Results.
| Example | Reference | Records | Largest deviation |
|---|---|---|---|
| Rectangular wall section | Closed form | 2 | 0% |
| L-shaped core section | Closed form | 2 | 0% |
Problem. Section integration also produces the geometric properties of the section. The centroid and area of a rectangular wall section and the offset centroid of an L-shaped core section are compared.
Reference document. The geometry comes from closed forms.
The area of a rectangular section and the centroid of an equal-leg L section are given by these relations.
Numerical model. The section geometry is computed directly from the section.
Rectangular wall section
Parameters. width = 4 · t = 0.3
Closed form. By symmetry the centroid lies at the midpoint
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| Centroid, x coordinate | 2 | 2 | 0% |
| Section area | 1.2 | 1.2 | 0% |
L-shaped core section
Parameters. leg = 4 · t = 0.3
Closed form. The area-weighted centroid of two equal legs lies at a quarter of the leg length
| Quantity | Reference | Computed | Deviation |
|---|---|---|---|
| Centroid, x coordinate | 1 | 1 | 0% |
| Centroid, y coordinate | 1 | 1 | 0% |