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Titrate:
Operator
COMB_SISM_MODAL
Date:
08/02/05
Author (S):
Y. PONS
,
J. PIGAT, L. VIVAN
Key
:
U4.84.01-F
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:
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HT-66/05/004/A
Organization (S):
EDF-R & D/AMA,
CS IF














Instruction manual
U4.8- booklet: Postprocessing and dedicated analyzes
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 the control
CALC_FONCTION
with the key word factor
SPEC_OSCI
[U4.32.04].
The 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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Code_Aster
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Titrate:
Operator
COMB_SISM_MODAL
Date:
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,
J. PIGAT, L. VIVAN
Key
:
U4.84.01-F
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2 Syntax

R [mode_stat] = COMB_SISM_MODAL
(
MODE_MECA = mode [mode_meca]
/
TOUT_ORDRE
=
“YES”
[DEFECT]
/
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
[DEFECT]
/
prec [R]
I
CRITERION
=
/
“RELATIVE”
[DEFECT]
/
“ABSOLUTE”
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 =/
“YES”
/
NODE
=
lno
[l_noeud]
/
GROUP_NO
=
lgrno [l_gr_noeud]
/
CENTER = (c1, c2, c3)
[l_R]
SPEC_OSCI = spec [tablecloth]
SCALE = echel
[R]
/
TRI_AXE = (p1, p2, p3)
[l_R]
SPEC_OSCI = spec [tablecloth]
SCALE = echel
[R]
/
TRI_SPEC = “YES”
[KN]
SPEC_OSCI= (spe1, spe2, spe3) [l_fonction]
ECHELLE= (ech1, ech2, ech3) [l_R]
NATURE
=
/
“ACCE”
[DEFECT]
/
“QUICKLY”
/
“DEPL”
)
CORR_FREQ
=
/
“YES”
[DEFECT]
/
“NOT”
COMB_MODE
=_F (
/STANDARD
=
/“SRSS”
/
“CQC”
/
“DPC”
/
“ABS”
/
“DSC”
DURATION
=
S
[R]
)
COMB_DIRECTION =_F (
/STANDARD
=
/“QUAD”
/
“NEWMARK”
)
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Titrate:
Operator
COMB_SISM_MODAL
Date:
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,
J. PIGAT, L. VIVAN
Key
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U4.84.01-F
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COMB_MULT_APPUI =_F (

/ALL = “YES”
/
NODE
=
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]
/NODE = 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”
TITRATE = tit
[l_Kn]
INFORMATION =
/1
[DEFECT]
/2
=_F IMPRESSION (/ALL
= “YES”
[DEFECT]
/
LEVEL
=
I
“SPEC_OSCI”
I
“MASS_EFFE”
I
“MAXI_GENE”
)
)
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Code_Aster
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Titrate:
Operator
COMB_SISM_MODAL
Date:
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J. PIGAT, L. VIVAN
Key
:
U4.84.01-F
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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 type
mode_meca
produced 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
sequence numbers (
NUME_ORDRE
)
or a list
l_mode
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 from frequencies
lfreqr8
, definite
by the operator
DEFI_LIST_REEL
[U4.34.01] (
lfreqr8
is thus a concept of the type
listr8)
.
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
CRITERION
=
“RELATIVE”
the interval of search is:
[inst (1 - prec), inst (1 + prec)]
“ABSOLUTE”
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 of a concept of the type
listr8
built
by the 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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Code_Aster
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Titrate:
Operator
COMB_SISM_MODAL
Date:
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Author (S):
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J. PIGAT, L. VIVAN
Key
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U4.84.01-F
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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
type
listr8
. 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 01
.
and for all the other modes
= 0 02
.

3.2.3 Operand
AMOR_GENE
/AMOR_GENE = amogene
One gives the name of the matrix of generalized damping
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.
The aforementioned is calculated by the control
POST_ELEM
[U4.81.22] with the key word
MASS_INER
.
The operand
MASS_INER
allows to provide the name of the concept produced by this control.

