SSLL107 - Validation of MACRO_CARA

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Organization (S)

: EDF-R & D/AMA

Manual 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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Problem of reference

1.1 Geometry

The geometry of the various sections is provided via a plane mesh. 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 tensile load F=1000N.

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 the reference mark

OXY

of description of the mesh 2D for the mesh 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

in the reference mark

GXY

IX_G_M

IY_G_M

IXY_G_M

2) In the same total reference mark, for the mesh obtained by symmetrization if

SYME_X

SYME_Y

surface:

SURFACE

position of the center of gravity:

CDG_X,

CDG_Y

moments and product of inertia of surface, in the center of gravity

in the reference mark

GXY

IX_G

IY_G

IXY_G

3) In the main reference mark of inertia

GYZ

. cross-section, whose denomination corresponds to

that used with the description of the elements of neutral fiber beam

[U4.24.01].

main moments of inertia of surface in the reference mark

GYZ

, usable for the calculation of rigidity

of bending of the beam:

IY_PRIN_G

and

IZ_PRIN_G

angle of flow of the reference mark

GXY

with the main reference mark of inertia

GYZ

ALPHA

characteristic distances, compared to the center of gravity

section for calculations of

maximum stresses:

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 the reference mark

PXY

IY_PRIN_P IZ_PRIN_P

: moments of inertia in the reference mark

PYZ

Mechanical characteristics:

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Identification

Significance

Constant of torsion

Position of the center of torsion/shearing

PCTX
PCTY
AX

Coefficient of shearing

Constant of roll

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

1.3E02

0.0

4.75E02

0.0

5.0E02

0.0E+00

5.0E02

5.5E03

4.750E02

8.0E03

1.30E02

8.0E03

9.4645E03

4.750E02

5.500E03

P10

8.0E03

1.300E02

P11

8.0E03

4.75E02

P12

5.5E03

5.0E02

P13

5.0E02

P14

5.5E03

4.75E02

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Results of modeling A

4.1 Values

tested

Identification Reference Aster %

difference

SURFACE 7.39E04

7.39E04

 0.043

ALPHA 1.35E+02

1.35E+02

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

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

0.026

Z_MAX

Z_MIN 1.83E02

 1.83E02

0.005

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5 Modeling

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 the key word

CARA_GEOM

POST_ELEM

, employee

also by

MACRO_CARA_POUTRE

to calculate the geometrical characteristics of a surface

plane.

5.2

Characteristics of the mesh

30 meshs QUAD8.

5.3 Functionalities

tested

Controls

POST_ELEM CARA_GEOM

SYME_X

SYME_Y

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5.4

Reference solution

For the complete section:

(

)

[

]

(

)

[

]

(

)

[

]

81132

76714

With

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

SURFACE 7.0685745E04

7.06858E04

 7.76E05

CDG_X 0.00000E+00

0.00000E+00

CDG_Y 0.00000E+00

0.00000E+00

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

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

POST_ELEM

, employee also by

MACRO_CARA_POUTRE

to calculate them

geometrical characteristics of a level surface.

epx

epy

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

7.2

Characteristics of the mesh

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

Controls

POST_ELEM CARA_GEOM

SYME_X

SYME_Y

7.4

Reference solution

(

)

(

)

(

)

(

)

[

]

With

(

)

(

)

[

]

968

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Results of modeling C

8.1 Values

tested

Identification

Reference

Aster

% difference

SURFACE 3.60000E04

3.60000E04

 2.26E13

ALPHA 9.00000E+01

9.00000E+01

0.00E+00

CDG_X 0.00000E+00

0.00000E+00

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

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 is carried out with the key word

SYME_Y = “YES”

, 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 mesh, C of co-ordinates (0.005, 0), and 2 different groups of meshs, which
correspond each one to the vertical half of the mesh (on both sides of the axis Cy).

9.2

Characteristics of the mesh

9.3 Functionalities

tested

Controls

MACRO_CARA_POUTRE SYME_Y

YES

MACRO_CARA_POUTRE ORIG_INER

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

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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

SURFACE 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

ALL

IX_P

3.60833E08

9.24E05

GR1

IX_P

3.60833E08

9.24E05

GR2

IX_P

7.21667E08

 4.62E05

ALL

IY_P

1.72333E09

1.93E04

GR1

IY_P

1.72333E09

1.93E04

GR2

IY_P

3.44667E09

 9.67E05

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11 Modeling

11.1 Characteristics of modeling

Hollow octagonal section, which one nets a quarter.

11.2 Characteristics of the mesh

11.3 Functionalities

tested

Controls

MACRO_CARA_POUTRE SYME_Y

YES

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

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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

13.1 Characteristics of modeling

Full circular section, of radius 0.025m. the 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 AP.

The characteristics of the section are introduced into

AFFE_CARA_ELEM

via variables python.

