3.1.7.3. LayeredMembraneSection
This command is used to construct a LayeredMembraneSection object. It is the abstract representation for the stress-strain behavior for a layered membrane element (based on the work of Rojas et al., 2016). The LayeredMembraneSection is similar to the RCLMS class, except that this class allows the use of nd materials available in OpenSees.
Fig. 3.1.7.4 LayeredMembraneSection: (a) Layer discretization; (b) Strain field; (c) Resultant stress field.
Command
section LayeredMembraneSection $secTag $total_thickness $nLayers -mat{$Material_tags} -thick{$Thicknesses} <-Eout $OutofPlaneModulus>
Parameter |
Type |
Description |
|---|---|---|
$secTag |
integer |
unique section tag |
$total_thickness |
float |
total section thickness |
$nLayers |
integer |
number of layers |
$Material_tags |
list int |
a list of nLayers nDMaterial tags |
$Thicknesses |
list float |
a list of nLayers layers thicknesses |
$OutofPlaneModulus |
float |
Elasticity modulus of out of plane (optional: default = 0.0) |
The following recorders are available with the LayeredMembraneSection.
Recorder |
Description |
|---|---|
panel_strain |
strains \(\varepsilon_{xx}\), \(\varepsilon_{yy}\), \(\gamma_{xy}\) |
panel_avg_stress |
resulting panel stresses \(\sigma_{xx}\), \(\sigma_{yy}\), \(\tau_{xy}\) |
panel_force |
membrane forces at panel level \(N_{x}\), \(N_{y}\), \(N_{xy}\) |
layer $ilayer $Response |
returns material $Response for a ilayer-th layer. For available $Response(s) refer to material |
Notes
MEFI element.Examples
For the development of this example, the RW-A20-P10-S38 wall specimen was employed (Tran, 2012). Uniaxial concrete and steel materials are defined, along with FSAM nDMaterials used within LMS sections to represent sections of types a and b, as illustrated in Fig. 3.1.7.1(a) for the RCLMS example.
Tcl Code
# ========================================================================================
# RW-A20-P10-S38 (Tran, 2012) - Definition of properties and creation of materials
# Basic units: N, mm
# ========================================================================================
# ----------------------------------------------------------------------------------------
# Create uniaxial steel materials
# ----------------------------------------------------------------------------------------
# steel X
set fyX 469.93; # fy
set bx 0.02; # strain hardening
# steel Y web
set fyYw 409.71; # fy
set byw 0.02; # strain hardening
# steel Y boundary
set fyYb 429.78; # fy
set byb 0.01; # strain hardening
# steel misc
set Es 200000.0; # Young's modulus
set R0 20.0; # initial value of curvature parameter
set A1 0.925; # curvature degradation parameter
set A2 0.15; # curvature degradation parameter
# build steel materials
uniaxialMaterial Steel02 1 $fyX $Es $bx $R0 $A1 $A2; # steel X
uniaxialMaterial Steel02 2 $fyYw $Es $byw $R0 $A1 $A2; # steel Y web
uniaxialMaterial Steel02 3 $fyYb $Es $byb $R0 $A1 $A2; # steel Y boundary
# ----------------------------------------------------------------------------------------
# Create uniaxial concrete materials
# ----------------------------------------------------------------------------------------
# unconfined
set fpc -47.09; # peak compressive stress
set ec0 -0.00232; # strain at peak compressive stress
set ft 2.13; # peak tensile stress
set et 0.00008; # concrete strain at tension cracking
set Ec 34766.59; # Young's modulus
# confined
set fpcc -53.78; # peak compressive stress
set ec0c -0.00397; # strain at peak compressive stress
set Ecc 36542.37; # Young's modulus
# build concrete materials
uniaxialMaterial ConcreteCM 4 $fpc $ec0 $Ec 7.16 1.016 $ft $et 1.2 10000; # unconfined concrete
uniaxialMaterial ConcreteCM 5 $fpcc $ec0c $Ecc 8.44 1.023 $ft $et 1.2 10000; # confined concrete
# define reinforcing ratios
set rouXw 0.0027; # X web
set rouXb 0.0082; # X boundary
set rouYw 0.0027; # Y web
set rouYb 0.0323; # Y boundary
# shear resisting mechanism parameters
set nu 0.35; # friction coefficient
set alfadow 0.005; # dowel action stiffness parameter
