# 3.1.9.7. MVLEM_3D Element¶

Developed and implemented by:
Kristijan Kolozvari (CSU Fullerton)
Kamiar Kalbasi (CSU Fullerton)
Kutay Orakcal (Bogazici University)
John Wallace (UCLA)

## 3.1.9.7.1. Description¶

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.

Fig. 3.1.9.4 Figure 1: MVLEM_3D Element Formulation

## 3.1.9.7.2. Input Parameters¶

Command

element MVLEM_3D eleTag iNode jNode kNode lNode m -thick {Thicknesses} -width {Widths} -rho {Reinforcing_ratios} -matConcrete {Concrete_tags} -matSteel {Steel_tags} -matShear {Shear_tag} <-CoR c> <-ThickMod tMod> <-Poisson Nu> <-Density Dens>

Parameter

Type

Description

eleTag

integer

unique element object tag

iNode jNode kNode lNode

4 integer

tags of element nodes defined in counterclockwise direction|

m

integer

number of element fibers

{Thicknesses}

m float

array of m fiber thicknesses

{Widths}

m float

array of m macro-fiber widths

{Reinforcing_ratios}

m float

array of m reinforcing ratios corresponding to macro-fibers

{Concrete_tags}

m float

array of m uniaxialMaterial tags for concrete

{Steel_tags}

m float

array of m uniaxialMaterial tags for steel

{Shear_tag}

m float

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)

## 3.1.9.7.3. Recorders¶

The following recorders are available with the MVLEM_3D element.

Recorder

Description

globalForce

Element global forces

Curvature

Element curvature

Shear_Force_Deformation

Element shear force-deformation relationship

Fiber_Strain

Vertical strains in m fibers along the cross-section

Fiber_Stress_Concrete

Vertical concrete stresses in m fibers along the cross-section

Fiber_Stress_Steel

Vertical steel stresses in m fibers along the cross-section

## 3.1.9.7.4. OpenSeesPy Documentation¶

OpenSeesPy user documetation for the MVLEM_3D element can be accessed from HERE.

## 3.1.9.7.5. Example¶

Specimen TUB (Beyer et al. 2008) is analyzed using the MVLEM_3D. Figure 2a shows the photo of the test specimen and the multidirectional displacement pattern applied at the top of the wall, while Figure 2b-c show the MVLEM_3D model of specimen TUB. Tcl Input files can be downloaded from MVLEM-3D GitHub Page.

Fig. 3.1.9.5 Figure 2: MVLEM_3D Model of Specimen TUB

Fig. 3.1.9.6 Figure 3: Animation of MVLEM_3D Analysis of Specimen TUB (displacement scale factor = 3.0)