I have just posted an update to my section properties spreadsheet, last discussed at:
Using Section Properties- Group
The new version can be downloaded from:
The main sheet provides section properties for a wide variety of defined shapes:
This sheet provides second moment of area about the X and Y axes, and about the shape centroid, but not about the principal axes.
This data can be calculated by going to the Coords_Shape sheet, and clicking the “Copy Shape Coordinates” and “Plot Coordinates” buttons:
This now calculates the second moment of area about the Principal Axes (Iu and Iv), but often it is useful to rotate the shape so that the principal axes are parallel to the X and Y axes.
This can be achieved by using the “grouped shapes” calculation. In the Group Properties table enter the “Rotation about centroid” value as – the calculated principal axis value, or enter a formula linking to the calculated alpha value (Cell I23), as shown below. Then click the Create new group button:
The displayed properties now include Iu and Iv, which are now equal to Ixc and Iyc, and Ixyc is equal to zero.
The rotated shape can be plotted on the Coords_Group sheet, by clicking the Plot Group button:
The principal axes are now parallel to the X and Y axes.
It is also possible to move the section centroid to the XY origin, by entering the appropriate offsets in the Group Properties table, and clicking the Create new group button:
The section corner coordinates are now relative to the section centroid, allowing easy calculation of the section modulus values for any corner point.
Note that the code for calculation of the rotated section properties has now been corrected to fix a problem when the rotated Alpha angle is exactly zero, and to plot the principal axes correctly, so the latest version should be downloaded from the link at the top of the page.