Code_Aster
®
Version
7.4
Titrate:
Macro-control DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE
Key
:
U4.42.04-C
Page
:
1/8
Instruction manual
U4.4- booklet: Modeling HT-66/05/004/A
Organization (S):
EDF-R & D/AMA
Instruction manual
U4.4- booklet: Modeling
Document: U4.42.04
Macro-control DEFI_CABLE_BP
1 Goal
The goal of this control is to calculate the initial profiles of voltage along the cables of
prestressed of a structure concrete. The data of calculation are the voltage applied at the ends and
other parameters characteristic of anchorings and materials. The relations used are those
prescribed by the BPEL 91.
The concept
cabl_precont
product can then be used by the operator
AFFE_CHAR_MECA
[U4.44.01], in order to define a mechanical loading of type
RELA_CINE_BP
, with an aim of calculating
the state of balance of the unit structure concrete/cables of prestressing. The resolution is carried out
by the operator
CALC_PRECONT
[U4.42.05] or by
STAT_NON_LINE
[U4.51.03].
Product a Structure of Data of the type
cabl_precont
.
Code_Aster
®
Version
7.4
Titrate:
Macro-control DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE
Key
:
U4.42.04-C
Page
:
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Instruction manual
U4.4- booklet: Modeling HT-66/05/004/A
2 Syntax
cabl_pr
[cabl_precont] = DEFI_CABLE_BP
(
MODEL
=
model, [model]
CHAM_MATER =
chmat,
[cham_mater]
CARA_ELEM
=
caelem, [cara_elem]
GROUP_MA_BETON
=
l_grmabe,
[l_gr_maille]
DEFI_CABLE =
(
/
GROUP_MA
=
grmaca, [gr_maille]
/
NET
=
l_maca, [l_maille]
/NOEUD_ANCRAGE
=
l_noa,
[l_noeud]
/
GROUPE_NO_ANCRAGE =
l_gnoa, [l_gr_noeud]
)
TYPE_ANCRAGE
=
l_tya,
[l_tx]
TENSION_INIT
=
f0,
[R]
RECUL_ANCRAGE
=
delta,
[R]
CONE =
(
RADIUS
=
radius,
[R]
LENGTH
=
length,
[R]
PRESENT =
l_pre,
[l_tx]
)
MESH
=
my,
[mesh]
RELIEVING =
(
R_J
=
rj,
[R]
)
TITRATE
=
l_titr, [l_tx]
);
Code_Aster
®
Version
7.4
Titrate:
Macro-control DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE
Key
:
U4.42.04-C
Page
:
3/8
Instruction manual
U4.4- booklet: Modeling HT-66/05/004/A
3 Operands
3.1 Operand
MODEL
MODEL = model
Concept produced by the operator
AFFE_MODELE
[U4.41.01] allowing to define the types
finite elements assigned to the meshs of the mesh.
3.2 Operand
CHAM_MATER
CHAM_MATER = chmat
Concept produced by the operator
AFFE_MATERIAU
[U4.43.02] allowing to affect materials
with the meshs of the mesh.
3.3 Operand
CARA_ELEM
CARA_ELEM = caelem
Concept produced by the operator
AFFE_CARA_ELEM
[U4.42.01] allowing to affect
mechanical and geometrical characteristics with the elements of the studied structure.
3.4 Operand
GROUP_MA_BETON
GROUP_MA_BETON = l_grmabe
Name of (or of) the group (S) of meshs of the mesh representing the structure concrete. One defines thus
precisely the locus of projection of the cables, preliminary stage to the determination
relations kinematics between the DDL of the nodes of the cables and the DDL of the nodes of
structure concrete.
Note: the groups of concrete meshs can have elastoplastic properties
different but characteristics suitable for
BPEL_BETON ()
must be identical.
3.5 Key word
DEFI_CABLE
DEFI_CABLE
Key word factor allowing the definition of a cable by designation of the topological entities of
mesh which represent it. The multiple occurrences are authorized, in order to be able to define
several cables.
/GROUP_MA = grmaca
Name of the group of meshs of the mesh representing the cable.
/
NET
=
l_maca
List meshs of the mesh representing the cable. Functionality incompatible with
key word CONE (to use GROUP_MA).
/NOEUD_ANCRAGE = l_noa
List nodes defining anchorings of the cable, i.e the ends. This list must
to comprise 2 arguments, neither more nor less.
