3. Operands#
3.1. Keyword MAX#
/MAX =
Find the x-axis where the maximum and the minimum are reached.
This operation is available on functions of a function or sheet nature.
Name of the function or functions whose maximums are being sought.
If f is a function, the product concept is a table whose access parameters are:
FONCTION, TYPE, the NOM_PARAde the function, the NOM_RESUde the function.
where we find respectively the name of the function, MAXI or MINI, the maximum/minimum x-axis, the maximum/minimum value.
When multiple factors are provided, the table contains the max (s) of the max, and the min (s) of the min.
If f is a tablecloth, the product concept is a table whose access parameters are:
FONCTION, TYPE, the NOM_PARAde the tablecloth, the name of the function parameter (NOM_PARA_FONC), the NOM_RESUdes functions.
◊ INTERVALLE =inter
List of reals defining the limits of the intervals over which the min and max of the functions will be searched.
inter is composed of real pairs, the first of which corresponds to the lower bound of the first|ninterval, the second corresponds to the upper bound of the first interval, and so on for the other intervals.
Inter is therefore composed of an even number of elements.
This keyword is not taken into account for table cloths.
3.2. Keyword NORME#
This keyword makes it possible to follow the convergence according to standard \({L}_{2}\) of a sequence of functions \({f}_{N}\) given in the form of a table. The result table has one row per function, the input parameters are NORME and FONCTION.
♦ FONCTION = f
Name of the tablecloth whose standard should be evaluated.
3.3. Keyword ECART_TYPE#
/ECART_TYPE =
We calculate the standard deviation of the function \(f(t)\) which is defined by:
\(\sigma \mathrm{=}\sqrt{\frac{1}{({t}_{\mathit{fin}}\mathrm{-}{t}_{\mathit{deb}})}{\mathrm{\int }}_{{t}_{\mathit{deb}}}^{{t}_{\mathit{fin}}}{(f(t)\mathrm{-}\stackrel{ˉ}{f})}^{2}\mathit{dt}}\) where \(\stackrel{ˉ}{f}\) is the average out of \([{t}_{\mathrm{deb}},{t}_{\mathrm{fin}}]\)
The keywords are the same as those provided under the keyword factor RMS.
The product concept is a table whose access parameters are:
FONCTION, METHODE, MOYENNE, INST_INIT,, INST_FIN, ECART_TYPE.
3.4. Keyword RMS#
/RMS =
We calculate the value RMS of the function \(f(t)\) which is defined by:
\(\mathrm{RMS}=\sqrt{\frac{1}{({t}_{\mathrm{fin}}-{t}_{\mathrm{deb}})}{\int }_{{t}_{\mathrm{deb}}}^{{t}_{\mathrm{fin}}}{f}^{2}(t)\mathrm{dt}}\)
Name of the function whose value RMS is calculated for.
Does not apply to tablecloth-type concepts.
Name of the METHODE that we use to calculate the integral.
Two methods are available: the “TRAPEZE” method (by default) and the “SIMPSON” method.
◊ INST_FIN = end,
Lower and upper limits of the integration interval.
If these values are not specified, the lower and upper discretization points (the order relationship being defined in relation to the x-axis parameter) are taken as the limit of the integration interval.
/prec,
/”RELATIF”, [DEFAUT]
We are looking for a discretization point of the function in an interval defined by the absolute or relative position around a value of the x-axis parameter for which the function must be estimated:
|
if CRITERE = “RELATIF” |
|
if CRITERE = “ABSOLU” |
The product concept is a table whose access parameters are:
FONCTION, METHODE, INST_INIT, INST_FIN, RMS.
3.5. Keyword NOCI_SEISME#
/NOCI_SEISME =
♦/FONCTION = f,
/SPEC_OSCI = sro,
Name of the function (accelerating signal \(a(t)\)) or the sheet in question that must be defined in DEFI_FONCTION [U4.31.02] with NOM_RESU =” ACCE “.
If we consider a sheet, only the spectral intensity calculation is available.
◊/OPTION =
Allows you to choose one or more of the following six harmful indices:
Give all of the six|indices of harmfulness,
Give the maximum of acceleration \(a(t)\), speed \(v(t)\), and displacement (obtained by integration)
\(\mathit{PGA}=\underset{t\in [{t}_{i},{t}_{f}]}{\mathit{max}}\left\{∣a(t)∣\right\}\), \(\mathrm{PGV}=\underset{t\in [{t}_{i},{t}_{f}]}{\mathrm{max}}\left\{∣v(t)∣\right\}\), \(\mathrm{PGD}=\underset{t\in [{t}_{i},{t}_{f}]}{\mathrm{max}}\left\{∣x(t)∣\right\}\)
Give the intensity of Arias \({I}_{A}=\frac{\pi }{2g}{\int }_{{t}_{i}}^{{t}_{f}}{a}^{2}(t)\mathit{dt}\)
where \(g\) is the acceleration due to gravity. This value should be taught using the PESANTEUR keyword.
