Benchmark solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

The modal analysis is carried out with the code SAMCEF. The spectral modal analysis is carried out with the code CASTEM 2000.


Benchmark results
----------------------


* Natural frequencies and modes calculated with SAMCEF.


* Axial, tangential, and normal displacements along the wall located in plane :math:`\mathrm{xOz}` (:math:`x` and :math:`z` positive) for modal recombinations :math:`\mathrm{CQC}` and :math:`\mathrm{SRSS}`. (Calculated taking into account 4 modes).

In order to improve the identification of modes, the spectrum is evaluated with a Fourier model. This modeling was carried out with the software SAMCEF. Since the spectrum is very dense (200 modes with a frequency lower than :math:`7\mathit{Hz}`), the following table only shows frequencies lower than :math:`4\mathrm{Hz}`. In this range, the cumulative effective mass according to :math:`z` is zero.


.. csv-table::

    "**No.** **h** **harmonic**", "**Frequencies** (:math:`\mathit{Hz}`)"
    "4", "1.14"
    "5", "1.17"
    "3", "1.24"
    "4", "1.35"
    "6", "1.45"
    "5", "1.50"
    "2", "1.53"
    "6", "1.62"
    "7", "1.70"
    "3", "1.73"
    "5", "1.93"
    "8", "1.96"
    "7", "2.03"
    "6", "2.09"
    "9", "2,26"
    "7", "2,28"
    "6", "2.42"
    "8", "2.45"
    "4", "2.47"
    "7", "2.55"
    "10", "2.60"
    "8", "2.67"
    "1", "2.80"
    "9", "2,82"
    "11", "2.98"
    "5", "3.01"
    "8", "3.04"
    "8", "3,10"
    "7", "3,10"
    "2", "3,20"
    "10", "3,21"
    "9", "3,29"
    "9", "3,37"
    "12", "3.40"
    "6", "3.56"
    "11", "3.65"
    "9", "3,70"
    "10", "3,80"
    "3", "3,81"
    "8", "3.83"
    "13", "3.86"
    "9", "3,91"



Uncertainty about the solution
---------------------------

Comparisons between codes.


Bibliographical references
---------------------------

The test case is based on the following reference:


1. P.L. GOULD and S.H. ABU - SITTA. *Dynamic response of structures to wind and earthquake loading.* PENTECH PRESS, 1980.