Results of modeling A
==============================


Natural frequencies
------------------


.. csv-table::

    "**MODE**", "**Reference**"
    ":math:`1` ", "2,18815E+00"
    ":math:`2` ", "5,30484E+00"



Global response on a full modal basis
----------------------------------------

Modes 1 and 2 are taken into account. The inertial (primary) and static (secondary) components of the response are directly accumulated at the level of the supports.


* **calculation no. 1**

COMB_MODE =' SRSS '


* response from support :math:`j\mathrm{=}1` (node :math:`\mathit{NO1}`): :math:`{R}_{1}=\sqrt{{\mathrm{Rm}}_{1}^{2}+{\text{Re}}_{1}^{2}}` with :math:`{\mathrm{Rm}}_{1}=\sqrt{{\mathrm{Rm}}_{11}^{2}+{\mathrm{Rm}}_{21}^{2}}` (cumulative modes)


* support response :math:`j\mathrm{=}2` (node :math:`\mathit{NO4}`): :math:`{R}_{2}=\sqrt{{\mathrm{Rm}}_{2}^{2}+{\text{Re}}_{2}^{2}}` with :math:`{\mathit{Rm}}_{2}\mathrm{=}\sqrt{{\mathit{Rm}}_{12}^{2}+{\mathit{Rm}}_{22}^{2}}`


* global response: :math:`R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}` (cumulative support)

absolute displacements: DEPL


.. csv-table::

    "**NOEUD**", "**Reference**"
    ":math:`\mathit{NO1}` ", "4,00000E-02"
    ":math:`\mathit{NO2}` ", "5,43820E-02"
    ":math:`\mathit{NO3}` ", "5,75544E-02"
    ":math:`\mathit{NO4}` ", "6,00000E-02"


nodal reactions: REAC_NODA


.. csv-table::

    "**NOEUD**", "**Reference**"
    ":math:`\mathit{NO1}` ", "5,36769E+01"
    ":math:`\mathit{NO4}` ", "7,44120E+01"



Overall response on an incomplete modal basis without static correction
--------------------------------------------------------

Only mode 1 is taken into account. The inertial (primary) and static (secondary) components of the response are directly accumulated at the level of the supports.


* **calculation no** 2

COMB_MODE =' SRSS '


* support response :math:`j\mathrm{=}1` (node :math:`\mathit{NO1}`): :math:`{R}_{1}=\sqrt{{\mathrm{Rm}}_{1}^{2}+{\text{Re}}_{1}^{2}}` with :math:`{\mathrm{Rm}}_{1}={\mathrm{Rm}}_{11}`


* support response :math:`j\mathrm{=}2` (node :math:`\mathit{NO4}`): :math:`{R}_{2}=\sqrt{{\mathrm{Rm}}_{2}^{2}+{\text{Re}}_{2}^{2}}` with :math:`{\mathrm{Rm}}_{2}={\mathrm{Rm}}_{12}`


* global response: :math:`R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}`

absolute displacements: DEPL


.. csv-table::

    "**NOEUD**", "**Reference**"
    ":math:`\mathit{NO1}` ", "4,00000E-02"
    ":math:`\mathit{NO2}` ", "5,43794E-02"
    ":math:`\mathit{NO3}` ", "5,73536E-02"
    ":math:`\mathit{NO4}` ", "6,00000E-02"


nodal reactions: REAC_NODA


.. csv-table::

    "**NOEUD**", "**Reference**"
    ":math:`\mathit{NO1}` ", "5,36743E+01"
    ":math:`\mathit{NO4}` ", "5,68312E+01"



Overall response on an incomplete modal basis with static correction
--------------------------------------------------------

Only mode 1 is involved in calculating the response. The static contribution of the neglected mode 2 is taken into account.


* **calculation no** 3

COMB_MODE =' SRSS '


* support response :math:`j\mathrm{=}1` (node :math:`\mathit{NO1}`): :math:`{R}_{1}=\sqrt{{\mathrm{Rm}}_{1}^{2}+{\mathrm{Rc}}_{1}^{2}+{\text{Re}}_{1}^{2}}` with :math:`{\mathrm{Rm}}_{1}={\mathrm{Rm}}_{11}`


* support response :math:`j\mathrm{=}2` (node :math:`\mathit{NO4}`): :math:`{R}_{2}=\sqrt{{\mathrm{Rm}}_{2}^{2}+{\mathrm{Rc}}_{2}^{2}+{\text{Re}}_{2}^{2}}` with :math:`{\mathrm{Rm}}_{2}={\mathrm{Rm}}_{12}`


* global response: :math:`R=\sqrt{{R}_{1}^{2}+{R}_{2}^{2}}`

absolute displacements: DEPL


.. csv-table::

    "**NOEUD**", "**Reference**", "**Tolerance**"
    ":math:`\mathit{NO1}` ", "4,00000E-02", "0.001"
    ":math:`\mathit{NO2}` ", "0.054389658", "0.001"
    ":math:`\mathit{NO3}` ", "0.058152653", "0.001"
    ":math:`\mathit{NO4}` ", "6,00000E-02", "0.001"


nodal reactions: REAC_NODA


.. csv-table::

    "**NOEUD**", "**Reference**", "**Tolerance**"
    ":math:`\mathit{NO1}` ", "53.6846755", "0.001"
    ":math:`\mathit{NO4}` ", "111.6190600", "0.001"



Partition of the primary and secondary components of the response
--------------------------------------------------------------

The inertial (primary) and static (secondary) components are treated separately.


* **calculation no** 4


* primary response on a full modal basis (modes 1 and 2)

COMB_MODE =' SRSS '


1. response from support :math:`j\mathrm{=}1` (node :math:`\mathit{NO1}`): :math:`{\mathrm{RI}}_{1}=\sqrt{{\mathrm{Rm}}_{11}^{2}+{\mathrm{Rm}}_{21}^{2}}` (accumulation on modes)


* support response :math:`j\mathrm{=}2` (node :math:`\mathit{NO4}`): :math:`{\mathrm{RI}}_{2}=\sqrt{{\mathrm{Rm}}_{12}^{2}+{\mathrm{Rm}}_{22}^{2}}`


* primary answer: :math:`\mathrm{RI}=\sqrt{{\mathrm{RI}}_{1}^{2}+{\mathrm{RI}}_{2}^{2}}`

relative displacements: DEPL


.. csv-table::

    "**NOEUD**", "**Reference**"
    "NO1 ", "0.00000E+00"
    "NO2 ", "4,12562E-02"
    "NO3 ", "6,60152E-03"
    "NO4 ", "0.00000E+00"


nodal reactions: REAC_NODA


.. csv-table::

    "**NOEUD**", "**Reference**"
    "NO1 ", "4,12562E+01"
    "NO4 ", "6,60152E+01"



* secondary response


1. secondary answer: :math:`\mathrm{RII}=\sqrt{{\text{Re}}_{1}^{2}+{\text{Re}}_{2}^{2}}`

training trips: DEPL


.. csv-table::

    "**NOEUD**", "**Reference**"
    "NO1 ", "4,00000E-02"
    "NO2 ", "3,54306E-02"
    "NO3 ", "5,71746E-02"
    "NO4 ", "6,00000E-02"


nodal reactions: REAC_NODA


.. csv-table::

    "**NOEUD**", "**Reference**"
    "NO1 ", "3,43386E+01"
    "NO4 ", "3,43386E+01"