Modélisation A ============== Caractéristiques de la modélisation et du maillage -------------------------------------------------- .. image:: images/10000201000002C100000269B2B922DFB5CA4F0C.png :width: 4.5965in :height: 4.022in .. _RefImage_10000201000002C100000269B2B922DFB5CA4F0C.png: Le maillage du modèle calculé avec *code_aster* est constitué de 3357 nœuds et de 3387 mailles dont 135 éléments de poutre droite de Timoshenko (dont 12 SEG2 par colonne, soit 108 pour les colonnes) et 3072 éléments plaque DKT (1024 par plancher). Afin d’assurer la continuité des degrés de liberté DRZ de rotation propre des poutres avec la rotation autour de la normale des plaques (non assurée automatiquement par *code_aster* ) des éléments de poutres sont ajoutés localement au bord des plaques DKT, au niveau des 27 raccords colonne-plancher (groupe de mailles 'JONCTIONS' dans le fichier de commande), pour assurer la transmission des rotations DRZ liées au mouvement plan de la plaque en rotation dans le plan :math:`(x,y)` . Le maillage du modèle calculé avec CASTEM 2000 est constitué de 3765 nœuds et de 7368 éléments dont 108 éléments poutre droite de Timoshenko et 6960 éléments de coque DKT. Le maillage du modèle calculé avec SAMCEF est constitué de 3360 nœuds et de 3180 éléments dont 108 éléments poutre droite de Mindlin et 3072 éléments de coque de Mindlin. Résultats de la modélisation A ------------------------------ Remarques ~~~~~~~~~ Pour un nœud :math:`i` donné, l’effort généralisé pour l’élément :math:`i-1` et pour l’élément :math:`i` est comparé respectivement dans les tableaux élément “bas” et élément “haut”. Les efforts sont donnés dans le repère local des éléments de poutre (repère principal d’inertie). Calcul de la base modale ~~~~~~~~~~~~~~~~~~~~~~~~ Fréquences propres en :math:`\mathrm{Hz}` .. csv-table:: "**Mode**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" "1", "1.512", "1.512", "0.036", "1.495", "1.11" "2", "2.052", "2.050", "0.125", "2.014", "1.93" "3", "2.365", "2.343", "0.916", "2.291", "3.24" "4", "4.848", "4.859", "0.237", "4.823", "0.522" "5", "7.488", "7.521", "0.448", "7.415", "0.99" "6", "8.388", "8.426", "0.456", "8.355", "0.392" "7", "8.547", "8.543", "0.037", "8.438", "1.30" "8", "15.185", "15.405", "1.428", "15.186", "0.004" +----------------------------------------------------------------+----------------------------------------------------------------+----------------------------------------------------------------+ | | | | | .. image:: images/100000000000025800000258A379CF693A6F8011.jpg | .. image:: images/100000000000025800000258158DB3D8EC25370D.jpg | .. image:: images/1000000000000258000002583F583A9E3ADE3EA7.jpg | | :width: 2.1189in | :width: 2in | :width: 2.0626in | | :height: 2.3689in | :height: 2.3626in | :height: 2.3626in | | | | | | | | | | .. _RefImage_100000000000025800000258A379CF693A6F8011.jpg: | .. _RefImage_100000000000025800000258158DB3D8EC25370D.jpg: | .. _RefImage_1000000000000258000002583F583A9E3ADE3EA7.jpg: | | | | | | | | | +----------------------------------------------------------------+----------------------------------------------------------------+----------------------------------------------------------------+ | Visualisation: Mode n° 1; | Mode n° 3; | Mode n° 7. | +----------------------------------------------------------------+----------------------------------------------------------------+----------------------------------------------------------------+ Masses modales effectives en :math:`\mathrm{kg}` +---------------------------+----------------+-----------------+----------------+------------+----------------+ | **Mode et direction** | **code_aster** | **CASTEM 2000** | **Écart en %** | **SAMCEF** | **Écart en %** | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | 1 | X | 2,129E+01 | 2.300E+01 | –7,451 | 2.070E+01 | 2,846 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Y | 1,115E+05 | 1.113E+05 | 0,127 | 1.102E+05 | 1,186 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Z | 