Cross-Section Properties (A, I, S, r)
Area, moment of inertia (I = b h^3/12 etc.), section modulus S = I/c, and radius of gyration r = sqrt(I/A) for a rectangle, solid round, pipe, or hollow tube. I scales with the cube of the depth, so orientation dominates. A design aid, not the engineer of record.
Formula and source
rectangle I = b h^3/12; round I = pi d^4/64; pipe I = pi(d^4 - di^4)/64; tube I = (b h^3 - bi hi^3)/12; S = I/c; r = sqrt(I/A).
The standard cross-section property formulas (mechanics of materials; AISC Manual shapes), by name.
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