Code_Aster
Version
7.4
Titrate:
Macro-command MACR_CARA_POUTRE


Date:
11/02/05
Author (S):
Key J-L.FLJOU
:
U4.42.02-E Page
: 1/8

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

Handbook of Utilization
U4.4- booklet: Modeling
Document: U4.42.02

Macro-command MACR_CARA_POUTRE

1 Goal
To calculate the characteristics of a cross section of beam starting from a grid 2D of
section.

It makes it possible to build a table of values, usable by command AFFE_CARA_ELEM
[U4.42.01] to assign characteristics of cross-sections to all the finite elements of beam
(modelings POU_D_E, POU_D_T, POU_C_T, POU_D_TG, POU_D_EM, POU_D_TGM) or of bar
(modeling BARRE) of unspecified section.

The characteristics necessary are defined in the note of reference [R3.08.03]. It is:


the geometrical characteristics (which can be calculated on the complete grid, half
grid with symmetry compared to X or with Y, quarter of grid with two symmetries by
report/ratio with X and Y),

characteristics of torsion: radius of torsion, constant of rigidity in torsion, position and
eccentricity of the center of torsion for the coupling inflection-torsion,

characteristics of shearing for the models with deformations of shearing action,

characteristics of warping for the models of “open” torsion of the sections
nonsymmetrical.

Product a table containing the characteristics of the section. Values contained in this
table can be introduced directly (via python) into command AFFE_CARA_ELEM
for a calculation of the beam type.
Handbook of Utilization
U4.4- booklet: Modeling
HT-66/05/004/A

Code_Aster
Version
7.4
Titrate:
Macro-command MACR_CARA_POUTRE


Date:
11/02/05
Author (S):
Key J-L.FLJOU
:
U4.42.02-E Page
: 2/8

2 Syntax

tabl_cara_geom = MACR_CARA_POUTRE (

UNITE_MAILLAGE =/20,
[DEFAUT]
/
iuni,
[I]
INFO
=
/
1
[DEFAUT]
/2
ORIG_INER
=
/
(xp, YP),
[l_R]
/
(0.0,
0.0) [DEFAUT]

# If one only wants the characteristics geometrical:

/
|
SYME_X
=
“OUI”,
|
SYME_Y
=
“OUI”,
GROUP_MA
=
lgm, [l_gr_maille]

# If one wants the characteristics geometrical and mechanical of one
section:

/GROUP_MA_BORD
=
lgb, [l_gr_maille]
NOEUD
=
ln,
GROUP_MA_INTE
=
lgi,

# If one wants the characteristics of a network of beams between two
floors:

/GROUP_MA_BORD
=
lgb, [l_gr_maille]
GROUP_MA
=
lgm, [l_gr_maille]
LONGUEUR
=
H,
MATERIAU
=
to subdue,
[to subdue]
CONNECTION =/“KNEE JOINT”,
/“ENCASTREMENT”,
NOEUD
=
ln,
)
Handbook of Utilization
U4.4- booklet: Modeling
HT-66/05/004/A

Code_Aster
Version
7.4
Titrate:
Macro-command MACR_CARA_POUTRE


Date:
11/02/05
Author (S):
Key J-L.FLJOU
:
U4.42.02-E Page
: 3/8

3 Operands

3.1 Operand
UNITE_MAILLAGE

UNITE_MAILLAGE

Logical number of unit for the reading of the grid 2D of the section of beam which one will calculate
characteristics with the Aster format: i.e. a grid which can be read by
LIRE_MAILLAGE.

Note:

If one must call several upon MACR_CARA_POUTRE in the same command file on
the same grid or of the different grids UNITE_MAILLAGE should then be changed.

3.2 Operands
SYME_X/SYME_Y

| SYME_X

Specify that the grid provided by the user corresponds to a half grid. The calculation of
characteristics of the cross-section takes account of a symmetry compared to X = 0.

|
SYME_Y

Specify that the grid provided by the user corresponds to a half grid. The calculation of
characteristics of the cross-section takes account of a symmetry compared to Y = 0.

The simultaneous use of the two options makes it possible to provide only one quarter of the grid.

The properties of symmetry are used to accelerate the calculation of the characteristics
geometrical.