5,203E–02 | 6.698E–02 | –22,319 | 5.816E–02 | –10,531 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | 2 | X | 9,559E+04 | 9.365E+04 | 2,068 | 9.294E+04 | 2,847 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Y | 1,532E+02 | 1.817E+02 | –15,689 | 1.683E+02 | –8,967 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Z | 1,002E–02 | 1.440E–02 | –30,405 | 1.500E–02 | –33,186 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | 3 | X | 1,063E+04 | 1.238E+04 | –14,202 | 1.201E+04 | –11,509 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Y | 4,954E+02 | 5.181E+02 | –4,399 | 5.010E+02 | –1,119 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Z | 6,074E–03 | 9.450E–03 | –35,736 | 8.390E–03 | –27,609 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | 4 | X | 9,222E–01 | 9.3722E–01 | –1,606 | 8.338E–01 | 10,599 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Y | 1,434E+04 | 1.438E+04 | –0,296 | 1.438E+04 | –0,247 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Z | 1,553E–01 | 2.066E–01 | –24,850 | 1.791E–01 | –13,286 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | 5 | X | 1,606E+04 | 1.582E+04 | 1,514 | 1.594E+04 | 0,749 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Y | 1,537E+01 | 1.751E+01 | –12,252 | 1.491E+01 | 3,096 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Z | 3,026E–02 | 4.386E–02 | –31,012 | 4.668E–02 | –35,178 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | 6 | X | 1,829E+02 | 3.9466E+02 | –53,662 | 1.901E+03 | –90,380 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Y | 3,771E+03 | 3.622E+03 | 4,112 | 1.300E+03 | 190,089 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Z | 1,282E–01 | 1.809E–01 | –29,145 | 1.336E–01 | –4,028 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | 7 | X | 2,064E+03 | 2.1461E+03 | –3,842 | 5.331E+02 | 287,105 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Y | 9,264E+01 | 2.7942E+02 | –66,846 | 2.627E+03 | –96,474 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Z | 1,449E–02 | 1.222E–02 | 18,522 | 2.709E–02 | –46,519 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | 8 | X | 4,932E+03 | 4.948E+03 | –0,346 | 4.974E+03 | –0,851 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Y | 1,130E+00 | 1.121E+00 | 0,752 | 1.035E+00 | 9,143 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Z | 5,731E+01 | 1.5420E+02 | –62,836 | 5.098E+01 | 12,411 | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | Cumul | X | 1,2948E+05 | 1,2936E+05 | 0,092% | 1,2832E+05 | 0,905% | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Y | 1,3037E+05 | 1,3030E+05 | 0,053% | 1,2919E+05 | 0,911% | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ | | Z | 5,7706E+01 | 1,5473E+02 | -62,706% | 5,1448E+01 | 12.16% | +-----------------------+---+----------------+-----------------+----------------+------------+----------------+ Remarque La norme d’erreur des modes calculés par la méthode de Sorensen de code_aster est toujours inférieure à :math:`{10}^{-9}` . Remarque La masse totale du bâtiment est de :math:`132552\mathrm{kg}` ; la forte orientation selon y des modes est due à la relative moindre inertie selon y des colonnes. La masse modale effective cumulée dans la direction :math:`x` du séisme obtenue par code_aster représente :math:`\text{97.678 \%}` de la masse totale. Remarque Les différences entre modélisations et logiciels sont assez fortes dans la direction :math:`z` , car elle est peu sollicitée dans ces modes. Réponse spectrale - méthode CQC ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Déplacements - colonne :math:`B` (en mètre) .. csv-table:: "**Altitude Z (m)**", "**Composante**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" "PM1: 1.5", "X", "1.829E–03", "1.717E–03", "6.466", "1.641E–03", "11.439" "", "Y", "2.303E–04", "2.276E–04", "1.190", "1.730E–03", "–86.686" "", "Z", "1.882E–06", "1.763E–06", "6.728", "2.112E–05", "–91.087" "PM2: 