What does the moment of inertia equation I = Ii + Aid^2 represent?

The equation ( I = I_i + A_{id}^2 ) describes the moment of inertia of a composite section about an axis. In this equation, ( I ) is the total moment of inertia of the entire composite section, ( I_i ) is the moment of inertia of a particular individual section about its own centroidal axis, ( A_i ) is the area of that section, and ( d ) is the distance from the centroid of the individual section to the centroid of the composite section.

This equation is derived from the parallel axis theorem, which allows for the calculation of the moment of inertia of various sections by including the contributions of each part with respect to a common axis. The total moment of inertia is thus the sum of the moments of inertia of individual sections adjusted for their distance from the centroid of the composite section.

In context, the other choices refer to different aspects of structural analysis. The overall moment around the centroid and effective moment of inertia might imply different calculations not represented by this specific formula. The contribution of added area may hint at adding the moment of inertia from more than one section, but it does not encompass the total moment of inertia of a composite section that this equation specifically articulates.