Code_Aster ®
Version
7.4
Titrate:
Macro-command DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE Key
:
U4.42.04-C Page
: 1/8
Organization (S): EDF-R & D/AMA
Handbook of Utilization
U4.4- booklet: Modeling
Document: U4.42.04
Macro-command DEFI_CABLE_BP
1 Goal
The goal of this command is to calculate the initial profiles of tension along the cables of
prestressed of a structure concrete. The data of calculation are the tension 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 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 operator CALC_PRECONT [U4.42.05] or by STAT_NON_LINE [U4.51.03].
Product Structure de Données of the cabl_precont type.
Handbook of Utilization
U4.4- booklet: Modeling HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Macro-command DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE Key
:
U4.42.04-C Page
: 2/8
2 Syntax
cabl_pr
[cabl_precont] = DEFI_CABLE_BP
(
MODELE
=
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]
/
MAILLE
=
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 = (
RAYON
=
radius,
[R]
LONGUEUR
=
length,
[R]
PRESENT =
l_pre,
[l_tx]
)
MAILLAGE
=
my,
[grid]
RELAXATION = (
R_J
=
rj,
[R]
)
TITER
=
l_titr, [l_tx]
);
Handbook of Utilization
U4.4- booklet: Modeling HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Macro-command DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE Key
:
U4.42.04-C Page
: 3/8
3 Operands
3.1 Operand
MODELE
MODELE = model
Concept produced by operator AFFE_MODELE [U4.41.01] allowing to define the types
finite elements assigned to the meshs of the grid.
3.2 Operand
CHAM_MATER
CHAM_MATER = chmat
Concept produced by operator AFFE_MATERIAU [U4.43.02] allowing to affect materials
with the meshs of the grid.
3.3 Operand
CARA_ELEM
CARA_ELEM = caelem
Concept produced by 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 grid 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 the characteristics specific to 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
grid 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 grid representing the cable.
/
MAILLE
=
l_maca
List meshs of the grid 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.
Handbook of Utilization
U4.4- booklet: Modeling HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Macro-command DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE Key
:
U4.42.04-C Page
: 4/8
3.6 Operand
TYPE_ANCRAGE
TYPE_ANCRAGE = l_tya
List arguments of the text type characterizing anchorings of the cable: “ACTIF” or “PASSIF”
(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 tension 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
output 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 constraints which the tensions 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 constraint (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:
radius
length
Real situation
Modeling EFF
Handbook of Utilization
U4.4- booklet: Modeling HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Macro-command DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE Key
:
U4.42.04-C Page
: 5/8
It should be noted that several rigid cones and thus several blocks are defined if key word PRESENT
two “OUI” (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 command DEFI_GROUP option TUNNEL.
methodology of extraction of the nodes contained in the cone is described in the document
U4.22.01 (command DEFI_GROUP).
/RAYON = radius
Radius of the cone.
/
LONGUEUR
=
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 “OUI” or “NON”, and make it possible to define the cone on
two anchorings (
PRESENT = (“YES”, “YES”,)
), on the first anchoring
(PRESENT = (“OUI”, “NON”,)) 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
MAILLAGE
MAILLAGE
Name of the grid on which one works. This concept is obligatory since key word CONE
is well informed. It will be removed in version 8.
3.11 Key word
RELAXATION
RELAXATION
Key word factor allowing the definition of a parameter for the taking into account of the losses of
tension by relieving of steel. This key word factor being optional, by defect losses of
tension 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:
J
R (J) =
with J in days
J + 9 × rm
surface of the concrete section
and rm =
average radius
perimeter of the concrete section
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 modelled with one
behavior of the type creep, one should not inform this key word in DEFI_CABLE_BP.
Handbook of Utilization
U4.4- booklet: Modeling HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Macro-command DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE Key
:
U4.42.04-C Page
: 6/8
3.12 Operand
TITER
TITER = 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 tension
in a cable of prestressed according to the regulations of
BPEL
The evolution of the tension (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 tension in the vicinity of anchoring
~
~
5
F (S)
~
F (S) = F (S) - X
µ
flu × F 0 + xret × F 0 + R (J) ×
×
-
× F (S)
0
1000
100
S
× y has
where S indicates the curvilinear X-coordinate along the cable. Parameters introduced into this expression
are:
·
F0
initial tension (NR);
·
X flu
standard rate of loss of tension by creep of the concrete, compared to the tension
initial;
·
xret
standard rate of loss of tension by shrinking of the concrete, compared to the tension
initial;
·
1000 relieving of steel at 1000 hours, expressed in %;
·
Its
surface of the cross-section of the cable defined in AFFE_CARA_ELEM;
·
y
stress ultimate elastic steel;
·
µ0
adimensional coefficient of relieving of prestressed steel.
R (J) is an adimensional function characterizing the evolution of relieving in time:
J
surface of the concrete section
R (J) =
with J in days and R =
average radius
J + 9 × R
m
m
perimeter of the concrete section
The function R (J) depend on the geometry of the structure, the value used is defined in
operator DEFI_CABLE_BP.
~
F (S) is the evolution of the tension 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)
2
is defined by the relation: FC (S) × F (S) = [FC (D)]
FC (S) indicates the evolution of the tension along the cable after taking into account of the losses by contact
between the cable and the concrete: FC (S) = F0 ex (
p - F - S)
indicate the cumulated angular deviation and the parameters introduced into the expression of FC (S)
are:
·
F coefficient of friction of the cable on the partly curved concrete, in rad1;
·
coefficient of friction per unit of length.
Handbook of Utilization
U4.4- booklet: Modeling HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Macro-command DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE Key
:
U4.42.04-C Page
: 7/8
Note:
·
The coefficients F,
, y and µ
1000
0 are to be informed in operator DEFI_MATERIAU
under key word BPEL_ACIER,
·
X and X
flu
ret is 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 tension by retreat to anchoring. This length is estimated using the relation
D
~
Ea Its =
(FC (S) - F (S)) ds
0
where Ea is the Young modulus of steel and the value of the retreat to anchoring. Thus Ea Its represents
the deformation energy (of the cable) due to the retreat with anchoring.
4.2 Evolution of the tension beyond the length where they apply
losses of tension by retreat to anchoring
5
F
C (S)
F (S) = F
µ
C (S) - X flu × F 0 + xret × F 0 + R (J) ×
×
-
× F
1000
0
C (S)
100
S
× y has
with the same notations as those introduced in the preceding paragraph.
Handbook of Utilization
U4.4- booklet: Modeling HT-66/05/004/A
Code_Aster ®
Version
7.4
Titrate:
Macro-command DEFI_CABLE_BP
Date:
01/02/05
Author (S):
S. MICHEL-PONNELLE, A. ASSIRE Key
:
U4.42.04-C Page
: 8/8
Intentionally white left page.
Handbook of Utilization
U4.4- booklet: Modeling HT-66/05/004/A
Outline document