3.0", "X", "5.411E–03", "5.108E–03", "5.935", "5.255E–03", "2.968" "1erplancher", "Y", "5.709E–04", "5.679E–04", "0.526", "3.304E–03", "–82.722" "", "Z", "3.764E–06", "3.526E–06", "6.729", "4.223E–05", "–91.087" "PM3: 4.5", "X", "9.762E–03", "9.243E–03", "5.608", "9.551E–03", "2.209" "", "Y", "9.277E–04", "9.246E–04", "0.331", "8.594E–03", "–89.205" "", "Z", "4.750E–06", "4.452E–06", "6.671", "5.540E–05", "–91.426" "PM4: 6.0", "X", "1.409E–02", "1.336E–02", "5.462", "1.381E–02", "2.047" "2èmeplancher", "Y", "1.259E–03", "1.255E–03", "0.296", "1.229E–02", "–89.756" "", "Z", "5.736E–06", "5.379E–06", "6.633", "6.857E–05", "–91.634" "PM5: 7.5", "X", "1.780E–02", "1.689E–02", "5.352", "1.747E–02", "1.890" "", "Y", "1.486E–03", "1.482E–03", "0.224", "1.539E–02", "–90.347" "", "Z", "6.014E–06", "5.642E–06", "6.598", "7.376E–05", "–91.846" "PM6: 9.0", "X", "2.085E–02", "1.980E–02", "5.319", "2.057E–02", "1.383" "3èmeplancher", "Y", "1.661E–03", "1.657E–03", "0.223", "1.789E–02", "–90.713" "", "Z", "6.293E–06", "5.905E–06", "6.567", "7.896E–05", "–92.029" Réaction en :math:`N` et Moment en :math:`\mathrm{N.m}` à l’encastrement de la colonne :math:`B` (groupe *nœud* 'PFE') .. csv-table:: "**Réaction ou moment**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" "Fx", "3.445E+04", "3.325E+04", "3.590", "3.362E+04", "2.460" "Fy", "1.644E+03", "1.629E+03", "0.916", "2.265E+03", "–27.405" "Fz", "4.015E+03", "3.761E+03", "6.729", "5.000E+03", "–19.694" "Mx", "2.986E+03", "2.975E+03", "0.348", "4.145E+03", "–27.967" "My", "8.488E+04", "8.135E+04", "4.336", "8.225E+04", "3.208" "Mz", "1.8460E–03", "1.772E–01", "–98.958", "2.165E+01", "-99.99" Réaction en :math:`N` *et Moment en* :math:`\mathrm{N.m}` à l’encastrement de la colonne centrale :math:`E` (groupe nœud 'PFE') .. csv-table:: "**Réaction/Moment**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" "Fx", "5.799E+04", "5341E+04", "8.552", "5.056E+04", "14.686" "Fy", "2.080E+03", "2.071E+03", "0.428", "2.849E+03", "–26.994" "Fz", "2.471E+02", "4.067E+02", "–39.247", "1.978E+03", "–87.504" "Mx", "3.419E+03", "3.417E+03", "0.044", "4.728E+03", "–27.691" "My", "1.202E+05", "1.116E+05", "7.705", "1.074E+05", "11.913" "Mz", "1.842E–03", "1.770E–01", "–98.959", "2.591E+01", "-99.99" Efforts généralisés de la colonne :math:`B` (en repère local) Tableau élément «bas» (voir remarque :numref:`v2.05.301-remarques`) .. csv-table:: "**Altitude Z (m)**", "**Composante**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" "PM1: 1.5", "N (N)", "4.015E+03", "3.7618E+03", "6.728", "5.000E+03", "–19.702" "PM1_BAS", "Vy (N)", "1.640E+03", "1.627E+03", "0.770", "2.260E+03", "–27.445" "", "Vz (N)", "3.441E+04", "3.323E+04", "3.528", "3.320E+04", "3.634" "", "MT (N.m)", "1.846E–03", "1.756E–01", "–98.949", "2.160E+01", "–99.99" "", "Mfy (N.m)", "3.325E+04", "3.151E+04", "5.522", "3.320E+04", "0.154" "", "Mfz (N.m)", "5.215E+02", "5.333E+02", "–2.227", "7.650E+02", "–31.835" "PM2: 3.0", "N (N)", "4.015E+03", "3.761E+03", "6.727", "4.999E+03", "–19.689" "1erplancher", "Vy (N)", "1.618E+03", "1.610E+03", "0.482", "2.230E+03", "–27.450" "PM2_BAS", "Vz (N)", "3.420E+04", "3.308E+04", "3.371", "3.286E+04", "4.073" "", "MT (N.m)", "1.846E–03", "1.645E–01", "–98.879", "2.160E+01", "–99.99" "", "Mfy (N.m)", "1.830E+04", "1.824E+04", "0.228", "1.750E+04", "4.603" "", "Mfz (N.m)", "1.925E+03", "1.891E+03", "1.771", "2.620E+03", "–26.542" "PM3: 4.5", "N (N)", "2.104E+03", "1.976E+03", "6.448", "2.636E+03", "–20.176" "PM3_BAS", "Vy (N)", "1.381E+03", "1.368E+03", "0.952", "1.930E+04", "–28.439" "", "Vz (N)", "3.061E+04", "3.000E+04", "2.010", "2.993E+04", "2.265" "", "MT (N.m)", "1.594E–03", "1.402E–01", "–98.863", "2.570E+01", "–99.99" "", "Mfy (N.m)", "1.434E+03", "1.390E+03", "3.161", "1.440E+03", "–0.385" "", "Mfz (N.m)", "1.295E+02", "1.342E+02", "–3.554", "1.890E+02", "–31.483" "PM4: 6.0", "N (N)", "2.104E+03", "1.976E+03", "6.450", "2.636E+03", "–20.187" "2èmeplancher", "Vy (N)", "1.324E+03", "1.315E+03", "0.618", "1.850E+03", "–28.458" "PM4_BAS", "Vz (N)", "2.993E+04", "2.941E+04", "1.751", "2.931E+04", "2.119" "", "MT (N.m)", "1.594E–03", "1.049E–01", "–98.481", "2.570E+01", "–99.99" "", "Mfy (N.m)", "4.583E+04", "4.471E+04", "2.480", "4.430E+04", "3.445" "", "Mfz (N.m)", "2.157E+03", "2.126E+03", "1.456", "2.990E+03", "–27.858" "PM5: 7.5", "N (N)", "5.956E+02", "5.629E+02", "5.817", "7.749E+02", "–23.133" "PM5_BAS", "Vy (N)", "7.279E+02", "7.312E+02", "–0.453", "1.040E+03", "–30.006" "", "Vz (N)", "1.935E+04", "1.934E+04", "0.039", "1.934E+04", "0.039" "", "MT (N.m)", "9.470E–04", "6.137E–02", "-98.457", "2.660E+01", "–99.99" "", "Mfy (N.m)", "1.234E+04", "1.184E+04", "4.184", "1.210E+04", "2.006" "", "Mfz (N.m)", "2.511E+02", "2.578E+02", "–2.607", "3.800E+02", "–33.921" Tableau élément «haut» (voir remarque :numref:`v2.05.301-remarques`) .. csv-table:: "**Altitude Z (m)**", "**Composante**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" "PM0: 0.0", "N (N)", "4.015E+03", "3.762E+03", "6.729", "-", "-" "PM0_HAUT", "Vy (N)", "1.644E+03", "1.629E+03", "0.928", "-", "-" "", "Vz (N)", "3.444E+04", "3.325E+04", "3.593", "-", "-" "", "MT (N.m)", "1.846E–03", "1.770E–01", "–98.957", "-", "-" "", "Mfy (N.m)", "8.488E+04", "8.135E+04", "4.336", "-", "-" "", "Mfz (N.m)", "2.986E+02", "2.975E+02", "0.348", "-", "-" "PM1: 1.5", "N (N)", "4.015E+03", "3.762E+03", "6.728", "5.000E+03", "–19.702" "PM1_HAUT", "Vy (N)", "1.640E+03", "1.621E+03", "1.149", "2.250E+03", "–27.123" "", "Vz (N)", "3.440E+04", "3.318E+04", "3.683", "3.300E+04", "4.258" "", "MT (N.m)", "1.846E–03", "1.717E–01", "–98.925", "2.160E+01", "–99.99" "", "Mfy (N.m)", "3.325E+04", "3.150E+04", "5.529", "3.260E+04", "1.997" "", "Mfz (N.m)", "5.215E+02", "5.331E+02", "–2.183", "7.640E+02", "–31.746" "PM2: 3.0", "N (N)", "2.104E+03", "1.976E+03", "6.454", "2.640E+03", "–20.289" "1erplancher", "Vy (N)", "1.419E+03", "1.386E+03", "2.319", "1.950E+03", "–27.233" "PM2_HAUT", "Vz (N)", "3.103E+04", "3.020E+04", "2.733", "3.010E+04", "3.094" "", "MT (N.m)", "1.595E–03", "1.540E–01", "–98.965", "2.570E+01", "–99.99" "", "Mfy (N.m)", "4.591E+04", "4.485E+04", "2.354", "4.500E+04", "2.022" "", "Mfz (N.m)", "1.976E+03", "1.935E+03", "2.095", "2.730E+03", "–27.610" "PM3: 4.5", "N (N)", "2.104E+03", "1.976E+03", "6.453", "2.640E+03", "–20.297" "PM3_HAUT", "Vy (N)", "1.381E+03", "1.344E+03", "2.739", "1.900E+03", "–-27.309" "", "Vz (N)", "3.061E+04", "2.974E+04", "2.917", "2.970E+04", "3.062" "", "MT (N.m)", "1.594E–03", "1.237E–01", "–98.712", "2.570E+01", "–99.99" "", "Mfy (N.m)", "1.434E+03", "1.391E+03", "3.109", "1.440E+03", "–0.385" "", "Mfz (N.m)", "1.295E+02", "1.345E+02", "–3.741", "1.900E+02", "–31.843" "PM4: 6.0", "N (N)", "5.960E+02", "5.630E+02", "5.847", "7.750E+02", "–23.103" "2èmeplancher", "Vy (N)", "7.978E+02", "7.660E+02", "4.147", "1.080E+03", "–26.130" "PM4_HAUT", "Vz (N)", "2.023E+04", "1.976E+04", "2.358", "1.970E+04", "2.696" "", "MT (N.m)", "9.477E–04", "8.407E–02", "–98.873", "2.670E+01", "–99.99" "", "Mfy (N.m)", "1.751E+04", "1.762E+04", "–0.636", "1.790E+04", "–2.179" "", "Mfz (N.m)", "8.967E+02", "8.675E+02", "3.363", "1.280E+03", "–29.945" "PM5: 7.5", "N (N)", "5.956E+02", "5.627E+02", "5.842", "7.750E+02", "–23.143" "PM5_HAUT", "Vy (N)", "7.279E+02", "6.933E+02", "4.987", "9.930E+02", "–26.693" "", "Vz (N)", "1.935E+04", "1.886E+04", "2.561", "1.890E+04", "2.360" "", "MT (N.m)", "9.470E–04", "3.736E–02", "–97.466", "2.660E+01", "–99.99" "", "Mfy (N.m)", "1.234E+04", "1.184E+04", "4.167", "1.210E+04", "2.006" "", "Mfz (N.m)", "2.511E+02", "2.579E+02", "–2.664", "3.810E+02", "–34.095" Réponse spectrale - méthode SRSS ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Déplacements – colonne :math:`B` (en :math:`m` ) .. csv-table:: "**Altitude Z (m)**", "**Composante**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" "PM1: 1.5", "X", "1.593E–03", "1.4749E–03", "7.998", "1.40E–03", "13.779" "N982", "Y", "2.767E–04", "2.795E–04", "–1.050", "1.47E–03", "–81.179" "", "Z", "2.253E+06", "2.156E–06", "4.469", "1.95E–05", "–88.447" "PM2: 