/
GROUPE_NOEUD_ANCRAGE
=
l_gnoa
List groups of nodes defining anchorings. The cardinal of this list must be
less than or equal to 2. In each group of node, one will not retain like anchoring
that the first node of the group.
Code_Aster
®
Version
7.4
Titrate:
Macro-control DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE
Key
:
U4.42.04-C
Page
:
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Instruction manual
U4.4- booklet: Modeling HT-66/05/004/A
3.6 Operand
TYPE_ANCRAGE
TYPE_ANCRAGE = l_tya
List arguments of the text type characterizing anchorings of the cable:
“ACTIVE”
or
“PASSIVE”
(only licit arguments). This list must comprise 2 arguments, neither more nor less, and must be
ordinate compared to the list of the nodes defining anchorings (operand
NOEUD_ANCRAGE
above). It should be noted that if several cables are defined in DEFI_CABLE then the first
argument of TYPE_ANCRAGE applies to all the first nodes which define anchorings.
Idem for the second argument.
Note:
The operator reconstitutes the driving related path of the first to the second anchoring of the cable
by traversing the meshs which represent it. Nonthe existence of a related path enters
two anchorings causes a program stop in fatal error.
Active anchorings are those where an initial voltage is applied.
3.7 Operand
TENSION_INIT
TENSION_INIT = f0
Value of the initial force applied to active anchorings of the cables.
This value must be positive.
3.8 Operand
RECUL_ANCRAGE
RECUL_ANCRAGE = delta
Value of the retreat to active anchorings of the cables.
This value must be positive.
3.9 Key word
CONE
CONE
This key word factor makes it possible to define a geometrical volume around anchorings, and to affect, in
exit of AFFE_CHAR_MECA key word RELA_CINE_BP, with all the nodes (concrete and cable) contained
in this volume, a kinematic relation of type LIAISON_SOLIDE (rigid body). The definition
this volume makes it possible to attenuate the stresses which the voltages at the ends generate of
cables on the concrete. In reality, this phenomenon is avoided thanks to the installation of a cone
of diffusion of stress (material harder than the concrete) which distributes the force of prestressed on
a great surface of the concrete. In practice, the practically right cone being, one defined a volume
cylindrical:
length
radius
Real situation
Modeling EFF
Code_Aster
®
Version
7.4
Titrate:
Macro-control DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE
Key
:
U4.42.04-C
Page
:
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Instruction manual
U4.4- booklet: Modeling HT-66/05/004/A
It should be noted that several rigid cones and thus several blocks are defined if the PRESENT key word
two “YES” (a block per end of the cable contains) and/or if several cables are defined under
DEFI_CABLE.
Note:
In practice, the cylinder is defined by control DEFI_GROUP option TUNNEL.
methodology of extraction of the nodes contained in the cone is described in the document
U4.22.01 (control DEFI_GROUP).
/RADIUS = radius
Radius of the cone.
/
LENGTH
=
length
Length of the cone, with the curvilinear direction X-coordinate on the cable. One defines the cone as
a succession of cylinder while stopping when the overall length of the cylinders is
equalize with the parameter length.
/PRESENT = l_pre
This list must comprise 2 arguments, neither more nor less, and must be ordered in glance
list of the nodes defining anchorings (operand
NOEUD_ANCRAGE
above).
The only valid arguments are “YES” or “NOT”, and make it possible to define the cone on
two anchorings (
PRESENT = (“YES”, “YES”,)
), on the first anchoring
(PRESENT = (“YES”, “NOT”,)) or on the second anchoring
(PRESENT = (“NOT”, “YES”,)). It should be noted that if several cables are defined in
DEFI_CABLE then the first argument of PRESENT applies to all the first
nodes which define anchorings. Idem for the second argument.
3.10 Key word
MESH
MESH
Name of the mesh on which one works. This concept is obligatory since the key word
CONE
is well informed. It will be removed in version 8.
3.11 Key word
RELIEVING
RELIEVING
Key word factor allowing the definition of a parameter for the taking into account of the losses of
voltage by relieving of steel. This key word factor being optional, by defect losses of
voltage by relieving of steel are not taken into account.
R_J = rj
Value of the adimensional function R (J) characterizing the evolution of the relieving of steel
in time; for example the BPEL 91 recommends:
R J
J
J
R
m
()
= + ×
9
with
J
in days
and
m
R =
surface of the concrete section
perimeter of the concrete section
average radius
This value must be positive or null.
