centimeter to the fourth

The second moment of area measures how far a section's material sits from the axis it bends about, weighted by the square of that distance. Because of the squaring, depth dominates: a rectangular beam of depth \(d\) has \(I = bd^3/12\), so doubling the depth multiplies the stiffness by eight while doubling the width only doubles it. That single fact explains why joists are installed on edge rather than flat, and why an I-beam puts most of its steel in flanges far from the neutral axis and only enough in the web to hold them apart.

The unit cm⁴ exists because the SI unit is unusably large. Working in m⁴ puts every real section at values like 8.36 × 10⁻⁵, which is hard to compare at a glance, while cm⁴ gives 8360. The value enters two of the most-used equations in structures: deflection, where \(\delta\) is inversely proportional to \(EI\), and bending stress, where \(\sigma = Mc/I\). Note that stiffness against deflection and strength against yield are different checks, and a long span is usually governed by deflection rather than by stress.