Second moment of area

Summary

The second moment of area of a plane region about an axis is the integral of the squared distance to the axis over the region. For the cross-section of a beam it measures how well the shape resists bending, and the bending stiffness of a beam is $EI$. It is a geometric quantity, the area analogue of the moment of inertia of a rigid body. Its dependence on the cube of the height explains why beams are made deep rather than wide. It also explains why I-beams put material far from the centroid.