J
corresponds to the date (in days) for which one wants to estimate the state of stress in
structure. For the case where, in the structural analysis, the bars would be modelized with one
behavior of the type creep, one should not inform this key word in DEFI_CABLE_BP.
Code_Aster
®
Version
7.4
Titrate:
Macro-control DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE
Key
:
U4.42.04-C
Page
:
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Instruction manual
U4.4- booklet: Modeling HT-66/05/004/A
3.12 Operand
TITRATE
TITRATE = l_titr
List arguments of the text type defining a title attached to the concept
[cabl_precont]
.
4
Theoretical complement: estimate of the losses of voltage
in a cable of prestressed according to the regulations of
BPEL
The evolution of the voltage (in Newton) along a cable of prestressing is calculated by using them
relations prescribed by the BPEL. These relations are as follows:
4.1
Evolution of the voltage in the vicinity of anchoring
F S
F S
X
F
X
F
R J
F S
S
F S
flu
ret
has
y
()
~ ()
()
~ ()
~ ()
=
-
×
+
×
+
×
×
×
-
×
0
0
1000
0
5
100
µ
where
S
indicate the curvilinear X-coordinate along the cable. Parameters introduced into this expression
are:
·
0
F
initial voltage (NR);
·
flu
X
standard rate of loss of voltage by creep of the concrete, compared to the voltage
initial;
·
ret
X
standard rate of loss of voltage by shrinking of the concrete, compared to the voltage
initial;
·
1000
relieving of steel at 1000 hours, expressed in %;
·
has
S
surface of the cross-section of the cable defined in AFFE_CARA_ELEM;
·
y
stress ultimate elastic steel;
·
0
µ
adimensional coefficient of relieving of prestressed steel.
R J
()
is an adimensional function characterizing the evolution of relieving in time:
R J
J
J
R
m
()
= + ×
9
with J in days and
m
R =
surface of the concrete section
perimeter of the concrete section
average radius
The function
R J
()
depending on the geometry of the structure, the value used is defined in
the operator
DEFI_CABLE_BP
.
~ ()
F S
is the evolution of the voltage in the vicinity of anchoring after taking into account of the loss by
retreat of anchoring and the losses by contact between the cable and the concrete.
~ ()
F S
is defined by the relation:
[
]
F S
F S
F D
C
C
() ~ ()
()
×
=
2
C
F S
()
indicate the evolution of the voltage along the cable after taking into account of the losses by contact
between the cable and the concrete:
(
)
C
F S
F
F
S
()
exp
=
-
-
0
indicate the cumulated angular deviation and the parameters introduced into the expression of
C
F S
()
are:
·
F
coefficient of friction of the cable on the partly curved concrete, in rad
1
;
·
coefficient of friction per unit of length.
Code_Aster
®
Version
7.4
Titrate:
Macro-control DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE
Key
:
U4.42.04-C
Page
:
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Instruction manual
U4.4- booklet: Modeling HT-66/05/004/A
Note:
·
Coefficients
F
y
,
,
µ
1000
0
and
are to be informed in operator DEFI_MATERIAU
under key word BPEL_ACIER,
·
X
X
flu
ret
and
are to be informed in operator DEFI_MATERIAU under the key word
BPEL_BETON.
The length D intervening in the expression of
~ ()
F S
is the length to which the loss applies
of voltage by retreat to anchoring. This length is estimated using the relation
(
)
has has
C
D
E S
F S
F S ds
=
-
()
~ ()
0
where
has
E
is the Young modulus of steel and
the value of the retreat to anchoring. Thus
has has
E S
represent
the deformation energy (of the cable) due to the retreat with anchoring.
4.2 Evolution of the voltage beyond the length where they apply
losses of voltage by retreat to anchoring
F S
F S
X
F
X
F
R J
F S
S
F S
C
flu
ret
C
has
y
C
()
()
()
()
()
=
-
×
+
×
+
×
×
×
-
×
0
0
1000
0
5
100
µ
with the same notations as those introduced in the preceding paragraph.
Code_Aster
®
Version
7.4
Titrate:
Macro-control DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE
Key
:
U4.42.04-C
Page
:
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Instruction manual
U4.4- booklet: Modeling HT-66/05/004/A
Intentionally white left page.