3.1.8.3. ReinforcedConcreteLayeredMembraneSection
This command is used to construct a ReinforcedConcreteLayeredMembraneSection object. It is the abstract representation for the stress-strain behavior for a reinforced concrete layered membrane element (based on the work of Rojas et al., 2016).
Fig. 3.1.8.1 ReinforcedConcreteLayeredMembraneSection: (a) Reinforced concrete wall; (b) Layer discretization.
Command
section ReinforcedConcreteLayeredMembraneSection $secTag $nSteelLayers $nConcLayers -reinfSteel{$RSteelAtEachLayer} –conc{$concAtEachLayer} -concThick{$Thicknesses}
Parameter |
Type |
Description |
|---|---|---|
$secTag |
integer |
unique section tag |
$nSteelLayers |
integer |
number of reinforced steel layers |
$nConcLayers |
integer |
number of concrete layers |
$RSteelAtEachLayer |
list int |
a list of nSteelLayers nDMaterial reinforced steel tags to be assigned to each layer |
$concAtEachLayer |
list int |
a list of nConcLayers nDMaterial concrete tags to be assigned to each layer |
$Thicknesses |
list float |
a list of nConcLayers concrete layers thicknesses |
The following recorders are available with the ReinforcedConcreteLayeredMembraneSection.
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 \(N_{x}\), \(N_{y}\), \(N_{xy}\) |
thetaPD |
principal strain direction \(\theta_{pd}\) |
CLayer $iClayer $Response |
returns material $Response for a iClayer-th concrete layer. For available $Response(s) refer to OrthotropicRAConcrete material |
RSLayer $iRSlayer $Response |
returns material $Response for a iRSlayer-th reinforcing steel layer. For available $Response(s) refer to SmearedSteelDoubleLayer material |
Fig. 3.1.8.2 ReinforcedConcreteLayeredMembraneSection: (a) Strain field; (b.1) Resultant stress field; (b.2) Concrete stresses; (b.3) Steel stresses.
Notes
OrthotropicRAConcrete and SmearedSteelDoubleLayer NDMaterials. It can also be used in a MEFI element.Examples
For the development of this example, the RW-A20-P10-S38 wall specimen was used (Tran, 2012). Uniaxial concrete and steel materials are defined, along with orthotropic layers for confined/unconfined concrete and distributed steel for the core and boundaries. Sections of types a and b are defined, composed of the layers created earlier.
Fig. 3.1.8.3 RW-A20-P10-S38 wall specimen: (a) Cross-sectional view ; (b) Layered view of the model.
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 Concrete02 4 $fpc $ec0 0.0 -0.037 0.1 $ft 1738.33; # unconfined concrete
uniaxialMaterial Concrete02 5 $fpcc $ec0c -9.42 -0.047 0.1 $ft 1827.12; # 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
# ----------------------------------------------------------------------------------------
# Create orthotropic concrete layers to represent unconfined and confined concrete
# ----------------------------------------------------------------------------------------
nDMaterial OrthotropicRAConcrete 6 4 $et $ec0 0.0 -damageCte1 0.175 -damageCte2 0.5; # unconfined concrete
nDMaterial OrthotropicRAConcrete 7 5 $et $ec0c 0.0 -damageCte1 0.175 -damageCte2 0.5; # confined concrete
# ----------------------------------------------------------------------------------------
# Create smeared steel layers to represent boundary and web reinforment
# ----------------------------------------------------------------------------------------
nDMaterial SmearedSteelDoubleLayer 8 1 2 $rouXw $rouYw 0.0; # steel web
nDMaterial SmearedSteelDoubleLayer 9 1 3 $rouXb $rouYb 0.0; # steel boundary
# ----------------------------------------------------------------------------------------
# Create ReinforcedConcreteLayeredMembraneSection sections composed of concrete and steel layers
# ----------------------------------------------------------------------------------------
set tw 152.4; # Wall thickness
set tnc 50.8; # unconfined concrete wall layer thickness
set tc 101.6; # confined concrete wall layer thickness
section RCLMS 10 1 1 -reinfSteel 8 -conc 6 -concThick $tw; # Section type b (wall web)
section RCLMS 11 1 2 -reinfSteel 9 -conc 6 7 -concThick $tnc $tc; # 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('Concrete02', 4, fpc, ec0, 0.0, -0.037, 0.1, ft, 1738.33) # unconfined concrete
ops.uniaxialMaterial('Concrete02', 5, fpcc, ec0c, -9.42, -0.047, 0.1, ft, 1827.12) # 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
# ----------------------------------------------------------------------------------------
# Create orthotropic concrete layers to represent unconfined and confined concrete
# ----------------------------------------------------------------------------------------
ops.nDMaterial('OrthotropicRAConcrete', 6, 4, et, ec0, 0.0, '-damageCte1', 0.175, '-damageCte2', 0.5) # unconfined concrete
ops.nDMaterial('OrthotropicRAConcrete', 7, 5, et, ec0c, 0.0, '-damageCte1', 0.175, '-damageCte2', 0.5) # confined concrete
# ----------------------------------------------------------------------------------------
# Create smeared steel layers to represent boundary and web reinforment
# ----------------------------------------------------------------------------------------
ops.nDMaterial('SmearedSteelDoubleLayer', 8, 1, 2, rouXw, rouYw, 0.0) # steel web
ops.nDMaterial('SmearedSteelDoubleLayer', 9, 1, 3, rouXb, rouYb, 0.0) # steel boundary
# ----------------------------------------------------------------------------------------
# Create ReinforcedConcreteLayeredMembraneSection sections composed of concrete and steel layers
# ----------------------------------------------------------------------------------------
tw = 152.4 # wall thickness
tnc = 50.8 # unconfined concrete wall layer thickness
tc = 101.6 # confined concrete wall layer thickness
ops.section('RCLMS', 10, 1, 1, '-reinfSteel', 8, '-conc', 6, '-concThick', tw) # Section type b (wall web)
ops.section('RCLMS', 11, 1, 2, '-reinfSteel', 9, '-conc', 6, 7, '-concThick', tnc, tc) # 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).