13.2 Characteristics of the mesh

A number of meshs: 52 TRIA6, 299 QUAD8

13.3 Functionalities

tested

Controls

MACRO_CARA_POUTRE

GROUP_MA_BORD

13.4 Reference solution

[] []

06796

9635

With

13592

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

[]

With

)

(

54648

)

(

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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

SURFACE

1.963495E03

1.46E06

1.166666E+00

1.166664E+00

 1.45E04

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

6.135900E07

6.135909E07

1.54E04

0.000000E+00

1.263839E18

1.26E18

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

0.000000E+00

9.814751E41

9.81E41

Y_MAX

2.500000E02

0.00E+00

Y_MIN

 2.500000E02

0.00E+00

Z_MAX

2.500000E02

0.00E+00

Z_MIN

 2.500000E02

0.00E+00

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

Identification

Reference

Aster

% difference

DEPL

2.546479E06

1.66E14

FORC_NOD
With

1.000000E+03

0.00E+00

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15 Modeling

15.1 Characteristics of modeling

Full rectangular section, of width 0.02m and height 0.05m. It 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).

GR2

GR1

B = 0.01

H = 0.025

15.2 Characteristics of the mesh

A number of meshs: 32 QUAD8

15.3 Functionalities

tested

Controls

MACRO_CARA_POUTRE GROUP_MA

MACRO_CARA_POUTRE LENGTH

0.0002

MACRO_CARA_POUTRE CONNECTION

EMBEDDING

MACRO_CARA_POUTRE MATERIAL

15.4 Reference solution

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

PLACE

SURFACE

CDG_X

CDG_Y

IX_G

IY_G

IXY_G

All

1.00E-03

2.08E-07

3.33E-08

GR1

5.00E-04

- 1.25E-02

2.60E-08

1.67E-08

GR2

5.00E-04

1.25E-02

2.60E-08

1.67E-08

PLACE

X_P

Y_P

IX_P

IY_P

IXY_P

IY_PRIN_P

IZ_PRIN_P

All

0.00E+00

2.08E-07 3.33E-08 0

3.33E-08

2.08E-07

GR1

0.00E+00

1.04E-07 1.67E-08 0

1.67E-08

1.04E-07

GR2

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

Code_Aster

Version

6.4

Titrate:

SSLL107 - Validation of

MACRO_CARA_POUTRE

Date:

02/06/03

Author (S)

J.M. PROIX

Key:

V3.01.107-A

Page:

19/24

Manual of Validation

V3.01 booklet: Linear statics of the linear structures

HT-66/03/008/A

16 Results of modeling G

16.1 Values

tested

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

Identification

Reference

Aster

% difference

SURFACE

1.0000000E03

1.000000E03

0.00E+00

ALPHA

9.0000000E+01

9.000000E+01

0.00E+00

1.2000000E+00

1.199951E+00

 0.004

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

9.9805000E08

9.968135E08

 0.124

0.0000000E+00

1.550963E18

1.55E18

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

SURFACE

5.00000E04

2.17E14

GR1

SURFACE

5.00000E04

4.34E14

ALL

1.20000E+00

1.19924E+00

 0.064

GR1

1.20000E+00

1.19922E+00

 0.065

GR2

1.20000E+00

1.19922E+00

 0.065

GR1

1.20000E+00

1.19922E+00

 0.065

GR2

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

 4.16E14

GR1

IX_G

2.60417E08

 1.28E04

GR2

IX_G

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

 2.00E04

GR2

IY_G

1.66667E08

 2.00E04

Code_Aster

Version

6.4

Titrate:

SSLL107 - Validation of

MACRO_CARA_POUTRE

Date:

02/06/03

Author (S)

J.M. PROIX

Key:

V3.01.107-A

Page:

20/24

Manual of Validation

V3.01 booklet: Linear statics of the linear structures

HT-66/03/008/A

17 Modeling

17.1 Characteristics of modeling

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

17.2 Characteristics of the mesh

A number of meshs: 236 QUAD8

17.3 Functionalities

tested

Controls

MACRO_CARA_POUTRE GROUP_MA_BORD

17.4 Reference solution

The approximate analytical values result from [bib1].

Identificatio
N

Reference

Numerical value

SURFACE

(

)

(

)

With

29.5

4.25300E+00

1.61800E+00

CDG_X

(

)

(

)

With

6.8602

CDG_Y

L/2

=2.8 [bib1]

4984

[bib2]

2.4984 [bib2]

()

=-15.43

 15.09 [bib4]

(

)

=9.52 E+4

8.69 E+04 [bib4]

Code_Aster

Version

6.4

Titrate:

SSLL107 - Validation of

MACRO_CARA_POUTRE

Date:

02/06/03

Author (S)

J.M. PROIX

Key:

V3.01.107-A

Page:

21/24

Manual of Validation

V3.01 booklet: Linear statics of the linear structures

HT-66/03/008/A

18 Results of modeling H

18.1 Values

tested

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

Identification

Reference

Aster %

difference

SURFACE 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

8.69 E+04 [bib4]

8.711924E+04

0.253

Code_Aster

Version

6.4

Titrate:

SSLL107 - Validation of

MACRO_CARA_POUTRE

Date:

02/06/03

Author (S)

J.M. PROIX

Key:

V3.01.107-A

Page:

22/24

Manual of Validation

V3.01 booklet: Linear statics of the linear structures

HT-66/03/008/A

19 Modeling

19.1 Characteristics of modeling

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

19.2 Characteristics of the mesh

A number of meshs: 300 QUAD8

19.3 Functionalities

tested

Controls

MACRO_CARA_POUTRE GROUP_MA_BORD

MACRO_CARA_POUTRE GROUP_MA_INTE

19.4 Reference solution

(

)

5401