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:
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: 1/22
Organization (S): EDF-R & D/AMA, CS IF
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U4.84.01 document
Operator COMB_SISM_MODAL
1 Goal
To calculate a dynamic response to single or multiple imposed movements.
In the case of the multiple excitation, the supports are animated different movements for one
direction given. These movements here are supposed to be décorrélés and independent.
These stresses are represented by spectra of response of oscillator representing a seism
or a shock. These spectra of oscillator can be given starting from a accélérogramme signal
seismic (real signal or synthetic signal) by command CALC_FONCTION with the key word factor
SPEC_OSCI [U4.32.04].
Operator COMB_SISM_MODAL allows to determine, in any point of the structure, the components
maximum of relative displacement, relative pseudovelocity, absolute pseudo-acceleration, them
maximum efforts generalized by element and maximum reactions to the supports.
These maxima of answer are calculated starting from the maximum answer of a simple oscillator,
associated each real clean mode taken into account. Several rules of recombination of
contributions of each clean mode and the contributions in each direction are available.
Product a concept of the mode_stat type.
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2 Syntax
R [mode_stat] = COMB_SISM_MODAL
(MODE_MECA = mode [mode_meca]
/TOUT_ORDRE
=
“OUI”
[DEFAUT]
/
NUME_ORDRE
=
l_ordre [l_I]
/
LIST_ORDRE
=
lordre
[listis]
/
NUME_MODE
=
l_mode
[l_I]
/
/
FREQ
=
l_freq
[l_R]
/
LIST_FREQ
=
lfreqr8
[listr8]
I PRECISION
=
/
1.D-3
[DEFAUT]
/
prec [R]
I CRITERION
=
/
“RELATIF”
[DEFAUT]
/
“ABSOLU”
MODE_CORR = acce [mode_stat_acce]
/
AMOR_REDUIT
=
amor
[l_R]
/
LIST_AMOR
=
lamor
[listr8]
/
AMOR_GENE
=
amogene
[matr_asse_gene_R]
MASS_INER = mass_iner [tabl_mass_iner]
EXCIT
=_F (/MONO_APPUI =/
“OUI”
/
NOEUD
=
lno
[l_noeud]
/
GROUP_NO
=
lgrno [l_gr_noeud]
/AXE = (c1, c2, c3) [l_R]
SPEC_OSCI = spec [tablecloth]
ECHELLE = echel
[R]
/
TRI_AXE = (p1, p2, p3)
[l_R]
SPEC_OSCI = spec [tablecloth]
ECHELLE = echel
[R]
/
TRI_SPEC = “YES”
[KN]
SPEC_OSCI= (spe1, spe2, spe3) [l_fonction]
ECHELLE= (ech1, ech2, ech3) [l_R]
NATURE
=
/
“ACCE”
[DEFAUT]
/
“VITE”
/
“DEPL”
)
CORR_FREQ
=
/
“OUI”
[DEFAUT]
/
“NON”
COMB_MODE
=_F (/TYPE
=
/“SRSS”
/
“CQC”
/
“DPC”
/
“ABS”
/
“DSC”
DUREE
=
S
[R]
)
COMB_DIRECTION =_F (
/TYPE
=
/“QUAD”
/
“NEWMARK”
)
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COMB_MULT_APPUI =_F (
/ALL = “YES”
/
NOEUD
=
lno
[l_noeud]
/
GROUP_NO
=lgrno [l_gr_noeud]
/TYPE_COMBI =/“QUAD”
/
“LINE”
)
DEPL_MULT_APPUI =_F (
NOM_CAS = nomcas
NUME_CAS = numcas
NOEUD_REFE = noeu
[node]
MODE_STAT = stat [mode_stat_depl]
/NOEUD = lno
[l_noeud]
/
GROUP_NO
=
lgrno
[l_gr_noeud]
I DX = dx
[R]
I DY = Dy
[R]
I DZ = dz
[R]
)
COMB_DEPL_APPUI =_F (
/ALL = “YES”
/
LIST_CAS
=
list
[l_nume]
/TYPE_COMBI =/“QUAD”
/
“LINE”
/
“ABS”
)
OPTION =
I
“DEPL”
I “QUICKLY”
I “ACCE_ABSOLU”
I “SIGM_ELNO_DEPL”
I “SIEF_ELGA_DEPL”
| “SIPO_ELNO_DEPL”
I “EFGE_ELNO_DEPL”
I “EFGE_ELNO_CART”
I “REAC_NODA”
I “FORC_NODA”
TITER = tit
[l_Kn]
INFO =/1
[DEFAUT]
/2
=_F IMPRESSION (/ALL = “YES”
[DEFAUT]
/
NIVEAU
=
I “SPEC_OSCI”
I “MASS_EFFE”
I “MAXI_GENE”
)
)
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3 Operands
3.1
Definition of the clean modes of the structure
3.1.1 Operand
MODE_MECA
MODE_MECA = mode
Name of the concept of the mode_meca type produces by one of the operators of modal analysis
MODE_ITER_SIMULT [U4.52.03] or MODE_ITER_INV [U4.52.04].
