A multi-layer shell element for shear walls based on OpenSEES--THUShell

Ref: Lu XZ, Xie LL, Guan H, Huang YL, Lu X, A shear wall element for nonlinear seismic analysis of super-tall buildings using OpenSees, Finite Elements in Analysis & Design, 2015, 98: 14-25.

The research group of Disaster Prevention and Mitigation in Tsinghua University has developed a multi-layer shell element for the simulation of shear wall components. The program can be downloaded at http://www.luxinzheng.net/download/OpenSEES/THUShell.zip.

Related Download: OpenSees Models for a 606m Mega-tall Building v0.1

The multi-layer shell element is based on the principles of composite material mechanics. It is made up of a number of layers with different thicknesses and different material properties (i.e., concrete layers or rebar layers), as shown in Figure 1(a). The strains and curvatures of the middle-layer of the shell element are firstly obtained during the computation, and the strains in other layers can be determined based on the “plane-in-plane” assumption. Then, the stress in each layer will be calculated through the material constitutive law, and the internal force of the shear element (force and bending moment along the section) can be determined via the numerical integration of the stress in all layers. The multi-layer shell element is capable of simulating coupled in-plane/out-of-plane bending as well as in-plane direct shear and coupled bending-shear behavior of RC shear walls. The rebars are smeared into one or more layers and these rebar layers can be either isotropic or orthotropic depending on the reinforcement ratio in the longitudinal and transverse directions, as shown in Figure 2(b).

(a)      Multi-layer shell element

(b)    Location of the rebar layers

Figure 1. The Principal of multi-layer shell element

In this research, the corresponding multi-dimensional concrete material model, steel reinforcement model and multi-layer shell element model are developed in OpenSEES. The multi-layer shell element is based on the ShellMITC4 element that is already provided by OpenSEES. The framework of the proposed multi-layer shell element in OpenSEES is shown in Figure 2.

Figure 2 .The framework of the multi-layer shell element in OpenSEES

1 Multi-dimensional concrete model.

This command is used to create the multi-dimensional concrete material model that is based on the damage mechanism and smeared crack model.

nDmaterial PlaneStressUserMaterial $matTag 40 7 $fc $ft $fcu $epsc0 $epscu $epstu $stc

$matTag

integer tag identifying material

$fc

concrete compressive strength at 28 days (positive)  

$ft

concrete tensile strength (positive)

$fcu

concrete crushing strength (negative)

$epsc0

concrete strain at maximum strength (negative)

$epscu

concrete strain at crushing strength (negative)

$epstu

ultimate tensile strain (positive)

$stc

shear retention factor

nDmaterial PlateFromPlaneStress $newmatTag $matTag $OutofPlaneModulus

$newmatTag

new integer tag identifying material deriving from pre-defined PlaneStressUserMaterial

$matTag

integer tag identifying PlaneStressUserMaterial

$OutofPlaneModulus

shear modulus of out plane

2. Multi-dimensional Reinforcement Material

This command is used to create the multi-dimensional reinforcement material.

nDmaterial PlateRebar $newmatTag $matTag $sita

$newmatTag

new integer tag identifying material deriving from pre-defined uniaxial steel material

$matTag

integer tag identifying uniaxial steel material

$sita

define the angle of steel layer, 90 º (longitudinal steel), 0º (tranverse steel)

3. Define the Section of the Multi-layer Shell element

This command will create the section of the multi-layer shell element, including the multi-dimensional concrete, reinforcement material and the corresponding thickness.

section LayeredShell $sectionTag $nLayers $matTag1 $thickness1...$matTagn $thicknessn

$sectionTag

unique tag among sections  

$nLayers

total numbers of layers

$matTag1

material tag of first layer

$thickness1

thickness of first layer

….

  

$matTagn

material tag of last layer

$thicknessn

thickness of last layer

4. Examples

Two solid shear wall specimens are chosen to demonstrate the feasibility of the proposed multi-layer shell element.

Table 1. Parameters of the specimen

Specimen

Dimension (mm)

(H “ W “ t)

High/width

Concrete strength

Width of boundary zone

Axial load ratio

Longitude reinforcement

Stirrups

SW1-1

2000“1000“125

2.0

C30

200

0.1

6D10

D6@80

SW2-1

1000“1000“125

1.0

C40

200

0.3

6D10

D6@80

Table 2. Parameters of the concrete

Specimen

fc(MPa)

ft(MPa)

fcu(MPa)

epsc0

epscu

epstu

stc

SW1-1

20.7

2.07

-4.14

-0.002

-0.006

0.001

0.08

SW2-1

30.8

3.08

-6.16

-0.002

-0.005

0.001

0.05

The stirrups is smeared into orthotropic rebar layers along 0º direction, whereas the longitude reinforcement is smeared into orthotropic rebar layers along 90º direction. The concentrated reinforcement in boundary zone is modeled with truss element, whose node is shared with the shell element to achieve the displacement compatibility.

The boundary zone and the other part of the wall are separately defined with two different multi-layer sections. The boundary zone is divided into 10 layers while the wall is divided into 8 layers.

(a) SW1-1

(b) SW2-1

Figure 3. Force-displacement of the specimens

Test date: Zhang HM, Study on the Performance-based Seismic Design Method for Shear Wall Structures, Doctoral Thesis, Tongji University, Shanghai, 2007.

By: Linlin XIE and Kaiqi LIN

Supervised by: Xinzheng LU, Yuli HUANG (ARUP) and Lieping YE

Download Address http://www.luxinzheng.net/download/OpenSEES/THUShell.zip