Background

The LIN3DRECTANGULARTUBE (or LIN2DRECTANGULARTUBE) class creates a line Section that is represented by its height \(h\), width \(b\), flange thickness \(t_f\), and web thickness \(t_w\). This class computes the cross-sectional properties such as area, shear area, inertias and so on. The figure shows a representation of the Lin2DRectangularTube and Lin3DRectangularTube

The section properties are:

Area properties: \(A = h\,b - (h - 2\,t_f)(b - 2\,t_w) \,, \; As_2 = 2\,h\,t_w \,, \; As_3 = 2\,b\,t_f \)
Inertia properties: \(I_{11} = I_{22} + I_{33} \,, \; I_{22} = \frac{1}{12} \left(h\,b^3 - (h - 2\,t_f)(b - 2\,t_w)^3 \right) \,, \; I_{33} = \frac{1}{12} \left( b\,h^3 - (b - 2\,t_w)(h - 2\,t_f)^3 \right)\)
Geometric center from bottom left corner (point of reference): \(x_3 = \frac{b}{2} \), and \(x_2 = \frac{h}{2}\)

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 Lin2DRectangularTube or Lin3DRectangularTube section using json format, use:

addSection(tag, name='Lin3DRectangularTube', 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.
  - 'tf' : is the flange thickness of the line cross section.
  - 'tw' : is the web thickness 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 LIN2DRECTANGULARTUBE section can be defined using the python interface as follows:
SVL.addSection(tag=1, name='Lin2DRectangularTube', model='Plain', attributes={'b': 0.30, 'h': 0.30, 'tw': 0.01, 'tf': 0.01, '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/Lin3DRectangularTube.cpp file provides the class implementation. A Lin3DRectangularTube section is created using the built-in json parse-structure provided in the Driver.hpp. A Lin3DRectangularTube is defined inside the "Sections" json field indicating its "Tag" as follows,

{
    "Sections": {
        "Tag": {
            "name" : "LIN3DRECTANGULARTUBE",
            "model" : "PLAIN",
            "attributes": {
                "h": double,
                "b": double,
                "tw": double,
                "tf": 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.
`tf`	The flange thickness of the cross section.
`tw`	The web thickness 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 LIN3DRECTANGULARTUBE / LIN2DRECTANGULARTUBE Section object is made of one Material.; The LIN3DRECTANGULARTUBE / LIN2DRECTANGULARTUBE Section is assumed to be use 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 LIN2DRECTANGULARTUBE section of height 0.30, width 0.30, and thickness 0.01, made of material 1 is defined:
{ "Sections": { "1": { "name" : "LIN2DRECTANGULAR", "model": "PLAIN", "attributes": { "h" : 0.75, "b" : 0.25, "tw" : 0.01, "tf" : 0.01, "material": 1 } } } }