Background

The LIN3DRECTANGULAR (or LIN2DRECTANGULAR) class creates a line Section class that is represented by its height \(h\), and width \(b\). This class computes the cross-sectional properties such as area, shear area, inertias and so on. The figure shows a representation of the Lin2DRectangular and Lin3DRectangular

The section properties are:

Area properties: \(A = b \, h \,, \; As_2 = \frac{5}{6} b \, h\,, \; As_3 = \frac{5}{6} b \, h\)
Inertia properties: \(I_{11} = \frac{1}{12} b \, h \left( b^2 + h^2 \right) \,, \; I_{22} = \frac{1}{12} h \, b^3 \,, \; I_{33} = \frac{1}{12} b \, h^3\)
Geometric center from bottom left corner (point of reference): \(\bar{x}_3 = \frac{b}{2}\), and \(\bar{x}_2 = \frac{h}{2}\)

REFERENCE:

MIDAS Civil User's Manual: analysis for civil structures, Area Moment of Inertia, Pages 77-78
MIDAS Civil User's Manual: analysis for civil structures, Effective Shear Areas, Pages 68-69

Pre-Analysis

The python Pre-Analysis in the 01-Pre_Process/Method/Attach.py file provides with an interface to populate the Entities dictionary. This file contains several functions to populate specific fields. For example, to create a Lin2DRectangular or Lin3DRectangular section using json format, use:

addSection(tag, name='Lin3DRectangular', model='Plain', attributes):
- tag : The identifier of this section, i.e., tag > -1
- name : Seismo-VLAB section class name
- model : model of the section, i.e., model=plain,fiber
- attributes : Specific properties for the created section, for example
  - 'h' : is the hight of the line cross section.
  - 'b' : is the width of the line cross section.
  - 'ip' : is the section insertion point.
  - 'theta' : is The section rotation angle about axis 1.
  - 'material' : is the material identifier the cross section is made out of.
Example

A LIN2DRECTANGULAR section can be defined using the python interface as follows:
SVL.addSection(tag=1, name='Lin2DRectangular', model='Plain', attributes={'b': 0.25, 'h': 0.75, 'material': 1})

Application
Please refer to the D01-ST_Lin_2DBernoulli_Elastic_Frame2.py file located at 03-Validations/01-Debugging/ to see an example on how to define a Lin2DRectangular section.

On the contrary, the 01-Pre_Process/Method/Remove.py file provides with an interface to depopulate the Entities dictionary. For example, to remove an already define Section, use:

delSection(tag):
- tag : The identifier of the section to be removed, i.e., tag > -1

Run-Analysis

The C++ Run-Analysis in the 02-Run_Process/03-Sections/01-Plain/Lin3DRectangular.cpp file provides the class implementation. A Lin3DRectangular section is created using the built-in json parse-structure provided in the Driver.hpp. A Lin3DRectangular is defined inside the "Sections" json field indicating its "Tag" as follows,

{
    "Sections": {
        "Tag": {
            "name" : "LIN3DRECTANGULAR",
            "model" : "PLAIN",
            "attributes": {
                "h": double,
                "b": double,
                "ip": double,
                "theta": double,
                "material": int
            }
        }
    }
}

Variable	Description
`Tag`	Unique Section object identifier.
`h`	The height of the cross section.
`b`	The width of the cross section.
`ip`	The insertion point, see Insertion Point.
`theta`	The section rotation angle, see Local Axes.
`material`	Material object identifier.

Attention: The LIN3DRECTANGULAR / LIN2DRECTANGULAR Section object is made of one Material.; The LIN3DRECTANGULAR / LIN2DRECTANGULAR Section is assumed to be used in linearized and finite deformations.; The stress/strain coordinates at Section::GetStrainAt() or Section::GetStressAt() must be refereed to the point of reference shown in figure.; If stress/strain are evaluated outside the section domain, the response is zero.; If not specified ip=10 and theta=0.0

Example

A LIN2DRECTANGULAR section of height 0.75, width 0.25 and made of material 1 is defined:
{ "Sections": { "1": { "name" : "LIN2DRECTANGULAR", "model": "PLAIN", "attributes": { "h" : 0.75, "b" : 0.25, "material": 1 } } } }