3.1.2 Operands
TOUT_ORDRE/NUME_ORDRE/NUME_MODE/LIST_ORDRE
/TOUT_ORDRE = “YES”
Default value which makes it possible to extract all the clean modes available in the concept mode.
/NUME_ORDRE = l_ordre
/NUME_MODE = l_mode
Extraction of the clean modes defined by a list l_ordre of sequence numbers (NUME_ORDRE)
or a list l_mode of numbers of modes (NUME_MODE).
/LIST_ORDRE = l_ordre
3.1.3 Operand
FREQ/LIST_FREQ/PRECISION/CRITERION
/FREQ = l_freq
Allows to extract the clean modes corresponding to a list from frequencies l_freq.
/LIST_FREQ = lfreqr8
Allows to extract the clean modes corresponding to a list of frequencies lfreqr8, definite
by operator DEFI_LIST_REEL [U4.34.01] (lfreqr8 is thus a concept of the listr8 type).
I PRECISION = prec
I CRITERION
=
These operands make it possible to indicate that one seeks all the clean modes of which
frequency is in the interval “inst ± prec”. By defect prec = 1.0D-3.
According to CRITERE =
“RELATIF” the interval of search is:
[inst (1 - prec), inst (1 + prec)]
“ABSOLU” the interval of search is:
[inst
-
prec,
inst
+
prec].
3.2
Definition of modal depreciation
Three possibilities exist to define modal depreciation: a list of reduced depreciation
provided by the user in the form of list of realities (l_R) or a concept of the listr8 type built
by operator DEFI_LIST_REEL [U4.34.01] or a matrix of damping generalized (matrix
of damping projected on the basis of real clean mode).
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3.2.1 Operand
AMOR_REDUIT
/AMOR_REDUIT = amor
This operand makes it possible to provide the list of the depreciation reduced in the form of a list of realities
(l_R). If the number of provided coefficients is lower than the numbers of clean modes taken in
count, the last coefficient is allotted to the mode corresponding and the following modes.
3.2.2 Operand
LIST_AMOR
/LIST_AMOR = lamor
This operand makes it possible to provide the list of the depreciation reduced in the form of a concept of
listr8 type. If the number of reduced depreciation is lower than the number of clean modes
taken into account, the last coefficient is affected with the following modes.
Example:
TOUT_ORDRE = “YES” LIST_AMOR = (“0.01”, “0.02”)
first mode = 0 0
. 1 and for all the other modes = 0 0
. 2
3.2.3 Operand
AMOR_GENE
/AMOR_GENE = amogene
One gives the name of the matrix of damping generalized amogene produced by the operator
PROJ_MATR_BASE [U4.63.12] or MACRO_PROJ_BASE [U4.63.11].
3.3 Operand
MASS_INER
To check the criterion of office plurality of the unit effective masses of the clean modes taken in
count in each direction, it is necessary to know the total mass of the structure.
This one is calculated by command POST_ELEM [U4.81.22] with key word MASS_INER.
Operand MASS_INER makes it possible to provide the name of the concept produced by this command.
3.4
Description of the excitation: key word EXCIT
The seismic excitation is defined by one or more spectra of oscillators. Those are calculated with
precondition by command CALC_FONCTION [U4.32.04] or read on a file by the command
LIRE_FONCTION [U4.32.02] with format “SEISME”. In both cases the produced concept is of
function type with two variables (tablecloth).
One uses for that the key word factor
EXCIT
and possibly operand CORR_FREQ.
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3.4.1 Operands
MONO_APPUI/NODE/GROUP_NO
Two situations are possible:
·
the structure is studied with the same movement of drive in all the supports: one
then use the operand MONO_APPUI = “OUI”
The key word factor EXCIT should appear only only once in this case.