3.0", "X", "4.714E–03", "4.386E–03", "7.475", "4.46E–03", "5.707" "1erplancher", "Y", "6.854E–04", "6.969E–04", "–1.653", "4.12E–03", "–83.364" "N1245", "Z", "4.506E–06", "4.312E–06", "4.469", "3.90E–05", "–88.447" "PM3: 4.5", "X", "8.508E–03", "7.939E–03", "7.169", "8.13E–03", "4.655" "N1530", "Y", "1.113E–03", "1.133E–03", "–1.797", "7.32E–03", "–84.798" "", "Z", "5.684E–06", "5.443E–06", "4.412", "5.12E–05", "–88.898" "PM4: 6.0", "X", "1.229E–02", "1.148E–02", "7.043", "1.18E–02", "4.153" "2èmeplancher", "Y", "1.510E–03", "1.538E–03", "–1.842", "1.05E–02", "–85.621" "N1815", "Z", "6.862E–06", "6.574E–06", "4.374", "6.33E–05", "–89.159" "PM5: 7.5", "X", "1.552E–02", "1.451E–02", "6.956", "1.49E–02", "4.187" "N2106", "Y", "1.780E–03", "1.815E–03", "–1.902", "1.31e–02", "–86.410" "", "Z", "7.195E–06", "6.896E–06", "4.338", "6.80E–06", "–89.419" "PM6: 9.0", "X", "1.820E–02", "1.701E–02", "6.944", "1.75E–02", "3.981" "3èmeplancher", "Y", "1.990E–03", "2.028E–03", "–1.902", "1.52E–02", "–86.908" "N2355", "Z", "7.528E–06", "7.217E–06", "4.303", "7.27E–06", "–89.646" Réaction en :math:`N` et Moment en :math:`\mathrm{N.m}` à l’encastrement de la colonne :math:`B` (nœud :math:`\mathrm{N758}` ) .. csv-table:: "**Réaction/Moment**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" "Fx", "2.999E+04", "2.854E+04", "5.040", "2.883E+04", "4.006" "Fy", "1.977E+03", "2.006E+03", "–1.434", "1.914E+03", "3.336" "Fz", "4.806E+03", "4.600E+03", "4.468", "4.254E+03", "12.973" "Mx", "3.587E+03", "3.657E+03", "–1.902", "3.510E+03", "2.203" "My", "7.393E+04", "6.985E+04", "5.830", "7.011E+04", "5.448" "Mz", "2.240E–03", "1.772E–01", "–98.736", "1.989E+01", "-99.99" Réaction en :math:`N` et Moment en :math:`\mathrm{N.m}` à l’encastrement de la colonne centrale :math:`E` (nœud :math:`\mathrm{N885}` ) .. csv-table:: "**Réaction/Moment**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" "Fx", "5.591E+04", "5.094E+04", "9.754", "4.797E+04", "16.558" "Fy", "2.499E+03", "2.545E+03", "–1.818", "2.413E+03", "3.571" "Fz", "2.472E+02", "4.068E+02", "–39.240", "1.972E+03", "–87.462" "Mx", "4.106E+03", "4.196E+03", "–2.161", "4.008E+03", "2.454" "My", "1.159E+05", "1.064E+05", "8.897", "1.019E+05", "13.769" "Mz", "2.236E–03", "1.770E–01", "–98.737", "2.288E+01", "–99.99" Efforts généralisés de la colonne :math:`B` Tableau élément «bas» (voir remarque :numref:`v2.05.301-remarques`) .. csv-table:: "**Altitude Z (m)**", "**Composante**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" "PM1: 1.5", "N (N)", "4.806E+03", "4.600E+03", "4.469", "4.250E+03", "13.082" "M3158, N982", "Vy (N)", "1.972E+03", "2.003E+03", "–1.580", "1.910E+03", "3.233" "", "Vz (N)", "2.995E+04", "2.853E+04", "4.979", "2.830E+04", "5.832" "", "MT (N.m)", "2.240E–03", "1.756E–01", "–98.725", "1.990E+01", "–99.99" "", "Mfy (N.m)", "2.898E+04", "2.706E+04", "7.088", "2.780E+04", "4.261" "", "Mfz (N.m)", "6.254E+02", "6.536E+02", "–4.319", "6.500E+02", "–3.781" "PM2: 3.0", "N (N)", "4.806E+03", "4.600E+03", "4.467", "4.250E+03", "13.078" "1erplancher", "Vy (N)", "1.944E+03", "1.980E+03", "–1.839", "1.890E+03", "2.867" "M3160, N1245", "Vz (N)", "2.977E+04", "2.840E+04", "4.825", "2.800E+04", "6.326" "", "MT (N.m)", "2.240E–03", "1.646E–01", "–98.639", "1.990E+01", "–99.99" "", "Mfy (N.m)", "1.590E+04", "1.566E+04", "1.513", "1.510E+04", "5.284" "", "Mfz (N.m)", "2.317E+03", "2.334E+03", "–0.746", "2.200E+03", "5.327" "PM3: 4.5", "N (N)", "2.515E+03", "2.414E+03", "4.184", "2.240E+03", "12.268" "M3162", "Vy (N)", "1.664E+03", "1.694E+03", "–1.789", "1.620E+03", "2.703" "", "Vz (N)", "2.670E+04", "2.578E+04", "3.551", "2.560E+04", "4.291" "", "MT (N.m)", "1.935E–03", "1.402E–01", "–98.621", "2.570E+01", "–99.99" "", "Mfy (N.m)", "1.246E+03", "1.152E+03", "8.141", "1.120E+03", "11.269" "", "Mfz (N.m)", "1.564E+02", "1.656E+02", "–5.535", "1.600E+02", "–2.217" "PM4: 6.0", "N (N)", "2.514E+03", "2.413E+03", "4.183", "2.240E+03", "12.253" "2èmeplancher", "Vy (N)", "1.592E+03", "1.626E+03", "–2.151", "1.560E+03", "2.033" "M3164, N1815", "Vz (N)", "2.611E+04", "2.528E+04", "3.308", "2.500E+04", "4.461" "", "MT (N.m)", "1.934E–03", "1.049E–01", "–98.156", "2.570E+01", "–99.99" "", "Mfy (N.m)", "3.993E+04", "3.840E+04", "3.962", "3.780E+04", "5.635" "", "Mfz (N.m)", "2.598E+03", "2.630E+03", "–1.242", "2.520E+03", "3.085" "PM5: 7.5", "N (N)", "7.130E+02", "6.904E+02", "3.270", "6.590E+02", "8.197" "M3166, N2106", "Vy (N)", "8.779E+02", "9.099E+02", "–3.521", "8.730E+02", "0.564" "", "Vz (N)", "1.693E+04", "1.663E+04", "1.802", "1.650E+04", "2.635" "", "MT (N.m)", "1.150E–03", "6.137E–02", "–98.128", "2.500E+01", "–99.99" "", "Mfy (N.m)", "1.075E+04", "1.017E+04", "5.675", "1.030E+04", "4.382" "", "Mfz (N.m)", "3.034E+02", "3.201E+02", "–5.243", "3.200E+02", "–5.199" Tableau élément «haut» (voir remarque :numref:`v2.05.301-remarques`) .. csv-table:: "**Altitude Z (m)**", "**Composante**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" "PM0: 0.0", "N (N)", "4.806E+03", "4.600E+03", "4.468", "-", "-" "M3157, N758", "Vy (N)", "1.977E+03", "2.006E+03", "–1.429", "-", "-" "", "Vz (N)", "2.998E+04", "2.854E+04", "5.043", "-", "-" "", "MT (N.m)", "2.240E–03", "1.770E–01", "–98.735", "-", "-" "", "Mfy (N.m)", "7.393E+04", "6.986E+04", "5.830", "-", "-" "", "Mfz (N.m)", "3.587E+03", "3.657E+03", "–1.902", "-", "-" "PM1: 1.5", "N (N)", "4.806E+03", "4.600E+03", "4.469", "4.250E+03", "13.082" "M3159, N982", "Vy (N)", "1.972E+03", "1.995E+03", "–1.176", "1.900E+03", "3.776" "", "Vz (N)", "2.995E+04", "2.848E+04", "5.140", "2.810E+04", "6.580" "", "MT (N.m)", "2.240E–03", "1.717E–01", "–98.696", "1.990E+01", "–99.99" "", "Mfy (N.m)", "2.898E+04", "2.706E+04", "7.096", "2.780E+04", "4.261" "", "Mfz (N.m)", "6.254E+02", "6.533E+02", "–4.276", "6.500E+02", "–3.781" "PM2: 3.0", "N (N)", "2.515E+03", "2.414E+03", "4.191", "2.240E+03", "12.280" "1erplancher", "Vy (N)", "1.709E+03", "1.716E+03", "–0.403", "1.640E+03", "4.231" "M3161, N1245", "Vz (N)", "2.706E+04", "2.595E+04", "4.269", "2.570E+04", "5.304" "", "MT (N.m)", "1.935E–03", "1.540E–01", "–98.744", "2.570E+01", "–99.99" "", "Mfy (N.m)", "4.009E+04", "3.856E+04", "3.969", "3.850E+04", "4.131" "", "Mfz (N.m)", "2.380E+03", "2.397E+03", "–0.703", "2.300E+03", "3.481" "PM3: 4.5", "N (N)", "2.515E+03", "2.413E+03", "4.193", "2.240E+03", "12.268" "M3163, N1530", "Vy (N)", "1.664E+03", "1.664E+03", "–0.025", "1.600E+03", "3.987" "", "Vz (N)", "2.670E+04", "2.555E+04", "4.469", "2.530E+04", "5.534" "", "MT (N.m)", "1.935E–03", "1.237E–01", "-98.437", "2.570E+01", "–99.99" "", "Mfy (N.m)", "1.246E+03", "1.153E+03", "8.084", "1.120E+03", "11.269" "", "Mfz (N.m)", "1.564E+02", "1.659E+02", "–5.734", "1.610E+02", "–2.824" "PM4: 6.0", "N (N)", "7.134E+02", "6.906E+02", "3.299", "6.590E+02", "8.255" "2èmeplancher", "Vy (N)", "9.610E+02", "9.506E+02", "1.087", "9.100E+02", "5.607" "M3165, N1815", "Vz (N)", "1.769E+04", "1.700E+04", "4.099", "1.680E+04", "5.325" "", "MT (N.m)", "1.150E–03", "8.407E–02", "–98.632", "2.500E+01", "–99.99" "", "Mfy (N.m)", "1.537E+04", "1.516E+04", "1.330", "1.540E+04", "–0.197" "", "Mfz (N.m)", "1.092E+03", "1.1021E+03", "–0.959", "1.060E+03", "2.974" "PM5: 7.5", "N (N)", "7.130E+02", "6.902E+02", "3.297", "6.580E+02", "8.362" "M3167, N2106", "Vy (N)", "8.779E+02", "8.644E+02", "1.561", "8.310E+02", "5.647" "", "Vz (N)", "1.693E+04", "1.622E+04", "4.345", "1.610E+04", "5.174" "", "MT (N.m)", "1.149E–03", "3.736E–02", "–96.925", "2.490E+01", "–99.99" "", "Mfy (N.m)", "1.075E+04", "1.017E+04", "5.654", "1.030E+04", "4.382" "", "Mfz (N.m)", "3.034E+02", "3.202E+02", "–5.282", "3.210E+02", "–5.494" Réponse spectrale - méthode ROSENBLUETH DSC ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Pour cette méthode, nous avons utilisé un temps de simulation de 30 secondes. Déplacements - colonne :math:`B` (en :math:`m` ) .. csv-table:: "**Altitude Z (m)**", "**Composante**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" "PM1: 1.5", "X", "1.858E–03", "1.746E–03", "6.396", "1.643E–3", "13.110" "N982", "Y", "2.230E–04", "2.197E–04", "1.493", "1.732E–3", "–87.124" "", "Z", "1.823E–06", "1.703E–06", "7.048", "2.113E–5", "–91.372" "PM2: 