titrate:
SSNL119 - Static Réponse of a BA beam with behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT Key
:
V6.02.119-A Page:
1/8

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

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.119

SSNL119 - Static Réponse of a concrete beam
armed (rectangular section) with behavior not
linear

Summary:

The problem consists in analyzing the response of a concrete beam reinforced via a modeling
multifibre beam [R3.08]. This test corresponds to a static analysis of a beam having a behavior
non-linear. The concrete is modelled with the law of behavior of Borderie in its version 1D [R7.01.07].

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL119 - Static Réponse of a BA beam with behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT Key
:
V6.02.119-A Page:
2/8

1 Characteristics
general

1.1 Geometry
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


1.2
Material properties

concrete: E = 37.272 MPa, = 0.2,
1
ft = 3.9 MPa, FC = 38.3 Mpa, FC = 2.0.10­3, Gf = 110 J/m

steel: E = 200.000 MPa, = 0.33, E = 400 MPa, AND = 3.280 MPa









1.3
Boundary conditions and loadings

Simple support in b: Dy = 0
Support “doubles” in a: dx = Dy = dz = 0 just as X-ray = ry = 0.

Loading: monotonous displacement Dy to the bottom applied to mid- span (deflection test 3 points).

NB: the transverse reinforcements are not taken into account in calculations.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL119 - Static Réponse of a BA beam with behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT Key
:
V6.02.119-A Page:
3/8

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) by half span while calculation
with ASTER (2 points per element) is realized with 8 elements by half span.
This difference in integration is the principal source of the differences noted in
paragraph 4.

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)


Steel is modelled by 4 specific fibers (AFFE_FIBER)

The concrete is modelled with the model of damage of Christian Borderie in version 1D
(LABORD_1D) [R7.01.07].
The parameters material used are as follows:

Y01 = 310 Pa
Y02 = 7000 Pa
A1 = 9,0.10-3 Pa1
A2 = 5,2.10-6 Pa1
B1 = 1,2
B2 = 2,0
1 = 106 Pa
2 = - 40.106 Pa
F = - 3,5.106 Pa
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL119 - Static Réponse of a BA beam with behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT Key
:
V6.02.119-A Page:
4/8

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”



“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



TOUT_SECT
“OUI”


GROUP_MA


AFFE_PONCT
CARA



VALE
“SURFACE”

MODEL AFFE_CHAR_MECA



DDL_IMPO
GROUP_NO


MODEL STAT_NON_LINE



CHAM_MATER


CARA_ELEM


EXCIT
CHARGE



FONCT_MULT


COMP_INCR
LABORD_1D



VMIS_CINE_LINE


NEWTON
MATRICE
“TANGENTE”


REAC_ITER
1

CONVERGENCE
RESI_GLOB_RELA



ITER_GLOB_MAXI


CALC_NO OPTION
“REAC_NODA”

REUSE


RESULTAT


CHAM_MATER


CARA_ELEM


EXCIT


CALC_ELEM OPTION
“EPSI_ELGA_DEPL”


REUSE


RESULTAT


MODELE


CHAM_MATER


CARA_ELEM



Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL119 - Static Réponse of a BA beam with behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT Key
:
V6.02.119-A Page:
5/8

4 Results

The following curves compare results ASTER with those of EFICOS [bib1]. Elements of
EFICOS have only one point of integration, which explains the light noted differences. Grid
EFICOS is composed of 20 elements of beam, the section is made up of 20 layers (calculation 2D).
1,4E+05
1,2E+05
1,0E+05
8,0E+04
6,0E+04
4,0E+04
ASTER
EFICOS
2,0E+04
0,0E+00
0
0,005
0,01
0,015
0,02
0,025
0,03

Be reproduced 4-a: Réaction on a support (NR) according to the arrow in the center (m)
0,012
0,01
ASTER
EFICOS
0,008
0,006
0,004
0,002
0
0
0,005
0,01
0,015
0,02
0,025
0,03

Appear 4-b: Déformation of the steels tended according to the arrow in the center
4,0E+06
3,0E+06
ASTER
EFICOS
2,0E+06
1,0E+06
0,0E+00
0
0,005
0,01
0,015
0,02
0,025
0,03

Appear 4-c: Extreme constraint concrete tended according to the arrow to the center
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL119 - Static Réponse of a BA beam with behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT Key
:
V6.02.119-A Page:
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0
0,005
0,01
0,015
0,02
0,025
0,03
0,0E+00
- 1,0E+07
ASTER
EFICOS
- 2,0E+07
- 3,0E+07
- 4,0E+07
- 5,0E+07

Appear 4-d: Extreme constraint compressed concrete according to the arrow in the center
4, E+08
3, E+08
2, E+08
ASTER
EFICOS
1, E+08
0, E+00
0
0,005
0,01
0,015
0,02
0,025
0,03

Appear 4th: Constraint steel tended according to the arrow to the center
0
0,005
0,01
0,015
0,02
0,025
0,03
- 5,0E+07
- 1,5E+08
- 2,5E+08
- 3,5E+08
ASTER
EFICOS
- 4,5E+08

Appear 4-f: Constraint steel compressed according to the arrow in the center
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL119 - Static Réponse of a BA beam with behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT Key
:
V6.02.119-A Page:
7/8

Tests of results (TEST_RESU) are carried out with each inflection on the curve arrow-reaction
[Figure 4-a], i.e. for arrows of 0,1 cm (not 2), 1,4 cm (not 12) and 3,08 cm (not 20).

PAS 2
EFICOS
ASTER
Relative error %




REACTION
1,71.104
1,78.104
4,20

Deformation



Tended steel
8,84.10-5
9,08.10-5
2,78

Constraint



Tended concrete
3,81.106
3,86.106
1,37

Constraint



Compressed concrete
­ 4,39.106
­ 4,41.106
0,46

Constraint



Tended steel
1,77.107
1,89.107
6,98

Constraint



Compressed steel
­ 2,10.107
­ 2,18.107
3,72


PAS 12
EFICOS
ASTER
Relative error %




REACTION
1,05.105
1,10.105
5,33

Deformation



Tended steel
1,90.10-3
1,93.10-3
1,72

Constraint



Tended concrete
2,64.104
2,71.104
2,67

Constraint



Compressed concrete
­ 3,35.107
­ 3,36.107
0,31

Constraint



Tended steel
3,80.108
3,97.108
4,26

Constraint



Compressed steel
­ 1,73.108
­ 1,83.108
6,19


PAS 20
EFICOS
ASTER
Relative error %




REACTION
1,24.105
1,24.105
0,07

Deformation



Tended steel
1,09.10-2
9,95.10-3
8,80

Constraint



Compressed concrete
­ 3,03.107
­ 2,98.107
1,65

Constraint



Tended steel
4,29.108
4,28.108
0,37

Constraint



Compressed steel
­ 4,01.108
­ 4,02.108
0,26


Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNL119 - Static Réponse of a BA beam with behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT Key
:
V6.02.119-A Page:
8/8

5 Bibliography

[1]
S. GHAVAMIAN, J. MAZARS: Strategy of calculations simplify for the analysis of the behavior
reinforced concrete structures: code EFICOS. Re-examined French of civil engineering 1998; 2: 61-
90

6
Summary of the results

The results obtained with Code_Aster are in rather good agreement with those of code EFICOS.

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A

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