CROSS-SECTION PROPERTIES

Cross-section properties are the geometric inputs to almost every structural calculation: area A, centroid ȳ, second moment of area I, section modulus S = I/c, polar moment J, and radius of gyration r = sqrt(I/A). For composite shapes, the parallel-axis theorem (I = I_local + A·d²) lets you combine simple primitives. This module supports rectangle, circle, hollow tube, I-beam, channel, T-section, and arbitrary polygons.

• A = ∫ dA
• ȳ = (∫ y·dA) / A
• I = ∫ y² dA
• S = I / c
• r = sqrt(I / A)
• J = Ix + Iy (polar)
• I_total = I_local + A·d² (parallel-axis)

References & StandardsAISC Steel Manual Part 1, Roark Table 1

Pick a section before sizing a beam, column, or shaft. The same library powers the beam-deflection module (I and c determine bending stress and deflection), the column module (r drives slenderness ratio), and the shaft module (J drives torsional stiffness). For rolled steel, look up properties in AISC tables; for custom shapes, build them up from primitives here.