4.2.7.11. MVLEM_3D - 3-D MVLEM Element for Flexure-Dominated RC Walls¶

Developed and implemented by:
Kristijan Kolozvari (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). 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 1: MVLEM_3D Element Formulation

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>)

`eleTag` (int)	unique element object tag
`eleNodes` (list (int))	a list of four element nodes defined in the counter-clockwise direction
`m` (int)	number of element uniaxial fibers
`thick` (list (float))	a list of `m` macro-fiber thicknesses
`widths` (list (float))	a list of `m` macro-fiber widths
`rho` (list (float))	a list of m reinforcing ratios corresponding to macro-fibers; for each fiber: \(rho_i = A_{s,i}/A_{gross,i} (1 < i < m)\)
`matConcreteTags` (list (int))	a list of `m` uniaxialMaterial tags for concrete
`matSteelTags` (list (int))	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)