## Section properties for groups of defined shapes

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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### 13 Responses to Section properties for groups of defined shapes

1. That’s a hug daily dosis I think. Still some good tips and trics.

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2. metroxx says:

Hello,
Is it possible to add find area of section above neutral axis and below?
With regards

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• metroxx says:

Mainly question: Is it possible to add calculation of First moment of area above neutral axis and below. It is used for example in EC2 calculation of prestressed section to shear resistance without needed reinforcement.

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• dougaj4 says:

On the Coords_Shape sheet, enter the coordinates for the section above the neutral axis, and click the “Recalc Section Properties” button.

This will give you the area of the shape (Area), and the distance from the neutral axis to the centroid (Yc, assuming you entered the NA on the X axis).

The first moment of area is then Area*Yc

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3. Robbie van Leeuwen says:

Great spreadsheet!

Big fan of your blog! I am in the processing of building something similar in MATLAB, however have used a sightly different approach where I have defined a boundary and used an open source meshing code to create a triangular mesh. I’ve got the flexural properties down, but I am trying to think about how I would approach calculating torsional properties (shear centre, J, Iw) for a set of triangles. Do you have any advice or resources that might guide me in the right direction?

Cheers,

Robbie

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• dougaj4 says:

Not really, other than that torsion is difficult. The finite element program I use does torsion by creating a mesh and doing a stress analysis on that. If you are working from a triangular mesh I think that’s the only approach that is going to work, since the connectivity of the mesh has a big effect on the torsional stiffness of the section.

If you do find a simpler way, I’d be really interested to hear of it.

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4. Brad Clarke says:

HI

Wanting properties for a Hollow Rectangle. Using Coords-Shape the area calc is wrong, it appears to be adding the area of the outer rectangle and the inner rectangle, rather than subtracting them. I note that you mention that you can use an E value of +1 for the outer rectangle, and -1 for the hole, but I cannot see where this can be entered in the Coords-Shape tab.

Brad

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• Brad Clarke says:

Hi

Just had a bit more of a look and found out that if you define the outer rectangle in one direction (say clockwise) and the inner rectangle in the opposite direction (say counter clockwise) then the area calcs properly.

Thanks for this, a great spreadsheet.
Brad

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• dougaj4 says:

Brad – yes, if you are entering coordinates by hand, that is the way to do it.

Using the Defshapes sheet you could use the hollow rectangle shape, but assuming you are doing a trial for something more complicated (or maybe the void is not central), the procedure is:
Select the rectangle shape and enter the outer dimensions.
Go down to the group table (starting row 42), delete any existing data, and enter offsets and rotation (I assume 0) and Elastic Modulus = 1.
Click the create new group button.
Enter the dimensions for the void in the shape table.
Enter X and Y offsets on the first row in the groups table, and Modulus = -1.
Click the “Add shapes to group” button.

The Group Properties results should update to the correct values.
You can then copy the group coordinates to the “Coords_Group” sheet, which should give the same results.
The “DefShapes” sheet will only copy the last shape you entered.

I haven’t used the group feature for some time, and I found the instructions a bit confusing myself (I initially assumed you left the outer rectangle in the top row of the group data, rather than deleting it). I’ll update the instructions, which I hope will make it clearer.

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• Brad Clarke says:

Thanks Doug

It was an offset hole in a rectangle (precast concrete panel) so I just manually entered the coords in the Coords_Shape tab after copying from the DefShapes (= 22). Simple panel so no real issues.

I’ll look further into the Groups for the next one I do.

Thanks again
Brad

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