Modélisation B
==============




Caractéristiques de la modélisation
-----------------------------------

On utilise une modélisation DKT. On réalise une analyse à l’ELS.




Caractéristiques du maillage
----------------------------

Le maillage contient 1 élément de type QUAD4.




Grandeurs testées et résultats
------------------------------



Pour les cas de chargements unidirectionnels, la marge est simplement égale à 1 - le coefficient de proportionnalité considéré pour efforts de rupture et l'angle critique est toujours égal à -90°.

+-----------------------+-------------------------------------+----------------------+---------------------------+
| **cas de chargement** | **Coefficient de proportionnalité** | **marge analytique** |**marge VERI_FERRAILLAGE** |
+-----------------------+-------------------------------------+----------------------+---------------------------+
| 1                     | 0.5                                 | 0.5                  |0.5                        |
+-----------------------+-------------------------------------+----------------------+---------------------------+
| 2                     | 2                                   | -1                   |-1.0                       |
+-----------------------+-------------------------------------+----------------------+---------------------------+
| 3                     | 0.7                                 | 0.3                  |0.314                      |
+-----------------------+-------------------------------------+----------------------+---------------------------+
| 4                     | 0.2                                 | 0.8                  |0.8                        |
+-----------------------+-------------------------------------+----------------------+---------------------------+
| 5                     | 0.0                                 | 1.0                  |1.0                        |
+-----------------------+-------------------------------------+----------------------+---------------------------+
| 6                     | 0.4                                 | 0.6                  |0.6                        |
+-----------------------+-------------------------------------+----------------------+---------------------------+
| 7                     | 0.7                                 | 0.3                  |0.316                      |
+-----------------------+-------------------------------------+----------------------+---------------------------+
| 8                     | 0.2                                 | 0.8                  |0.8                        |
+-----------------------+-------------------------------------+----------------------+---------------------------+


Pour chaque cas de chargement, les paramètres liés à l'état d'équilibre sont calculés avec le logiciel de calcul STBEAM [bib2]_. Les contraintes (en MPa) calculées avec STBEAM et POST_VERI_FERRAILLAGE sont reportées dans les tableaux suivants:

+--------------------------+------------+---------------------------+
| **cas de chargement 1**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |0.0         |0.0                        |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |-200.05     |-200                       |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |-200.05     |-200                       |
+--------------------------+------------+---------------------------+

+--------------------------+------------+---------------------------+
| **cas de chargement 2**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |0.0         |0.0                        |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |-400        |-400                       |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |-400        |-400                       |
+--------------------------+------------+---------------------------+

+--------------------------+------------+---------------------------+
| **cas de chargement 3**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |12.596      |12.598                     |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |-280.02     |-279.936                   |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |89.51       |89.456                     |
+--------------------------+------------+---------------------------+

+--------------------------+------------+---------------------------+
| **cas de chargement 4**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |3.6         |3.599                      |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |8.07        |8.065                      |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |42.36       |42.334                     |
+--------------------------+------------+---------------------------+

+--------------------------+------------+---------------------------+
| **cas de chargement 5**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |0.0         |0.0                        |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |0.0         |0.0                        |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |0.0         |0.0                        |
+--------------------------+------------+---------------------------+

+--------------------------+------------+---------------------------+
| **cas de chargement 6**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |7.2         |7.2                        |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |100.86      |100.80                     |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |100.86      |100.80                     |
+--------------------------+------------+---------------------------+

+--------------------------+------------+---------------------------+
| **cas de chargement 7**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |12.596      |12.598                     |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |89.51       |89.456                     |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |-280.02     |-279.936                   |
+--------------------------+------------+---------------------------+

+--------------------------+------------+---------------------------+
| **cas de chargement 8**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |3.6         |3.599                      |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |42.36       |42.334                     |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |8.07        |8.065                      |
+--------------------------+------------+---------------------------+

Pour le cas de chargement multidirectionnels, la marge et l'angle critique sont calculés avec la formule :eq:`marge-theta`.


+-----------------------+-------------------------------------+-------------------------------------+
|                       | **marge**                           | **angle critique**                  |
+-----------------------+--------------+----------------------+--------------+----------------------+
|**cas de chargement**  |**analytique**|**VERI_FERRAILLAGE**  |**analytique**|**VERI_FERRAILLAGE**  |
+-----------------------+--------------+----------------------+--------------+----------------------+
| 9                     | -0.194       |-0.194                | -45°         |-44.99°               |
+-----------------------+--------------+----------------------+--------------+----------------------+
| 10                    | 0.149        |0.148                 | 0°           |-2.703E-14            |
+-----------------------+--------------+----------------------+--------------+----------------------+