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Code_Aster
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Version
7.1
Titrate:
SSNV164 - Setting in voltage of cables of prestressing
Date:
02/06/03
Author (S):
S. MICHEL-PONNELLE
Key
:
V6.04.164-A
Page:
1/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA















Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.164



SSNV164 - Setting in voltage of cables of
prestressed in a beam 3D



Summary

One considers a concrete beam reinforced with section square, composed of two sections of 10 meters
length, having respectively one and four square meters of section. The beam is vertical, weakest
section in bottom. It is embedded at its base, and contains 5 rectilinear cables of prestressing.
One tests here the phasage setting in prestressing, i.e. the setting in successive voltage of different
cables.
The functionalities particular to test are as follows:
·
the operator
DEFI_CABLE_BP
: determination of the relations kinematics between the DDL of the nodes
of a cable and DDL of the nodes “close” to a concrete structure modelized by elements
3D and calculation of the voltages in a cable under the friction effect and of the retreat of anchoring,
·
the operator
AFFE_CHAR_MECA
associated the key word
RELA_CINE_BP
,
·
the operator
CALC_PRECONT
: setting in voltage of the cables of prestressing.

The results obtained are validated by comparison with the computer code CASTEM 2000.
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Code_Aster
®
Version
7.1
Titrate:
SSNV164 - Setting in voltage of cables of prestressing
Date:
02/06/03
Author (S):
S. MICHEL-PONNELLE
Key
:
V6.04.164-A
Page:
2/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
1
Problem of reference
1.1 Geometry
One considers a concrete beam reinforced with section square, composed of two sections of 10 meters
of length, having respectively one and four square meters of section. The beam is vertical,
weaker section in bottom. It is embedded at its base, and contains 5 cables of prestressing
rectilinear.
The five cables which cross all the length of the beam are located as on plan Ci
below:
Appear 1.1-a: Positioning of the cables in the beam
The section of each cable is 25 cm
2
.

1.2
Properties of materials
Material concrete constituting the beam:
·
Young modulus:
E
B
= 4. 10
5
MPa
·
Poisson's ratio:
= 0,2
·
density:
= 2500 kg/m
3
Material steel constituting the cable:
·
Young modulus:
E
B
= 1,93 10
5
MPa
·
Poisson's ratio:
= 0,3
·
density:
= 7850 kg/m
3
Characteristic concerning the setting in voltage of the cables:
·
retreat of anchoring = 1 mm
·
linear coefficient of friction: 0,0015 m
- 1
·
force voltage at the end of a cable: 3,75 10
6
NR
·
age of dismantling 150 days
·
age of setting in voltage of the first cables 300 days
1m
0.225m
0.225m
1
3
2
4
5
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Code_Aster
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Version
7.1
Titrate:
SSNV164 - Setting in voltage of cables of prestressing
Date:
02/06/03
Author (S):
S. MICHEL-PONNELLE
Key
:
V6.04.164-A
Page:
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Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
1.3
Boundary conditions and loadings
The base of the beam is locked in direction Z. the two translatory movements per report/ratio
with OX and OY are locked as well as the rotational movement around OZ.
The sequence of loading is as follows:
·
at 300 days, put in voltage of 2 cables (1 and 2) by their lower end,
·
at 450 days, put in voltage of 2 additional cables (3 and 4) always by their end
lower,
·
at 600 days, put in voltage of the last cable (5) by its two ends.
The beam is obviously subjected to gravity.


2
Reference solution
The reference solution was obtained by the ECA with CASTEM 2000, with a mesh containing
2080 cubic elements with 20 nodes and 100 elements of cable.
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Code_Aster
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Version
7.1
Titrate:
SSNV164 - Setting in voltage of cables of prestressing
Date:
02/06/03
Author (S):
S. MICHEL-PONNELLE
Key
:
V6.04.164-A
Page:
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Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
The concrete beam is represented by 2080 elements
MECA_HEXA8
, supported per as many meshs
hexahedrons with 8 nodes. The 5 cables are represented using 20 elements
MECA_BARRE
each one
supported per as many segments with 2 nodes. The figure below shows the mesh of the beam.
Appear 3.1-a: Description of the mesh
The material concrete is defined by the behaviors
ELAS
and
BPEL_BETON
: parameters
characteristics of this relation are fixed at 0 bus one does not wish to include the losses of voltage
had with the shrinking and the creep of the concrete.
The material steel for the cables is defined by the behaviors
ELAS
and
BPEL_ACIER
.
nonnull values for
BPEL_ACIER
relate to friction (
FROT_LINE
=1,5 10
- 3
m
- 1
) and limit
of elasticity since a zero value is illicit (
SY
= 1,94 10
11
AP). The radius of the cables is 2,8209
10
- 2
Mr.