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 the control
CALC_FONCTION
[U4.32.04] or read on a file by the control
LIRE_FONCTION
[U4.32.02] with the format
“SEISM”
. In both cases the produced concept is of
type
function
with two variables (tablecloth).
One uses for that the key word factor
EXCIT
and possibly the operand
CORR_FREQ
.
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Titrate:
Operator
COMB_SISM_MODAL
Date:
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J. PIGAT, L. VIVAN
Key
:
U4.84.01-F
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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
use the operand then
MONO_APPUI = “YES”
The key word factor
EXCIT
must 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
/NODE = lno
/GROUP_NO = lgrno
3.4.2 Excitation along an axis
/
CENTER = (c1, c2, c3)
SPEC_OSCI = spec
SCALE = echel
In this case one provides:
·
the cosine Directors
(c1 c2 c3)
axis of excitation in the TOTAL reference mark of
definition of the mesh: coefficients
c1
,
c2
,
c3
are renormés by the control,
·
the operand
SPEC_OSCI
only one spectrum of oscillator waits where
spec
is the name of
tablecloth to be used,
·
the operand
SCALE
allows to define a scale factor
echel
to apply to
all points of the spectrum
spec
.
Example:
For an excitation with 45° compared to the TOTAL reference mark, a spectrum of ground
sol_0_1
fixed with 0.1g and a scale factor allowing to simulate a fixed spectrum with 0.25g:
CENTER
= (
“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
SCALE = 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,
·
the operand
SPEC_OSCI
only one spectrum of oscillator waits where
spec
is the name of
tablecloth to be used,
·
the operand
SCALE
allows to define a scale factor
echel
to apply 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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Titrate:
Operator
COMB_SISM_MODAL
Date:
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Y. PONS
,
J. PIGAT, L. VIVAN
Key
:
U4.84.01-F
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:
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3.4.4 Excitation
triaxial
with three different spectra
/
TRI_SPEC = “YES”
SPEC_OSCI = (spe1, spe2, spe3)
SCALE = (ech1, ech2, ech3)
In this case one provides:
·
the operand
TRI_SPEC
:
“YES”
,
·
the operand
SPEC_OSCI
awaits three spectra of oscillators where
(spe1 spe2 spe3)
is the list of the names of the tablecloths to be used,
·
the operand
SCALE
allows 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
'
QUICKLY
“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
pseudo speed
acce
depl
pseudo acceleration
max
R
read
max
R
read
=
=
-
=
=
-

2
The operand
CORR_FREQ:
“YES”
allows to correct these values to take into account
the damping of the clean mode:
quickly
depl
speed
acce
depl
acceleration
max
R
read
max
R
read
=
-
=
=
-
=
1
1
2
2
2
(
)
If one provides a spectrum of answer of speed (
NATURE
=
“QUICKLY”
) the operand
CORR_FREQ
will be
necessary to correct
depl
max
and
acce
max
if necessary. In the same way for a spectrum of
response in acceleration (
NATURE = “ACCE”
) to correct
depl
max
and
quickly
max
.
In all the cases, one will take care not to use like data
SPEC
a spectrum of
pseudo-size.
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Titrate:
Operator
COMB_SISM_MODAL
Date:
08/02/05
Author (S):
Y. PONS
,
J. PIGAT, L. VIVAN
Key
:
U4.84.01-F
Page
:
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U4.8- booklet: Postprocessing and dedicated analyzes
HT-66/05/004/A
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, stresses) 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 stress. 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
R
X
where
X
represent one of the directions of the reference mark
TOTAL
of definition of the mesh
(
)
X Y Z
,
or
a particular direction (cf operand
CENTER
). The directional answer is given by:
R
R
R
R
X
D
T
E
=
+
+
2
2
2
·
R
D
combined response of the modal oscillators established by the key word
COMB_MODE
[§ 3.6.1]
·
R
T
represent the correction of the static effects of the neglected modes (pseudo mode) [§ 3.6.2]
·
R
E
contribution of the movement of drive (
R
E
= 0
in mono support)
The rule of combination of the directional answers is defined by the 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 structure
R
D
, in a direction of seism, is obtained by one of
possible combinations (defined by the operand
TYPE
) of the contributions of each mode
clean taken into account. Each clean mode is regarded as an oscillator independent of
answer
R
R
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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Operator
COMB_SISM_MODAL
Date:
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Y. PONS
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J. PIGAT, L. VIVAN
Key
:
U4.84.01-F
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For an excitation mono support the answer
R
R
oscillator
R
is given by:
R
p S
R
R
R
R
=
2
R
·
R
modal size (displacement, generalized effort, reaction) associated the mode
clean of index
R
·
P
R
factor of modal participation associated the mode
R
in the studied direction
·
S
R
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
the operand
TYPE
.

3.6.1.1 Combination
quadratic
TYPE = “SRSS”
This combination (Public garden Root off Sum off Public gardens) corresponds to the assumption of strict independence
oscillators associated with each clean mode:
R
R
D
R
R 1
nmod
=
=
2
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
R
R
=
1
1 2
1
2
2
with the coefficient of correlation:
ij
I J I
J
I I
J
J
I
J
I
J
I J I
J
I
J
I
J
I
J
=
+
-
+
+
+
+
8
4
4
2
2 2
2
2
2
2
2
2
(
)
(
)
(
)
(
)

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:
=
=
MOD
1
N
R
R
D
R
R
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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COMB_SISM_MODAL
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J. PIGAT, L. VIVAN
Key
:
U4.84.01-F
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:
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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 Guides 1.92 - February 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 sum (Double Sum Combination):
R
R R
D
R
R R
R
R
R
=
1
1 2
1
2
2
It requires an additional data, the duration
S
“strong” phase of the seism defined by
the operand
DURATION
.
The coefficient of correlation is then:
ij
I
J
I
I
J
J
I
I
I
I
I
I
S
= +
-
+