Note:

Key words SYME_X and SYME_Y are used only for the calculation of the characteristics
geometrical. Mechanical characteristics (constant of torsion, constant of
warping, coefficients of shearing) do not hold account of it. To calculate them, it is necessary
thus to net the section in entirety. This is why SYME_X and SYME_Y cannot be
informed simultaneously with GROUP_MA_BORD.

3.3
Calculation of the mechanical characteristics

GROUP_MA_BORD = lgb

lgb indicates one (or several) group of meshs (SEG2 or SEG3) describing the contour (closed) of
the section with a grid. It is the presence of this key word which involves the calculation of the characteristics
mechanics of the section (cf [U4.42.01] AFFE_CARA_ELEM, key word POUTRE).

GROUP_MA_INTE = lgi

lgi indicates one or more groups of meshs describing contours of possible holes. This
data is used for calculation of the constant of torsion.

GROUP_MA = lgm

lgm corresponds to a list of groups of meshs for which the calculation of the characteristics must
to be carried out independently. This functionality makes it possible in particular to seek them
characteristics of beam equivalent to several disjoined sections. If one wishes the calculation of
mechanical characteristics for each group of mesh, it is then necessary to give a group of
meshs of edge by section (using key word GROUP_MA_BORD). The lists lgb and lgm must
then to correspond.
Handbook of Utilization
U4.4- booklet: Modeling
HT-66/05/004/A

Code_Aster
Version
7.4
Titrate:
Macro-command MACR_CARA_POUTRE


Date:
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Author (S):
Key J-L.FLJOU
:
U4.42.02-E Page
: 4/8

ORIG_INER = (xp, YP)

This key word defines the point where the inertial characteristics of the section are calculated.
values of the moments of inertia are then provided in this point and to the center of gravity of the section
(for all the grid or for each group of mesh if GROUP_MA is specified).

NOEUD = ln,

For the calculation of the coefficients of shearing (if key word GROUP_MA_BORD is present), one is
brought to solve a thermal problem on the section (or each group of the list lgm), with
for only boundary condition a source term. This can produce messages of alarm due
with the presence of null pivots, without the quality of the result being affected. To avoid these
messages of alarm, it is possible to give a node (or a list of nodes if lgm is
data) for which the temperature is imposed.

3.4
Case of network of beams

LONGUEUR = H,
MATERIAU
=
to subdue,
LIAISON =
/“ROTULE”,
/“ENCASTREMENT”,

These three key words allow the calculation of the coefficients of shearing equivalent to one
together of parallel beams (posts) located between two floors, distant the length h.
The sections of these beams are defined by key word GROUP_MA.
They all are made up of same linear elastic material (key word MATERIAU). The connection
with the lower floor of type “embedding is”. That with the higher floor is
indicated by key word LIAISON.

Handbook of Utilization
U4.4- booklet: Modeling
HT-66/05/004/A

Code_Aster
Version
7.4
Titrate:
Macro-command MACR_CARA_POUTRE


Date:
11/02/05
Author (S):
Key J-L.FLJOU
:
U4.42.02-E Page
: 5/8

4
Definition of the produced sizes

4.1
Reference marks used for the geometrical characteristics

Two reference marks are used:

reference mark OXY of description of the grid 2D;
the principal reference mark of Gyz inertia. cross-section, whose denomination corresponds to that
used with the description of the elements of neutral fiber beam Gx [U4.42.01].

Z
Y
Y
(princi
CDG_X
stake)
Y_MAX
TESTSTEMX
_M
Z_MAX
R
y (principal)
X
Y
G
_M
_
Y
I
G
NR
Z_MIN
ALPHA
CD
X
O


Definition of the geometrical magnitudes relating to a section of beam

4.2
Sizes available in the produced table

4.2.1 Characteristics
geometrical

These characteristics are given in the table for all the grid and each group of
list lgm (which can correspond to a half or a quarter of the section if key words SYME_X or
SYME_Y are present).

4.2.1.1 Characteristics of the grid read


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

Handbook of Utilization
U4.4- booklet: Modeling
HT-66/05/004/A

Code_Aster
Version
7.4
Titrate:
Macro-command MACR_CARA_POUTRE


Date:
11/02/05
Author (S):
Key J-L.FLJOU
:
U4.42.02-E Page
: 6/8

4.2.1.2 Characteristics of the section of beam


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
principal moments of inertia of surface in the Gyz reference mark, usable for the calculation of the 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 Gyz inertia: 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.
X_P, Y_P: not calculation of the geometrical moments of inertia
IX_P, IY_P, IXY_P: geometrical moments of inertia in reference mark PXY
IY_PRIN_P, IZ_PRIN_P: moments of inertia in the Pyz reference mark.
IXR2, IYR2, IYR2_PRIN_G, IZR2_PRIN_G, IXR2_P, IYR2_P: useful characteristics for
the geometrical matrix of rigidity of elements POU_D_TG and POU_D_T_GM.

