Section : Perimeter sections
Perimeter definition
The outline of a perimeter section is defined by a series of coordinates describing a polyline. The polyline is automatically closed to form a polygon so an end point coincident with the start point need not be entered. Polyline segments may not intersect.
In addition, any number of voids may be defined in the section, again by a series of coordinates describing an unclosed polyline of non-intersecting segments. Voids may not intersect with each other or with the outline.
The section displayed in the wizard is as viewed from end 1 of the element towards end 2.
The centroid is calculated for the section and the section is assumed to lie centred at its centroid, – not at the datum coordinates.
Import options
The section can be imported or exported from a DXF file. For the import to work the DXF file should contain only LWPOLYLINE or POLYLINE entities that described the perimeter and void in the section. The export option allows the section to be exported as a series of LWPOLYLINE entities.
The bridge beam option is only enabled if the bridge beam database is available. This gives access to standard bridge beam sections. These are stored as perimeter sections in GSA, but have associated tendon positions stored as point voids along with the section geometry.
The shear factors, and , are also set as zero.
Calculate torsion constant
This option uses a purpose-built solver for the calculation of the torsion constant. The calculation will accept any arbitrarily defined perimeter section as input, as long as the perimeter is a valid section shape and the section area is sufficiently thick-walled (see below). No further input is necessary in setting up the analysis. Due to the increased complexity of this method, when selecting this option there may be a brief but noticeable delay when proceeding through to the next page of the Section Wizard as the Wizard constructs and solves the torsion problem.
The calculation of the torsion constant makes use of a numerical technique that is designed for use specifically on thick-walled sections - that is, section shapes with a sufficient area enclosed within the perimeter boundary relative to the perimeter length. Thin-walled sections are best considered as a separate concern and are typically solved using specific thin-walled theory. This theory is not currently implemented in this solver and hence it is not recommended to calculate the value of for thin-walled sections in this case. Section shapes that are considered to be too thin will prompt a warning message to the user, given at the point during the wizard when the value of is calculated.
Internally, the solver makes use of the ‘membrane analogy’ to construct and solve a particular case of the Poisson problem. The differential equations along with the specific boundary conditions prescribed for the torsion problem are assembled and solved numerically by application of boundary element method (BEM) in a dedicated solver.
Perimeter sections
There are two types of geometric section: perimeter and line segment. Both are described in terms of 2D vertices. A perimeter section is specified by a polygon to define the section outline and, optionally, one or more further polygons to define voids within the outline.
The syntax for geometric sections gives instructions for constructing the shape of the section. The section must start with a flag to give the type of geometric section. This followed by a series of instructions defining the shape of the section, separated by spaces. The instructions that are used are:
| Type | Type code |
|---|---|
| Perimeter | P |
| Line segment | L |
and
| Instruction | Values | Code |
|---|---|---|
| Move to position | (x, y) | `M(x |
| Line to position | (x, y) | `L(x |
| Set thickness | t | T(t) |
The (x,y) coordinates referred to here are in section definition axes. These translate to (−y,z) coordinates in element axes. (See Section profile for more information on this.) This translation happens automatically requiring no action by the user.
Thickness is only required for line segment section.
In general a geometric section is defined as
GEO <Type(unit)> <Instruction> <Instruction>…
The available units are m, cm, mm, ft and in, defaulting to mm.
So for example a rectangular section 200mm wide and 400mm deep defined as a perimeter section would be:
GEO P M(0|0) L(200|0) L(200|400) L(0|400) L(0|0)
or a hollow rectangular section 200mm wide and 400mm deep with wall thickness of 10mm defined as a perimeter:
GEO P M(0|0) L(200|0) L(200|400) L(0|400) L(0|0)
M(10|10) L(190|10) L(190|390) L(10|390) L(10|10)
A rectangular section 12.5in by 4.5in defined as perimeter section would be:
GEO P(in) M(0|0) L(4.5|0) L(4.5|12.5) L(0|12.5) L(0|0)