·
the structure is studied with several different movements of drive (excitation multi
supports): one specifies with each occurrence of the key word factor the nodes or groups of
nodes concerned with the described excitation
/NOEUD = lno
/GROUP_NO = lgrno
3.4.2 Excitation along an axis
/
AXE = (c1, c2, c3)
SPEC_OSCI = spec
ECHELLE = echel
In this case one provides:
·
the cosine directors (c1 c2 c3) of the axis of excitation in reference mark GLOBAL of
definition of the grid: the coefficients c1, c2, c3 are renormés by the command,
·
operand SPEC_OSCI awaits only one spectrum of oscillator where spec is the name of
tablecloth to be used,
·
operand ECHELLE makes it possible to define a scale factor echel to be applied to
all points of the spectrum spec.
Example:
For an excitation with 45° compared to reference mark GLOBAL, a spectrum of ground sol_0_1
fixed with 0.1g and a scale factor allowing to simulate a fixed spectrum with 0.25g:
AXE
= (
“1.”,
“1.”,
“0.”),
SPEC_OSCI=sol_0_1,
ECHELLE=2.5,
3.4.3 Triaxial excitation with only one spectrum
/
TRI_AXE = (p1, p2, p3)
SPEC_OSCI = spec
ECHELLE = echel
In this case one provides:
·
weighting coefficients (p1 p2 p3) to apply to the spectrum of ocillator
for each direction X, Y and Z,
·
operand SPEC_OSCI awaits only one spectrum of oscillator where spec is the name of
tablecloth to be used,
·
operand ECHELLE makes it possible to define a scale factor echel to be applied to
all points of the spectrum spec, independently of the weighting coefficients
of direction.
Example:
For an excitation with a weighting of 1. in X and Y (plane horizontal) and 0.66 in
Z (vertical), a spectrum of fixed ground with 0.1g and a scale factor allowing to simulate one
fixed spectrum with 0,25g:
TRI_AXE= (“1.”, “1.”, “0.66”),
SPEC_OSCI=sol_0_1,
ECHELLE=2.5,
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3.4.4 Excitation
triaxial
with three different spectra
/
TRI_SPEC = “YES”
SPEC_OSCI = (spe1, spe2, spe3)
ECHELLE = (ech1, ech2, ech3)
In this case one provides:
·
operand TRI_SPEC: “OUI”,
·
operand SPEC_OSCI awaits three spectra of oscillators where (spe1 spe2 spe3)
is the list of the names of the tablecloths to be used,
·
operand ECHELLE makes it possible to define three scale factors (ech1 ech2 ech3)
to apply independently to all the points of each spectrum.
Example:
For an excitation spe1 in X, spe2 in Y and spe3 in Z, with three scale factors
different:
TRI_SPEC=' OUI',
SPEC_OSCI= (spe1 spe2 spe3),
ECHELLE= (ech1 ech2 ech3),
3.4.5 Operand
NATURE
NATURE
This operand makes it possible to specify the size of the spectrum of oscillator. By defect one uses one
spectrum of acceleration “ACCE”. It is possible to more rarely use of other sizes: speed
“VITE” or displacement “DEPL”.
3.4.6 Operand
CORR_FREQ
CORR_FREQ
To calculate the components of answer of speed or in acceleration starting from a spectrum
of oscillator of the size displacement (NATURE = “DEPL”) one is led to multiply each
value one or twice by R pulsation of the real clean mode (oscillating not deadened). In all
rigor the oscillator R is deadened and its own pulsation is
R
1
2
-
and R is only
own pseudo-pulsation. By defect one thus obtains:
quickly
= depl = pseudovelocity
max
R
read
acce
= 2 depl = pseudo - acceleration
max
R
read
Operand CORR_FREQ: “OUI” makes it possible to correct these values to take into account
the damping of the clean mode:
quickly
=
1 - 2 depl
= speed
max
R
read
acce
= 2 1 - 2
(
) depl
= acceleration
max
R
read
If one provides a spectrum of answer of speed (NATURE = “VITE”) operand CORR_FREQ will be
necessary to correct deplmax and accemax so necessary. In the same way for a spectrum of
response in acceleration (NATURE = “ACCE”) to correct deplmax and vitemax.
In all the cases, one will take care not to use like data SPEC a spectrum of
pseudo-size.
