3.1.7.2. 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. 3.1.7.1 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. 3.1.7.2 ReinforcedConcreteLayeredMembraneSection: (a) Strain field; (b.1) Resultant stress field; (b.2) Concrete stresses; (b.3) Steel stresses.

Notes

1. The ReinforcedConcreteLayeredMembraneSection should be used in conjunction with OrthotropicRAConcrete and SmearedSteelDoubleLayer NDMaterials. It can also be used in a MEFI element.

2. The section can also be referred to as RCLayeredMembraneSection or RCLMS.

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. 3.1.7.3 RW-A20-P10-S38 wall specimen: (a) Cross-sectional view ; (b) Layered view of the model.

1. 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)

2. 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:

1. 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).

2. 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).