The locked DDL are as follows:
DZ
for the lower face
DX
and
DY
for the points located on the axis of symmetry of the beam
DX
for the point (0.5 0. 0.) and
DY
for the point (­ 0.5 0. 0.)

The voltage F
0
= 3,75 10
6
NR is applied to the lower nodes of cables 1, 2, 3 and 4 and to both
ends for cable 5.
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Code_Aster
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Version
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Titrate:
SSNV164 - Setting in voltage of cables of prestressing
Date:
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S. MICHEL-PONNELLE
Key
:
V6.04.164-A
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V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
The loading is carried out in 4 pitches of time:
·
T =150 S, taken into account of gravity:
STAT_NON_LINE
with the boundary conditions,
gravity and the relations kinematics for all the cables. Cables not contributing
with the rigidity of the model, to them is affected a law of behavior `
WITHOUT
'(forced null),
·
T = 300 S, put in voltage of cables 1 and 2:
CALC_PRECONT
with the boundary conditions,
cables 1 and 2 being cables to be put in voltage, cables 3, 4 and 5 being inactive,
·
T = 450 S, put in voltage of cables 3 and 4:
CALC_PRECONT
with the boundary conditions,
the relations kinematics for cables 1 and 2, cables 3 and 4 being cables to be put
in voltage, cable 5 being inactive,
·
T = 600 S, put in voltage of cable 5:
CALC_PRECONT
with the boundary conditions, them
relations kinematics for cables 1, 2, 3 and 4, cable 5 being the cable to be put in
voltage.
3.2
Stages of calculation and functionalities tested
The main stages of calculation correspond to the functionalities which one wishes to validate:
·
operator
DEFI_MATERIAU
: definition of the relations of behavior
BPEL_BETON
with
default values and
BPEL_ACIER
, in the case of loss by linear friction,
·
operator
DEFI_CABLE_BP
: determination of a profile of voltage along the cable of
prestressed, by taking of account losses by linear friction and losses by retreat
of anchoring; calculation of the coefficients of the relations kinematics between the DDL of the nodes of
cable and the DDL of the nodes “close” to the beam out of concrete, in the case of a beam
modelized by elements 3D,
·
operator
AFFE_CHAR_MECA
: definition of a loading of the type
RELA_CINE_BP (RELA_CINE = ' OUI')
,
·
operator
STAT_NON_LINE
, option
COMP_INCR
: calculation of the state of balance by holding account
loading of the type
RELA_CINE_BP
, in the case of a beam modelized by
elements 3D,
·
law of behavior
WITHOUT
,
·
macro-control
CALC_PRECONT
with a nonvirgin initial state, that there is or not
inactive cables, that there are one or more cables to put in voltage.
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Code_Aster
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Version
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Titrate:
SSNV164 - Setting in voltage of cables of prestressing
Date:
02/06/03
Author (S):
S. MICHEL-PONNELLE
Key
:
V6.04.164-A
Page:
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Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
4
Results of modeling A
One compares the value extracted the field
SIEF_ELNO_ELGA
with reference obtained with CASTEM
and this for the various characteristic moments (nonnull voltage) and for nodes équirépartis
along the cables.
The component to which the test relates is the voltage in the cables
NR
.
The tolerance of relative variation compared to the reference is worth 0.1% for the phase of setting in voltage then
1% for the following stages.
4.1
Voltage in cable 1
T = 300 S
Node
Net
Value of reference
Computed value
Relative variation
N1 M5655
3,648.10
6
NR
3,6494.10
6
NR
0,038%
N6 M5660
3,675.10
6
NR
3,6769.10
6
NR
0,051%
N11 M5664
3,693.10
6
NR
3,6952.10
6
NR
0,059%
N16 M5670
3,667.10
6
NR
3,6638.10
6
NR
­ 0,087%
N101 M5674
3,640.10
6
NR
3,6419.10
6
NR
0,052%
T = 450 S
Node
Net
Value of reference
Computed value
Relative variation
N1 M5655
3,561.10
6
NR
3,5634.10
6
NR
0,068%
N6 M5660
3,588.10
6
NR
3,5903.10
6
NR
0,063%
N11 M5664
3,628.10
6
NR
3,6132.10
6
NR
­ 0,408%
N16 M5670
3,645.10
6
NR
3,6418.10
6
NR
­ 0,088%
N101 M5674
3,629.10
6
NR
3,6224.10
6
NR
­ 0,183%

