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Version
7.1
Titrate:
SSNV164 - Mise in tension of cables of prestressing
Date:
02/06/03
Author (S):
Key S. MICHEL-PONNELLE
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Organization (S): EDF-R & D/AMA
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.164
SSNV164 - Mise in tension 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 tension of different
cables.
The functionalities particular to test are as follows:
· 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 modelled by elements
3D and calculation of the tensions in a cable under the friction effect and of the retreat of anchoring,
· operator AFFE_CHAR_MECA associated with key word RELA_CINE_BP,
· operator CALC_PRECONT: setting in tension of the cables of prestressing.
The results obtained are validated by comparison with the computer code CASTEM 2000.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
7.1
Titrate:
SSNV164 - Mise in tension of cables of prestressing
Date:
02/06/03
Author (S):
Key S. MICHEL-PONNELLE
:
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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.
1
3
0.225m
5
1m
2
4
0.225m
The five cables which cross all the length of the beam are located as on plan Ci
below:
Appear 1.1-a: Positionnement of the cables in the beam
The section of each cable is 25 cm2.
1.2
Properties of materials
Material concrete constituting the beam:
· Young modulus:
Eb = 4. 105 MPa
· Poisson's ratio:
= 0,2
· density:
= 2500 kg/m3
Material steel constituting the cable:
· Young modulus:
Eb = 1,93 105 MPa
· Poisson's ratio:
= 0,3
· density:
= 7850 kg/m3
Characteristic concerning the setting in tension of the cables:
· retreat of anchoring = 1 mm
· linear coefficient of friction: 0,0015 M-1
· force tension at the end of a cable: 3,75 106 NR
· age of dismantling 150 days
· age of setting in tension of the first cables 300 days
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
7.1
Titrate:
SSNV164 - Mise in tension of cables of prestressing
Date:
02/06/03
Author (S):
Key S. MICHEL-PONNELLE
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1.3
Boundary conditions and loadings
The base of the beam is blocked in direction Z. Les two translatory movements per report/ratio
with OX and OY are blocked as well as the rotational movement around OZ.
The sequence of loading is as follows:
· at 300 days, put in tension of 2 cables (1 and 2) by their lower end,
· at 450 days, put in tension of 2 additional cables (3 and 4) always by their end
lower,
· at 600 days, put in tension 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 grid containing
2080 cubic elements with 20 nodes and 100 elements of cable.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
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Version
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Titrate:
SSNV164 - Mise in tension of cables of prestressing
Date:
02/06/03
Author (S):
Key S. MICHEL-PONNELLE
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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 grid of the beam.
Appear 3.1-a: Description of the grid
The material concrete is defined by behaviors ELAS and BPEL_BETON: parameters
characteristics of this relation are fixed at 0 bus one does not wish to include the losses of tension
had with the shrinking and the creep of the concrete.
The material steel for the cables is defined by behaviors ELAS and BPEL_ACIER.
nonnull values for BPEL_ACIER relate to friction (FROT_LINE=1,5 10-3 M-1) and the limit
of elasticity since a zero value is illicit (SY = 1,94 1011 Pa). The radius of the cables is 2,8209
10-2 Mr.
The blocked 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 F0 tension = 3,75 106 NR is applied to the lower nodes of cables 1, 2, 3 and 4 and to both
ends for cable 5.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
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Version
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Titrate:
SSNV164 - Mise in tension of cables of prestressing
Date:
02/06/03
Author (S):
Key S. MICHEL-PONNELLE
:
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The loading is carried out in 4 steps 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, one affects to them a law of behavior “SANS” (forced null),
· T = 300 S, put in tension of cables 1 and 2: CALC_PRECONT with the boundary conditions,
cables 1 and 2 being cables to be put in tension, cables 3, 4 and 5 being inactive,
· T = 450 S, put in tension 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 tension, cable 5 being inactive,
· T = 600 S, put in tension 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
tension.
