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Date:
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Author (S):
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Key: V3.01.107-A Page: 1/24

Organization (S): EDF-R & D/AMA
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
Document: V3.01.107

SSLL107 - Validation of MACRO_CARA_POUTRE

Summary:

The whole of modelings of this test make it possible to validate the macro_commande calculation of
characteristics of section of beam, MACRO_CARA_POUTRE, for all the options suggested. Sections
studied are different according to modelings.

Modeling A validates the calculation of the characteristics of section of a corner type.
Modeling B validates the calculation of the characteristics of a circular section.
Modeling C validates the calculation of the characteristics of a rectangular section.
Modeling D validates the calculation of the characteristics of an alveolate rectangular section.
Modeling E validates the calculation of the characteristics of an octagonal section.
Modeling F validates the calculation of the characteristics of a circular section with a sequence
on a calculation of beam.
Modeling G validates the calculation of a network of 2 rectangular beams of section.
Modeling H validates the calculation of the characteristics of a mean section out of U.
Modeling I validates the calculation of the constant of torsion for a perforated section.

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1
Problem of reference

1.1 Geometry

The geometry of the various sections is provided via a plane grid. It are different for
each modeling, and will thus be described in the corresponding paragraphs.

Modeling G also implements the chained calculation of the characteristics of a section
circular, and the use of these characteristics in a calculation of a right beam, L=1m length,
in pure traction.

1.2
Material properties

Without object, except for modeling G, where the treated beam has a Young modulus of 2.E11Pa and one
Poisson's ratio of 0.3.

1.3
Boundary conditions and loadings

Without object, except for modeling G: the right beam is embedded at an end, and is subjected to
the other end with a tractive effort F=1000N.

2
Reference solution

2.1
Method of calculation used for the reference solution

Since the solutions are specific to each modeling, they are described in
corresponding paragraphs. They are drawn mainly from [bib1] and [bib2];

2.2
Results of reference

One describes here the characteristics calculated by MACRO_CARA_POUTRE [R3.08.03]:

Characteristics geometrical of the sections

1) In reference mark OXY of description of the grid 2D for the grid provided by the user
surface: AIRE_M
position of the center of gravity: CDG_X_M, CDG_Y_M
moments and product of inertia of surface, in the center of gravity G in reference mark GXY: IX_G_M,
IY_G_M, IXY_G_M
2) In the same total reference mark, for the grid obtained by symmetrization if SYME_X or SYME_Y:
surface: AIRE
position of the center of gravity: CDG_X, CDG_Y
moments and product of inertia of surface, in the center of gravity G in reference mark GXY: IX_G, IY_G,
IXY_G
3) In the principal reference mark of inertia GYZ. cross-section, whose denomination corresponds to
that used with the description of the elements of neutral fiber beam GX [U4.24.01].
principal moments of inertia of surface in reference mark GYZ, usable for the calculation of rigidity
of inflection of the beam: IY_PRIN_G and IZ_PRIN_G
angle of flow of reference mark GXY to the principal reference mark of inertia GYZ: ALPHA
characteristic distances, compared to the center of gravity G of the section for calculations of
maximum constraints: Y_MAX, Y_MIN, Z_MAX, Z_MIN and R_MAX.
4) In the total reference mark, in a point P provided by the user:
X_P Y_P: not calculation of the moments of inertia
IX_P IY_P IXY_P: moments of inertia in reference mark PXY
IY_PRIN_P IZ_PRIN_P: moments of inertia in reference mark PYZ.

Mechanical characteristics:
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Identification
Significance
CT
Constant of torsion
EY
Position of the center of torsion/shearing
EZ
Position of the center of torsion/shearing
PCTX
PCTY
AX
Coefficient of shearing
AY
Coefficient of shearing
JG
Constant of warping

2.3
Uncertainty on the solution

Analytical solution.

2.4 References
bibliographical

[1]
PILKEY W.D.: “Formulated for stress, Strain and Structural Matrices”. Wiley & Idiots,
New York, 1994.
[2]
D. BLEVINS: Formulated for natural frequency and shape mode.
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3 Modeling
With

3.1
Characteristics of modeling

Corner section:

The co-ordinates of the points are:

P1
0.0
0.0
P2
1.3E02
0.0
P3
4.75E02
0.0
P4
5.0E02
0.0E+00
P5
5.0E02
5.5E03
P6
4.750E02
8.0E03
P7
1.30E02
8.0E03
P8
9.4645E03
9.4645E03
P9
4.750E02
5.500E03
P10
8.0E03
1.300E02
P11
8.0E03
4.75E02
P12
5.5E03
5.0E02
P13
0.
5.0E02
P14
5.5E03
4.75E02

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3.2
Characteristics of the grid

182 meshs TRIA6.