# ----------------------------------------------------------------------------------------
# Create FSAM nDMaterial
# ----------------------------------------------------------------------------------------
nDMaterial FSAM 6 0.0 1 2 4 $rouXw $rouYw $nu $alfadow; # Web (unconfined concrete)
nDMaterial FSAM 7 0.0 1 3 5 $rouXb $rouYb $nu $alfadow; # Boundary (confined concrete)
# ----------------------------------------------------------------------------------------
# Create LayeredMembraneSection section
# ----------------------------------------------------------------------------------------
set tw 152.4; # Wall thickness
section LMS 10 $tw 1 -mat 6 -thick $tw; # Section type b (wall web)
section LMS 11 $tw 1 -mat 7 -thick $tw; # Section type a (wall boundary)
Python Code
# ========================================================================================
# RW-A20-P10-S38 (Tran, 2012) - Definition of properties and creation of materials
# Basic units: N, mm
# ========================================================================================
# ----------------------------------------------------------------------------------------
# Create uniaxial steel materials
# ----------------------------------------------------------------------------------------
# steel x
fyX = 469.93 # fy
bx = 0.02 # strain hardening
# steel Y web
fyYw = 409.71 # fy
byw = 0.02 # strain hardening
# steel Y boundary
fyYb = 429.78 # fy
byb = 0.01 # strain hardening
# steel misc
Es = 200000.0 # Young's modulus
R0 = 20.0 # initial value of curvature parameter
A1 = 0.925 # curvature degradation parameter
A2 = 0.15 # curvature degradation parameter
# build steel materials
ops.uniaxialMaterial('Steel02', 1, fyX, Es, bx, R0, A1, A2) # steel X
ops.uniaxialMaterial('Steel02', 2, fyYw, Es, byw, R0, A1, A2) # steel Y web
ops.uniaxialMaterial('Steel02', 3, fyYb, Es, byb, R0, A1, A2) # steel Y boundary
# ----------------------------------------------------------------------------------------
# Create uniaxial concrete materials
# ----------------------------------------------------------------------------------------
# unconfined
fpc = -47.09 # peak compressive stress
ec0 = -0.00232 # strain at peak compressive stress
ft = 2.13 # peak tensile stress
et = 0.00008 # strain at peak tensile stress
Ec = 34766.59 # Young's modulus
# confined
fpcc = -53.78 # peak compressive stress
ec0c = -0.00397 # strain at peak compressive stress
Ecc = 36542.37 # Young's modulus
# build concrete materials
ops.uniaxialMaterial('ConcreteCM', 4, fpc, ec0, Ec, 7.16, 1.016, ft, et, 1.2, 10000) # unconfined concrete
ops.uniaxialMaterial('ConcreteCM', 5, fpcc, ec0c, Ecc, 8.44, 1.023, ft, et, 1.2, 10000) # confined concrete
# define reinforcing ratios
rouXw = 0.0027 # X web
rouXb = 0.0082 # X boundary
rouYw = 0.0027 # Y web
rouYb = 0.0323 # Y boundary
# shear resisting mechanism parameters
nu = 0.35 # friction coefficient
alfadow = 0.005 # dowel action stiffness parameter
# ----------------------------------------------------------------------------------------
# Create FSAM nDMaterial
# ----------------------------------------------------------------------------------------
ops.nDMaterial('FSAM', 6, 0.0, 1, 2, 4, rouXw, rouYw, nu, alfadow) # Web (unconfined concrete)
ops.nDMaterial('FSAM', 7, 0.0, 1, 3, 5, rouXb, rouYb, nu, alfadow) # Boundary (confined concrete)
# ----------------------------------------------------------------------------------------
# Create LayeredMembraneSection section
# ----------------------------------------------------------------------------------------
tw = 152.4 # Wall thickness
ops.section('LMS', 10, tw, 1, '-mat', 6, '-thick', tw) # Section type b (wall web)
ops.section('LMS', 11, tw, 1, '-mat', 7, '-thick', tw) # Section type a (wall boundary)
REFERENCES:
Rojas, F., Anderson, J. C., Massone, L. M. (2016). A nonlinear quadrilateral layered membrane element with drilling degrees of freedom for the modeling of reinforced concrete walls. Engineering Structures, 124, 521-538. (link).
Tran, T. A. (2012). Experimental and Analytical Studies of Moderate Aspect Ratio Reinforced Concrete Structural Walls. Ph.D. Dissertation, Department of Civil and Environmental Engineering, University of California, Los Angeles. (link).
Code Developed by: F. Rojas (University of Chile), M.J. Núñez (University of Chile).