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


Geometry
---------

It is a 40 meter high beam, whose lower part (between altitudes 0 and 10 meters) is composed of stiff material while the upper part (above the 10-meter mark) is more flexible; the whole is equipped with a spring at the lower end (Table 1.1-1).



+------------------------------------------+---------------------------+
|                                          |H                          |
+ .. image:: images/Shape1.gif             +                           +
|                                          | S                         |
+                                          +                           +
|                                          | R O                       |
+------------------------------------------+---------------------------+


**Table** 1.1-1 **: Simplified Template**



Point coordinates:


.. csv-table::

    "Knots", ":math:`X` (:math:`m`)", ":math:`Y` (:math:`m`)", ":math:`Z` (:math:`m`)"
    ":math:`O` ", "0. ", "0. ", "-1."
    ":math:`R` ", "0. ", "0. ", "0."
    ":math:`S` ", "0. ", "0. ", "10."
    ":math:`H` ", "0. ", "0. ", "40."


**Table** 1.1-2 **: Node coordinates**



Characteristics of the sections:


.. csv-table::

    "", "Outer radius :math:`{R}_{\mathit{ext}}` (:math:`m`)", "Thickness :math:`{E}_{p}` (:math:`m`)", "GROUP_MA"
    "write off", "10. ", "1. "," RADIER"
    "built", "10. ", "1. "," BATI"


**Table** 1.1-3 **: Section characteristics**


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


.. csv-table::

    "", "Poisson's ratio", "Young's modulus"
    :math:`({N\text{.}m}^{-2})`)", "Density
    :math:`({\mathit{kg}\text{.}m}^{-3})` "," GROUP_MA"
    "write off", "0.2"," :math:`3.5\text{ }E+10` "," :math:`2.5\text{ }E+03` "," RADIER"
    "frame", "0.2"," :math:`3.5\text{ }E+08` "," "," :math:`2.5\text{ }E+03` "," BATI"


**Table** 1.2-1


.. csv-table::

    "", "Stiffness in x
    :math:`({N\text{.}\mathit{kg}}^{-1})` ", "Y-stiffness
    :math:`({N\text{.}\mathit{kg}}^{-1})`)", "Stiffness in z
    :math:`({N\text{.}\mathit{kg}}^{-1})`)", "Mass
    :math:`(\mathit{kg})` "," GROUP_MA"
    "soil", ":math:`1\text{.}\text{ }E+13` "," :math:`1\text{.}\text{ }E+13` "," "," :math:`1\text{.}\text{ }E+13` ", "0. "," SOL"


**Table** 1.2-2 **: Material Properties**


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

Boundary conditions:

Knot :math:`O`: :math:`DX=DZ=0`

Knot :math:`R`: :math:`DRY=0`

All knots: :math:`DY=DRX=DRZ=0`

Single-support seismic loads, identical in all 3 directions:

Reduced depreciation taken into account: 0.07


.. image:: images/10000200000003E9000002C0141C5FF130C587A8.png
    :width: 6.3374in
    :height: 4.4555in


.. _RefImage_10000200000003E9000002C0141C5FF130C587A8.png:

**Fig. 1.3-1: Elastic response spectrum**

**abscissa: frequency (** :math:`\mathit{Hz}` **)/ordinate: acceleration (** :math:`g` **)**