.. _LayeredMembraneSection: 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. .. figure:: LMS_figure.png :align: center :figclass: align-center :width: 60% :name: LMS_FIG LayeredMembraneSection: (a) Layer discretization; (b) Strain field; (c) Resultant stress field. .. admonition:: Command section LayeredMembraneSection $secTag $total_thickness $nLayers -mat{$Material_tags} -thick{$Thicknesses} <-Eout $OutofPlaneModulus> .. csv-table:: :header: "Parameter", "Type", "Description" :widths: 10, 10, 40 $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. .. csv-table:: :header: "Recorder", "Description" :widths: 20, 40 panel_strain, "strains :math:`\varepsilon_{xx}`, :math:`\varepsilon_{yy}`, :math:`\gamma_{xy}`" panel_avg_stress, "resulting panel stresses :math:`\sigma_{xx}`, :math:`\sigma_{yy}`, :math:`\tau_{xy}`" panel_force, "membrane forces at panel level :math:`N_{x}`, :math:`N_{y}`, :math:`N_{xy}`" layer $ilayer $Response, "returns material $Response for a ilayer-th layer. For available $Response(s) refer to material" .. admonition:: Notes | 1. The **LayeredMembraneSection** can be used in a ``MEFI`` element. | 2. The section can also be referred to as **LMS**. .. admonition:: 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. 1. **Tcl Code** .. code-block:: tcl # ======================================================================================== # 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) 2. **Python Code** .. code-block:: python # ======================================================================================== # 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).