Following a discussion at Eng-Tips, I have modified the section properties spreadsheet (presented here) so that section properties can be found for groups of defined shapes, including provision for translation and rotation of each shape, and application of different E values.
The new spreadsheet may be downloaded from Section Properties07.zip, including full open source code.
The procedure is:
- Select a shape from the drop-down list on the “DefShapes” sheet and enter the required dimensions.
- In the Group Properties table (further down on the same sheet) enter details of X and Y offsets, rotations, and Elastic Modulus values for one or more copies of this shape.
- Click the “Create new group” button. The Group Properties table will update.
- Different shapes may be added by following the same procedure as above, then click the “Add shapes to group” button.
Holes inside a shape may be defined using Elastic Modulus values of 1 and -1 for the shape and holes respectively.
The grouped shapes may be plotted on the “Coords_Group” sheet, which also recalculates section properties, based on end point coordinates. Note that properties on the “Coords_Group” sheet will be slightly different from those shown in the Group Properties table for any shape including curves because the calculation on that sheet models curves as a series of short straight lines. For any polygonal shape the results should be exactly the same (within machine precision).
Examples of input and results are shown in the screen-shots below.
Create 6 equilateral triangles, offset so that the tip is at the origin, and rotated through 60 degree increments
Resulting hexagon
Create new group with 0.5 dia. circle
Add 25 mm diameter holes at 0.45 m from the centre with 30 degree increment
Resulting group and section properties
Add 4 equal angles to an I section; offset and rotated to I section internal corners
Resulting group and section properties
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