Reference problem
=====================

The POST_COMBINAISON command calculates linear combinations of various calculation results associated with user-defined coefficients.

:math:`{C}_{i}\text{}\text{}\text{}=\text{}\text{}\text{}({\alpha }_{i\mathrm{,1}}\times {Q}_{1})\text{}\text{}\text{}+\text{}\text{}\text{}({\alpha }_{i\mathrm{,2}}\times {Q}_{2})`

Where:

- is the combination number

- Q1 is the result/table from a first finite element calculation

- Q2 is the result/table from a first finite element calculation

- αi,1 is the coefficient associated with Q1

- αi,2is the coefficient associated with Q2

- This is the result of the combination made.


Geometry
---------

The model models half of a typical building of a nuclear installation on a 1/4 scale. Elle

consists of three walls V01/02, V03 and V04 placed in a U shape as well as three floors

trapezoidal. Openings are pierced in the V01/02 and V03 sails. Each floor is

supported by a horizontal beam as well as by a vertical column. The model is asymmetric so

to promote twisting movements. The geometric characteristics of the model are

presented on and on the.


.. image:: images/1000020100000229000001E8B973AA8D2BA72807.png
    :width: 4.1634in
    :height: 3.6744in


.. _RefImage_1000020100000229000001E8B973AA8D2BA72807.png:

**Figure** 1.1-a **: Dimensions of the Smart 2013 model (Elevation view — Dimensions in mm)**

The thickness of the sails and slabs is 0.1 m. The thickness of the sole and the support of the pole is 0.25m.

The beams have a rectangular section :math:`0.325m\times 0.15m`.

The posts have a :math:`0.2m\times 0.2m` square section.


.. image:: images/10000201000001FA00000175CA841DE6F5A884C2.png
    :width: 3.848in
    :height: 2.8366in


.. _RefImage_10000201000001FA00000175CA841DE6F5A884C2.png:

**Figure** 1.1-b **: Dimensions of the Smart 2013 model (Plan view — Dimensions in mm)**


Material properties
----------------------

The spring stiffness of the spring pad under the sole and the post support are:


* k_x = 6.e8


* k_y = 2.e8


* k_z = 2.e9


* k_rx=5.e9


* k_ry = 5.e9


* k_rz=1.e11


For load 1:
~~~~~~~~~~~~~~~~~~~~~~~~

Young's module:.


* Beams, posts, walls and slabs: :math:`E=14200\mathit{MPa}`


* Base and pole support: :math:`E=3200000\mathit{MPa}`

Poisson's ratio:.


* Beams, posts and walls: :math:`\nu =0`


* Slabs, footing and pole support: :math:`\nu =\mathrm{0,2}`

Density:


* Beams, posts, sails, sole and pole support :math:`\rho =2500\mathit{kg}/m\mathrm{³}`


* Level 1 panel: :math:`\rho =2500+2450/0.1\mathit{kg}/m\mathrm{³}`


* Level 2 panel: :math:`\rho =2500+2570/0.1\mathit{kg}/m\mathrm{³}`


* Level 3 panel: :math:`\rho =2500+2150/0.1\mathit{kg}/m\mathrm{³}`

Depreciation:


* AMOR_ALPHA = 0.000454728


* AMOR_BETA = 0.718078321


For load 2:
~~~~~~~~~~~~~~~~~~~~~~~~

Young's module:.


* Beams, posts and walls: :math:`E=32000\mathit{MPa}`


* Tiles: :math:`E=16000\mathit{MPa}`


* Base and pole support: :math:`E=3200000\mathit{MPa}`

Poisson's ratio:.


* Beams, posts and walls: :math:`\nu =0`


* Slabs, footing and pole support: :math:`\nu =\mathrm{0,2}`

Density:


* Beams :math:`\rho =2500\mathit{kg}/m\mathrm{³}`


* Level 1 panel: :math:`\rho =2500+2450/0.1\mathit{kg}/m\mathrm{³}`


* Level 2 panel: :math:`\rho =2500+2570/0.1\mathit{kg}/m\mathrm{³}`


* Level 3 panel: :math:`\rho =2500+2150/0.1\mathit{kg}/m\mathrm{³}`

Depreciation:


* AMOR_ALPHA = 0.000454728


* AMOR_BETA = 0.718078321


Boundary conditions and loads
-------------------------------------


Loading 1
~~~~~~~~~~~~

The structure is subject to its own weight.


Loading 2
~~~~~~~~~~~~

The structure is subject to seismic stresses.

Combination CQC (Full Quadratic Combination) is calculated via COMB_SISM_MODAL for the spectra described below.

*Next X*:

Spectrum SP_HXa2 has a damping of 0.02.

Spectrum SP_HXa5 has a damping of 0.05.

Spectrum SP_HXa7 has a damping of 0.07.

Spectrum SP_HXa10 has a damping of 0.1.


.. image:: images/10000201000003810000022D40FB6901F7FE215B.png
    :width: 4.7047in
    :height: 2.9209in


.. _RefImage_10000201000003810000022D40FB6901F7FE215B.png:

*Next* *Y*:

Spectrum SP_HYa2 has a damping of 0.02.

Spectrum SP_HYa5 has a damping of 0.05.

Spectrum SP_HYa7 has a damping of 0.07.

Spectrum SP_HYa10 has a damping of 0.1.


.. image:: images/100002010000036C0000023B9FCD34D2C9FC4A2E.png
    :width: 4.8465in
    :height: 3.1583in


.. _RefImage_100002010000036C0000023B9FCD34D2C9FC4A2E.png:

*Next* *Z*:

Spectrum SP_HZa2 has a damping of 0.02.

Spectrum SP_HZa5 has a damping of 0.05.

Spectrum SP_HZa7 has a damping of 0.07.

Spectrum SP_HZa10 has a damping of 0.1.


.. image:: images/100002010000032E000001EDAD9D1D8F3AB39581.png
    :width: 4.939in
    :height: 2.9909in


.. _RefImage_100002010000032E000001EDAD9D1D8F3AB39581.png:

The combination CQCS is then deduced and used to evaluate the field resulting from the seismic calculation.