.. include:: sub.txt

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MVLEM_3D - 3-D MVLEM Element for Flexure-Dominated RC Walls 
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| Developed and implemented by: 
| `Kristijan Kolozvari <mailto:kkolozvari@fullerton.edu>`_ (CSU Fullerton)
| Kamiar Kalbasi (CSU Fullerton)
| Kutay Orakcal (Bogazici University)
| John Wallace (UCLA)

The MVLEM_3D model (Figure 1a) is a three-dimensional four-node element with 24 DOFs for nonlinear analysis of flexure-controlled non-rectangular reinforced concrete walls subjected to multidirectional loading. The model is an extension of the two-dimensional, two-node Multiple-Vertical-Line-Element-Model (`MVLEM <https://opensees.berkeley.edu/wiki/index.php/MVLEM_-_Multiple-Vertical-Line-Element-Model_for_RC_Walls>`_). The baseline MVLEM, which is essentially a line element for rectangular walls subjected to in-plane loading, is extended to a three-dimensional model formulation by: 1) applying geometric transformation of the element in-plane degrees of freedom that convert it into a four-node element formulation (Figure 1b), as well as by incorporating linear elastic out-of-plane behavior based on the Kirchhoff plate theory (Figure 1c). The in-plane and the out-of-plane element behaviors are uncoupled in the present model.

This element shall be used in Domain defined with **-ndm 3 -ndf 6**.

.. figure:: MVLEM_3D_formulation.jpg
	:align: center
	:figclass: align-center

	**Figure 1: MVLEM_3D Element Formulation**
	
.. function:: element('MVLEM_3D', eleTag,*eleNodes,m, '-thick', *thick,'-width',*widths,'-rho',*rho,'-matConcrete',*matConcreteTags,'-matSteel',*matSteelTags,'-matShear',matShearTag,<'-CoR',c>,<'-ThickMod',tMod>,<'-Poisson',Nu>,<'-Density',Dens>)
   :noindex:

   ===================================   ===========================================================================
   ``eleTag`` |int|                      unique element object tag
   ``eleNodes`` |listi|                  a list of four element nodes defined in the counter-clockwise direction
   ``m`` |int|                           number of element uniaxial fibers
   ``thick`` |listf|                     a list of ``m`` macro-fiber thicknesses
   ``widths`` |listf|                    a list of ``m`` macro-fiber widths
   ``rho`` |listf|                       a list of m reinforcing ratios corresponding to macro-fibers; for each fiber: :math:`rho_i = A_{s,i}/A_{gross,i} (1 < i < m)`
   ``matConcreteTags`` |listi|           a list of ``m`` uniaxialMaterial tags for concrete
   ``matSteelTags`` |listi|              a list of ``m`` uniaxialMaterial tags for steel
   ``matShearTag`` |int|                 tag of uniaxialMaterial for shear material
   
   ``c`` |float|                         location of center of rotation from the base (optional; default = 0.4 (recommended))
   ``tMod`` |float|                      thickness multiplier (optional; default = 0.63 equivalent to 0.25Ig for out-of-plane bending)
   ``Nu`` |float|                        Poisson ratio for out-of-plane bending (optional; default = 0.25)
   ``Dens`` |float|                      density (optional; default = 0.0)
   ===================================   ===========================================================================

.. seealso::

   More information available `HERE <https://kkolozvari.github.io/MVLEM-3D/>`_ and in the following reference:
   
   K. Kolozvari, K. Kalbasi, K. Orakcal & J. W. Wallace, "Three-Dimensional Model for Nonlinear Analysis of Slender Flanged Reinforced Concrete Walls", Engineering Structures, `Volume 236, 1 June 2021, 112105 <https://www.sciencedirect.com/science/article/pii/S0141029621002558>`_.