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3.5
Rules of combination
To evaluate one raising of the response of the structure, one reasons size by size
(internal displacement, speed or acceleration, efforts, constraints) starting from the modal values
associated the clean modes taken into account. For each size, one will treat
independently each speed, degree of freedom (fields to the nodes of displacement or
acceleration), or each component of torque (internal efforts) or constraint. It is what us
let us call the answer R in the statement of the rules of combination.
Several levels of combinations are necessary:
·
combination of the clean modes,
·
static correction by pseudo mode,
·
combination according to the directions of seism.
In the case of an analysis multi-supports, the rules of combination are modified to hold account
various excitations applied to groups of supports. It is also possible to calculate
separately primary and secondary components of the answer.
3.6
Rules of combination for an excitation mono-support
The total response of the structure R is obtained by combination of the directional answers
X-ray where X represents one of the directions of reference mark GLOBAL of definition of grid (X, Y, Z) or
a particular direction (cf operand AXE). The directional answer is given by:
R = R2 + R2 + R2
X
D
T
E
·
Rd answer combined of the modal oscillators established by key word COMB_MODE [§ 3.6.1]
·
Rt represents the correction of the static effects of the neglected modes (pseudo mode) [§ 3.6.2]
·
Re contribution of the movement of drive (Re = 0 in mono support)
The rule of combination of the directional answers is defined by key word COMB_DIRECTION
[§ 3.6.3].
3.6.1 Combination of the clean modes: key word COMB_MODE
COMB_MODE
The response of the Rd structure, in a direction of seism, is obtained by one of
possible combinations (defined by operand TYPE) of the contributions of each mode
clean taken into account. Each clean mode is regarded as an oscillator independent of
Rr answer defined by (,
R
R). The answer is read by interpolation in the spectrum of oscillator
signal of excitation in this direction.
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For an excitation mono support the Rr answer of the oscillator R is given by:
p
R
R
=
S
R
R
2
R
R
·
R modal size (displacement, generalized effort, reaction) associated the mode
clean of index R
·
Pr factor of modal participation associated the mode R in the studied direction
·
Sr value of the spectrum of answer, for example in pseudo acceleration, for
the oscillator R
Several rules of combination of the clean modes are available. They are chosen by
operand TYPE.
3.6.1.1 Combination
quadratic
TYPE = “SRSS”
This combination (Square Root off Sum off Squares) corresponds to the assumption of strict independence
oscillators associated with each clean mode:
nmod
R =
R2
D
R
r=1
Let us note that this rule of combination, although very usually used, can be badly adapted
when the assumption of independence is not checked for nearby clean modes or with
important damping.
3.6.1.2 Complete quadratic combination TYPE = “CQC”
The quadratic combination (established by DER KIUREGHIAN [bib1]) makes a correction to the rule
the preceding one by introducing coefficients of correlation depending on depreciation and on
distances between close clean modes (cf [R4.05.03]):
R = R R
D
R R
R
R
1 2
1
2
R
R
1
2
with the coefficient of correlation:
8
(+)
I J I
J
I I
J
J
I
J
ij =
2
(
- 2 2
) +
4 2
(
+ 2) + 4 2
(
+ 2 2
)
2
I
J
I J I
J
I
J
I
J
I
J
3.6.1.3 Summon absolute values TYPE = “ABS”
This combination corresponds to an assumption of complete dependence of the oscillators associated with
each clean mode:
N MOD
R =
D
rR
R =1
Let us note that this rule of combination is to be disadvised, because it is too strongly preserving and
conduit with a systematic oversizing.
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3.6.1.4 Combination with rule of the 10% TYPE = “DPC”
The close modes (of which the frequencies different from less than 10%) are initially combined by
summation of the absolute values. The values resulting from this first combination are then
combined quadratically. This method was proposed by American payment U.S. Nuclear
Regulatory Commission (Regulatory Guide 1.92 - Février 1976) to attenuate the conservatism of
preceding method. It remains at fault for structures with an own frequency spectrum
dense.
3.6.1.5 Combination of ROSENBLUETH TYPE = “DSC”
This rule (proposed by E. ROSENBLUETH and J. ELORDY [bib2]) introduced a correlation enters
modes, different from that of method CQC. The answers of the oscillators are combined by
double nap (Double Sum Combination):
R = R R
D
R R
R
R
1 2
1
2
R
R
1
2
It requires an additional data, the duration S of the “strong” phase of the seism defined by
operand DUREE.