3.0", "X", "5.499E–03", "5.194E–03", "5.864", "5.241E–3", "4.917" "1 erplancher", "Y", "5.528E–04", "5.4825E–04", "0.827", "4.845E–3", "–88.590" "N1245", "Z", "3.646E–06", "3.406E–06", "7.048", "4.225E–5", "–91.370" "PM3: 4.5", "X", "9.919E–03", "9.398E–03", "5.534", "9.560E–3", "3.751" "N1530", "Y", "8.983E–04", "8.927E–04", "0.631", "8.603E–3", "–89.558" "", "Z", "4.601E–06", "4.300E–06", "6.991", "5.453E–5", "–91.699" "PM4: 6.0", "X", "1.432E–02", "1.359E–02", "5.386", "1.383E–2", "3.548" "2èmeplancher", "Y", "1.219E–03", "1.212E–03", "0.596", "1.23E–2", "–90.087" "N1815", "Z", "5.557E–06", "5.195E–06", "6.953", "6.861E–5", "–91.901" "PM5: 7.5", "X", "1.808E–02", "1.717E–02", "5.273", "1.748E–2", "3.434" "N2106", "Y", "1.439E–03", "1.431E–03", "0.525", "1.54E–2", "–90.657" "", "Z", "5.827E–06", "5.450E–06", "6.918", "7.381E–5", "–92.105" "PM6: 9.0", "X", "2.119E–02", "2.013E–02", "5.239", "2.059E–2", "2.892" "3ème plancher", "Y", "1.609E–03", "1.600E–03", "0.524", "1.79E–2", "–91.015" "N2355", "Z", "6.097E–06", "5.704E–06", "6.886", "7.901E–5", "–92.283" Réaction en :math:`N` et Moment en :math:`\mathrm{N.m}` à l’encastrement de la colonne :math:`B` (nœud :math:`\mathrm{N758}`) .. csv-table:: "**Réaction/Moment**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" "Fx", "3.501E+04", "3.381E+04", "3.524", "3.368E+04", "3.938" "Fy", "1.592E+03", "1.572E+03", "1.223", "2.270E+03", "–29.885" "Fz", "3.889E+03", "3.633E+03", "7.050", "5.007E+03", "–22.330" "Mx", "2.891E+03", "2.872E+03", "0.647", "4.154E+03", "–30.410" "My", "8.626E+04", "8.273E+04", "4.267", "8.236E+04", "4.738" "Mz", "1.787E–03", "1.772E–01", "-98.992", "2.170E+01", "–99.99" Réaction en :math:`N` et Moment en :math:`\mathrm{N.m}` à l’encastrement de la colonne centrale :math:`E` (nœud :math:`\mathrm{N885}`) .. csv-table:: "**Réaction/Moment**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" "Fx", "5.827E+04", "5.374E+04", "8.432", "5.061E+04", "15.148" "Fy", "2.014E+03", "1.999E+03", "0.724", "2.855E+03", "–29.471" "Fz", "2.471E+02", "4.067E+02", "–39.252", "1.979E+03", "–87.515" "Mx", "3.310E+03", "3.298E+03", "0.343", "4.738E+03", "–30.136" "My", "1.208E+05", "1.122E+05", "7.586", "1.075E+05", "12.386" "Mz", "1.783E–03", "1.770E–01", "-98.993", "2.601E+01", "–99.99" Efforts généralisés de la colonne :math:`B` Tableau élément «bas» (voir remarque :numref:`v2.05.301-remarques`) .. csv-table:: "**Altitude Z (m)**", "**Composante**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" "PM1: 1.5", "N (N)", "3.889E+03", "3.633E+03", "7.048", "5.007E+03", "–22.327" "", "Vy (N)", "1.588E+03", "1.570E+03", "1.070", "2.266E+03", "–29.938" "", "Vz (N)", "3.497E+04", "3.380E+04", "3.461", "3.325E+04", "5.172" "", "MT (N.m)", "1.786E–03", "1.756E–01", "–98.983", "2.169E+01", "–99.99" "", "Mfy (N.m)", "3.378E+04", "3.204E+04", "5.445", "3.264E+04", "3.507" "", "Mfz (N.m)", "5.050E+02", "5.149E+02", "–1.933", "7.659E+02", "–34.067" "PM2: 3.0", "N (N)", "3.889E+03", "3.632E+03", "7.047", "5.007E+03", "–22.330" "1erplancher", "Vy (N)", "1.566E+03", "1.554E+03", "0.785", "2.235E+03", "–29.911" "M3160, N1245", "Vz (N)", "3.476E+04", "3.364E+04", "3.304", "3.290E+04", "5.646" "", "MT (N.m)", "1.786E–03", "1.646E–01", "–98.915", "2.167E+01", "–99.99" "", "Mfy (N.m)", "1.861E+04", "1.858E+04", "0.181", "1.752E+04", "6.243" "", "Mfz (N.m)", "1.863E+03", "1.825E+03", "2.075", "2.623E+03", "–28.960" "PM3: 4.5", "N (N)", "2.039E+03", "1.910E+03", "6.770", "2.641E+03", "–22.799" "M3162, N1530", "Vy (N)", "1.338E+03", "1.321E+03", "1.255", "1.934E+03", "–30.834" "", "Vz (N)", "3.109E+04", "3.050E+04", "1.931", "2.997E+04", "3.751" "", "MT (N.m)", "1.543E–03", "1.402E–01", "–98.900", "2.573E+01", "–99.99" "", "Mfy (N.m)", "1.441E+03", "1.397E+03", "3.154", "1.447E+03", "–0.374" "", "Mfz (N.m)", "1.253E+02", "1.295E+02", "–3.277", "1.900E+02", "–34.035" "PM4: 6.0", "N (N)", "2.039E+03", "1.910E+03", "6.767", "2.640E+03", "–22.780" "2èmeplancher", "Vy (N)", "1.282E+03", "1.270E+03", "0.924", "1.859E+03", "–31.030" "M3164, N1815", "Vz (N)", "3.040E+04", "2.990E+04", "1.675", "2.935E+04", "3.594" "", "MT (N.m)", "1.542E–03", "1.049E–01", "–98.53", "2.573E+01", "–99.99" "", "Mfy (N.m)", "4.656E+04", "4.546E+04", "2.413", "4.436E+04", "4.969" "", "Mfz (N.m)", "2.089E+03", "2.053E+03", "1.759", "2.999E+03", "–30.340" "PM5: 7.5", "N (N)", "5.775E+02", "5.441E+02", "6.129", "7.773E+02", "–25.708" "M3166, N2106", "Vy (N)", "7.058E+02", "7.068E+02", "–0.143", "1.045E+03", "–32.457" "", "Vz (N)", "1.964E+04", "1.965E+04", "–0.056", "1.937E+04", "1.389" "", "MT (N.m)", "9.165E–04", "6.137E–02", "–98.51", "2.669E+01", "–100.00" "", "Mfy (N.m)", "1.254E+04", "1.205E+04", "4.116", "1.210E+04", "3.652" "", "Mfz (N.m)", "2.431E+02", "2.488E+02", "–2.314", "3.815E+02", "–36.283" Tableau élément «haut» (voir remarque :numref:`v2.05.301-remarques`) .. csv-table:: "**Altitude** :math:`Z(m)`", "**Composante**", "**code_aster**", "**CASTEM 2000**", "**Écart en %**", "**SAMCEF**", "**Écart en %**" ":math:`\mathrm{PM0}:0.0`", "N (N)", "3.889E+03", "3.633E+03", "7.050", "–", "–" ":math:`\mathrm{M3157}` , :math:`\mathrm{N758}`", "Vy (N)", "1.592E+03", "1.573E+03", "1.229", "–", "–" "", "Vz (N)", "3.501E+04", "3.382E+04", "3.527", "–", "–" "", "MT (N.m)", "1.787E–03", "1.770E–01", "–98.991", "–", "–" "", "Mfy (N.m)", "8.626E+04", "8.273E+04", "4.267", "–", "–" "", "Mfz (N.m)", "2.891E+03", "2.872E+03", "0.647", "–", "–" ":math:`\mathrm{PM1}:1.5`", "N (N)", "3.889E+03", "3.633E+03", "7.048", "5.007E+03", "–22.327" ":math:`\mathrm{M3159}` , :math:`\mathrm{N982}`", "Vy (N)", "1.587E+03", "1.564E+03", "1.451", "2.255E+03", "–29.596" "", "Vz (N)", "3.497E+04", "3.375E+04", "3.620", "3.306E+04", "5.773" "", "MT (N.m)", "1.786E–03", "1.718E–01", "–98.96", "2.168E+01", "–99.99" "", "Mfy (N.m)", "3.378E+04", "3.204E+04", "5.452", "3.263E+04", "3.539" "", "Mfz (N.m)", "5.050E+02", "5.147E+02", "–1.891", "7.655E+02", "–34.033" ":math:`\mathrm{PM2}:3.0`", "N (N)", "2.039E+03", "1.910E+03", "7.358", "2.641E+03", "–22.791" ":math:`\mathrm{M3161}` , :math:`\mathrm{N1245}`", "Vy (N)", "1.374E+03", "1.339E+03", "2.625", "1.374E+03", "–-29.711" "", "Vz (N)", "3.153E+04", "3.071E+04", "2.659", "3.017E+04", "4.493" "", "MT (N.m)", "1.543E–03", "1.540E–01", "–98.99", "2.572E+01", "–99.99" "", "Mfy (N.m)", "4.663E+04", "4.559E+04", "2.271", "4.51E+04", "3.363" "", "Mfz (N.m)", "1.914E+03", "1.869E+02", "2.396", "2.742E+03", "–30.190" ":math:`\mathrm{PM3}:4.5`", "N (N)", "2.039E+03", "1.909E+03", "6.775", "2.641E+03", "–22.799" ":math:`\mathrm{M3163}` , :math:`\mathrm{N1530}`", "Vy (N)", "1.338E+03", "1.298E+03", "3.049", "1.902E+03", "–29.670" "", "Vz (N)", "3.110E+04", "3.023E+04", "2.843", "2.969E+04", "4.734" "", "MT (N.m)", "1.543E–03", "1.237E–01", "–97.75", "2.573E+01", "–99.99" "", "Mfy (N.m)", "1.442E+03", "1.398E+03", "3.095", "4.440E+04", "0.110" "", "Mfz (N.m)", "1.253E+02", "1.298E+02", "–3.464", "1.904E+02", "–34.174" "PM4: 6.0", "N (N)", "5.778E+03", "5.442E+02", "6.158", "7.775E+02", "–25.689" "2èmeplancher", "Vy (N)", "7.731E+03", "7.402E+02", "4.444", "1.087E+03", "–28.875" ":math:`\mathrm{M3165}` , :math:`\mathrm{N1815}`", "Vz (N)", "2.054E+04", "2.008E+04", "2.267", "1.977E+04", "3.887" "", "MT (N.m)", "9.172E–04", "8.407E–02", "–98.909", "2.670E+01", "–100.00" "", "Mfy (N.m)", "1.776E+04", "1.789E+04", "–0.745", "1.797E+04", "–1.176" "", "Mfz (N.m)", "8.696E+02", "8.388E+02", "3.663", "1.284E+03", "–32.273" ":math:`\mathrm{PM5}:7.5`", "N (N)", "5.775E+02", "5.440E+02", "6.153", "7.771E+02", "–25.689" ":math:`\mathrm{M3167}` , :math:`\mathrm{N2106}`", "Vy (N)", "7.058E+02", "6.704E+02", "5.279", "9.968E+02", "–29.191" "", "Vz (N)", "1.964E+04", "1.916E+04", "2.466", "1.891E+04", "3.848" "", "MT (N.m)", "9.165E–04", "3.736E–02", "–97.547", "2.669E+01", "–100.00" "", "Mfy (N.m)", "1.254E+04", "1.204E+04", "4.099", "1.211E+04", "3.566" "", "Mfz (N.m)", "2.431E+02", "2.490E+02", "–2.369", "3.816E+02", "–36.299"