The moment-area method — using theorems relating the change in slope and the tangential deviation between two points on a beam's elastic curve to the area and moment of the M/EI diagram — can be extended to non-prismatic beams or beams with variable moment of inertia by treating the beam as a series of piecewise-prismatic segments, each with its own constant flexural rigidity, so a distinct M/EI diagram ordinate is computed per segment rather than assuming uniform EI throughout the span. This approximation, while not exact for a continuously varying moment of inertia, yields results of acceptable engineering accuracy and demonstrates that concentrating additional moment of inertia in regions of highest bending moment reduces deflection and slope more efficiently (per unit of added material) than uniformly increasing the moment of inertia across the entire span. This belongs to structural mechanics / strength of materials, within the broader topic of beam deflection theory, alongside the differential equation of the elastic curve and the method of superposition.
The moment-area method — using theorems relating the change in slope and the tangential deviation between two points on a beam's elastic curve to the area and moment of the M/EI diagram — can be exte…