The coefficient of correlation is then:
- 1
'
- '
2
I
J
1
ij =
+
“+”
I
I
J
J
where
2
'= 1 - 2
'
and '=
I
I
I
I
I + S I
3.6.2 Static correction by pseudo-mode: operand MODE_CORR
The modal base used is in general incomplete. The evaluation of raising response to one
seismic excitation requires, so a correction by a term representing the contribution
statics of the neglected clean modes, in each direction of seism.
For each direction of the seism, one carries out this correction, while adding to the modal base, one
pseudo-mode obtained starting from a static mode, field of displacement of the nodes of
structure subjected to a constant acceleration in the direction considered defined by:
K = M
·
K stamps rigidity of the structure
·
M stamps of mass of the structure
·
unit field in the direction of the seism
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The pseudo-mode is obtained by withdrawing the static contributions of the modes taken into account:
nmod Pr
= -
R with:
2
R =1 R
· R clean mode of index R
·
R
P factor of participation in the direction
In this direction, for each size, the contribution of the neglected modes is given by:
N MOD
R = R - R
T
S
R
r=1
Rs is the size associated with the static mode
MODE_CORR = acce
This key word makes it possible to provide it (S) field (S) of displacement of the nodes of the structure
subjected to a constant acceleration in one (or several) direction (S), field (S) calculated (S) by
operator MODE_STATIQUE with key word PSEUDO_MODE [U4.52.14]. For any direction of
seism where the answer is calculated, one calculates a pseudo-mode if acce is provided.
3.6.3 Combination according to the directions: key word COMB_DIRECTION
COMB_DIRECTION
Two rules of combination of the directional answers are available. They are selected
by operand TYPE.
3.6.3.1 Quadratic combination: TYPE = “QUAD”
This combination corresponds to the assumption of strict independence of the answers in each
direction:
R = R2 + R2 + R2
X
Y
Z
3.6.3.2 Combination of NEWMARK: TYPE = “NEWMARK”
For each direction I (X, Y, Z), one calculates the 8 values:
R = ± R
± 0 4
, R ± 0 4
, R
I
X
Y
Z
What leads, by circular shift, with 24 values and
R = max (IH)
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3.7
Case of an excitation multi-supports
Two processing are envisaged [bib 3]:
·
Calculation of the total answer
·
Calculation of the primary and secondary components of the answer
In the case of the multiple excitation, these supports are animated different movements for one
direction given. These movements here are supposed to be décorrélés and independent.
3.7.1 Calculation of the total answer
Compared to the mono-support, an additional combination is necessary. The flow diagram for treatment
becomes:
·
For each support or groups supports subscripted by I, subjected to a different excitation, one calculates
directional answers of Rxi supports defined by:
R
= R2 + R2 + R2
X I
D I
T I
I.E.(internal excitation)
-
Rdi answer combined of the modal oscillators established by key word COMB_MODE [§ 3.6.1]
-
Rti represents the correction of the static effects of the neglected modes. The term differs from
case mono support. Calculation similar but is utilized the fields of displacement of
structure subjected to a unit acceleration of support I in direction X [bib3].
-
Rei contribution of the movement of drive of support I (Rei 0 in multi-support)
established by key word DEPL_MULT_APPUI [§ 3.7.4]
·
One calculates directional answers X-ray by combination of the directional answers
Rxi supports. The rule of combination is defined by key word COMB_MULT_APPUI [§ 3.7.3].
The total answer R of the structure is obtained by combination of directional answers X-ray.
regulate combination is defined by key word COMB_DIRECTION [§ 3.6.3].
3.7.2 Partition of the primary and secondary components of the answer
For the seismic analysis of supported pipings multi, the partition of the inertial components and
quasi static of the answer can prove to be necessary for a post processing RCC-M [bib3].
3.7.2.1 Inertial primary component
It is about the inertial response induced by the accelerations imposed on anchorings (SRO). One
renewed the processing adopted for the total response by removing the contribution of the movement
of drive.
·
For each support or groups supports subscripted by I, subjected to a different excitation, one calculates
directional answers of supports primary education IH X I defined by:
2
2
IH X I = Rdi + Ti
R
-
Rdi answer combined of the modal oscillators established by key word COMB_MODE [§ 3.6.1]
-
Rti represents the correction of the static effects of the neglected modes. The term differs from
case mono support. Calculation similar but is utilized the fields of displacement of
structure subjected to a unit acceleration of support I in direction X [bib3].
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·
One calculates directional answers X-ray by combination of the directional answers
Rxi supports. The rule of combination is defined by key word COMB_MULT_APPUI [§ 3.7.3].
