Section Geometry

1 · Input data

The geometric properties of a section you define, from pure geometry: the centroid (x̄, ȳ) and the section height, the area A, the second moments of area I_x and I_y about the centroidal axes, the section moduli S_x and S_y to the extreme fibres in both directions, the radii of gyration r_x and r_y, and — where the plastic neutral axis falls at mid-depth — the plastic modulus Z_x. No code standard governs this page, and none is needed: a geometric property is a property of the shape, not of the material, and there is no provision, no coefficient and no table behind it. What a code governs is what is done with these numbers. Every formula the page applies is printed in the solution, symbol by symbol, with each part’s own contribution shown, so the arithmetic can be checked by hand. Choose a shape, give every dimension it asks for in inches, and press Compute the properties. A dimension that is missing, zero or negative is refused by name and nothing is computed. The I-shape, the T-shape and the L-shape are built from rectangles and the fillets are ignored.

2 · Solution