Give the destructive power \({P}_{d}=\frac{{I}_{A}}{{\nu }_{0}^{c}}=\frac{{\pi }^{3}}{2g}{\int }_{{t}_{i}}^{{t}_{f}}{v}^{2}(t)\mathrm{dt}\)
where \(g\) must be filled in with the PESANTEUR keyword
Give the cumulative absolute value of speed \(\mathit{CAV}={\int }_{{t}_{i}}^{{t}_{f}}∣a(t)∣\mathit{dt}\)
duration of strong phase (Arias intensity being an increasing monotonic function):
Minimum duration \({t}_{\text{sup}}-{t}_{\mathrm{inf}}\) such as, for terminals \({b}_{\text{inf}},{b}_{\text{sup}}\):
\({b}_{\text{inf}}\times {I}_{A}⩽\frac{\pi }{2g}{\int }_{{t}_{\mathit{inf}}}^{{t}_{\text{sup}}}{a}^{2}(f)\mathit{dt}⩽{b}_{\text{sup}}\times {I}_{A}\)
where \(g\) must be filled in with the PESANTEUR keyword.
The resulting table contains \({t}_{\mathit{inf}}\) under DEBUT_PHAS_FORT.
This indicator is based on the spectral pseudo-acceleration of the structure and depends on its fundamental frequency.
A damage, characterized by a decrease in this natural frequency, is taken into account by the integration of spectral pseudo-accelerations \({S}_{a}(f,\eta )\) .over a frequency range:
\({\mathit{ASA}}_{R}=\frac{1}{R{f}_{0}}{\int }_{(1-R){f}_{0}}^{{f}_{0}}{S}_{a}(f,\eta )\mathit{df}\)
where R refers to the ratio defining the integration domain and \(\eta\) is the reduced depreciation. The value of the ratio can be entered by the user using the RATIO keyword. By default, \({\mathit{ASA}}_{40}\) is determined with R=0.4 and reduced damping \(\eta =0.05\). The keyword FREQ_PAS is used to define the integration step. The spectral pseudo-acceleration will be normalized to the NORME specified (by default 1.0).
“INTE_SPEC”
Housner spectral intensity, between frequencies \({f}_{\mathrm{deb}},{f}_{\mathrm{fin}}\), \({S}_{V}(f,\eta )\) designating the Oscillator Response Spectrum in pseudo-velocities for reduced damping \(\eta\):
\({I}_{H}={\int }_{{f}_{\mathit{deb}}}^{{f}_{\mathit{fin}}}\frac{{S}_{V}(f,\eta )}{{f}^{2}}\mathit{df}\)
\(\text{ACCE\_SUR\_VITE}=\frac{\underset{t\in [{t}_{i},{t}_{f}]}{\mathit{max}}\left\{∣a(t)∣\right\}}{\underset{t\in [{t}_{i},{t}_{f}]}{\mathit{max}}\left\{∣\nu (t)∣\right\}}\)
Depending on the option, you have to fill in certain parameters, if you indicate no option, by default, you calculate all the indices so you have to fill in everything. The integration method is the “TRAPEZE” method.
INST_FIN = end,
Lower and upper bounds of the time interval in question.
If these values are not specified, the lower and upper discretization points (the order relationship being defined in relation to the x-axis parameter) are taken as the limit of the interval.
PRECISION =/0.001,
/prec,
CRITERE =/'ABSOLU',
/”RELATIF”, [DEFAUT]
We are looking for a discretization point of the function in an interval defined by the absolute or relative position around a value of the x-axis parameter for which the function must be estimated:
*[inst*(1-prec) , inst*(1+prec)] |
if CRITERE = “RELATIF” |
|
if CRITERE = “ABSOLU” |
*[freq*(1-prec) , freq*(1+prec)] |
if CRITERE = “RELATIF” |
|
if CRITERE = “ABSOLU” |
COEF = r1
Integration constant, by default 0. In the “MAXI” option, we calculate the speed and the displacement by two successive integrations of the damping, so we must enter COEF if we do not want to take it by default.
FREQ_INIT = fdeb,
FREQ_FIN = end,
Frequencies representing the two integration terminals for calculating the Housner spectral intensity. These must be between the extremes of the frequency base defining the array SRO, otherwise an interpolation problem arises. By default, these two frequencies are set to \(\mathrm{0,4}\mathrm{Hz}\) and \(\mathrm{10Hz}\).
AMOR_REDUIT = am
Reduced damping, for the calculation of the Oscillator Response Spectrum in that of the Housner spectral intensity.
FREQ = free
iron = \(({\Phi }_{\mathrm{1,}}\mathrm{...},{\Phi }_{i},\mathrm{...})\). List of frequencies.
LIST_FREQ = lfreq
List of frequencies provided under a listr8 concept.
NORME = R2
The oscillator spectrum will be normalized to the value R2 (value of the pseudo-acceleration).
BORNE_INF = nothing,
BORNE_SUP = bsup,
Boundaries limiting the part of intensity Arias defining the initial and final moments of the strong phase (between \(({b}_{\text{inf}})\text{\%}\) and \(({b}_{\text{sup}})\text{\%}\) of \({({I}_{A})}_{\mathrm{max}}\)) of the earthquake (we often take 5% and 95%).
PESANTEUR
Acceleration of Gravity. Since its value depends on the units of the model, this keyword is mandatory for the indices INTE_ARIAS, POUV_DEST, DUREE_PHAS_FORT.
3.6. Operand TITRE#
◊ TITRE = t
Title attached to the concept produced by this operator [U4.03.01].
3.7. Operand INFO#
◊ INFO
If INFO =2, we print the function (IMPR_FONCTION format TABLEAU) in the file MESSAGE.