3.3 Functionalities
tested

Commands



MACRO_CARA_POUTRE GROUP_MA_BORD


3.4
Reference solution

No the exact analytical solution. The values are values of nonregression.
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4
Results of modeling A

4.1 Values
tested

Identification Reference Aster %
difference
AIRE 7.39E04
7.39E04
0.043
ALPHA 1.35E+02
1.35E+02
0
CDG_X 1.53E02
1.53E02
0.131
CDG_Y 1.53E02
1.53E02
0.131
CT 1.43E08
1.60E08
11.0
EY 0.00E+00
7.13E08
0
EZ 1.60E02
1.51E02
0.001
IX_G 1.64E07
1.64E07
0.138
IXR2_P 1.41E08
1.39E08
1.295
IXY_G 9.50E08
9.49E08
0.066
IY_G 1.64E07
1.64E07
0.138
IY_PRIN_G 6.95E08 6.93E08
0.303
IYR2_P 1.41E08
1.39E08
1.295
IZ_PRIN_G 2.60E07 2.59E07
0.321
PCTX 4.00E03
4.67E03
6.66E04
PCTY 4.00E03
4.67E03
6.66E04
R_MAX 3.79E02
3.79E02
0.018
Y_MAX 3.54E02
3.54E02
0.013
Y_MIN 3.54E02
3.54E02
0.013
2.17E02
2.17E02
0.026
Z_MAX


Z_MIN 1.83E02
1.83E02
0.005

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5 Modeling
B

5.1
Characteristics of modeling

Section external circle of radius R=0.025m and thickness 0.005m. One represents only one quarter of
section. This modeling makes it possible to test key word CARA_GEOM of POST_ELEM, employee
also by MACRO_CARA_POUTRE to calculate the geometrical characteristics of a surface
plane.

y
R
G
Z
ep


5.2
Characteristics of the grid

30 meshs QUAD8.


5.3 Functionalities
tested

Commands



POST_ELEM CARA_GEOM
SYME_X
SYME_Y
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5.4
Reference solution

For the complete section:

With = [2
R - (
R
- ep) 2]
- 4
2
= 76714
.
1
10 m

I

=
I

=

-
-
=
-

y
Z
[4
R (
R ep) 4]
7
4
81132
.
1
10 m
4

I

=

-
-
p
[4
R (
R ep) 4]
2

6
Results of modeling B

6.1 Values
tested

Identification Reference
Aster %
difference
AIRE_M 1.76714E04
1.76714E04
7.76E05
CDG_X_M 1.438288E02 1.43829E02
1.25E04
CDG_Y_M 1.438288E02 1.43829E02
1.25E04
IX_G_M 8.7265757E09
8.7266E09
2.78E04
IY_G_M 8.7265757E09
8.7266E09
2.78E04
IXY_G_M 7.72837E09 7.7284E09
3.83E04
AIRE 7.0685745E04
7.06858E04
7.76E05
CDG_X 0.00000E+00
0.00000E+00
0
CDG_Y 0.00000E+00
0.00000E+00
0
IX_G 1.81132E07
1.81132E07
4.19E06
IY_G 1.81132E07
1.81132E07
4.19E06
IXY_G 0.00000E+00
0.00000E+00

IY_PRIN_G 1.81132E07 1.81132E07
4.19E06
IZ_PRIN_G 1.81132E07 1.81132E07
4.19E06
Y_MIN 2.50000E02
2.50000E02
0.00E+00
Y_MAX 2.50000E02
2.50000E02
0.00E+00
Z_MIN 2.50000E02
2.50000E02
0.00E+00
Z_MAX 2.50000E02
2.50000E02
0.00E+00
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7 Modeling
C

7.1
Characteristics of modeling

Rectangular section digs which one represents a quarter. This modeling makes it possible to test the word
key CARA_GEOM of POST_ELEM, employee also by MACRO_CARA_POUTRE to calculate them
geometrical characteristics of a level surface.


y
epy
X
G
hy
epx
hx


Hx=0.02m, Hy=0.05m, epx=0.002m, epy=0.005m.