T = 600 S
Node
Net
Value of reference
Computed value
Relative variation
N1 M5655
3,519.10
6
NR
3,5214.10
6
NR
0,069%
N6 M5660
3,546.10
6
NR
3,5479.10
6
NR
0,055%
N11 M5664
3,597.10
6
NR
3,5730.10
6
NR
­ 0,666%
N16 M5670
3,635.10
6
NR
3,6308.10
6
NR
­ 0,115%
N101 M5674
3,614.10
6
NR
3,6046.10
6
NR
­ 0,260%
4.2
Voltage in cable 3
T = 450 S
Node
Net
Value of reference
Computed value
Relative variation
N41 M5695
3,647.10
6
NR
3,6494.10
6
NR
0,066%
N46 M5700
3,675.10
6
NR
3,6769.10
6
NR
0,051%
N51 M5705
3,695.10
6
NR
3,6914.10
6
NR
­ 0,097%
N56 M5710
3,667.10
6
NR
3,6638.10
6
NR
­ 0,087%
N103 M5714
3,640.10
6
NR
3,6419.10
6
NR
0,052%
T = 600 S
Node
Net
Value of reference
Computed value
Relative variation
N41 M5695
3,605.10
6
NR
3,6075.10
6
NR
0,070%
N46 M5700
3,632.10
6
NR
3,6346.10
6
NR
0,070%
N51 M5705
3,662.10
6
NR
3,6720.10
6
NR
0,272%
N56 M5710
3,655.10
6
NR
3,6529.10
6
NR
­ 0,058%
N103 M5714
3,625.10
6
NR
3,6241.10
6
NR
­ 0,024%
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Code_Aster
®
Version
7.1
Titrate:
SSNV164 - Setting in voltage of cables of prestressing
Date:
02/06/03
Author (S):
S. MICHEL-PONNELLE
Key
:
V6.04.164-A
Page:
7/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
4.3
Voltage in cable 5
T = 600 S
Node
Net
Value of reference
Computed value
Relative variation
N81 M5735
3,647.10
6
NR
3,6494.10
6
NR
0,066%
N86 M5740
3,674.10
6
NR
3,6768.10
6
NR
0,078%
N91 M5745
3,695.10
6
NR
3,6952.10
6
NR
0,005%
N96 M5750
3,674.10
6
NR
3,6714.10
6
NR
­ 0,072%
N105 M5754
3,647.10
6
NR
3,6494.10
6
NR
0,066%
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Code_Aster
®
Version
7.1
Titrate:
SSNV164 - Setting in voltage of cables of prestressing
Date:
02/06/03
Author (S):
S. MICHEL-PONNELLE
Key
:
V6.04.164-A
Page:
8/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
5
Summary of the results
It is noted that the macro-control makes it possible to obtain the voltage given by the BPEL (guaranteed by
procedure implemented by CASTEM) with a very good precision since the variation is lower than
0.1%. In addition, the effect of the setting in voltage of the cables on the remainder of the structure and in particular
on the already tended cables, is completely satisfactory since the variation enters the reference solution and it
aster calculation is lower than 1%, whereas the mesh of reference was quadratic and calculation carried out
here used linear meshs.