3.2
Stages of calculation and functionalities tested
The principal 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 tension 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
modelled 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 modelled by
elements 3D,
· law of behavior SANS,
· macro-command CALC_PRECONT with a nonvirgin initial state, that there is or not
inactive cables, that there are one or more cables to put in tension.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
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Titrate:
SSNV164 - Mise in tension of cables of prestressing
Date:
02/06/03
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Key S. MICHEL-PONNELLE
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4
Results of modeling A
One compares the value extracted field SIEF_ELNO_ELGA with reference obtained with CASTEM
and this for the various characteristic moments (nonnull tension) and for nodes équirépartis
along the cables.
The component to which the test relates is the tension in the cables NR.
The tolerance of relative variation compared to the reference is worth 0.1% for the phase of setting in tension then
1% for the following stages.
4.1
Tension in cable 1
T = 300 S
Node
Net
Value of reference
Computed value
Relative variation
N1 M5655 3,648.106 NR
3,6494.106 NR
0,038%
N6 M5660 3,675.106 NR
3,6769.106 NR
0,051%
N11 M5664 3,693.106 NR
3,6952.106 NR
0,059%
N16 M5670 3,667.106 NR
3,6638.106 NR
0,087%
N101 M5674
3,640.106 NR
3,6419.106 NR
0,052%
T = 450 S
Node
Net
Value of reference
Computed value
Relative variation
N1 M5655
3,561.106 NR
3,5634.106 NR
0,068%
N6 M5660
3,588.106 NR
3,5903.106 NR
0,063%
N11 M5664
3,628.106 NR
3,6132.106 NR
0,408%
N16 M5670
3,645.106 NR
3,6418.106 NR
0,088%
N101 M5674
3,629.106 NR
3,6224.106 NR
0,183%
T = 600 S
Node
Net
Value of reference
Computed value
Relative variation
N1 M5655
3,519.106 NR
3,5214.106 NR
0,069%
N6 M5660
3,546.106 NR
3,5479.106 NR
0,055%
N11 M5664
3,597.106 NR
3,5730.106 NR
0,666%
N16 M5670
3,635.106 NR
3,6308.106 NR
0,115%
N101 M5674
3,614.106 NR
3,6046.106 NR
0,260%
4.2
Tension in cable 3
T = 450 S
Node
Net
Value of reference
Computed value
Relative variation
N41 M5695
3,647.106 NR
3,6494.106 NR
0,066%
N46 M5700
3,675.106 NR
3,6769.106 NR
0,051%
N51 M5705
3,695.106 NR
3,6914.106 NR
0,097%
N56 M5710
3,667.106 NR
3,6638.106 NR
0,087%
N103 M5714
3,640.106 NR
3,6419.106 NR
0,052%
T = 600 S
Node
Net
Value of reference
Computed value
Relative variation
N41 M5695
3,605.106 NR
3,6075.106 NR
0,070%
N46 M5700
3,632.106 NR
3,6346.106 NR
0,070%
N51 M5705
3,662.106 NR
3,6720.106 NR
0,272%
N56 M5710
3,655.106 NR
3,6529.106 NR
0,058%
N103 M5714
3,625.106 NR
3,6241.106 NR
0,024%
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
7.1
Titrate:
SSNV164 - Mise in tension of cables of prestressing
Date:
02/06/03
Author (S):
Key S. MICHEL-PONNELLE
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4.3
Tension in cable 5
T = 600 S
Node
Net
Value of reference
Computed value
Relative variation
N81 M5735
3,647.106 NR
3,6494.106 NR
0,066%
N86 M5740
3,674.106 NR
3,6768.106 NR
0,078%
N91 M5745
3,695.106 NR
3,6952.106 NR
0,005%
N96 M5750
3,674.106 NR
3,6714.106 NR
0,072%
N105 M5754
3,647.106 NR
3,6494.106 NR
0,066%
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
Code_Aster ®
Version
7.1
Titrate:
SSNV164 - Mise in tension of cables of prestressing
Date:
02/06/03
Author (S):
Key S. MICHEL-PONNELLE
:
V6.04.164-A Page:
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5
Summary of the results
It is noted that the macro-command makes it possible to obtain the tension 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 tension 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 grid of reference was quadratic and calculation carried out
here used linear meshs.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/03/008/A
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