=
-
= +
-
1
1
2
2
1
2
'
'
'
'
'
'
'
where
and

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
stamp rigidity of the structure
·
M
stamp of mass of the structure
·
unit field in the direction of the seism
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Operator
COMB_SISM_MODAL
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J. PIGAT, L. VIVAN
Key
:
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:
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Pseudo-mode
is obtained by withdrawing the static contributions of the modes taken into account:
R
nmod
1
R
R
R
p
-
=
=
2
with:
·
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:
R
R
R
T
S
R
R
N
=
-
=
1
MOD
S
R
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
nodes of the structure
subjected to a constant acceleration in one (or several) direction (S), field (S) calculated (S) by
the operator
MODE_STATIQUE
with the 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 the 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
R
R
R
X
Y
Z
=
+
+
2
2
2

3.6.3.2 Combination of NEWMARK:
TYPE = “NEWMARK”
For each direction
(
)
I X Y Z
,
, the 8 values are calculated:
R
R
R
R
I
X
Y
Z
= ±
±
±
0 4
0 4
,
,
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 supports
R
xi
defined by:
R
R
R
R
X I
D I
T I
I.E.(internal excitation)
=
+
+
2
2
2
-
R
di
combined response of the modal oscillators established by the key word
COMB_MODE
[§ 3.6.1]
-
R
Ti
represent 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].
-
R
I.E.(internal excitation)
contribution of the movement of drive of the support
I
(
R
I.E.(internal excitation)
0
in multi-support)
established by the key word
DEPL_MULT_APPUI
[§ 3.7.4]
·
The directional answers are calculated
R
X
by combination of the directional answers
supports
R
xi
. The rule of combination is defined by the key word
COMB_MULT_APPUI
[§ 3.7.3].
The total answer
R
structure is obtained by combination of the directional answers
R
X
.
regulate combination is defined by the 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
I
X
I
R
defined by:
2
2
Ti
di
I
X
I
R
R
R
+
=
-
R
di
combined response of the modal oscillators established by the key word
COMB_MODE
[§ 3.6.1]
-
R
Ti
represent 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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·
The directional answers are calculated
R
X
by combination of the directional answers
supports
R
xi
. The rule of combination is defined by the key word
COMB_MULT_APPUI
[§ 3.7.3].
The total answer
R
structure is obtained by combination of the directional answers
R
X
.
regulate combination is defined by the 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 contribution
R
I.E.(internal excitation)
movement of drive of the support
I
established by the key word
DEPL_MULT_APPUI
[§ 3.7.4]
·
Combinations of the various contributions of support
R
I.E.(internal excitation)
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 occurrences of the key word
COMB_DEPL_APPUI
is 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 the 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
/
NODE
=
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 the 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
R
X
Xj
=
2

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:
(
)
+
=
2
2
Xk
Xj
R
R
R
where
J
indicate 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. The aforementioned is established with
to leave the static modes of the structure:
max
I
I
S
I
E
R
=
with:
if
static mode for the support
I
I max
maximum displacement of the 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 type
mode_stat
product 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
-
max
I
where
is affected displacement with the node of reference
noeu
in the direction considered.

3.7.4.4 Operands
NODE
/
GROUP_NO
/NODE = 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 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”
=
2j
E
E
R
R

3.7.5.3 Combination
linear
TYPE = “LINE”
=
K
E
E
R
R


3.7.5.4 Combination in absolute value
TYPE = “ABS”
=
L
E
E
R
R
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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:
(
)
(
)
+
+
=
2
2
2
L
E
K
E
J
E
II
R
R
R
R
where
J
indicate the supports combined quadratically,
K
linearly combined supports and
L
supports combined in absolute value.

3.7.5.6 Examples
of application
· Displacement expressed in a local reference mark R
loc
(X, y, Z) different from the total reference mark R
glob
(X, Y, Z)
Axes X, y and Z of R
loc
are built by 3 successive rotations of angle
, and around
axes X, Y and Z of R
glob
.
To simplify the example, it is considered that R
loc
results from R
glob
by a single rotation around
axis X and of angle
and that local displacement U
X
support S located with the node NS is
given along axis X of R
loc
.
This loading case results from the linear combination of 2 static modes and results in
algebraic summation of the 2 following loadings:
- DX=u displacement
X
cos
deplX along axis X
- DY=u displacement
X
sin
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 line of a ship 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 capture 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
“QUICKLY”
relative speed
“ACCE_ABSOLU”
absolute acceleration = relative acceleration + acceleration
of drive
“SIGM_ELNO_DEPL”
stresses by elements with the nodes
“SIEF_ELGA_DEPL”
stresses by elements at the points of integration
“SIPO_ELNO_DEPL”
stresses 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
TITRATE
TITRATE = T
Titrate attached to the concept produced by this operator [U4.03.01].
3.10 Operand
INFORMATION
INFORMATION
/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:
/
ALL =
“YES”
/LEVEL
=
“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
ALL = “YES”
, 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 controls
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 the 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 the 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” Carryforward 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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