Having recently come upon a scenario in practice where existing multiple beams needed to be enhanced in order to support the moment and deflection from an increased load, it seems important to consider the relevance of statics – from academics to design.
Moment of Inertia
The moment of inertia for different shapes can be found in multiple sources, specifically the AISC Steel Construction Manual
We will focus on the areas of beams.
A = b*h
y = the height of the specific areas center of gravity from a specified datum
y_bar = the location of the combined center of gravity for a shape from the total
I = bh^3/12
Section Modulus
The section modulus is
S = I/y
In design, the moment of inertia can be used to select a required section based on the ultimate load on a beam. For steel information, see the AISC Steel Construction Manual