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Custom Shape
Draw a section as a polygon and get its properties exactly: area, centroid, Ix / Iy, Sx / Sy, Zx / Zy, radii of gyration and the torsion constant, by the shoelace and parallel-axis formulae. For a built-up or non-catalog shape the tables do not carry. The properties are geometry, not a code check - the design provisions are applied by whichever module then uses the section.
Section geometry — shoelace area/centroid, parallel-axis I, S, Z, r, J
What it checks
The module calculates the geometric properties of a custom cross-section defined by a polygon. It accepts outer boundary vertices and optional hole polygons to represent built-up or non-catalog shapes. The design method is purely geometric, utilizing the shoelace formula for area and centroid, and parallel-axis formulae for moments of inertia.
The sequence of checks involves computing the signed area and centroid of the simple polygon. It then determines the second moments about the origin and applies the parallel-axis theorem to find properties about the centroidal axes. The module also calculates the torsion constant and plastic section moduli by binary-searching for the plastic neutral axis, ensuring holes are subtracted at every step for accuracy.
What it reports
- Area - The total cross-sectional area, calculated using the shoelace formula with holes subtracted.
- Centroid - The coordinates (cx, cy) of the centroid of the simple polygon, undefined if the area is zero.
- Moments of Inertia - The second moments of area Ix and Iy about the centroidal axes, derived from origin moments via the parallel-axis theorem.
- Section Moduli - The elastic section moduli Sx and Sy, calculated from the moments of inertia and extreme fiber distances.
- Plastic Moduli - The plastic section moduli Zx and Zy, determined by finding the plastic neutral axis where areas are equal.
- Radius of Gyration - The radii of gyration r, derived from the area and moments of inertia.
- Torsion Constant - The torsion constant J, calculated for the polygonal section.
- Perimeter - The total perimeter of the polygon, including the boundaries of any holes.
Code references
The engine cites Section geometry — shoelace area/centroid, parallel-axis I, S, Z, r, J. The calculations rely on the shoelace formula for signed area and centroid, and the parallel-axis theorem for second moments. The plastic neutral axis is found by binary search for equal areas, with specific handling for holes to ensure accuracy in ring-like shapes.
Limits
The module provides geometric properties only and does not perform code checks or strength verifications. The centroid calculation is undefined if the area is zero. The properties are geometry, not a code check; the design provisions are applied by whichever module then uses the section. Results are engineering aids; the engineer of record is responsible for the design.
This module ships in the desktop app
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