4.2.2 Characteristics
“mechanical”

These characteristics are provided in the table for all the grid and each group of mesh
list lgm.

4.2.2.1 Characteristics of torsion

constant of torsion: CT
The resolution of a stationary thermal problem of unknown factor phi makes it possible to determine
constant of torsion and stresses shear.
radius of torsion: RT
The radius of torsion “RT” can vary along external contour; indeed, for a section
unspecified, shearings due to torsion vary on the edge. One chooses to take the value of
Rt leading to shearings maximum on the external edge, i.e. the maximum value of Rt
(in absolute value) on external contour. Moreover, if the section is alveolate, there are several
“several radii of torsion”: Rt = 2 * A (K)/L (K) (or A (K) represents the surface of the cell K and L (K) sound
perimeter).
If one is satisfied to seek the maximum value of shearing, it is necessary to take the maximum of
Rt values obtained on the external edge and the cells.
Position of the center of torsion (point C) in reference mark GXY: PCTX and PCTY. One deduces some
the eccentricity of the center of torsion (component of CG in the principal reference mark of Gyz inertia): EY and
EZ.
Constant of warping (usable for modelings POU_D_TG and POU_D_TGM with
7 degrees of freedom): JG

4.2.2.2 Characteristics of shearing

The coefficients of shearing are given, in the principal reference mark of Gyz inertia, in the form of
report/ratio (> 1) of the total surface to the actually sheared surface: AY and AZ

4.3
Assignment of the sizes in AFFE_CARA_ELEM

The values contained in this table can be in command AFFE_CARA_ELEM for one
calculation of the beam type.

In AFFE_CARA_ELEM, the characteristics are to be provided in the principal reference mark of inertia (G, y, Z).
Quantities required (IY, IZ.) correspond to those calculated in the principal reference mark of inertia
defined starting from G, X, Y (IY_PRIN_G, IZ_PRIN…).

It is thus necessary to take guard with directing well the local reference mark of the elements of beam (key word
ORIENTATION of AFFE_CARA_ELEM) in order to affect the quantities correctly.

It is possible to directly provide (via variables python) the characteristics of the sections
(general) resulting from a calculation with MACR_CARA_POUTRE. This is implemented in the test
SSLL107F.
Handbook of Utilization
U4.4- booklet: Modeling
HT-66/05/004/A

Code_Aster
Version
7.4
Titrate:
Macro-command MACR_CARA_POUTRE


Date:
11/02/05
Author (S):
Key J-L.FLJOU
:
U4.42.02-E Page
: 7/8

5 Examples
of use

5.1
Characteristic of a section in angle with equal wings

(50 X 50 X 8) treated by test SSLL107A [V1.01.105].

5.1.1 Section
studied

Y
R1
To = 0.0500
E
= 0.0080
R = 0.0050
With
R1 = 0.0025
E
R
E
R1 X
With


5.1.2 Command file

TCARA = MACR_CARA_POUTRE (GROUP_MA_BORD = “LSURF”, NODE = “N1”, INFORMATION = 2)
or LSURF is the group of the linear meshs of the contour of the section.

5.1.3 Characteristics
geometrical obtained

The characteristics of the grid are identical to those of the section. They are in conformity with those
found in the “Catalog of iron and steel products OTUA: Condition of uses in construction
metal - 1959 "

AIRE_M
=
AIRE
=
7.39E-4
CDG_X_M
=
CDG_X
=
1.53148E-02
CDG_Y_M
=
CDG_Y
=
1.53148E-02
IX_G_M
=
IX_G
=
1.64141E-07
IY_G_M
=
IY_G
=
1.64141E-07
IXY_G_M
=
IXY_G
=
- 9.48843E-08
IY_PRIN_G