The total answer R of the structure is obtained by combination of directional answers X-ray.
regulate combination is defined by key word COMB_DIRECTION [§ 3.6.3].
3.7.2.2 Differential secondary component
It is about the static response induced by seismic differential displacements of anchorings
(movement of drive):
· Calculation of the Rei contribution of the movement of drive of support I established by the key word
DEPL_MULT_APPUI [§ 3.7.4]
·
Combinations of the various contributions of Rei support defined by the key word
COMB_DEPL_APPUI [§ 3.7.5].
It is thus possible to reconstitute:
·
lawful loading cases corresponding to:
- an overall movement of part of the supports in a given direction
- a displacement mentioned in a local reference mark different from the total reference mark of stress
seismic inertial
· answers directional by combining the adequate contributions of supports
· the total secondary answer.
Examples are proposed in [§ 3.7.5.6].
3.7.3 Key word COMB_MULT_APPUI
COMB_MULT_APPUI
The occurrences of this key word make it possible to define the directional combinations of support
to form the total response of the structure.
If the occurrences of key word COMB_DEPL_APPUI are present, it is the primary component
answer which is treated.
The combination of the contributions of each movement of support can be combined of
various manners, defined by operand TYPE_COMBI:
·
quadratic combination
·
linear combination
3.7.3.1 Operands
ALL/NODE/GROUP_NO
/ALL = “YES”
Allows to choose that all the supports are combined with the rule defined by TYPE
/
NOEUD
=
lno
[l_noeud]
/GROUP_NO = lgrno
[l_group_no]
Allows to define the list of the supports (or groups of supports) which are combined with the rule
defined by operand TYPE_COMBI in the same occurrence of the key word
COMB_MULT_APPUI.
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3.7.3.2 Combination
quadratic
TYPE = “QUAD”
R = R2
X
Xj
3.7.3.3 Combination
linear
TYPE = “LINE”
R = R
X
Xk
3.7.3.4 Different rules of combination on the various supports
The rule of combination can be the same one for all the supports [§ 3.7.3.1] or differentiated according to
supports or groups of supports defined by an occurrence of the key word factor
COMB_MULT_APPUI. In this case the total answer - or the primary component of the answer if
COMB_DEPL_APPUI is present - is obtained by:
R = 2
R +
Xj
(RXk) 2
where J indicates the supports combined quadratically and K linearly combined supports.
3.7.4 Word
key
DEPL_MULT_APPUI
DEPL_MULT_APPUI
The movement of drive of the structure not being uniform this key word makes it possible to define
contribution to the total response of a list of supports or groups of supports. This one is established with
to leave the static modes of the structure:
I
E
R = siimax
with:
if
static mode for support I
imax maximum displacement of support I compared to a support of reference (for
which I max = 0)
3.7.4.1 Operand
NOM_CAS/NUME_CAS
NOM_CAS = nomcas
Character string defining the name of the loading case
NUME_CAS = numecas
Number of the loading case
3.7.4.2 Operand
MODE_STAT
MODE_STAT = stat
Name of the static modes if, concept of the mode_stat type produces by the operator
MODE_STATIQUE [U4.52.14]
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3.7.4.3 Operand
NOEUD_REFE
NOEUD_REFE = noeu
Node of reference per report/ratio to which relative displacements of the supports are defined.
If this operand is present, the maximum displacement applied to support I is worth
-
imax
where
is affected displacement with the node of reference noeu in the direction considered.
3.7.4.4 Operands
NODE/GROUP_NO
/NOEUD = lno
/GROUP_NO = lgrno
List names of nodes (or groups of nodes) corresponding to the supports concerned with
occurrence of the key word factor DEPL_MULT_APPUI.
3.7.4.5 Operands
DX/DY/DZ
I DX = dx
I DY = Dy
I DZ = dz
Value of maximum relative displacement of the supports concerned, direction by direction.
3.7.5 Word
key
COMB_DEPL_APPUI
COMB_DEPL_APPUI
The occurrences of this key word define the combinations of the lawful loading cases
intervening in the secondary component of the answer.
