Code_Aster ®
Version
5.7
Titrate:
SSLL112 - Circular Voûte under uniform pressure


Date:
20/08/02
Author (S):
Key J.M. PROIX
:
V3.01.112-A Page:
1/4

Organization (S): EDF/AMA
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
Document: V3.01.112

SSLL112 - Circular Voûte under uniform pressure

Summary:

This test makes it possible to check the internal efforts on the curved model of beam POU_C_T.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A

Code_Aster ®
Version
5.7
Titrate:
SSLL112 - Circular Voûte under uniform pressure


Date:
20/08/02
Author (S):
Key J.M. PROIX
:
V3.01.112-A Page:
2/4

1
Problem of reference

1.1 Geometry
1.1.1 Arch circular


R
p
y
B
With
X

Appear 1.1.1-a

Radius: R = 1 m

1.2
Properties of materials

Young modulus:
E = 2. 1011 Pa
Poisson's ratio:
= 0.3

1.3
Boundary conditions and loading

Boundary condition:

DX = DY = DZ = DRX = 0 on point A
DY = DZ = 0 on the point B

Loading: Force distributed

p = 100N/m on AB

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

Code_Aster ®
Version
5.7
Titrate:
SSLL112 - Circular Voûte under uniform pressure


Date:
20/08/02
Author (S):
Key J.M. PROIX
:
V3.01.112-A Page:
3/4

2
Reference solutions

2.1
Method of calculation used for the reference solutions

The beam of the figure [Fgure 1.1.1-a] checks the equilibrium equations (plane problem).

dN
FD
DM
V =
, N+
y = - p R,
+R V =
0
y
D
D
y

D

(p: normal constant loading divided into any point of the beam).
NR (), Vy (), Mz () indicate the efforts (normal, edge and moment bending) in a point of the vault
expressed in the local reference mark.

Their integration with the limiting conditions:

V ()
0 = 0, M ()
0 =0
y
Z

give:

V =


-

y ()
0, M () = 0, NR () = p.
R

2.2
Results of reference

Interior efforts for = 0°, 6°, 42° and 60°.

2.3
Uncertainty on the solution

Analytical solution.

2.4 References
bibliographical

[1]
Report/ratio n° 2314/A of Institut Aérotechnique “Proposition and realization of new cases
tests missing with the validation beams ASTER “

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

Code_Aster ®
Version
5.7
Titrate:
SSLL112 - Circular Voûte under uniform pressure


Date:
20/08/02
Author (S):
Key J.M. PROIX
:
V3.01.112-A Page:
4/4

3 Modeling
With

3.1
Characteristics of modeling

The model is composed of 30 elements curved beam of Timoshenko.

3.2
Characteristics of the grid

It consists of 30 elements POU_C_T.

3.3 Functionalities
tested


Commands


AFFE_CARA_ELEM
POUTRE
SECTION
CERCLE
CALC_ELEM
OPTION
EFGE_ELNO_DEPL
SIGM_ELNO_DEPL
AFFE_CHAR_MECA
FORCE_POUTRE
VY

4
Results of modeling A

4.1 Values
tested

Type of effort
Reference
Aster Variation
(%)
Vy (0°) 0.0000
5.E-5
5.E-5
Vy (6°) 0.0000
5.E-5
5.E-5
NR (60°) ­ 1.000E+02
­ 9.99E+01
0.1
MFZ (42°) 0.0000
3.93E05
3.93E05

5
Summary of the results

The normal effort in the vault (only effort not no one) is calculated with a good precision (0,1%) for
adopted modeling.

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

Outline document