=
2.59025E-07
IZ_PRIN_G

=
6.92568E-08

ALPHA
= 45
2
2
OG
=
(CDG_X +CDG_Y) = 2.166E-02
Y_ MIN
= - OG
= - 2.166E - 02

2
2
Y_ MAX
=
(A-R +
cos/4
-

1)
(e-R1)
(
) R
OG
1.465E
02
1




+
-
=
Z_ MIN
= - A cos (/4)
= - 3.536E - 02
Z_ MAX
=
With cos (/4)
= 3.536E - 02
2
2
R_ MAX
=
A/2 + (A cos (/4) - OG)
= 3.792E - 02
Handbook of Utilization
U4.4- booklet: Modeling
HT-66/05/004/A

Code_Aster
Version
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Titrate:
Macro-command MACR_CARA_POUTRE


Date:
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Author (S):
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:
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: 8/8

5.1.4 Characteristics
mechanics

CT =
1.596E8
RT =
1.164E2
PCT_X = 4.665E3
PCT_Y = 4.665E3
EY =
1.51E2
EZ =
0
AY =
2.174
AZ =
2.174

5.2
Full rectangle (treaty by test ZZZZ105G)

5.2.1 Section
studied

y



B
B


B = 0.01

GR2
H
H = 0.025


3 groups of meshs are defined:
0



X
GR1 corresponds to the part y

0
GR1
H

GR2 corresponds to the part y 0

LR1 corresponds to the linear meshs of contour

5.2.2 Order

TCARS = MACR_CARA_POUTRE (GROUP_MA_BORD = “LR1”, NODE = “N64”)

5.2.3 Characteristics
geometrical obtained

LIEU
AIRE_M
CDG_X_M
CDG_Y_M
IX_G_M
IY_G_M
IXY_G_M
0.000003
1.00E-03

4.24E-18 - 3.39E-18 2.08E-07
3.33E-08
2.65E-23
GR1
5.00E-04

2.20E-17 - 1.25E-02 2.60E-08
1.67E-08
3.97E-23
GR2
5.00E-04
- 8.47E-18
1.25E-02
2.60E-08
1.67E-08
5.62E-23












LIEU

AIRE
CDG_X
CDG_Y IX_G IY_G IXY_G IY_PRIN_G IZ_PRIN_G ALPHA
0.000003
1.00E-03 4.24E-18 - 3.39E-18 2.08E-07 3.33E-08 2.65E-23 3.33E-08 2.08E-07 9.00E+01
GR1
5.00E-04 2.20E-17 - 1.25E-02 2.60E-08 1.67E-08 3.97E-23 1.67E-08 2.60E-08 9.00E+01
GR2
5.00E-04 - 8.47E-18 1.25E-02 2.60E-08 1.67E-08 5.62E-23 1.67E-08 2.60E-08 9.00E+01

LIEU
X_P


Y_P
IX_P
IY_P
IXY_P

IY_PRIN_P
IZ_PRIN_P
0.000003
0.00E+00
0.00E+00
2.08E-07 3.33E-08 2.65E-23
3.33E-08
2.08E-07

GR1
0.00E+00
0.00E+00
1.04E-07 1.67E-08 - 9.79E-23
1.67E-08
1.04E-07

GR2
0.00E+00
0.00E+00
1.04E-07 1.67E-08 3.31E-24
1.67E-08
1.04E-07


LIEU
Y_MAX
Z_MAX
Y_MIN
Z_MIN
R_MAX
0.000003
2.50E-02

1.00E-02 - 2.50E-02 - 1.00E-02 2.69E-02
GR1
2.50E-02

2.25E-02 - 2.50E-02
2.50E-03 3.36E-02
GR2
2.50E-02
- 2.50E-03 - 2.50E-02 - 2.25E-02 3.36E-02

LIEU
CT


AY





AZ
EY
EZ
PCTX
PCTY
JG

0.000003

-


-



-
-
-
-
-
-

GR1
3.43E-08
1.20E+00
1.20E+00
9.00E-17
- 3.97E-18
2.60E-17 - 1.25E-02 -

GR2
3.43E-08
1.20E+00
1.20E+00
- 4.03E-17
1.19E-16
- 1.27E-16 1.25E-02 -


LIEU
RT

0.000003 1.93871E-2
GR1
1.56391E-2
GR2
1.56391E-2

Handbook of Utilization
U4.4- booklet: Modeling
HT-66/05/004/A

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