Code_Aster
®
Version
6.4
Titrate:
SSNL120 - Cyclic response of the law of behavior of the concrete
Date:
16/07/03
Author (S):
S. GHAVAMIAN, L. DAVENNE, F. GATUINGT
Key
:
V6.02.120-A
Page:
1/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA, LMT Cachan
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.120
SSNL120 - Cyclic response of the law
of behavior of the concrete (model of Borderie)
Summary:
In this example one tests the model of behavior of the concrete of Borderie [R7.01.07] in his version 1D
using a multifibre element of beam [R3.08] under axial stress. The loading is composed of
traction with loading and unloading followed by compression also with loading and unloading. It
allows to test resistances in traction and compression, to highlight the phenomenon of
refermeture of fissures and to test the anelastic deformations.
Code_Aster
®
Version
6.4
Titrate:
SSNL120 - Cyclic response of the law of behavior of the concrete
Date:
16/07/03
Author (S):
S. GHAVAMIAN, L. DAVENNE, F. GATUINGT
Key
:
V6.02.120-A
Page:
2/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/03/008/A
1 Characteristics
general
1.1 Geometry
Beam comforts length unit, of square section on side unit:
1 m
With
B
X
y
1 m
Z
y
1 m
1.2
Material properties
Young modulus: E = 2. 10
10
AP
Resistance in traction: Rt = 4. 10
6
AP
Resistance in compression: Rc = 40. 10
6
AP
1.3
Boundary conditions
Embedding in a: dx = Dy = dz = 0 and X-ray = ry = rz = 0.
1.4 Loadings
One decreases to grow and the axial deformation (via a displacement imposed out of B
according to X) according to the following sequence:
Moment Deformation
0 0,0
1 1,4.10
4
2 0,5.10
4
3 1,0.10
3
4 4,0.10
3
5 2,0.10
3
6 5,0.10
3
7 0,0
2
Reference solution
The reference solution is the uniaxial response of the model for the parameters selected materials.
This solution was obtained using the code Eficos (code with multi-layer beams 2D [bib1]) in
which this law was established.
3 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
6.4
Titrate:
SSNL120 - Cyclic response of the law of behavior of the concrete
Date:
16/07/03
Author (S):
S. GHAVAMIAN, L. DAVENNE, F. GATUINGT
Key
:
V6.02.120-A
Page:
3/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/03/008/A
4 Modeling
With
4.1
Characteristics of modeling A
Longitudinal mesh of the beam:
We have 2 nodes and 1 element
(POU_D_EM)
.
With
B
The concrete part of the cross section of the beam is with a grid (
AFFE_SECT
) by 4 fibers:
Note:
The problem being 1D, only one fiber could seem sufficient, but that would lead to
to have null terms in the matrix of rigidity (the own inertia of fibers not being taken
in account) and with an error at the time of the solution of the system of equations.
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
6.4
Titrate:
SSNL120 - Cyclic response of the law of behavior of the concrete
Date:
16/07/03
Author (S):
S. GHAVAMIAN, L. DAVENNE, F. GATUINGT
Key
:
V6.02.120-A
Page:
4/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/03/008/A
4.2 Functionalities
tested
Controls
AFFE_MODELE MESH
AFFE
ALL
PHENOMENON
MODELING
“YES”
“MECHANICAL”
“POU_D_EM”
DEFI_MATERIAU
“ELAS”
“LABORD_1D'
AFFE_MATERIAU
GROUP_MA
MATER
AFFE_CARA_ELEM BEAM
ORIENTATION
AFFE_SECT
GROUP_MA
SECTION
GROUP_MA
CARA
GROUP_MA
MAILLAGE_SECT
TOUT_SECT
GROUP_MA
“ANGL_VRIL”
“YES”
MODEL AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
MODEL STAT_NON_LINE
CHAM_MATER
CARA_ELEM
EXCIT
COMP_INCR
NEWTON
CHARGE
FONCT_MULT
LABORD_1D
STAMP
“TANGENT”
CALC_NO OPTION
REUSE
RESULT
CHAM_MATER
CARA_ELEM
EXCIT
“REAC_NODA”
CALC_ELEM OPTION
REUSE
RESULT
MODEL
CHAM_MATER
CARA_ELEM
“DEGE_ELNO_DEPL”
Code_Aster
®
Version
6.4
Titrate:
SSNL120 - Cyclic response of the law of behavior of the concrete
Date:
16/07/03
Author (S):
S. GHAVAMIAN, L. DAVENNE, F. GATUINGT
Key
:
V6.02.120-A
Page:
5/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/03/008/A
5
Results of modeling A
The stress-strain curve is represented on the figure below:
- 45,0
- 40,0
- 35,0
- 30,0
- 25,0
- 20,0
- 15,0
- 10,0
- 5,0
0,0
5,0
- 5,0
- 4,0
- 3,0
- 2,0
- 1,0
0,0
1,0
Deformation (x1000)
One tests the stresses obtained for the deformations imposed on the moments indicated in
paragraph [§1.4]:
Moment Reference Aster
Relative error %
1 1,707816
10
6
1,707816
10
6
<
10
3
2 0,247022
10
6
0,247022
10
6
<
10
3
3 0,068862
10
6
0,068862
10
6
<
10
3
4 22,2404
10
6
22,2404
10
6
<
10
3
5 2,14356
10
6
2,14356
10
6
<
10
3
6 16,3512
10
6
16,3512
10
6
<
10
3
One also tests the maximum stresses (traction and compression) and the deformations
corresponding
Peaks in stress
Reference
Aster
Relative error %
Traction
Stress
Deformation
3,86138 10
6
1,036 10
4
3,86138 10
6
1,036 10
4
< 10
3
< 10
3
Compression
Stress
Deformation
40,9496 10
6
1,810
- 3
40,9496 10
6
1,810
3
< 10
3
< 10
3
Code_Aster
®
Version
6.4
Titrate:
SSNL120 - Cyclic response of the law of behavior of the concrete
Date:
16/07/03
Author (S):
S. GHAVAMIAN, L. DAVENNE, F. GATUINGT
Key
:
V6.02.120-A
Page:
6/6
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/03/008/A
6
Summary of the results
The results obtained with Code_Aster are in very good agreement with those of code EFICOS.