Maximising the beam stiffness
The product EI is termed the "beam stiffness", or sometimes the "flexural rigidity". It is often given the symbol Σ. It is a measure of how strongly the beam resists deflection under bending moments. It is analogous to the Young's modulus in uniaxial loading (with the curvature being analogous to the uniaxial strain and the bending moment being analogous to the uniaxial stress). For a given material, the beam stiffness is maximised by maximising the value of I . This is done by using sectional shapes for which most of the sectional area is remote from the neutral axis.
For example, a beam of square cross-section is stiffer than a circular beam with the same area, since a circle has a larger proportion of the section near the neutral axis. A hollow square section is even stiffer. Taking this rationale still further leads to I-section beams and sandwich panels.