Definition of the quantities produced ================================== Structure element coordinate system -------------------------------- The figure shows the coordinate system associated with the structural element. Axis :math:`X` represents the neutral axis of the structural element. The mechanical characteristics are necessarily given in the main axes of the right section [:ref:`R3.08.01 `] of the element: :math:`{Y}_{\mathit{principal}}` and :math:`{Z}_{\mathit{principal}}`. .. image:: images/100000000000025800000167AC066ED5834B066C.png :width: 4.7244in :height: 2.8272in .. _RefImage_100000000000025800000167AC066ED5834B066C.png: **Figure** 3.1-a: Structure element coordinate system **.** Markers used for geometric characteristics -------------------------------------------------------- Two reference points are used: • the :math:`\mathit{OYZ}` coordinate system for describing the 2D mesh; • the main inertia coordinate system :math:`\mathrm{Gyz}`. in the right section, whose name corresponds to that used in the description of neutral fiber beam elements :math:`\mathrm{Gx}` [:ref:`U4.42.01 `]. **Note:** The mesh that is at the input of the command is in 2D and must therefore be given in the :math:`\mathit{oxy}` axes. Coordinates :math:`z` must all be the same. The MACR_CARA_POUTRE command maps the :math:`x` and :math:`Y` axes to, :math:`y` and :math:`Z`. .. image:: images/10000000000002580000026BE62EE0D04E5E67F1.png :width: 3.9366in :height: 4.0634in .. _RefImage_10000000000002580000026BE62EE0D04E5E67F1.png: **Figure** 3.2-a: **Definition of geometric quantities relating to a section of a beam.** Sizes available in the produced table -------------------------------------------- Geometric characteristics ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ These characteristics are given in the table for the entire mesh and for each group in the **lgm** list (which can correspond to a half or a quarter of the section if the keywords SYME_Y or SYME_Z are present). Characteristics of the mesh read ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ • area: A_M • center of gravity position: CDG_Y_M, CDG_Z_M • moments and product of inertia of air, at the center of gravity :math:`G` in the :math:`\mathit{GYZ}` coordinate system: IY_G_M IZ_G_M IYZ_G_M Characteristics of the beam section ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ • area: A • center of gravity position: CDG_Y, CDG_Z • moments and product of inertia of air, at the center of gravity :math:`G` in the :math:`\mathit{GYZ}` coordinate system: IY_GIZ_G IYZ_G • main moments of inertia of air in frame :math:`\mathrm{Gyz}`, usable for calculating the flexural stiffness of the beam: IY and IZ • angle of transition from coordinate system :math:`\mathit{GYZ}` to the main inertia coordinate system :math:`\mathrm{Gyz}`: ALPHA • characteristic distances, in relation to the center of gravity :math:`G` of the section for maximum stress calculations: Y_ MAX, Y_ MIN, Z_ MAX, Z_ MIN and R_ MAX. • RY and RZ: maximum of Y_ MIN and Y_ MAX and of Z_ MIN and Z_ MAX. • Y_P, Z_P: point for calculating geometric moments of inertia • IY_P, IZ_P, IYZ_P: geometric moments of inertia in the PYZ coordinate system • IY_P, IZ_P: moments of inertia in the coordinate system :math:`\mathrm{Pyz}`. • IYR2_G, IZR2_G, IYR2, IZR2, IXR2_P, IYR2_P: characteristics useful for the geometric rigidity matrix of the elements POU_D_TG and POU_D_TGM. For more details on the definition of quantities see [:ref:`R3.08.04 `]: :math:`{I}_{\mathrm{yr}}^{2}={\int }_{S}y({y}^{2}+{z}^{2})\mathrm{dS}` :math:`{I}_{\mathrm{zr}}^{2}={\int }_{S}z({y}^{2}+{z}^{2})\mathrm{dS}` "Mechanical" characteristics ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ These characteristics are provided in the table for the entire mesh and for each mesh group in the **lgm** list. Torsion characteristics ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ • torsional constant: JX Solving a stationary thermal problem with unknown :math:`\mathrm{\varphi }` makes it possible to determine the torsional constant and the shear stresses. *Note:* *When the section is made up of thin elements* (tubes, reconstituted sections,...) *, it is necessary to have several meshes in this thickness in order to correctly calculate the characteristics related to the twist. *The torsional characteristics are obtained by the resolution* :math:`\mathrm{\Delta }\mathrm{\varphi }` *on the section, so the mesh must be able to solve this equation.* **It is necessary to have more than** **three linear meshes or** **two meshes** **squared in the thickness** **to solve correctly** :math:`\mathrm{\Delta }\mathrm{\varphi }` **.In case of doubt about the value found, it is possible to obtain an approximate value,* *by* *applying the formula given in* [:ref:`1, p *p. 200, table 3.6.5 <1, p*p. 200, table 3.6.5>`] . * • torsional radius: RT The radius of torsion :math:`\mathrm{Rt}` may vary along the outer contour; in fact, for any section, the shear due to the twist varies along the edge. We choose to take the value of :math:`\mathrm{Rt}` leading to the maximum shears on the outer edge, that is to say the maximum value of :math:`\mathrm{Rt}` (in absolute value) on the outer contour. In addition, if the section is honeycombed, we have several "several radii of torsion": :math:`\mathrm{Rt}=2\ast A(k)/L(k)` (where :math:`A(k)` represents the area of the cell :math:`k` and :math:`L(k)` its perimeter). If we are simply looking for the maximum shear value, we must take the maximum of the :math:`\mathrm{Rt}` values obtained on the outer edge and on the cells. • Position of the center of torsion (point :math:`C`) in the GYZ coordinate system: PCTY and PCTZ. From this we deduce the eccentricity of the center of torsion (component of :math:`\mathrm{CG}` in the main inertia coordinate system Gyz): EY and EZ. • Warpage constant (usable for models POU_D_TG and pou_d_tgm with 7 degrees of freedom): JG. Shear characteristics ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The coefficients :math:`{A}_{y}` and :math:`{A}_{z}` are given, in the main inertia coordinate system :math:`\mathrm{Gyz}`, in the form of the ratio (:math:`>1`) of the total area to the area actually sheared. Assigning quantities in AFFE_CARA_ELEM --------------------------------------------- The characteristics contained in this table and that can be used in AFFE_CARA_ELEM have the same names as the characteristics expected under the CARA keyword of the AFFE_CARA_ELEM command. The results calculated by MACR_CARA_POUTRE can simply be sent to AFFE_CARA_ELEM via the TABLE_CARA keyword.