7.2
Characteristics of the grid

The co-ordinates of the nodes are:

N1 8.00E-03 0.00E+00
N2 8.00E-03 2.00E-02
N3 0.00E+00 2.00E-02
N4 0.00E+00 2.50E-02
N5 1.00E-02 2.50E-02
N6 1.00E-02 0.00E+00
N7 8.00E-03 6.6667E-03
N8 8.00E-03 1.3333E-02
N9 4.00E-03 2.00E-02
N10 5.00E-03 2.50E-02
N11 1.00E-02 1.66667E-02
N12 1.00E-02 8.3333E-03

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7.3 Functionalities
tested

Commands



POST_ELEM CARA_GEOM
SYME_X
SYME_Y

7.4
Reference solution

With = H H
-
-
-
-
=
y Z
(H2 ep H2 ep
6
.
3 10 m
y
y) (Z
Z)
4
2
1

I

=


-
-
-
-
=
X
[3
H H

H2 ep H2 ep
10
23
.
1
m
y
Z
(y
y) (Z
) 3
Z
]
7
4
12

1
I

=


y
[3
H H


- H - ep

2

H - ep

2

10
968
.
1
-
=
Z
y
(Z
Z) (y
) 3
y
]
8
12
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8
Results of modeling C

8.1 Values
tested

Identification
Reference
Aster
% difference
AIRE 3.60000E04
3.60000E04
2.26E13
ALPHA 9.00000E+01
9.00000E+01
0.00E+00
CDG_X 0.00000E+00
0.00000E+00
0
CDG_Y 0.00000E+00
0.00000E+00
0.00E+00
IX_G 1.23000E07
1.23000E07
6.46E14
IXY_G_M 1.11111E09 1.11111E09 1.00E04
IY_G 1.96800E08
1.96800E08
2.52E13
IY_PRIN_G 1.96800E08 1.96800E08
2.52E13
IZ_PRIN_G 1.23000E07 1.23000E07
6.46E14
R_MAX 2.69258E02
2.69260E02
6.54E04
Y_MAX 2.50000E02
2.50000E02
0.00E+00
Y_MIN 2.50000E02
2.50000E02
0.00E+00
Z_MAX 1.00000E02
1.00000E02
0.00E+00
Z_MIN 1.00000E02
1.00000E02
0.00E+00

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9 Modeling
D

9.1
Characteristics of modeling

Hollow rectangular section. This modeling makes it possible to test MACRO_CARA_POUTRE to calculate
geometrical and mechanical characteristics of a level surface.
Two calculations are carried out:

first with the key word SYME_Y = “OUI is carried out”, i.e. that the section
considered is obtained by symmetry around the axis Y (alveolate section). Moreover inertias
are calculated compared to the point of co-ordinates (0, 0.025) (key word ORIG_INER),
second is carried out without symmetry, on the section with a grid, with a calculation of inertias with
center grid, C of co-ordinates (0.005, 0), and 2 different groups of meshs, which
correspond each one to the vertical half of the grid (on both sides of the axis Cy).

9.2
Characteristics of the grid
40 meshs QUAD4.
Co-ordinates of the nodes nodes of
rectangle are:
N1 0.00E+00 2.50E02
N2 0.00E+00 2.50E02
N3 1.00E02 2.50E02
N4 1.00E02 2.50E02
N5 2.00E03 2.00E02
N6 2.00E03 2.00E02
N7 8.01E03 2.00E02
N8 8.01E03 2.00E02
N9 0.00E+00 0.00E+00


9.3 Functionalities
tested

Commands



MACRO_CARA_POUTRE SYME_Y
OUI

MACRO_CARA_POUTRE ORIG_INER



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10 Results of modeling D

10.1 Values
tested

For the section symmetrized according to OY, the geometrical characteristics are:

Identification
Reference
Aster
% difference
AIRE_M 2.600E04
2.6000E04
1.25E13
AIRE 5.200E04
5.2000E04
1.25E13
ALPHA 9.000E+01
9.0000E+01
0.00E+00
CDG_X_M 5.000E03
5.0000E03
5.20E14
CDG_X 0.000E+00
0.0000E+00
0.00E+00
CDG_Y_M 0.000E+00
1.4008E18
1.40E18
CDG_Y 0.000E+00
1.4002E18
1.40E18
IX_G_M 7.21667E08
7.21667E08
4.62E05
IX_G 1.44333E07
1.44333E07
2.31E04
IX_P 4.69333E07
4.69333E07
7.10E05
IXY_G_M 0.000E+00
4.332E26
4.33E26
IXY_G 0.000E+00
4.332E26
4.33E26
IY_G_M 3.44667E09
3.446667E09
9.67E05
IY_G 1.98933E08
1.989333E08
1.68E04
IY_PRIN_G 1.98933E08 1.989333E08
1.68E04
IY_P 1.98933E08
1.989333E08
1.68E04
IZ_PRIN_G 1.44333E07
1.443333E07
2.31E04
R_MAX 2.69260E02
2.692582E02
6.54E04
Y_MAX 2.500E02
2.5000E02
0.00E+00
Y_MIN 2.500E02
2.5000E02
0.00E+00
Z_MAX 1.000E02
1.0000E02
1.73E14
Z_MIN 1.000E02
1.0000E02
1.73E14

For the not symmetrized section, the geometrical characteristics are:

Place
Identification
Reference
Aster
% difference
TOUT
IX_P
3.60833E08
3.60833E08
9.24E05
GR1
IX_P
3.60833E08
3.60833E08
9.24E05
GR2
IX_P
7.21667E08
7.21667E08
4.62E05
TOUT
IY_P
1.72333E09
1.72333E09
1.93E04
GR1
IY_P
1.72333E09
1.72333E09
1.93E04
GR2
IY_P
3.44667E09
3.44667E09
9.67E05

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11 Modeling
E

11.1 Characteristics of modeling

Hollow octagonal section, which one nets a quarter.

11.2 Characteristics of the grid
N1 2.30969E-02 0.00000E+00
N2 2.30969E-02 9.56708E-03
N3 9.56708E-03 2.30969E-02
N4 0.00000E+00 2.30969E-02
N5 2.11835E-02 0.00000E+00
N6 2.11835E-02 8.77452E-03
N7 8.77452E-03 2.11835E-02
N8 0.00000E+00 2.11835E-02


11.3 Functionalities
tested

Commands


MACRO_CARA_POUTRE SYME_Y
OUI

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12 Results of modeling E

12.1 Values
tested

For the section symmetrized according to OY, the geometrical characteristics are:

Identification
Reference
Aster
% difference
ALPHA 9.00000E+01
9.000000E+01
0.00E+00

IXY_G 0.00000E+00
0.000000E+00
0.00E+00

IY_G 7.28824E08
7.288478E08
0.003

IY_PRIN_G 7.28824E08
7.288478E08
0.003

IZ_PRIN_G 7.28824E08
7.288478E08
0.003

R_MAX 2.50000E02
2.500000E02
4.58E13

Y_MAX 2.30967E02
2.309698E02
0.001

Y_MIN 2.30967E02
2.309698E02
0.001

Z_MAX 2.30967E02
2.309698E02
0.001

Z_MIN 2.30967E02
2.309698E02
0.001

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13 Modeling
F

13.1 Characteristics of modeling

Full circular section, of radius 0.025m. Les characteristics calculated are then used
directly in a calculation of right beam (L=1m length), in pure traction (F=1000N).
Young modulus is worth 2.E11 Pa.

The characteristics of the section are introduced into AFFE_CARA_ELEM via variables python.

13.2 Characteristics of the grid

A number of meshs: 52 TRIA6, 299 QUAD8

13.3 Functionalities
tested

Commands


MACRO_CARA_POUTRE
GROUP_MA_BORD


13.4 Reference solution

With = [2
R]
3
-
2
= 9635
.
1
10 m

I

=
I

=

-
=

y
Z
[4
R]
7
4
06796
.
3
10 m
4
10
With

=
With

=


y
Z
9
4
R
- 7
C
=
I

=


X

= 13592
.
6
10
2

Pure traction of a beam of full circular section, L=1m length, subjected to a force
F=1000N:

With = [R2

]
F
U (X) =
X
EA
F
U (L) =
L
- 6
= 54648
.
2
10 m
EA
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14 Results of modeling F

14.1 Values
tested

For the section symmetrized according to OY, the geometrical characteristics are:

Identification
Reference
Aster
% difference
AIRE
1.963495E03
1.963495E03
1.46E06
AY
1.166666E+00
1.166664E+00
1.45E04
AZ
1.166666E+00
1.166664E+00
1.45E04
CDG_X
0.000000E+00
1.033285E19
1.03E19
CDG_Y
0.000000E+00
3.715818E19
3.72E19
CT
6.135900E07
6.135909E07
1.54E04
EY
0.000000E+00
1.263839E18
1.26E18
EZ
0.000000E+00
9.610445E20
9.61E20
IX_G
3.067961E07
3.067960E07
1.99E05
IXY_G
0.000000E+00
2.774478E22
2.77E22
IY_G
3.067961E07
3.067960E07
1.99E05
IY_PRIN_G 3.067961E07

3.067960E07
1.99E05
IZ_PRIN_G
3.067961E07
3.067960E07
1.99E05
JG
0.000000E+00
9.814751E41
9.81E41
Y_MAX
2.500000E02
2.500000E02
0.00E+00
Y_MIN
2.500000E02
2.500000E02
0.00E+00
Z_MAX
2.500000E02
2.500000E02
0.00E+00
Z_MIN
2.500000E02
2.500000E02
0.00E+00

For the calculation of traction of beam, the result is:

Identification
Reference
Aster
% difference
DEPL
2.546479E06
2.546479E06
1.66E14
FORC_NOD
1.000000E+03
1.000000E+03
0.00E+00
With

Handbook of Validation
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Code_Aster
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Titrate:
SSLL107 - Validation of MACRO_CARA_POUTRE


Date:
02/06/03
Author (S):
J.M. PROIX
Key: V3.01.107-A Page: 18/24

15 Modeling
G

15.1 Characteristics of modeling

Full rectangular section, of width 0.02m and height 0.05m. Elle is divided into two
rectangles respective heights 0.025m, in order to test the calculation of the characteristics on
groups of meshs for a network here made up of two parallel beams, ranging between two
floors distant of L=0.0002 (what makes it possible to obtain characteristics (coefficient of
shearing) very close to that of the complete section).
y
B
B
B = 0.01
GR2
H
H = 0.025
0
X
GR1
H


15.2 Characteristics of the grid

A number of meshs: 32 QUAD8

15.3 Functionalities
tested

Commands



MACRO_CARA_POUTRE GROUP_MA


MACRO_CARA_POUTRE LENGTH
0.0002

MACRO_CARA_POUTRE CONNECTION
ENCASTREMENT

MACRO_CARA_POUTRE MATERIAL



15.4 Reference solution

Geometrical characteristics for the complete section and each half-section:

LIEU
AIRE
CDG_X
CDG_Y
IX_G
IY_G
IXY_G
All
1.00E-03

0
0
2.08E-07
3.33E-08
0
GR1
5.00E-04

0
- 1.25E-02
2.60E-08
1.67E-08
0
GR2
5.00E-04

0
1.25E-02
2.60E-08
1.67E-08
0

LIEU
X_P


Y_P
IX_P
IY_P
IXY_P

IY_PRIN_P
IZ_PRIN_P
All
0.00E+00
0.00E+00
2.08E-07 3.33E-08 0

3.33E-08
2.08E-07

GR1
0.00E+00
0.00E+00
1.04E-07 1.67E-08 0


1.67E-08
1.04E-07

GR2
0.00E+00
0.00E+00
1.04E-07 1.67E-08 0

1.67E-08
1.04E-07



Coefficients of shearing: for each rectangular section, it is worth

Ay = Az = 2
.
1.
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16 Results of modeling G

16.1 Values
tested

For the complete section, the geometrical and mechanical characteristics are:

Identification
Reference
Aster
% difference
AIRE
1.0000000E03
1.000000E03
0.00E+00
ALPHA
9.0000000E+01
9.000000E+01
0.00E+00
AY
1.2000000E+00
1.199951E+00
0.004
AZ
1.2000000E+00
1.199218E+00
0.065
CDG_X
0.0000000E+00
1.032683E19
1.03E19
CDG_Y
0.0000000E+00
2.669725E19
2.67E19
CT
9.9805000E08
9.968135E08
0.124
EY
0.0000000E+00
1.550963E18
1.55E18
EZ
0.0000000E+00
4.792477E18
4.79E18
IX_G
2.0833333E07
2.083333E07
1.60E06
IXY_G
0.0000000E+00
1.395261E24
1.40E24
IY_G
3.3333330E08
3.333333E08
1.00E05
PCTX
0.0000000E+00
4.895746E18
4.90E18
PCTY
0.0000000E+00
1.817936E18
1.82E18
Y_MAX
2.5000000E02
2.500000E02
0.00E+00
Y_MIN
2.5000000E02
2.500000E02
0.00E+00
Z_MAX
1.0000000E02
1.000000E02
1.73E14
Z_MIN
1.0000000E02
1.000000E02
1.73E14