3.7.5.1 Operands
ALL/LISTE_CAS
/ALL = “YES”
All the loading cases defined under the occurrences of DEPL_MULT_APPUI are combined
with a single rule specified by TYPE
/LISTE_CAS = list
Numbers of the loading cases combined with the rule specified by TYPE
3.7.5.2 Combination
quadratic
TYPE = “QUAD”
R =
E
2nd
R J
3.7.5.3 Combination
linear
TYPE = “LINE”
R =
E
E
R K
3.7.5.4 Combination in absolute value TYPE = “ABS”
R =
E
R it
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3.7.5.5 Different rules of combination on the various loading cases
The rule of combination can be the same one for all the cases of displacement of anchoring or
differentiated according to the groups of cases defined by an occurrence of the key word factor
COMB_DEPL_APPUI. In this case the secondary total answer is obtained by:
R =
II
2
R +
E J
(Rek) 2 + (Rel) 2
where J indicates the supports combined quadratically, K supports combined linearly and L
supports combined in absolute value.
3.7.5.6 Examples
of application
· Displacement expressed in a local reference mark Rloc (X, y, Z) different from the total reference mark Rglob (X, Y, Z)
Axes X, y and Z of Rloc are built by 3 successive rotations of angle, and around
axes X, Y and Z of Rglob.
To simplify the example, it is considered that Rloc results from Rglob by a single rotation around
axis X and of angle and that local displacement ux of the support S located with the node NS is
given along axis X of Rloc.
This loading case results from the linear combination of 2 static modes and results in
algebraic summation of the 2 following loadings:
- displacement DX=uxcos deplX along axis X
- displacement DY=uxsin deplY along the axis Y
The static modes of support following directions X and Y are calculated beforehand.
The taking into account of the loading case is written with following syntax:
DEPL_MULT_APPUI= (
_F (
NOM_CAS=' uxcos',
NUME_CAS=1,
MODE_STAT=modstat,
NOEUD=' NS',
DX=deplX,
),
_F (
NOM_CAS=' uxsin',
NUME_CAS=2,
MODE_STAT=modstat,
NOEUD=' NS',
DY=deplY,
),
),
COMB_DEPL_APPUI= (
_F (
LIST_CAS= (“1”, “2”),
TYPE_COMBI
=
“LINE”
),
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· Overall movement in a direction
Let us consider a line anchored on 3 supports S1, S2 and S3. An overall movement U is
applied to the S1 supports, S2 in direction X. the S3 support related to the crossing of a building is
presumedly fixed.
The static modes of support in direction X on the level of the supports S1 and S2 are
calculated beforehand.
The taking into account of the loading case is written with following syntax:
DEPL_MULT_APPUI= (
_F (NOM_CAS=' depl_S1_X',
NUME_CAS=1,
MODE_STAT=modstat,
NOEUD=' NS1',
DX=U,
),
_F (NOM_CAS=' depl_S2_X',
NUME_CAS=2,
MODE_STAT=modstat,
NOEUD=' NS2',
DX=U,
),
),
COMB_DEPL_APPUI= (
_F (
LIST_CAS= (“1”, “2”),
TYPE_COMBI
=
“LINE”
),
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· Response by direction and total secondary office plurality
Let us consider a line anchored on 2 supports S1 and S2 and seismic differential displacements
following:
- S1 support: U1, V1 and W1 in directions X, Y and Z
- S2 support: U2, V2 and W2 in directions X, Y and Z
The 6 static modes of support are calculated beforehand.
The data entry of the various loading cases is carried out under the occurrences of DEPL_MULT_APPUI:
DEPL_MULT_APPUI= (
# S1 support with node NS1
_F (
NOM_CAS=' depl_S1_X',
NUME_CAS=1,
MODE_STAT=modstat,
NOEUD=' NS1',
DX=U1,
),
_F (
NOM_CAS=' depl_S1_Y',
NUME_CAS=2,
MODE_STAT=modstat,
NOEUD=' NS1',
DY=V1,
),
_F (
NOM_CAS=' depl_S1_Z',
NUME_CAS=3,
MODE_STAT=modstat,
NOEUD=' NS1',
DZ=W1,
),
# S2 support with node NS2
_F (
NOM_CAS=' depl_S2_X',
NUME_CAS=4,
MODE_STAT=modstat,
NOEUD=' NS2',
DX=U2,
),
_F (
NOM_CAS=' depl_S2_Y',
NUME_CAS=5,
MODE_STAT=modstat,
NOEUD=' NS2',
DY=V2,
),
_F (
NOM_CAS=' depl_S2_Z',
NUME_CAS=6,
MODE_STAT=modstat,
NOEUD=' NS2',
DZ=W2,
),
),
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The directional answers are established under the occurrences of COMB_DEPL_APPUI:
COMB_DEPL_APPUI= (
# office plurality following X
_F (
LIST_CAS= (“1”, “4”),
TYPE_COMBI
=
“QUAD”,
),
# office plurality following Y
_F (
LIST_CAS= (“2”, “5”),
TYPE_COMBI
=
“QUAD”,
),
# office plurality following Z
_F (
LIST_CAS= (“3”, “6”),
TYPE_COMBI
=
“QUAD”,
),
),
The secondary total answer is formed by the quadratic office plurality of the directional answers. It
is calculated automatically [§ 3.7.3.5].
