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
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Organization (S):
EDF/AMA, CS IF
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
V3.01.014 document
SSLL14 - Plane gantry 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 modelized with elements linear (SEG2) and subjected to four loadings (distributed or
specific).
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:
2/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
D
C
E
With
B
L
H
has
y
X
F
1
F
2
M
P
L = 20 m
H = 8 m
= 4 m have
Sections AD, EB
I
1
= 5. E4 m
4
Sections cd., EC
I
2
= 2.5 E4 m
4
The gantry consists of symmetrical beams of sections, so that IY=IZ.
One takes account only of the energy of bending, 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 AP
1.3
Boundary conditions and loadings
Feet of articulated posts A and B.
Loadings
Nodal force out of C:
F
y
= 2000 NR = F
1
Nodal force in D:
F
X
= 10 000 NR = F
2
Moment in D:
M
X
= 100 000 N.m = M
Force distributed on section cd.:
P
Z
= 3000 NR/m
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:
3/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
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].
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:
4/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
D
C
E
With
B
y
X
·
Modeling
POU_D_E
·
10 elements section by section, is 40 elements SEG2
·
Displacement in the plan: D
Z
= 0 on all the mesh
·
Feet of articulated posts A and B: D
X
= D
y
= 0
3.2
Characteristics of the mesh
Sections AD and EB: inertia
I
1
= 5e4 m
4
Sections cd. and EC: inertia
I
2
= 2.5 E4 m
4
3.3 Functionalities
tested
AFFE_CHAR_MECA
FORCE_NODALE:
FORCE_POUTRE:
Fx, Fy, Mz
Fy
CALC_ELEM
“EFGE_ELNO_DEPL”
CALC_NO
“REAC_NODA”
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:
5/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
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 3.10
6
Reaction of A Dx
4881.487
4881.47 2.10
4
Reaction of A Dy
10000.00
10000.0 2.10
4
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 3.10
6
Reaction of A Dx
5976.297
5976.31 1.10
4
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 3.10
6
Reaction of A Dx
4576.394
4576.38 2.10
4
Reaction of A Dy
5000.00
5000.0 0
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
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
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.