For the two disjoined groups, one obtains:

Identification place
Reference
Aster
% difference
GR2
AIRE
5.00000E04
5.00000E04
2.17E14
GR1
AIRE
5.00000E04
5.00000E04
4.34E14
TOUT
AY
1.20000E+00
1.19924E+00
0.064
GR1
AY
1.20000E+00
1.19922E+00
0.065
GR2
AY
1.20000E+00
1.19922E+00
0.065
GR1
AZ
1.20000E+00
1.19922E+00
0.065
GR2
AZ
1.20000E+00
1.19922E+00
0.065
GR1
CDG_X
0.00000E+00
1.59374E19
1.59E19
GR2
CDG_X
0.00000E+00
2.11345E19
2.11E19
GR1
CDG_Y
1.25000E02
1s.25000E02
1.39E14
GR2
CDG_Y
1.25000E02
1.25000E02
4.16E14
GR1
IX_G
2.60417E08
2.60417E08
1.28E04
GR2
IX_G
2.60417E08
2.60417E08
1.28E04
GR1
IXY_G
0.00000E+00
1.57868E24
1.58E24
GR2
IXY_G
0.00000E+00
1.98030E24
1.98E24
GR1
IY_G
1.66667E08
1.66667E08
2.00E04
GR2
IY_G
1.66667E08
1.66667E08
2.00E04

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Key: V3.01.107-A Page: 20/24

17 Modeling
H

17.1 Characteristics of modeling

Section out of U, of dimension l=20mm, and thickness e=0.5mm


17.2 Characteristics of the grid

A number of meshs: 236 QUAD8

17.3 Functionalities
tested

Commands



MACRO_CARA_POUTRE GROUP_MA_BORD



17.4 Reference solution

The approximate analytical values result from [bib1].

Identificatio
Reference
Numerical value
N
AIRE
With = it
2 + (L - 2nd) E = E (L
3 - 2nd)
29.5
AY

4.25300E+00
AZ

1.61800E+00
CDG_X
X = 20 + 25
.
0
- 2
/
6.8602
G
(it
(L E) E) A
CDG_Y
L/2
10
CT
12
.
1
2.4984 [bib2]
3
3
C =
L E = 12
.
1
the =2.8 [bib1]
3
I I
i=,
1 3
1
3 3
3 3
C = L E
I
I
= L E
I
I
= 2.4984 [bib2]
3
2
2
2
2
i=,
1 3
Li + E L L
I
I
+ E L
I
EY
0
0
EZ
E
=-15.43
15.09 [bib4]
Z = - xg - (3/7) L +
25
.
0
JG
J
5
= 5/84
=9.52 E+4
8.69 E+04 [bib4]
G
(
) L E
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18 Results of modeling H

18.1 Values
tested

For the complete section, the geometrical and mechanical characteristics are:

Identification
Reference
Aster %
difference
AIRE 29.5
2.9500000E+01

0.00E+00
AY 4.25300E+00
4.4862058E+00

5.483
AZ 1.61800E+00
1.916878E+00

18.472
CDG_X 6.8602 6.860169E+00

0.015
CDG_Y 10
1.00000E+01

2.31E13
CT 2.4984
2.449398E+00

1.9
EY 0 4.E-11

4.18E11
EZ 15.43 1.507743E+01

0.089
JG
8.69 E+04 [bib4]
8.711924E+04
0.253

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Date:
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Author (S):
J.M. PROIX
Key: V3.01.107-A Page: 22/24

19 Modeling
I

19.1 Characteristics of modeling

Hollow circular section, of external radius 10mm, and thickness 1mm.

19.2 Characteristics of the grid

A number of meshs: 300 QUAD8

19.3 Functionalities
tested

Commands



MACRO_CARA_POUTRE GROUP_MA_BORD


MACRO_CARA_POUTRE GROUP_MA_INTE



19.4 Reference solution

4
R
(R - E) 4
4
C
=
I

=

-
=
97
.
5401
m
X

2
2




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20 Results of modeling I

20.1 Values
tested

The constant of torsion is worth:

Identification
Reference
Aster %
difference
CT 5401.97
5391.48
0.194

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21 Summary of the results

This test makes it possible simultaneously to check the correct operation of the command
MACRO_CARA_POUTRE for various types of sections.

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