If the impression of the directional answers is not necessary, the total answer can be calculated
directly under only one occurrence of COMB_DEPL_APPUI:
COMB_DEPL_APPUI= (
# total answer
_F (
TOUT=' OUI',
TYPE_COMBI
=
“QUAD”,
),
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3.8
Option of calculation: operand OPTION
OPTION
List sizes (options of calculation) modal which one wants to determine the combined answer:
“DEPL”
relative displacement
“VITE”
relative speed
“ACCE_ABSOLU”
absolute acceleration = relative acceleration + acceleration
of drive
“SIGM_ELNO_DEPL”
constraints by elements with the nodes
“SIEF_ELGA_DEPL”
constraints by elements at the points of integration
“SIPO_ELNO_DEPL”
constraints in the section of beam broken up into
contributions of each generalized effort
“EFGE_ELNO_DEPL”
efforts generalized by elements with the nodes
“EFGE_ELNO_CART”
efforts generalized by elements with the nodes in
total Cartesian reference mark
“REAC_NODA”
reactions to the supports
“FORC_NODA”
internal efforts
3.9 Operand
TITER
TITER = T
Titrate attached to the concept produced by this operator [U4.03.01].
3.10 Operand
INFO
INFO
/1:
impression on the file “message” of following information:
·
name of the modal base used,
·
a number of clean vectors selected,
·
regulate selected modal combination,
·
options of calculation requested.
/2:
idem 1
3.11 Word
key
IMPRESSION
IMPRESSION
Impression on the file “result” of following information:
/
TOUT =
“OUI”
/NIVEAU
=
“SPEC_OSCI”
Values of the excitation corresponding to different
modes
“MASS_EFFE”
modal sizes in the direction of the excitation and
office plurality of the effective mass
“MAXI_GENE”
Maximum generalized contributions
With TOUT = “OUI”, one obtains the impressions corresponding to the whole of the 3 levels
defined above.
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The impression in the file “result” of the computed fields is carried out via the commands
IMPR_RESU [U4.91.01] or POST_RELEVE_T [U4.81.21] by specifying the suitable sequence numbers.
For an excitation mono support following 3 directions X, Y and Z:
· directional answers [§3.6]:
sequence numbers 1, 2 and 3 for the answers according to X, Y and Z
· combination of the directional answers if COMB_DIRECTION is present [§3.6.3]:
sequence number 4
For an excitation multi supports according to 3 directions X, Y and Z:
· If key word COMB_DEPL_APPUI misses, the primary and secondary components of
answer are cumulated:
- directional answers [§3.7.3]:
sequence numbers 1, 2 and 3 for the answers according to X, Y and Z
- combination of the directional answers if COMB_DIRECTION is present [§3.6.3]:
sequence number 4
· If key word COMB_DEPL_APPUI is present, the primary and secondary components of
answer are separate:
- primary component:
- directional answers [§3.7.3]:
sequence numbers 1, 2 and 3 for the answers according to X, Y and Z
- combination of the directional answers if COMB_DIRECTION is present [§3.6.3]:
sequence number 4
- secondary component
- fields resulting from the combinations of loading case of displacement indicated under N
occurrences of COMB_DEPL_APPUI [§3.7.5.2, §3.7.5.3, §3.7.5.4]
sequence number 200 for occurrence 1
sequence number 200+i for occurrence I
sequence number 200+n for occurrence N
- total quadratic office plurality [§3.7.5.5]
sequence number 200+n+1
4 Bibliography
[1]
“A response spectrum method for random vibrations” Report UCB/EERC - 80/15 Berkeley
(1980)
[2]
“Response off linear systems to some transient disturbances” Proceedings, Fourth World
conference one earthquake engineering - Santiago off Chile (1969)
[3]
Seismic response by spectral method [R4.05.03].
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