Code_Aster ®
Version
5.0
Titrate:
SSLL14 ­ plane Portique articulated in foot

Date
:

21/03/02
Author (S):
J.M. PROIX, L. VIVAN Key
:
V3.01.014-A Page:
1/6

Organization (S): EDF/AMA, CS IF
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
V3.01.014 document

SSLL14 - Plane Portique articulated in foot

Summary

This test relates to the study of a gantry made up of hurled beams, articulated in foot, in static analysis
linear.

The gantry is modelled with elements linear (SEG2) and subjected to four loadings (distributed or
specific).

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SSLL14 ­ plane Portique articulated in foot

Date
:

21/03/02
Author (S):
J.M. PROIX, L. VIVAN Key
:
V3.01.014-A Page:
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1
Problem of reference

1.1 Geometry

F1
L = 20 m
H = 8 m
C
= 4 m have
P
has
F2
D
E
M
H
y
With
B
X
L
Sections AD, EB
I1 = 5. E4 m4
Sections cd., EC
I2 = 2.5 E4 m4


The gantry consists of symmetrical beams of sections, so that IY=IZ.
One takes account only of the energy of inflection, because the beams are very slim. This is why them
other characteristics of section of beam do not intervene.

1.2
Material properties

Isotropic linear elastic material:

E = 2.1 E11 Pa

1.3
Boundary conditions and loadings

Feet of articulated posts A and B.

Loadings

Nodal force out of C:
Fy = ­ 2000 NR = F1
Nodal force in D:
Fx = ­ 10 000 NR = F2
Moment in D:
MX = ­ 100 000 N.m = M
Force distributed on section cd.:
Pz = ­ 3000 NR/m
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
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Titrate:
SSLL14 ­ plane Portique articulated in foot

Date
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21/03/02
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J.M. PROIX, L. VIVAN Key
:
V3.01.014-A Page:
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2
Reference solution

2.1
Method of calculation used for the reference solution

The method of calculation and the solution are exposed in the document [V3.90.01].

2.2
Results of reference

Horizontal and vertical reactions at point A.
Bending moment out of C.

Displacements horizontal and vertical of the point C.

2.3
Uncertainty on the solution

Analytical solution.

2.4 References
bibliographical

[1]
F.VOLDOIRE: Calculation of an elastic hyperstatic plane gantry [V3.90.01].
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SSLL14 ­ plane Portique articulated in foot

Date
:

21/03/02
Author (S):
J.M. PROIX, L. VIVAN Key
:
V3.01.014-A Page:
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3 Modeling
With

3.1
Characteristics of modeling

C
D
E
y
With
B
X

·
Modeling POU_D_E
·
10 elements section by section, is 40 elements SEG2
·
Displacement in the plan: Dz = 0 on all the grid
·
Feet of articulated posts A and B: Dx = Dy = 0

3.2
Characteristics of the grid

Sections AD and EB: I1 inertia = 5e4 m4

Sections cd. and EC: I2 inertia = 2.5 E4 m4

3.3 Functionalities
tested

AFFE_CHAR_MECA
FORCE_NODALE:
Fx, Fy, Mz
FORCE_POUTRE:
Fy
CALC_ELEM
“EFGE_ELNO_DEPL”

CALC_NO
“REAC_NODA”


Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
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Titrate:
SSLL14 ­ plane Portique articulated in foot

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21/03/02
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J.M. PROIX, L. VIVAN Key
:
V3.01.014-A Page:
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4
Results of modeling A

4.1 Values
tested

Loading Value
tested
Reference
Aster
% difference
Effort distributed p on CD
Displacement out of C Dx
0.0110476
0.0110472 0.003

Displacement out of C Dy
­ 0.012422374
­ 0.0124233 0.004

Moment out of C Dz
18672.994
18673.20 3.10-6

Reaction of A Dx
5175.37
5175.36 2.10-4

Reaction of A Dy
24233.24
24233.2 2.10-4





Force concentrated F1 out of C
Displacement out of C Dx
0.00000
0.0000 0

Displacement out of C Dy
­ 0.01497330
­ 0.0149734 0.005

Moment out of C Dz
41422.161
41422.40 3.10­6

Reaction of A Dx
4881.487
4881.47 2.10­4

Reaction of A Dy
10000.00
10000.0 2.10­4





Force concentrated F2 in D
Displacement out of C Dx
­ 0.03000956
­ 0.0300098 0.001

Displacement out of C Dy
­ 0.00299466
­ 0.00299450 0.005

Moment out of C Dz
8284.432
8284.34 3.10­6

Reaction of A Dx
5976.297
5976.31 1.10­4

Reaction of A Dy
4000.00
4000.0 0





Moment out of C
Displacement out of C Dx
0.0273532
0.0273536 0.001

Displacement out of C Dy
­ 0.001215646
­ 0.00121583 0.015

Moment out of C Dz
4916.724
4916.62 3.10­6

Reaction of A Dx
4576.394
4576.38 2.10­4

Reaction of A Dy
5000.00
5000.0 0
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.0
Titrate:
SSLL14 ­ plane Portique articulated in foot

Date
:

21/03/02
Author (S):
J.M. PROIX, L. VIVAN Key
:
V3.01.014-A Page:
6/6

5
Summary of the results

The results obtained with modeling POU_D_E are in very good agreement with the solution
analytical and thus validate the calculation of lattice of beams subjected to efforts specific or distributed.

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A

Outline document