Modélisation A
==============




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

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




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

Le maillage contient 1 élément de type QUAD4.




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



Pour la configuration 1, 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                   |-0.99                     |
+-----------------------+-------------------------------------+----------------------+--------------------------+
| 3                     | 0.7                                 | 0.3                  |0.303                     |
+-----------------------+-------------------------------------+----------------------+--------------------------+
| 4                     | 0.2                                 | 0.8                  |0.801                     |
+-----------------------+-------------------------------------+----------------------+--------------------------+
| 5                     | 0.8                                 | 0.2                  |0.199                     |
+-----------------------+-------------------------------------+----------------------+--------------------------+
| 6                     | 0.0                                 | 1.0                  |1.0                       |
+-----------------------+-------------------------------------+----------------------+--------------------------+
| 7                     | 0.4                                 | 0.6                  |0.599                     |
+-----------------------+-------------------------------------+----------------------+--------------------------+
| 8                     | 0.7                                 | 0.3                  |0.303                     |
+-----------------------+-------------------------------------+----------------------+--------------------------+
| 9                     | 0.2                                 | 0.8                  |0.801                     |
+-----------------------+-------------------------------------+----------------------+--------------------------+
| 10                    | 0.8                                 | 0.2                  |0.199                     |
+-----------------------+-------------------------------------+----------------------+--------------------------+

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**  |-217.44     |-217.392                   |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |-217.44     |-217.392                   |
+--------------------------+------------+---------------------------+

+--------------------------+------------+---------------------------+
| **cas de chargement 2**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |0.0         |0.0                        |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |-434.35     |-434.782                   |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |-434.35     |-434.782                   |
+--------------------------+------------+---------------------------+

+--------------------------+------------+---------------------------+
| **cas de chargement 3**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |17.39       |17.393                     |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |-327.92     |-327.849                   |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |97.98       |-97.979                    |
+--------------------------+------------+---------------------------+

+--------------------------+------------+---------------------------+
| **cas de chargement 4**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |7.47        |7.475                      |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |-46.37      |-46.363                    |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |48.04       |-48.036                    |
+--------------------------+------------+---------------------------+

+--------------------------+------------+---------------------------+
| **cas de chargement 5**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |21.99       |21.993                     |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |92.11       |92.113                     |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |263.76      |263.749                    |
+--------------------------+------------+---------------------------+

+--------------------------+------------+---------------------------+
| **cas de chargement 6**  | **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 7**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |9.744       |9.744                      |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |94.74       |94.731                     |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |94.74       |94.736                     |
+--------------------------+------------+---------------------------+

+--------------------------+------------+---------------------------+
| **cas de chargement 8**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |17.39       |17.393                     |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |97.98       |-97.979                    |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |-327.92     |-327.849                   |
+--------------------------+------------+---------------------------+

+--------------------------+------------+---------------------------+
| **cas de chargement 9**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |7.47        |7.475                      |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |48.04       |-48.036                    |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |-46.37      |-46.363                    |
+--------------------------+------------+---------------------------+

+--------------------------+------------+---------------------------+
|**cas de chargement 10**  | **STBEAM** | **POST_VERI_FERRAILLAGE** |
+--------------------------+------------+---------------------------+
|**Contrainte max béton**  |21.99       |21.993                     |
+--------------------------+------------+---------------------------+
|**Contrainte acier inf**  |263.76      |263.749                    |
+--------------------------+------------+---------------------------+
|**Contrainte acier sup**  |92.11       |92.113                     |
+--------------------------+------------+---------------------------+

Pour la configuration 2, la marge est calculée avec la formule :eq:`marge-theta`.

+-----------------------+----------------------+--------------------------+
| **cas de chargement** | **marge analytique** |**marge VERI_FERRAILLAGE**|
+-----------------------+----------------------+--------------------------+
| 1                     | 0.173                |0.173                     |
+-----------------------+----------------------+--------------------------+
| 2                     | 0.345                |0.345                     |
+-----------------------+----------------------+--------------------------+
| 3                     | 0.346                |0.345                     |
+-----------------------+----------------------+--------------------------+
| 4                     | 0.75                 |0.749                     |
+-----------------------+----------------------+--------------------------+

Pour la configuration 3, la marge est evidement nulle pour tous les cas de chargement.

+-----------------------+-------------------------+--------------------------+
| **cas de chargement** | **marge FEUILLE DIPDE** |**marge VERI_FERRAILLAGE**|
+-----------------------+-------------------------+--------------------------+
| 1                     | 0.0                     |0.02                      |
+-----------------------+-------------------------+--------------------------+
| 2                     | 0.0                     |0.0006                    |
+-----------------------+-------------------------+--------------------------+
| 3                     | 0.0                     |0.004                     |
+-----------------------+-------------------------+--------------------------+
| 4                     | 0.0                     |-0.0006                   |
+-----------------------+-------------------------+--------------------------+

Pour la configuration 4, les résultats sont identiques à ceux de la configuration 1.