Code_Aster
®
Version
6.0
Titrate:
SSNL119 - Static response of a BA beam to behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key
:
V6.02.119-A
Page:
1/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
Organization (S):
EDF-R & D/AMA, LMT Cachan
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.119
SSNL119 - Static response 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 modelized with the law of behavior of Borderie in its version 1D [R7.01.07].
Code_Aster
®
Version
6.0
Titrate:
SSNL119 - Static response of a BA beam to behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key
:
V6.02.119-A
Page:
2/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
1 Characteristics
general
1.1 Geometry
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
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
steel: E = 200.000 MPa,
= 0.33,
E
= 400 MPa, E
T
= 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.
Code_Aster
®
Version
6.0
Titrate:
SSNL119 - Static response of a BA beam to behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key
:
V6.02.119-A
Page:
3/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
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) 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 main source of the differences noted in
paragraph 4.
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)
Steel is modelized by 4 specific fibers (
AFFE_FIBER
)
The concrete is modelized with the model of damage of Christian Borderie in version 1D
(
LABORD_1D
) [R7.01.07].
The parameters material used are as follows:
Y
01
= 310 AP
Y
02
= 7000 AP
With
1
= 9,0.10
- 3
AP
1
With
2
= 5,2.10
- 6
AP
1
B
1
= 1,2
B
2
= 2,0
1
= 10
6
AP
2
= - 40.10
6
AP
F
= - 3,5.10
6
AP
Code_Aster
®
Version
6.0
Titrate:
SSNL119 - Static response of a BA beam to behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key
:
V6.02.119-A
Page:
4/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
3.2 Functionalities
tested
Controls
CREA_MAILLAGE CREA_GROUP_MA
AFFE_MODELE MESH
AFFE
ALL
“YES”
PHENOMENON
“MECHANICAL”
MODELING
“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
“YES”
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
STAMP
“TANGENT”
REAC_ITER
1
CONVERGENCE
RESI_GLOB_RELA
ITER_GLOB_MAXI
CALC_NO OPTION
“REAC_NODA”
REUSE
RESULT
CHAM_MATER
CARA_ELEM
EXCIT
CALC_ELEM OPTION
“EPSI_ELGA_DEPL”
REUSE
RESULT
MODEL
CHAM_MATER
CARA_ELEM
Code_Aster
®
Version
6.0
Titrate:
SSNL119 - Static response of a BA beam to behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key
:
V6.02.119-A
Page:
5/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
4 Results
The following curves compare the ASTER results with those of EFICOS [bib1]. Elements of
EFICOS have only one point of integration, which explains the light noted differences. Mesh
EFICOS is composed of 20 elements of beam, the section is made up of 20 layers (calculation 2D).
0,0E+00
2,0E+04
4,0E+04
6,0E+04
8,0E+04
1,0E+05
1,2E+05
1,4E+05
0
0,005
0,01
0,015
0,02
0,025
0,03
ASTER
EFICOS
Appear 4-a:
Reaction on a support (NR) according to the arrow in the center (m)
0
0,002
0,004
0,006
0,008
0,01
0,012
0
0,005
0,01
0,015
0,02
0,025
0,03
ASTER
EFICOS
Appear 4-b:
Deformation of the steels tended according to the arrow to the center
0,0E+00
1,0E+06
2,0E+06
3,0E+06
4,0E+06
0
0,005
0,01
0,015
0,02
0,025
0,03
ASTER
EFICOS
Appear 4-c:
Extreme stress concrete tended according to the arrow to the center
Code_Aster
®
Version
6.0
Titrate:
SSNL119 - Static response of a BA beam to behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key
:
V6.02.119-A
Page:
6/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
- 5,0E+07
- 4,0E+07
- 3,0E+07
- 2,0E+07
- 1,0E+07
0,0E+00
0
0,005
0,01
0,015
0,02
0,025
0,03
ASTER
EFICOS
Appear 4-d:
Extreme stress compressed concrete according to the arrow in the center
0, E+00
1, E+08
2, E+08
3, E+08
4, E+08
0
0,005
0,01
0,015
0,02
0,025
0,03
ASTER
EFICOS
Appear 4th:
Stress steel tended according to the arrow to the center
- 4,5E+08
- 3,5E+08
- 2,5E+08
- 1,5E+08
- 5,0E+07
0
0,005
0,01
0,015
0,02
0,025
0,03
ASTER
EFICOS
Appear 4-f:
Stress steel compressed according to the arrow in the center
Code_Aster
®
Version
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Titrate:
SSNL119 - Static response of a BA beam to behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key
:
V6.02.119-A
Page:
7/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
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).
NOT 2
EFICOS
ASTER
Relative error %
REACTION
1,71.10
4
1,78.10
4
4,20
Deformation
Tended steel
8,84.10
- 5
9,08.10
- 5
2,78
Stress
Tended concrete
3,81.10
6
3,86.10
6
1,37
Stress
Compressed concrete
4,39.10
6
4,41.10
6
0,46
Stress
Tended steel
1,77.10
7
1,89.10
7
6,98
Stress
Compressed steel
2,10.10
7
2,18.10
7
3,72
NOT 12
EFICOS
ASTER
Relative error %
REACTION
1,05.10
5
1,10.10
5
5,33
Deformation
Tended steel
1,90.10
- 3
1,93.10
- 3
1,72
Stress
Tended concrete
2,64.10
4
2,71.10
4
2,67
Stress
Compressed concrete
3,35.10
7
3,36.10
7
0,31
Stress
Tended steel
3,80.10
8
3,97.10
8
4,26
Stress
Compressed steel
1,73.10
8
1,83.10
8
6,19
NOT 20
EFICOS
ASTER
Relative error %
REACTION
1,24.10
5
1,24.10
5
0,07
Deformation
Tended steel
1,09.10
- 2
9,95.10
- 3
8,80
Stress
Compressed concrete
3,03.10
7
2,98.10
7
1,65
Stress
Tended steel
4,29.10
8
4,28.10
8
0,37
Stress
Compressed steel
4,01.10
8
4,02.10
8
0,26
Code_Aster
®
Version
6.0
Titrate:
SSNL119 - Static response of a BA beam to behavior
Date:
22/11/02
Author (S):
S. MILL, L. DAVENNE, F.GATUINGT
Key
:
V6.02.119-A
Page:
8/8
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/02/001/A
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.